question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
|---|---|---|
<p>I am assuming that zero (rest) mass particles don't interact gravitationally with each other and other particles. Does that mean they experience a "flat" spacetime instead of a curved one? I find it a little hard to imagine that. Also, does this mean massless particles can pass through an event horizon (not the singularity itself, I assume there would be some other way of interaction that would prohibit that).</p> | g7779 | [
0.01797485165297985,
0.01838979311287403,
0.0129645811393857,
-0.0018454435048624873,
0.043678563088178635,
0.059171464294195175,
-0.006626475136727095,
0.0174687672406435,
-0.02039201185107231,
-0.07278791815042496,
-0.007966887205839157,
-0.052841898053884506,
0.02506313845515251,
-0.03296292573213577,
-0.06480950117111206,
0.017055310308933258,
0.04875367507338524,
0.005158648826181889,
-0.02318750135600567,
0.05872578173875809,
0.031981129199266434,
0.009221331216394901,
-0.0015709950821474195,
-0.007890780456364155,
-0.04403381794691086,
0.023347122594714165,
-0.012044910341501236,
-0.002531906822696328,
-0.03939773887395859,
-0.046300288289785385,
0.04812471568584442,
0.038843534886837006,
0.016583632677793503,
-0.026099545881152153,
0.016005197539925575,
-0.025075703859329224,
-0.003359816037118435,
0.027705518528819084,
-0.018771078437566757,
-0.019376462325453758,
0.026528507471084595,
0.03194276615977287,
0.0198129341006279,
-0.018207915127277374,
0.01898813433945179,
0.06678388267755508,
-0.027447273954749107,
0.008828636258840561,
0.0280614010989666,
-0.023058976978063583,
-0.0030768897850066423,
-0.009980783797800541,
-0.012164878658950329,
0.00006321826367639005,
-0.014581788331270218,
0.0003545139916241169,
0.04559125378727913,
-0.012972705066204071,
0.10308369249105453,
0.0633528083562851,
0.007717850152403116,
-0.005181606858968735,
0.06609087437391281,
-0.002075653290376067,
0.014697172679007053,
0.02722088061273098,
-0.057670895010232925,
0.015064172446727753,
0.04072494059801102,
0.010021031834185123,
0.03967007249593735,
0.010318313725292683,
-0.05224206671118736,
-0.041041046380996704,
-0.03631395846605301,
0.08026543259620667,
0.00902767013758421,
0.01287832111120224,
-0.0163830928504467,
-0.08050494641065598,
-0.03337632864713669,
-0.03460220620036125,
0.01453357096761465,
0.0021261044312268496,
0.08246427029371262,
-0.02681764028966427,
-0.016662370413541794,
-0.10482131689786911,
0.002122656675055623,
0.04276693984866142,
0.05053448677062988,
-0.018390607088804245,
0.016912313178181648,
0.022613130509853363,
-0.016102857887744904,
-0.010849489830434322,
0.0318317785859108,
0.05726077780127525,
0.007561784237623215,
-0.009470113553106785,
-0.036067020148038864,
0.021381517872214317,
0.0020470102317631245,
0.013763152062892914,
0.017764942720532417,
-0.0024255223106592894,
-0.05005558207631111,
-0.00036575415288098156,
0.09239961206912994,
-0.023336617276072502,
-0.020629212260246277,
-0.018455246463418007,
-0.03413103520870209,
0.01723683625459671,
-0.02797827683389187,
-0.03163168206810951,
0.057757098227739334,
-0.017651734873652458,
-0.017527112737298012,
0.031602468341588974,
-0.03158499300479889,
0.04340570420026779,
-0.052930280566215515,
0.05069607496261597,
-0.03992678225040436,
-0.009202671237289906,
0.024914324283599854,
0.004864315502345562,
-0.03052167221903801,
-0.02004311978816986,
-0.012099145911633968,
0.009013759903609753,
-0.031828612089157104,
0.017101649194955826,
-0.05388587713241577,
-0.029784422367811203,
0.006718046963214874,
-0.04011433199048042,
-0.004872528836131096,
0.0020817110780626535,
-0.0032995925284922123,
-0.007401990704238415,
-0.027368387207388878,
0.01576966419816017,
0.0058494615368545055,
-0.03403756022453308,
-0.02171931602060795,
0.01568341813981533,
-0.0015952400863170624,
0.0841788575053215,
-0.00714466068893671,
0.07970499247312546,
0.03860010206699371,
-0.03086812049150467,
0.014763393439352512,
0.01464555598795414,
0.008001508191227913,
-0.01677773892879486,
0.00989636592566967,
0.01804497465491295,
0.08498753607273102,
-0.028050562366843224,
0.0274173766374588,
-0.00985910464078188,
-0.06633102893829346,
-0.028341256082057953,
-0.03938848525285721,
-0.060269564390182495,
0.03605397790670395,
-0.0612059086561203,
-0.017882557585835457,
-0.027555007487535477,
-0.040835440158843994,
0.11658629029989243,
-0.026012495160102844,
-0.031360555440187454,
-0.058396052569150925,
0.05583720654249191,
0.017430219799280167,
-0.053655531257390976,
-0.012169665656983852,
-0.05416971072554588,
-0.03235958144068718,
-0.04604161158204079,
0.0001985239505302161,
-0.0281008780002594,
-0.018521638587117195,
0.023913750424981117,
-0.013078439980745316,
0.012680496089160442,
-0.014707162044942379,
-0.08428479731082916,
0.05098385736346245,
0.03363404795527458,
0.06287896633148193,
0.012345700524747372,
0.04842820391058922,
-0.019619539380073547,
0.00898285023868084,
0.004749965388327837,
0.03634681552648544,
0.05373771861195564,
0.013777610845863819,
0.0063612740486860275,
0.009420426562428474,
-0.06060011312365532,
0.021704766899347305,
-0.0021442968863993883,
-0.031856901943683624,
-0.031170031055808067,
0.04957541078329086,
-0.004023031797260046,
0.047955580055713654,
-0.02405419573187828,
-0.04820853844285011,
0.02724478207528591,
-0.06082410365343094,
0.021912718191742897,
0.07269012928009033,
-0.013884421437978745,
-0.02131313644349575,
-0.000715979200322181,
-0.01683982089161873,
-0.0011511793127283454,
0.02915550023317337,
0.00762674817815423,
-0.04312979802489281,
-0.03154406696557999,
-0.020225610584020615,
0.06687816977500916,
-0.040054671466350555,
0.004183607641607523,
-0.021208856254816055,
0.006600277964025736,
0.034494902938604355,
0.005452618468552828,
0.014681296423077583,
-0.055081453174352646,
0.023144057020545006,
0.019393332302570343,
-0.009609265252947807,
-0.07886820286512375,
-0.022214656695723534,
-0.003778532613068819,
0.05564364418387413,
-0.03806309774518013,
0.014805280603468418,
0.02760138548910618,
-0.02667166106402874,
-0.007541611324995756,
0.02564924769103527,
-0.023542946204543114,
-0.01987859420478344,
0.018793860450387,
0.018190043047070503,
-0.03236959129571915,
-0.010905425995588303,
0.019321823492646217,
-0.09084826707839966,
-0.00563380541279912,
0.007181218825280666,
-0.02078545279800892,
-0.028940163552761078,
0.05987502634525299,
-0.033603210002183914,
-0.05792708322405815,
-0.012133777141571045,
0.02185347117483616,
-0.022430583834648132,
0.020426692441105843,
-0.03700561448931694,
0.03949381038546562,
0.012943542562425137,
0.05530061572790146,
-0.02531687542796135,
0.008297807537019253,
-0.023779666051268578,
0.0488632470369339,
0.0017118509858846664,
-0.03575699031352997,
0.03966978192329407,
0.015106133185327053,
-0.03124619834125042,
-0.005881120916455984,
-0.009063668549060822,
-0.058557044714689255,
-0.03465956076979637,
0.024988839402794838,
0.015607273206114769,
-0.044879764318466187,
0.026862043887376785,
-0.0051688505336642265,
0.04464227706193924,
-0.014573723077774048,
0.02207917533814907,
-0.006717901211231947,
-0.04760671406984329,
-0.0027435917872935534,
-0.0027059095446020365,
0.044127847999334335,
-0.03143793344497681,
-0.014927222393453121,
-0.0025416468270123005,
-0.02205405756831169,
-0.07034839689731598,
0.031200841069221497,
0.0014376933686435223,
-0.07040289789438248,
-0.0204232856631279,
-0.0605209581553936,
-0.004451956134289503,
0.04965634271502495,
0.045721206814050674,
0.044527217745780945,
-0.026993844658136368,
0.0021762787364423275,
-0.031238006427884102,
-0.024407966062426567,
-0.017345983535051346,
0.010475345887243748,
0.0034531543496996164,
-0.010886091738939285,
0.022549038752913475,
-0.01640479825437069,
-0.026091042906045914,
0.0461261160671711,
0.034853581339120865,
-0.0023229713551700115,
-0.048410821706056595,
0.0335734561085701,
-0.02372804470360279,
-0.011217888444662094,
-0.004650256596505642,
-0.0031850847881287336,
0.036690182983875275,
-0.03257160633802414,
0.019336797297000885,
0.017509233206510544,
0.07394170761108398,
0.033254459500312805,
-0.008341853506863117,
0.024858735501766205,
0.0006018046988174319,
-0.008156140334904194,
-0.0065384008921682835,
0.040142763406038284,
-0.016786284744739532,
-0.06526792049407959,
0.026034321635961533,
-0.017620522528886795,
0.049775172024965286,
-0.012074372731149197,
-0.0040137688629329205,
-0.0317147821187973,
0.021969152614474297,
0.01341096218675375,
-0.02167147770524025,
0.04614894464612007,
0.032012082636356354,
-0.025474710389971733,
0.0598304308950901,
-0.018339864909648895,
0.006570920813828707,
0.03821369633078575,
0.017676062881946564,
-0.06435589492321014,
-0.04164598137140274,
-0.0598369836807251,
0.01660855859518051,
-0.0002930517657659948,
0.05828676372766495,
0.015783119946718216,
-0.03125137463212013,
0.03129405900835991,
0.036102548241615295,
-0.023458346724510193,
0.022897042334079742,
0.04584764316678047,
-0.009780402295291424,
-0.017963841557502747,
0.035067349672317505,
-0.03634637966752052,
-0.005682272370904684,
0.022107653319835663,
-0.001364812022075057,
0.04965171217918396,
-0.0786912739276886,
-0.03380356729030609,
-0.033567726612091064,
0.015175248496234417,
0.04699931666254997,
-0.04047848656773567,
0.02762691117823124,
-0.053920384496450424,
0.02432606741786003,
0.006908581592142582,
0.03624897450208664,
-0.002394750015810132,
0.03560296446084976,
0.010508392937481403,
-0.002663182560354471,
0.10972867161035538,
-0.004396423231810331,
-0.039144713431596756,
0.08739916980266571,
0.015136457048356533,
0.009715290740132332,
-0.033963944762945175,
-0.00269745453260839,
-0.01472727581858635,
0.0105729466304183,
0.00817165058106184,
-0.021240150555968285,
-0.03935954347252846,
0.06399393081665039,
-0.003158851759508252,
0.025078222155570984,
-0.019016271457076073,
-0.006981506012380123,
-0.010277277790009975,
-0.019276417791843414,
-0.03114217519760132,
-0.05245893448591232,
0.03137193247675896,
-0.012795403599739075,
0.009528158232569695,
0.0269363634288311,
-0.001725466689094901,
-0.09499827772378922,
0.027636587619781494,
-0.010181800462305546,
0.007328258827328682,
0.0033205123618245125,
0.020194295793771744,
-0.0663205161690712,
0.05667684227228165,
-0.021205728873610497,
0.023708879947662354,
0.03353254869580269,
0.00063516286900267,
0.09062318503856659,
0.002813936211168766,
0.005811307113617659,
-0.006955989636480808,
0.004262908827513456,
0.05473015084862709,
-0.012904664501547813,
-0.07988598942756653,
-0.0062131257727742195,
0.008121988736093044,
-0.027934707701206207,
-0.03090677224099636,
-0.05750683695077896,
-0.05922818183898926,
-0.027561526745557785,
0.019008943811058998,
-0.012176227755844593,
0.0832539051771164,
-0.01801956258714199,
0.005805052816867828,
-0.0659051313996315,
-0.049527306109666824,
0.054294437170028687,
0.03930056467652321,
0.007461718283593655,
-0.01411286648362875,
-0.018465613946318626,
0.035252273082733154,
-0.07406727969646454,
-0.00506036588922143,
-0.053877707570791245,
0.0285209771245718,
-0.0089672626927495,
0.03660247102379799,
-0.03762389346957207,
-0.026350274682044983,
-0.008651246316730976,
-0.0890059620141983,
0.013299583457410336,
-0.05025951564311981,
-0.0066635869443416595,
-0.004327982664108276,
0.04284703731536865,
-0.0316523052752018,
-0.018947837874293327,
0.08800151944160461,
-0.007272304967045784,
0.01583053730428219,
0.027230553328990936,
-0.0027233725413680077,
-0.01739558018743992,
-0.03629203513264656,
-0.028074324131011963,
-0.015008971095085144,
-0.011481307446956635,
0.0408555269241333,
-0.005814397241920233,
-0.04447300732135773,
-0.035832397639751434,
-0.0035296387504786253,
-0.01928127184510231,
-0.013008213602006435,
0.034211281687021255,
0.014317587949335575,
-0.05796511843800545,
0.03972991928458214,
-0.01454097405076027,
-0.07966958731412888,
-0.01018170453608036,
0.011930068023502827,
-0.02360738255083561,
0.02289736270904541,
-0.028705567121505737,
0.05808327719569206,
0.006360387429594994,
0.014195341616868973,
-0.01328000333160162,
-0.002684436272829771,
-0.019874826073646545,
0.0305838193744421,
-0.009320084936916828,
-0.01755361631512642,
0.0066885449923574924,
-0.01601427048444748,
0.027567163109779358,
-0.0612492673099041,
-0.015175892040133476,
0.030285034328699112,
0.03479070961475372,
0.07783898711204529,
-0.002033966826274991,
-0.004032567609101534,
0.029228465631604195,
-0.008496018126606941,
0.008801435120403767,
-0.06912145018577576,
0.026187587529420853,
0.05670639127492905,
0.1094105988740921,
-0.024575768038630486,
-0.05060628429055214,
-0.007257313001900911,
-0.026614869013428688,
0.043973423540592194,
-0.01744997501373291,
0.0375838503241539,
0.010136639699339867,
0.07542233169078827,
0.031761229038238525,
-0.028284719213843346,
-0.07192692905664444,
0.030491868034005165,
-0.008645594120025635,
0.043993137776851654,
-0.0360204316675663,
0.044996216893196106,
0.048002395778894424,
-0.002097344258800149,
-0.014308816753327847,
-0.06746669858694077,
0.020593037828803062,
0.03431948646903038,
0.02266349270939827,
-0.05491764098405838,
0.01180718932300806,
0.0006045650807209313,
-0.03991664573550224,
-0.052157774567604065,
0.0651296004652977,
-0.07621068507432938,
0.004886610899120569,
0.029009630903601646,
0.034451425075531006,
-0.022606298327445984,
-0.0025909689720720053,
-0.031489185988903046,
-0.016598748043179512,
-0.006516095716506243,
-0.06132274121046066,
0.043790802359580994,
0.007294504437595606,
0.012968424707651138,
0.08878424018621445,
-0.06143385171890259,
0.034375324845314026,
0.010188273154199123,
-0.05103006213903427,
0.018111297860741615,
0.0034217447973787785,
0.07215368002653122,
-0.008250049315392971,
-0.03371117636561394,
0.014079143293201923,
-0.010151177644729614,
-0.031069407239556313,
0.010470602661371231,
-0.05228608846664429,
0.006512081250548363,
-0.06359101831912994,
0.03334997594356537,
-0.036862973123788834,
0.03318199887871742,
0.04715544357895851,
0.06172339245676994,
0.03975449502468109,
0.0029653131496161222,
-0.0461270697414875,
0.026378553360700607,
0.0433901809155941,
0.03479083254933357,
-0.009488874115049839,
0.050853535532951355,
-0.002892483025789261,
-0.0078038438223302364,
0.021563516929745674,
-0.04456539824604988,
-0.08102640509605408,
-0.03314710035920143,
-0.0027018256951123476,
-0.0613320954144001,
0.02517905831336975,
-0.028731100261211395,
0.00022373626416083425,
-0.01519786100834608,
0.016004158183932304,
-0.014454237185418606,
-0.00953815970569849,
0.02158057689666748,
0.0007860144833102822,
-0.0022780424915254116,
-0.020089343190193176,
0.016987986862659454,
0.0025840899907052517,
0.003961128182709217,
-0.007581300102174282,
0.02512328140437603,
0.009560997597873211,
-0.023248661309480667,
0.07144373655319214,
-0.033888187259435654,
0.07581610232591629,
0.05798535421490669,
-0.0011519150575622916,
0.05177487060427666,
-0.10554694384336472,
0.012244848534464836,
0.009640435688197613,
0.02386428229510784,
-0.014950101263821125,
-0.03867111727595329,
-0.029558636248111725,
-0.016226673498749733,
-0.007640922907739878,
0.0358528196811676,
-0.01732071302831173,
-0.00013346251216717064,
-0.06071731075644493,
-0.0004340937011875212,
0.04138094559311867,
-0.03044392168521881,
-0.051621757447719574,
-0.008240832947194576,
0.012908892706036568,
-0.009120939299464226,
-0.03326600044965744,
0.01829383336007595,
0.059073157608509064,
0.012327448464930058,
-0.015047268941998482,
0.027618953958153725,
0.008253226988017559,
-0.066430002450943,
-0.05310037359595299,
0.009006615728139877,
0.0039057089015841484,
-0.07343551516532898,
-0.06709212064743042,
0.06345612555742264,
0.025220423936843872,
0.04313215985894203,
0.05118696391582489,
0.010007870383560658,
0.03580844774842262,
0.05208318307995796,
-0.013596946373581886,
0.07366181164979935,
0.058958057314157486,
0.04765861853957176,
-0.03184831514954567,
0.01336128544062376,
-0.028836240991950035,
0.05459471419453621,
-0.027755100280046463,
-0.01638510636985302,
-0.03340282663702965,
-0.044757358729839325,
0.010336751118302345,
0.06336383521556854,
-0.012776205316185951,
-0.021900711581110954,
-0.01728510670363903,
0.06535199284553528,
-0.012609544210135937,
-0.004847664386034012,
0.07997269928455353,
0.02055342122912407,
-0.01609613373875618,
-0.03975486382842064,
-0.005103896372020245,
0.03976135328412056,
0.04014590010046959,
0.06053192541003227,
-0.04905475303530693,
0.03548360615968704,
-0.020522190257906914,
-0.022560078650712967,
0.009068692103028297,
0.015405330806970596,
0.038838308304548264,
-0.03794591501355171,
-0.02004196308553219,
-0.007294151932001114,
0.01993137039244175,
-0.03914192318916321,
0.007639220915734768,
0.016562514007091522,
-0.02854265831410885,
0.00840002205222845,
0.014944118447601795,
-0.005784573033452034,
0.01449329499155283,
0.029026897624135017,
-0.02332150936126709,
0.04627484083175659,
-0.042800288647413254,
-0.0025215367786586285,
-0.01738584414124489,
-0.026850884780287743,
-0.018126416951417923,
0.009616173803806305,
0.02672707661986351,
0.0005691102123819292,
-0.011998248286545277,
-0.02283654920756817,
-0.04617408290505409,
-0.007210867013782263,
0.03394632041454315,
0.007024023681879044,
0.0316113717854023,
-0.0012368436437100172,
-0.001959054032340646,
0.013607680797576904,
-0.03374664485454559,
0.02380334585905075,
0.040916841477155685,
-0.05880403518676758,
-0.01680869609117508,
0.0017556336242705584,
-0.0277545265853405,
-0.009526100941002369,
0.009947586804628372,
-0.02830539084970951,
-0.018201852217316628,
0.027082789689302444,
-0.04300124570727348,
0.02347256802022457,
0.06654854118824005,
0.024249756708741188
] |
<p>I am in an introductory physics class and we have been working with Gravitational Potential Energy, Elastic Potential Energy, Kinetic Energy and the Law of Conservation of Energy in relation to bungee cords. Recently, we delved into the topic of efficiency and with it I came upon the following stumbling block. </p>
<p>For a project, we need to design a bungee cord for an egg (Average mass: 57.3g +/- 3.0g) falling from a height of 10.0m, and try to get the egg's stopping point as close as possible to the ground. We also need to take efficiency into account.</p>
<p>Now I completely understand the basics of the calculation. Pick a desired stretch, use that to determine cord length, use that to determine the spring constant of the cord, etc. However, when you bring efficiency into account things get more complicated. Energy definitely escapes the system as the egg falls and the cord is stretched. Energy escapes in the cord as a result of internal friction, and during the fall as a result of air resistance. I think air resistance should be negligible given the mass of the egg and the shortness of the drop. I have scoured the internet for a model to determine the energy loss of the system due to internal friction to no avail. <strong>So...My question is, how can I quantify and predict the internal friction of the bungee cord, then use that to determine the % efficiency of my system?</strong></p>
<p>Sorry if my question's a little long and/or misplaced and/or I'm making some kind of mistake in my thinking here. This is my first post on the site.</p>
<p><strong>Edit:</strong> Here is all the given information for this problem:</p>
<ul>
<li>Average mass of the group of eggs being used: 57.3g</li>
<li>Standard Deviation: 3.0g</li>
<li>Height: 10.0m</li>
<li>Desired height at the egg's lowest point: 0.10m</li>
</ul> | g7780 | [
0.015056881122291088,
0.03840278461575508,
0.016107898205518723,
0.004428114276379347,
-0.026450634002685547,
0.009878329001367092,
0.04964902251958847,
-0.016660302877426147,
-0.10409881919622421,
-0.006935223937034607,
-0.030149780213832855,
-0.05374870076775551,
-0.008350515738129616,
0.03051287867128849,
0.05213744193315506,
0.03488515317440033,
0.08885180950164795,
-0.04486684128642082,
0.04701559618115425,
-0.055077824741601944,
-0.02433631382882595,
0.018443984910845757,
-0.010376252233982086,
-0.010589277371764183,
-0.03202155977487564,
0.05148416757583618,
0.027532227337360382,
-0.0019659269601106644,
-0.05486258491873741,
0.009180593304336071,
-0.027332516387104988,
-0.04215915501117706,
0.0184552650898695,
-0.0852598324418068,
-0.076772041618824,
0.03337777405977249,
0.06023783981800079,
-0.009850858710706234,
-0.012263581156730652,
0.012811977416276932,
0.025288330391049385,
-0.08295094221830368,
-0.019241593778133392,
0.022215602919459343,
-0.03283211216330528,
0.03535405173897743,
0.007833852432668209,
-0.016682131215929985,
-0.011571232229471207,
-0.031768105924129486,
-0.02052474580705166,
0.06503646075725555,
0.0449008084833622,
-0.026809489354491234,
0.01919611357152462,
0.02713417075574398,
0.012965625151991844,
-0.03285180404782295,
0.013752183876931667,
0.007687651086598635,
-0.010897203348577023,
0.025964615866541862,
-0.010759958066046238,
-0.049544960260391235,
0.020078275352716446,
-0.011791771277785301,
-0.030345512554049492,
-0.020715823397040367,
0.019825110211968422,
0.04464112967252731,
0.027230320498347282,
0.0022650747559964657,
-0.003592762863263488,
-0.002655685180798173,
-0.030037008225917816,
-0.0314280167222023,
-0.007466983515769243,
0.0198333952575922,
0.02245384082198143,
0.014951188117265701,
-0.02792687714099884,
0.06368400901556015,
-0.0663892924785614,
-0.017960039898753166,
0.09142687171697617,
-0.01108179148286581,
-0.0034935709554702044,
-0.01635797508060932,
-0.06882042437791824,
-0.001452624099329114,
0.03264811262488365,
-0.0006596722523681819,
0.07029462605714798,
0.02574334107339382,
-0.05625664442777634,
-0.020783578976988792,
0.008492701686918736,
0.04244410991668701,
0.047781072556972504,
-0.008499653078615665,
0.006452864035964012,
-0.04903443902730942,
-0.026826482266187668,
-0.0028878513257950544,
-0.024214893579483032,
0.028796156868338585,
0.07904449850320816,
-0.021294765174388885,
0.024333704262971878,
-0.029747791588306427,
0.0033777840435504913,
0.0061723641119897366,
-0.05439838021993637,
-0.06370473653078079,
-0.02018212340772152,
-0.07793037593364716,
0.057855263352394104,
0.006116272881627083,
-0.003913204651325941,
0.05025153607130051,
-0.03142490237951279,
0.01639684848487377,
0.007212774828076363,
-0.0033034600783139467,
-0.0075889225117862225,
-0.0196437519043684,
0.017825601622462273,
-0.021669993177056313,
0.0008116876124404371,
0.011667009443044662,
-0.005571374204009771,
-0.015221544541418552,
0.028334887698292732,
-0.017120392993092537,
0.027919460088014603,
0.004372382536530495,
0.016626209020614624,
0.06026419997215271,
0.01047471072524786,
0.015976225957274437,
-0.015693964436650276,
-0.02386958710849285,
-0.007039970252662897,
0.015422981232404709,
-0.008533972315490246,
0.07920784503221512,
-0.008127926848828793,
-0.0029533652123063803,
0.037982188165187836,
-0.0037440170999616385,
0.03690414875745773,
0.0684981718659401,
-0.002410787856206298,
-0.03352915495634079,
0.03622756153345108,
-0.00860833004117012,
-0.0045369816944003105,
0.0026612204965204,
-0.006016410421580076,
0.0023406711407005787,
0.03207158297300339,
-0.02189432829618454,
0.0675809234380722,
0.00018966587958857417,
-0.0541180819272995,
0.025580063462257385,
0.02157794125378132,
-0.032910481095314026,
0.004832924343645573,
-0.020464424043893814,
-0.0480022169649601,
-0.03304770961403847,
0.07452110946178436,
0.0675654262304306,
-0.08166955411434174,
0.028760867193341255,
0.11572805047035217,
-0.027631940320134163,
0.011724435724318027,
-0.024181770160794258,
0.0858963131904602,
0.006428014487028122,
0.06566779315471649,
0.009352085180580616,
-0.028306953608989716,
0.03141331300139427,
0.06115575134754181,
-0.015364544466137886,
-0.01533297449350357,
-0.02786870114505291,
0.013334875926375389,
0.042466286569833755,
0.030791033059358597,
-0.07422760128974915,
-0.042817581444978714,
0.014671728946268559,
0.05184531211853027,
0.01348137017339468,
-0.03870942443609238,
-0.007635440211743116,
0.025238849222660065,
0.014092499390244484,
-0.010473194532096386,
0.010123900137841702,
0.003738400526344776,
0.007365011610090733,
-0.0016578270588070154,
0.040378082543611526,
0.00902199000120163,
-0.020274175330996513,
0.05831974744796753,
0.0091866971924901,
-0.016264554113149643,
0.05383288115262985,
0.009551775641739368,
0.012660736218094826,
-0.01824149303138256,
0.005624865647405386,
-0.012450125068426132,
0.03500752151012421,
-0.023433268070220947,
0.004282043781131506,
0.05338573455810547,
0.030626941472291946,
-0.046432387083768845,
-0.035189446061849594,
0.00776635529473424,
-0.06154198572039604,
-0.0156333576887846,
-0.022697241976857185,
0.018397454172372818,
0.02587604895234108,
-0.0034049861133098602,
-0.03620164096355438,
0.022873280569911003,
0.04977203905582428,
-0.004386080428957939,
-0.020741991698741913,
0.025906477123498917,
-0.029624156653881073,
0.06069551780819893,
-0.045657750219106674,
-0.013468329794704914,
-0.02593161351978779,
0.0401129350066185,
-0.020023541525006294,
0.05432604253292084,
-0.020454932004213333,
-0.015364429913461208,
0.053922150284051895,
0.06356257945299149,
0.04578497260808945,
-0.038409020751714706,
-0.015879087150096893,
-0.03498217090964317,
0.03690651059150696,
-0.08196932077407837,
0.01315149012953043,
0.016135746613144875,
-0.0435417965054512,
-0.01218339055776596,
-0.0777200311422348,
0.024134866893291473,
0.07146624475717545,
-0.05084231495857239,
-0.005583090707659721,
-0.003475081641227007,
-0.10584286600351334,
0.015723831951618195,
0.020560039207339287,
-0.027575241401791573,
0.035744521766901016,
-0.0400974377989769,
0.025692177936434746,
0.02851029299199581,
-0.09176325052976608,
0.011946247890591621,
-0.006683912593871355,
-0.04304644465446472,
0.021287761628627777,
0.030605806037783623,
0.0026109872851520777,
-0.0059499796479940414,
0.05240844190120697,
0.04708681255578995,
-0.047137949615716934,
-0.02371056005358696,
0.055897440761327744,
0.019932979717850685,
-0.01621372252702713,
-0.02616035006940365,
0.030462637543678284,
0.0443730428814888,
0.030449919402599335,
0.021166671067476273,
0.049294281750917435,
0.02734684944152832,
0.005371779203414917,
-0.054688867181539536,
-0.030510853976011276,
-0.02665860764682293,
-0.007231525611132383,
-0.030936799943447113,
0.05714147910475731,
-0.03532697632908821,
0.0956173911690712,
-0.01798318326473236,
-0.02732439897954464,
0.0047592162154614925,
-0.001480329199694097,
-0.01090280432254076,
0.01287816185504198,
0.040595728904008865,
-0.05077507719397545,
-0.030945925042033195,
-0.044256776571273804,
0.008555890992283821,
0.004961139988154173,
-0.0039765723049640656,
0.01589970663189888,
0.006022268906235695,
-0.06846492737531662,
0.014788725413382053,
-0.022840719670057297,
-0.034330226480960846,
0.03490472584962845,
-0.07110834121704102,
-0.024053996428847313,
-0.05773654952645302,
-0.03501613810658455,
0.0011238505830988288,
0.012194369919598103,
-0.03962726891040802,
-0.00454019894823432,
0.009507892653346062,
-0.0530426949262619,
-0.013785229995846748,
0.0039262110367417336,
-0.0026834201999008656,
0.044085778295993805,
-0.08337198942899704,
-0.04006999731063843,
-0.008523977361619473,
-0.01867343857884407,
-0.0006798892864026129,
-0.013194099068641663,
0.015324992127716541,
-0.010293512605130672,
-0.012956173159182072,
-0.051826946437358856,
0.09951574355363846,
-0.031347889453172684,
0.011341373436152935,
0.028780754655599594,
0.02077421359717846,
0.019124655053019524,
-0.03634853661060333,
0.035382501780986786,
-0.03390372544527054,
0.06117403134703636,
0.009982059709727764,
-0.03377451002597809,
0.025932492688298225,
-0.0038740853779017925,
-0.028066467493772507,
-0.07717456668615341,
-0.02852819301187992,
0.030709359794855118,
-0.008703439496457577,
-0.002941044745966792,
-0.024605678394436836,
0.05262652412056923,
-0.03070608340203762,
0.0113750658929348,
-0.014953382313251495,
-0.05607301741838455,
0.08784496784210205,
0.016751762479543686,
0.003571369219571352,
0.01826661452651024,
0.04752358794212341,
0.012628103606402874,
-0.02353651076555252,
0.01710563339293003,
0.002317917998880148,
0.041275568306446075,
0.024215390905737877,
0.009683138690888882,
0.03538722172379494,
0.01134756114333868,
0.0015856152167543769,
-0.0872160941362381,
0.00555714825168252,
-0.001200093305669725,
0.034963615238666534,
0.024060368537902832,
0.020639076828956604,
-0.020169319584965706,
-0.03687303513288498,
0.07096946984529495,
0.018870577216148376,
-0.003008406376466155,
-0.014578256756067276,
0.033451102674007416,
0.04817087948322296,
-0.002186310011893511,
0.04025609418749809,
-0.030227407813072205,
0.023921938613057137,
0.0015470607904717326,
0.0533442422747612,
-0.07476329058408737,
0.030345257371664047,
-0.06432637572288513,
0.001930102240294218,
-0.05312957242131233,
0.00102325645275414,
-0.011941692791879177,
-0.016381753608584404,
0.006849824916571379,
0.025450564920902252,
0.03203345090150833,
-0.030673576518893242,
-0.04028891772031784,
-0.06710036098957062,
0.021750489249825478,
0.0295692328363657,
0.019692683592438698,
0.02797803282737732,
-0.053454380482435226,
-0.00975776743143797,
-0.023722564801573753,
-0.04679981246590614,
0.0017129458719864488,
-0.08733005076646805,
0.0590534433722496,
0.04061037674546242,
0.011824745684862137,
-0.033509913831949234,
0.025856902822852135,
-0.004287223797291517,
0.020961934700608253,
0.003338919021189213,
0.022763691842556,
0.020733525976538658,
0.05232244357466698,
-0.06311502307653427,
-0.007593097630888224,
-0.004873699974268675,
-0.020351391285657883,
0.022581441327929497,
0.008294465951621532,
-0.023128589615225792,
0.021523846313357353,
-0.022703757509589195,
0.052345775067806244,
-0.011329040862619877,
-0.01973968744277954,
0.023943977430462837,
0.01628604158759117,
-0.005531941540539265,
0.012067542411386967,
-0.017167041078209877,
-0.009515064768493176,
-0.023064764216542244,
-0.003060949733480811,
-0.015583526343107224,
-0.009444169700145721,
0.03772161900997162,
0.014024524949491024,
-0.018039299175143242,
0.0006068186485208571,
0.061133284121751785,
0.05996394157409668,
-0.007594008930027485,
0.04042290151119232,
-0.014814530499279499,
0.022399384528398514,
0.07176686823368073,
-0.006147101521492004,
-0.041057098656892776,
0.025033747777342796,
-0.058962125331163406,
-0.037831056863069534,
-0.01355375163257122,
-0.007782205007970333,
-0.03104802779853344,
-0.012651676312088966,
0.057722240686416626,
0.024913916364312172,
0.020892567932605743,
0.006015433929860592,
0.008847682736814022,
-0.00010542179370531812,
0.013006331399083138,
-0.00034371839137747884,
0.05297037214040756,
-0.015370653942227364,
-0.05255093425512314,
-0.009554506279528141,
-0.05195273831486702,
0.03718400374054909,
-0.04578452557325363,
0.011642510071396828,
-0.006116482429206371,
0.003486447734758258,
0.012221465818583965,
-0.04809338599443436,
-0.05110961198806763,
0.05099542811512947,
-0.046597570180892944,
0.07053028792142868,
0.03488561138510704,
-0.030330533161759377,
0.00006395152013283223,
0.04488898813724518,
-0.0019303447334095836,
0.04865628853440285,
-0.027381550520658493,
0.012116237543523312,
0.05531791225075722,
-0.007475648541003466,
-0.002723144367337227,
0.025542674586176872,
0.02843646891415119,
-0.006486446596682072,
-0.10640978068113327,
-0.007748751901090145,
-0.013979557901620865,
0.03796422481536865,
-0.03318466246128082,
-0.025085343047976494,
-0.026240335777401924,
-0.024206722155213356,
0.003355414140969515,
-0.009141483344137669,
0.020545892417430878,
-0.030854176729917526,
0.030550537630915642,
-0.0636136531829834,
-0.02050114795565605,
-0.030446209013462067,
0.016959624364972115,
-0.030268903821706772,
-0.01694156602025032,
-0.048580411821603775,
-0.07921086996793747,
-0.043223682790994644,
0.021918591111898422,
-0.05578240379691124,
0.033468298614025116,
0.05625654011964798,
0.04395950585603714,
0.0027897164691239595,
-0.01785716973245144,
0.03620898723602295,
0.026986971497535706,
-0.04272502660751343,
0.02214110642671585,
0.08796894550323486,
0.009745686315000057,
0.03029068559408188,
0.008628110401332378,
0.023077979683876038,
0.04942051321268082,
-0.04856402054429054,
-0.0382579043507576,
-0.026647772639989853,
0.019620219245553017,
0.04952829331159592,
0.04226499795913696,
0.00594704132527113,
-0.00719405198469758,
0.048791587352752686,
0.03068636916577816,
0.027639899402856827,
-0.05424067750573158,
-0.10415711998939514,
-0.049497123807668686,
-0.00549034820869565,
0.03228481858968735,
0.011223097331821918,
0.02041095308959484,
-0.06174653023481369,
-0.0362045094370842,
-0.013020887970924377,
-0.005494500510394573,
-0.02956528216600418,
-0.02920321375131607,
-0.03764133155345917,
-0.008139142766594887,
0.039067186415195465,
-0.011703185737133026,
0.016688503324985504,
-0.02973184734582901,
0.006503814831376076,
0.0025410321541130543,
-0.030246522277593613,
0.0005710714613087475,
0.04573260620236397,
0.011488759890198708,
-0.03157123550772667,
0.010920435190200806,
-0.0674547478556633,
0.03524386137723923,
-0.0008721174672245979,
0.0015314259799197316,
0.033220209181308746,
-0.0001690150093054399,
-0.03620636835694313,
-0.01937115751206875,
0.06336082518100739,
0.01568019576370716,
0.03133096918463707,
0.007926642894744873,
0.0569511242210865,
-0.013477739877998829,
-0.007770085707306862,
0.028883574530482292,
-0.05439703166484833,
0.01885536126792431,
0.008789967745542526,
0.059670861810445786,
-0.04904787242412567,
0.0439649373292923,
0.03218575194478035,
-0.016629701480269432,
0.030283724889159203,
-0.001309688319452107,
-0.005458039231598377,
0.00030690868152305484,
0.042114876210689545,
-0.0011583751766011119,
-0.036917794495821,
-0.05482029169797897,
0.08327565342187881,
-0.01532849669456482,
0.01028415933251381,
0.036435339599847794,
0.041172970086336136,
-0.016808662563562393,
0.04211869090795517,
0.01526810135692358,
0.06944606453180313,
-0.05262654274702072,
0.033526401966810226,
0.026943108066916466,
-0.01316822599619627,
-0.007475077174603939,
0.009290729649364948,
-0.027732480317354202,
-0.01010337844491005,
-0.030363259837031364,
0.0009304282139055431,
-0.00330657372251153,
0.01547076553106308,
-0.03657519072294235,
0.017454009503126144,
0.02173345349729061,
-0.02406715415418148,
0.00015736024943180382,
-0.040544938296079636,
0.03615555539727211,
0.0036160433664917946,
0.033310987055301666,
0.006104211788624525,
-0.027498401701450348,
-0.04595587030053139,
-0.037569332867860794,
-0.012044817209243774,
0.01401708647608757,
-0.05408615991473198,
-0.04927965998649597,
-0.02127634547650814,
0.026025164872407913,
-0.006800852715969086,
-0.020457036793231964,
-0.0603402741253376,
-0.06745735555887222,
0.0008469229214824736,
0.002544957213103771,
0.023256784304976463,
-0.08360270410776138,
0.011243091896176338,
0.013621424324810505,
0.04897831007838249,
-0.039650190621614456,
-0.04174758493900299,
0.03335745632648468,
-0.0033635711297392845,
-0.05410788208246231,
0.08539378643035889,
0.005051553715020418,
-0.04497793689370155,
-0.02443915419280529,
0.06968516111373901,
0.002835210645571351,
-0.0008494675275869668,
0.0566444993019104,
-0.0013055155286565423,
0.05357784777879715,
0.02048671990633011,
0.03081762045621872,
-0.011373873800039291,
-0.06414362043142319,
0.037878528237342834,
-0.04590562731027603,
-0.021625876426696777,
-0.09296165406703949,
0.026562783867120743,
0.016776641830801964,
0.0061460696160793304,
0.038192324340343475,
0.025294184684753418,
-0.007914099842309952,
0.036951929330825806,
-0.027509208768606186,
-0.014226159080862999,
-0.024424873292446136,
-0.009795840829610825,
-0.03304401412606239,
0.01102842204272747,
0.011718552559614182,
-0.04437228664755821,
0.01659739762544632,
-0.020899860188364983,
0.0035534200724214315,
0.04523773118853569,
-0.052332259714603424,
-0.054958753287792206,
0.03260401263833046,
-0.024808861315250397,
0.0504082515835762,
-0.0339135080575943,
-0.009155657142400742,
-0.02048993669450283,
0.01358737051486969,
-0.009814308024942875,
-0.038128044456243515,
0.0587860532104969,
-0.02326793223619461,
-0.04337681829929352,
-0.05687236040830612,
-0.012032286264002323,
0.0631832405924797,
-0.010764937847852707,
-0.019523510709404945,
0.041338805109262466,
-0.001964250113815069,
-0.019436433911323547,
0.0449833944439888,
-0.021282248198986053,
-0.008018547669053078,
0.03803548961877823,
-0.008448765613138676,
-0.016325347125530243,
-0.0005216856952756643,
0.014506073668599129,
-0.04980890080332756,
-0.0009619271731935441,
-0.0369599424302578,
0.04069386050105095,
0.002440344775095582,
-0.006737673655152321,
-0.01256808452308178,
-0.06683892756700516,
0.01622428558766842,
0.035602252930402756
] |
<p>I'm an engineering student and have a few ideas to bat at the scientific community. First premise is based upon common sense. I understand that if I am standing on a skateboard on a relatively smooth surface and a stone of significant mass is thrown to me and I catch it, the momentum of the projectile is transferred to me causing a forward acceleration. </p>
<p>My question: Suppose that a system is designed to provided constant acceleration in space utilizing the aforementioned intuitive concept. In the simplest form I can idealize such a system as a basketball constantly striking a flat surface. Opposed to a ball consider an arbitrary mass striking a greater mass. I suppose that if creative means are applied to control the striking action (e.g. magnetism, mechanical means) then this action can be repeated to provide constant acceleration without the use of carrying fuel loads. Would it not be possible to reset the system to an initial state without canceling the resulting acceleration? </p>
<p>Due to the length of this question I will post the next question later. Thx</p> | g7781 | [
0.049298908561468124,
0.06143664941191673,
0.0022277364041656256,
0.019096555188298225,
-0.008043671026825905,
0.04507569223642349,
0.029918106272816658,
-0.003820482874289155,
-0.053741712123155594,
-0.015987418591976166,
-0.005264812149107456,
0.010882110334932804,
0.031122364103794098,
0.00801350548863411,
-0.023573055863380432,
0.008232228457927704,
0.05784700810909271,
-0.016167141497135162,
0.022447682917118073,
0.02708473615348339,
-0.003065353725105524,
-0.03201424330472946,
-0.026190554723143578,
-0.02904173545539379,
-0.01721150241792202,
-0.004152240231633186,
0.019976994022727013,
-0.013972258195281029,
-0.020263928920030594,
-0.05708671733736992,
-0.01939271204173565,
-0.04343545809388161,
-0.01625269278883934,
-0.013331882655620575,
-0.04805542901158333,
0.013313821516931057,
0.01573799178004265,
-0.04040773957967758,
-0.03404554724693298,
0.0011827758280560374,
-0.014286926947534084,
-0.0412488617002964,
-0.00019997794879600406,
0.008003137074410915,
0.03932516276836395,
0.07090260088443756,
0.006668717600405216,
-0.03720344603061676,
-0.017221178859472275,
0.002156864618882537,
-0.04167438670992851,
-0.03172212094068527,
-0.04631607234477997,
-0.022704467177391052,
-0.015922198072075844,
0.02509334124624729,
0.01200740784406662,
0.01060506235808134,
0.009069396182894707,
-0.03234226629137993,
-0.07118809223175049,
0.024375075474381447,
-0.004279220476746559,
-0.05775044485926628,
0.05505571514368057,
-0.019951995462179184,
-0.020534513518214226,
0.04090673848986626,
-0.003419274929910898,
0.01308293454349041,
0.06788444519042969,
-0.0336015447974205,
-0.05017876252532005,
-0.034272391349077225,
0.010304144583642483,
0.03900793194770813,
-0.051545239984989166,
0.006946387700736523,
-0.03320454806089401,
0.04734690859913826,
-0.020228153094649315,
-0.017674677073955536,
0.06671248376369476,
-0.0390273742377758,
0.0735294371843338,
-0.014772813767194748,
-0.016441047191619873,
0.0034562991932034492,
-0.0790954977273941,
-0.03853122144937515,
0.02793682925403118,
0.027606066316366196,
0.05769303813576698,
0.053576964884996414,
-0.061121903359889984,
-0.007595917209982872,
-0.016236085444688797,
0.05306404083967209,
-0.005334370769560337,
0.01779254898428917,
-0.04395630955696106,
-0.01724865660071373,
-0.012750772759318352,
-0.02231922186911106,
0.00528749218210578,
-0.05293036997318268,
0.06222689524292946,
-0.0056874630972743034,
0.013945477083325386,
-0.01164711732417345,
0.04502195119857788,
-0.08056572079658508,
-0.020063290372490883,
-0.0356578603386879,
-0.0615704171359539,
-0.006964680273085833,
0.08556529879570007,
0.022296935319900513,
-0.04420224949717522,
0.021058885380625725,
-0.024129008874297142,
-0.01879483088850975,
-0.03803712874650955,
0.04191535711288452,
-0.017000600695610046,
0.00830977875739336,
-0.012192882597446442,
-0.02766617201268673,
-0.018043508753180504,
-0.009396263398230076,
-0.0033138596918433905,
-0.006404625717550516,
-0.0004078461497556418,
0.0036659627221524715,
-0.019215809181332588,
-0.008871300145983696,
0.016565626487135887,
0.0003962731861975044,
0.04122148081660271,
-0.0029087159782648087,
-0.0076513695530593395,
0.010848574340343475,
-0.03673383966088295,
0.0064502498134970665,
-0.018437333405017853,
0.049958355724811554,
0.003227092092856765,
-0.01490158773958683,
0.04670232906937599,
0.033654216676950455,
0.006219362840056419,
0.07186590135097504,
-0.0006145359948277473,
-0.03677194565534592,
0.06618034839630127,
-0.01146586425602436,
0.03460616245865822,
0.025120165199041367,
-0.006124868988990784,
-0.006724378559738398,
0.07831670343875885,
0.012905699200928211,
0.03864810988306999,
-0.0024152228143066168,
-0.07963582873344421,
0.01177145354449749,
-0.033337369561195374,
-0.03328033536672592,
-0.000031539333576802164,
-0.006699615158140659,
-0.051921673119068146,
-0.030583282932639122,
0.01189444400370121,
0.07005387544631958,
-0.02825152315199375,
-0.020242230966687202,
0.02877148985862732,
-0.03358582779765129,
-0.019211260601878166,
-0.07158342003822327,
-0.022216325625777245,
0.013088976964354515,
0.034552011638879776,
0.06762294471263885,
0.021666763350367546,
0.038285400718450546,
0.04339134320616722,
0.07015080749988556,
-0.019970647990703583,
-0.031390152871608734,
0.025049932301044464,
-0.019795304164290428,
-0.0281191635876894,
0.03390704467892647,
-0.03730645775794983,
0.006789303384721279,
0.06624291092157364,
0.03320594131946564,
-0.03557819500565529,
-0.005125958006829023,
-0.008773906156420708,
0.06398613750934601,
-0.008844416588544846,
-0.03501609340310097,
0.011265280656516552,
-0.021555781364440918,
0.020276376977562904,
-0.0005597565905191004,
-0.030203595757484436,
0.017529521137475967,
0.09068194031715393,
0.05157380923628807,
-0.025481004267930984,
0.034900765866041183,
-0.0005174181424081326,
-0.026506155729293823,
0.03338538482785225,
0.01739581488072872,
0.05188024044036865,
-0.013147774152457714,
-0.016446372494101524,
-0.0016795139526948333,
-0.002925717504695058,
0.005600637756288052,
-0.040820326656103134,
-0.01705177128314972,
0.003943595569580793,
0.004112285561859608,
0.0026754778809845448,
0.030088862404227257,
-0.04060841724276543,
0.05050086975097656,
0.05224810913205147,
-0.027792440727353096,
0.05791444703936577,
0.027966637164354324,
0.03005492128431797,
-0.014283865690231323,
0.012689637020230293,
0.004134438931941986,
-0.0019299561390653253,
-0.01082312036305666,
-0.005391829647123814,
-0.0545608289539814,
0.017312385141849518,
-0.08897870779037476,
0.06740477681159973,
0.002537152962759137,
0.022252514958381653,
-0.01889692060649395,
-0.0369768850505352,
-0.016304638236761093,
-0.08789898455142975,
0.004606111440807581,
-0.02027875743806362,
-0.006514302454888821,
-0.03475961089134216,
0.03489922732114792,
-0.08315549790859222,
-0.024835996329784393,
-0.004721151199191809,
-0.02113257348537445,
-0.0394519567489624,
0.051177263259887695,
-0.04461969807744026,
0.005541111808270216,
-0.010045723058283329,
-0.028874864801764488,
-0.03954850509762764,
0.04367765411734581,
-0.03779923543334007,
0.018710503354668617,
0.04062909632921219,
0.12951603531837463,
-0.014892149716615677,
0.00503933010622859,
0.014816176146268845,
-0.027347229421138763,
-0.0034704534336924553,
0.01377931796014309,
-0.0024569579400122166,
-0.01336726639419794,
-0.027316948398947716,
-0.02426500804722309,
0.019938955083489418,
0.014717723242938519,
0.023219620808959007,
-0.016992995515465736,
-0.03206169977784157,
0.0011004237458109856,
-0.01924395188689232,
-0.004216332454234362,
0.024948203936219215,
0.012919020839035511,
-0.06070363521575928,
0.09845028072595596,
-0.013996697962284088,
-0.03221845626831055,
-0.0035830880515277386,
0.039388127624988556,
-0.0004444450023584068,
-0.0048746285028755665,
0.0069855512119829655,
0.00007434676081174985,
-0.042009007185697556,
0.06023304536938667,
-0.0526006780564785,
0.007089040707796812,
0.028078598901629448,
-0.00022236128279473633,
-0.022591477259993553,
0.07311614602804184,
0.015459553338587284,
0.045205600559711456,
-0.04341108351945877,
-0.046005040407180786,
0.03702469915151596,
-0.03404725715517998,
0.005188957788050175,
-0.018208574503660202,
-0.0024957379791885614,
0.003996538929641247,
0.01883622258901596,
0.013023089617490768,
0.02471647970378399,
0.09362945705652237,
-0.05149964615702629,
0.0380864217877388,
-0.05069361999630928,
-0.004318819381296635,
0.045423075556755066,
0.1057509034872055,
-0.008987623266875744,
-0.06280617415904999,
-0.02280423231422901,
-0.03794264793395996,
-0.01464718859642744,
0.006817592773586512,
0.055165261030197144,
0.02274686098098755,
0.000769590784329921,
0.0011142913717776537,
-0.05647711828351021,
-0.034607574343681335,
0.031309641897678375,
0.03994521126151085,
0.02266009896993637,
-0.026211317628622055,
-0.013560283929109573,
-0.02070700377225876,
0.06742175668478012,
0.009909636341035366,
0.0038758553564548492,
0.00036880761035718024,
-0.022452516481280327,
0.028328310698270798,
0.025788914412260056,
0.04315267503261566,
-0.0006627060356549919,
-0.017638923600316048,
-0.07476408034563065,
-0.017889149487018585,
-0.0025728598702698946,
0.0510418601334095,
0.014950796030461788,
0.044134628027677536,
-0.03394971787929535,
0.008612670935690403,
-0.040239691734313965,
-0.04165879637002945,
0.006294317077845335,
-0.03952963277697563,
-0.04544027894735336,
-0.03825623169541359,
-0.002968576969578862,
-0.013905491679906845,
-0.014582499861717224,
-0.020766064524650574,
-0.060708869248628616,
0.01553276926279068,
0.03487059101462364,
0.024700509384274483,
-0.0026196218095719814,
-0.004993528593331575,
-0.004865463823080063,
0.08162404596805573,
-0.03668965399265289,
0.0037512374110519886,
0.029655713587999344,
0.03315136954188347,
0.024318773299455643,
-0.03086082637310028,
0.0010261016432195902,
-0.0032757921144366264,
0.029071878641843796,
0.04449915885925293,
-0.05531265214085579,
-0.10630101710557938,
-0.0008156888070516288,
0.007352983113378286,
0.059530749917030334,
0.04156825318932533,
-0.013397871516644955,
-0.009773749858140945,
-0.029064781963825226,
0.016899606212973595,
0.0520666278898716,
-0.01623816415667534,
-0.04534575715661049,
0.002613017801195383,
-0.010010598227381706,
-0.011185123585164547,
-0.029334738850593567,
-0.0764310359954834,
-0.026856666430830956,
-0.009865651838481426,
0.0369030199944973,
0.055437780916690826,
-0.010393817909061909,
0.037335049360990524,
0.02171551063656807,
0.0301460400223732,
0.024050967767834663,
-0.021887827664613724,
0.010376361198723316,
0.016366994008421898,
-0.02447229065001011,
-0.014980616047978401,
0.013874607160687447,
0.006726300809532404,
0.008896617218852043,
0.03905709087848663,
0.008218369446694851,
0.018524175509810448,
-0.031160492449998856,
0.019980786368250847,
-0.05672110617160797,
0.04838433861732483,
0.025328503921628,
0.03139786794781685,
0.04676057770848274,
-0.006229952909052372,
-0.008777615614235401,
-0.01604791171848774,
-0.020162111148238182,
0.10105891525745392,
-0.005679361056536436,
-0.0011586010223254561,
-0.016365299001336098,
-0.024799425154924393,
-0.0191408209502697,
-0.031981874257326126,
-0.005257900338619947,
-0.0033441861160099506,
-0.013767613098025322,
-0.0005487968446686864,
-0.08697877079248428,
-0.002683473750948906,
0.016842812299728394,
-0.008316761814057827,
0.023140331730246544,
0.008662177249789238,
-0.004164720885455608,
-0.011773735284805298,
-0.01930142194032669,
-0.005440360866487026,
0.010807844810187817,
0.02042514644563198,
-0.043521009385585785,
-0.02169136144220829,
0.07409770786762238,
0.04947932809591293,
0.001221617334522307,
0.08044283837080002,
0.00537186861038208,
-0.03289427608251572,
0.004368050489574671,
0.009026716463267803,
0.05144849419593811,
-0.009685839526355267,
-0.0045632109977304935,
-0.052882276475429535,
-0.03618023172020912,
-0.03980395197868347,
0.03138228878378868,
0.004465906415134668,
-0.0030711626168340445,
-0.012666156515479088,
0.01049892883747816,
0.002118556061759591,
0.052477143704891205,
0.056106261909008026,
-0.0019228145247325301,
-0.03514225780963898,
0.013159049674868584,
-0.021492160856723785,
-0.045259617269039154,
-0.014711844734847546,
-0.05793941393494606,
0.003120026784017682,
-0.014180467464029789,
-0.03878255933523178,
0.018682807683944702,
0.05665761977434158,
-0.008652281947433949,
0.015642771497368813,
0.011397743597626686,
-0.04401766136288643,
0.0034960543271154165,
0.07951991260051727,
-0.04333470016717911,
0.09141996502876282,
0.0648992583155632,
0.030266353860497475,
-0.02421991527080536,
-0.012476957403123379,
0.007642657030373812,
-0.06974934041500092,
-0.04694763943552971,
-0.02365156263113022,
0.028829658403992653,
-0.01701824553310871,
-0.020249320194125175,
0.01836160384118557,
-0.0385102815926075,
0.0519697405397892,
-0.02036152593791485,
-0.0144402626901865,
-0.043367475271224976,
0.12003935873508453,
0.026320884004235268,
-0.03416549041867256,
0.02068566530942917,
-0.028796225786209106,
-0.07721329480409622,
-0.03556838631629944,
0.000247762945946306,
0.025018662214279175,
0.02430221624672413,
-0.04424048960208893,
-0.07247956842184067,
-0.06111011281609535,
0.06066364422440529,
0.06071773171424866,
0.00041596157825551927,
-0.03870738670229912,
-0.025936409831047058,
0.005072744097560644,
0.05180684104561806,
-0.09454767405986786,
-0.018009889870882034,
0.04115677997469902,
-0.005751218181103468,
-0.04838087782263756,
-0.01316773984581232,
0.03622288629412651,
-0.07418574392795563,
0.039435844868421555,
-0.012048172764480114,
-0.05662719905376434,
0.028456931933760643,
-0.004045153968036175,
0.0326184518635273,
0.010975898243486881,
0.03610167279839516,
-0.001102629117667675,
-0.000985874910838902,
-0.016218535602092743,
0.04816953092813492,
-0.01026215311139822,
0.042350396513938904,
0.0068404218181967735,
-0.038151562213897705,
0.014619429595768452,
0.01799832098186016,
-0.0328618660569191,
-0.04784929007291794,
0.010050302371382713,
-0.08480459451675415,
0.06902549415826797,
-0.014812454581260681,
0.012732057832181454,
0.015133041888475418,
-0.030153950676321983,
-0.019113173708319664,
-0.030278561636805534,
-0.08048131316900253,
-0.031297340989112854,
0.01733528822660446,
-0.061102788895368576,
-0.0021884392481297255,
-0.016891732811927795,
-0.032614193856716156,
-0.022912517189979553,
-0.08806488662958145,
0.01591896265745163,
-0.022150708362460136,
0.01788514107465744,
-0.007973384112119675,
0.013353127986192703,
0.03687569126486778,
0.013095058500766754,
-0.005161053966730833,
-0.027780070900917053,
-0.006171569228172302,
0.06580322235822678,
0.014498477801680565,
0.0018698020139709115,
0.01808816008269787,
-0.024193309247493744,
-0.04025372490286827,
-0.011699458584189415,
0.008509109728038311,
0.021635953336954117,
-0.012062461115419865,
0.01917334273457527,
0.0023672468960285187,
-0.02385743334889412,
0.0003601453499868512,
-0.024012072011828423,
0.006254417821764946,
0.004174407105892897,
0.06464710831642151,
-0.04802047088742256,
0.038138531148433685,
-0.026230795308947563,
-0.003348197788000107,
0.040204063057899475,
0.038553401827812195,
0.021304909139871597,
-0.0005372051382437348,
0.011692899279296398,
-0.000997596187517047,
0.08001317828893661,
0.02586539275944233,
0.062451526522636414,
0.04615793004631996,
0.06833286583423615,
0.0041153570637106895,
-0.03267668932676315,
-0.06115460768342018,
0.06678877025842667,
0.004058979917317629,
0.07816603034734726,
-0.026277747005224228,
-0.03687245026230812,
0.030093783512711525,
-0.008848043158650398,
-0.0008969783666543663,
0.014064601622521877,
-0.018241412937641144,
-0.06849522888660431,
-0.018248839303851128,
0.007548993453383446,
-0.04615679010748863,
0.05595779046416283,
-0.006134481634944677,
0.019342681393027306,
0.06276258081197739,
-0.0600823312997818,
-0.03837126865983009,
-0.0021550694946199656,
0.05783715471625328,
-0.04192217066884041,
-0.04762987419962883,
0.012681775726377964,
0.050478655844926834,
-0.005416980944573879,
0.03352903202176094,
0.039226047694683075,
0.0417860671877861,
-0.0043011996895074844,
-0.006814060267060995,
0.02324097417294979,
-0.001117777545005083,
0.041449759155511856,
-0.00491100549697876,
0.01251131109893322,
0.023599721491336823,
0.024042736738920212,
-0.00679677864536643,
0.017144575715065002,
-0.007350356318056583,
0.03660499304533005,
-0.035602740943431854,
0.031393587589263916,
-0.00887821801006794,
0.08775845170021057,
0.03195223584771156,
-0.058074530214071274,
0.004063460044562817,
0.02004961669445038,
0.07625621557235718,
0.012243716046214104,
0.014476330950856209,
-0.03462882339954376,
0.01840520091354847,
0.030476830899715424,
0.008028589189052582,
-0.022153940051794052,
0.025263996794819832,
-0.02569759078323841,
0.04111415520310402,
0.02959546633064747,
-0.011513815261423588,
0.00860197190195322,
-0.037925008684396744,
-0.024875907227396965,
-0.054922498762607574,
0.0017584003508090973,
-0.01788022182881832,
0.020345186814665794,
0.005731591489166021,
0.01972724311053753,
-0.07492896169424057,
0.018120067194104195,
-0.008182479999959469,
0.03462902829051018,
0.00627318536862731,
-0.0021923042368143797,
-0.04653748497366905,
0.029261073097586632,
0.0012524055782705545,
-0.034597739577293396,
0.015888135880231857,
-0.040851544588804245,
-0.0592770129442215,
-0.03950414061546326,
-0.020596060901880264,
0.025591975077986717,
0.03424781933426857,
-0.03354407474398613,
0.008583560585975647,
-0.0027008375618606806,
0.005028445273637772,
0.002285605063661933,
-0.003922647796571255,
-0.01565585285425186,
-0.06772597134113312,
0.004956174176186323,
-0.05846795812249184,
-0.03487265482544899,
0.0031991302967071533,
-0.022601256147027016,
0.05302564427256584,
-0.009295593947172165,
0.00884855818003416,
0.02563902549445629,
0.047505997121334076,
-0.025862978771328926,
0.06654636561870575,
-0.02784177102148533,
-0.11785160005092621,
0.011316755786538124,
0.04929719492793083,
0.021425383165478706,
-0.004557004198431969,
0.015077462419867516,
0.023551473394036293,
-0.005301904398947954,
-0.020091554149985313,
-0.005039840470999479,
-0.013680141419172287,
-0.07265007495880127,
-0.06030159816145897,
-0.0065835448913276196,
0.02486262656748295,
0.037308864295482635
] |
<p>In a question titled <a href="http://physics.stackexchange.com/questions/2041/how-are-classical-optics-phenomena-explained-in-qed-snells-law">How are classical optics phenomena explained in QED (Snell's law)?</a> Marek talked about the probability amplitude for photons of a given path. He said that it was $\exp(iKL)$, and that "...this is very simplified picture but I don't want to get too technical so..." </p>
<p>I want to know how it arises, even if it is technical. I find it very strange. If we compare it to the case of a particle obeying the Schrodinger equation, we have $\exp(iS/h)$ where $S$ is the action of a given path. $S$ is what we want to minimize(in the classical limit). In this case the path is a space-time path. </p>
<p>But in the other case, of the photon, where $L$ is that we have to minimize(in the classical limit or if you want in the geometrical optics limit) the paths are only in space, and I can't find any temporal dependence. </p>
<p>when I check any book about QED, I can read about the photon propagator (about space-time paths) but I never have found out about the expression $\exp(iKL)$.</p>
<p>In general terms I find hard to relate what Feynman teaches in his book with what I have read in the "formal QED books" like Sokolov, Landau, Feynman or Greiner.</p> | g7782 | [
0.010232110507786274,
0.0569767951965332,
-0.0019122305093333125,
0.04734956473112106,
0.021958205848932266,
0.017171381041407585,
0.05219294875860214,
0.02002968266606331,
0.01839515008032322,
-0.0019550397992134094,
-0.009640514850616455,
-0.03295481577515602,
0.06310628354549408,
0.032651811838150024,
-0.00598817877471447,
-0.009789581410586834,
0.03454180806875229,
0.008744141086935997,
0.07411371171474457,
-0.011551384814083576,
-0.038387563079595566,
0.013594076037406921,
-0.016487715765833855,
-0.023497777059674263,
-0.01638353057205677,
0.033073410391807556,
0.06723818182945251,
-0.00710638239979744,
-0.04398566856980324,
-0.03081369400024414,
0.01730104722082615,
-0.05914195254445076,
0.04177793860435486,
-0.05349237844347954,
0.01550605334341526,
-0.030438292771577835,
0.052984338253736496,
-0.016594815999269485,
0.00852606724947691,
0.0032212729565799236,
0.03500151261687279,
-0.06893354654312134,
0.012188209220767021,
-0.021919405087828636,
0.016935428604483604,
0.018588146194815636,
0.0020913027692586184,
0.02431345172226429,
-0.04891670122742653,
-0.017456267029047012,
-0.033951204270124435,
0.05112384259700775,
0.04985123500227928,
0.004484432749450207,
0.049499355256557465,
0.044706519693136215,
0.012026474811136723,
-0.023375337943434715,
0.08392665535211563,
0.05481725558638573,
0.031586822122335434,
0.00475021218881011,
0.05671355873346329,
0.02608759142458439,
0.08771798759698868,
-0.05233184993267059,
-0.03362321853637695,
-0.03472834825515747,
-0.0193562600761652,
0.03869518265128136,
0.021503880620002747,
-0.04872385784983635,
-0.04816979169845581,
-0.033941593021154404,
-0.011692089959979057,
0.04110860824584961,
0.019447308033704758,
0.0046022734604775906,
0.07260876148939133,
0.02273751236498356,
-0.049368709325790405,
-0.026651866734027863,
0.0054400647059082985,
-0.00621197372674942,
0.04166428744792938,
0.03713987022638321,
0.009113993495702744,
-0.004241824150085449,
0.014897545799612999,
-0.03632283955812454,
-0.012241832911968231,
-0.025766581296920776,
0.10175156593322754,
0.021656157448887825,
-0.0012889711651951075,
-0.016153521835803986,
-0.04006626084446907,
0.0611037015914917,
0.010045954957604408,
-0.01699274219572544,
-0.03710777312517166,
-0.014900065958499908,
0.029568862169981003,
0.018181627616286278,
-0.06769590079784393,
0.01855718344449997,
0.012261980213224888,
-0.017826253548264503,
0.0337863527238369,
0.020371831953525543,
-0.03177797421813011,
-0.014850693754851818,
-0.07275238633155823,
-0.03548894822597504,
-0.01781770959496498,
0.0074168602004647255,
0.026414958760142326,
-0.02341430075466633,
0.004622035659849644,
0.058001503348350525,
0.021659402176737785,
-0.03004138544201851,
-0.0025969594717025757,
0.06419039517641068,
0.017749376595020294,
0.07359877973794937,
-0.004795784130692482,
-0.00746977049857378,
0.04765286669135094,
0.03255230560898781,
0.07581852376461029,
0.03222806751728058,
-0.008892646059393883,
0.022427499294281006,
-0.011673182249069214,
0.02457500994205475,
0.03057164140045643,
-0.0344657376408577,
0.02310618944466114,
-0.01940409280359745,
0.010645942762494087,
0.0026861075311899185,
-0.005453588906675577,
-0.05425850674510002,
-0.03544371947646141,
0.022271867841482162,
0.006467602215707302,
-0.015961093828082085,
-0.011267668567597866,
-0.018187470734119415,
0.005070554558187723,
0.03268352895975113,
-0.011062334291636944,
-0.026498276740312576,
0.047381117939949036,
-0.027547817677259445,
-0.003696128260344267,
-0.014593730680644512,
-0.0756785050034523,
-0.049874112010002136,
0.05138961598277092,
-0.004142035264521837,
0.010176748968660831,
0.01532161608338356,
-0.039292801171541214,
0.023533130064606667,
0.011903525330126286,
-0.059815406799316406,
0.0018187250243499875,
-0.04393051937222481,
-0.02214568480849266,
-0.05420827120542526,
0.01187089178711176,
0.041529495269060135,
-0.08927543461322784,
0.07580039650201797,
0.0000722962649888359,
-0.016300281509757042,
-0.0021230801939964294,
0.008022374473512173,
-0.03721187636256218,
0.034247931092977524,
0.015148387290537357,
-0.015761911869049072,
-0.015222185291349888,
0.02230606973171234,
0.008012927137315273,
0.05463384464383125,
-0.026368319988250732,
-0.045091062784194946,
0.00553983123973012,
-0.049987949430942535,
0.0023605888709425926,
0.029385851696133614,
0.0010535645997151732,
-0.0005731919081881642,
-0.008377139456570148,
-0.0875585526227951,
-0.014158057980239391,
-0.01840372011065483,
0.00018405575247015804,
0.04892437160015106,
-0.012383289635181427,
0.006281272973865271,
0.04933790862560272,
-0.01930069550871849,
0.004021666012704372,
0.011059482581913471,
0.014572987332940102,
-0.01713666133582592,
0.0540006197988987,
-0.007136297412216663,
0.009304373525083065,
0.040230512619018555,
-0.02244921773672104,
-0.053704265505075455,
-0.009391735307872295,
-0.022100217640399933,
0.043591707944869995,
0.0055275531485676765,
-0.004480812698602676,
-0.05661148577928543,
0.014258293434977531,
0.0072533548809587955,
-0.044513411819934845,
-0.0034293713979423046,
-0.04612935706973076,
-0.004279088228940964,
0.00691666454076767,
0.0745956227183342,
-0.09425294399261475,
-0.023688724264502525,
-0.047259263694286346,
0.0041307006031274796,
0.0625511109828949,
-0.0008155438699759543,
0.004057663958519697,
-0.01679622381925583,
0.058798011392354965,
0.004733595997095108,
0.0019862463232129812,
-0.014698827639222145,
-0.01782272942364216,
0.015075147151947021,
-0.020032191649079323,
-0.06479448080062866,
0.031108738854527473,
-0.021210474893450737,
-0.005404255352914333,
0.041617389768362045,
0.04256296902894974,
-0.005877908319234848,
0.020098835229873657,
-0.0346076637506485,
-0.0394299179315567,
0.0013201457913964987,
-0.03024599701166153,
0.06078445166349411,
-0.06596794724464417,
0.0038393812719732523,
-0.006535565480589867,
0.06097862496972084,
-0.047838978469371796,
-0.018571944907307625,
0.009233716875314713,
-0.009775145910680294,
0.017953509464859962,
0.037881068885326385,
0.01877351477742195,
0.008488618768751621,
-0.052974481135606766,
0.08617470413446426,
-0.019403837621212006,
0.0032763590570539236,
0.023100566118955612,
0.009210778400301933,
-0.00950175616890192,
-0.0010286382166668773,
0.05878661200404167,
-0.05634427070617676,
0.02268349565565586,
-0.04463771730661392,
-0.03444020077586174,
-0.0012226998805999756,
0.0040833791717886925,
-0.06851710379123688,
0.10654132068157196,
0.09167668223381042,
0.0002606339112389833,
0.002339255064725876,
-0.08847866952419281,
-0.03365003690123558,
-0.035572342574596405,
0.024031812325119972,
-0.0879661813378334,
0.026857422664761543,
0.01760200224816799,
-0.02677558735013008,
-0.0045235371217131615,
0.01091191079467535,
-0.04141305387020111,
-0.01908820867538452,
0.011379130184650421,
0.00548943504691124,
0.04042939096689224,
0.02804885432124138,
-0.03985114023089409,
-0.09676194190979004,
0.04889623448252678,
-0.015368438325822353,
0.029131915420293808,
0.023285778239369392,
-0.032607391476631165,
0.014490493573248386,
0.0008517097448930144,
0.03670176491141319,
-0.048165079206228256,
0.05424311012029648,
0.012709216214716434,
0.03212011978030205,
-0.08021867275238037,
-0.012375793419778347,
-0.024485519155859947,
-0.0262590479105711,
0.07606631517410278,
-0.03640832379460335,
-0.013593423180282116,
-0.01706565171480179,
-0.02980458363890648,
0.0045391167514026165,
0.004171616397798061,
-0.06108199805021286,
-0.04129127040505409,
-0.01984761655330658,
-0.02990555204451084,
-0.03647809848189354,
-0.05916757136583328,
-0.024379855021834373,
0.022026319056749344,
-0.010601402260363102,
0.016663292422890663,
-0.029493240639567375,
-0.0922977551817894,
0.02200854755938053,
-0.04948225989937782,
0.016938259825110435,
0.002583178458735347,
0.029129626229405403,
0.0375344380736351,
-0.011939392425119877,
0.014173522591590881,
-0.00008155499381246045,
0.02079678513109684,
0.04270176216959953,
-0.039834752678871155,
0.08411875367164612,
-0.014439085498452187,
0.05912119150161743,
0.11797935515642166,
-0.05121513828635216,
-0.011077695526182652,
-0.0012278292560949922,
0.0031743827275931835,
-0.01993381790816784,
0.0011726253433153033,
-0.018900375813245773,
0.015984460711479187,
0.006731425877660513,
0.03842215985059738,
0.010214021429419518,
-0.0029458790086209774,
-0.02185196429491043,
-0.0197476577013731,
0.04083983227610588,
0.025502504780888557,
-0.008939781226217747,
-0.01037821639329195,
0.02284218557178974,
-0.07197919487953186,
0.0012500365264713764,
-0.044236503541469574,
0.051479779183864594,
0.07661538571119308,
0.008410687558352947,
0.040979884564876556,
0.04654968902468681,
-0.07662530988454819,
0.00030621426412835717,
0.02491891384124756,
0.010499491356313229,
0.00877097062766552,
-0.03887758404016495,
-0.023808350786566734,
-0.023594139143824577,
0.00457963440567255,
0.043446749448776245,
0.04957474023103714,
-0.0408361554145813,
-0.004167653154581785,
0.012466118671000004,
0.021744903177022934,
0.040171362459659576,
0.04230219125747681,
0.055235326290130615,
-0.01914440095424652,
0.019927866756916046,
0.0367114432156086,
-0.06905797123908997,
-0.020371105521917343,
-0.014696543104946613,
-0.014363818801939487,
-0.02315921150147915,
-0.010875324718654156,
-0.06920982152223587,
0.017207734286785126,
0.05668438598513603,
0.028186598792672157,
-0.09161978214979172,
-0.02660188265144825,
-0.007681403774768114,
0.017907507717609406,
-0.020093711093068123,
-0.016772249713540077,
-0.04596384987235069,
0.03154579550027847,
0.013029517605900764,
-0.0010861294576898217,
-0.02474982477724552,
-0.021264929324388504,
-0.07301865518093109,
0.009135615080595016,
0.003105559153482318,
0.03498974069952965,
-0.007745776325464249,
-0.06679913401603699,
0.037643417716026306,
-0.009126006625592709,
0.0502835288643837,
0.008884092792868614,
0.0494852289557457,
0.05053994432091713,
-0.03501966595649719,
0.029102426022291183,
-0.028048524633049965,
0.03758455067873001,
0.006800932344049215,
-0.012409198097884655,
-0.0347408652305603,
-0.019328156486153603,
-0.05195404589176178,
-0.021846244111657143,
0.02554274909198284,
-0.009708568453788757,
-0.08203152567148209,
-0.0029730526730418205,
-0.039147164672613144,
-0.0752425268292427,
0.045663826167583466,
0.042799465358257294,
0.018949173390865326,
-0.08207602053880692,
-0.0015427994076162577,
0.011738147586584091,
-0.036679934710264206,
0.05610891804099083,
-0.03444064408540726,
-0.07942599058151245,
0.02387307584285736,
-0.02726808935403824,
-0.02837953343987465,
0.03657010197639465,
0.03819490596652031,
0.022854777052998543,
-0.04548690468072891,
-0.012453228235244751,
-0.04703310504555702,
-0.03741410747170448,
0.01960020884871483,
-0.027554845437407494,
-0.037397995591163635,
0.001649558893404901,
-0.011229436844587326,
-0.014044422656297684,
-0.006625293288379908,
-0.02643227018415928,
0.025914505124092102,
0.024211620911955833,
-0.020191775634884834,
-0.005168151576071978,
-0.03953239694237709,
0.06643560528755188,
-0.058089833706617355,
0.02116028405725956,
0.02578779309988022,
-0.01725025102496147,
-0.03594641387462616,
0.042164355516433716,
0.0004905264941044152,
0.022662153467535973,
-0.019810223951935768,
-0.059024810791015625,
-0.029451711103320122,
-0.033466026186943054,
-0.0024659771006554365,
0.0023310633841902018,
0.03490931913256645,
0.013017774559557438,
-0.03384913504123688,
-0.03357425704598427,
0.023569127544760704,
0.06054341048002243,
0.0014211570378392935,
-0.018717363476753235,
0.059384655207395554,
0.03684077039361,
-0.008133998140692711,
-0.05284886434674263,
0.01969384029507637,
0.032648198306560516,
-0.032092273235321045,
-0.010674653574824333,
0.006742772646248341,
-0.04324309527873993,
-0.017307139933109283,
0.01774631440639496,
-0.0020265444181859493,
-0.04049964249134064,
-0.0562688484787941,
0.03729909285902977,
-0.0013269538758322597,
-0.014349175617098808,
0.039178602397441864,
0.01875247433781624,
0.016663946211338043,
-0.008276049979031086,
-0.05946027487516403,
0.03652545064687729,
0.029111061245203018,
0.0038166723679751158,
-0.017254050821065903,
-0.042543455958366394,
-0.014073819853365421,
0.01953156292438507,
-0.006469087675213814,
0.003761888947337866,
-0.029254915192723274,
-0.03431640937924385,
0.0066567822359502316,
0.05916802957653999,
-0.027902426198124886,
-0.006407808978110552,
-0.022829866036772728,
0.031130284070968628,
-0.015691952779889107,
-0.007573004346340895,
0.01827787607908249,
-0.047968242317438126,
0.02718348614871502,
-0.05888183042407036,
-0.012514865025877953,
0.10403680056333542,
0.015259847044944763,
0.05147922784090042,
-0.013006247580051422,
0.0030665264930576086,
-0.057827427983284,
-0.02157115563750267,
-0.02254188247025013,
0.048090867698192596,
0.07730118930339813,
-0.005980545189231634,
0.0528300404548645,
0.002102899830788374,
0.05073075741529465,
0.018754076212644577,
0.04237726330757141,
0.009584929794073105,
-0.04794176295399666,
-0.07814916223287582,
-0.008185380138456821,
-0.02802586928009987,
0.07393306493759155,
0.037063486874103546,
-0.03524712473154068,
-0.05761106684803963,
0.075533427298069,
-0.005228042136877775,
-0.006670868955552578,
0.005995683837682009,
0.04726999253034592,
-0.027042115107178688,
-0.006737446878105402,
-0.021266981959342957,
0.0031651153694838285,
-0.02772531285881996,
-0.030016455799341202,
0.04653986170887947,
-0.013711136765778065,
0.02129855751991272,
0.016245324164628983,
-0.003502360312268138,
0.009149136953055859,
0.009954001754522324,
-0.02548249065876007,
0.02545662224292755,
0.049047354608774185,
-0.02587645687162876,
-0.005341013893485069,
0.03987742215394974,
-0.0204728115350008,
0.032976582646369934,
0.021080777049064636,
-0.041623711585998535,
-0.008461284451186657,
-0.013882645405828953,
-0.05177256092429161,
-0.022027524188160896,
0.03565458953380585,
-0.022205248475074768,
0.005581586621701717,
-0.021258432418107986,
0.017150122672319412,
0.004340209066867828,
-0.001562492921948433,
0.018731532618403435,
0.040193233639001846,
-0.004155315924435854,
-0.004443853162229061,
0.022309744730591774,
0.04068360850214958,
0.02051009237766266,
0.023009298369288445,
0.0021042826119810343,
0.0494605228304863,
-0.04608432203531265,
0.031132064759731293,
-0.04188898205757141,
0.05292948707938194,
-0.01656355708837509,
0.04674587771296501,
0.045903682708740234,
0.02720632031559944,
0.030431395396590233,
-0.019976647570729256,
-0.042917877435684204,
0.011233084835112095,
-0.0120927719399333,
0.013244525529444218,
-0.0685056522488594,
-0.012084261514246464,
0.021084684878587723,
-0.04871423542499542,
-0.03055396117269993,
0.008417618460953236,
0.034274496138095856,
-0.016085390001535416,
-0.018489396199584007,
0.040608327835798264,
0.019640516489744186,
-0.126697838306427,
-0.03643491491675377,
-0.00105115189217031,
-0.03002113290131092,
0.022892791777849197,
0.0297288466244936,
0.014556844718754292,
0.027338093146681786,
-0.017330799251794815,
-0.04150177910923958,
0.018305962905287743,
0.016523385420441628,
-0.037090003490448,
-0.0248873271048069,
0.02629559300839901,
0.0003361219714861363,
0.0006467641796916723,
-0.009655235335230827,
0.051973264664411545,
-0.038269080221652985,
0.04053426906466484,
0.023640818893909454,
0.01875597983598709,
0.025363031774759293,
-0.036436229944229126,
0.006395000498741865,
0.017309041693806648,
-0.05113346129655838,
-0.023909494280815125,
0.028872931376099586,
0.00325745134614408,
-0.023505495861172676,
-0.024463441222906113,
-0.011082219891250134,
-0.031077519059181213,
0.04665996506810188,
0.017386043444275856,
0.03276236355304718,
0.030234690755605698,
0.02765301801264286,
0.047756344079971313,
0.007482931483536959,
-0.03013482131063938,
-0.01939271204173565,
0.02142522856593132,
0.012808906845748425,
-0.007553968578577042,
0.016462860628962517,
-0.08984358608722687,
0.001312983687967062,
-0.0020128446631133556,
-0.00697453273460269,
0.011826538480818272,
0.007545506581664085,
0.05026591941714287,
0.02588815987110138,
0.02855849638581276,
0.01398689579218626,
0.0786585807800293,
-0.0018353824270889163,
0.02140582539141178,
-0.0014344145311042666,
-0.016120856627821922,
-0.04788988083600998,
-0.024538565427064896,
0.010907584801316261,
0.014364145696163177,
0.024023862555623055,
-0.05952038615942001,
-0.005723316688090563,
-0.03397892415523529,
0.0024237376637756824,
-0.05256921052932739,
-0.024020547047257423,
0.019014908000826836,
-0.010672902688384056,
0.018124355003237724,
-0.028553465381264687,
0.06666219979524612,
-0.010815848596394062,
0.02704189158976078,
0.008026824332773685,
-0.08546795696020126,
0.013330028392374516,
-0.01398677472025156,
-0.04679042100906372,
-0.04744041711091995,
0.023700948804616928,
-0.05259030684828758,
0.0023039821535348892,
0.027534956112504005,
-0.027969110757112503,
0.03734070062637329,
-0.034293074160814285,
0.054140642285346985,
0.05726708471775055,
-0.08350039273500443,
0.03578423708677292,
-0.01980270817875862,
0.015521091409027576,
0.04008323699235916,
0.023387396708130836,
-0.036986224353313446,
0.0233863927423954,
-0.023082325235009193,
-0.044525984674692154,
-0.013135448098182678,
-0.028182463720440865,
0.007826592773199081
] |
<p>I'm pretty certain that the answer to the question in the title is a no, but I don't understand why. I have some basic misunderstanding of quantum processes that I’d like clarified in the form of asking questions about a hypothetical scenario. </p>
<p>So, let’s say we have a pair of entangled photons…</p>
<p>1) Is it possible to prepare an entangled pair such that it can be known that, for example, the photon going down a certain path will be measured 25% of the time to be horizontally polarized and 75% likely to be vertically polarized? I guess this would be some sort of quantum decoherence? Partial collapse?</p>
<p>2) If that is possible, then would it also be possible to measure that photon’s diagonal polarization in order to "reset" the horizontal-vertical probability back to 50-50?
I've seen a trick done where you take some polarizing filters and stack them horizontal on top of vertical, so that no light gets through. But when you slide a diagonally oriented filter between them, some light does get through, because the horizontal/vertical polarization information gets "reset" when measured against the diagonal filter.</p>
<p>3) If these two things are possible, then wouldn’t it be possible to send information along the entangled pair? If you sent bursts of 1000 photons and were able to measure them all, and found that the first burst had ~750 vertically polarized photons but the second burst had ~500 vertically polarized photons, then wouldn’t you know that the second burst had their diagonal measurements taken? Or would that not work because the extra measurements "break" the entanglement..? </p>
<p>4) Along with that, how many times can the photon pairs be measured before there are no longer entangled? Just once? Or maybe just once per state/qubit/aspect (such as polarization angle)? I understand that measuring the photon would necessarily change it (like with the polarization filter trick), but then how do scientists measure the polarization angles of two photons like in experiments of Bell’s inequality?</p>
<p>I know that somewhere along the line, what I've described cannot be possible. If it were, then you could easily send information faster than light. E.g., say you had a photon-entanglement-generator-and-probability-fixer station in between two planets, 1 light year from the planet Foo and .99 light years from the planet Bar. After a year's time, after the photon stream has propagated to both planets, scientists on Bar could measure diagonally polarization of 1000 photons to encode a 1 or not measure to encode a 0. Then scientists on the planet Foo could measure vertically polarity and decode the 1s and 0s based on the statistical readings. The Bar scientists could encode that such a message and the Foo scientists would "instantly" receive the message. Except it would actually be from the past, since Foo is 1.99 years outside the Bar light cone. So since this is impossible, what am I misunderstanding?</p>
<p>Thanks for answering, and thanks for putting up with yet another clueless but curious layman.</p> | g7783 | [
-0.03497621417045593,
0.011208970099687576,
0.0083191879093647,
0.010052737779915333,
0.028564058244228363,
0.016930198296904564,
-0.003906149882823229,
0.002622191095724702,
0.008299050852656364,
0.030006974935531616,
-0.003046590369194746,
0.016112100332975388,
-0.010728167369961739,
-0.027505313977599144,
-0.023296568542718887,
0.004232032690197229,
0.1007670983672142,
-0.037938762456178665,
0.031111350283026695,
-0.031409889459609985,
-0.00038825799128971994,
-0.0021305514965206385,
-0.014371383935213089,
-0.04441891238093376,
-0.04488424211740494,
-0.04996277764439583,
0.00769116822630167,
-0.05950513854622841,
-0.06944795697927475,
-0.0013855926226824522,
-0.029698699712753296,
-0.0901259109377861,
0.022678975015878677,
-0.0380229726433754,
-0.03606482595205307,
-0.06756360083818436,
-0.01144326850771904,
-0.05730336159467697,
0.030162306502461433,
0.04392455890774727,
0.07103331387042999,
-0.009543935768306255,
0.057287152856588364,
-0.08144111931324005,
0.05766575410962105,
0.00252446997910738,
0.05591827630996704,
-0.005363091826438904,
0.038732849061489105,
-0.03254018351435661,
-0.0005200719460844994,
-0.035294778645038605,
0.035407643765211105,
0.05235684663057327,
0.006623389199376106,
0.13531799614429474,
0.05071026086807251,
0.004034749232232571,
0.07054047286510468,
0.015314682386815548,
0.011675437912344933,
-0.06238560751080513,
0.022168073803186417,
-0.02381112612783909,
0.019039124250411987,
0.01791747286915779,
-0.06662362068891525,
-0.024702994152903557,
0.018778808414936066,
-0.0013835716526955366,
0.012766594998538494,
0.021420566365122795,
-0.00794468354433775,
-0.048532675951719284,
0.05525164678692818,
0.06820610165596008,
-0.03454799950122833,
-0.00825075525790453,
0.014937172643840313,
0.06306896358728409,
-0.0006071229581721127,
-0.004599505569785833,
0.01608331687748432,
-0.01563214883208275,
0.0928560420870781,
0.022026393562555313,
-0.01862175762653351,
-0.0493633858859539,
-0.020898262038826942,
0.02283698134124279,
0.02521301433444023,
-0.049004700034856796,
0.067474365234375,
0.0748131275177002,
-0.0366164892911911,
-0.031876470893621445,
-0.02981061115860939,
0.018492722883820534,
0.01607373356819153,
0.04281752184033394,
-0.04600493982434273,
0.026130156591534615,
-0.02629806660115719,
0.028941292315721512,
-0.02622704766690731,
-0.003909760620445013,
0.0388508066534996,
-0.01971345953643322,
-0.034903235733509064,
-0.02729986421763897,
-0.06933911144733429,
0.014944071881473064,
-0.07102188467979431,
-0.02541016787290573,
-0.04204661399126053,
-0.011568102985620499,
0.08484852313995361,
0.01333772111684084,
-0.03581451252102852,
0.047440845519304276,
0.01988859847187996,
0.03812885284423828,
0.000671197718475014,
0.0673580914735794,
-0.05352122709155083,
0.07075309008359909,
-0.036867838352918625,
0.04941638559103012,
0.02396279387176037,
-0.02036435529589653,
0.020519010722637177,
0.02940000221133232,
-0.011205422692000866,
0.03476087003946304,
0.011663027107715607,
-0.016771677881479263,
0.08334601670503616,
0.046634137630462646,
0.01688797026872635,
0.022996287792921066,
-0.007118722423911095,
-0.02017049677670002,
-0.020495178177952766,
-0.010584685951471329,
0.022061211988329887,
0.029507290571928024,
-0.03736230731010437,
0.015385971404612064,
0.028921417891979218,
-0.004173584748059511,
0.01682744361460209,
0.015535708516836166,
0.02657451666891575,
-0.04179133474826813,
-0.016362512484192848,
-0.02221778780221939,
0.018797488883137703,
0.0034311639610677958,
0.03162205219268799,
0.06787307560443878,
0.04851172864437103,
0.0588233545422554,
0.001989297568798065,
-0.02824677899479866,
-0.00830387044698,
0.02607015147805214,
-0.0032950451131910086,
-0.043777164071798325,
-0.02796839363873005,
-0.06583399325609207,
-0.05822170153260231,
0.023162148892879486,
0.04570585489273071,
0.02960740588605404,
-0.013041009195148945,
0.13404394686222076,
0.00484171649441123,
-0.04529587924480438,
-0.01014182809740305,
0.022783873602747917,
-0.041337981820106506,
0.05792833864688873,
-0.01446846779435873,
-0.005691010504961014,
-0.006689027417451143,
-0.05800015479326248,
0.01656327210366726,
0.023426607251167297,
-0.048710234463214874,
-0.036262936890125275,
-0.007827221415936947,
-0.03215894475579262,
-0.06568550318479538,
0.0036682123318314552,
-0.023151114583015442,
-0.022801941260695457,
0.023200474679470062,
-0.012999357655644417,
0.01763293333351612,
0.037043336778879166,
-0.05644470453262329,
0.027374660596251488,
0.01264127530157566,
0.003093797480687499,
-0.022020669654011726,
-0.007511339616030455,
0.028906987980008125,
-0.05835229530930519,
-0.01655588671565056,
-0.02432953007519245,
0.027938976883888245,
-0.028997832909226418,
-0.01909695193171501,
-0.01895301043987274,
0.029382428154349327,
-0.021140003576874733,
0.020133409649133682,
0.02197670005261898,
0.0018805572763085365,
-0.022115441039204597,
-0.007569167297333479,
-0.022459708154201508,
0.015234100632369518,
-0.010377674363553524,
-0.026417769491672516,
-0.005047204438596964,
-0.09961392730474472,
-0.034863755106925964,
-0.030114054679870605,
0.03327973186969757,
-0.031239882111549377,
0.004432479850947857,
0.019082730636000633,
-0.00855043064802885,
0.01739398017525673,
0.10099536180496216,
0.0020663414616137743,
0.023022254928946495,
0.008149433881044388,
-0.033553872257471085,
0.0013803925830870867,
-0.014230013824999332,
-0.05423954874277115,
0.08059954643249512,
0.055006083101034164,
-0.01854698173701763,
-0.0024626082740724087,
-0.009234846569597721,
0.014174075797200203,
0.04432724416255951,
0.052081137895584106,
0.010259606875479221,
-0.0079015688970685,
0.015008924528956413,
-0.04157327488064766,
-0.04542326554656029,
0.052197035402059555,
-0.027899503707885742,
-0.057905107736587524,
-0.019899681210517883,
0.0006056010606698692,
-0.0021827840246260166,
-0.003272571135312319,
-0.037820108234882355,
0.008922425098717213,
0.0025149693246930838,
-0.009207102470099926,
0.017394855618476868,
0.025125358253717422,
0.04112353175878525,
-0.030794616788625717,
0.05834052711725235,
0.0736970528960228,
0.05602239444851875,
-0.021805457770824432,
-0.01586444117128849,
-0.039336588233709335,
-0.018755871802568436,
-0.02455907128751278,
-0.0058856322430074215,
-0.03669172525405884,
0.02756340242922306,
-0.025145575404167175,
0.044365499168634415,
0.025687381625175476,
0.020800702273845673,
0.015284513123333454,
0.007971259765326977,
0.010930024087429047,
0.10447779297828674,
-0.041894104331731796,
0.017485570162534714,
0.04285252094268799,
0.027701398357748985,
-0.08197121322154999,
0.011176309548318386,
0.003191411728039384,
-0.05480547994375229,
-0.001361696282401681,
-0.03894571587443352,
-0.02374858967959881,
0.009762831963598728,
0.005485902074724436,
0.04111418500542641,
0.05021959915757179,
-0.02040547877550125,
-0.10570075362920761,
0.00643219193443656,
0.032094720751047134,
-0.018662068992853165,
-0.006000169552862644,
0.0714363381266594,
-0.0078116306103765965,
0.002355471020564437,
0.04607691615819931,
-0.057157259434461594,
-0.001244720770046115,
0.015125417150557041,
-0.033978186547756195,
0.03564930707216263,
0.01357690803706646,
0.006560483481734991,
-0.03523894399404526,
-0.0019313566153869033,
0.07430265098810196,
-0.0028404633048921824,
-0.0483294278383255,
0.05093429237604141,
-0.05976734682917595,
-0.019063612446188927,
0.04327453672885895,
-0.01194195356220007,
0.03253534436225891,
0.03430001437664032,
0.015345423482358456,
-0.0664186179637909,
-0.04605654627084732,
-0.01026290375739336,
0.055684592574834824,
0.001725430367514491,
0.024095995351672173,
-0.032161321491003036,
-0.033332496881484985,
0.03232404589653015,
0.06378336995840073,
0.0034608717542141676,
-0.04791814088821411,
0.0066525982692837715,
0.014836510643362999,
-0.025979559868574142,
0.0185294970870018,
0.027653800323605537,
0.018652690574526787,
-0.02634836919605732,
0.005935160908848047,
0.054155491292476654,
0.040208231657743454,
0.02828788571059704,
0.025479843840003014,
0.013488516211509705,
-0.01845317706465721,
-0.011427639983594418,
0.004246317315846682,
-0.03690880909562111,
-0.040542781352996826,
0.02062465250492096,
-0.02848677895963192,
0.021172519773244858,
-0.001657813205383718,
0.03138628229498863,
-0.01695888303220272,
-0.004532863851636648,
-0.03907656669616699,
-0.022178493440151215,
-0.030117996037006378,
-0.035502344369888306,
0.02792075276374817,
-0.02627464383840561,
-0.015795214101672173,
0.045339617878198624,
-0.010861975140869617,
0.01940000429749489,
0.08145304769277573,
-0.0022341134026646614,
0.04319840297102928,
0.04216725379228592,
-0.007935856468975544,
-0.019450150430202484,
-0.01650558039546013,
0.023071888834238052,
-0.00009248685819329694,
0.016573330387473106,
-0.020293544977903366,
-0.032988540828228,
0.02434401400387287,
0.008640005253255367,
0.0042960490100085735,
-0.033865466713905334,
-0.004717226140201092,
-0.01535612903535366,
-0.012707899324595928,
-0.00366034684702754,
-0.009233657270669937,
0.050708603113889694,
-0.029763562604784966,
-0.02292764186859131,
-0.01871536672115326,
0.017777467146515846,
-0.050115037709474564,
0.009024498984217644,
0.04512409493327141,
-0.018862547352910042,
-0.02629747800529003,
-0.04271966591477394,
0.03988641873002052,
0.033359136432409286,
0.011224656365811825,
-0.01676315814256668,
0.024983739480376244,
0.007934258319437504,
0.03496063873171806,
0.0808214619755745,
0.05602260306477547,
-0.0029331843834370375,
0.02331806905567646,
0.06157071515917778,
0.01710350066423416,
-0.018162395805120468,
0.021108753979206085,
-0.05037608742713928,
0.1118178740143776,
-0.015234992839396,
-0.007958367466926575,
-0.005076725967228413,
0.01818852126598358,
-0.038730379194021225,
-0.04100785404443741,
-0.01511647179722786,
0.019920803606510162,
0.025152891874313354,
0.024872558191418648,
0.005826899316161871,
0.0008533617947250605,
-0.022979246452450752,
-0.030651243403553963,
0.019523637369275093,
0.008145579136908054,
-0.01470878254622221,
0.03098479099571705,
-0.008152014575898647,
-0.0402505099773407,
0.05091627687215805,
-0.026341209188103676,
-0.05990292876958847,
-0.038601212203502655,
-0.04111279919743538,
0.018289674073457718,
0.05303645879030228,
-0.02851129323244095,
0.041148945689201355,
-0.06575287133455276,
0.03744048997759819,
-0.005885534454137087,
0.0020221383310854435,
-0.0030448741745203733,
-0.08893929421901703,
-0.0436340793967247,
-0.009251792915165424,
-0.10747158527374268,
0.01493208110332489,
-0.07126347720623016,
0.011548910290002823,
0.005324809346348047,
0.04517883062362671,
-0.0589631125330925,
-0.012957150116562843,
-0.043545596301555634,
0.047632619738578796,
0.004138600081205368,
-0.06245234236121178,
0.01551754865795374,
-0.010456751100718975,
-0.006777993869036436,
-0.00886174663901329,
-0.020826123654842377,
0.01875986158847809,
-0.05717427283525467,
-0.01643480360507965,
0.00905283447355032,
-0.014928458258509636,
-0.0008436356438323855,
-0.03912568837404251,
0.009775147773325443,
-0.025886164978146553,
-0.06085268408060074,
-0.04222388193011284,
-0.012368452735245228,
-0.034226249903440475,
-0.004042333923280239,
-0.0113403694704175,
-0.005767574068158865,
0.0631457269191742,
0.0266906525939703,
-0.011863801628351212,
0.015665924176573753,
-0.0011177577544003725,
-0.0014600460417568684,
0.02180829644203186,
-0.01204881351441145,
0.043751414865255356,
-0.08411570638418198,
-0.017652055248618126,
0.0025824347976595163,
0.03061692602932453,
0.030201658606529236,
-0.054879140108823776,
-0.01812995783984661,
0.029854971915483475,
-0.028852296993136406,
-0.04684072732925415,
-0.013421175070106983,
-0.000461274670669809,
-0.005077851004898548,
0.04909500852227211,
0.005420612171292305,
-0.032510846853256226,
-0.10706769675016403,
0.059395067393779755,
0.018826235085725784,
0.023398229852318764,
0.05147024989128113,
0.022639434784650803,
0.02396984025835991,
-0.036111775785684586,
-0.035674646496772766,
-0.07000723481178284,
0.04548340290784836,
-0.003548651235178113,
0.021374395117163658,
0.025910601019859314,
-0.011506689712405205,
-0.012615310028195381,
0.0320909209549427,
0.061994872987270355,
-0.023518502712249756,
-0.024299684911966324,
0.0001629555190447718,
-0.044763922691345215,
-0.0029839379712939262,
-0.004506154917180538,
0.018985984846949577,
-0.014800048433244228,
-0.011006779037415981,
-0.013086216524243355,
-0.05395294353365898,
0.00855965819209814,
-0.010219438001513481,
-0.040801484137773514,
0.04072890058159828,
0.008870217949151993,
0.06383538991212845,
-0.025074679404497147,
0.025353221222758293,
0.0060712071135640144,
-0.033044423907995224,
-0.0357554629445076,
-0.005305263213813305,
0.024885494261980057,
0.019835716113448143,
0.04266546294093132,
0.003115569707006216,
-0.0289910901337862,
-0.0813148245215416,
0.03181394562125206,
-0.011116696521639824,
-0.008515395224094391,
-0.011707796715199947,
-0.02023540996015072,
-0.0240824855864048,
-0.05655601620674133,
-0.025656739249825478,
0.013259699568152428,
0.010900826193392277,
0.029301248490810394,
-0.0009081299649551511,
0.029166346415877342,
-0.045111171901226044,
0.008278368040919304,
0.01984040066599846,
-0.0714808851480484,
-0.04448999464511871,
-0.03366641700267792,
-0.02311493270099163,
-0.05797717347741127,
-0.06431667506694794,
-0.023727376013994217,
0.05792435631155968,
0.04186205938458443,
-0.036869436502456665,
0.037506647408008575,
-0.0054184431210160255,
-0.02878066524863243,
0.013532347977161407,
-0.0344882570207119,
-0.023304292932152748,
0.036057837307453156,
-0.021336792036890984,
0.024062711745500565,
0.07127966731786728,
-0.03267902508378029,
-0.002583213383331895,
-0.04786279425024986,
0.023515505716204643,
-0.00919654592871666,
-0.027903052046895027,
-0.01722709648311138,
0.015492920763790607,
-0.01433270238339901,
0.0021667673718184233,
0.045676253736019135,
0.004497379530221224,
-0.021789098158478737,
0.016246197745203972,
-0.0369609110057354,
-0.02384994924068451,
0.040689777582883835,
0.04005367308855057,
-0.01675378903746605,
0.041323963552713394,
0.08763379603624344,
0.009087597951292992,
-0.018976803869009018,
0.01834772527217865,
0.005817788187414408,
0.022236745804548264,
0.0177660770714283,
-0.03759301081299782,
0.035807691514492035,
0.0004131641471758485,
0.00209103524684906,
0.07203415781259537,
0.02334548905491829,
0.026929441839456558,
0.047875240445137024,
-0.0206874068826437,
0.06853307038545609,
0.03283693268895149,
-0.022831112146377563,
-0.033956464380025864,
0.03372114151716232,
-0.00773416506126523,
0.02073855698108673,
-0.03248509019613266,
0.009968066588044167,
-0.011023524217307568,
0.07793720066547394,
0.02134297601878643,
0.0023159354459494352,
-0.020595593377947807,
-0.04284382984042168,
0.008013507351279259,
-0.1064373254776001,
0.004130515269935131,
-0.041493143886327744,
0.00547504797577858,
-0.030549807474017143,
0.0048129442147910595,
-0.07444527745246887,
-0.048206180334091187,
-0.03330100700259209,
0.03491587936878204,
-0.05047740042209625,
-0.014827835373580456,
0.019974585622549057,
-0.005569087341427803,
-0.021877285093069077,
0.014843531884253025,
0.01995585300028324,
-0.07166548818349838,
0.005337993614375591,
0.058899909257888794,
0.018674718216061592,
-0.007700126152485609,
-0.009545973502099514,
0.004022529348731041,
0.034835875034332275,
0.006074067670851946,
-0.00014793637092225254,
-0.0062629771418869495,
-0.015175359323620796,
-0.02113731950521469,
-0.0074735041707754135,
0.02851966582238674,
-0.005682480055838823,
-0.016100198030471802,
0.01845637895166874,
0.021509109064936638,
0.03398166596889496,
0.017081035301089287,
-0.044932328164577484,
-0.01648898236453533,
-0.048811450600624084,
0.02897675149142742,
-0.02840699441730976,
0.02766323834657669,
-0.03163536638021469,
-0.0064088525250554085,
-0.023494262248277664,
-0.0018884665332734585,
-0.009273642674088478,
0.0416821613907814,
0.04356125369668007,
-0.035506680607795715,
0.002286252100020647,
-0.03626479208469391,
-0.046827252954244614,
-0.08008242398500443,
-0.015663160011172295,
0.01704292930662632,
-0.021040713414549828,
-0.023729681968688965,
0.024334251880645752,
0.0011738286120817065,
0.0004110175941605121,
-0.012278299778699875,
0.07319720089435577,
-0.009777449071407318,
0.03285204991698265,
0.025360599160194397,
-0.02056458406150341,
0.03740277141332626,
0.02888544276356697,
-0.044988963752985,
0.0008642377215437591,
0.04660936817526817,
0.06422796100378036,
0.014746247790753841,
0.02674924209713936,
-0.01405760645866394,
0.03888680413365364,
-0.030253533273935318,
0.00026741932379081845,
-0.008401610888540745,
-0.008560032583773136,
0.028527216985821724,
-0.021700521931052208,
-0.033320214599370956,
0.036805737763643265,
-0.015379512682557106,
-0.032776203006505966,
-0.0034462036564946175,
0.05528774857521057,
0.0221000574529171,
0.05408892780542374,
0.029523799195885658,
-0.03582193702459335,
0.03985483944416046,
-0.022824451327323914,
0.02584279328584671,
-0.02639833465218544,
0.005548796150833368,
0.009703422896564007,
0.00623778160661459,
-0.05985928326845169,
-0.07940076291561127,
0.0011079978430643678,
0.015391695313155651,
0.03116098791360855
] |
<p>I was digging into <a href="http://latticeqcd.blogspot.com/2005/12/nielsen-ninomiya-theorem.html" rel="nofollow">Nielson-Ninomiya Theorem</a> and doubler fermions, as well as solutions to these problems using <a href="http://arxiv.org/abs/hep-lat/9410018" rel="nofollow">Domain Wall Fermions</a> and <a href="http://arxiv.org/abs/hep-lat/0405024" rel="nofollow">overlap lattice fermions</a>, both of which make effective use of a 5th dimension.</p>
<p>Does this imply that our universe is either a continuous 3+1 dimensional space, or a space that is 4+1 dimensions on a lattice?</p> | g7784 | [
-0.003458290360867977,
0.04740249365568161,
-0.011871127411723137,
-0.03007439151406288,
-0.037748876959085464,
0.004448755644261837,
0.04824099689722061,
-0.0011424169642850757,
-0.048178765922784805,
-0.006209213752299547,
-0.014489518478512764,
-0.010415730997920036,
-0.035956211388111115,
0.052934013307094574,
-0.02442396618425846,
-0.006869730073958635,
-0.011033070273697376,
-0.011257242411375046,
0.02011978253722191,
-0.008812179788947105,
0.001821998506784439,
0.026005910709500313,
0.026194749400019646,
-0.062469206750392914,
0.03847149759531021,
0.006409742403775454,
0.03452611714601517,
-0.04351117089390755,
-0.034451618790626526,
0.010702008381485939,
0.06630805879831314,
-0.06097418814897537,
0.03443039581179619,
-0.025317305698990822,
-0.03929606452584267,
-0.011049982160329819,
0.06754184514284134,
0.024905284866690636,
0.05359475687146187,
-0.0673205628991127,
0.01996111311018467,
0.014632485806941986,
-0.016412369906902313,
0.023002659901976585,
0.007191448472440243,
0.03229429945349693,
-0.03774743154644966,
-0.005152770318090916,
0.06761542707681656,
0.00063848786521703,
-0.020908908918499947,
0.03223259001970291,
0.006962853949517012,
0.021309752017259598,
0.0035952504258602858,
0.0002780803188215941,
0.00876539759337902,
-0.012434347532689571,
0.0536608025431633,
0.01452688779681921,
-0.04342235252261162,
0.0005404081894084811,
0.027966417372226715,
0.062475427985191345,
0.07062548398971558,
0.031880933791399,
-0.054589781910181046,
0.01055061910301447,
0.01872391253709793,
-0.07114826887845993,
0.030355097725987434,
0.007420045789331198,
0.023983070626854897,
0.015485145151615143,
0.009942925535142422,
0.0577254593372345,
-0.014266517013311386,
-0.0022162306122481823,
-0.03062763437628746,
0.015190638601779938,
-0.009312992915511131,
-0.05525600165128708,
-0.05182350426912308,
-0.011293902061879635,
0.06838628649711609,
0.00027551737730391324,
-0.027406930923461914,
-0.03816070035099983,
-0.03745141252875328,
-0.012142367660999298,
0.0344209261238575,
0.07312963902950287,
0.014356423169374466,
0.025651587173342705,
0.024722076952457428,
0.01581321470439434,
0.034347981214523315,
0.001931955455802381,
0.03397504612803459,
-0.01888757385313511,
-0.06046823039650917,
0.059926651418209076,
0.10692503303289413,
-0.02010732889175415,
-0.008455262519419193,
0.046750374138355255,
0.06047932803630829,
-0.010768854059278965,
-0.04899473115801811,
0.0241714920848608,
-0.03143153339624405,
-0.0010727365734055638,
-0.008590694516897202,
0.003048505401238799,
0.013656599447131157,
0.006180059164762497,
0.06212858110666275,
-0.013138970360159874,
-0.04237578809261322,
0.0629359781742096,
0.028462685644626617,
0.04911534860730171,
0.08051890879869461,
0.02371862344443798,
-0.037518229335546494,
-0.0028835670091211796,
0.015509807504713535,
0.031939152628183365,
0.03530242294073105,
-0.00592260854318738,
-0.003481756430119276,
0.027901308611035347,
0.017327014356851578,
0.0374329648911953,
0.003868733998388052,
-0.009823299944400787,
0.03252978250384331,
-0.014064757153391838,
-0.018388738855719566,
0.026097435504198074,
-0.0065247793681919575,
0.0021468396298587322,
0.005590899847447872,
-0.02685043029487133,
-0.011059991084039211,
-0.01818116381764412,
-0.01061246171593666,
-0.015081603080034256,
-0.04391128942370415,
0.017984235659241676,
0.02010985091328621,
0.07918304204940796,
-0.06363429129123688,
0.01713687740266323,
0.005976704880595207,
0.024713164195418358,
0.010852765291929245,
-0.006313880905508995,
0.03923370689153671,
-0.13616329431533813,
-0.04114033281803131,
0.0011002621613442898,
-0.04231198504567146,
-0.026235559955239296,
0.003085824428126216,
-0.05898715555667877,
0.06413770467042923,
-0.04096711426973343,
-0.04891495034098625,
-0.003107319353148341,
-0.043107666075229645,
0.03133968636393547,
-0.014434228651225567,
-0.018493523821234703,
0.00500267231836915,
0.0468069426715374,
-0.03615133464336395,
0.00318852043710649,
-0.017160391435027122,
0.006909341551363468,
-0.013498093001544476,
-0.006762222852557898,
0.01877683773636818,
0.020510105416178703,
-0.011032970622181892,
0.04518944025039673,
-0.03182397037744522,
-0.02542814239859581,
0.04086551442742348,
-0.01911371760070324,
0.009820322506129742,
-0.029665572568774223,
0.0637212023139,
0.058012835681438446,
0.049790769815444946,
-0.01862143538892269,
0.029645627364516258,
-0.04168816655874252,
-0.025000397115945816,
-0.03560076281428337,
-0.019222132861614227,
0.0041185165755450726,
0.06230456382036209,
0.00974864698946476,
0.0631079375743866,
0.04977717623114586,
-0.03146965056657791,
0.025781424716114998,
0.036302417516708374,
-0.016272513195872307,
-0.03548066318035126,
-0.015646887943148613,
-0.017068352550268173,
0.016478976234793663,
0.008045720867812634,
-0.014714234508574009,
-0.0428774319589138,
0.00006133397982921451,
-0.03989237919449806,
0.024891791865229607,
-0.03409783914685249,
-0.0003026337071787566,
0.05843917280435562,
0.02873462252318859,
-0.010761194862425327,
-0.005358900409191847,
-0.015307665802538395,
0.021282292902469635,
0.06690816581249237,
0.005342509131878614,
-0.0955059751868248,
-0.02332969196140766,
0.003311540000140667,
-0.04719778895378113,
0.005347707308828831,
0.03770070523023605,
-0.03126262500882149,
0.024475811049342155,
-0.017856845632195473,
0.05306851118803024,
0.04039900004863739,
-0.018529366701841354,
-0.09171971678733826,
-0.028503211215138435,
0.0675242468714714,
-0.005346127785742283,
0.05356675013899803,
0.002277906285598874,
-0.058521002531051636,
-0.013169665820896626,
-0.013728054240345955,
-0.01815900392830372,
0.02441391721367836,
0.0277476217597723,
-0.0008725608349777758,
0.037633009254932404,
0.03759074583649635,
-0.008148735389113426,
-0.023493962362408638,
-0.026334170252084732,
0.05091747269034386,
-0.06535759568214417,
0.023649336770176888,
0.12290652841329575,
0.024612154811620712,
-0.03832068666815758,
0.011654265224933624,
0.04648464918136597,
-0.05213386192917824,
0.024155808612704277,
0.04489351063966751,
0.0018632233841344714,
0.0024445271119475365,
-0.03664736822247505,
-0.019706761464476585,
0.023062899708747864,
0.027646761387586594,
-0.04007020965218544,
0.03787059709429741,
0.024411410093307495,
0.0388408824801445,
0.06696777790784836,
-0.07230644673109055,
-0.013431803323328495,
0.028250714763998985,
-0.02163013070821762,
-0.03622632101178169,
-0.004764663986861706,
-0.018784133717417717,
0.014071053825318813,
0.021689189597964287,
-0.016169873997569084,
0.0004909209674224257,
0.020279331132769585,
-0.009759926237165928,
0.02516709640622139,
-0.024409441277384758,
-0.04262928664684296,
-0.02765137329697609,
0.030723994597792625,
-0.037495747208595276,
-0.00250539043918252,
-0.03316504880785942,
-0.03629264980554581,
-0.0012356224469840527,
-0.033729348331689835,
-0.0378219336271286,
-0.021834401413798332,
-0.04648258909583092,
-0.06175292655825615,
0.004432779736816883,
0.07721888273954391,
-0.030134208500385284,
0.03216226398944855,
-0.027748804539442062,
0.0070054498501122,
0.025164302438497543,
-0.005341856274753809,
0.05585634335875511,
-0.007112191990017891,
0.006043854635208845,
0.012103268876671791,
0.015369395725429058,
-0.0037599336355924606,
0.01052554976195097,
0.07104174792766571,
0.02391131781041622,
-0.000987343955785036,
0.021690616384148598,
0.04088897630572319,
-0.011398856528103352,
-0.02562004141509533,
0.004710503853857517,
0.011310804635286331,
-0.03579889237880707,
-0.049773238599300385,
-0.06659164279699326,
-0.004580025561153889,
0.06402164697647095,
0.06308870017528534,
-0.0758495032787323,
0.018643734976649284,
-0.048102665692567825,
0.004490481689572334,
0.012432349845767021,
0.055052176117897034,
-0.021926743909716606,
0.07141022384166718,
-0.02888355404138565,
0.025802558287978172,
0.0030285927932709455,
0.00976518914103508,
0.023743683472275734,
-0.043683238327503204,
-0.007651886902749538,
0.009349608793854713,
-0.012065907008945942,
0.013670122250914574,
0.05211726203560829,
-0.038080163300037384,
0.06120198965072632,
0.008589527569711208,
0.010930906981229782,
-0.025135809555649757,
-0.01886783167719841,
0.04531457647681236,
-0.013045446015894413,
0.07136183232069016,
-0.010228275321424007,
0.01793784834444523,
0.007560285739600658,
-0.05486496910452843,
-0.040038757026195526,
-0.046319086104631424,
0.03129296749830246,
-0.016531700268387794,
-0.038900502026081085,
-0.0714697539806366,
0.04192987084388733,
-0.010206549428403378,
0.00818299874663353,
0.050348758697509766,
0.014487743377685547,
0.005932620260864496,
-0.06032107397913933,
0.05768606811761856,
-0.054138973355293274,
-0.03319529816508293,
-0.03276193514466286,
-0.02210131473839283,
0.049314070492982864,
0.012789193540811539,
-0.054429661482572556,
0.01482909545302391,
0.029967043548822403,
0.005067432764917612,
0.017010588198900223,
0.019560709595680237,
-0.019673289731144905,
-0.007882966659963131,
0.006416143849492073,
-0.012637248262763023,
0.05269094929099083,
-0.01204412616789341,
0.040201615542173386,
-0.059828244149684906,
-0.0013074591988697648,
0.009104369208216667,
0.006798346992582083,
0.00031204710830934346,
-0.009299753233790398,
0.06272865831851959,
-0.012908922508358955,
-0.022938383743166924,
0.08797997236251831,
-0.04756133258342743,
-0.03741796314716339,
-0.04245481640100479,
-0.00901853572577238,
-0.026124291121959686,
0.01865796558558941,
0.09243249893188477,
-0.0457497276365757,
0.0058264341205358505,
0.06840158253908157,
0.025232769548892975,
0.0008179592550732195,
-0.0034071903210133314,
-0.011394048109650612,
0.004090616945177317,
-0.01653330586850643,
0.08305926620960236,
-0.007578959222882986,
0.042857058346271515,
-0.030663063749670982,
0.0031993708107620478,
-0.06997021287679672,
0.01594436727464199,
0.038412682712078094,
0.00876158382743597,
0.02935120277106762,
-0.07185796648263931,
-0.030721278861165047,
-0.007120028603821993,
-0.03912633657455444,
0.023974759504199028,
-0.07401259988546371,
-0.013956382870674133,
-0.03067478910088539,
-0.008784553967416286,
0.049537915736436844,
0.02881491929292679,
-0.04069419205188751,
0.0076217614114284515,
0.0017426229314878583,
-0.05483081564307213,
-0.014080038294196129,
0.05362650752067566,
0.07011354714632034,
0.02833452820777893,
-0.05783531814813614,
-0.01714515872299671,
0.036341309547424316,
0.04778154566884041,
-0.016218652948737144,
-0.03463614359498024,
-0.022450117394328117,
-0.04913053289055824,
-0.04999341070652008,
0.010829398408532143,
0.054327066987752914,
0.017478274181485176,
-0.06341718882322311,
-0.04463778808712959,
-0.009066974744200706,
-0.03199020028114319,
-0.02942320704460144,
0.019592702388763428,
-0.018681123852729797,
0.02686457335948944,
0.006509822327643633,
-0.08114390075206757,
0.03556026145815849,
0.0058300551027059555,
0.007629306521266699,
0.053457945585250854,
-0.012503554113209248,
-0.014688365161418915,
0.008539029397070408,
0.008613409474492073,
-0.03765076398849487,
-0.0075843073427677155,
-0.003884694306179881,
0.03860725089907646,
0.0008016002248041332,
-0.03982635587453842,
-0.02719211019575596,
-0.03286555036902428,
-0.012323557399213314,
0.024736054241657257,
0.0018517798744142056,
-0.0036871605552732944,
0.0367882065474987,
0.0027207359671592712,
-0.01980597712099552,
0.043177440762519836,
0.05405955761671066,
-0.04496543109416962,
-0.04758451133966446,
-0.01793922297656536,
0.028572794049978256,
-0.008436709642410278,
-0.007315046153962612,
-0.01073358952999115,
-0.007526705041527748,
-0.04345448687672615,
-0.05819933861494064,
0.003203204134479165,
-0.01501521561294794,
-0.047202277928590775,
-0.024084514006972313,
0.06951141357421875,
-0.00028529137489385903,
-0.028744319453835487,
0.04304677993059158,
-0.013060632161796093,
0.03840703144669533,
-0.0817127600312233,
-0.015717804431915283,
0.07765872776508331,
0.032506171613931656,
0.011879007332026958,
-0.017713308334350586,
0.050246402621269226,
-0.014456981793045998,
-0.008649209514260292,
0.01902824454009533,
-0.006250744219869375,
0.019314059987664223,
-0.014412439428269863,
0.004940347746014595,
-0.06852171570062637,
-0.013477117754518986,
0.02435535192489624,
-0.04402793198823929,
-0.01631978154182434,
-0.02792254462838173,
0.022480057552456856,
-0.012535283342003822,
0.014787045307457447,
-0.05931062251329422,
-0.0610785074532032,
-0.05292048677802086,
0.02668372355401516,
-0.04050580412149429,
-0.02285628393292427,
0.00780135951936245,
0.0022316337563097477,
-0.0028551165014505386,
-0.009378175251185894,
0.050901785492897034,
0.027521971613168716,
0.0016112843295559287,
-0.06398073583841324,
-0.044282715767621994,
-0.013292787596583366,
-0.02173842117190361,
0.0031701356638222933,
0.00652588065713644,
-0.00836543831974268,
0.037154294550418854,
0.018002640455961227,
-0.017040424048900604,
0.03778880462050438,
-0.023222217336297035,
-0.01682315208017826,
-0.04370047152042389,
-0.03162873163819313,
-0.060744911432266235,
0.02592792548239231,
0.02081705443561077,
-0.03080064058303833,
0.019083121791481972,
-0.045816510915756226,
0.018802309408783913,
0.004583035595715046,
0.001094882027246058,
-0.01483116764575243,
0.001839959411881864,
-0.030787324532866478,
-0.04037560895085335,
-0.02436378039419651,
-0.02561052143573761,
-0.018440894782543182,
-0.028704794123768806,
-0.04021228477358818,
-0.026987193152308464,
-0.01690041460096836,
-0.07849650830030441,
0.06693848222494125,
0.0332193523645401,
0.017409147694706917,
0.025248346850275993,
0.005509665701538324,
-0.02488618716597557,
0.07255102694034576,
-0.0248995553702116,
-0.02347864769399166,
-0.0041044424287974834,
0.04545976594090462,
0.014262557961046696,
0.06220420077443123,
-0.02086433209478855,
0.026318127289414406,
0.03170614317059517,
-0.09885247051715851,
-0.018362198024988174,
-0.02381662093102932,
0.034377943724393845,
0.03481671214103699,
0.019978569820523262,
-0.03789723664522171,
-0.012857618741691113,
0.0014221429591998458,
0.028302617371082306,
0.05554267019033432,
-0.019505690783262253,
-0.018960677087306976,
0.033431682735681534,
0.033334001898765564,
-0.02514548972249031,
-0.00678615877404809,
0.07114414125680923,
0.021070290356874466,
-0.060781367123126984,
-0.03291736915707588,
-0.027623644098639488,
0.06641887128353119,
-0.05109092965722084,
0.017594357952475548,
-0.05369978025555611,
-0.008676464669406414,
0.053988102823495865,
0.005654897540807724,
0.042889222502708435,
0.013325502164661884,
0.0034489831887185574,
0.005186533555388451,
-0.03238668292760849,
0.0023200458381325006,
0.018160611391067505,
-0.006852173246443272,
-0.029880749061703682,
-0.0318196564912796,
-0.08724265545606613,
0.011982028372585773,
0.021910488605499268,
0.019333157688379288,
-0.08452493697404861,
-0.044880423694849014,
0.01202284637838602,
-0.016226932406425476,
-0.018962126225233078,
0.015856236219406128,
0.011167805641889572,
0.027700433507561684,
0.05794011056423187,
0.03371160849928856,
-0.05624254047870636,
-0.012324323877692223,
-0.0397392138838768,
-0.009962808340787888,
-0.002480895956978202,
0.0284075066447258,
-0.0005731105920858681,
-0.024733765050768852,
-0.04486303776502609,
0.04002184420824051,
0.08982887119054794,
-0.026069484651088715,
0.06581468880176544,
0.039277076721191406,
-0.04047807306051254,
0.015335512347519398,
0.017456747591495514,
0.0416460819542408,
0.036682482808828354,
-0.022326316684484482,
-0.009561633691191673,
0.02789223939180374,
0.06345546990633011,
-0.001729727489873767,
0.0010386474896222353,
-0.033461153507232666,
-0.022466881200671196,
0.04027842357754707,
0.02358696609735489,
0.013099370524287224,
-0.025268564000725746,
-0.035222213715314865,
-0.02840254455804825,
0.005901342257857323,
-0.04969712719321251,
-0.014065397903323174,
0.05514923855662346,
-0.056433599442243576,
-0.013064374215900898,
0.032731473445892334,
0.012544399127364159,
0.03492933511734009,
-0.011652011424303055,
0.08183158934116364,
0.017059579491615295,
0.09471239149570465,
0.04107266291975975,
-0.002706114435568452,
-0.037594787776470184,
-0.003975774627178907,
0.07803720235824585,
-0.000734026893042028,
0.00046564306830987334,
-0.03318340703845024,
-0.008082103915512562,
-0.0522012896835804,
-0.01701175421476364,
-0.03184418007731438,
-0.03801129758358002,
-0.03289142623543739,
0.041764065623283386,
0.07535100728273392,
0.00813521072268486,
0.016053427010774612,
-0.05728611722588539,
-0.0025935762096196413,
-0.05590745061635971,
0.03941730037331581,
0.03690878674387932,
0.0036842150148004293,
0.040844518691301346,
-0.028637727722525597,
-0.029686003923416138,
-0.032635435461997986,
-0.01590711995959282,
-0.054236989468336105,
-0.029810098931193352,
-0.012543188408017159,
-0.07356547564268112,
-0.00514264265075326,
0.015518046915531158,
-0.026693278923630714,
-0.03429076820611954,
-0.012959105893969536,
0.0006890433724038303,
0.028969140723347664,
0.028476865962147713,
-0.009940610267221928,
-0.059795182198286057,
-0.006722850725054741,
-0.004259573295712471,
0.042001765221357346,
0.01958061009645462,
0.010948443785309792,
0.013969610445201397,
-0.00797363929450512,
-0.03382008522748947,
-0.002503305906429887,
-0.007860316894948483,
0.011915797367691994
] |
<p>In organic light emitting diodes, only singlet excitons contribute to the light emission (this is flouresence). Everything I read, say that triplet excitons cannot recombine on the same timescale as the singlets because spin selection rules forbid it. </p>
<p>Can anyone expand on how the spin selection rules allow for singlet and not triplet emission? </p> | g7785 | [
-0.017872221767902374,
0.045390501618385315,
0.004414033144712448,
-0.022524796426296234,
0.052259646356105804,
-0.054612427949905396,
-0.012903574854135513,
0.07734476029872894,
0.027344731613993645,
0.012312471866607666,
-0.027314040809869766,
-0.008952194824814796,
0.04423927515745163,
-0.021898355334997177,
-0.04173790290951729,
0.034268856048583984,
0.00015270212315954268,
0.037567198276519775,
0.06398048996925354,
0.02385551668703556,
-0.0816691517829895,
0.0015240957727655768,
-0.06210099905729294,
-0.06050857529044151,
-0.03028576448559761,
0.007980171591043472,
0.0283000897616148,
-0.029370157048106194,
-0.015625014901161194,
0.00899922288954258,
0.04965627193450928,
0.014446533285081387,
0.024622786790132523,
0.03452763333916664,
0.02819894254207611,
-0.035078030079603195,
0.03840990364551544,
-0.004564812406897545,
-0.020944848656654358,
0.04797067493200302,
0.014144698157906532,
0.00989228580147028,
-0.012884081341326237,
-0.05971912294626236,
-0.04883996769785881,
0.031312454491853714,
0.043751977384090424,
-0.004803747870028019,
-0.002253667451441288,
-0.002744820900261402,
0.02262791059911251,
0.0023809969425201416,
-0.0045034633949398994,
-0.007944643497467041,
0.02150006778538227,
-0.035819366574287415,
-0.060881681740283966,
0.0325315035879612,
0.07238621264696121,
-0.01095977146178484,
-0.06088509410619736,
0.0437513031065464,
0.015534892678260803,
0.043626174330711365,
0.04218122363090515,
-0.007195769809186459,
0.03305111452937126,
0.007615973707288504,
0.05254403501749039,
0.02315947413444519,
-0.0009057065472006798,
0.00846815574914217,
0.0010058468906208873,
-0.008373220451176167,
0.0072386604733765125,
0.02578986994922161,
0.014423074200749397,
-0.01802578568458557,
-0.03083011507987976,
0.04825248196721077,
-0.02223794162273407,
0.0027490302454680204,
0.0027999109588563442,
0.04495895653963089,
0.011097796261310577,
0.07265739887952805,
-0.017268160358071327,
-0.022987762466073036,
0.017138445749878883,
0.0038979623932391405,
0.06015009433031082,
-0.05298670008778572,
0.04099980741739273,
-0.03786661475896835,
-0.000188657664693892,
0.004569241311401129,
0.02557041309773922,
0.04317876696586609,
-0.023828526958823204,
0.016378281638026237,
-0.008020525798201561,
-0.00420021777972579,
0.03456449136137962,
-0.00005278725438984111,
-0.02877526544034481,
0.03570961952209473,
-0.01433796901255846,
0.020766068249940872,
-0.018612446263432503,
0.027305401861667633,
-0.04450126737356186,
-0.023612266406416893,
-0.0033323406241834164,
-0.05128311738371849,
-0.052217286080121994,
0.030318649485707283,
0.05473704636096954,
-0.06056245416402817,
0.02872532233595848,
0.04172537475824356,
0.03915894776582718,
-0.014053556136786938,
0.0017571692587807775,
0.06964068859815598,
-0.0330454558134079,
-0.021035801619291306,
-0.008510817773640156,
-0.021204618737101555,
0.005483889952301979,
-0.03007473796606064,
-0.007544725202023983,
0.003755973419174552,
0.0016509159468114376,
-0.02540489099919796,
0.025893906131386757,
0.015081592835485935,
0.042079780250787735,
-0.035517193377017975,
0.04325350001454353,
-0.033663809299468994,
0.027750926092267036,
0.010932850651443005,
0.020762180909514427,
-0.04731586202979088,
-0.024881411343812943,
0.003727148985490203,
0.048311375081539154,
0.021419543772935867,
0.029356207698583603,
0.009907936677336693,
0.01991669461131096,
0.04175037145614624,
0.013220097869634628,
-0.05560633912682533,
0.00962698645889759,
-0.039424698799848557,
0.015041434206068516,
-0.032819636166095734,
-0.05208789184689522,
-0.014040601439774036,
0.01633770950138569,
-0.023400356993079185,
-0.06744203716516495,
-0.03361092880368233,
-0.026805253699421883,
0.004147895611822605,
-0.007506198715418577,
-0.03271450102329254,
-0.014576026238501072,
-0.032567884773015976,
-0.006036753300577402,
0.018133988603949547,
-0.01712309755384922,
-0.005604241043329239,
0.02450304478406906,
0.00677953427657485,
-0.012805313803255558,
-0.01232993882149458,
-0.042977191507816315,
0.026010461151599884,
-0.02435324154794216,
0.015548483468592167,
-0.02819700352847576,
0.04144385829567909,
-0.0037686792202293873,
-0.028606506064534187,
-0.032633692026138306,
0.010472838766872883,
-0.009555607102811337,
0.049943458288908005,
-0.028957001864910126,
0.021876640617847443,
0.04271703585982323,
-0.011671352200210094,
-0.03425316885113716,
-0.04050048068165779,
0.0038710529915988445,
-0.03908531367778778,
-0.05004563555121422,
-0.0407240204513073,
-0.032372474670410156,
-0.02634441666305065,
-0.014473365619778633,
0.035735245794057846,
0.020781664177775383,
0.016276773065328598,
-0.0006167883984744549,
0.0021238168701529503,
0.10267265141010284,
0.0016046593664214015,
-0.011039734818041325,
0.07596062868833542,
-0.032882507890462875,
0.027161547914147377,
-0.05866359919309616,
-0.05817555636167526,
0.02287871018052101,
-0.011650965549051762,
0.012034076265990734,
-0.04027590528130531,
0.015439414419233799,
0.003665281692519784,
0.04457154870033264,
0.03549034520983696,
-0.015369095839560032,
0.018673265352845192,
-0.047750212252140045,
0.005275804083794355,
0.016737740486860275,
0.05289847403764725,
-0.03567259758710861,
-0.02481985278427601,
-0.02428556978702545,
-0.019488094374537468,
0.04012758657336235,
0.06435221433639526,
0.00989339966326952,
0.03119877353310585,
-0.04526209086179733,
-0.008556310087442398,
-0.028224047273397446,
0.014088267460465431,
-0.02800576202571392,
-0.033279143273830414,
-0.025359680876135826,
-0.04964454472064972,
0.08158772438764572,
-0.01963016577064991,
-0.033830463886260986,
0.033945802599191666,
-0.010082393884658813,
0.004883045330643654,
0.0013504419475793839,
0.0417550690472126,
-0.07131597399711609,
-0.014428135938942432,
0.03422204405069351,
0.01798362284898758,
-0.02409542165696621,
0.014471132308244705,
-0.013933692127466202,
-0.05935985594987869,
0.03696839511394501,
0.0040864176116883755,
-0.001389809651300311,
-0.01091306284070015,
0.006253515835851431,
-0.04880731552839279,
-0.012988234870135784,
-0.04518106207251549,
-0.06195785105228424,
0.03795068711042404,
-0.047390665858983994,
-0.02590424381196499,
-0.004550599958747625,
0.045240212231874466,
0.010621253401041031,
0.02601051703095436,
-0.03405013307929039,
0.014655173756182194,
-0.00589714152738452,
-0.03914439678192139,
-0.006201183423399925,
-0.04068516567349434,
0.034093227237463,
-0.02574915438890457,
0.04286343604326248,
-0.01593090407550335,
-0.023389168083667755,
0.03303547576069832,
-0.044653479009866714,
-0.03566860035061836,
0.020395739004015923,
-0.059022240340709686,
0.027461299672722816,
-0.08083634823560715,
-0.022495709359645844,
0.0052466606721282005,
-0.006756788119673729,
0.10066203773021698,
0.02134830318391323,
0.04496641084551811,
-0.008324669674038887,
0.02053324691951275,
0.060768723487854004,
0.036627642810344696,
-0.04668672755360603,
-0.05626500025391579,
-0.02581200934946537,
0.05625542998313904,
-0.015355514362454414,
0.018855933099985123,
-0.041730526834726334,
0.06388210505247116,
-0.003672732738777995,
-0.03683551028370857,
-0.029867488890886307,
0.0788993164896965,
0.01302549708634615,
-0.023257384076714516,
0.0009971047984436154,
0.03818577900528908,
-0.039076901972293854,
-0.009786640293896198,
0.03472280129790306,
0.01790277473628521,
-0.027760669589042664,
-0.041822247207164764,
-0.05927271395921707,
0.018094109371304512,
0.06389441341161728,
0.010451440699398518,
0.006078857462853193,
0.010610741563141346,
-0.04586244747042656,
-0.013575525023043156,
0.022132566198706627,
0.04594757780432701,
-0.01605910249054432,
0.019170979037880898,
0.03289389610290527,
0.010901405476033688,
-0.1201632171869278,
-0.04572470113635063,
0.002451627980917692,
0.018160387873649597,
-0.060308460146188736,
0.011880675330758095,
0.050788745284080505,
-0.011611038818955421,
0.048251207917928696,
-0.015496063977479935,
-0.0085056833922863,
0.02473943680524826,
0.015385481528937817,
-0.011048651300370693,
0.009580341167747974,
0.023163653910160065,
0.03168933466076851,
0.015268324874341488,
-0.024774029850959778,
-0.02076445333659649,
0.06173890456557274,
-0.030628766864538193,
0.013652005232870579,
0.006148842163383961,
-0.0014286405639722943,
0.07333224266767502,
0.09213701635599136,
-0.0010409846436232328,
-0.05505490303039551,
0.027529366314411163,
-0.008361664600670338,
-0.007266846019774675,
-0.0224863700568676,
0.012278646230697632,
0.05599124729633331,
0.04123232141137123,
-0.07793153077363968,
0.052720315754413605,
-0.0218187402933836,
0.04403349757194519,
-0.04206830635666847,
0.044310811907052994,
0.015383212827146053,
0.07622668892145157,
-0.05631541460752487,
-0.012817264534533024,
-0.07746963202953339,
-0.005672386381775141,
-0.005165653768926859,
-0.009853201918303967,
-0.014729481190443039,
-0.02836003340780735,
0.020557846873998642,
0.01362594310194254,
0.05715644359588623,
-0.044393204152584076,
0.030279692262411118,
0.032847970724105835,
-0.06242958828806877,
-0.004477291367948055,
-0.030588647350668907,
-0.03881653770804405,
0.04374030977487564,
0.04550974816083908,
0.022237101569771767,
0.029087068513035774,
0.039593011140823364,
0.007881303317844868,
-0.029827512800693512,
0.06292134523391724,
-0.024669408798217773,
0.05384714901447296,
0.009655231609940529,
-0.046391330659389496,
0.05937040224671364,
-0.029535934329032898,
0.005002943333238363,
-0.0018363900016993284,
0.043609537184238434,
-0.0324893593788147,
-0.051518067717552185,
-0.0022599848452955484,
0.0007497185724787414,
0.040154311805963516,
0.03524315357208252,
-0.006702226586639881,
0.007735926192253828,
-0.028106005862355232,
0.01865517348051071,
0.005428807809948921,
0.004013947676867247,
-0.06023215502500534,
-0.05376424640417099,
0.023946473374962807,
0.035721857100725174,
0.035588882863521576,
-0.031216740608215332,
-0.011021224781870842,
0.04396440461277962,
-0.04002014547586441,
0.03578519448637962,
-0.0199119970202446,
-0.014070131815969944,
0.03821847587823868,
-0.04717105254530907,
-0.021656403318047523,
0.027380796149373055,
-0.036231063306331635,
0.013282482512295246,
-0.037031855434179306,
-0.03214158117771149,
-0.017205316573381424,
-0.007240171078592539,
-0.023650074377655983,
-0.054077211767435074,
-0.02702724188566208,
0.059215009212493896,
0.0790703222155571,
-0.1142323911190033,
-0.020347360521554947,
-0.022673234343528748,
-0.020431049168109894,
-0.0008138276753015816,
0.024978656321763992,
-0.05590410903096199,
0.013801687397062778,
-0.05893554538488388,
-0.017750149592757225,
0.009694674983620644,
-0.051597822457551956,
0.021604709327220917,
0.06757953017950058,
0.00854481477290392,
-0.034699391573667526,
0.044912029057741165,
0.0037986026145517826,
0.020863045006990433,
-0.004678715486079454,
-0.023351993411779404,
-0.0901649072766304,
0.022162113338708878,
-0.006188693922013044,
0.0349896065890789,
-0.030880436301231384,
0.0029488045256584883,
-0.013517778366804123,
0.04768150672316551,
-0.0663389191031456,
0.023085063323378563,
0.04334331676363945,
-0.03818050026893616,
-0.007135508581995964,
0.01031531859189272,
0.06835589557886124,
0.001104784314520657,
-0.006187365856021643,
-0.023510228842496872,
-0.019544290378689766,
-0.015475853346288204,
0.03476222604513168,
0.016270138323307037,
-0.005212313495576382,
-0.04437399283051491,
0.012267634272575378,
0.0173942968249321,
-0.07263746857643127,
-0.028832100331783295,
-0.03637155517935753,
-0.0007077392074279487,
-0.006108046043664217,
0.008581592701375484,
-0.021255264058709145,
0.011028490029275417,
-0.055952660739421844,
-0.03845905885100365,
0.00041473197052255273,
0.05192713439464569,
-0.019573405385017395,
-0.04416169598698616,
0.031963396817445755,
-0.050959184765815735,
-0.05125180631875992,
0.009846995584666729,
-0.044920191168785095,
-0.045441169291734695,
0.026190895587205887,
0.0543590784072876,
0.06546080857515335,
0.032670650631189346,
0.03811059892177582,
0.012539230287075043,
0.0386984646320343,
0.04034051299095154,
-0.060771215707063675,
0.0053448136895895,
0.016651619225740433,
0.010082995519042015,
0.027227679267525673,
-0.04585976526141167,
-0.03750045597553253,
-0.014826007187366486,
0.0386076457798481,
0.009286384098231792,
-0.04538736119866371,
0.02243865840137005,
-0.0005159141728654504,
-0.05477726832032204,
0.015052852220833302,
0.037097182124853134,
0.09535626322031021,
-0.019465414807200432,
-0.03595167025923729,
0.00040395575342699885,
0.06454271823167801,
-0.017579952254891396,
-0.01940278522670269,
0.05601685121655464,
0.028160784393548965,
-0.055329062044620514,
0.04444047808647156,
0.017206212505698204,
-0.013221555389463902,
-0.0037728426977992058,
0.037214405834674835,
-0.017878457903862,
-0.022133804857730865,
-0.03404130041599274,
-0.01794475130736828,
0.017830241471529007,
-0.045614320784807205,
0.010005745105445385,
0.023897308856248856,
-0.015358834527432919,
-0.00828300416469574,
0.004782692529261112,
-0.010215257294476032,
-0.057454466819763184,
-0.06874486058950424,
-0.003059589536860585,
0.04346540570259094,
0.004600983578711748,
-0.05005825683474541,
-0.0402807891368866,
0.016879456117749214,
-0.02966647408902645,
0.0013703893637284636,
0.018045268952846527,
0.04077012836933136,
0.022275058552622795,
-0.007375336717814207,
-0.05598423257470131,
0.003004751168191433,
0.009171762503683567,
-0.0030676526948809624,
-0.011669386178255081,
0.032754432410001755,
-0.00948740728199482,
-0.055731359869241714,
0.019005658105015755,
0.04898253455758095,
-0.0007489065174013376,
-0.0008478793897666037,
-0.001295045716688037,
0.07506377249956131,
-0.06428300589323044,
0.008104747161269188,
-0.00013134807522874326,
0.03456978499889374,
-0.032758235931396484,
-0.030313491821289062,
-0.04273479804396629,
-0.011722180061042309,
-0.021686596795916557,
-0.030260741710662842,
-0.05037911981344223,
0.0799117386341095,
0.03435516357421875,
0.05527327582240105,
-0.0004389026144053787,
-0.06613769382238388,
0.02868806943297386,
-0.006763460114598274,
0.013183631002902985,
0.056097645312547684,
0.023630479350686073,
0.01358182542026043,
-0.010444840416312218,
0.023687727749347687,
0.020591797307133675,
0.010063855908811092,
-0.04487525671720505,
0.07042748481035233,
-0.00621491763740778,
-0.01344947051256895,
-0.04927865415811539,
-0.06693489849567413,
-0.002495888853445649,
0.0432707853615284,
0.025095347315073013,
0.0409097857773304,
0.059645626693964005,
0.03790507838129997,
-0.014756166376173496,
0.0009637657785788178,
0.01339498721063137,
-0.016655271872878075,
0.037523552775382996,
-0.020206861197948456,
0.058446381241083145,
-0.03004826046526432,
-0.012087642215192318,
0.07659240067005157,
0.0018745085690170527,
0.015419289469718933,
-0.015589173883199692,
0.03019714169204235,
-0.03752538189291954,
-0.043526239693164825,
-0.03210948035120964,
-0.02652180753648281,
-0.02470945380628109,
-0.003053168300539255,
0.03342484310269356,
-0.023901350796222687,
-0.002389565808698535,
-0.014165841042995453,
0.029626403003931046,
-0.039902303367853165,
-0.0014695527497678995,
-0.052777986973524094,
-0.049108922481536865,
-0.026368089020252228,
-0.042552415281534195,
-0.05549045279622078,
-0.010152571834623814,
0.10093078017234802,
-0.02189500443637371,
-0.04522676765918732,
-0.06726260483264923,
0.04948723316192627,
0.033267468214035034,
-0.027049601078033447,
-0.026051897555589676,
-0.009090285748243332,
-0.07511954754590988,
0.025354791432619095,
0.010783223435282707,
0.002721569035202265,
0.017541147768497467,
0.008792949840426445,
0.006413936614990234,
0.01596623845398426,
-0.05342334881424904,
0.07320563495159149,
0.03305080160498619,
-0.014630268327891827,
0.035595692694187164,
0.05397956445813179,
0.03276314213871956,
-0.022203953936696053,
-0.01317193266004324,
-0.01264272816479206,
0.008603684604167938,
-0.019123896956443787,
0.0007200326072052121,
0.012915872037410736,
0.052038222551345825,
-0.009858391247689724,
-0.05304373428225517,
0.024958990514278412,
-0.04811268672347069,
0.06586939096450806,
0.0067197950556874275,
0.04283483698964119,
-0.05449604243040085,
0.054789114743471146,
-0.0026781519409269094,
0.05575963482260704,
-0.021716533228754997,
-0.004615284036844969,
-0.025134047493338585,
0.051893625408411026,
0.00036993634421378374,
-0.0723550096154213,
0.034422919154167175,
-0.008897657506167889,
0.09321334958076477,
-0.017587995156645775,
-0.015971152111887932,
-0.02916191704571247,
-0.04425942897796631,
0.05974014475941658,
-0.0011007633293047547,
0.07549486309289932,
0.018914585933089256,
0.008050634525716305,
-0.040762078016996384,
0.0006861781002953649,
0.009709087200462818,
0.03138291463255882,
0.03875806927680969,
-0.06449732184410095,
-0.029433734714984894,
0.016405727714300156,
-0.0348544716835022,
-0.001524131279438734,
0.0018779253587126732,
0.05223609879612923,
-0.055544763803482056,
0.007286070380359888,
0.01182605978101492,
0.03300316259264946,
0.0753098800778389,
-0.051050931215286255,
0.006642830558121204,
-0.00002721123928495217,
0.03241785243153572,
-0.00009172485442832112,
-0.03647182881832123,
0.047728631645441055,
-0.028337107971310616,
-0.026250358670949936,
0.057641737163066864,
-0.029275992885231972,
-0.050478462129831314,
0.025052914395928383
] |
<blockquote>
<p>I have given one-dimensional motion of the particle directed
horizontally. A problem says: "<em>...Show that for this given motion
Conservation of Energy Law holds.</em>".</p>
</blockquote>
<p>Since Energy can intuitively be thought of an operation that changes something over time, energy being conserved essentially means that the motion is not a function of time, but position only?</p>
<p>I.e. does energy conservation mean that a process is time-independent?</p> | g7786 | [
0.07954540103673935,
0.027377227321267128,
0.002815233077853918,
0.025290923193097115,
0.029110070317983627,
-0.026911761611700058,
0.021782606840133667,
0.013050025328993797,
-0.02411271259188652,
0.010241353884339333,
-0.01279038842767477,
0.0253888051956892,
-0.03159266710281372,
0.013402816839516163,
-0.027375347912311554,
-0.016263041645288467,
0.0851166769862175,
0.010672150179743767,
-0.014095941558480263,
0.07520138472318649,
0.003348831320181489,
-0.010806586593389511,
-0.005363003816455603,
0.013983641751110554,
0.06493846327066422,
-0.0474000982940197,
0.05014733225107193,
-0.08219853043556213,
-0.04383213818073273,
-0.014033627696335316,
0.022403623908758163,
-0.006987593602389097,
0.06746464967727661,
-0.03201056644320488,
-0.05120807886123657,
-0.039999380707740784,
0.12333935499191284,
-0.00894996989518404,
0.09972812980413437,
0.02650480717420578,
-0.0040121800266206264,
0.02396545186638832,
0.007442277390509844,
-0.02670179307460785,
0.08196857571601868,
-0.01917148195207119,
-0.008691484108567238,
-0.03423868864774704,
-0.02434556931257248,
-0.009470690041780472,
0.011360830627381802,
0.029968880116939545,
0.022343197837471962,
0.0243256576359272,
-0.016450049355626106,
-0.030131177976727486,
0.001804616185836494,
0.014633769169449806,
0.023939425125718117,
0.03158992528915405,
0.003728181589394808,
0.01063196174800396,
0.049912117421627045,
-0.005022995173931122,
0.03974195197224617,
-0.07619083672761917,
-0.07721300423145294,
-0.014027240686118603,
0.05010506883263588,
0.010547623038291931,
0.05905239284038544,
-0.009564111940562725,
-0.017726263031363487,
-0.0023576123639941216,
0.03797241672873497,
0.028173189610242844,
-0.009879807941615582,
-0.029022295027971268,
-0.04760486260056496,
-0.010750939138233662,
-0.06327661871910095,
0.014180213212966919,
0.031897515058517456,
0.008413032628595829,
0.09491145610809326,
0.007035619113594294,
0.018854310736060143,
-0.014204079285264015,
-0.0544535368680954,
0.028637949377298355,
-0.0010342642199248075,
-0.017818545922636986,
0.07585469633340836,
0.023474423214793205,
-0.01704736426472664,
-0.011938841082155704,
-0.05464346706867218,
0.05330166220664978,
0.0007129092700779438,
0.004301833920180798,
-0.01491219736635685,
-0.0032625554595142603,
-0.03483506292104721,
-0.02638433873653412,
0.06332704424858093,
0.004677095450460911,
0.011702192947268486,
0.013246867805719376,
-0.053074322640895844,
-0.029395530000329018,
0.07124770432710648,
-0.05503673106431961,
-0.035625506192445755,
-0.02378050982952118,
-0.024529483169317245,
-0.042297977954149246,
0.1056659147143364,
-0.0038063316605985165,
0.023853855207562447,
0.028526166453957558,
-0.006462596356868744,
0.01613771729171276,
0.010347588919103146,
0.044747620820999146,
-0.012460595928132534,
0.029577596113085747,
-0.009961074218153954,
0.005019485484808683,
0.0034072089474648237,
0.00503148976713419,
0.015662213787436485,
-0.0009245566907338798,
0.03502798080444336,
0.015542431734502316,
-0.013735177926719189,
0.03633856773376465,
0.004924409091472626,
0.028665008023381233,
0.023195110261440277,
-0.018953930586576462,
-0.02587166801095009,
-0.0017069774912670255,
-0.0027620610781013966,
0.0020367505494505167,
-0.023965701460838318,
0.011024205014109612,
-0.004753113724291325,
-0.044728584587574005,
0.043480608612298965,
0.0055842590518295765,
-0.03814302012324333,
0.10493078082799911,
-0.04826146364212036,
-0.048686061054468155,
0.11785157024860382,
-0.022703316062688828,
0.008157787844538689,
0.01962043158710003,
-0.017588309943675995,
0.011443580500781536,
0.05245070904493332,
0.018113603815436363,
0.03339606150984764,
-0.024423304945230484,
-0.08096910268068314,
-0.02549947239458561,
0.012635349296033382,
-0.05815751105546951,
0.02701280452311039,
-0.07399478554725647,
-0.06169041991233826,
-0.03029225580394268,
0.001207006280310452,
0.057399503886699677,
-0.0441584587097168,
0.044287629425525665,
-0.02796534262597561,
-0.06974305957555771,
0.011831979267299175,
-0.0479399599134922,
-0.0017904380802065134,
-0.01320064626634121,
0.032666418701410294,
-0.010001401416957378,
0.030317531898617744,
0.04878934100270271,
0.011410144157707691,
-0.00688672810792923,
-0.0828872099518776,
-0.04728497192263603,
-0.018026426434516907,
0.011465759947896004,
-0.003980160690844059,
0.05977100506424904,
-0.033187806606292725,
-0.007072465494275093,
0.005659126676619053,
-0.04719003662467003,
-0.07092336565256119,
0.007790132891386747,
-0.0023498230148106813,
0.04080642759799957,
0.043701108545064926,
0.02625107392668724,
0.030938202515244484,
-0.00941416248679161,
0.046220168471336365,
-0.00990109983831644,
0.0029263945762068033,
-0.026247207075357437,
0.05905945226550102,
0.0017157495021820068,
-0.02413613721728325,
-0.02010374329984188,
0.040619995445013046,
-0.04978047311306,
-0.008261571638286114,
0.016322312876582146,
-0.02477048896253109,
-0.04455456882715225,
-0.10001664608716965,
-0.022406267002224922,
0.048588596284389496,
0.02490057423710823,
0.009897119365632534,
-0.015223009511828423,
-0.04696361720561981,
-0.0305339302867651,
-0.031238190829753876,
0.05656075105071068,
-0.06919249892234802,
-0.013561168685555458,
-0.023169249296188354,
-0.02481970191001892,
0.04791150242090225,
0.03707149252295494,
-0.02206917479634285,
0.08486539125442505,
0.06587395817041397,
0.02460668422281742,
0.002720337128266692,
-0.02778066322207451,
0.008353685028851032,
-0.0566796250641346,
0.01679936982691288,
-0.01452717836946249,
0.06070404872298241,
0.022663524374365807,
-0.015407717786729336,
-0.04797656089067459,
0.030795993283391,
0.011124284006655216,
-0.02022583782672882,
0.019988663494586945,
0.04975630342960358,
-0.02990560233592987,
0.010916593484580517,
0.0029000199865549803,
-0.021867502480745316,
-0.04075925424695015,
-0.0091490363702178,
-0.06459822505712509,
0.037474483251571655,
0.010249463841319084,
0.01804567128419876,
-0.04721098393201828,
-0.007429707329720259,
-0.0009847116889432073,
-0.0111057935282588,
-0.014288372360169888,
-0.01871318370103836,
0.03511326387524605,
-0.010468639433383942,
0.06479935348033905,
-0.050098810344934464,
-0.011191006749868393,
0.04414373263716698,
-0.013040031306445599,
-0.0043215262703597546,
-0.016329627484083176,
0.0018299553776159883,
-0.02401384525001049,
-0.0709339901804924,
0.029934626072645187,
0.05001147836446762,
0.0088462820276618,
0.009727622382342815,
-0.00249797897413373,
-0.022266298532485962,
-0.027904663234949112,
-0.054875027388334274,
0.03799682483077049,
0.03109615668654442,
0.0015305507695302367,
-0.019235102459788322,
0.03710305318236351,
-0.04030761867761612,
-0.0416996031999588,
-0.026198113337159157,
0.02937789261341095,
-0.040574781596660614,
-0.001496711978688836,
-0.018250111490488052,
0.02750876545906067,
0.09169743210077286,
0.04575250670313835,
-0.09747037291526794,
-0.03620418161153793,
0.04252355918288231,
0.0027082243468612432,
-0.00045132660306990147,
0.07405611127614975,
-0.012051287107169628,
0.010960706509649754,
-0.03774945065379143,
-0.025714389979839325,
-0.05359234660863876,
-0.05711626261472702,
0.00767073780298233,
-0.006890239659696817,
-0.033570799976587296,
-0.015118603594601154,
0.018012546002864838,
-0.009801716543734074,
-0.011844638735055923,
-0.007557705510407686,
-0.0671788901090622,
0.00513670826330781,
-0.01990468241274357,
0.005415104795247316,
-0.03270033001899719,
0.004833732265979052,
0.036449383944272995,
-0.02225368656218052,
0.027051305398344994,
-0.07477699965238571,
-0.02761138789355755,
-0.0063938600942492485,
0.04721279442310333,
-0.011975441128015518,
0.012676149606704712,
-0.005152939353138208,
-0.019722813740372658,
0.03271082788705826,
0.03765357285737991,
-0.021123886108398438,
-0.02300247550010681,
0.03411494567990303,
0.009396353736519814,
0.02579445019364357,
0.071564219892025,
-0.028405072167515755,
0.007238391786813736,
-0.022518454119563103,
-0.006812722887843847,
0.02602190151810646,
0.01952984556555748,
0.06390637904405594,
-0.05870668217539787,
0.008955630473792553,
-0.019608929753303528,
-0.011800860054790974,
0.007882465608417988,
0.03275289759039879,
0.0013565578265115619,
0.03284084424376488,
-0.0026102459523826838,
-0.04001430422067642,
0.029600689187645912,
-0.009359466843307018,
-0.01680568791925907,
-0.038340430706739426,
-0.0011533121578395367,
0.01599418930709362,
0.004252533428370953,
-0.008033711463212967,
0.032466813921928406,
-0.005128115881234407,
-0.029793886467814445,
0.006189094390720129,
-0.004442605655640364,
-0.011240610852837563,
0.0066353436559438705,
0.0403749905526638,
0.0199220422655344,
0.05637555569410324,
-0.022378861904144287,
0.031160691753029823,
0.020597102120518684,
0.00272595533169806,
0.03472350537776947,
-0.019089730456471443,
0.023998938500881195,
-0.033882591873407364,
-0.006742824800312519,
0.018319008871912956,
0.04487065598368645,
-0.05701472982764244,
-0.02074551209807396,
-0.02552087791264057,
-0.0046845898032188416,
-0.06836442649364471,
0.007676290813833475,
-0.019418055191636086,
0.022086327895522118,
0.025218939408659935,
0.06404715031385422,
-0.05665683001279831,
-0.034511059522628784,
-0.010242613032460213,
0.02777879126369953,
-0.0004213593783788383,
-0.034941285848617554,
-0.030295616015791893,
-0.004975209943950176,
-0.026603009551763535,
0.00301467371173203,
-0.0022247405722737312,
0.0456160306930542,
0.03614014759659767,
0.042495135217905045,
0.06821145862340927,
-0.00891854427754879,
-0.043049972504377365,
0.0007501750369556248,
0.09031574428081512,
0.016224149614572525,
-0.026282833889126778,
-0.02155415341258049,
-0.053624339401721954,
0.01071876659989357,
0.014361667446792126,
0.028693750500679016,
-0.03456396237015724,
-0.06373541802167892,
0.02489149570465088,
0.00427702721208334,
0.022080466151237488,
0.01941836252808571,
0.06758046895265579,
0.06729967892169952,
-0.014722359366714954,
0.009589826688170433,
0.012046520598232746,
-0.008314453065395355,
0.05808351933956146,
0.017866207286715508,
-0.046736422926187515,
-0.02131015807390213,
-0.04267292469739914,
0.010710169561207294,
0.08141349256038666,
-0.043559782207012177,
-0.0025394458789378405,
0.008784192614257336,
-0.023641284555196762,
-0.00339944614097476,
-0.03850970044732094,
0.013508963398635387,
0.04694100469350815,
-0.05989690124988556,
-0.027177199721336365,
0.01991105079650879,
0.023199914023280144,
-0.014572707004845142,
0.01142298523336649,
-0.015639040619134903,
0.02853991650044918,
-0.04311352223157883,
0.012631122022867203,
0.029871637001633644,
0.012088078074157238,
-0.002771624829620123,
-0.004111174494028091,
-0.029420489445328712,
-0.00017317768651992083,
-0.005886575672775507,
-0.01801309362053871,
0.07858365774154663,
-0.01734505221247673,
-0.02234252169728279,
-0.04432044178247452,
0.022078096866607666,
0.030741628259420395,
0.03804636001586914,
-0.022792181000113487,
-0.05969686061143875,
0.011550158262252808,
0.03521682694554329,
-0.014703668653964996,
0.003993902821093798,
0.020320583134889603,
-0.008468872867524624,
-0.013255173340439796,
0.017650283873081207,
-0.04735225811600685,
-0.005906797479838133,
-0.00473078154027462,
0.0031160677317529917,
-0.016307499259710312,
-0.045425478368997574,
-0.07599740475416183,
-0.039725009351968765,
-0.001564798760227859,
0.0036039436236023903,
0.024078158661723137,
0.006923690438270569,
0.02996031381189823,
-0.08094128221273422,
-0.022907689213752747,
-0.019699689000844955,
0.017479686066508293,
-0.023420583456754684,
0.02320043183863163,
0.014998913742601871,
-0.04151265695691109,
0.030254798009991646,
0.022190097719430923,
-0.07329774647951126,
-0.009370295330882072,
0.06512397527694702,
0.03564148023724556,
0.0835437998175621,
0.012121576815843582,
0.02678523398935795,
0.008268573321402073,
-0.08956198394298553,
-0.01682117022573948,
-0.03032158873975277,
0.0728812888264656,
0.02413184568285942,
-0.0339871309697628,
-0.03344053775072098,
-0.006438244599848986,
-0.06968072056770325,
0.014253704808652401,
-0.022555064409971237,
0.014151548035442829,
0.004154059570282698,
0.013193017803132534,
-0.014161653816699982,
-0.046893052756786346,
0.02745104767382145,
0.023417670279741287,
-0.07214830815792084,
0.020881297066807747,
-0.08849700540304184,
-0.019730163738131523,
0.0039400095120072365,
-0.07008282095193863,
0.024405663833022118,
0.00755702517926693,
0.009373921900987625,
-0.05519247055053711,
0.022370031103491783,
0.018863217905163765,
0.030491311103105545,
-0.055786408483982086,
0.02259794808924198,
0.009218492545187473,
-0.00597282312810421,
0.025264302268624306,
0.036056142300367355,
-0.010038905777037144,
0.061372656375169754,
-0.051318030804395676,
0.023128315806388855,
-0.02351377159357071,
0.007631280925124884,
0.026567934080958366,
-0.0011786053655669093,
0.016669632866978645,
-0.007752190809696913,
0.05613669380545616,
0.007366078440099955,
-0.018325267359614372,
-0.06830655783414841,
-0.00788915529847145,
-0.11793402582406998,
0.0317533016204834,
-0.005774194374680519,
-0.01602095179259777,
0.035864606499671936,
-0.04410944879055023,
0.01246174331754446,
0.03458552435040474,
-0.025935962796211243,
-0.018597105517983437,
0.08054006099700928,
0.061284467577934265,
-0.029546992853283882,
-0.027848277240991592,
-0.024951672181487083,
0.03966207802295685,
-0.005325610749423504,
-0.0034586398396641016,
-0.02681039646267891,
0.002927036490291357,
-0.03372642397880554,
-0.0003786795132327825,
-0.005804469808936119,
-0.010436425916850567,
-0.017552796751260757,
-0.1028972864151001,
-0.037319596856832504,
0.08764896541833878,
-0.0432196781039238,
0.07437650114297867,
-0.005143306218087673,
-0.026700064539909363,
-0.04011619836091995,
0.05023773014545441,
0.017729222774505615,
-0.04596146568655968,
-0.012912090867757797,
-0.023249903693795204,
0.02775794081389904,
0.009852087125182152,
-0.0033756408374756575,
-0.026562398299574852,
0.01490369439125061,
0.05147257074713707,
0.029739927500486374,
-0.013439086265861988,
0.036263786256313324,
0.0032586692832410336,
-0.06368530541658401,
0.008031105622649193,
0.03457166999578476,
0.03662585839629173,
-0.025229111313819885,
0.017801927402615547,
-0.055378615856170654,
0.031048370525240898,
-0.02227403223514557,
0.006332710385322571,
-0.062112994492053986,
0.05438138172030449,
0.007032576948404312,
0.027221566066145897,
-0.036263395100831985,
0.017087025567889214,
0.02400534227490425,
0.026334477588534355,
-0.08491965383291245,
-0.010970713570713997,
0.04995238035917282,
0.02191648632287979,
-0.03433164954185486,
-0.03595936298370361,
0.00598874082788825,
0.061499323695898056,
-0.01898662932217121,
-0.04030412808060646,
0.004540559835731983,
0.020739100873470306,
-0.03149929642677307,
-0.008730443194508553,
0.007858378812670708,
-0.05055176466703415,
0.0030019062105566263,
-0.09638648480176926,
0.025897406041622162,
0.016133731231093407,
0.008985066786408424,
0.05469473451375961,
-0.018430259078741074,
-0.03459972143173218,
0.0408468022942543,
-0.03677187114953995,
-0.005706614349037409,
-0.01824166439473629,
-0.011499520391225815,
0.04238541051745415,
0.006272835191339254,
0.03813377767801285,
0.02797289751470089,
0.04668109863996506,
-0.012695963494479656,
0.013667529448866844,
0.012081936001777649,
0.004923297557979822,
-0.02469991147518158,
-0.02515450306236744,
-0.032980967313051224,
0.032462142407894135,
-0.013972459360957146,
-0.007852466776967049,
-0.01119245495647192,
-0.01057386863976717,
-0.04390261322259903,
0.04664319381117821,
0.05473579466342926,
-0.038095664232969284,
0.006651916075497866,
-0.019386708736419678,
0.07057434320449829,
0.019927559420466423,
-0.03102843463420868,
0.016016123816370964,
-0.011065331287682056,
-0.022739198058843613,
0.0005456621875055134,
0.04535023868083954,
-0.0028041955083608627,
-0.050319742411375046,
-0.021288996562361717,
-0.05422579124569893,
-0.031494203954935074,
0.038691360503435135,
0.0013223242713138461,
-0.008804094046354294,
-0.020198890939354897,
0.024101246148347855,
0.046589240431785583,
0.004970377776771784,
-0.0021861593704670668,
0.012000196613371372,
0.022480344399809837,
0.04336792230606079,
0.017102520912885666,
-0.009782535023987293,
-0.0799037292599678,
-0.06853599846363068,
0.03055056743323803,
0.017314165830612183,
-0.01643740013241768,
-0.026640765368938446,
0.035322681069374084,
-0.017779015004634857,
0.012927287258207798,
-0.01602736860513687,
-0.012131474912166595,
0.017373202368617058,
0.04041700065135956,
0.01576251909136772,
0.0368933342397213,
-0.013789752498269081,
-0.018109796568751335,
0.024585479870438576,
0.009310022927820683,
-0.024928297847509384,
-0.04141629487276077,
-0.01811867579817772,
0.00033965124748647213,
-0.029480312019586563,
0.01970953308045864,
0.004442357458174229,
0.026737632229924202,
0.0033535612747073174,
0.06460221111774445,
0.04112003743648529,
-0.051186710596084595,
-0.019510120153427124,
0.021695973351597786,
-0.031448230147361755,
0.0155513696372509,
-0.0023775147274136543,
0.014010904356837273,
0.01748797670006752,
-0.029351556673645973,
0.029496509581804276,
0.014691324904561043,
-0.05257204547524452,
-0.003670645644888282,
-0.03976241499185562,
0.03984225168824196,
0.04646247625350952
] |
<p>May be this question might have already been asked but i couldn't find it, so let me know if its already there.</p>
<p>Consider a potential, $V(x) = -\frac{1}{|x|}$ and if we apply this to a one dimensional Schrodinger's equation, I'd like to know the solution for the wave function in 1-D. Does it have a simple analytical solution? Does it have any oscillatory behavior like $$\psi(x,t) = P(x) e^{ikx}e^{i\omega t}$$ I mean will there be a factor like $e^{ikx}$ ? From the internet search, looking at one-dimensional hydrogen atom, first of all i am not sure whether there is any analytical solution, but I guess it was suggested that an exponential decay, something like $$P(x) = e^{-\alpha x}$$ is present. But I am not sure about presence of oscillations like $e^{ikx}$. Hence I'd appreciate some suggestions and clarification.</p>
<p>PS : I am not interested in Hydrogen atom, but in this specific 1-D potential.</p> | g7787 | [
-0.013180694542825222,
0.014726167544722557,
-0.006922774948179722,
-0.03421167656779289,
0.03943100571632385,
0.007538427133113146,
0.018239496275782585,
0.02131439745426178,
0.0016306460602208972,
-0.010229633189737797,
0.02587823010981083,
0.008049766533076763,
0.025316771119832993,
0.08511491119861603,
-0.019068291410803795,
-0.01286697294563055,
0.048865094780921936,
-0.0008867907454259694,
-0.03791038319468498,
-0.050032444298267365,
-0.00520899286493659,
-0.006133220158517361,
0.019715161994099617,
-0.013816941529512405,
0.059164561331272125,
0.0014538519317284226,
0.03399212658405304,
-0.0033771744929254055,
0.0030841126572340727,
0.025023886933922768,
-0.06163426861166954,
0.026480278000235558,
0.08530759811401367,
-0.046595990657806396,
0.018146270886063576,
0.058498892933130264,
0.04915812984108925,
0.0048140850849449635,
0.03493126109242439,
-0.041852325201034546,
0.0045757535845041275,
-0.048902738839387894,
0.049182645976543427,
-0.0237263310700655,
0.04933600872755051,
-0.013614499941468239,
-0.018397195264697075,
0.022501643747091293,
0.027004901319742203,
0.010338813997805119,
0.03819281980395317,
0.005998682230710983,
0.0651174932718277,
0.024077007547020912,
-0.023655397817492485,
-0.003150560427457094,
0.018138865008950233,
-0.04193153977394104,
0.029005642980337143,
0.09786678105592728,
0.010357581079006195,
-0.0023752327542752028,
0.07395155727863312,
-0.00815287884324789,
0.07645653933286667,
-0.055136147886514664,
-0.014070054516196251,
-0.014551661908626556,
0.025428447872400284,
-0.056567151099443436,
0.03786628320813179,
-0.06720028817653656,
-0.02742023393511772,
-0.011946204118430614,
0.03475593030452728,
0.07389163970947266,
-0.01960194669663906,
-0.06433942168951035,
-0.017691221088171005,
-0.015064011327922344,
-0.005501367151737213,
-0.04354604706168175,
0.04900255799293518,
0.0111685860902071,
0.08086733520030975,
-0.007775777485221624,
0.024207331240177155,
-0.019618788734078407,
0.014703255146741867,
-0.029468083754181862,
-0.037003595381975174,
-0.03468352183699608,
-0.014799581840634346,
-0.0933312326669693,
0.010710137896239758,
-0.030952738597989082,
-0.04709409177303314,
0.022826889529824257,
-0.031143810600042343,
-0.005596448201686144,
-0.003108808770775795,
-0.012629986740648746,
0.01760496385395527,
-0.0084528848528862,
0.017895115539431572,
-0.019289830699563026,
-0.05059688910841942,
-0.031153839081525803,
-0.0025722477585077286,
-0.03700414299964905,
-0.005148217547684908,
-0.022851452231407166,
-0.046685002744197845,
-0.033612824976444244,
-0.03136349841952324,
-0.0009832291398197412,
0.007052351254969835,
-0.017351774498820305,
-0.009575031697750092,
0.012061161920428276,
-0.012835429050028324,
0.003702157875522971,
0.07262217998504639,
0.017221949994564056,
-0.02723991870880127,
0.07568620145320892,
-0.025781797245144844,
-0.005120341200381517,
0.002422098768875003,
0.03737026825547218,
0.014440766535699368,
0.05981874465942383,
-0.021464668214321136,
-0.03156314790248871,
-0.023122306913137436,
0.047250665724277496,
0.004501290153712034,
0.02411285974085331,
0.005722599569708109,
0.0019705339800566435,
0.03317493200302124,
-0.05959451198577881,
-0.004260244779288769,
0.026454022154211998,
-0.06368312984704971,
0.04626196250319481,
-0.015139027498662472,
-0.013177908025681973,
0.014969520270824432,
0.03003137744963169,
0.00011774725135182962,
0.02544650062918663,
0.001590597559697926,
-0.06172607094049454,
-0.033614229410886765,
0.003062962321564555,
-0.021993784233927727,
0.0418262742459774,
-0.028831027448177338,
0.0021120498422533274,
-0.0008288320968858898,
0.050094280391931534,
0.004680970683693886,
0.029920263215899467,
-0.050259068608284,
0.01659354194998741,
-0.00427235709503293,
-0.028702929615974426,
-0.02393696829676628,
-0.04311342164874077,
0.029847992584109306,
-0.011161143891513348,
0.02194683626294136,
0.01863112859427929,
-0.014836196787655354,
0.01683846488595009,
0.0016321238363161683,
-0.03804207965731621,
-0.007027709856629372,
0.030238624662160873,
0.022382155060768127,
-0.06243167072534561,
0.0016009025275707245,
-0.05077600106596947,
0.011283821426331997,
0.007809940725564957,
-0.02203129604458809,
0.016350941732525826,
-0.04476511478424072,
0.008401118218898773,
0.02355298213660717,
-0.020569851621985435,
0.03794759511947632,
0.006796910893172026,
0.006065111607313156,
0.015822166576981544,
0.008913991041481495,
-0.08486030250787735,
-0.058453138917684555,
-0.005141832400113344,
-0.03300754353404045,
0.056213971227407455,
0.022773828357458115,
0.011129218153655529,
0.04483426734805107,
-0.0017050241585820913,
0.049436602741479874,
0.0023744467180222273,
0.029321465641260147,
-0.03875560313463211,
0.02172418311238289,
0.002231279853731394,
-0.019099049270153046,
0.013180303387343884,
-0.024701032787561417,
-0.040866605937480927,
0.026907840743660927,
0.011303724721074104,
-0.05957683548331261,
0.03934536874294281,
-0.0002668524393811822,
-0.007126763463020325,
-0.03697584941983223,
0.037003982812166214,
-0.012131831608712673,
0.015809426084160805,
-0.053010012954473495,
-0.00003380857015145011,
-0.03329430893063545,
0.052872151136398315,
-0.07237463444471359,
0.04235851392149925,
-0.00043998018372803926,
-0.06754012405872345,
0.024161627516150475,
0.02900867536664009,
-0.06428838521242142,
-0.03394134342670441,
0.008195540867745876,
-0.024765340611338615,
0.005978972651064396,
-0.05964496731758118,
-0.04495156928896904,
-0.009320169687271118,
0.07439575344324112,
-0.046216998249292374,
-0.00032296209246851504,
0.01112363114953041,
0.007369914557784796,
-0.034027520567178726,
0.022785406559705734,
-0.0020435305777937174,
-0.02053583227097988,
0.057050712406635284,
-0.01964142732322216,
-0.032761383801698685,
0.014047120697796345,
0.032402295619249344,
-0.007095367647707462,
-0.03890877589583397,
-0.027195336297154427,
-0.004769168794155121,
0.01822195015847683,
-0.016414165496826172,
-0.012640648521482944,
-0.042460061609745026,
-0.01679118163883686,
0.03752098232507706,
-0.036325257271528244,
-0.01830228418111801,
-0.017335819080471992,
0.017318548634648323,
-0.02370278723537922,
0.05790777876973152,
-0.06920921802520752,
0.0028759767301380634,
0.0036283740773797035,
-0.03180890157818794,
0.050007037818431854,
-0.05204023793339729,
-0.04047122597694397,
0.024928707629442215,
-0.039972223341464996,
0.04354039952158928,
0.011808165349066257,
-0.009887316264212132,
0.08225122094154358,
-0.007771249860525131,
0.022317172959446907,
-0.01974206045269966,
-0.012800252996385098,
0.0055726878345012665,
-0.028040166944265366,
0.06850139796733856,
-0.047120850533246994,
0.009641117416322231,
0.0245346762239933,
-0.04277149215340614,
0.00017318796017207205,
0.08537366986274719,
0.024648655205965042,
0.019845301285386086,
-0.009984346106648445,
0.0026871266309171915,
0.02688930369913578,
-0.03298233449459076,
-0.05059758946299553,
-0.001113899634219706,
0.04540613293647766,
0.012528964318335056,
0.02060416154563427,
0.0983206108212471,
0.010504717007279396,
0.0020171029027551413,
-0.04862705245614052,
0.013170742429792881,
-0.019757471978664398,
-0.031472936272621155,
-0.010268273763358593,
-0.018981579691171646,
-0.030453624203801155,
-0.07540407031774521,
-0.030122948810458183,
0.02268866077065468,
0.02952449955046177,
-0.006710815243422985,
-0.06636416912078857,
-0.04309151694178581,
-0.017425846308469772,
-0.0036054120864719152,
-0.020926237106323242,
-0.015203068032860756,
0.02350175753235817,
-0.01632687635719776,
-0.042753033339977264,
-0.018087975680828094,
-0.031691521406173706,
0.046643372625112534,
-0.005090551450848579,
0.03912581875920296,
-0.0213632695376873,
-0.0339374914765358,
0.027388636022806168,
0.04241481423377991,
0.02285625971853733,
-0.031805068254470825,
-0.06111813336610794,
0.020859267562627792,
0.05012628808617592,
-0.029031509533524513,
-0.023592131212353706,
-0.02904658578336239,
0.040626686066389084,
0.023358939215540886,
-0.0014458434889093041,
-0.00004642623389372602,
0.06509793549776077,
0.02553502470254898,
-0.04112894460558891,
0.02252962812781334,
-0.021397322416305542,
-0.07812030613422394,
0.06491954624652863,
0.0734710544347763,
-0.020281361415982246,
-0.02001160755753517,
-0.007803282700479031,
0.06946379691362381,
-0.002310154028236866,
-0.035137295722961426,
0.026531914249062538,
-0.00636389059945941,
0.10185439884662628,
0.0421205572783947,
0.003397151129320264,
-0.008825445547699928,
-0.07498740404844284,
0.00929742306470871,
0.01804620586335659,
0.04345840960741043,
0.011047611944377422,
-0.012241948395967484,
0.03232758119702339,
0.00401550717651844,
0.057845547795295715,
-0.034836456179618835,
-0.010772604495286942,
0.0000753100830479525,
0.019010843709111214,
-0.03301767259836197,
0.03786628693342209,
-0.028195368126034737,
0.0308625940233469,
0.07308337092399597,
0.033090654760599136,
0.00725491251796484,
-0.02685442939400673,
-0.030005168169736862,
-0.09687977284193039,
0.027165487408638,
0.026110518723726273,
-0.07385823875665665,
0.030911270529031754,
0.01440109871327877,
0.04828867316246033,
0.024921176955103874,
0.04438535496592522,
-0.06754913181066513,
-0.022966304793953896,
-0.04360868036746979,
-0.008858954533934593,
0.012712626717984676,
0.001178352627903223,
-0.0030423044227063656,
-0.057837679982185364,
-0.004222194664180279,
0.058229412883520126,
-0.003760305931791663,
0.048581790179014206,
0.02316521666944027,
0.010875707492232323,
0.0007125426200218499,
0.0026843929663300514,
0.017501262947916985,
-0.04152432456612587,
-0.03769274055957794,
0.07666146010160446,
0.014241510070860386,
-0.05646863579750061,
-0.03837187588214874,
-0.005952795036137104,
0.005292826797813177,
0.04680575802922249,
0.021175308153033257,
-0.010384145192801952,
0.028572620823979378,
0.0036255414597690105,
-0.04973747208714485,
0.015369603410363197,
-0.0012666614493355155,
0.06371796131134033,
0.015190946869552135,
0.03627569600939751,
0.02501046098768711,
-0.001518942997790873,
0.03742823377251625,
-0.009887663647532463,
-0.043292563408613205,
-0.028245456516742706,
-0.0471789725124836,
-0.005364877171814442,
0.05692458525300026,
-0.038276612758636475,
-0.05126218870282173,
0.024894705042243004,
-0.057742536067962646,
-0.028942469507455826,
0.0014505895087495446,
-0.007803658023476601,
0.046487439423799515,
0.00221579079516232,
-0.06279134005308151,
0.007612336426973343,
-0.017584295943379402,
0.02498806081712246,
-0.02682563103735447,
0.015879595652222633,
-0.0006785703590139747,
-0.08165482431650162,
0.009577536024153233,
0.06105266883969307,
-0.017570480704307556,
0.01851467229425907,
0.02352023683488369,
0.06736774742603302,
-0.08616024255752563,
-0.03343532234430313,
-0.0015174148138612509,
-0.04510529711842537,
-0.0837719589471817,
0.0039619929157197475,
-0.06099555641412735,
0.03490741550922394,
0.0033480743877589703,
0.008053782396018505,
-0.05760424956679344,
0.0035608336329460144,
0.04714076966047287,
-0.05447826161980629,
-0.010997136123478413,
0.025015873834490776,
0.06095331534743309,
-0.0208435021340847,
-0.021533573046326637,
0.03156870976090431,
-0.05803124979138374,
0.020889494568109512,
-0.01099630817770958,
-0.009972376748919487,
0.042368270456790924,
-0.04118332266807556,
-0.01401758473366499,
-0.04656946286559105,
-0.013226587325334549,
-0.002009886084124446,
0.09599719196557999,
-0.002590019488707185,
-0.027792589738965034,
-0.02800854481756687,
-0.00515065249055624,
-0.04733830317854881,
-0.04029574990272522,
-0.011549076065421104,
0.07771901041269302,
0.0712442398071289,
-0.031314969062805176,
-0.0891677588224411,
0.021163618192076683,
-0.03504592180252075,
-0.0253352839499712,
0.034088678658008575,
0.0624520517885685,
-0.051025740802288055,
0.002914572600275278,
0.06639805436134338,
0.03853592649102211,
-0.038046348839998245,
-0.04230089113116264,
-0.018242692574858665,
0.022854629904031754,
0.04507950693368912,
0.0238176416605711,
-0.03209265321493149,
0.012446867302060127,
0.05314598232507706,
0.012468424625694752,
-0.021926499903202057,
-0.01531912013888359,
-0.031043339520692825,
0.035043779760599136,
0.018042361363768578,
0.0018020287388935685,
0.019938232377171516,
0.0037333345972001553,
-0.04907849803566933,
0.011501643806695938,
-0.01494980975985527,
0.07089371234178543,
0.022241761907935143,
-0.004510641563683748,
-0.027039043605327606,
-0.027014486491680145,
-0.041649118065834045,
-0.012050769291818142,
0.006756122689694166,
0.0318196676671505,
0.05761256441473961,
-0.027450447902083397,
0.0027876095846295357,
0.0020538282115012407,
0.004860966000705957,
0.057093363255262375,
0.05770320072770119,
0.00006146998930489644,
-0.006200108211487532,
0.004711022134870291,
0.047991346567869186,
-0.059026844799518585,
0.011676130816340446,
0.044423189014196396,
-0.058480314910411835,
0.024001924321055412,
0.07412673532962799,
0.00006755401409463957,
-0.011680732481181622,
-0.01240547001361847,
-0.026763631030917168,
-0.042483940720558167,
-0.02310224063694477,
0.006800925824791193,
-0.04332345351576805,
0.03650389984250069,
0.07735028862953186,
0.01943102478981018,
0.01919212006032467,
-0.00815532822161913,
-0.02583826147019863,
-0.07206788659095764,
0.062517911195755,
0.044054511934518814,
-0.04688176512718201,
0.011126365512609482,
-0.014480198733508587,
-0.02104944922029972,
0.009711180813610554,
-0.025945810601115227,
0.03860190138220787,
-0.006729958578944206,
-0.041523922234773636,
0.014024412259459496,
0.08302029967308044,
0.030294125899672508,
-0.023161308839917183,
-0.013969755731523037,
-0.009809832088649273,
0.04683174937963486,
-0.029208753257989883,
0.007971559651196003,
-0.014311560429632664,
0.05136803537607193,
-0.0007501285872422159,
0.05581466481089592,
-0.03437584638595581,
-0.0316874198615551,
0.023796888068318367,
-0.06186060979962349,
0.09849172085523605,
0.0396745428442955,
0.020670928061008453,
0.006995851173996925,
0.03527482971549034,
-0.011966387741267681,
0.008200769312679768,
-0.0017259669257327914,
-0.01473976206034422,
-0.016942469403147697,
-0.03868769481778145,
-0.04665309190750122,
0.044084638357162476,
-0.01673537865281105,
0.028846418485045433,
0.023878592997789383,
0.014150315895676613,
0.019232796505093575,
-0.04402470961213112,
-0.005474936217069626,
-0.027772819623351097,
0.013024885207414627,
-0.0087582403793931,
-0.004294713027775288,
-0.03424958884716034,
0.02736278809607029,
0.05702126398682594,
-0.006003459915518761,
-0.0776052251458168,
-0.0021136379800736904,
0.04312654212117195,
0.02099643647670746,
-0.10242070257663727,
0.011408811435103416,
0.05579318478703499,
-0.016886461526155472,
-0.008064036257565022,
0.012916107662022114,
0.03996077552437782,
-0.04727509617805481,
-0.012881669215857983,
0.021292535588145256,
-0.028398456051945686,
-0.01901230961084366,
0.00010341235611122102,
-0.030872095376253128,
0.017800740897655487,
0.0325624980032444,
-0.035195570439100266,
0.07460825890302658,
0.02516935206949711,
-0.005436270963400602,
0.0038739682640880346,
-0.028269296512007713,
0.04550928622484207,
-0.026690499857068062,
0.004089278634637594,
0.0010139524238184094,
0.016138140112161636,
0.030116910114884377,
-0.015650121495127678,
0.012193777598440647,
-0.009794787503778934,
-0.026032285764813423,
0.009857204742729664,
0.00812038779258728,
0.05417690426111221,
-0.00001675594648986589,
-0.008036582730710506,
0.019787857308983803,
-0.0588226318359375,
-0.03107600286602974,
-0.01996961422264576,
0.07032172381877899,
-0.012425248511135578,
0.021268602460622787,
0.008804195560514927,
-0.06827037781476974,
-0.024411650374531746,
-0.0342826247215271,
-0.010249893181025982,
-0.009654413908720016,
-0.05717132240533829,
0.03246571496129036,
-0.0038221559952944517,
-0.025182878598570824,
0.05791031941771507,
0.031693439930677414,
-0.023163853213191032,
-0.06826586276292801,
-0.02117292769253254,
-0.07727053016424179,
-0.0001578329101903364,
-0.007865792140364647,
0.04923877492547035,
0.010800551623106003,
0.04528585076332092,
-0.033712297677993774,
0.08232998847961426,
0.021712500602006912,
-0.03553575649857521,
-0.004730085376650095,
0.051368482410907745,
0.004406397230923176,
-0.0026131237391382456,
0.029568107798695564,
0.009017333388328552,
-0.04242900758981705,
0.003345258068293333,
0.0013671490596607327,
-0.06223843991756439,
-0.03622179850935936,
0.04326854646205902,
-0.028118174523115158,
0.008126895874738693,
0.02149278111755848,
-0.00830799899995327,
0.003679438028484583,
-0.025321029126644135,
-0.04205050319433212,
0.01362614892423153,
-0.006554931867867708,
-0.007014380767941475,
0.044065508991479874,
0.0070561752654612064,
-0.05204996466636658,
0.011979242786765099,
-0.04181061312556267,
0.059665825217962265,
0.01534244418144226,
-0.03384203836321831,
-0.008159258402884007,
0.05650825425982475,
0.006736516486853361,
-0.008424029685556889,
0.018995001912117004,
-0.02019129879772663,
-0.0003619213530328125,
0.03283563628792763,
-0.07709498703479767,
0.00734471483156085,
0.015112588182091713,
-0.025677522644400597,
-0.015977902337908745,
0.04626479744911194,
0.033551838248968124,
-0.07199633866548538,
0.03127327933907509,
0.016612466424703598,
-0.04744483530521393,
0.008544087409973145,
0.02079167775809765
] |
<p>I am currently designing a heat sink for OPA 549. Among the many considerations, for example, the choice of material, the geometry of heat sink, the design of fins and all the parameters that come into play during the modelling, I am most curious about the simple choice of material.
Copper has more conductivity than Aluminium while the heat capacity of Aluminium is more than twice of copper. So naturally there has to be a trade off between the two. And I have no constraint on weight. I cannot use the combination of the two as there is bonding problem. My question is simple- Which one to use and why?
Relevant details: Max Power 90W; Forced Convection with 21 cfm; Overall thermal resistance is around 0.5 SI units.
thanks in advance</p> | g7788 | [
0.07125800102949142,
0.0024317491333931684,
0.023178517818450928,
0.013956672511994839,
0.026265300810337067,
0.007275672163814306,
-0.000526092597283423,
0.037897344678640366,
-0.058106664568185806,
-0.009613464586436749,
0.05919533595442772,
0.07050081342458725,
-0.015911022201180458,
-0.02882775105535984,
0.047517381608486176,
0.04047911614179611,
0.01313211303204298,
-0.010649146512150764,
-0.004183619748800993,
0.020942052826285362,
0.01711372472345829,
-0.022855760529637337,
-0.023858610540628433,
0.006883866153657436,
-0.02780643105506897,
-0.04430973529815674,
-0.0731569156050682,
0.02628018707036972,
-0.05900098383426666,
-0.03824362903833389,
0.012172805145382881,
-0.010672347620129585,
0.0001235313102370128,
-0.044476043432950974,
-0.09183134138584137,
0.008053360506892204,
0.03475946933031082,
0.015871938318014145,
-0.034961193799972534,
0.03104032762348652,
-0.04132670909166336,
0.029016487300395966,
0.00944577157497406,
0.008622921071946621,
0.031195057556033134,
-0.062144629657268524,
0.00998480524867773,
-0.07522859424352646,
0.0134350024163723,
0.03453952446579933,
0.0298690814524889,
-0.017072992399334908,
0.006218939088284969,
-0.02626127004623413,
-0.032393403351306915,
-0.03516740724444389,
0.01006203331053257,
0.026126328855752945,
-0.020898543298244476,
0.02142186649143696,
-0.03998847305774689,
0.07703953981399536,
-0.06555963307619095,
-0.058561183512210846,
0.018323885276913643,
0.024339742958545685,
0.05455220490694046,
-0.007100410759449005,
0.016627032309770584,
0.004274002276360989,
-0.00768545176833868,
-0.020655395463109016,
-0.016741981729865074,
-0.1000087633728981,
0.00894747395068407,
-0.012978782877326012,
-0.015705076977610588,
-0.02288724295794964,
0.09580425918102264,
-0.01604597643017769,
-0.004327985458076,
0.0091837327927351,
0.048176079988479614,
0.00024778422084636986,
0.015412593260407448,
0.028818100690841675,
-0.08062499016523361,
0.01647897996008396,
-0.03830347955226898,
-0.024937236681580544,
-0.00624040886759758,
-0.010637100785970688,
0.03337106853723526,
-0.02250734157860279,
0.0257877167314291,
0.055183250457048416,
-0.006661669816821814,
-0.004268759395927191,
0.01622840017080307,
-0.009002228267490864,
-0.03577972576022148,
0.008071794174611568,
-0.01287033874541521,
0.02909681759774685,
-0.0024764486588537693,
-0.03757815435528755,
0.025105277076363564,
0.05641518160700798,
-0.06032655015587807,
0.022697540000081062,
0.009010040201246738,
0.030426856130361557,
-0.028861580416560173,
-0.04179462790489197,
-0.011831723153591156,
0.009292209520936012,
0.01247391663491726,
-0.028780095279216766,
-0.009041416458785534,
-0.03995799273252487,
-0.04291914775967598,
-0.03736455366015434,
0.029346134513616562,
0.01827280968427658,
0.049986567348241806,
0.009352842345833778,
0.042293332517147064,
0.08999677002429962,
0.062094300985336304,
-0.02681208774447441,
0.006218341179192066,
0.003255760297179222,
-0.06416404247283936,
-0.02453332021832466,
-0.000595659192185849,
-0.013207800686359406,
0.018340740352869034,
-0.0399467907845974,
0.01539885438978672,
-0.029020734131336212,
-0.032776448875665665,
-0.042904917150735855,
-0.02337874099612236,
-0.025262707844376564,
-0.010534410364925861,
0.03271746262907982,
-0.044394031167030334,
0.051392558962106705,
-0.02212587371468544,
0.04683374986052513,
0.020074455067515373,
0.0579928494989872,
0.00960584171116352,
0.005374357104301453,
-0.052553389221429825,
-0.008732006885111332,
-0.004467320162802935,
-0.005332723259925842,
-0.00513129448518157,
-0.049223531037569046,
-0.0005358082125894725,
0.04914408549666405,
0.008225692436099052,
-0.011409315280616283,
-0.06031741574406624,
-0.00020054263586644083,
-0.022126169875264168,
-0.01265120878815651,
-0.008660977706313133,
-0.02830384112894535,
0.016057515516877174,
-0.032643724232912064,
-0.03202574700117111,
0.03685547783970833,
0.039246197789907455,
-0.010067461058497429,
0.08065345138311386,
0.01940232329070568,
0.05874205380678177,
-0.04485033079981804,
0.016314247623085976,
0.021249879151582718,
0.027620233595371246,
0.04953177273273468,
0.004108669701963663,
0.04507702961564064,
0.05503313988447189,
0.018827596679329872,
-0.03076077625155449,
0.03542224317789078,
-0.06333915889263153,
-0.00449061905965209,
-0.06746518611907959,
-0.00099085527472198,
-0.012340755201876163,
0.06136126443743706,
0.04664849117398262,
-0.044527627527713776,
-0.06791287660598755,
-0.00487870816141367,
0.037571534514427185,
-0.04704174026846886,
-0.040797967463731766,
0.032764408737421036,
0.0046579246409237385,
0.042435482144355774,
-0.0636344850063324,
0.03870823234319687,
0.09596942365169525,
-0.043227873742580414,
-0.028166012838482857,
0.01992659643292427,
-0.02300478145480156,
-0.005206449888646603,
0.0453893281519413,
-0.017419012263417244,
-0.022832782939076424,
0.02527647279202938,
-0.03331463411450386,
0.008911333046853542,
0.06743673235177994,
-0.0014760030899196863,
0.01475007925182581,
-0.006388773676007986,
-0.02916228398680687,
0.0005886155413463712,
0.025794534012675285,
0.013321254402399063,
0.01758967712521553,
0.04675240069627762,
-0.05358150601387024,
-0.039295047521591187,
0.06541357934474945,
0.00005796761979581788,
-0.003559504635632038,
-0.009917983785271645,
0.002735075308009982,
-0.005618021357804537,
-0.031214512884616852,
0.01227207388728857,
0.02154393121600151,
-0.03224650397896767,
-0.05734047666192055,
-0.07701431214809418,
0.038715410977602005,
-0.001263964339159429,
0.016419539228081703,
0.007116304244846106,
0.05419902503490448,
0.01881515420973301,
0.00028851506067439914,
-0.03317950665950775,
-0.02033950760960579,
-0.04144151508808136,
-0.045362360775470734,
0.0283803753554821,
0.008301605470478535,
0.012615847401320934,
0.0466676764190197,
0.02160656452178955,
0.03083767183125019,
-0.05154817923903465,
0.024477794766426086,
0.01612723618745804,
-0.08633570373058319,
0.04328031837940216,
-0.058897558599710464,
-0.07201367616653442,
0.05629028007388115,
0.0305384062230587,
-0.0005919592222198844,
0.006467756815254688,
0.003504716092720628,
0.014479825273156166,
0.03601404279470444,
-0.017621882259845734,
-0.01995905674993992,
-0.06906569004058838,
0.037387099117040634,
-0.019452868029475212,
0.035271525382995605,
-0.008162676356732845,
-0.0005615613772533834,
0.02707665041089058,
0.027882946655154228,
0.024924222379922867,
-0.030381735414266586,
0.002476935973390937,
0.04568623751401901,
0.0021803868003189564,
-0.0010961765656247735,
0.010594029910862446,
-0.018646972253918648,
-0.016779905185103416,
0.028751209378242493,
-0.02780505269765854,
0.030976319685578346,
-0.01222452986985445,
-0.017886798828840256,
-0.0020465608686208725,
0.014809520915150642,
0.0291123166680336,
-0.05364760011434555,
-0.033642057329416275,
0.06077263504266739,
0.07301205396652222,
-0.03794426843523979,
-0.05551491677761078,
0.029409844428300858,
0.032450977712869644,
0.006425742991268635,
0.006047375500202179,
0.031482018530368805,
-0.009232565760612488,
-0.03886745125055313,
-0.051938746124506,
-0.009823895059525967,
-0.024496493861079216,
-0.017403336241841316,
-0.060931239277124405,
0.03523695096373558,
0.019035452976822853,
0.025262203067541122,
-0.042672816663980484,
-0.03326990827918053,
0.0600619837641716,
0.005126666277647018,
0.004666654858738184,
-0.04565319046378136,
0.05748030170798302,
-0.02609499916434288,
-0.0013625641586259007,
0.0010299425339326262,
0.012896683067083359,
-0.05394240468740463,
-0.00041052376036532223,
-0.0006578665343113244,
0.03440562263131142,
0.011291957460343838,
0.03991517797112465,
-0.010399656370282173,
0.005157732404768467,
0.002328741131350398,
0.0019450627733021975,
-0.003210020251572132,
0.0045607974752783775,
0.008181104436516762,
0.11267313361167908,
-0.054869942367076874,
-0.0027809629682451487,
0.03039044514298439,
-0.03827742114663124,
-0.0014638399006798863,
0.036468952894210815,
-0.024731043726205826,
-0.03487620875239372,
0.022197064012289047,
0.004915522877126932,
-0.012871489860117435,
0.03029298037290573,
0.04067418724298477,
0.0024492479860782623,
-0.0022919722832739353,
-0.08956050872802734,
-0.005828518886119127,
0.047402989119291306,
-0.004134519025683403,
-0.016428744420409203,
-0.030115744099020958,
-0.07381550967693329,
0.025064555928111076,
-0.019881393760442734,
-0.009833072312176228,
-0.02490418218076229,
0.10176557302474976,
0.036244072020053864,
0.042796432971954346,
0.025647373870015144,
-0.023305540904402733,
0.03385928273200989,
-0.0321497842669487,
0.04258399456739426,
0.011532874777913094,
0.04484330862760544,
-0.039709970355033875,
-0.003867420135065913,
0.005823747254908085,
0.003915936220437288,
-0.08268172293901443,
-0.0564822293817997,
-0.05908861756324768,
-0.02548622526228428,
-0.042690861970186234,
0.007561366073787212,
-0.03953244537115097,
-0.00021631801791954786,
0.0017362035578116775,
0.007452060934156179,
-0.038853615522384644,
-0.022453220561146736,
-0.03869936615228653,
0.015353715978562832,
0.011226714588701725,
0.011953421868383884,
0.012070592492818832,
-0.0833529531955719,
-0.025155505165457726,
-0.05190371721982956,
-0.05004539340734482,
-0.03204714506864548,
-0.006106932647526264,
0.032056260854005814,
0.013216882944107056,
0.02654424123466015,
-0.004176939371973276,
-0.05112355947494507,
-0.034220196306705475,
0.02327888458967209,
0.05258098989725113,
-0.004215293098241091,
-0.019395552575588226,
0.004057875368744135,
-0.04359100013971329,
-0.022040950134396553,
0.04197590798139572,
-0.01218116469681263,
-0.007970334030687809,
0.0025015862192958593,
-0.014188452623784542,
0.014733787626028061,
0.012931667268276215,
0.030087780207395554,
-0.009123273193836212,
-0.034063857048749924,
-0.007423488888889551,
0.07111921906471252,
0.041880037635564804,
0.05415784567594528,
-0.043621741235256195,
0.018980303779244423,
-0.03214086964726448,
-0.002512120408937335,
-0.03350256383419037,
-0.019188305363059044,
-0.003359053749591112,
0.02706919237971306,
-0.013225180096924305,
-0.050945233553647995,
-0.05209219083189964,
-0.019027886912226677,
0.05243932828307152,
-0.016237497329711914,
-0.020403975620865822,
0.006259233225136995,
0.00950875598937273,
0.03913750872015953,
-0.010204688645899296,
-0.0036691452842205763,
0.09452059864997864,
0.028765227645635605,
0.003202413208782673,
0.014110429212450981,
0.00911560095846653,
-0.034487903118133545,
0.020878221839666367,
0.006789701525121927,
0.021591423079371452,
-0.026000065729022026,
-0.03891238942742348,
0.004401777405291796,
0.013339141383767128,
-0.0012932125246152282,
0.023051798343658447,
0.06518855690956116,
-0.03032638318836689,
0.046464256942272186,
0.015847377479076385,
-0.03473960608243942,
-0.03138406202197075,
0.03551526740193367,
-0.019795628264546394,
0.02154679223895073,
-0.006496854592114687,
-0.026793723925948143,
0.023108119145035744,
-0.05231932923197746,
0.0025399888399988413,
-0.017980514094233513,
0.07662786543369293,
0.013564429245889187,
0.05706845223903656,
0.01774616912007332,
0.006551824510097504,
0.029865814372897148,
-0.014351108111441135,
0.060936346650123596,
0.03238510340452194,
0.021367663517594337,
0.03924019634723663,
-0.036210790276527405,
0.03322143107652664,
0.015724463388323784,
-0.028446901589632034,
0.035062525421381,
-0.006121648009866476,
0.027375180274248123,
0.09274965524673462,
0.002567008836194873,
0.03660684451460838,
-0.034210454672575,
-0.002004362642765045,
-0.012278785929083824,
-0.015478304587304592,
-0.03563614934682846,
-0.017099348828196526,
-0.06915678083896637,
0.030399896204471588,
-0.001587998354807496,
0.0012663544621318579,
-0.019495798274874687,
0.02242903597652912,
-0.00013481131463777274,
-0.006440240889787674,
0.05145754665136337,
0.010994982905685902,
-0.06164693832397461,
-0.019515419378876686,
0.00013507468975149095,
0.008039905689656734,
-0.06980205327272415,
0.0703858882188797,
0.07412373274564743,
0.03510674461722374,
0.012497496791183949,
-0.0009553795680403709,
-0.0057478295639157295,
-0.02922326885163784,
0.034876227378845215,
0.027847591787576675,
-0.01407369039952755,
-0.016180038452148438,
-0.04723617061972618,
0.023335697129368782,
0.06946731358766556,
0.004163126461207867,
0.041010621935129166,
0.005919620860368013,
0.04413619264960289,
-0.014043450355529785,
0.017665741965174675,
0.026114221662282944,
-0.07512465864419937,
-0.005470653064548969,
-0.011817854829132557,
0.05876952037215233,
0.02857207879424095,
0.08570879697799683,
-0.00802113302052021,
0.032673049718141556,
0.02705003134906292,
0.020313356071710587,
-0.032513346523046494,
0.041467562317848206,
-0.04934689775109291,
0.038659241050481796,
-0.03241448849439621,
-0.0911785438656807,
-0.050285402685403824,
-0.01990477927029133,
0.006875932216644287,
0.007281688041985035,
-0.057111237198114395,
0.012800965458154678,
-0.027200397104024887,
0.020521732047200203,
0.029515448957681656,
-0.07295375317335129,
0.03176625072956085,
0.025814685970544815,
-0.011572948656976223,
0.0073284124955534935,
-0.051740825176239014,
0.006594846956431866,
0.019858835265040398,
0.0017480016686022282,
0.02704712748527527,
-0.008620606735348701,
-0.018649211153388023,
-0.01519838534295559,
-0.019538437947630882,
-0.01635018363595009,
-0.018297294154763222,
0.08278743922710419,
0.07120081037282944,
-0.03959779068827629,
0.025184927508234978,
-0.0013723697047680616,
-0.010989862494170666,
0.03769252076745033,
0.017400112003087997,
0.010224433615803719,
0.02378728985786438,
0.00533277029171586,
0.019723791629076004,
0.04064076393842697,
0.057185981422662735,
0.09347988665103912,
-0.014593712985515594,
0.008059128187596798,
0.012024398893117905,
-0.01969628594815731,
0.027317633852362633,
0.03776108846068382,
0.014247912913560867,
-0.03727497532963753,
0.007008047308772802,
0.010496612638235092,
-0.03702697902917862,
-0.012763305567204952,
0.03951111063361168,
0.06978445500135422,
-0.021660052239894867,
-0.019908282905817032,
-0.05332973226904869,
0.019742600619792938,
0.014336621388792992,
-0.07243242859840393,
0.06237993389368057,
0.006104009225964546,
0.012085571885108948,
0.01683674566447735,
-0.021873487159609795,
-0.01275578886270523,
0.02782735601067543,
-0.051971856504678726,
0.0036323941312730312,
0.0004231906495988369,
0.030509697273373604,
-0.007068022154271603,
0.037519000470638275,
-0.055778734385967255,
0.012757488526403904,
0.005799524486064911,
0.07122176885604858,
-0.004647537134587765,
-0.06142442673444748,
-0.01678628847002983,
-0.014950690791010857,
-0.08986858278512955,
0.010480205528438091,
-0.03478185459971428,
-0.028276430442929268,
-0.056272875517606735,
-0.005229356698691845,
0.02728177420794964,
-0.00586299505084753,
-0.07908862829208374,
0.054765764623880386,
0.03977843374013901,
0.06532420963048935,
0.016938472166657448,
0.024263251572847366,
-0.013451660051941872,
0.04349726438522339,
0.033368755131959915,
-0.007460834924131632,
-0.0029223242308944464,
-0.017918922007083893,
0.051560938358306885,
-0.06392060965299606,
0.028618762269616127,
-0.01090208999812603,
-0.0020766728557646275,
-0.02041538432240486,
-0.01143449917435646,
-0.006603275425732136,
0.007871927693486214,
-0.01419731043279171,
-0.02934334985911846,
-0.0002163953467970714,
0.0004353147523943335,
-0.05269123241305351,
0.012901922687888145,
-0.014360909350216389,
0.0011751402635127306,
-0.052808184176683426,
-0.0154381413012743,
0.0031435545533895493,
0.03875086084008217,
0.04087448492646217,
-0.015606053173542023,
-0.014424593187868595,
-0.014570530503988266,
-0.02535741962492466,
-0.005368645768612623,
0.06885413825511932,
-0.04216402396559715,
0.008271655067801476,
0.0522635355591774,
-0.010029532946646214,
0.006037356797605753,
0.008789983578026295,
0.019075747579336166,
0.02690877392888069,
-0.027747027575969696,
0.01356838271021843,
0.04429863020777702,
0.006394034251570702,
-0.02099461480975151,
-0.011316622607409954,
0.08680234849452972,
0.005457128863781691,
0.012222345918416977,
0.035375624895095825,
-0.06749437749385834,
-0.04564881697297096,
-0.06540465354919434,
-0.04815303534269333,
-0.055288176983594894,
-0.01051343884319067,
0.03504756838083267,
-0.06556958705186844,
0.024125881493091583,
-0.0028563763480633497,
-0.02960227057337761,
-0.001149103743955493,
-0.039277028292417526,
-0.03373858705163002,
-0.0835353210568428,
0.019125791266560555,
-0.004797639790922403,
-0.03376684710383415,
-0.05346272140741348,
-0.06528466194868088,
-0.02182593196630478,
-0.0015116306021809578,
-0.013555985875427723,
0.04478222131729126,
-0.01907283253967762,
0.0048834956251084805,
-0.015563205815851688,
0.012351290322840214,
-0.060980625450611115,
0.0008153792005032301,
0.04243093729019165,
-0.05289420485496521,
-0.06604074686765671,
0.06988655030727386,
0.02177683636546135,
-0.020572490990161896,
-0.056829292327165604,
0.10148534178733826,
-0.07282938063144684,
-0.013646982610225677,
-0.004093221388757229,
0.04141181334853172,
0.006745771039277315,
0.02180352620780468,
-0.03804553300142288,
0.05249728634953499,
0.01592019945383072,
-0.0071329390630126,
-0.06573708355426788,
-0.013817111030220985,
0.02258315309882164,
0.047245483845472336,
-0.011872799135744572,
0.0006937377620488405
] |
<p>I am just reading at the beginnin of <a href="http://backreaction.blogspot.de/2013/06/passing-through-cosmic-walls.html" rel="nofollow">this</a> nice article, that axions could be responsible for spontaneously breaking of a symmetry in the early universe.</p>
<p>Does anybody know which symmetry is alluded to and how the mechanism of spontaneous symmetry breaking exactly works in this particular case?</p>
<p>I'd like to learn in some more detail about this.</p> | g7789 | [
0.01840941049158573,
0.060947924852371216,
-0.002507529454305768,
-0.009576570242643356,
0.03027438186109066,
-0.031434256583452225,
0.05407000333070755,
0.025879008695483208,
-0.02452131360769272,
-0.012778561562299728,
-0.030669094994664192,
0.03305783122777939,
0.010798102244734764,
0.013246225193142891,
0.008906783536076546,
-0.013283883221447468,
0.037517424672842026,
0.014510011300444603,
0.05168396607041359,
0.0006565586663782597,
-0.022330330684781075,
0.028454730287194252,
-0.0282992422580719,
-0.051787182688713074,
0.046437595039606094,
0.0007131471065804362,
-0.010328278876841068,
-0.040928538888692856,
-0.023057756945490837,
-0.029659966006875038,
0.054641369730234146,
0.030516304075717926,
0.008893758989870548,
-0.04210694506764412,
-0.0007711004000157118,
-0.047958776354789734,
0.03373292461037636,
0.014257076196372509,
0.025397222489118576,
-0.0373184010386467,
-0.02794983983039856,
0.016568807885050774,
0.015053000301122665,
-0.01664774678647518,
-0.051225993782281876,
-0.004033578094094992,
0.0003045632329303771,
-0.0670514851808548,
-0.04708811640739441,
-0.07484123110771179,
-0.005828302353620529,
0.046107761561870575,
0.059780824929475784,
0.01699410192668438,
-0.012378149665892124,
-0.0181717686355114,
0.013403743505477905,
0.0036483064759522676,
0.07840988785028458,
0.00037550978595390916,
-0.02785310335457325,
0.04303278774023056,
0.045067764818668365,
0.0299950260668993,
0.060130078345537186,
0.015368400141596794,
0.028509363532066345,
0.0526576042175293,
0.017887141555547714,
0.029922040179371834,
0.03737179562449455,
-0.009201793931424618,
0.00919739343225956,
0.012206324376165867,
-0.024936618283391,
0.0037541643250733614,
0.050466958433389664,
-0.0008990830392576754,
-0.01630968414247036,
0.07492470741271973,
-0.005854947026818991,
0.005781759973615408,
-0.06475143134593964,
0.02193552628159523,
0.03548942878842354,
-0.007844630628824234,
-0.014620679430663586,
-0.0057523176074028015,
-0.04333418235182762,
-0.031039876863360405,
0.01295995619148016,
-0.02315056510269642,
-0.039640530943870544,
-0.04504486173391342,
0.013047028332948685,
-0.0018712393939495087,
-0.028252368792891502,
0.03697087615728378,
-0.06254184991121292,
-0.00902794860303402,
-0.017855724319815636,
-0.005594155285507441,
0.03431754559278488,
-0.02221774123609066,
0.012434817850589752,
0.024426348507404327,
0.07581092417240143,
-0.059603095054626465,
-0.019207898527383804,
0.00926029309630394,
-0.0015486996853724122,
-0.01202310249209404,
-0.017346888780593872,
0.02754952199757099,
0.023850001394748688,
-0.006101032719016075,
0.11432217806577682,
-0.022671973332762718,
0.04928664118051529,
0.028004558756947517,
-0.03757904842495918,
0.016333768144249916,
-0.06659847497940063,
0.005259052850306034,
-0.07494321465492249,
0.010539212264120579,
0.045018281787633896,
-0.07749885320663452,
0.08557658642530441,
-0.006466235965490341,
-0.04308684915304184,
0.014584844931960106,
0.028033388778567314,
0.026284234598279,
-0.008425421081483364,
0.041252367198467255,
0.05089225247502327,
0.00797182135283947,
0.010350952856242657,
-0.029070448130369186,
0.011543583124876022,
0.005774862598627806,
0.028971794992685318,
0.0013160302769392729,
0.04668894782662392,
-0.07358948141336441,
0.0028027875814586878,
-0.00737158115953207,
0.03968753293156624,
-0.008844127878546715,
-0.04094559699296951,
0.01700071059167385,
0.0038780260365456343,
-0.022648783400654793,
-0.03988063335418701,
-0.034573234617710114,
0.04162093251943588,
0.007558060809969902,
-0.05477408692240715,
-0.03847771883010864,
0.08053498715162277,
-0.007021605037152767,
0.014745018444955349,
-0.01546473242342472,
-0.06999725103378296,
0.03515525907278061,
-0.007010618690401316,
-0.053265225142240524,
0.03815397620201111,
-0.016155188903212547,
-0.040464743971824646,
0.033877480775117874,
0.004685092251747847,
0.09689111262559891,
0.008392563089728355,
0.07787740230560303,
0.05476663261651993,
0.019039250910282135,
0.02577422559261322,
0.007640116848051548,
0.01295110210776329,
-0.02276916615664959,
-0.023044876754283905,
0.020246047526597977,
0.02258838713169098,
-0.027960097417235374,
0.0005856721545569599,
-0.02025878243148327,
0.0030675355810672045,
-0.01967453770339489,
0.02417493425309658,
0.023222822695970535,
0.027178265154361725,
0.02574986405670643,
-0.009414699859917164,
-0.012106806971132755,
0.023739054799079895,
0.03560848534107208,
-0.06853985786437988,
0.02540917880833149,
-0.0021399036049842834,
0.01614953950047493,
-0.04849660024046898,
-0.0211289431899786,
0.0030698832124471664,
-0.005849855486303568,
-0.026184529066085815,
0.010611249133944511,
0.0242838803678751,
-0.028656216338276863,
0.05891263857483864,
0.00483119860291481,
-0.03566037863492966,
-0.03478847071528435,
-0.04677283391356468,
0.039969321340322495,
0.02617148868739605,
0.01641007326543331,
-0.0029918355867266655,
0.02085050754249096,
-0.0198996402323246,
-0.010422482155263424,
0.05131327733397484,
0.030932174995541573,
0.018199356272816658,
0.002179363975301385,
0.01218138262629509,
-0.02632978931069374,
0.0049133216962218285,
-0.015834927558898926,
-0.05235772952437401,
0.06316756457090378,
-0.0040524741634726524,
-0.03997486084699631,
0.02314177341759205,
0.0029064370319247246,
-0.0004946407279931009,
-0.015216362662613392,
0.008801735937595367,
-0.005690610967576504,
-0.00814808625727892,
-0.016811387613415718,
-0.03644765913486481,
-0.0010544535471126437,
0.015356323681771755,
-0.014488027431070805,
0.0162179134786129,
-0.10019528865814209,
-0.0072863404639065266,
0.003723770147189498,
0.06052049249410629,
-0.05310988798737526,
-0.07434839010238647,
-0.02139928936958313,
-0.020649932324886322,
0.003016688395291567,
0.060705479234457016,
0.11014274507761002,
-0.031261131167411804,
-0.0683649554848671,
0.0026276668068021536,
0.018522262573242188,
0.03693544864654541,
0.012150396592915058,
-0.018722286447882652,
-0.04485362395644188,
-0.005195299629122019,
0.012004022486507893,
-0.013972419314086437,
0.017485057935118675,
0.00033231329871341586,
0.06917314976453781,
-0.0369759202003479,
0.02384660206735134,
-0.053511034697294235,
-0.03921874612569809,
-0.008170964196324348,
-0.10180724412202835,
0.038177814334630966,
-0.019126012921333313,
-0.0362100824713707,
0.011168748140335083,
0.02075718715786934,
-0.03006475232541561,
0.060377337038517,
-0.026931293308734894,
-0.06166525185108185,
-0.0003212880401406437,
-0.04201100394129753,
0.019680554047226906,
-0.003662016475573182,
0.003202552907168865,
-0.025917459279298782,
-0.019609635695815086,
0.01000302005559206,
0.05007615312933922,
-0.007018187548965216,
0.0014801810029894114,
-0.08976157754659653,
0.0032764715142548084,
0.0029701595194637775,
-0.07132165879011154,
0.0017322854837402701,
0.02034624107182026,
-0.041819214820861816,
0.045426566153764725,
0.005265098065137863,
0.02924586832523346,
0.03971109911799431,
-0.0271515604108572,
-0.01444252859801054,
0.028303131461143494,
-0.008985345251858234,
0.023568332195281982,
0.004993414040654898,
0.02309371903538704,
-0.07125674188137054,
-0.014849508181214333,
0.021844837814569473,
-0.0365179181098938,
-0.07349333167076111,
0.043524786829948425,
0.011925365775823593,
-0.01064083818346262,
0.0019934328738600016,
-0.06044735759496689,
-0.02577781118452549,
0.011463205330073833,
-0.06123676151037216,
-0.013219901360571384,
0.010004610754549503,
-0.07192333787679672,
0.011903408914804459,
-0.053081199526786804,
-0.04225451499223709,
0.012213598005473614,
-0.06739506870508194,
-0.033915650099515915,
-0.03544428572058678,
-0.007645806297659874,
-0.008074721321463585,
-0.022751381620764732,
-0.003388381330296397,
-0.012898496352136135,
0.02293817326426506,
0.0615902878344059,
0.03787211701273918,
-0.006373330485075712,
0.015317671932280064,
0.034236740320920944,
0.02869166061282158,
0.0366099514067173,
-0.0196517501026392,
-0.0015651308931410313,
-0.02470003254711628,
0.02188202179968357,
0.05967490375041962,
0.01684499718248844,
0.018321283161640167,
-0.033212535083293915,
0.04623435437679291,
-0.0712682455778122,
-0.01432761549949646,
0.01903798244893551,
-0.0469561405479908,
0.0468745194375515,
-0.006796000525355339,
-0.00805422943085432,
0.0491979643702507,
0.012797648087143898,
0.04442794248461723,
-0.002220059046521783,
-0.047343552112579346,
-0.014882716350257397,
0.008196881040930748,
0.029623068869113922,
0.056932199746370316,
-0.026205144822597504,
-0.029049020260572433,
-0.0032058656215667725,
0.02633182518184185,
0.0005803104140795767,
0.06904516369104385,
0.026460571214556694,
0.049731090664863586,
0.045600783079862595,
-0.04921192675828934,
-0.014410966075956821,
-0.03905676677823067,
-0.10392144322395325,
0.08441760390996933,
-0.005134388338774443,
0.009592481888830662,
-0.05146346986293793,
-0.007016573566943407,
0.01803184300661087,
-0.026920491829514503,
-0.008744074031710625,
-0.010907084681093693,
0.04406518489122391,
-0.0069246175698935986,
0.027187172323465347,
-0.0030726154800504446,
-0.0017464611446484923,
0.03083581104874611,
0.008871329948306084,
0.0009752259938977659,
-0.005207155365496874,
-0.008212405256927013,
0.0190968569368124,
0.06448297947645187,
0.06528649479150772,
-0.013499442487955093,
-0.0815519317984581,
0.017862999811768532,
0.026586009189486504,
0.005911555141210556,
-0.01909700781106949,
0.04368989169597626,
-0.0193801186978817,
0.0036201365292072296,
-0.020223423838615417,
-0.011993157677352428,
-0.010449615307152271,
-0.00922562088817358,
0.07776062935590744,
0.019510306417942047,
-0.0799948051571846,
0.021553628146648407,
0.00021379934332799166,
-0.006199724040925503,
-0.03429953008890152,
-0.018522432073950768,
-0.00989680178463459,
-0.056544121354818344,
-0.0029564197175204754,
-0.029212407767772675,
0.05694659426808357,
-0.029074199497699738,
0.05313875526189804,
0.10845084488391876,
0.0005732035497203469,
0.013641925528645515,
-0.03607584536075592,
0.0549032986164093,
0.0394878163933754,
-0.092849001288414,
-0.028379932045936584,
0.016959216445684433,
0.009540562517940998,
0.00010126660345122218,
0.022914143279194832,
0.02815699204802513,
-0.0010161035461351275,
-0.0054326727986335754,
-0.03224899619817734,
-0.02854333072900772,
0.07404546439647675,
0.059236813336610794,
0.015213189646601677,
-0.059087205678224564,
-0.065747931599617,
0.043025676161050797,
0.022459998726844788,
0.03303951770067215,
0.05150729790329933,
0.021026378497481346,
-0.024781331419944763,
0.0020058259833604097,
-0.004304133355617523,
0.006923978682607412,
-0.007617576513439417,
-0.05484333634376526,
0.02671259641647339,
0.022407226264476776,
-0.038694631308317184,
0.015237723477184772,
-0.047444071620702744,
0.006683452054858208,
0.0005383515963330865,
0.030982432886958122,
0.019691122695803642,
0.009655592031776905,
-0.05467211455106735,
-0.03555678203701973,
-0.01424665842205286,
-0.019262047484517097,
-0.018133088946342468,
-0.07779551297426224,
-0.016998181119561195,
-0.0017935829237103462,
0.008709915913641453,
0.011785895563662052,
-0.059389740228652954,
0.0037671306636184454,
-0.051016539335250854,
0.023121120408177376,
-0.03468666970729828,
-0.04001927375793457,
0.004991681315004826,
-0.02718341536819935,
0.051361240446567535,
0.007375338114798069,
-0.0032770249526947737,
0.04581759497523308,
-0.01606760174036026,
0.05131063982844353,
-0.004533133469521999,
-0.03074992261826992,
0.01968020386993885,
0.0026084226556122303,
-0.06545551121234894,
-0.010497655719518661,
-0.01763775758445263,
-0.0015030670911073685,
0.01063735131174326,
0.020516211166977882,
-0.010560124181210995,
0.012019800953567028,
-0.056785717606544495,
-0.07244008779525757,
0.03108172118663788,
0.005974151659756899,
-0.016829201951622963,
-0.0066978903487324715,
0.0040361639112234116,
-0.0614318922162056,
0.006206062622368336,
0.01681801676750183,
-0.017799530178308487,
-0.04950065165758133,
-0.00550306448712945,
0.09379181265830994,
-0.007922117598354816,
0.05243026092648506,
-0.051467206329107285,
0.018802260980010033,
-0.005163965746760368,
-0.005681807640939951,
-0.025411337614059448,
-0.008673111908137798,
-0.026900706812739372,
0.021263638511300087,
-0.01525453943759203,
-0.06154350936412811,
-0.03216561675071716,
-0.08878328651189804,
0.05955833941698074,
0.058113232254981995,
-0.0012026994954794645,
-0.010731334798038006,
0.03949449956417084,
0.006270831450819969,
-0.02056160941720009,
-0.07562395930290222,
0.05306117236614227,
0.027012065052986145,
-0.05153200030326843,
-0.04609261825680733,
-0.05532059073448181,
0.03007778339087963,
0.055713798850774765,
0.022993342950940132,
0.023537591099739075,
-0.04996791481971741,
-0.022537410259246826,
-0.018642187118530273,
-0.04206062853336334,
0.09025444090366364,
0.09628031402826309,
0.0430629700422287,
0.07024911791086197,
-0.038260649889707565,
0.030059631913900375,
0.021140001714229584,
0.000439001276390627,
-0.03161002695560455,
-0.010509027168154716,
-0.02283640205860138,
0.023824254050850868,
0.021056637167930603,
-0.05669454485177994,
0.05988190695643425,
-0.035897932946681976,
-0.06342079490423203,
0.017520060762763023,
0.004779900889843702,
0.01647426374256611,
0.06811776012182236,
-0.05301804468035698,
-0.02789064310491085,
-0.03280632570385933,
-0.03672314062714577,
0.018015693873167038,
-0.018859386444091797,
0.03297913819551468,
0.046345051378011703,
-0.011583153158426285,
-0.05647917836904526,
-0.0026924568228423595,
0.005858959164470434,
-0.024502642452716827,
0.025949425995349884,
-0.0006418645498342812,
0.0702427476644516,
0.016064723953604698,
0.020770395174622536,
0.038620252162218094,
0.01918426714837551,
0.01915418915450573,
0.022647293284535408,
0.06888072937726974,
0.01911325380206108,
0.03509027138352394,
-0.021042395383119583,
0.02322840504348278,
-0.04745173826813698,
0.01677047088742256,
-0.02464178204536438,
0.04350315034389496,
0.029883094131946564,
0.00890656840056181,
-0.05812068656086922,
-0.040635447949171066,
0.022258037701249123,
0.055667199194431305,
-0.02546915039420128,
0.03213649243116379,
0.02257630042731762,
0.02114129438996315,
-0.03482430428266525,
-0.01509132795035839,
0.04680377244949341,
-0.02534600906074047,
-0.07475912570953369,
-0.0002976146643050015,
-0.049755509942770004,
0.0053749093785882,
0.053059715777635574,
0.04133271798491478,
0.0017922773258760571,
0.01925126276910305,
0.014691243879497051,
0.0082580940797925,
-0.004771572072058916,
-0.005508434493094683,
-0.04109484329819679,
0.0061659011989831924,
-0.022972052916884422,
-0.054001908749341965,
-0.0010257262038066983,
-0.001542871119454503,
-0.013748890720307827,
0.002835702383890748,
-0.0013538809726014733,
0.011544852517545223,
-0.0037120075430721045,
0.015823591500520706,
-0.003754453733563423,
-0.11466070264577866,
-0.04757383093237877,
0.06501329690217972,
0.009120556525886059,
-0.01951630786061287,
-0.05355384573340416,
-0.015254260040819645,
0.02015148289501667,
-0.0008994428208097816,
-0.001970555866137147,
0.018958592787384987,
-0.0482892245054245,
-0.025944551452994347,
-0.05813128873705864,
0.022338103502988815,
-0.011850391514599323,
-0.002075859112665057,
0.051141634583473206,
-0.007260644342750311,
0.06557851284742355,
-0.03489891439676285,
0.01932191476225853,
0.0353689081966877,
-0.04278494790196419,
-0.01705878973007202,
-0.01835319586098194,
0.06660561263561249,
-0.03286587819457054,
0.06494896113872528,
-0.025644149631261826,
-0.013023272156715393,
-0.022081976756453514,
-0.028473511338233948,
-0.0334116593003273,
-0.03986242040991783,
0.02205783687531948,
0.0043396358378231525,
0.013434933498501778,
0.02603800594806671,
0.010683516971766949,
-0.0005290947156026959,
0.00338488700799644,
0.010671520605683327,
0.001271864166483283,
-0.02095642127096653,
0.008610817603766918,
-0.020529424771666527,
0.0070377313531935215,
0.011638732627034187,
-0.02663494646549225,
0.016370778903365135,
-0.09597840905189514,
0.04056623578071594,
0.07042452692985535,
-0.0167983565479517,
0.03780242055654526,
0.006620506756007671,
-0.024288924410939217,
0.087410107254982,
0.043571412563323975,
0.06753692030906677,
0.0007215550285764039,
-0.004709738306701183,
-0.01214300375431776,
-0.0469815656542778,
-0.022495020180940628,
0.06897122412919998,
0.02121908962726593,
-0.032873332500457764,
-0.014829629100859165,
0.016152935102581978,
0.016975997015833855,
-0.002935761585831642,
0.004365468397736549,
0.032196301966905594,
-0.009706294164061546,
0.03308846428990364,
0.02633899822831154,
-0.04555138200521469,
0.022323153913021088,
-0.009100892581045628,
0.00622513284906745,
0.006669473368674517,
0.0028790710493922234,
-0.03807181119918823,
-0.019281726330518723,
-0.008565792813897133,
-0.022601675242185593,
0.03532987833023071,
-0.014571992680430412,
-0.047769807279109955,
0.04326460883021355,
-0.026652678847312927,
-0.000887055357452482,
-0.023812510073184967,
-0.03196018561720848,
0.003080989932641387,
-0.043754421174526215,
-0.00294890021905303,
-0.019106566905975342,
0.008402341045439243,
0.0417284294962883,
0.009864768013358116,
0.0477282740175724,
0.004588298033922911,
-0.0190399382263422,
-0.016978995874524117,
-0.0020468339789658785,
0.017091179266572
] |
<p>So far I have only actually calculated dimensional regularization and I just know about the idea of cutoff regularization. From what I understand, as the name suggests, you just ignore momentum as from some high value and integrate the virtual momenta until this arbitrary chosen value. Depending on which value you chose, and thereby to what order you consider the Feynman diagrams, you get a (little bit) different result. </p>
<p>Now what I was wondering is, why don't people just cutoff exactly at the value that corresponds to the momentum of the process you want to consider, if there is some specific experiment you want to calculate. E.g. if someone wants to calculate some cross section of an experiment that will be/has been done at CERN, why don't they just consider exactly the momentum that the virtual particle must (maximally) have (due to momentum conservation of the particles that are smashed together)? Intuitively it seems (to me) that this must give the best result. And let us ignore of course, that physicists that calculate cross sections for CERN probably do not use cutoff regularization.</p> | g7790 | [
0.042520105838775635,
-0.010448629967868328,
0.011517309583723545,
0.009684033691883087,
0.03352775424718857,
0.01889740116894245,
0.02702036313712597,
0.06665930896997452,
-0.026995202526450157,
0.0022555412724614143,
0.004322218708693981,
-0.021265268325805664,
-0.013963897712528706,
0.004401062149554491,
0.014311451464891434,
-0.054259032011032104,
0.00767561886459589,
-0.0027018210384994745,
0.00773819861933589,
-0.002665999811142683,
-0.05502576008439064,
-0.010323325172066689,
0.029405107721686363,
-0.008679080754518509,
-0.05788419768214226,
-0.018466414883732796,
-0.05854687839746475,
0.03025161847472191,
-0.06986387819051743,
0.019826257601380348,
0.02910994179546833,
0.015242562629282475,
0.02160261571407318,
-0.02183365635573864,
-0.06739084422588348,
-0.005357092246413231,
-0.0047470820136368275,
0.020030440762639046,
-0.01023906096816063,
-0.028209034353494644,
0.03803210332989693,
-0.061673883348703384,
-0.012709515169262886,
-0.0078733516857028,
-0.04320809245109558,
0.03287798538804054,
-0.063421331346035,
-0.0049490355886518955,
-0.009726590476930141,
-0.02190646156668663,
0.011889535002410412,
0.005734139587730169,
0.021205458790063858,
0.05537538230419159,
0.040407028049230576,
0.04619156941771507,
0.001873170374892652,
0.017209235578775406,
0.02925042435526848,
-0.011147047393023968,
-0.0024309996515512466,
0.0027862866409122944,
-0.015138514339923859,
-0.02433633804321289,
0.030298013240098953,
-0.06458514928817749,
-0.044556960463523865,
-0.020471099764108658,
-0.015733882784843445,
0.05869278684258461,
0.03678251802921295,
-0.022097690030932426,
-0.03224010020494461,
0.01594078354537487,
0.00811381358653307,
0.045288871973752975,
-0.014329434372484684,
0.006391799543052912,
0.024962488561868668,
0.01223804708570242,
-0.07060115039348602,
0.003999946638941765,
0.040982685983181,
-0.01586347445845604,
0.06908705830574036,
0.05091717839241028,
0.0407906100153923,
0.022250212728977203,
-0.002537494758144021,
-0.016437333077192307,
0.008615335449576378,
-0.03696193918585777,
0.03202527388930321,
-0.017556259408593178,
-0.06131560355424881,
-0.02616424858570099,
-0.03106565773487091,
0.053533270955085754,
0.02640630304813385,
0.01439585629850626,
-0.018196003511548042,
0.07225634157657623,
-0.053030312061309814,
-0.013578019104897976,
-0.01888640969991684,
-0.00966483075171709,
0.04676869884133339,
0.032383039593696594,
0.06749340891838074,
-0.04455069452524185,
-0.05050717294216156,
-0.06950850784778595,
-0.02628793939948082,
0.006674544885754585,
-0.004568736534565687,
0.009523654356598854,
0.06785716116428375,
-0.04818331077694893,
-0.0016209795139729977,
0.017841069027781487,
0.07729608565568924,
-0.0060798474587500095,
0.013072744011878967,
0.055469077080488205,
-0.03167545795440674,
-0.008288397453725338,
-0.036781150847673416,
0.05024858936667442,
0.0020387964323163033,
-0.029589612036943436,
-0.036061905324459076,
-0.021236177533864975,
-0.029164277017116547,
0.03197098895907402,
0.0006032609380781651,
-0.030332818627357483,
-0.009623602963984013,
0.0029838047921657562,
0.021939607337117195,
-0.030538076534867287,
-0.024381449446082115,
0.02780977077782154,
-0.03601020202040672,
-0.04997793585062027,
-0.014082693494856358,
-0.044437382370233536,
-0.007096103858202696,
-0.007315298542380333,
-0.004545415751636028,
0.030189383774995804,
0.05364428088068962,
0.08523929864168167,
-0.0048734815791249275,
0.020524173974990845,
0.0292043536901474,
0.01728467270731926,
0.035219982266426086,
-0.035023197531700134,
0.04062797874212265,
0.02791169285774231,
0.01702185720205307,
0.010654513724148273,
-0.048310596495866776,
-0.003594564041122794,
-0.046384721994400024,
0.002245083451271057,
0.02278243750333786,
-0.05765986815094948,
-0.05953349173069,
-0.07716169953346252,
-0.0513678677380085,
0.03830432519316673,
0.04029037430882454,
0.05654474347829819,
0.0011099980911239982,
0.06272528320550919,
0.009084401652216911,
0.07873933017253876,
0.03393039107322693,
0.06654076278209686,
-0.019423076882958412,
0.021985504776239395,
0.03422371670603752,
0.0007309751817956567,
0.04517868161201477,
0.0020953721832484007,
0.006095663644373417,
0.043820708990097046,
-0.019455093890428543,
-0.033706385642290115,
0.05290284380316734,
-0.03011317551136017,
-0.034966543316841125,
0.016851017251610756,
-0.07681218534708023,
-0.009050453081727028,
0.005070003680884838,
-0.010059908963739872,
-0.025141721591353416,
0.06399070471525192,
-0.025138014927506447,
0.04662404954433441,
-0.030850881710648537,
0.05367642268538475,
0.022387422621250153,
-0.010185406543314457,
0.03088117390871048,
-0.011228726245462894,
0.03635918349027634,
-0.036149173974990845,
0.037516940385103226,
0.0003653659950941801,
0.0019154903711751103,
0.023762907832860947,
-0.019102275371551514,
-0.03001728095114231,
0.008985287509858608,
0.014983116649091244,
0.017792558297514915,
0.027881819754838943,
-0.0061944457702338696,
-0.056671131402254105,
0.04565395042300224,
0.009104382246732712,
-0.06930005550384521,
0.01130176242440939,
-0.025426732376217842,
0.015847301110625267,
0.02023356407880783,
0.011431999504566193,
-0.03857117518782616,
-0.024479391053318977,
-0.050592537969350815,
-0.007132941856980324,
0.025734897702932358,
0.02281872369349003,
-0.028347158804535866,
-0.03329680114984512,
0.045999675989151,
0.06272493302822113,
0.03382830694317818,
0.01386896800249815,
-0.014617432840168476,
-0.015580188482999802,
0.035374123603105545,
-0.038717810064554214,
0.04658234119415283,
-0.008521008305251598,
-0.051389794796705246,
-0.02316434122622013,
-0.045756831765174866,
0.03571949526667595,
-0.0025074202567338943,
-0.03880219906568527,
-0.02734997868537903,
-0.02030176855623722,
0.019217556342482567,
0.027662431821227074,
-0.04288383200764656,
0.014475640840828419,
0.03336092829704285,
0.03982382267713547,
-0.00008841324597597122,
0.051761891692876816,
-0.04210131615400314,
0.050382547080516815,
0.025086482986807823,
0.063541479408741,
-0.001195102697238326,
-0.0028007521759718657,
-0.0025492243003100157,
0.05453331768512726,
0.0014384347014129162,
0.043620042502880096,
0.0594807006418705,
-0.02111644856631756,
0.023333672434091568,
-0.03277585282921791,
0.0451352521777153,
-0.02539936453104019,
-0.06060367077589035,
0.03278273716568947,
-0.049964435398578644,
0.0076584843918681145,
0.012778677977621555,
-0.008637087419629097,
0.028879383578896523,
-0.022224901244044304,
-0.020730065181851387,
0.009526106528937817,
-0.016766441985964775,
-0.056646134704351425,
-0.0030932961963117123,
0.014217793010175228,
0.05229200795292854,
0.03868354484438896,
0.07048357278108597,
-0.016725806519389153,
-0.01615378074347973,
-0.025576069951057434,
-0.06939422339200974,
-0.006881318520754576,
-0.009113184176385403,
0.028647208586335182,
0.06801058351993561,
0.043978575617074966,
-0.013022913597524166,
-0.011112893931567669,
-0.0795554369688034,
-0.025211593136191368,
-0.013207203708589077,
0.08419600129127502,
0.01666760817170143,
-0.0029957182705402374,
0.025135699659585953,
-0.019251396879553795,
0.004456543363630772,
-0.006900647189468145,
-0.03704160079360008,
-0.0063079288229346275,
-0.022769300267100334,
-0.008675648830831051,
0.0671956017613411,
0.00008293366408906877,
0.0301007479429245,
0.05263938009738922,
-0.024384906515479088,
0.006835501175373793,
-0.008833548985421658,
-0.023425709456205368,
0.03353019058704376,
0.0758960023522377,
0.01974656619131565,
-0.010769696906208992,
-0.09363258630037308,
-0.16689109802246094,
-0.05501334369182587,
0.017751697450876236,
0.06523807346820831,
-0.014760630205273628,
0.013088473118841648,
-0.005369297228753567,
0.029051270335912704,
0.013229483738541603,
0.05545990169048309,
-0.00464799115434289,
0.0029499006923288107,
0.047069814056158066,
-0.01809096336364746,
-0.06218009814620018,
0.0021224694792181253,
0.05506894364953041,
-0.007089049089699984,
0.01742446981370449,
-0.021475285291671753,
0.06629937887191772,
0.002180760959163308,
0.03846001997590065,
0.040727488696575165,
0.0008685021311976016,
0.01165038999170065,
0.022723739966750145,
-0.03732035309076309,
-0.02602340094745159,
-0.025091158226132393,
-0.023547455668449402,
-0.017532091587781906,
0.059260912239551544,
-0.015829848125576973,
-0.010225208476185799,
0.011448448523879051,
0.04633037745952606,
-0.0016684195725247264,
0.0002585641050245613,
-0.03344140574336052,
-0.004053124692291021,
0.005040026735514402,
0.090518519282341,
-0.0029737786389887333,
0.005198710132390261,
0.004380187019705772,
0.02738594263792038,
0.02638792060315609,
-0.025047708302736282,
-0.02136656455695629,
-0.03693641349673271,
-0.08281540870666504,
0.040816109627485275,
-0.01218455657362938,
-0.017871135845780373,
0.04508531093597412,
-0.08270776271820068,
-0.016416063532233238,
0.01906554028391838,
0.003104888368397951,
-0.018769945949316025,
0.024765290319919586,
-0.04071769863367081,
0.013396590948104858,
0.03084222972393036,
-0.06168487295508385,
-0.0013053520815446973,
0.005783992353826761,
0.0008322689682245255,
0.05648977681994438,
0.00713470671325922,
-0.020678702741861343,
0.013512374833226204,
-0.029039576649665833,
0.015967736020684242,
-0.009261047467589378,
0.002631006995216012,
-0.004396996460855007,
-0.07988997548818588,
0.04928676784038544,
-0.0508308969438076,
-0.020497871562838554,
-0.042732272297143936,
0.005768939852714539,
-0.0034665174316614866,
0.04911036044359207,
-0.03690533712506294,
0.025188976898789406,
0.015186329372227192,
0.03230324387550354,
0.04508110508322716,
0.03136610984802246,
-0.04695264250040054,
0.00624132389202714,
-0.07075778394937515,
0.09866239875555038,
-0.005608700215816498,
-0.04051857441663742,
0.0037464408669620752,
-0.04074573889374733,
0.006489252671599388,
-0.04735081270337105,
0.0494157075881958,
-0.06396596133708954,
0.07181299477815628,
0.05412652716040611,
-0.03416654095053673,
0.017459256574511528,
0.006945948116481304,
-0.04933880642056465,
0.035164445638656616,
-0.03795301169157028,
-0.013104433193802834,
-0.04627801850438118,
0.03513173386454582,
-0.04927974194288254,
0.0010675075463950634,
-0.06113174185156822,
-0.048245593905448914,
0.04021240770816803,
-0.024817941710352898,
-0.014004315249621868,
0.026832174509763718,
0.08184833079576492,
0.02413913980126381,
-0.07877519726753235,
-0.0108850272372365,
-0.0429614782333374,
-0.034560222178697586,
-0.0070861829444766045,
0.02967938967049122,
-0.04032231867313385,
-0.026855487376451492,
-0.03015792928636074,
0.01274485420435667,
0.018781717866659164,
-0.008374192751944065,
0.0009746912401169538,
-0.01688392460346222,
-0.021401556208729744,
0.05509098246693611,
-0.0030439221300184727,
0.024288559332489967,
0.05043796822428703,
-0.027459364384412766,
-0.03208112716674805,
-0.012248220853507519,
0.05248086526989937,
0.007092475891113281,
-0.03368305042386055,
0.040987707674503326,
-0.03323850780725479,
-0.05591382458806038,
-0.010312825441360474,
-0.007426155731081963,
-0.021248240023851395,
0.027148431167006493,
0.04415418207645416,
-0.029430611059069633,
0.0031950725242495537,
-0.044770777225494385,
0.019048012793064117,
-0.02347843535244465,
-0.05473307520151138,
-0.05705529451370239,
0.0008925008005462587,
-0.013436643406748772,
-0.0483645424246788,
-0.0329144261777401,
-0.0552937276661396,
0.03519870713353157,
0.059149060398340225,
-0.035091448575258255,
0.02500741370022297,
-0.0023664410691708326,
0.05416638404130936,
0.02968287095427513,
0.0625637099146843,
0.01721969246864319,
-0.023819468915462494,
0.008060161024332047,
0.01741553470492363,
-0.02228657715022564,
-0.023293089121580124,
-0.054280560463666916,
0.008341781795024872,
-0.007677929475903511,
0.04396110773086548,
-0.01970403641462326,
0.010966324247419834,
-0.042363934218883514,
-0.051600463688373566,
-0.04384267330169678,
0.024266405031085014,
0.03321058303117752,
0.010606327094137669,
-0.04696540907025337,
-0.011226309463381767,
0.0470011867582798,
-0.1066160500049591,
-0.043950822204351425,
0.009096954017877579,
0.0031989114359021187,
0.00847875326871872,
-0.022861823439598083,
-0.05647551268339157,
0.03589324653148651,
-0.016782276332378387,
0.03725098446011543,
0.0010732952505350113,
-0.03766946867108345,
0.02166060358285904,
-0.02368541806936264,
0.012099899351596832,
-0.0731901302933693,
-0.029409348964691162,
-0.0627538412809372,
-0.025118790566921234,
0.004828643519431353,
-0.030447598546743393,
0.014072560705244541,
-0.007976964116096497,
0.00659263227134943,
-0.05625409260392189,
-0.022034255787730217,
-0.017739200964570045,
-0.03605674207210541,
-0.000045580145524581894,
-0.0531567819416523,
0.0020098842214792967,
-0.01766091026365757,
-0.023015055805444717,
-0.029953937977552414,
0.007635786663740873,
0.012889543548226357,
-0.027079487219452858,
0.0021574620623141527,
0.015451405197381973,
0.016926338896155357,
-0.004312113858759403,
0.03910328075289726,
0.021739274263381958,
-0.05840672552585602,
-0.02888815477490425,
-0.023481279611587524,
0.007760787848383188,
0.03674281761050224,
0.0906262993812561,
-0.08076874166727066,
0.03376384451985359,
0.0301161278039217,
-0.0018487905617803335,
-0.036745499819517136,
0.07376904785633087,
0.030533229932188988,
-0.024416200816631317,
0.022016314789652824,
0.01359612587839365,
-0.03351711481809616,
-0.008806126192212105,
-0.029320143163204193,
0.029670605435967445,
-0.055048346519470215,
-0.05065978318452835,
-0.0062682437710464,
0.08317983895540237,
0.022780442610383034,
-0.032699353992938995,
0.026754047721624374,
0.045883599668741226,
0.07963419705629349,
0.0071098413318395615,
0.0036002597771584988,
0.004841359797865152,
-0.010696452111005783,
0.01129150390625,
0.05506701394915581,
-0.045181967318058014,
0.0018590978579595685,
0.023707250133156776,
-0.010049041360616684,
-0.05559944733977318,
0.002755203749984503,
0.010592829436063766,
-0.014582649804651737,
0.010351870208978653,
-0.036306511610746384,
0.05150517076253891,
0.03679275140166283,
0.03959786519408226,
0.06502273678779602,
-0.02826068550348282,
0.0037932954728603363,
0.07703941315412521,
-0.021993327885866165,
-0.06170486658811569,
0.035175468772649765,
0.04151158034801483,
0.05333855748176575,
0.03336355462670326,
0.03975430503487587,
-0.01761360839009285,
0.04458783566951752,
-0.006079079583287239,
0.013186240568757057,
-0.018514441326260567,
0.02444530837237835,
0.04748682305216789,
0.018338292837142944,
0.007859745994210243,
-0.0068439822643995285,
0.02930643782019615,
0.011032132431864738,
-0.05696048587560654,
-0.0036244364455342293,
0.01165302749723196,
-0.02917836792767048,
0.028297994285821915,
-0.033137064427137375,
0.022670796141028404,
0.009966702200472355,
-0.049645181745290756,
0.04647964611649513,
0.0511939562857151,
-0.020888984203338623,
-0.03299029916524887,
-0.009717625565826893,
0.015951940789818764,
-0.018369944766163826,
0.032090529799461365,
-0.03706897050142288,
-0.019678499549627304,
-0.054388660937547684,
0.034764159470796585,
-0.054341819137334824,
-0.006767518352717161,
-0.019995754584670067,
-0.07710107415914536,
-0.0187215693295002,
0.07749556005001068,
-0.03013506904244423,
0.03006526082754135,
0.025593556463718414,
-0.07500811666250229,
0.029023829847574234,
0.016728084534406662,
0.06684455275535583,
-0.027068059891462326,
-0.0577949620783329,
-0.02876812219619751,
0.04361071437597275,
-0.055376797914505005,
0.059110116213560104,
-0.01903715915977955,
0.02220132388174534,
-0.01811027340590954,
-0.021715564653277397,
0.04034329950809479,
-0.030711468309164047,
0.023573635146021843,
0.02562752738595009,
0.044815633445978165,
-0.027006756514310837,
0.029405741021037102,
0.00931581761687994,
0.0693337544798851,
-0.05195597931742668,
0.015993887558579445,
0.019563745707273483,
0.03182373568415642,
0.009408707730472088,
0.02082541584968567,
-0.04315739497542381,
-0.056227196007966995,
0.0024898541159927845,
-0.0021743238903582096,
-0.007486787624657154,
0.012851093895733356,
-0.019428960978984833,
-0.03296881541609764,
-0.00420761201530695,
-0.05481616035103798,
0.004769151099026203,
0.07642918825149536,
-0.009811731986701488,
0.015265002846717834,
0.001033230684697628,
0.025524547323584557,
0.002248660661280155,
0.06269127875566483,
-0.0038759259041398764,
-0.030276862904429436,
0.0015934969997033477,
-0.017031555995345116,
0.07039918005466461,
0.03711787983775139,
-0.026992401108145714,
0.023056427016854286,
0.06281767040491104,
-0.006332986522465944,
-0.003340978641062975,
-0.017751961946487427,
-0.022197222337126732,
-0.029168499633669853,
-0.011481254361569881,
-0.006722902413457632,
-0.0320325642824173,
-0.004015432205051184,
-0.018615804612636566,
-0.028254752978682518,
-0.02230558730661869,
-0.037149474024772644,
0.017280010506510735,
0.0010665958980098367,
0.021038562059402466,
0.017944127321243286,
0.010331603698432446,
0.0037111197598278522,
0.024134710431098938,
-0.009629253298044205,
-0.03536044806241989,
-0.03677275776863098,
-0.0006165525410324335,
-0.03023109957575798,
0.021756311878561974,
-0.01604500599205494,
0.018239298835396767,
0.023851854726672173,
0.05059099942445755,
0.0014814581954851747,
-0.015953633934259415,
-0.030104296281933784,
0.027028290554881096
] |
<p>I was attending my philosophy class and in the middle of student presentations, I found myself mentally wondering off and thinking about light. After a few minutes of trying to piece together how the sun works I came to ask a question I could not answer myself. Why does each individual photon have such a low amount of energy? I am hit by photons all day and I find it amazing that I am not vaporized. Am I simply too physically big for the photons to harm me much, or perhaps the Earth's magnetic field filters out enough harmful causes such as gammy rays?</p> | g7791 | [
0.0017165748868137598,
0.05597830191254616,
-0.004544917494058609,
0.019632961601018906,
0.006796632893383503,
0.05982723832130432,
0.045301008969545364,
0.04591166228055954,
-0.01070073340088129,
-0.051949191838502884,
0.07081159949302673,
0.018824908882379532,
-0.0012201201170682907,
0.003453706158325076,
-0.018040917813777924,
0.004714377224445343,
0.08072147518396378,
-0.00278146518394351,
0.07068577408790588,
0.017918389290571213,
-0.033700741827487946,
-0.01914440467953682,
0.01845618151128292,
-0.06879885494709015,
-0.024359680712223053,
0.032018519937992096,
0.02348235994577408,
-0.0059721814468503,
-0.016664307564496994,
-0.046996429562568665,
0.02300911955535412,
-0.04296761751174927,
0.024202140048146248,
-0.03890971094369888,
-0.016039585694670677,
-0.04991229623556137,
0.014493752270936966,
0.03947680816054344,
-0.009363573044538498,
0.02148284949362278,
0.03547265753149986,
-0.007423481438308954,
0.06581135839223862,
-0.03711148723959923,
0.01546263974159956,
0.0262907687574625,
0.03952851891517639,
0.0006453864043578506,
0.020018182694911957,
-0.04378289356827736,
-0.0013461236376315355,
-0.07118066400289536,
0.026896264404058456,
0.04706965759396553,
0.06323906034231186,
-0.03470616787672043,
0.007919419556856155,
-0.007243306841701269,
0.05357673019170761,
0.05976743623614311,
0.030547432601451874,
0.007618137635290623,
0.009401097893714905,
0.010358179919421673,
-0.01871900074183941,
-0.04308682307600975,
-0.031144294887781143,
-0.08016844838857651,
0.011190002784132957,
0.027321573346853256,
0.007599199656397104,
-0.025121212005615234,
-0.05526292696595192,
-0.04354872554540634,
0.060333047062158585,
-0.021949000656604767,
0.02708100527524948,
0.055273450911045074,
0.01889456808567047,
0.035218801349401474,
-0.010253114625811577,
-0.032259970903396606,
-0.0025725695304572582,
-0.055977147072553635,
0.07009820640087128,
-0.03237077593803406,
-0.0389723964035511,
-0.025467095896601677,
-0.010594585910439491,
0.00961903017014265,
0.05170637369155884,
-0.024059966206550598,
0.11779414117336273,
0.014500695280730724,
-0.020342888310551643,
0.024110672995448112,
0.03694085404276848,
0.047359343618154526,
-0.03430510684847832,
0.006569538731127977,
-0.03782515972852707,
-0.005994869861751795,
-0.028064893558621407,
0.04214586690068245,
0.04880547523498535,
-0.0027691004797816277,
-0.03563697636127472,
-0.02334284596145153,
0.024160664528608322,
0.03962448984384537,
-0.02657042071223259,
-0.0032286308705806732,
-0.08231878280639648,
-0.0717611014842987,
-0.03796127438545227,
0.018721969798207283,
0.08748603612184525,
-0.05912851542234421,
0.03300125151872635,
0.03519370034337044,
0.04921881854534149,
0.036828961223363876,
-0.012844396755099297,
0.03512024134397507,
-0.013647571206092834,
-0.010351334698498249,
0.027619216591119766,
0.003351351246237755,
0.011101540178060532,
-0.021380916237831116,
-0.029909376055002213,
-0.04144789278507233,
-0.05588220804929733,
-0.013464760035276413,
0.041573796421289444,
0.03144215792417526,
0.011194897815585136,
0.029317691922187805,
0.019024036824703217,
-0.012267198413610458,
0.06410379707813263,
0.005450760945677757,
0.011276697739958763,
-0.02317124791443348,
-0.03760206326842308,
0.028766684234142303,
-0.020277617499232292,
-0.03122873418033123,
0.012235456146299839,
0.025611262768507004,
0.06357162445783615,
0.02301172912120819,
-0.003739069914445281,
-0.06933297216892242,
0.05913529172539711,
-0.033135004341602325,
0.033962130546569824,
-0.016325760632753372,
-0.07690360397100449,
0.0038669882342219353,
0.02694394625723362,
0.037681944668293,
0.010565540753304958,
-0.022598747164011,
-0.03833288326859474,
0.012918383814394474,
0.010320371948182583,
-0.04485587775707245,
-0.04014727100729942,
0.014283052645623684,
-0.05046004056930542,
-0.012929392978549004,
0.017602529376745224,
0.004390175919979811,
-0.04810911789536476,
0.026291489601135254,
0.08149208873510361,
-0.05863848701119423,
0.005078071262687445,
0.005839846562594175,
-0.004289388656616211,
-0.02413228154182434,
0.010073777288198471,
-0.08486573398113251,
0.02076045610010624,
-0.013420937582850456,
-0.053726352751255035,
0.007415017578750849,
-0.024741437286138535,
-0.02530086599290371,
-0.01756495051085949,
0.00197610049508512,
0.01385978702455759,
-0.08345073461532593,
-0.011290043592453003,
-0.034833990037441254,
0.015550509095191956,
0.01450181845575571,
-0.05519430711865425,
0.02379870042204857,
-0.0782918855547905,
0.04113595187664032,
-0.014174608513712883,
0.009625573642551899,
0.04735790565609932,
0.02913827635347843,
-0.019757993519306183,
-0.00961146131157875,
0.03813561424612999,
-0.06014956906437874,
0.07037290930747986,
-0.03481147810816765,
0.017610929906368256,
0.044243358075618744,
-0.0338289812207222,
-0.03819798305630684,
-0.01937742345035076,
-0.008603162132203579,
0.0011267211521044374,
0.032980095595121384,
0.0009589549736119807,
0.014055496081709862,
0.0465262308716774,
-0.005937718786299229,
0.02077082172036171,
0.0564773865044117,
-0.06138048321008682,
-0.06462536007165909,
-0.006301734130829573,
-0.004041701089590788,
-0.04377538710832596,
0.044730294495821,
0.04352699965238571,
0.006644421257078648,
-0.000209533391171135,
0.04089853912591934,
-0.05306575447320938,
-0.03657400608062744,
-0.015182588249444962,
-0.03329872339963913,
-0.0030078731942921877,
-0.014391286298632622,
0.019960835576057434,
-0.007935456931591034,
0.007286191917955875,
-0.0951305404305458,
0.0023053449112921953,
-0.002183373784646392,
-0.07103165984153748,
0.007651741150766611,
0.046139150857925415,
-0.02113940753042698,
-0.010462689213454723,
0.01989057846367359,
-0.010976136662065983,
-0.0020768947433680296,
-0.0008304381626658142,
0.07876044511795044,
0.0037248129956424236,
-0.03852223977446556,
-0.02751740999519825,
-0.088711217045784,
-0.012950805947184563,
-0.0007314804242923856,
-0.017294565215706825,
0.019492272287607193,
-0.02709687128663063,
-0.0032374488655477762,
0.06581123173236847,
-0.000847741262987256,
0.03407413512468338,
0.05290716513991356,
0.016646357253193855,
0.01246151514351368,
0.059473831206560135,
-0.01123047899454832,
-0.029540181159973145,
0.03510689735412598,
0.023539206013083458,
-0.03494831174612045,
-0.003191707655787468,
0.04543806239962578,
-0.06980093568563461,
-0.027987146750092506,
0.09030929207801819,
-0.09304645657539368,
-0.028423897922039032,
0.01622016914188862,
-0.0031770924106240273,
-0.05164628475904465,
-0.029453033581376076,
0.003379397327080369,
0.03638235852122307,
0.0070721725933253765,
-0.02973116561770439,
0.012158150784671307,
0.02842319756746292,
-0.020931394770741463,
-0.10568816214799881,
0.01855744980275631,
0.025850804522633553,
0.02968623675405979,
-0.005677337292581797,
0.0036714118905365467,
-0.07622366398572922,
0.002385389758273959,
-0.05025799199938774,
-0.05345238000154495,
-0.03607897832989693,
0.004165889695286751,
-0.039118442684412,
0.045266278088092804,
0.022492438554763794,
0.06481598317623138,
-0.05242688208818436,
-0.007059301715344191,
-0.035562220960855484,
0.0024690567515790462,
0.014944317750632763,
0.029606875032186508,
-0.02231510356068611,
0.03591081500053406,
-0.0199296735227108,
-0.011735610663890839,
0.034306224435567856,
0.023433666676282883,
-0.01475970447063446,
-0.05153772607445717,
0.019549313932657242,
-0.003700411645695567,
-0.022792290896177292,
-0.07063198834657669,
-0.06114771589636803,
0.011220593005418777,
-0.02060501091182232,
0.011778772808611393,
-0.045282576233148575,
-0.01734798215329647,
0.07471884787082672,
-0.020660394802689552,
-0.06982012838125229,
0.011750507168471813,
-0.059987008571624756,
-0.04771608114242554,
0.029666384682059288,
0.0424947664141655,
-0.019601892679929733,
-0.036306656897068024,
0.029015274718403816,
-0.011058238334953785,
0.027897706255316734,
0.018566222861409187,
-0.03114105947315693,
-0.010067833587527275,
-0.0504404753446579,
-0.004893108271062374,
-0.00007883107173256576,
0.0240092184394598,
0.004315127152949572,
-0.008930744603276253,
0.009270493872463703,
0.023114847019314766,
0.02379104122519493,
-0.02023502252995968,
-0.008289680816233158,
0.044739704579114914,
-0.047569390386343,
0.004347560461610556,
0.018712664023041725,
0.02732767164707184,
0.00846054870635271,
-0.00029801620985381305,
-0.03756377100944519,
0.04511177912354469,
-0.019568270072340965,
-0.050992999225854874,
0.05441509932279587,
-0.01564973033964634,
-0.049739986658096313,
-0.017868470400571823,
0.029454907402396202,
-0.008161420002579689,
0.05572236329317093,
0.021040260791778564,
0.038340456783771515,
0.028862273320555687,
-0.012239668518304825,
-0.006211092695593834,
-0.0243009515106678,
0.012992944568395615,
-0.001067113596946001,
-0.07641085982322693,
-0.04692956432700157,
0.008539393544197083,
0.013839980587363243,
-0.0037913909181952477,
0.029318001121282578,
-0.03839578106999397,
0.026527833193540573,
0.0057403529062867165,
0.0227854922413826,
0.03987957909703255,
0.04793591797351837,
-0.013263218104839325,
0.019925139844417572,
0.044633954763412476,
0.026018407195806503,
-0.022545482963323593,
-0.007137383799999952,
-0.008658289909362793,
0.037557054311037064,
0.028021039441227913,
-0.026957593858242035,
-0.07289257645606995,
0.013856800273060799,
0.03210785984992981,
0.028318481519818306,
-0.007134263403713703,
0.027104295790195465,
-0.02541213296353817,
-0.003860397497192025,
0.04836514592170715,
0.0053693680092692375,
-0.017805464565753937,
-0.012087599374353886,
0.07896057516336441,
0.05952376499772072,
0.007368453778326511,
0.015072157606482506,
0.02212969772517681,
0.039553675800561905,
0.02474679797887802,
-0.04216322675347328,
0.03272268548607826,
0.045063164085149765,
0.022076167166233063,
-0.041483666747808456,
-0.003260666271671653,
0.040044303983449936,
0.08891833573579788,
0.1017463281750679,
-0.019386611878871918,
0.03837092965841293,
-0.004697440657764673,
0.04692887142300606,
0.00842961948364973,
-0.011243374086916447,
-0.001898448565043509,
-0.07317022979259491,
-0.014885171316564083,
0.015052062459290028,
-0.040393438190221786,
-0.017967799678444862,
-0.056500982493162155,
0.012029777280986309,
0.004616353660821915,
-0.03303172066807747,
-0.0019164037657901645,
0.028440402820706367,
0.08449497073888779,
-0.09246096760034561,
0.03132837265729904,
0.011612157337367535,
0.023810407146811485,
0.025872746482491493,
-0.02325013093650341,
-0.04607682675123215,
0.025804491713643074,
-0.06832258403301239,
-0.033993180841207504,
-0.012223286554217339,
0.020648948848247528,
-0.016897227615118027,
-0.02471216581761837,
-0.0061056953854858875,
-0.03266052529215813,
-0.04781568422913551,
-0.03774230182170868,
-0.041536830365657806,
0.0003178628103341907,
0.03316348418593407,
0.03208097442984581,
-0.02176150679588318,
0.019358163699507713,
-0.005080251023173332,
0.05754823237657547,
-0.046963684260845184,
0.0686720758676529,
-0.028495153412222862,
-0.028074972331523895,
-0.028144637122750282,
-0.036942288279533386,
-0.017688484862446785,
-0.018223395571112633,
-0.005975685548037291,
0.0020847145933657885,
0.0376872681081295,
-0.0007508019334636629,
0.00859009101986885,
-0.0504390224814415,
-0.018999401479959488,
0.0010301376460120082,
-0.04912596940994263,
-0.03989510238170624,
0.04725513607263565,
-0.02871733345091343,
0.01266813836991787,
-0.03987699747085571,
0.040260858833789825,
0.0306193046271801,
-0.018271900713443756,
-0.017054682597517967,
0.03387119621038437,
0.03583679348230362,
0.04894256964325905,
-0.0348547101020813,
-0.02445261739194393,
0.028357362374663353,
0.06452475488185883,
0.00805624295026064,
-0.017650997266173363,
0.04863784834742546,
0.008664509281516075,
0.03111819177865982,
0.07720932364463806,
-0.02572023496031761,
-0.06567148864269257,
-0.035292867571115494,
0.013853265903890133,
-0.006994599476456642,
0.02256317436695099,
0.030446326360106468,
0.035433974117040634,
-0.02606355771422386,
-0.033971820026636124,
-0.028808148577809334,
0.0190094243735075,
-0.02271835319697857,
0.03659134730696678,
0.025897111743688583,
-0.024789508432149887,
-0.04486854746937752,
0.026885202154517174,
0.056152790784835815,
0.01585620827972889,
0.032581448554992676,
-0.004243672825396061,
-0.0013536671176552773,
0.03460276871919632,
0.019399702548980713,
-0.007491554599255323,
0.018182173371315002,
0.04921448603272438,
-0.03193126991391182,
-0.020782368257641792,
0.01900690235197544,
-0.03006603568792343,
0.005779898725450039,
0.026468714699149132,
-0.014016861096024513,
0.03545102849602699,
0.030534513294696808,
-0.011252151802182198,
-0.010319025255739689,
0.01716790162026882,
-0.04237182065844536,
0.02075185999274254,
-0.07738186419010162,
0.0004201059928163886,
0.04757823050022125,
0.024088000878691673,
0.053710464388132095,
0.027780774980783463,
0.0008903598063625395,
-0.0064481934532523155,
-0.02311711758375168,
0.023008573800325394,
0.00809295941144228,
-0.08732550591230392,
-0.04329511150717735,
0.027493305504322052,
-0.001367824268527329,
0.03703351318836212,
-0.09900867938995361,
0.04388890787959099,
-0.0019675279036164284,
-0.0146620012819767,
-0.00046387684415094554,
0.042961485683918,
-0.031631916761398315,
-0.012193023227155209,
0.01618485152721405,
0.005210391245782375,
0.03543759137392044,
-0.03510314226150513,
-0.04617050662636757,
0.07081502676010132,
-0.04923110082745552,
-0.03813157230615616,
-0.02571163885295391,
0.03377433493733406,
0.001296068076044321,
0.014425245113670826,
-0.02998124621808529,
0.037009626626968384,
0.050366587936878204,
-0.05046181008219719,
0.0323759987950325,
-0.04677126929163933,
0.04801568016409874,
-0.027282966300845146,
0.02682492509484291,
-0.03938473388552666,
-0.0014285390498116612,
-0.037792883813381195,
-0.05080922693014145,
-0.021469485014677048,
0.008606063202023506,
0.01404478307813406,
-0.033556628972291946,
-0.03219879791140556,
-0.033970266580581665,
0.03182435408234596,
-0.02267371118068695,
0.053401317447423935,
0.07428383082151413,
-0.002567383460700512,
0.038130488246679306,
0.03598647937178612,
0.021938038989901543,
-0.02620789222419262,
-0.011010567657649517,
0.00041544940904714167,
0.11501096934080124,
0.006124904844909906,
0.0442134253680706,
-0.03882557526230812,
-0.026286546140909195,
0.009839054197072983,
-0.02382666990160942,
0.013042614795267582,
-0.032821591943502426,
0.007549408823251724,
0.01980438642203808,
-0.027393251657485962,
0.030914057046175003,
-0.01433460135012865,
-0.03917347267270088,
0.04030240327119827,
-0.0012703564716503024,
-0.005337085109204054,
0.009704386815428734,
0.0535382479429245,
-0.02093341015279293,
0.03146863728761673,
0.03811495378613472,
-0.06873509287834167,
-0.008837922476232052,
-0.014522640034556389,
-0.11429324001073837,
-0.013530497439205647,
0.03142910823225975,
-0.005256786942481995,
-0.003552759997546673,
0.0052249073050916195,
0.05639400705695152,
0.012384123168885708,
-0.043458301573991776,
0.02008502185344696,
-0.02992888353765011,
-0.03096039965748787,
-0.01328402291983366,
-0.08852118998765945,
-0.017043963074684143,
-0.022484462708234787,
0.006779526360332966,
-0.03232619911432266,
0.037095699459314346,
0.03493082523345947,
-0.033225756138563156,
0.02024085447192192,
0.038231898099184036,
0.020169515162706375,
0.007912421599030495,
-0.004325649701058865,
0.01950845494866371,
-0.016999486833810806,
0.007185188587754965,
0.012926995754241943,
-0.004701079800724983,
-0.000979674281552434,
-0.04963989928364754,
0.018778931349515915,
-0.019723251461982727,
-0.018363744020462036,
-0.03483904153108597,
0.054289404302835464,
0.007135485764592886,
0.026911184191703796,
-0.027164392173290253,
-0.004317483399063349,
-0.005229868460446596,
-0.023496439680457115,
-0.014566950500011444,
0.036847759038209915,
0.06477833539247513,
0.009319563396275043,
0.00898091122508049,
0.0024426188319921494,
-0.010011794045567513,
0.03618231043219566,
-0.0015701522352173924,
-0.011923377402126789,
0.0331948958337307,
0.04715384542942047,
0.0040042647160589695,
-0.014063149690628052,
0.01745622418820858,
-0.01134045235812664,
-0.00969032384455204,
-0.021719854325056076,
0.007987934164702892,
-0.010077742859721184,
0.001330871251411736,
0.014260351657867432,
-0.04988681152462959,
0.07173661887645721,
-0.05264255777001381,
0.03206059709191322,
0.011718451976776123,
-0.011538264341652393,
-0.01177232712507248,
-0.028975673019886017,
-0.06637966632843018,
-0.006633552722632885,
0.015009255148470402,
0.020776528865098953,
-0.032267432659864426,
0.03575404733419418,
-0.013866317458450794,
0.012827939353883266,
-0.0012190173147246242,
-0.04094316437840462,
0.038880448788404465,
0.0006799258990213275,
0.0009667735430411994,
-0.07698164135217667,
0.006877236533910036,
0.03583911061286926,
-0.010614154860377312,
-0.034552544355392456,
0.04972219094634056,
-0.006727446801960468,
0.026912203058600426,
0.05021842196583748,
-0.06821594387292862,
0.05255512893199921,
0.0023334401194006205,
-0.015630820766091347,
-0.022489214316010475,
-0.010282667353749275,
-0.05071689188480377,
-0.014197267591953278,
0.02265262044966221,
0.025971442461013794,
-0.03946182504296303,
0.026904843747615814,
-0.042410001158714294
] |
<p>I would like some <strong>super simple computational code for solving magnetohydrodynamics problems</strong>. High accuracy nor performance is not my concern. I wan't it just to visually explore qualitative behavior of plasma. Important for me is:</p>
<ul>
<li><strong>Generality</strong> - it should not be specialised on any particular subproblem
of MHD </li>
<li><strong>Easy to get it work</strong> - does not require any libraries difficult to instal. Input is strightforward and well documented by some examples</li>
<li><strong>Easy to read and modify</strong> - you can read the code and learn about MHD solution from it. You can use this code as starting point for your own MHD code development </li>
</ul>
<p>Something as simple as this <a href="http://www.openprocessing.org/sketch/10419" rel="nofollow">Navier stokes solver</a> would be best</p>
<p>best would be something in python-numpy or java, but C++ or Fortran is not a big problem for me.</p>
<p><strong>Up to now I found:</strong></p>
<p>some libraries ( <a href="http://certik.github.io/mhd-hermes/index.html" rel="nofollow">MHD-Hermes</a> and <a href="https://code.google.com/p/python-mhd/" rel="nofollow">python-mhd</a> ) which are in python, but doesn't seem to have any documantation or examples how to use it.</p>
<p>and this
<a href="http://www.cita.utoronto.ca/~pen/MHD/" rel="nofollow"><em>A Free, Fast, Simple and Efficient TVD MHD Code</em></a> which is in frotran but has just 400 lines</p>
<p>I was thinking about writing something by myself but I wan't to be sure there is nothing similar already avaible. </p> | g7792 | [
0.07197591662406921,
-0.007302140351384878,
0.006507935933768749,
-0.05953764170408249,
-0.0030911832582205534,
-0.04443731904029846,
-0.055742956697940826,
0.043113309890031815,
-0.03752848133444786,
-0.01686667464673519,
0.050559189170598984,
0.003412653459236026,
0.028609415516257286,
0.039355866611003876,
-0.023871315643191338,
0.010186770930886269,
-0.00020711336401291192,
0.017832258716225624,
-0.007267100736498833,
0.05667935311794281,
-0.003080883529037237,
0.06031413748860359,
0.02634832076728344,
-0.03974440321326256,
-0.03019302524626255,
0.004421595484018326,
-0.014633775688707829,
-0.013788962736725807,
-0.023825006559491158,
-0.009497035294771194,
-0.04621567204594612,
-0.02772710658609867,
-0.01093667559325695,
-0.05439968407154083,
-0.024041274562478065,
0.04058624804019928,
-0.01771528832614422,
-0.0029070160817354918,
0.039404552429914474,
0.000934446114115417,
0.00006365154695231467,
-0.023057032376527786,
0.055532414466142654,
0.0019501333590596914,
0.03475681319832802,
-0.04603291675448418,
0.016268884763121605,
-0.02292346954345703,
-0.10100168734788895,
-0.0002583939640317112,
0.028421733528375626,
-0.03351404517889023,
0.0639350414276123,
-0.020500198006629944,
-0.029712598770856857,
0.008838945999741554,
-0.03450514003634453,
-0.04794906824827194,
-0.000025831806851783767,
-0.004275045823305845,
0.02707066386938095,
0.013370612636208534,
0.02936313860118389,
-0.04991110414266586,
-0.008137628436088562,
0.01338741835206747,
-0.026402894407510757,
-0.0737452581524849,
0.02832571603357792,
0.06341733038425446,
0.014447787776589394,
-0.0020928680896759033,
-0.01662420853972435,
-0.050840750336647034,
0.01861598528921604,
0.011048848740756512,
0.004370750393718481,
-0.016374872997403145,
0.08145537972450256,
-0.020288201048970222,
-0.07186976820230484,
-0.0005090057966299355,
-0.0404486246407032,
0.0022596782073378563,
0.03445393964648247,
0.0053083328530192375,
-0.026008103042840958,
0.049646176397800446,
0.044049885123968124,
-0.09379992634057999,
-0.04242746904492378,
0.012081368826329708,
0.025066019967198372,
-0.049754347652196884,
0.034327682107686996,
-0.005567442625761032,
0.010192547924816608,
0.04087891802191734,
0.013812528923153877,
-0.04429921507835388,
-0.023378638550639153,
-0.05311698839068413,
-0.0121962521225214,
-0.005078619346022606,
-0.02311314269900322,
-0.0003127755771856755,
0.025536799803376198,
0.03681444749236107,
-0.015172697603702545,
-0.02180747129023075,
0.008138355799019337,
-0.04375322535634041,
-0.03744228929281235,
0.008369183167815208,
-0.0023163349833339453,
-0.02236032672226429,
0.021142102777957916,
-0.04083880037069321,
-0.01231339480727911,
0.01985487900674343,
-0.02984488382935524,
-0.005589259788393974,
0.06071760877966881,
0.03499797731637955,
0.04051852226257324,
-0.02769458293914795,
0.006145841907709837,
0.048947326838970184,
0.010927288793027401,
-0.050014957785606384,
0.06709413230419159,
-0.04167763516306877,
-0.04267169535160065,
0.020542500540614128,
-0.03584569692611694,
0.02430901676416397,
0.021571682766079903,
0.039130356162786484,
0.002903544344007969,
-0.025736737996339798,
0.04385324567556381,
-0.03584744408726692,
0.007524625398218632,
-0.003615292254835367,
0.039752792567014694,
-0.012363525107502937,
-0.019828759133815765,
0.01525878719985485,
0.06675492972135544,
0.0021671843715012074,
0.011684841476380825,
0.0031347814947366714,
0.015210357494652271,
-0.02040504477918148,
0.01273413933813572,
-0.01138256024569273,
0.0075551713816821575,
0.0050913128070533276,
-0.011668551713228226,
-0.0055722808465361595,
-0.002010679105296731,
-0.004749909043312073,
0.0011159890564158559,
-0.020836733281612396,
-0.01005870383232832,
0.022715453058481216,
0.0422186478972435,
0.00111285038292408,
-0.027323659509420395,
0.004079718142747879,
-0.06076360121369362,
-0.03168787434697151,
0.03912263736128807,
0.04247434437274933,
-0.024472717195749283,
0.012157895602285862,
0.02671111933887005,
-0.031652625650167465,
0.02326289564371109,
-0.00004708269261755049,
-0.007637654896825552,
-0.019733697175979614,
0.04061419144272804,
0.014670266769826412,
-0.029435034841299057,
0.04642248526215553,
-0.04915362596511841,
0.013782578520476818,
-0.09557408094406128,
-0.006328714080154896,
0.0020415352191776037,
0.06557539850473404,
0.02597435750067234,
0.04692794755101204,
-0.060359887778759,
-0.0026899001095443964,
-0.027711477130651474,
-0.01728190667927265,
-0.030041592195630074,
-0.00001717610939522274,
0.0058457753621041775,
0.036674175411462784,
0.04959673434495926,
0.06922823190689087,
-0.02698885090649128,
0.024243216961622238,
0.0563303679227829,
-0.01663917861878872,
0.041780341416597366,
-0.004985055420547724,
0.004617368336766958,
0.07512792199850082,
-0.06665132194757462,
0.02939850464463234,
0.030332956463098526,
-0.06764832884073257,
-0.046147480607032776,
-0.029250502586364746,
-0.1069551557302475,
-0.025378907099366188,
0.056522175669670105,
-0.03539722412824631,
-0.03216157108545303,
0.030781036242842674,
-0.006810513325035572,
-0.025217488408088684,
0.0285914596170187,
0.040401387959718704,
0.04438922181725502,
-0.06433117389678955,
-0.035083428025245667,
0.031126225367188454,
0.014680782333016396,
-0.033841315656900406,
0.06603778153657913,
0.05768975615501404,
-0.049456849694252014,
-0.016432272270321846,
0.0009100690949708223,
0.06437806040048599,
-0.01782277785241604,
0.010180060751736164,
0.061003781855106354,
-0.04057195037603378,
0.01674644462764263,
-0.05787389725446701,
0.06679631769657135,
-0.005546271800994873,
0.02872764691710472,
0.019878944382071495,
0.021686945110559464,
-0.06289022415876389,
0.009445364587008953,
0.004629338160157204,
-0.029233889654278755,
0.039534009993076324,
0.0009016179828904569,
-0.0252541471272707,
0.01893615908920765,
0.006500364281237125,
0.02176755666732788,
0.05721844732761383,
-0.00021996239956934005,
0.0046910811215639114,
-0.054153185337781906,
0.0299695897847414,
-0.04409406706690788,
-0.03271360695362091,
0.013736892491579056,
-0.07134319841861725,
-0.018029168248176575,
0.04416472837328911,
0.03938787057995796,
-0.014352912083268166,
-0.018145140260457993,
0.05395819991827011,
0.08172381669282913,
0.008485591039061546,
0.039676062762737274,
0.02349911443889141,
-0.019535424187779427,
-0.09283146262168884,
0.03050932288169861,
0.016518158838152885,
0.005966161843389273,
-0.01514430996030569,
-0.039651043713092804,
0.018958888947963715,
-0.02440515346825123,
0.01390538364648819,
-0.018733380362391472,
-0.03264386206865311,
-0.029150035232305527,
-0.06438815593719482,
-0.045169852674007416,
0.03163277730345726,
-0.012441053986549377,
0.003913010470569134,
0.007823175750672817,
-0.0046704839915037155,
0.019881056621670723,
0.03966424614191055,
0.035343799740076065,
0.06386075168848038,
-0.030644718557596207,
-0.023508621379733086,
-0.020450802519917488,
-0.05202282592654228,
0.0011068008607253432,
-0.0021976237185299397,
0.09074269235134125,
-0.03120466321706772,
-0.012623506598174572,
0.05085630342364311,
0.007349021267145872,
0.019400998950004578,
-0.028236037120223045,
-0.030948296189308167,
0.024229316040873528,
0.0329502634704113,
-0.015417355112731457,
-0.06458887457847595,
0.00871232058852911,
-0.09342668950557709,
0.023013023659586906,
0.040245428681373596,
-0.018684953451156616,
-0.04671357199549675,
-0.013860045932233334,
0.02243058569729328,
-0.012738346122205257,
0.058032359927892685,
0.05695898085832596,
0.04533972218632698,
-0.04365624114871025,
-0.04179680347442627,
-0.04859514161944389,
0.01639588177204132,
0.002508812816813588,
-0.05649571865797043,
-0.0022531815338879824,
-0.10469359904527664,
-0.03642239049077034,
-0.037753935903310776,
-0.004294510930776596,
0.008763774298131466,
0.05802527442574501,
-0.017393657937645912,
0.01123582199215889,
-0.021829433739185333,
0.08115891367197037,
0.030995739623904228,
0.057080939412117004,
-0.03554939478635788,
-0.002842486370354891,
-0.034385062754154205,
0.023251904174685478,
-0.032521214336156845,
0.05275648459792137,
0.026608996093273163,
-0.06507425010204315,
0.03025980293750763,
-0.07078786194324493,
0.016912709921598434,
-0.03740387037396431,
0.06987331062555313,
0.03293539583683014,
0.0258327703922987,
-0.0024663410149514675,
-0.08555550128221512,
0.038152940571308136,
0.0387355238199234,
0.04454512521624565,
-0.020997488871216774,
-0.020650405436754227,
-0.024253996089100838,
-0.06120847538113594,
-0.004263422451913357,
0.022299733012914658,
0.0742599293589592,
0.025563424453139305,
-0.013135370798408985,
0.006713873241096735,
0.04524979367852211,
-0.015982715412974358,
-0.04013362526893616,
0.024099625647068024,
0.0651630312204361,
-0.0004268971970304847,
-0.04676150158047676,
0.019091803580522537,
-0.02785620652139187,
0.000782866554800421,
-0.009255779907107353,
0.02225903794169426,
-0.03918468579649925,
0.029316198080778122,
0.004572619684040546,
-0.01424552034586668,
-0.004460163414478302,
-0.00428761774674058,
-0.04518540948629379,
0.02139299549162388,
0.06380420923233032,
-0.030324121937155724,
-0.07333838194608688,
-0.03036503866314888,
-0.05185108631849289,
0.0010193753987550735,
-0.03364608809351921,
-0.0031916676089167595,
-0.0695425271987915,
0.044267620891332626,
-0.02429240755736828,
0.04085851460695267,
0.010682923719286919,
0.01593237929046154,
-0.002509043086320162,
0.0051146503537893295,
-0.02567657269537449,
-0.0042825196869671345,
0.05569373816251755,
-0.012103235349059105,
-0.013113435357809067,
0.0035389848053455353,
-0.005596712231636047,
0.050185322761535645,
-0.004346491768956184,
0.06869305670261383,
0.00006698586366837844,
0.006775733549147844,
-0.027817467227578163,
0.0082687484100461,
0.01355527713894844,
0.005989055149257183,
0.010772100649774075,
-0.028617631644010544,
-0.020647486671805382,
-0.05598310008645058,
0.013651146553456783,
-0.0004167832084931433,
0.023416804149746895,
0.0531536228954792,
-0.021821238100528717,
-0.035127196460962296,
0.04370613768696785,
-0.01782570779323578,
-0.002312521915882826,
-0.06448002904653549,
-0.02093808725476265,
-0.058651965111494064,
-0.010304921306669712,
-0.038158804178237915,
0.04067712277173996,
-0.03368071839213371,
0.013581712730228901,
-0.017276888713240623,
0.0034195363987237215,
0.044780801981687546,
0.04615670442581177,
-0.05110691860318184,
0.015249417163431644,
-0.009104060009121895,
-0.0009922554017975926,
-0.0034593769814819098,
0.012105227448046207,
0.0001174386779894121,
-0.028950948268175125,
-0.025257058441638947,
-0.029786186292767525,
0.02862892672419548,
0.06651709228754044,
0.05481642112135887,
-0.09148143976926804,
0.029325438663363457,
0.02151310443878174,
0.0321146696805954,
-0.019788919016718864,
0.005357516463845968,
0.0066373771987855434,
-0.009363575838506222,
0.07727894186973572,
0.03538420796394348,
0.05983349308371544,
0.0481623038649559,
0.016515741124749184,
-0.009635010734200478,
0.01836128532886505,
-0.03677201643586159,
-0.05407516285777092,
-0.023928599432110786,
0.010568254627287388,
0.005030416417866945,
0.01439356803894043,
-0.03039301559329033,
-0.025954507291316986,
0.020595733076334,
0.012224795296788216,
-0.029817337170243263,
-0.009605785831809044,
-0.050518836826086044,
0.002265837974846363,
-0.048246778547763824,
-0.01678765006363392,
0.016401052474975586,
0.018587816506624222,
0.010329720564186573,
0.016192937269806862,
-0.006201969459652901,
0.05165253207087517,
-0.014027496799826622,
-0.02086298167705536,
0.03188461437821388,
0.022947587072849274,
-0.018876349553465843,
0.021559877321124077,
-0.013183653354644775,
0.02395220845937729,
-0.015862181782722473,
-0.0371335968375206,
0.06610425561666489,
-0.0017259630840271711,
0.06391386687755585,
0.04708120599389076,
-0.010295307263731956,
0.013519623316824436,
-0.041732367128133774,
-0.0009582629427313805,
0.010114233009517193,
0.04590390995144844,
0.019504066556692123,
0.01290750503540039,
-0.017926855012774467,
0.006478677038103342,
-0.04028410464525223,
-0.024557076394557953,
-0.013630096800625324,
-0.012115776538848877,
-0.029050717130303383,
0.01982078142464161,
0.06615839898586273,
0.07318779826164246,
0.051775332540273666,
0.020467912778258324,
-0.04202989861369133,
-0.05348100885748863,
0.016252020373940468,
-0.00154177809599787,
0.04106318578124046,
-0.07916116714477539,
-0.03207596763968468,
-0.01658402383327484,
0.036597393453121185,
-0.024283839389681816,
-0.02297862060368061,
0.034705668687820435,
0.017810702323913574,
-0.0666179358959198,
0.0032815365120768547,
-0.008003320544958115,
-0.010487455874681473,
-0.03163871541619301,
-0.02368711680173874,
0.04500645026564598,
-0.006012899335473776,
0.018846621736884117,
-0.04530640318989754,
-0.04538096860051155,
0.04461120441555977,
0.05429350584745407,
-0.05177067965269089,
-0.04844023659825325,
-0.015358625911176205,
-0.06356092542409897,
0.07637940347194672,
-0.008262026123702526,
0.024850521236658096,
0.04932289198040962,
-0.010174626484513283,
-0.012970689684152603,
0.009684804826974869,
0.04158468171954155,
0.04199089854955673,
0.00042798073263838887,
0.00974897388368845,
0.01108136959373951,
-0.008072149008512497,
0.040679145604372025,
0.01194099709391594,
-0.02906319499015808,
-0.016438396647572517,
-0.016792969778180122,
-0.010177616961300373,
-0.03872736543416977,
0.0225148256868124,
0.016255801543593407,
-0.0036728759296238422,
-0.037270188331604004,
-0.035059332847595215,
0.024094916880130768,
-0.04327324777841568,
0.0018753305776044726,
-0.06616493314504623,
0.00487255584448576,
-0.0056057400070130825,
-0.008151286281645298,
-0.00899889413267374,
0.044001828879117966,
-0.0476745180785656,
-0.04501449689269066,
0.04808414727449417,
0.02905552089214325,
-0.06639087945222855,
-0.04201791435480118,
-0.029916200786828995,
-0.06490028649568558,
0.029607439413666725,
-0.002795768901705742,
0.05723489448428154,
0.02494344860315323,
-0.027652300894260406,
-0.052872803062200546,
0.021278833970427513,
-0.001166552072390914,
-0.039784085005521774,
0.030074050650000572,
-0.04495878890156746,
-0.0176017377525568,
0.045625586062669754,
-0.024052608758211136,
0.08140876889228821,
-0.015163568779826164,
0.009871303103864193,
0.08349521458148956,
0.006846299394965172,
-0.023372909054160118,
-0.03989933431148529,
0.020306706428527832,
0.07200269401073456,
0.07662966847419739,
-0.027207644656300545,
0.005990725941956043,
0.07041038572788239,
-0.04393140599131584,
0.002513877348974347,
-0.06535501033067703,
0.003362523391842842,
0.03465024009346962,
-0.06052769720554352,
0.0042102523148059845,
0.05816562846302986,
0.00971593614667654,
0.03024427592754364,
0.03600860759615898,
0.01050037331879139,
0.05062315985560417,
-0.036717429757118225,
-0.012196782045066357,
-0.013615988194942474,
0.02615123987197876,
0.01839417591691017,
0.056389179080724716,
-0.00416456488892436,
0.007004966028034687,
0.07840574532747269,
0.04526287317276001,
-0.059197839349508286,
-0.01907534711062908,
0.047652002424001694,
0.005953953135758638,
0.02510030008852482,
0.018126893788576126,
-0.03914245218038559,
0.043064918369054794,
-0.004855628125369549,
-0.004963996820151806,
-0.0019154718611389399,
-0.012866036035120487,
-0.01978273317217827,
-0.05039434880018234,
-0.04433500021696091,
0.017651136964559555,
-0.004131924360990524,
-0.028769144788384438,
0.04098983481526375,
-0.04687304422259331,
-0.0547027513384819,
0.013344181701540947,
0.03817104548215866,
-0.003950939979404211,
0.01966540701687336,
0.02222200483083725,
0.0329061783850193,
-0.013297348283231258,
-0.029572293162345886,
0.014632142148911953,
0.008338116109371185,
-0.05182597041130066,
0.11840420216321945,
0.022213149815797806,
0.02593100257217884,
0.006093234289437532,
0.006198953837156296,
0.032314375042915344,
-0.03299226984381676,
0.028706258162856102,
0.017443254590034485,
-0.020480476319789886,
-0.030811572447419167,
-0.024851910769939423,
-0.034913141280412674,
0.06474138051271439,
-0.014927458018064499,
-0.00699655944481492,
0.023055270314216614,
0.010150153189897537,
-0.012162855826318264,
0.006168603431433439,
-0.0005724194925278425,
0.05326427146792412,
-0.018809620290994644,
-0.01778089441359043,
0.04377712309360504,
-0.002218319335952401,
0.02027856558561325,
-0.006298440042883158,
-0.030399741604924202,
0.02645186521112919,
-0.030799780040979385,
-0.007934192195534706,
0.024492019787430763,
-0.0819343775510788,
0.013070832006633282,
0.017563432455062866,
-0.024883165955543518,
-0.026744022965431213,
-0.04704835265874863,
-0.04606696590781212,
0.004413917660713196,
0.039140406996011734,
0.040652692317962646,
-0.042064376175403595,
-0.058333270251750946,
-0.014173065312206745,
0.035107992589473724,
-0.0035396397579461336,
-0.03483859449625015,
0.05611148849129677,
0.019257500767707825,
-0.028563255444169044,
0.042934782803058624,
0.010207590647041798,
0.01126189436763525,
-0.0753214955329895,
-0.03493252396583557,
-0.03318842500448227,
0.037181828171014786,
-0.01021213736385107,
0.020673168823122978,
0.018725251778960228,
-0.00878249853849411,
-0.03643675893545151,
0.006453900597989559,
-0.008479362353682518,
0.05207635834813118,
0.028539836406707764,
-0.03295430168509483,
-0.026714816689491272
] |
<p>I know that we can make water solid with high pressure, so I think water will be solid in the deep ocean?</p>
<p>If that is true, the depth of the ocean would be limited because water will become ice? Anyone know that maximum depth? </p> | g7793 | [
0.03207672759890556,
0.03774034231901169,
0.007733203936368227,
0.01187102124094963,
0.021695952862501144,
0.07573341578245163,
0.001050765858963132,
-0.0016032642452046275,
-0.026224346831440926,
-0.053232163190841675,
-0.044435054063797,
0.01086508296430111,
0.020010633394122124,
-0.05752823129296303,
-0.02082270011305809,
-0.0024136491119861603,
-0.03686649724841118,
-0.05101027339696884,
-0.028649942949414253,
-0.007449011784046888,
-0.0006002616719342768,
-0.05264132842421532,
0.052527617663145065,
0.0032374784350395203,
-0.07736280560493469,
0.06947042793035507,
-0.013034733012318611,
-0.03167625889182091,
0.026161061599850655,
0.05107540264725685,
0.06933527439832687,
0.011746774427592754,
-0.0026906298007816076,
0.0016571355517953634,
0.013873065821826458,
-0.03468700870871544,
-0.03365170210599899,
0.0013589448062703013,
0.07698426395654678,
-0.038016997277736664,
-0.005336476489901543,
0.012517271563410759,
-0.0427626371383667,
-0.00963188149034977,
-0.04815354943275452,
-0.019431142136454582,
-0.0488230362534523,
-0.0020692027173936367,
-0.041198138147592545,
-0.017782432958483696,
0.05292405188083649,
0.021094197407364845,
-0.01601378619670868,
-0.004363561514765024,
-0.026221849024295807,
0.03378235176205635,
0.011973211541771889,
0.014148501679301262,
0.00848163291811943,
-0.04616441950201988,
0.014928111806511879,
0.010444317944347858,
0.020557688549160957,
0.033464301377534866,
0.04328684136271477,
0.038615450263023376,
-0.01129731722176075,
0.02562553808093071,
0.005756442900747061,
-0.011655952781438828,
0.039811767637729645,
-0.027024533599615097,
-0.022336293011903763,
0.016534164547920227,
0.005276079755276442,
0.025006156414747238,
0.029589632526040077,
0.05411112308502197,
0.020290344953536987,
-0.022153247147798538,
0.01787089928984642,
0.002975569572299719,
-0.017080241814255714,
0.00380966835655272,
0.008837773464620113,
0.031901951879262924,
-0.00264920387417078,
0.007378600537776947,
0.015436815097928047,
0.0013319310965016484,
-0.07046831399202347,
-0.013302238658070564,
0.0015697685303166509,
-0.0429852157831192,
0.08041536808013916,
-0.01135313231498003,
0.036599013954401016,
-0.0043933638371527195,
-0.007937139831483364,
-0.002558373147621751,
-0.013143463060259819,
-0.02098187804222107,
0.06497800350189209,
-0.016656503081321716,
0.027712594717741013,
-0.014612960629165173,
0.05438311770558357,
-0.051243606954813004,
0.04370782896876335,
-0.03214861452579498,
0.04591917246580124,
-0.041365355253219604,
0.0021726081613451242,
0.02844512090086937,
-0.05053273215889931,
0.02931746281683445,
-0.027594903483986855,
-0.006601789500564337,
0.0066467891447246075,
0.03986312448978424,
0.030682705342769623,
0.03278264403343201,
0.015196632593870163,
0.06137266382575035,
-0.03264162689447403,
0.05577247217297554,
0.01736004836857319,
0.010824884288012981,
0.007440702058374882,
-0.0424637533724308,
-0.015542849898338318,
0.05158979073166847,
-0.033447857946157455,
-0.04473445937037468,
0.010274132713675499,
0.0011333378497511148,
-0.06888291239738464,
-0.010453260503709316,
0.025159651413559914,
0.03522665798664093,
0.01111211534589529,
0.06475922465324402,
0.034953512251377106,
0.04804893210530281,
0.00038728213985450566,
-0.05309624969959259,
-0.030969960615038872,
0.06816338747739792,
-0.006522990297526121,
0.05051587522029877,
0.0034777410328388214,
-0.00045140209840610623,
0.06123150512576103,
0.00914806965738535,
0.021512307226657867,
0.027273323386907578,
-0.022300541400909424,
0.03461484611034393,
0.024271870031952858,
-0.01759694516658783,
-0.0047407615929841995,
0.005084341857582331,
-0.023417888209223747,
-0.004035032354295254,
-0.02524530701339245,
0.006019532680511475,
-0.0344189815223217,
0.06486771255731583,
-0.02380107343196869,
0.07308697700500488,
-0.004597220104187727,
0.049111876636743546,
-0.033329591155052185,
0.041479986160993576,
0.04508884996175766,
-0.014735388569533825,
0.05657883733510971,
0.016558721661567688,
0.015947453677654266,
-0.04008150100708008,
0.011025122366845608,
0.030612975358963013,
-0.030608326196670532,
-0.07287801802158356,
-0.027835333719849586,
0.021194694563746452,
-0.0256404560059309,
-0.015782760456204414,
-0.010121752507984638,
0.02389572560787201,
-0.012546722777187824,
0.006376214325428009,
0.01896519772708416,
0.03793342784047127,
0.06847652047872543,
-0.027561364695429802,
0.04181550070643425,
-0.01770007237792015,
-0.02793317288160324,
0.05303586274385452,
-0.010815983638167381,
0.017543761059641838,
0.04708503186702728,
0.01882774382829666,
-0.006142454221844673,
0.0646108016371727,
0.01586845889687538,
0.006959913298487663,
0.011633320711553097,
0.019741985946893692,
0.012353822588920593,
-0.012848923914134502,
-0.03481502830982208,
0.006651571951806545,
0.03590765222907066,
0.07706495374441147,
-0.04971562325954437,
0.02054988406598568,
0.010850472375750542,
-0.0192751232534647,
-0.02333296276628971,
-0.016316363587975502,
-0.010608836077153683,
0.04452468827366829,
-0.03927569091320038,
-0.041331853717565536,
0.012712338007986546,
-0.0020632892847061157,
0.0324862040579319,
0.01510381605476141,
0.023880543187260628,
0.010986819863319397,
0.015421796590089798,
-0.01560383103787899,
0.013186605647206306,
0.032694149762392044,
-0.05168687924742699,
-0.025905515998601913,
-0.005836188327521086,
-0.019107168540358543,
-0.04771018400788307,
-0.015423312783241272,
-0.030076541006565094,
-0.01830984465777874,
0.003342007752507925,
-0.04442335665225983,
-0.01445590890944004,
0.0254465751349926,
0.10761922597885132,
0.060543425381183624,
0.021324846893548965,
-0.04725370183587074,
-0.06463263183832169,
0.028584839776158333,
0.009549245238304138,
-0.009302850812673569,
0.007111836690455675,
0.09969808161258698,
-0.03281126916408539,
-0.053222306072711945,
0.03137625753879547,
0.021702155470848083,
-0.01409237738698721,
0.027752166613936424,
-0.044190093874931335,
0.03361944109201431,
-0.03896402567625046,
0.015583067201077938,
0.024888519197702408,
0.011531663127243519,
-0.0027134129777550697,
0.07583291083574295,
-0.06450676172971725,
0.03621850535273552,
-0.028716882690787315,
-0.02540591172873974,
-0.02307472564280033,
-0.013220265507698059,
0.019402585923671722,
-0.039785344153642654,
0.0486140176653862,
0.02006601169705391,
0.0017193785170093179,
0.037613630294799805,
-0.010639309883117676,
-0.012450367212295532,
-0.0767727717757225,
-0.024138949811458588,
0.01476568728685379,
0.016945788636803627,
0.03713611513376236,
-0.014599508605897427,
0.021579941734671593,
-0.005249903071671724,
0.023538313806056976,
0.047186315059661865,
0.03506706655025482,
0.024373412132263184,
-0.004102816805243492,
0.022320181131362915,
-0.005780232138931751,
-0.01310819573700428,
-0.013486039824783802,
0.06767190247774124,
-0.06777282059192657,
0.011721254326403141,
-0.021773643791675568,
-0.02865617163479328,
-0.06065768748521805,
-0.0066351075656712055,
-0.022228365764021873,
0.04116049408912659,
-0.06906656920909882,
0.035201482474803925,
-0.03851356357336044,
-0.0036520890425890684,
0.01200968399643898,
0.031194953247904778,
0.02075594663619995,
-0.10812930017709732,
-0.035044487565755844,
-0.02118086628615856,
0.022258169949054718,
0.012754884548485279,
0.003659709356725216,
0.09142781794071198,
-0.01644500344991684,
-0.013557957485318184,
-0.09598638862371445,
-0.00548074534162879,
0.0556890070438385,
0.006024556700140238,
-0.044140495359897614,
0.0732833743095398,
-0.04513167589902878,
0.0022693639621138573,
0.060638926923274994,
-0.009036879986524582,
0.033754944801330566,
0.05378304421901703,
0.044663187116384506,
0.008553476072847843,
0.000806111260317266,
-0.01770893484354019,
-0.016408875584602356,
0.006997869350016117,
-0.05867750942707062,
-0.02988491952419281,
-0.04937697947025299,
0.027659496292471886,
0.03725823760032654,
-0.006391817703843117,
-0.035786982625722885,
-0.010502916760742664,
0.02742939628660679,
0.04299946129322052,
-0.0010907093528658152,
0.07631932944059372,
0.003298275638371706,
-0.031933389604091644,
0.0233236625790596,
-0.03299611434340477,
0.11589833348989487,
-0.01951627992093563,
-0.04903781786561012,
-0.0065562529489398,
-0.03994261100888252,
-0.04285125434398651,
-0.05689450353384018,
0.0069785634987056255,
-0.03327994793653488,
-0.07727965712547302,
0.025536105036735535,
0.0358477346599102,
0.05290568619966507,
-0.036181747913360596,
0.0029875459149479866,
0.026812009513378143,
-0.006663910113275051,
-0.010400990024209023,
0.0969211533665657,
0.028366809710860252,
0.03590868413448334,
-0.020599858835339546,
-0.028412405401468277,
0.011162525974214077,
-0.023653939366340637,
-0.019376903772354126,
0.002271759556606412,
-0.014635270461440086,
-0.0011913516791537404,
-0.020617399364709854,
-0.008302119560539722,
-0.001630955608561635,
0.02609400451183319,
-0.06534748524427414,
-0.02650672383606434,
0.023363258689641953,
-0.056131646037101746,
-0.014891387894749641,
-0.01570490002632141,
0.00923969317227602,
-0.005230598151683807,
-0.01648315228521824,
0.0584859624505043,
-0.035419486463069916,
0.04052043333649635,
-0.004768770188093185,
-0.04970255866646767,
-0.024555770680308342,
0.07798880338668823,
-0.027492865920066833,
-0.02084301970899105,
0.016969306394457817,
-0.00339734205044806,
-0.0306561216711998,
-0.0479012131690979,
-0.02069409005343914,
-0.02362341433763504,
0.02625754475593567,
-0.005653033498674631,
0.040619466453790665,
-0.05242240056395531,
-0.002663835184648633,
-0.038415953516960144,
0.035385072231292725,
-0.001738718361593783,
-0.04469132050871849,
-0.03606696426868439,
-0.012947604060173035,
-0.01897008717060089,
-0.04392330348491669,
-0.0010110015282407403,
-0.01919625513255596,
0.053485576063394547,
0.042121242731809616,
-0.00361991161480546,
-0.05244700238108635,
0.0022257433738559484,
0.026545150205492973,
-0.05410223454236984,
0.015812383964657784,
0.0563664585351944,
0.04068974405527115,
0.02753722108900547,
0.06142023578286171,
-0.026751363649964333,
0.00688612274825573,
-0.013146631419658661,
-0.0068467529490590096,
-0.01658746413886547,
-0.011353052221238613,
-0.009682320058345795,
-0.0053264060989022255,
0.01388782262802124,
0.006880573462694883,
-0.02474568970501423,
0.004520705435425043,
-0.03287738561630249,
0.04996846988797188,
-0.07085543870925903,
0.00042720805504359305,
-0.0344984196126461,
0.08266548812389374,
0.004682756029069424,
-0.06943640857934952,
-0.009440531954169273,
-0.02791047841310501,
-0.02780650183558464,
0.06222290173172951,
0.001856932183727622,
0.0670786201953888,
0.039403703063726425,
0.11611537635326385,
-0.010483844205737114,
-0.01423521526157856,
-0.012193145230412483,
0.0030787144787609577,
0.009412958286702633,
-0.042357489466667175,
0.0015019840793684125,
0.030057230964303017,
-0.025886086747050285,
-0.022697938606142998,
0.0411301851272583,
0.0810401514172554,
-0.05986754596233368,
-0.0009843300795182586,
0.020177556201815605,
0.024069765582680702,
-0.030436189845204353,
-0.0166106428951025,
-0.01455756276845932,
-0.012430996634066105,
-0.10816342383623123,
-0.0000953727139858529,
-0.01593332551419735,
-0.009086518548429012,
-0.06740172207355499,
0.02586202882230282,
0.04383578896522522,
-0.040133267641067505,
0.043221838772296906,
-0.01435161754488945,
0.006396167445927858,
-0.030036399140954018,
0.0632329061627388,
-0.05997411906719208,
0.02630538120865822,
0.04341191053390503,
-0.003279151627793908,
-0.025957388803362846,
-0.046633657068014145,
-0.007979480549693108,
0.09888386726379395,
-0.04549224302172661,
-0.0420856736600399,
0.047851357609033585,
0.015857772901654243,
0.005361905321478844,
0.01296277903020382,
-0.03909342736005783,
0.049517080187797546,
0.03594977408647537,
-0.03685932606458664,
0.006351357791572809,
-0.03283290937542915,
-0.009075609967112541,
0.04013555869460106,
0.03191476687788963,
0.03484959527850151,
0.045435529202222824,
0.04640243574976921,
-0.06797195971012115,
0.02575461007654667,
-0.024792633950710297,
-0.03999565914273262,
0.030483873561024666,
0.04599953070282936,
0.014805334620177746,
0.0606631301343441,
0.026709722355008125,
-0.02906186506152153,
0.07995449006557465,
0.02838636003434658,
0.008278796449303627,
0.007411218248307705,
0.07749374955892563,
0.00924853328615427,
-0.026157069951295853,
0.006095084827393293,
-0.03282145783305168,
-0.05418017879128456,
-0.03901664540171623,
-0.013583479449152946,
-0.015236555598676205,
0.01833837851881981,
0.033847346901893616,
0.0691329687833786,
-0.038417574018239975,
0.007753700949251652,
0.11233781278133392,
-0.07132599502801895,
-0.017404697835445404,
-0.008402055129408836,
-0.03665784373879433,
-0.018585368990898132,
-0.01747366413474083,
0.07895399630069733,
0.009366973303258419,
0.03690510243177414,
0.00009990451508201659,
-0.002370932139456272,
-0.04434259235858917,
-0.0008945430163294077,
-0.03178538382053375,
0.016964945942163467,
0.006952668074518442,
-0.005931936204433441,
-0.04087110236287117,
-0.007532194256782532,
-0.02837749943137169,
-0.003196807811036706,
0.0323411263525486,
-0.01930626668035984,
0.019441938027739525,
-0.018790574744343758,
-0.014771909452974796,
-0.027789387851953506,
0.009806626476347446,
0.008935051038861275,
0.031110307201743126,
-0.021588295698165894,
-0.028623610734939575,
0.019496707245707512,
-0.014875893481075764,
0.015903878957033157,
-0.016439009457826614,
-0.005095893517136574,
0.042807966470718384,
0.008458280935883522,
0.06774534285068512,
0.011992424726486206,
0.04480050131678581,
-0.017554549500346184,
-0.006358621176332235,
0.026844481006264687,
0.10387150943279266,
-0.02086271531879902,
0.019281424582004547,
-0.07539879530668259,
-0.012181256897747517,
0.036990415304899216,
-0.04522018879652023,
-0.011771473102271557,
-0.041425202041864395,
0.011379479430615902,
0.006853976286947727,
0.02939886599779129,
0.008260917849838734,
-0.02220146171748638,
-0.05424356460571289,
-0.06689686328172684,
-0.023662365972995758,
-0.01856296695768833,
0.010438220575451851,
0.011198236607015133,
0.0537085197865963,
0.02015739306807518,
-0.016336586326360703,
0.03561361879110336,
-0.05274571105837822,
0.011934318579733372,
0.0283042062073946,
-0.007668175734579563,
0.01809893175959587,
0.050749633461236954,
0.014997501857578754,
0.044129855930805206,
-0.05309770256280899,
0.029412919655442238,
-0.03279586881399155,
0.021441949531435966,
0.028493840247392654,
-0.036148492246866226,
-0.0021031503565609455,
-0.005423724185675383,
-0.03912702947854996,
-0.07556454837322235,
-0.019276490435004234,
0.0015687301056459546,
-0.02509700320661068,
-0.01930905692279339,
-0.02291114255785942,
-0.007423778530210257,
-0.006792018190026283,
0.008416575379669666,
-0.05318853631615639,
0.010185889899730682,
0.004195955581963062,
-0.0037709393072873354,
0.011367445811629295,
-0.0004136360948905349,
-0.04688159376382828,
0.009357833303511143,
-0.008125611580908298,
0.013161332346498966,
0.010510793887078762,
-0.03369301185011864,
0.0069276997819542885,
0.01223316602408886,
-0.03532404452562332,
-0.0015362094854936004,
-0.019765660166740417,
0.01019001193344593,
-0.016987664625048637,
-0.009060194715857506,
-0.014355368912220001,
0.01192642655223608,
0.014092362485826015,
0.02103659138083458,
0.05380087345838547,
-0.06516724824905396,
0.0017495080828666687,
0.01548049133270979,
-0.04874633997678757,
-0.024016285315155983,
-0.011973528191447258,
-0.028453165665268898,
0.007719705812633038,
-0.06379824131727219,
-0.026751602068543434,
0.01004076935350895,
-0.06043989583849907,
0.04094761610031128,
-0.00867091678082943,
0.014366076327860355,
0.03720609098672867,
0.05055759847164154,
-0.03899211809039116,
-0.03187696263194084,
0.06109237298369408,
-0.03086337074637413,
-0.035161424428224564,
-0.06841479986906052,
0.01377303060144186,
-0.019957900047302246,
0.018216324970126152,
-0.027135424315929413,
-0.06772714108228683,
-0.046561598777770996,
0.05052783340215683,
-0.0349569097161293,
-0.04123670607805252,
-0.0019219423411414027,
0.007756481878459454,
-0.026859622448682785,
-0.04813331365585327,
-0.04722806438803673,
-0.055083006620407104,
-0.04236728698015213,
-0.013841785490512848,
-0.029455386102199554,
-0.024331839755177498,
-0.08667783439159393,
0.007455157581716776,
0.05989842116832733,
-0.05175185948610306,
-0.007392131257802248,
-0.014624632894992828,
-0.003582525998353958,
-0.02315736934542656,
-0.021555239334702492,
-0.04597611352801323,
0.04963184520602226,
-0.047425225377082825,
-0.011618779972195625,
0.02966604009270668,
0.032490164041519165,
0.015479485504329205,
0.019541477784514427,
0.05159522965550423,
-0.022436540573835373,
-0.03486643359065056,
0.038091517984867096,
-0.0208442360162735,
-0.04198345169425011,
0.06306114792823792,
-0.015369663946330547,
-0.03883952274918556,
-0.03920884057879448,
-0.003766476409509778,
0.021724529564380646,
-0.0003480112354736775,
0.03625791519880295,
-0.03358844667673111,
0.003608149476349354,
-0.04771491885185242,
0.02602265775203705,
-0.036385759711265564,
0.009728128090500832,
0.0063257296569645405,
0.07814639061689377,
-0.032423920929431915,
-0.02033800072968006,
-0.028911752626299858,
0.03795500099658966,
-0.02909177914261818
] |
<p>In a gravitational field, the gravitational force acting on a body (of mass m) at a point x metres away from the attracting body (of mass M) is $\frac{GMm}{x^2}$. Integrating this force from a point at infinity to x gives $-\frac{GMm}{x}$, or the work done by the gravitational field on the mass in moving the mass from a point at infinity to x. Then, the gravitational potential at point x is $-\frac{GM}{x}$.</p>
<p>However, the definition that my school gives is : "Gravitational potential at a point in a gravitational field is the amount of work done by an <strong>external agent</strong> in moving one unit of mass from a point at infinity to the point in the gravitational field, without any acceleration". The lecturers explained that as a body moves closer to the attracting body, it accelerates and gains kinetic energy. In order to maintain a constant velocity, negative work must be done by an external agent to remove this extra kinetic energy.</p>
<p>Now I am very confused, because both seem valid to me. What does "gravitational potential" actually mean?</p> | g7794 | [
0.04398872330784798,
0.07351313531398773,
-0.004997116047888994,
0.026140807196497917,
0.03204294294118881,
0.04166572913527489,
0.021085720509290695,
0.024686500430107117,
-0.09997561573982239,
0.009532725438475609,
-0.01598452404141426,
0.035561949014663696,
0.023509513586759567,
-0.03760329261422157,
0.012711452320218086,
-0.030764911323785782,
0.09943854808807373,
-0.0025754300877451897,
0.030372340232133865,
0.03080384060740471,
-0.010940936394035816,
0.024663681164383888,
-0.0019615814089775085,
-0.026131680235266685,
-0.011526577174663544,
0.01058367919176817,
0.07696323841810226,
-0.005436094477772713,
-0.04028138145804405,
-0.06666158884763718,
-0.0031287753954529762,
-0.00248888717032969,
0.02455478347837925,
-0.033064667135477066,
-0.03504679724574089,
0.015418825671076775,
0.09507062286138535,
0.029965870082378387,
-0.003495759330689907,
-0.0404391847550869,
-0.024666802957654,
-0.021588729694485664,
0.014255762100219727,
0.00648243073374033,
-0.0019050172995775938,
0.028989505022764206,
0.0018957254942506552,
-0.03886665031313896,
0.03861605376005173,
-0.02923189289867878,
0.004685989115387201,
0.02480575628578663,
0.000033695821912260726,
-0.015530428849160671,
0.00338609516620636,
0.046580806374549866,
0.039704225957393646,
-0.0153276938945055,
0.023834295570850372,
-0.035667359828948975,
0.047595713287591934,
-0.030174169689416885,
0.04373551905155182,
-0.03173964098095894,
0.009954228065907955,
-0.029368139803409576,
-0.08017513155937195,
-0.01087014377117157,
-0.051442768424749374,
0.005604226142168045,
-0.01336154155433178,
-0.042111705988645554,
-0.017336411401629448,
-0.01011660136282444,
-0.03865785524249077,
-0.000570239033550024,
0.055176299065351486,
0.0008872089674696326,
0.03498591110110283,
-0.005938156507909298,
0.013405286706984043,
-0.062072016298770905,
0.06165023520588875,
0.010676434263586998,
0.06248517706990242,
-0.015765827149152756,
-0.03359793499112129,
0.019965607672929764,
-0.03158964589238167,
0.02832048572599888,
0.016712838783860207,
0.027439668774604797,
0.04815215617418289,
-0.0047172862105071545,
-0.059962768107652664,
0.041516467928886414,
-0.01958647556602955,
0.05097651854157448,
-0.054666370153427124,
-0.025378920137882233,
-0.023136477917432785,
-0.03487851843237877,
0.007581065874546766,
0.005381516646593809,
0.044832807034254074,
-0.00884885061532259,
-0.001676058047451079,
0.019674129784107208,
0.03918679058551788,
0.029793864116072655,
-0.02065432071685791,
-0.010136513039469719,
-0.033612243831157684,
-0.08482510596513748,
-0.042899440973997116,
-0.03914191201329231,
0.04297095537185669,
-0.00484916428104043,
0.03261908143758774,
0.04417945817112923,
-0.04320136830210686,
0.058344516903162,
-0.03421716392040253,
0.055425792932510376,
-0.03601550683379173,
-0.01309705339372158,
-0.016369303688406944,
0.031711895018815994,
0.005010963883250952,
-0.01753421314060688,
-0.005170389078557491,
-0.03648761287331581,
-0.005866805091500282,
-0.011603661812841892,
-0.009173396974802017,
0.02449648827314377,
-0.029271122068166733,
-0.022278601303696632,
0.007033139932900667,
0.051182959228754044,
-0.02607777714729309,
-0.04201972484588623,
0.01163436472415924,
-0.005390686448663473,
-0.03275647386908531,
0.10196781158447266,
-0.04959609732031822,
0.039287228137254715,
0.05591319501399994,
-0.019612113013863564,
0.052072200924158096,
0.07447627931833267,
0.00403599813580513,
-0.0828738883137703,
0.07302360981702805,
-0.014880628325045109,
-0.021034838631749153,
0.045220814645290375,
-0.023161690682172775,
0.06554807722568512,
0.1193683072924614,
-0.016667965799570084,
0.06666755676269531,
0.01399211585521698,
-0.03062128834426403,
0.024012118577957153,
-0.0233664121478796,
-0.055955562740564346,
0.005812374409288168,
0.026789916679263115,
-0.05568800866603851,
0.002112406538799405,
0.02079934813082218,
0.03792495280504227,
-0.026027051731944084,
0.0036544702015817165,
0.01602453552186489,
-0.015590982511639595,
-0.04336875304579735,
0.04210050031542778,
-0.02434637024998665,
-0.03962114825844765,
0.011530586518347263,
-0.023720571771264076,
-0.02563176304101944,
-0.01923210918903351,
0.007967701181769371,
0.06147294491529465,
-0.011191915720701218,
0.015620972029864788,
-0.007124288473278284,
-0.018119070678949356,
0.029076850041747093,
0.049841102212667465,
-0.03354217857122421,
0.07355837523937225,
0.02368125692009926,
-0.03733211010694504,
-0.007339353207498789,
-0.003129030345007777,
-0.04181770235300064,
0.06422293186187744,
0.016000207513570786,
-0.03385841101408005,
0.07566912472248077,
-0.008446664549410343,
0.0031366695184260607,
0.011902942322194576,
0.05223622918128967,
0.004099278710782528,
-0.02352972701191902,
-0.03262771666049957,
0.02588546648621559,
-0.010107878595590591,
0.01043485477566719,
-0.06313329190015793,
-0.09306175261735916,
0.024347422644495964,
-0.0009173068101517856,
-0.005406043026596308,
-0.04449789971113205,
0.05928483605384827,
0.02295382134616375,
-0.011078494600951672,
-0.09287463873624802,
-0.005413594655692577,
-0.009619669988751411,
-0.021137459203600883,
0.0037264246493577957,
-0.009648689068853855,
-0.06184638664126396,
0.05134402588009834,
-0.0015585966175422072,
-0.027789000421762466,
0.04579557478427887,
0.03218935430049896,
-0.03693507984280586,
0.034061502665281296,
-0.027896879240870476,
0.027196919545531273,
-0.017779426649212837,
-0.04474553465843201,
-0.06473833322525024,
-0.049201175570487976,
0.03783918172121048,
-0.008202641271054745,
0.07368145883083344,
0.009389850310981274,
0.0184680987149477,
-0.000220004134462215,
0.02771138958632946,
0.023820510134100914,
-0.043016210198402405,
0.02120782621204853,
0.028607860207557678,
-0.00553552620112896,
-0.08035983890295029,
0.017998358234763145,
-0.07465032488107681,
-0.0053010061383247375,
0.008731705136597157,
-0.035012636333703995,
0.0206455085426569,
0.03150473162531853,
-0.045000068843364716,
0.028176385909318924,
-0.07648784667253494,
0.02113848365843296,
0.02752820961177349,
0.0457778200507164,
-0.002057333244010806,
0.032791174948215485,
0.01139138638973236,
0.03363689407706261,
-0.03116524964570999,
-0.06953388452529907,
-0.0012064612237736583,
-0.017487075179815292,
0.015546529553830624,
-0.005292132496833801,
-0.03364880755543709,
-0.010897941887378693,
-0.004408056382089853,
0.017428698018193245,
0.021907292306423187,
-0.02653827890753746,
0.008977655321359634,
0.014271327294409275,
-0.0402885340154171,
-0.05535220354795456,
0.03179844468832016,
0.02365751750767231,
0.06846458464860916,
0.008392579853534698,
-0.00323738856241107,
0.0333964079618454,
0.0003022152232006192,
-0.044116370379924774,
-0.007355371490120888,
-0.03655466064810753,
-0.005141938105225563,
-0.009293709881603718,
-0.05143221840262413,
0.00985001865774393,
0.025559447705745697,
0.019918806850910187,
-0.030205048620700836,
-0.04815880209207535,
-0.047943998128175735,
-0.0041890861466526985,
-0.006708624307066202,
0.06595613062381744,
0.021298155188560486,
0.005157782230526209,
-0.02232448011636734,
0.007819145917892456,
-0.026646975427865982,
-0.037997689098119736,
-0.0377628356218338,
-0.004161506425589323,
0.06370750814676285,
-0.04343774542212486,
-0.010817321948707104,
0.02547864429652691,
0.031482916325330734,
0.0281732939183712,
-0.029132727533578873,
-0.004713950678706169,
-0.052407972514629364,
-0.03173192963004112,
0.017410896718502045,
-0.0028348464984446764,
-0.05807599797844887,
-0.0025546604301780462,
-0.03221255913376808,
-0.05207184702157974,
-0.0100912069901824,
0.007761531975120306,
0.05765432491898537,
-0.0033051425125449896,
0.02714136242866516,
0.048278745263814926,
-0.052272897213697433,
0.02118982933461666,
-0.033683255314826965,
0.0315934494137764,
-0.005994983948767185,
-0.0016520610079169273,
-0.00961786974221468,
-0.0075585427694022655,
-0.028628911823034286,
-0.019533229991793633,
0.01637844368815422,
-0.03258185461163521,
-0.033653825521469116,
-0.04805020987987518,
-0.011382393538951874,
0.01873655989766121,
-0.07049671560525894,
0.05799096077680588,
-0.0023476749192923307,
-0.009162464179098606,
0.015354255214333534,
0.10672439634799957,
0.02416332997381687,
-0.021639211103320122,
-0.010302629321813583,
-0.03614049032330513,
0.02367597445845604,
-0.0006927535869181156,
0.04251763969659805,
-0.08091291785240173,
0.025190550833940506,
0.015459545888006687,
0.047702353447675705,
-0.03354818746447563,
0.014423555694520473,
-0.021545711904764175,
0.0030075511895120144,
0.009303630329668522,
0.09275501221418381,
0.027649544179439545,
-0.059713952243328094,
0.033087484538555145,
0.059528470039367676,
0.01904613897204399,
-0.03532269597053528,
-0.02203345112502575,
0.07399291545152664,
-0.05996284261345863,
-0.023716414347290993,
-0.03611777722835541,
0.004499106202274561,
0.03945665806531906,
0.00632814085111022,
0.008964013308286667,
-0.010495038703083992,
0.016903189942240715,
0.038161180913448334,
0.06829211115837097,
0.022331207990646362,
0.05143182352185249,
-0.0322076678276062,
0.035591449588537216,
-0.03889322280883789,
-0.0201511662453413,
0.028639083728194237,
-0.03861607611179352,
-0.009884175844490528,
-0.024524660781025887,
-0.007997330278158188,
-0.002577098784968257,
-0.018032103776931763,
-0.05112428963184357,
0.0027551178354769945,
-0.020482204854488373,
0.014362029731273651,
0.013356364332139492,
0.0210932195186615,
0.029786746948957443,
0.021758800372481346,
0.030870862305164337,
0.03699806332588196,
-0.02460324764251709,
-0.04032820463180542,
0.10627057403326035,
0.03830016404390335,
0.05242377519607544,
-0.024598268792033195,
-0.01103986892849207,
-0.002723290817812085,
0.0532304123044014,
-0.0002569339412730187,
0.03586197644472122,
-0.03845825418829918,
0.10244230926036835,
0.00577373243868351,
0.010184493847191334,
0.0667584016919136,
0.014983098953962326,
0.0757785439491272,
0.07676994055509567,
-0.004931761883199215,
-0.025754371657967567,
0.020950371399521828,
0.027659909799695015,
-0.026288088411092758,
-0.040408942848443985,
-0.03072640672326088,
-0.052312351763248444,
-0.10399840772151947,
0.014034388586878777,
0.0028389287181198597,
-0.03280407935380936,
0.01533446367830038,
0.0512971505522728,
0.0071899015456438065,
-0.039122965186834335,
-0.0357869528234005,
-0.005610238295048475,
-0.025162076577544212,
-0.003932563588023186,
0.0069495923817157745,
0.02434975653886795,
0.07342167943716049,
0.01114713866263628,
-0.04064345732331276,
-0.03755646571516991,
-0.0611552894115448,
0.022718477994203568,
-0.023429878056049347,
0.026031160727143288,
0.018570976331830025,
0.016286903992295265,
0.022973131388425827,
0.03129737451672554,
-0.0017783398507162929,
0.00862729549407959,
0.047121673822402954,
-0.04165980592370033,
0.0007678123656660318,
0.03916291519999504,
0.03979983180761337,
-0.038071922957897186,
-0.008858243003487587,
0.0011709985556080937,
-0.035573139786720276,
0.04258304089307785,
0.02289048209786415,
-0.010036706924438477,
0.054335396736860275,
-0.04307185113430023,
-0.012515829876065254,
-0.048613835126161575,
0.0000818754342617467,
0.027910033240914345,
0.029641782864928246,
-0.004263793583959341,
0.01965516246855259,
-0.004280215594917536,
-0.04693213477730751,
0.012804950587451458,
-0.058822982013225555,
-0.023410361260175705,
-0.014653130434453487,
0.10662834346294403,
0.017001697793602943,
-0.043088123202323914,
-0.012964698486030102,
0.05092455446720123,
-0.01882297359406948,
0.039038676768541336,
0.033944349735975266,
0.0343896709382534,
0.02245744690299034,
-0.031109552830457687,
0.025408245623111725,
-0.06312572211027145,
-0.038203950971364975,
0.012150229886174202,
0.03851587325334549,
0.056048326194286346,
-0.012805466540157795,
-0.05852755904197693,
0.010200755670666695,
0.01887810043990612,
-0.015713663771748543,
0.024248721078038216,
-0.03865169733762741,
0.02580224722623825,
-0.00020655093248933554,
-0.0344940647482872,
0.014698821119964123,
0.03973245620727539,
-0.04586966708302498,
-0.02383270114660263,
-0.01160468440502882,
-0.020708562806248665,
0.07204661518335342,
-0.031625907868146896,
0.015344482846558094,
-0.04605266824364662,
-0.004588293377310038,
0.05341855436563492,
-0.07700933516025543,
0.03736333176493645,
-0.03804472088813782,
-0.043464574962854385,
0.014738736674189568,
-0.10003691166639328,
-0.013493524864315987,
-0.03056102804839611,
0.013243362307548523,
-0.0468921959400177,
-0.015247230418026447,
0.03055989369750023,
-0.009206626564264297,
0.003185459179803729,
-0.030918404459953308,
-0.07972153276205063,
-0.009619537740945816,
-0.014490561559796333,
-0.0026829338166862726,
-0.06314751505851746,
0.038728296756744385,
-0.04473811388015747,
0.01971895433962345,
-0.05276218801736832,
0.0459892675280571,
0.00954271201044321,
0.010920869186520576,
0.03356720134615898,
0.0002990998618770391,
0.0001141517423093319,
-0.02578849159181118,
0.039780646562576294,
0.000694902497343719,
-0.0225696824491024,
-0.02590451017022133,
0.04693998768925667,
0.01328733004629612,
-0.008749364875257015,
0.03127529099583626,
-0.10600093007087708,
-0.026066480204463005,
0.06138540059328079,
-0.026704484596848488,
-0.029655221849679947,
0.05416035279631615,
0.0066403974778950214,
-0.002434138674288988,
-0.02348601631820202,
-0.051259227097034454,
-0.005959720816463232,
-0.020826799795031548,
-0.042905524373054504,
-0.03606972098350525,
0.02671113796532154,
-0.0004887809627689421,
0.023170607164502144,
-0.0036014574579894543,
0.01857340894639492,
0.018972285091876984,
-0.013647861778736115,
0.03874815255403519,
0.022600091993808746,
-0.034734711050987244,
-0.015190289355814457,
-0.03629148378968239,
-0.005523638799786568,
-0.023132305592298508,
0.022628935053944588,
-0.008706138469278812,
0.023890722543001175,
0.05444876477122307,
0.0016058849869295955,
-0.0007623802521266043,
-0.015273687429726124,
-0.06112011522054672,
-0.012486608698964119,
-0.003984010312706232,
-0.03235829249024391,
0.06212557107210159,
-0.003207690780982375,
0.031215624883770943,
0.027362363412976265,
-0.025236349552869797,
0.03751301392912865,
0.02066137082874775,
-0.01802058331668377,
-0.043651338666677475,
0.004532855004072189,
-0.061471953988075256,
0.02169874683022499,
-0.010970067232847214,
0.03464464843273163,
-0.03357492759823799,
0.06299266964197159,
0.05473964288830757,
-0.0017884880071505904,
-0.03510114923119545,
-0.011781980283558369,
0.010954204015433788,
-0.03337373211979866,
-0.02465374395251274,
-0.03287193551659584,
-0.009470337070524693,
0.017592739313840866,
-0.001052467618137598,
-0.0021609619725495577,
-0.06636857986450195,
-0.05833204835653305,
0.013890914618968964,
0.015492026694118977,
-0.0388936847448349,
0.025768712162971497,
-0.028224676847457886,
0.01657307706773281,
0.023809531703591347,
-0.08692621439695358,
0.02677406743168831,
-0.008258970454335213,
0.005372248124331236,
0.042720504105091095,
-0.025547539815306664,
0.036285143345594406,
-0.011503014713525772,
-0.013547789305448532,
-0.03475452959537506,
-0.018577825278043747,
0.007305752020329237,
0.006621453911066055,
-0.024797167629003525,
-0.03424760326743126,
-0.005540429148823023,
0.046840593218803406,
-0.014584695920348167,
-0.017171809449791908,
-0.007246057037264109,
-0.05276728793978691,
0.008042791858315468,
0.0423671118915081,
-0.01065362710505724,
0.02938820794224739,
-0.038551684468984604,
-0.013833818025887012,
-0.033729832619428635,
0.009402688592672348,
-0.008591501042246819,
0.021241936832666397,
0.04663969948887825,
0.014782222919166088,
0.015989694744348526,
0.028701838105916977,
0.013330034911632538,
-0.04379893094301224,
0.020798930898308754,
0.06089400500059128,
0.03147641941905022,
0.005172856617718935,
-0.014237986877560616,
-0.049567922949790955,
-0.02747155725955963,
0.011468565091490746,
-0.002940898761153221,
0.011129406280815601,
0.015072115696966648,
-0.010777645744383335,
-0.009932590648531914,
0.016783947125077248,
0.006686655338853598,
-0.005839494522660971,
0.010244767181575298,
-0.027837593108415604,
-0.011465996503829956,
0.03261096775531769,
0.00048776320181787014,
0.04030760005116463,
0.007495431695133448,
-0.051467545330524445,
0.018670329824090004,
0.019997969269752502,
-0.00989703182131052,
-0.05454033613204956,
-0.08471238613128662,
0.030487723648548126,
-0.034182578325271606,
-0.0011489192256703973,
0.008792495355010033,
-0.019249308854341507,
-0.06568887829780579,
-0.020008474588394165,
-0.04582269489765167,
0.01147349365055561,
0.0027326506096869707,
-0.0018905318574979901,
0.023961730301380157,
-0.030490180477499962,
-0.012770074419677258,
0.04371311143040657,
0.012344805523753166,
-0.05809924378991127,
0.010776286013424397,
0.05133036896586418,
0.012304284609854221,
-0.009924052283167839,
-0.04331959784030914,
0.10850061476230621,
0.05229142680764198,
0.029055893421173096,
0.03348546102643013,
0.038411229848861694,
-0.0304842758923769,
0.015799107030034065,
0.017809469252824783,
-0.06913531571626663,
-0.01415594294667244,
0.04742966592311859,
0.005400525406002998,
-0.0030639301985502243,
0.011304391548037529,
0.004789307247847319,
-0.03204343840479851,
-0.011770551092922688,
0.0043650101870298386,
-0.01046083029359579,
0.029893428087234497,
-0.006374269723892212
] |
<p>Would a projectile fired in space and assuming there were no stars or planets in the way, would the projectile continue on to infinity, since the x-component of the projectile's velocity never changes from it's original? </p> | g7795 | [
0.019353024661540985,
0.002232591388747096,
0.04012693092226982,
-0.032963283360004425,
0.023638885468244553,
0.005161432549357414,
-0.06268874555826187,
0.04342217370867729,
-0.01515381969511509,
-0.06769769638776779,
-0.03922095522284508,
0.05168082192540169,
0.0314803309738636,
-0.04044099897146225,
0.0011233590776100755,
-0.04618251696228981,
0.07108638435602188,
-0.0026380817871540785,
-0.0006769070168957114,
0.08519109338521957,
-0.000397874420741573,
-0.02610190585255623,
0.035378728061914444,
0.0051932185888290405,
-0.03322531282901764,
-0.04979356750845909,
0.02502312697470188,
-0.010916126891970634,
-0.055832456797361374,
-0.021803949028253555,
0.04277217388153076,
0.017328811809420586,
-0.039879653602838516,
-0.013043698854744434,
-0.0008220814052037895,
-0.044243186712265015,
-0.03296932205557823,
0.047054070979356766,
0.003952521365135908,
-0.014734813012182713,
-0.008722677826881409,
-0.03155345842242241,
0.014860600233078003,
0.008459090255200863,
-0.0009764691349118948,
0.008071809075772762,
0.04296686500310898,
0.03802800923585892,
0.013077921234071255,
-0.04874643683433533,
-0.06735935062170029,
0.004589664749801159,
-0.0030753454193472862,
0.009394073858857155,
0.0032054446637630463,
0.01821564882993698,
0.010446779429912567,
-0.04135405272245407,
0.06843189895153046,
0.02372816391289234,
-0.0057836975902318954,
-0.054825808852910995,
-0.026260865852236748,
0.002617049729451537,
0.026239505037665367,
-0.08307863771915436,
-0.06001691520214081,
0.02595466561615467,
-0.001547263003885746,
0.00018933662795461714,
0.09247667342424393,
-0.03466818109154701,
-0.06529948115348816,
-0.042205650359392166,
-0.05885111168026924,
0.0111572640016675,
0.02620820142328739,
0.04307345300912857,
-0.011573637835681438,
0.04841003566980362,
-0.04696447029709816,
0.008975458331406116,
0.09788019210100174,
-0.0540129691362381,
0.021653849631547928,
-0.021841878071427345,
0.05492383614182472,
-0.048140738159418106,
-0.0421154759824276,
0.03480890393257141,
-0.02146143466234207,
0.054661575704813004,
-0.006368129048496485,
0.015935834497213364,
-0.008032288402318954,
-0.04459334537386894,
-0.03795890882611275,
0.08139722049236298,
0.02726820670068264,
0.008206497877836227,
-0.0024287353735417128,
0.004808435682207346,
0.03546510636806488,
-0.027011629194021225,
0.05772756412625313,
-0.027277348563075066,
0.061238355934619904,
-0.010721237398684025,
0.02119877003133297,
-0.04038025066256523,
0.0032733967527747154,
-0.10885416716337204,
-0.0036879635881632566,
-0.031692031770944595,
0.015910696238279343,
0.01442550029605627,
0.048070065677165985,
-0.011510099284350872,
0.07629971206188202,
0.07806079834699631,
0.008985414169728756,
0.0002411736495560035,
-0.05417507886886597,
0.02509930729866028,
-0.03881184756755829,
0.001591669162735343,
-0.010242024436593056,
-0.017657596617937088,
-0.021663939580321312,
-0.05459170788526535,
-0.03083609975874424,
-0.008562860079109669,
0.02412470430135727,
0.01755433715879917,
-0.050973597913980484,
-0.013347690925002098,
0.019562775269150734,
-0.03435444086790085,
-0.00809997133910656,
-0.007902923040091991,
0.023509126156568527,
0.030462075024843216,
0.012533240020275116,
0.03354205563664436,
-0.02469557896256447,
0.05077267810702324,
-0.012187466025352478,
-0.015150505118072033,
0.024386636912822723,
-0.01847974583506584,
-0.008464666083455086,
0.029486117884516716,
0.029366539791226387,
0.026387320831418037,
-0.010479692369699478,
-0.049674004316329956,
0.03930976614356041,
0.011875919066369534,
-0.01097097061574459,
-0.05020109936594963,
0.03137402608990669,
0.038375124335289,
0.021664105355739594,
-0.005592167843133211,
-0.10215061157941818,
-0.020568594336509705,
-0.11615131050348282,
-0.03184564784169197,
-0.008808494545519352,
-0.016232889145612717,
-0.024258045479655266,
-0.03174903616309166,
0.026744021102786064,
0.022338908165693283,
0.01607024483382702,
0.017422344535589218,
-0.004167923703789711,
-0.00190601812209934,
-0.047174274921417236,
-0.009567590430378914,
-0.0228379275649786,
0.03463052213191986,
-0.02405403181910515,
0.00044485347461886704,
0.029928840696811676,
-0.02154705673456192,
0.03269004076719284,
0.05513054132461548,
-0.03465127944946289,
-0.015545567497611046,
-0.026091555133461952,
-0.03750135004520416,
0.016058973968029022,
0.07279986888170242,
0.024710586294531822,
-0.010469808243215084,
0.002913689473643899,
-0.0367138534784317,
-0.027276264503598213,
0.023175569251179695,
-0.02711111307144165,
0.09283538162708282,
0.030638260766863823,
0.039368223398923874,
-0.007279965095221996,
-0.04555905610322952,
-0.009681659750640392,
-0.011846572160720825,
0.0033831424079835415,
-0.008660053834319115,
0.08294269442558289,
0.018134497106075287,
-0.03247131407260895,
0.07028651982545853,
0.008141542784869671,
-0.007839102298021317,
-0.005010899156332016,
0.045223504304885864,
0.02769320458173752,
0.054538544267416,
-0.03275607153773308,
0.01946159079670906,
0.04025772213935852,
-0.05770557001233101,
-0.000887046626303345,
-0.0018440259154886007,
-0.027040043845772743,
-0.012629308737814426,
0.04513562470674515,
0.04878384247422218,
0.005194487050175667,
-0.012909365817904472,
-0.010470624081790447,
-0.029534079134464264,
0.03727097809314728,
-0.03374093025922775,
0.005375322885811329,
0.0228206105530262,
-0.016703391447663307,
0.0078001427464187145,
0.01799124665558338,
0.009824037551879883,
-0.01173908170312643,
-0.0415518656373024,
0.06565642356872559,
-0.09008636325597763,
-0.00903680082410574,
0.013116244226694107,
0.03435909003019333,
-0.00964859127998352,
-0.036745741963386536,
0.013570732437074184,
-0.05636211484670639,
0.032523490488529205,
-0.027640560641884804,
-0.04916970059275627,
-0.021179748699069023,
0.021979622542858124,
-0.09048672765493393,
-0.05412766709923744,
-0.05020856857299805,
-0.021516725420951843,
-0.06780635565519333,
-0.03233303502202034,
-0.01744522526860237,
0.038071852177381516,
-0.022876422852277756,
0.024188963696360588,
-0.034767016768455505,
0.03144681826233864,
-0.016748741269111633,
0.0007447522948496044,
0.01999894343316555,
0.05816031992435455,
-0.02022106572985649,
0.04922320321202278,
-0.009181380271911621,
-0.004252833314239979,
0.03790810704231262,
0.008157793432474136,
-0.007678682915866375,
0.02005617879331112,
-0.01697610504925251,
0.018753279000520706,
0.061731502413749695,
-0.02339889109134674,
0.038201186805963516,
0.0170876644551754,
-0.014945329166948795,
-0.030911654233932495,
0.02438162826001644,
0.021009664982557297,
0.04260190203785896,
-0.028529254719614983,
0.007706278935074806,
0.059544868767261505,
0.031668975949287415,
-0.04628020152449608,
0.0012653679586946964,
0.011597882956266403,
0.007541600614786148,
0.0013155053602531552,
-0.0026666491758078337,
-0.013997472822666168,
-0.006139053497463465,
0.018812187016010284,
-0.028968248516321182,
0.01240555103868246,
0.01495295949280262,
-0.017451701685786247,
0.09351854026317596,
0.09335937350988388,
0.0036548227071762085,
0.09530358016490936,
0.006220388691872358,
-0.03852701932191849,
-0.019652873277664185,
0.0367097444832325,
0.02569947950541973,
0.03257185220718384,
-0.01899360679090023,
-0.03647246211767197,
0.0412963442504406,
0.0017909681191667914,
-0.0005960278795100749,
0.02214946039021015,
-0.015396223403513432,
0.01439876388758421,
-0.027813436463475227,
0.027334582060575485,
-0.03473904728889465,
0.041050974279642105,
0.0006086790235713124,
-0.017641734331846237,
-0.03010174073278904,
0.03369350731372833,
-0.002734050853177905,
0.019310206174850464,
0.0390796959400177,
0.12318243086338043,
0.0505637526512146,
0.015322376973927021,
-0.007587363012135029,
0.005116025917232037,
0.05391237512230873,
0.00617387006059289,
0.051674723625183105,
-0.03648408502340317,
0.003151715500280261,
-0.01718452014029026,
0.059353094547986984,
-0.0536009855568409,
0.015740761533379555,
0.026879029348492622,
-0.049956467002630234,
0.0394437313079834,
0.04422533139586449,
0.04559532552957535,
0.005595644004642963,
-0.06466930359601974,
-0.004903050605207682,
-0.03728386387228966,
0.0215037539601326,
0.046375520527362823,
0.013525567948818207,
0.02812664769589901,
-0.004514794796705246,
-0.06548628956079483,
0.004198448266834021,
0.033281855285167694,
-0.0031938960310071707,
-0.05837381258606911,
-0.06164342910051346,
-0.025553112849593163,
-0.014653014950454235,
0.0020666129421442747,
0.03810907527804375,
-0.011381643824279308,
-0.024293314665555954,
0.004236261826008558,
0.07417023181915283,
-0.03591403737664223,
-0.013301300816237926,
-0.015383525751531124,
0.02248617447912693,
0.017688486725091934,
-0.004814980085939169,
-0.012555582448840141,
0.034955915063619614,
-0.023082440719008446,
0.05894453823566437,
-0.07166897505521774,
0.04474393278360367,
-0.03355996683239937,
0.023157278075814247,
-0.018553825095295906,
-0.02541542425751686,
-0.06600973010063171,
-0.026479098945856094,
-0.01159319095313549,
0.03000653348863125,
0.05212783068418503,
0.010121607221662998,
-0.030909443274140358,
0.03665585815906525,
-0.015847869217395782,
0.029019558802247047,
-0.024997541680932045,
-0.02217373065650463,
-0.03896620497107506,
-0.0012569243554025888,
0.019416719675064087,
0.005408015567809343,
0.0352187380194664,
-0.0358547680079937,
-0.011730686761438847,
0.010949035175144672,
0.025171440094709396,
-0.06502366065979004,
-0.027941793203353882,
0.0040694233030080795,
-0.005742273759096861,
0.0024685338139533997,
0.03273746743798256,
0.08460645377635956,
-0.03540998324751854,
-0.03449272736907005,
-0.023219015449285507,
-0.01814224384725094,
0.047388602048158646,
-0.015226992778480053,
0.01499524898827076,
0.03512740135192871,
0.04879692941904068,
-0.03757253661751747,
0.037602584809064865,
-0.01711415685713291,
0.006087836809456348,
0.03664897009730339,
0.034868184477090836,
0.05481049045920372,
0.0522850900888443,
0.03430014103651047,
0.006514540873467922,
-0.07152529060840607,
0.08382484316825867,
-0.018214402720332146,
-0.03232041373848915,
0.04003271088004112,
-0.00297339609824121,
-0.022340646013617516,
-0.02738329954445362,
-0.06388325989246368,
-0.011260165832936764,
-0.03801986202597618,
-0.04748062416911125,
-0.03563910722732544,
0.020904624834656715,
0.026282094419002533,
0.03786616772413254,
-0.0518200509250164,
-0.07743950188159943,
0.014744235202670097,
0.044193509966135025,
0.00812503695487976,
0.009379261173307896,
0.016037574037909508,
-0.0318460687994957,
-0.031029455363750458,
0.03186691552400589,
-0.001598635339178145,
0.04946411773562431,
0.02221526950597763,
0.08966768532991409,
-0.0300016850233078,
-0.0574600026011467,
-0.003333545522764325,
-0.008521473966538906,
-0.00381927820853889,
0.008249828591942787,
-0.033953409641981125,
-0.003891539294272661,
0.03657002002000809,
-0.030810652300715446,
0.020214123651385307,
0.0015480535803362727,
-0.05544351041316986,
-0.029315417632460594,
-0.010737696662545204,
-0.001558985561132431,
0.004619669169187546,
0.011803701519966125,
-0.016547836363315582,
0.0024786684662103653,
0.01292379479855299,
-0.011562615633010864,
-0.045248717069625854,
-0.02941524237394333,
0.02536504901945591,
0.023019881919026375,
-0.08308812230825424,
-0.0020297905430197716,
0.026840373873710632,
0.010730094276368618,
-0.06438596546649933,
0.005402862560003996,
-0.003961718175560236,
0.019813114777207375,
-0.03891133889555931,
0.017458600923419,
-0.015119551680982113,
0.059262990951538086,
-0.021687647327780724,
0.024363340809941292,
0.05017368495464325,
0.012588527984917164,
-0.030250463634729385,
-0.014065894298255444,
0.03725390136241913,
0.01905081421136856,
0.04987898841500282,
-0.07074546068906784,
0.011140401475131512,
0.019622618332505226,
0.03373584896326065,
0.0741075873374939,
-0.030298231169581413,
-0.05073530599474907,
-0.09165950119495392,
0.04985949397087097,
0.01573461852967739,
-0.02073054574429989,
-0.0234860647469759,
-0.025616036728024483,
-0.049746155738830566,
-0.0062084076926112175,
0.010358545929193497,
0.023982161656022072,
0.03645269572734833,
-0.03644554689526558,
-0.0861222892999649,
-0.004389020614326,
0.023823587223887444,
0.03284902125597,
-0.008554117754101753,
-0.023554682731628418,
-0.06290200352668762,
0.002305205911397934,
0.02686270885169506,
-0.0712135061621666,
-0.09071870148181915,
0.026616986840963364,
0.01280196849256754,
0.007320854812860489,
-0.00012713047908619046,
0.026837924495339394,
0.0011627578642219305,
0.04785453900694847,
-0.030454449355602264,
-0.060807179659605026,
-0.00042887782910838723,
-0.010707731358706951,
0.009425022639334202,
0.006470757070928812,
-0.002406802959740162,
-0.021952880546450615,
0.03512090444564819,
-0.06601766496896744,
0.057972174137830734,
0.00914329756051302,
-0.013319971971213818,
-0.0010126333218067884,
-0.013714475557208061,
-0.0128214992582798,
0.020663132891058922,
-0.04000679776072502,
-0.005275358911603689,
-0.023062951862812042,
-0.027097901329398155,
0.01316924300044775,
0.02959544025361538,
0.032555580139160156,
0.010396920144557953,
0.008348880335688591,
-0.004941883962601423,
0.059371743351221085,
0.007306108716875315,
0.01496049016714096,
0.04262658208608627,
-0.027034161612391472,
-0.04819241166114807,
-0.04967892915010452,
0.02791924960911274,
-0.018220599740743637,
-0.07850691676139832,
0.019915493205189705,
-0.00892767682671547,
0.007216603495180607,
0.022379320114850998,
0.009963851422071457,
-0.011975694447755814,
0.04611962288618088,
0.032448910176754,
0.02442208118736744,
0.016551773995161057,
0.01625053770840168,
-0.014735942706465721,
0.008889768272638321,
0.047287728637456894,
0.026013066992163658,
0.015559176914393902,
0.03491140902042389,
0.022047502920031548,
0.02441546879708767,
-0.04558132588863373,
0.010072540491819382,
0.012055518105626106,
-0.04542164504528046,
-0.010184695944190025,
0.033057522028684616,
0.09432148933410645,
-0.04751339182257652,
-0.06463462859392166,
0.006850534584373236,
-0.007991714403033257,
0.02065013349056244,
-0.02448933944106102,
0.07838355004787445,
0.0283542238175869,
-0.027438586577773094,
0.010395434685051441,
-0.002911402378231287,
0.01651710830628872,
0.024010786786675453,
0.004179707262665033,
0.052741747349500656,
0.0257033109664917,
0.03268788754940033,
-0.005482962355017662,
-0.005873167887330055,
0.017666662111878395,
-0.033555127680301666,
-0.017663471400737762,
-0.001298334333114326,
-0.03998357057571411,
0.04427693039178848,
0.028518827632069588,
-0.06755127012729645,
-0.04894644394516945,
-0.026398269459605217,
-0.05350526049733162,
-0.030520642176270485,
-0.05435493215918541,
0.027925673872232437,
-0.029157616198062897,
0.010172567330300808,
-0.020481642335653305,
-0.016431760042905807,
0.002197753172367811,
-0.06712613254785538,
-0.03351254388689995,
-0.014276579953730106,
-0.037125274538993835,
0.027644064277410507,
0.006956595461815596,
0.03196713700890541,
0.033800628036260605,
-0.01253883820027113,
0.01087050512433052,
0.041106387972831726,
0.04278809577226639,
0.022790001705288887,
0.005917640868574381,
0.009760801680386066,
0.016809679567813873,
-0.0027689968701452017,
-0.00511179817840457,
0.00906476192176342,
-0.011286737397313118,
0.06712586432695389,
0.058075740933418274,
0.02653888426721096,
0.005344478879123926,
0.03135400265455246,
-0.05043935030698776,
-0.0453520342707634,
-0.014456646516919136,
-0.00008897342922864482,
0.0191639494150877,
-0.051397599279880524,
-0.00423352001234889,
0.01944124512374401,
0.03850709646940231,
-0.03542593494057655,
0.031100792810320854,
-0.01684149168431759,
0.005990064237266779,
0.024380885064601898,
0.04418572038412094,
-0.04064294323325157,
-0.04946083575487137,
0.027217842638492584,
0.021584592759609222,
-0.04783876612782478,
0.017817260697484016,
0.021252578124403954,
-0.04061642661690712,
0.021393148228526115,
-0.01987222209572792,
-0.03220907598733902,
-0.029693856835365295,
0.062197279185056686,
-0.01026615034788847,
-0.0202472023665905,
-0.030235813930630684,
0.021251017227768898,
0.014250445179641247,
-0.011501782573759556,
0.004575543105602264,
0.04340079054236412,
-0.0459776446223259,
0.02262258343398571,
0.012957827188074589,
-0.015075668692588806,
0.012101560831069946,
-0.015492089092731476,
-0.09078674018383026,
-0.01578887179493904,
0.0025462855119258165,
-0.10701918601989746,
0.025596100836992264,
-0.028453240171074867,
-0.010953755117952824,
0.02930706925690174,
-0.03932691365480423,
-0.019170846790075302,
-0.0026143076829612255,
-0.019086485728621483,
-0.0406729020178318,
-0.006846706848591566,
-0.053614649921655655,
-0.01647312007844448,
0.03602941334247589,
-0.027565086260437965,
-0.007543032523244619,
-0.02403634786605835,
0.04609654098749161,
0.013826148584485054,
0.06301082670688629,
-0.01101510040462017,
0.09647717326879501,
0.005746989045292139,
-0.06556632369756699,
0.0429309606552124,
0.0006684725522063673,
-0.0033838048111647367,
-0.00778112281113863,
0.03314854949712753,
-0.008867460303008556,
-0.01115855947136879,
0.01597272790968418,
0.0034523294307291508,
0.0046980120241642,
-0.055895350873470306,
-0.014110071584582329,
-0.08752309530973434,
0.008609320037066936,
0.011469056829810143
] |
<p>One page 5 in Landau & Lifshitz <em>Fluid Mechanics</em> (2nd edition), the authors pose the following problem:</p>
<blockquote>
<p>Write down the equations for one-dimensional motion of an ideal fluid in terms > of the variables $a$, $t$, where $a$ (called a <em>Lagrangian variable</em>) is the
$x$ coordinate of a fluid particle at some instant $t=t_0$.</p>
</blockquote>
<p>The authors then go on to give their solutions and assumptions. Here are the important parts:</p>
<blockquote>
<p>The coordinate $x$ of a fluid particle at an instant $t$ is regarded as a
function of $t$ and its coordinate $a$ at the initial instant: $x=x(a,t)$.</p>
</blockquote>
<p>For the condition of mass conversation the authors arrive at (where $\rho_0 = \rho(a)$ the given initial density distribution):</p>
<blockquote>
<p>$$ \rho\,\mathrm{d}x = \rho_0 \mathrm{d}a $$</p>
</blockquote>
<p>or alternatively:</p>
<blockquote>
<p>$$ \rho\left(\frac{\partial x}{\partial a}\right)_t = \rho_0 $$</p>
</blockquote>
<p>Now the authors go on to write out Euler's equation, where I start to miss something. With the velocity of the fluid particle $v=\left(\frac{\partial x}{\partial t}\right)_a$ and $\left(\frac{\partial v}{\partial t}\right)_a$ the rate of change of the velocity of the particle during its motion, they write:</p>
<blockquote>
<p>$$ \left(\frac{\partial v}{\partial t}\right)_a = -\frac{1}{\rho_0} \left(\frac{\partial p}{\partial a}\right)_t
$$</p>
</blockquote>
<p><strong>How are the authors arriving at that equation?</strong></p>
<p>In particular, when looking at Euler's equation:
$$
\frac{\partial\mathbb{v}}{\partial t} + \left( \mathbf{v} \cdot \textbf{grad} \right) \mathbf{v} = - \frac{1}{\rho} \textbf{grad}\, p
$$
what happens with the second term on the LHS $\left( \mathbf{v} \cdot \textbf{grad} \right) \mathbf{v}$? Why does it not appear in the authors' solution?</p> | g7796 | [
0.08870221674442291,
-0.024671517312526703,
0.004745422396808863,
-0.030438169836997986,
0.1032467857003212,
0.033982910215854645,
0.015834761783480644,
0.014972900971770287,
-0.08122246712446213,
0.0014787028776481748,
-0.0020890510641038418,
0.0381755605340004,
0.02560451254248619,
0.06515486538410187,
-0.012928313575685024,
0.04574643447995186,
0.09175501763820648,
-0.009252066724002361,
0.006280500907450914,
-0.005373021587729454,
-0.0174231119453907,
0.008347309194505215,
0.020491136237978935,
-0.03654658421874046,
0.01624905690550804,
-0.0294914823025465,
0.04733895882964134,
-0.03906230255961418,
-0.04433690756559372,
0.00959879718720913,
0.03301999717950821,
0.023972878232598305,
-0.00204167771153152,
-0.10682883858680725,
-0.05766423046588898,
-0.024211106821894646,
0.0875665470957756,
-0.0038158120587468147,
0.029089441522955894,
-0.0501311719417572,
0.05909634381532669,
-0.06485197693109512,
-0.0012303012190386653,
-0.01968643069267273,
-0.014270101673901081,
0.007495375350117683,
-0.045058347284793854,
-0.047776006162166595,
-0.02729819528758526,
0.02188403531908989,
0.04133933410048485,
0.10106729716062546,
-0.0064965710043907166,
-0.0004269930941518396,
0.015520426444709301,
0.07861416786909103,
0.01458707358688116,
0.00262203230522573,
0.06505485624074936,
0.015398207120597363,
0.029375765472650528,
-0.03726734220981598,
-0.006826413795351982,
-0.032684892416000366,
0.02751416526734829,
-0.03162875771522522,
-0.056838274002075195,
-0.011430090293288231,
0.012688630260527134,
-0.00021310726879164577,
-0.05980469286441803,
-0.036692261695861816,
-0.013411104679107666,
-0.08267264813184738,
-0.0351228304207325,
0.014962764456868172,
-0.004373758099973202,
-0.018343906849622726,
0.04961095005273819,
-0.03268299624323845,
-0.03616900369524956,
0.028319567441940308,
0.0013895512092858553,
0.010331803001463413,
0.07302655279636383,
0.039312634617090225,
0.0034803301095962524,
-0.0025545430835336447,
-0.03760787472128868,
0.0026076100766658783,
-0.04262310639023781,
-0.009803492575883865,
0.01239329855889082,
0.019800951704382896,
-0.006227834150195122,
-0.05175138637423515,
-0.015424514189362526,
0.020033150911331177,
-0.025085914880037308,
0.03943108394742012,
-0.013214404694736004,
0.0009508626535534859,
0.0010320252040401101,
0.004348184447735548,
-0.030062468722462654,
-0.00942516140639782,
0.04608668014407158,
0.04163027182221413,
-0.009854430332779884,
-0.0007826767396181822,
-0.02925330027937889,
-0.015341239050030708,
-0.014743482694029808,
-0.04727090895175934,
-0.027703111991286278,
0.004953224211931229,
0.048986323177814484,
-0.005863407161086798,
-0.013257395476102829,
0.051649585366249084,
-0.04205506294965744,
-0.010760434903204441,
0.02001776546239853,
0.05825301259756088,
0.0032243195455521345,
0.018075130879878998,
0.009833162650465965,
0.00789592880755663,
0.028367329388856888,
0.017113475129008293,
-0.0002679216559045017,
0.013978622853755951,
0.033826716244220734,
-0.007621611934155226,
0.00504101300612092,
0.03482916206121445,
0.032984569668769836,
0.05442868918180466,
0.007644889876246452,
-0.015505827032029629,
0.05608588829636574,
-0.031309764832258224,
0.00501624308526516,
-0.016635945066809654,
-0.042229101061820984,
0.05285430699586868,
-0.004118268843740225,
-0.046704355627298355,
0.024717746302485466,
-0.036573655903339386,
-0.02049264870584011,
0.06539498269557953,
0.012278919108211994,
0.03672563284635544,
-0.04613868519663811,
0.02738826535642147,
0.08370114117860794,
-0.016384392976760864,
-0.001756590441800654,
0.024976937100291252,
0.05874589830636978,
-0.04203680530190468,
0.02751016430556774,
0.025804925709962845,
-0.04959156736731529,
0.07563409954309464,
0.04659436270594597,
-0.10038424283266068,
0.021902773529291153,
-0.04534900560975075,
-0.0430300310254097,
-0.0465228334069252,
-0.028836285695433617,
0.033369969576597214,
-0.002656143857166171,
0.039580829441547394,
0.00023248032084666193,
-0.04199039191007614,
-0.0011852085590362549,
0.04443615302443504,
0.0123145068064332,
-0.04000779241323471,
0.07695568352937698,
-0.059671252965927124,
-0.05147065594792366,
-0.03178561478853226,
-0.026883501559495926,
0.036945000290870667,
-0.05728483572602272,
-0.021710745990276337,
-0.027539309114217758,
-0.026377663016319275,
-0.009506753645837307,
0.04272530600428581,
0.006040704436600208,
-0.01248357817530632,
0.0172113049775362,
-0.09903871268033981,
-0.0429052971303463,
0.06271609663963318,
0.002638466190546751,
0.04673448204994202,
0.05018049106001854,
0.05771409720182419,
-0.027812626212835312,
-0.008226841688156128,
-0.026411468163132668,
-0.029597273096442223,
0.013288894668221474,
0.011185619980096817,
0.03388800472021103,
-0.037198424339294434,
-0.061946362257003784,
0.038699351251125336,
-0.003485524095594883,
-0.041950248181819916,
0.019339654594659805,
0.01629798300564289,
-0.01623685099184513,
-0.0008459920063614845,
-0.05446990951895714,
-0.04538769647479057,
-0.007276648655533791,
0.0043829018250107765,
-0.045107435435056686,
-0.004761021584272385,
-0.026318157091736794,
-0.030710773542523384,
-0.055607207119464874,
0.045647718012332916,
-0.010667376220226288,
0.006194861140102148,
-0.04268995672464371,
0.012274675071239471,
0.06633209437131882,
0.005001050420105457,
-0.02744011953473091,
0.0685238167643547,
0.06131121888756752,
0.024702981114387512,
-0.04387263208627701,
-0.018593696877360344,
-0.01790754310786724,
-0.003317122347652912,
0.036716170608997345,
0.02059014141559601,
0.1006954163312912,
-0.03911712393164635,
-0.013327991589903831,
0.027630211785435677,
0.02447095885872841,
-0.02894054353237152,
0.019317684695124626,
-0.0250658318400383,
0.028185522183775902,
-0.032778944820165634,
-0.012566797435283661,
0.007866152562201023,
0.012363837100565434,
0.015523599460721016,
-0.032683830708265305,
-0.001595954643562436,
-0.002597612561658025,
0.039940863847732544,
-0.11619682610034943,
0.012954470701515675,
-0.015150466002523899,
0.028272554278373718,
0.03999817743897438,
-0.024035215377807617,
0.0027038478292524815,
0.036970093846321106,
0.04558933153748512,
0.07093651592731476,
-0.016309088096022606,
0.019465191289782524,
-0.023446548730134964,
-0.06529276072978973,
0.02218056656420231,
0.006776872090995312,
-0.023914124816656113,
-0.003482791827991605,
-0.03329329192638397,
0.008902204222977161,
-0.010569910518825054,
-0.08701099455356598,
0.01676744967699051,
0.016528911888599396,
-0.02361758053302765,
-0.04312099143862724,
0.01016505528241396,
0.06305357068777084,
0.013326370157301426,
-0.01004936546087265,
-0.0004934095195494592,
0.05906158685684204,
-0.008524510078132153,
-0.00427171029150486,
-0.01657012477517128,
0.010611780919134617,
0.02740468829870224,
-0.002691899659112096,
-0.03122146986424923,
0.0749707743525505,
0.010753304697573185,
-0.00918937474489212,
-0.007266214583069086,
-0.00979094859212637,
0.013166988268494606,
0.021158592775464058,
0.06813988089561462,
0.0435451976954937,
0.04022298380732536,
-0.09064382314682007,
-0.015011155046522617,
0.0005304834921844304,
-0.007968106307089329,
-0.025397194549441338,
0.004587700590491295,
-0.02101411670446396,
-0.07487361878156662,
-0.03043542057275772,
0.053489647805690765,
-0.005399294197559357,
0.07553987205028534,
0.0013835853897035122,
-0.029286546632647514,
0.01238210778683424,
-0.02984912507236004,
-0.018761802464723587,
-0.005629184655845165,
0.01666196808218956,
0.031060082837939262,
-0.05115476995706558,
-0.007430240511894226,
-0.07430923730134964,
-0.011780857108533382,
0.06508102267980576,
0.06850111484527588,
-0.019834144040942192,
-0.02389558032155037,
0.03555284067988396,
-0.03535915166139603,
0.05354831740260124,
0.035658545792102814,
-0.08055825531482697,
-0.006348314695060253,
0.007228866685181856,
0.021865710616111755,
0.0445711612701416,
-0.020490523427724838,
0.05027424916625023,
0.022184476256370544,
0.007861847057938576,
-0.01303055975586176,
0.014905188232660294,
0.08369630575180054,
0.004880647175014019,
0.02471633069217205,
-0.002743629040196538,
-0.002209217520430684,
-0.035973187536001205,
-0.035188302397727966,
0.08896352350711823,
-0.008301670663058758,
0.011845985427498817,
0.017829352989792824,
-0.02102578803896904,
-0.028597334399819374,
0.012834957800805569,
0.020525852218270302,
-0.03479490801692009,
0.005617460235953331,
0.04641987755894661,
0.012602074071764946,
-0.05850687995553017,
-0.008441240526735783,
0.04879530519247055,
-0.044012587517499924,
0.034416019916534424,
0.05477207526564598,
0.003977264743298292,
0.019467053934931755,
0.008688293397426605,
-0.006006904412060976,
0.0030490478966385126,
-0.06303518265485764,
0.01466129906475544,
0.01066452544182539,
-0.06768631935119629,
0.04814926162362099,
0.046813566237688065,
-0.0077413409017026424,
0.05260525643825531,
-0.004491541069000959,
0.02797824703156948,
0.06425052881240845,
0.033109117299318314,
-0.009700916707515717,
0.008482648991048336,
-0.006295220460742712,
-0.06051163747906685,
-0.052529387176036835,
-0.04659843444824219,
-0.012248488143086433,
-0.029940830543637276,
0.02304370515048504,
-0.03876584395766258,
0.014322074130177498,
-0.017594436183571815,
0.040403638035058975,
-0.012050791643559933,
0.02557324804365635,
-0.015249366872012615,
-0.02595355175435543,
-0.015082728117704391,
-0.02136632800102234,
-0.02471713349223137,
-0.019141165539622307,
-0.04672697186470032,
0.049970921128988266,
0.0049277422949671745,
-0.01256017666310072,
-0.02492796629667282,
0.034982699900865555,
0.02888704091310501,
0.06379352509975433,
0.020994408056139946,
0.0007226855377666652,
-0.07739230990409851,
-0.037450894713401794,
0.00995673518627882,
-0.024113545194268227,
0.0718294233083725,
-0.03164695203304291,
0.027950292453169823,
0.030043084174394608,
0.00914432667195797,
0.012060971930623055,
0.11194252967834473,
0.03077392280101776,
-0.0312996506690979,
-0.010367898270487785,
-0.0173280518501997,
0.014712494798004627,
0.03069102019071579,
0.001348846941255033,
-0.010795768350362778,
0.04391421377658844,
-0.00533391535282135,
0.015881715342402458,
0.07112935185432434,
0.025894084945321083,
0.011844011954963207,
0.01298915222287178,
0.0050792088732123375,
0.0013364768819883466,
0.024470418691635132,
0.008718703873455524,
-0.02060694433748722,
-0.03095226362347603,
-0.010004984214901924,
0.019078582525253296,
-0.011468686163425446,
-0.00020301822223700583,
-0.01839590258896351,
0.004258543718606234,
-0.027939874678850174,
-0.06256995350122452,
-0.08760324120521545,
0.017817461863160133,
-0.007553539704531431,
-0.040215764194726944,
-0.019111067056655884,
0.044049739837646484,
0.04272790253162384,
0.00878662709146738,
-0.007263493724167347,
0.013074707239866257,
-0.06258651614189148,
0.003068248275667429,
0.0013467323733493686,
0.01284630224108696,
0.04781012237071991,
0.006792485248297453,
-0.031477682292461395,
-0.0026523673441261053,
0.009790821000933647,
-0.03137509152293205,
0.026664206758141518,
0.01469308789819479,
-0.018691079691052437,
-0.04983852058649063,
-0.012869144789874554,
-0.06717240810394287,
-0.013730496168136597,
0.017748920246958733,
-0.03522380068898201,
-0.010887045413255692,
0.007923777215182781,
-0.10041535645723343,
-0.04194003343582153,
-0.040333788841962814,
-0.019222943112254143,
0.01243670005351305,
0.05524930730462074,
0.01006993092596531,
0.010880501940846443,
-0.03759248927235603,
0.0315224826335907,
0.06398382037878036,
0.018898895010352135,
0.05205736681818962,
-0.00001114714268624084,
0.02571404166519642,
-0.04572092741727829,
0.009002616629004478,
-0.0421665795147419,
0.017116939648985863,
-0.04760361462831497,
0.01990174688398838,
0.01633669063448906,
0.04157216101884842,
0.01187452208250761,
0.014449253678321838,
-0.006696885451674461,
-0.058752935379743576,
-0.01819051429629326,
-0.05630611255764961,
0.05849071219563484,
-0.061073362827301025,
0.02871609479188919,
-0.0033298751804977655,
0.030927635729312897,
-0.027030451223254204,
-0.03839718922972679,
-0.024011578410863876,
-0.043504223227500916,
0.0034463328775018454,
-0.010614797472953796,
-0.03684420511126518,
-0.010547908022999763,
-0.0625901073217392,
0.04762988165020943,
-0.01839478500187397,
0.07855542004108429,
-0.0014329556142911315,
0.007337210234254599,
0.05533554032444954,
-0.029830852523446083,
0.004943451378494501,
-0.0006155879236757755,
0.0032672230154275894,
0.023382505401968956,
-0.009908848442137241,
-0.031092464923858643,
0.006005501840263605,
-0.0158978383988142,
-0.01023250911384821,
-0.03850525617599487,
-0.012148324400186539,
-0.03876342996954918,
0.02162986993789673,
0.005581495352089405,
0.021401360630989075,
0.007895075716078281,
-0.0002993330708704889,
0.02587074227631092,
0.01927926205098629,
-0.043405931442976,
-0.02822134830057621,
0.051683176308870316,
0.028588222339749336,
-0.027042970061302185,
0.08287501335144043,
0.006030062213540077,
-0.031147649511694908,
-0.058688219636678696,
-0.04727208986878395,
0.0014625340700149536,
-0.04932747036218643,
0.015737013891339302,
0.03622664883732796,
-0.032790567725896835,
0.00014850948355160654,
-0.039874784648418427,
-0.053361911326646805,
-0.037450481206178665,
0.0317981094121933,
0.04084852710366249,
-0.026362096890807152,
-0.04465576261281967,
-0.0622568242251873,
-0.039267320185899734,
0.0014603098388761282,
-0.0027388238813728094,
-0.001862144097685814,
-0.03925076499581337,
-0.048816025257110596,
0.04604124277830124,
0.018976230174303055,
0.013938858173787594,
-0.01022365316748619,
0.001750591560266912,
-0.02222534827888012,
0.022915953770279884,
-0.04424166679382324,
0.039491768926382065,
0.024221358820796013,
0.04118756204843521,
-0.0238629262894392,
-0.010441075079143047,
0.00025413924595341086,
0.022464200854301453,
0.030790766701102257,
-0.05165039375424385,
0.02753392606973648,
0.07543782144784927,
0.0068360487930476665,
-0.0411871112883091,
0.02151249349117279,
-0.00530714588239789,
-0.004161479417234659,
-0.0614316388964653,
0.030101848766207695,
-0.008170067332684994,
-0.04017021134495735,
-0.004293257370591164,
0.027857830747961998,
0.005252076778560877,
0.09320587664842606,
-0.03283674269914627,
-0.04694431275129318,
0.01628907397389412,
0.004308621399104595,
0.01578102633357048,
-0.02487719990313053,
0.03992711007595062,
0.03483698517084122,
0.024332057684659958,
-0.0007104675751179457,
0.044844288378953934,
0.0357501320540905,
-0.02715892344713211,
-0.032165080308914185,
0.010387475602328777,
-0.007301720324903727,
0.020936336368322372,
-0.12330222874879837,
-0.026429004967212677,
0.0012774744536727667,
-0.012065570801496506,
-0.005998364649713039,
0.00991637259721756,
0.04354538396000862,
0.008660397492349148,
0.024601783603429794,
-0.004781808238476515,
-0.019195804372429848,
-0.004921379033476114,
-0.0473216213285923,
-0.03089609183371067,
0.02015761286020279,
0.01606544852256775,
-0.03866707161068916,
0.040292590856552124,
0.0036942996084690094,
-0.02685929648578167,
0.06492409855127335,
-0.05223240703344345,
0.01589183323085308,
-0.01648533344268799,
-0.02863982319831848,
0.025440890341997147,
0.04974064975976944,
0.012370649725198746,
0.051197350025177,
0.07455036044120789,
0.025231556966900826,
-0.0168626606464386,
-0.0010400133905932307,
0.02690114453434944,
0.011166232638061047,
-0.034364040940999985,
-0.016165772452950478,
-0.013424268923699856,
-0.038986433297395706,
-0.005115763749927282,
0.0006427849875763059,
-0.022180112078785896,
0.011616416275501251,
0.045213621109724045,
0.03653353825211525,
0.046996716409921646,
-0.05403001606464386,
-0.012910585850477219,
-0.003650825470685959,
0.06665697693824768,
-0.0109574468806386,
0.051892779767513275,
0.026582160964608192,
-0.022472476586699486,
-0.024990525096654892,
0.04521000385284424,
0.0005417142529040575,
-0.012811051681637764,
0.051978107541799545,
-0.034508612006902695,
-0.010762304067611694,
-0.03196531906723976,
-0.004830218385905027,
-0.010264554060995579,
0.0029833815060555935,
-0.048083141446113586,
0.0236015897244215,
0.025086550042033195,
-0.010265805758535862,
0.0064477138221263885,
0.03835432231426239,
-0.04047747701406479,
-0.021840697154402733,
-0.03134242072701454,
-0.06191233918070793,
-0.05478833243250847,
-0.006842972710728645,
-0.00824335590004921,
-0.029661720618605614,
-0.013416976667940617,
-0.0398656390607357,
-0.0013805970083922148,
-0.06573521345853806,
-0.01087508350610733,
0.01648113504052162,
0.05849709361791611,
-0.04049161076545715,
-0.030976641923189163,
0.03264031931757927,
-0.008420574478805065,
0.02786044217646122,
0.0033544579055160284,
-0.05652957409620285,
-0.045669522136449814,
-0.01339946873486042,
0.00784417986869812,
-0.030850427225232124,
-0.008826939389109612,
-0.033313166350126266,
0.02565230242908001,
0.00513444235548377,
0.002584555884823203,
0.04403113201260567,
0.03688434511423111,
-0.022359535098075867,
0.01128718163818121,
-0.005332587752491236,
-0.04106718301773071,
0.0030580523889511824,
0.05520453676581383,
0.009393131360411644,
-0.030148189514875412,
-0.047188423573970795,
-0.052622225135564804,
0.02493446320295334,
-0.017870116978883743,
0.037662237882614136,
0.007507555652409792,
0.025737430900335312,
0.0015593310818076134
] |
<p>Got two accelerometers that are measuring accelerations oriented at +/- 45 deg from horizontal. I am looking to determine the conversion of the accelerometer measured data to accelerations in the vertical and horizontal direction. Can I use coordinate system conversion below ?</p>
<p>$$F_{Vertical} = (F_1 + F_2) \cos(\frac{\pi}{4})$$</p>
<p>$$F_{Horizontal} = (F_1 - F_2) \cos (\frac{\pi}{4})$$
<img src="http://i.stack.imgur.com/KKydJ.jpg" alt="enter image description here"></p>
<p>I don't know phase relationship, but I can assume they are out of phase since I know the vertical acceleration is high and the horizontal acceleration is small.</p>
<p>Are the conversions above correct ?</p> | g7797 | [
0.039836131036281586,
-0.018307991325855255,
-0.003830120898783207,
-0.014899940229952335,
0.05538295954465866,
-0.01391051895916462,
-0.007501355372369289,
0.00012706013512797654,
-0.08884509652853012,
-0.030957579612731934,
-0.0012640393106266856,
0.041134919971227646,
-0.02069868892431259,
0.0034511189442127943,
0.016151191666722298,
-0.02198249287903309,
0.018474990501999855,
-0.008337833918631077,
-0.040894437581300735,
0.01392768882215023,
0.044745028018951416,
-0.011317958123981953,
-0.06168954819440842,
-0.03495986387133598,
0.06790947169065475,
-0.024410605430603027,
0.008880157954990864,
-0.060297802090644836,
-0.09804663807153702,
0.011324073188006878,
0.016269827261567116,
0.0220303013920784,
0.023999279364943504,
-0.011943304911255836,
-0.002151364693418145,
-0.052317772060632706,
0.020086120814085007,
-0.010354002937674522,
0.0010052435100078583,
-0.027238840237259865,
0.05053571239113808,
-0.02126152440905571,
0.05573143810033798,
0.011043494567275047,
0.026134656742215157,
-0.041115161031484604,
-0.026726234704256058,
-0.006036017090082169,
-0.0042211818508803844,
0.020260319113731384,
-0.0342041477560997,
0.030670402571558952,
-0.026463838294148445,
0.06496718525886536,
-0.036710623651742935,
0.10010535269975662,
0.03292226046323776,
0.005960831884294748,
0.05502323433756828,
0.03650946915149689,
-0.08944648504257202,
0.001295517897233367,
0.05636388435959816,
-0.04733775183558464,
0.06304808706045151,
0.016228267922997475,
-0.008244987577199936,
-0.03930399566888809,
0.006408961955457926,
-0.025905093178153038,
0.021432947367429733,
-0.01547599583864212,
0.048419978469610214,
0.007648383732885122,
-0.019845908507704735,
0.009302089922130108,
-0.0030367476865649223,
-0.0628364235162735,
0.001511037116870284,
0.009953273460268974,
-0.002135057235136628,
-0.0004258384869899601,
0.00687412079423666,
-0.02253669872879982,
0.07807283103466034,
0.0020518156234174967,
0.02016354352235794,
0.034617990255355835,
-0.020522091537714005,
-0.024733873084187508,
0.0020372753497213125,
0.029134970158338547,
0.07146722078323364,
0.045042265206575394,
-0.050561025738716125,
0.0026133458595722914,
-0.015769027173519135,
0.0759727731347084,
0.04009968787431717,
-0.012440016493201256,
-0.05016302317380905,
0.013856309466063976,
0.009670861065387726,
-0.020976856350898743,
0.008221063762903214,
-0.015979446470737457,
0.0789414495229721,
0.01207016035914421,
-0.006704343948513269,
-0.08852004259824753,
-0.012962797656655312,
-0.020016035065054893,
-0.039814360439777374,
-0.06154588982462883,
-0.012678969651460648,
0.026245875284075737,
0.06282762438058853,
0.03921259567141533,
0.02983376383781433,
0.016088616102933884,
0.06055580452084541,
-0.022777831181883812,
0.027023687958717346,
0.07626616954803467,
-0.029651494696736336,
-0.02755752205848694,
-0.008579413406550884,
-0.012486528605222702,
0.06177397444844246,
-0.03517357259988785,
-0.025721518322825432,
-0.03673851862549782,
0.04276508837938309,
-0.008064310997724533,
0.005167632829397917,
-0.02416694164276123,
0.05984057858586311,
0.016320226714015007,
0.03432281315326691,
0.011891782283782959,
-0.010486726649105549,
-0.0727357417345047,
-0.006714262533932924,
-0.013586698099970818,
0.01968456618487835,
0.03314312919974327,
-0.02704945206642151,
0.014551087282598019,
0.07465265691280365,
0.05093131214380264,
-0.024755258113145828,
0.021548885852098465,
0.014766545034945011,
-0.001087756478227675,
0.0059576877392828465,
-0.04907664284110069,
-0.008590981364250183,
-0.0023003967944532633,
-0.01231470238417387,
-0.027147959917783737,
0.006522321607917547,
0.010045547038316727,
0.04411621019244194,
0.011477510444819927,
-0.045179545879364014,
-0.013468476943671703,
-0.04231930151581764,
-0.04503479599952698,
-0.014181961305439472,
-0.023904945701360703,
-0.033166103065013885,
0.03638482466340065,
0.05735298618674278,
-0.020542584359645844,
0.01894882135093212,
0.06441229581832886,
-0.00980998482555151,
0.011741912923753262,
0.05695051699876785,
0.015903687104582787,
-0.007993154227733612,
0.017942531034350395,
0.012925243005156517,
0.008793655782938004,
-0.018518753349781036,
-0.027196703478693962,
0.07559769600629807,
0.03669271245598793,
-0.08574487268924713,
0.03254019469022751,
0.026353854686021805,
-0.007362314499914646,
-0.05357205495238304,
0.03477907553315163,
-0.030769940465688705,
-0.007627076469361782,
-0.023175697773694992,
0.0003352898929733783,
-0.014749366790056229,
0.04312620684504509,
0.025396522134542465,
0.03504544869065285,
0.03495197370648384,
0.0199295524507761,
0.07988277822732925,
-0.03695552796125412,
0.00826067104935646,
-0.05717173591256142,
-0.0009424469317309558,
0.04714732617139816,
-0.053235262632369995,
0.07223440706729889,
-0.030542707070708275,
0.013467575423419476,
0.029457321390509605,
-0.037810761481523514,
0.06970363855361938,
-0.0030498069245368242,
-0.02960234135389328,
0.03746573254466057,
-0.013149330392479897,
-0.006335125304758549,
0.04783569648861885,
-0.0178834181278944,
0.010609193705022335,
-0.02623843401670456,
-0.018154526129364967,
-0.008758620359003544,
-0.009447956457734108,
-0.045692767947912216,
-0.024809665977954865,
-0.001524211373180151,
0.004383530467748642,
-0.001341851195320487,
0.054848991334438324,
0.03475572541356087,
-0.029764359816908836,
0.011662717908620834,
0.009244871325790882,
0.07466533035039902,
-0.012576834298670292,
-0.06417249143123627,
-0.01783333159983158,
-0.04712413251399994,
0.09245984256267548,
0.009101959876716137,
0.08684023469686508,
0.08551889657974243,
-0.005159866530448198,
0.013487067073583603,
-0.0028189283329993486,
0.00791965238749981,
-0.0632341280579567,
0.006873362697660923,
-0.05291815847158432,
0.015620417892932892,
-0.03173566982150078,
-0.0028145057149231434,
-0.02185416780412197,
-0.03004472516477108,
-0.01849554479122162,
-0.06512369960546494,
-0.03519834578037262,
0.027780117467045784,
-0.021259672939777374,
-0.016026370227336884,
-0.019800253212451935,
0.0004293735255487263,
0.0360141396522522,
-0.0019939467310905457,
0.013496486470103264,
0.04505135118961334,
0.02706088498234749,
0.06906184554100037,
-0.031519241631031036,
-0.02808775193989277,
0.024722665548324585,
0.013987094163894653,
0.013483203947544098,
0.0018952015088871121,
-0.015980415046215057,
0.0004427876556292176,
0.02106425352394581,
0.06888251006603241,
0.06065059080719948,
0.06863658130168915,
-0.007912810891866684,
0.004829956218600273,
-0.022000698372721672,
0.03756362199783325,
-0.013948099687695503,
-0.017198471352458,
0.03539547696709633,
-0.03724516183137894,
-0.008242644369602203,
0.032100386917591095,
0.05746600776910782,
-0.02528807893395424,
0.06715267896652222,
0.015563499182462692,
0.031984299421310425,
-0.02150103822350502,
-0.012097739614546299,
0.01880747079849243,
0.0017751657869666815,
-0.007256068754941225,
-0.027290495112538338,
-0.03366323560476303,
-0.02393222600221634,
-0.04029626026749611,
-0.0755067765712738,
-0.0037001597229391336,
0.003492660354822874,
0.009320523589849472,
-0.030106302350759506,
-0.03602280095219612,
-0.004138730466365814,
-0.008890527300536633,
0.0061277104541659355,
0.0200627613812685,
-0.06321251392364502,
-0.09200670570135117,
-0.006351122632622719,
0.01910104602575302,
0.01028304360806942,
0.007788191083818674,
-0.007430621888488531,
0.013695886358618736,
-0.00740030175074935,
-0.034046098589897156,
-0.005019984673708677,
-0.047088176012039185,
0.04655875638127327,
-0.02189360000193119,
-0.008977841585874557,
-0.005447093863040209,
-0.06598710268735886,
0.004827017895877361,
-0.014668911695480347,
-0.004773509223014116,
-0.02611188217997551,
0.027215013280510902,
-0.031703393906354904,
0.027273230254650116,
-0.028113579377532005,
-0.011167078278958797,
0.03128941357135773,
0.031548239290714264,
0.0157172754406929,
-0.08069209009408951,
-0.016942521557211876,
0.028238637372851372,
0.0292687825858593,
-0.020237548276782036,
-0.024767687544226646,
0.007320600561797619,
0.05381922051310539,
0.05816815793514252,
-0.07432393729686737,
0.03260970488190651,
-0.025209974497556686,
-0.012144097127020359,
-0.014295855537056923,
0.02617836371064186,
-0.049430929124355316,
-0.012217960320413113,
-0.080684132874012,
0.05419037863612175,
-0.0284387469291687,
-0.05891004577279091,
0.005868218373507261,
-0.03200560063123703,
0.05532781779766083,
-0.042633410543203354,
-0.02709672972559929,
-0.08569987118244171,
0.013645135797560215,
-0.05980849266052246,
-0.011707499623298645,
0.0537443608045578,
-0.0014672060497105122,
-0.004275456070899963,
0.012589538469910622,
-0.010014653205871582,
0.0317155122756958,
-0.022279534488916397,
0.002400389639660716,
0.03811731934547424,
-0.0020727310329675674,
-0.044851019978523254,
0.03484824299812317,
-0.04700181633234024,
-0.048007965087890625,
0.04624653235077858,
0.021270692348480225,
-0.010798902250826359,
0.03142809495329857,
0.006872229278087616,
-0.013349363580346107,
0.030114496126770973,
-0.03762414678931236,
-0.031249409541487694,
0.019385389983654022,
0.022941000759601593,
-0.021607128903269768,
0.05654827132821083,
-0.0024862682912498713,
-0.02496935799717903,
-0.012239579111337662,
0.007821159437298775,
0.004747398197650909,
0.006348979659378529,
0.04341605305671692,
-0.01734231784939766,
0.05371208116412163,
0.014809289947152138,
0.03608325868844986,
-0.0287916362285614,
0.03647204115986824,
-0.016535937786102295,
0.012875996530056,
0.060673486441373825,
0.054873500019311905,
-0.018080368638038635,
0.0014896754873916507,
0.11445590108633041,
0.005015289410948753,
-0.03603275865316391,
-0.015101665630936623,
0.06087624654173851,
0.011005581356585026,
0.006208134815096855,
0.0975802019238472,
0.006691711023449898,
-0.03410254046320915,
0.022293247282505035,
-0.012926478870213032,
0.03668342903256416,
0.04605661332607269,
0.02451026812195778,
-0.015338285826146603,
-0.0008406529086641967,
-0.008283067494630814,
-0.03751984238624573,
-0.03141475096344948,
0.043939393013715744,
-0.018336905166506767,
-0.025133280083537102,
0.011388005688786507,
-0.0636875331401825,
0.00040797857218421996,
-0.02066495642066002,
-0.02852538600564003,
0.009116634726524353,
-0.016518782824277878,
-0.022093700245022774,
0.020855525508522987,
0.005567902233451605,
-0.033024273812770844,
0.030925169587135315,
-0.04387430101633072,
-0.009212653152644634,
0.01440149825066328,
-0.03744710609316826,
-0.0010630745673552155,
-0.010140295140445232,
-0.04561270400881767,
-0.039398420602083206,
-0.049762826412916183,
-0.005839018151164055,
-0.017507556825876236,
-0.07790033519268036,
0.018958693370223045,
0.025032980367541313,
0.06643716245889664,
0.03257346525788307,
-0.014878234826028347,
0.01698419265449047,
0.026738598942756653,
-0.017937973141670227,
-0.015475289896130562,
0.015570631250739098,
0.03185510262846947,
-0.04412843659520149,
-0.015737706795334816,
0.042348816990852356,
-0.017578531056642532,
-0.022704334929585457,
0.02792428992688656,
-0.02968372218310833,
-0.04705779254436493,
0.038243331015110016,
-0.005810202099382877,
-0.05069000646471977,
0.016404828056693077,
0.0059343366883695126,
-0.007081148214638233,
-0.06383838504552841,
-0.009183880873024464,
-0.0035918017383664846,
-0.050325289368629456,
0.06691707670688629,
-0.010876981541514397,
0.0398007407784462,
-0.007672119420021772,
0.04859359189867973,
0.07335744798183441,
0.0035108732990920544,
0.03952925652265549,
0.029356984421610832,
0.005650634411722422,
0.034600939601659775,
0.015181252732872963,
0.0003266561252530664,
-0.01598103903234005,
-0.0286399032920599,
0.010595248080790043,
0.019676772877573967,
0.014467326924204826,
-0.0556841604411602,
0.06291983276605606,
-0.030323266983032227,
0.05735226348042488,
0.008693451061844826,
-0.0005674753920175135,
-0.024435726925730705,
-0.020113565027713776,
-0.003342360956594348,
0.017528418451547623,
-0.030622247606515884,
-0.01805354468524456,
-0.024329774081707,
-0.0062140184454619884,
-0.009710180573165417,
-0.015085442923009396,
-0.03983234614133835,
-0.04503213241696358,
-0.0358688123524189,
0.049105990678071976,
-0.016817204654216766,
-0.06924504786729813,
0.004866034723818302,
0.004556972533464432,
0.042612940073013306,
-0.04894547536969185,
0.025135019794106483,
-0.03330564871430397,
0.0024838868994265795,
-0.010532173328101635,
0.05795121565461159,
-0.0493241548538208,
0.05677557364106178,
0.013527699746191502,
-0.07966645807027817,
-0.022100072354078293,
0.0563553124666214,
-0.017506984993815422,
0.03205239027738571,
0.0013524983078241348,
-0.02388128824532032,
0.07983214408159256,
-0.038812678307294846,
0.027539202943444252,
0.03161479905247688,
-0.0031492963898926973,
-0.003508302615955472,
0.03341032937169075,
0.024616654962301254,
-0.0008417986100539565,
0.020694607868790627,
0.010931947268545628,
-0.043811582028865814,
-0.04426664113998413,
0.0735202506184578,
0.05061325058341026,
-0.011136595159769058,
-0.04588470607995987,
0.031763505190610886,
0.023915881291031837,
-0.005063030403107405,
-0.0156557634472847,
-0.019175684079527855,
-0.031059173867106438,
-0.004412276670336723,
-0.029687251895666122,
0.015590953640639782,
-0.025323117151856422,
-0.01022409275174141,
-0.039110392332077026,
-0.06656655669212341,
-0.04901770502328873,
0.002001846907660365,
-0.028417881578207016,
0.03098296746611595,
-0.024199433624744415,
-0.005015878938138485,
0.022062409669160843,
0.043810464441776276,
-0.004125111270695925,
0.045311711728572845,
0.05139145627617836,
0.011605454608798027,
0.01721910759806633,
-0.018870072439312935,
-0.010395260527729988,
-0.04417669400572777,
-0.016315272077918053,
0.08148587495088577,
0.04101232811808586,
-0.06693123281002045,
-0.051264066249132156,
-0.016103731468319893,
-0.03563535585999489,
0.03521621227264404,
0.021002687513828278,
0.04588836804032326,
0.08080603927373886,
-0.022146428003907204,
-0.005827519576996565,
0.011159922927618027,
0.02107924222946167,
-0.009807930327951908,
-0.06529085338115692,
-0.03771505877375603,
-0.04126247763633728,
0.012214628048241138,
0.008821574971079826,
0.008894301019608974,
0.03186769038438797,
0.02197924628853798,
-0.03071463108062744,
-0.01124659739434719,
0.04246063902974129,
-0.04749348387122154,
0.04071689397096634,
0.08902459591627121,
-0.024699680507183075,
-0.0027984194457530975,
0.04254522547125816,
0.06881692260503769,
0.03541521728038788,
0.015268394723534584,
-0.05385935306549072,
0.02516046352684498,
-0.07380081713199615,
-0.024341268464922905,
0.022571900859475136,
-0.012524080462753773,
-0.03580470383167267,
0.06549835950136185,
0.013070105575025082,
-0.020224805921316147,
0.004079986363649368,
0.047883134335279465,
-0.03546144813299179,
0.026994597166776657,
0.04119034484028816,
0.04713239148259163,
0.005839346908032894,
0.009096469730138779,
-0.026291796937584877,
-0.040052689611911774,
-0.015589485876262188,
0.013662111945450306,
-0.04250657185912132,
-0.04085367172956467,
-0.0213357862085104,
0.008698396384716034,
-0.016770895570516586,
-0.05221734195947647,
0.010697977617383003,
-0.017183024436235428,
-0.027028203010559082,
-0.008265877142548561,
0.010911804623901844,
0.03033583052456379,
-0.010068411938846111,
-0.0410081148147583,
-0.022442679852247238,
0.02971121110022068,
-0.022635018453001976,
0.014120086096227169,
-0.010728539898991585,
0.03791842237114906,
-0.0548204742372036,
0.051947854459285736,
0.010066164657473564,
-0.009803012944757938,
0.015770768746733665,
-0.025388026610016823,
-0.10282040387392044,
0.01233754213899374,
0.043477583676576614,
-0.039574507623910904,
0.00754019059240818,
-0.0007016806048341095,
0.0112041300162673,
0.06889719516038895,
-0.02975991927087307,
-0.00493002450093627,
0.089727021753788,
0.03475265949964523,
-0.016273438930511475,
0.04816652461886406,
-0.00037564142257906497,
-0.005279660224914551,
0.006290994118899107,
-0.04197847843170166,
0.022749366238713264,
-0.030787665396928787,
-0.04242401942610741,
0.042746998369693756,
0.0000956949224928394,
0.029449399560689926,
0.01783759891986847,
0.0296051986515522,
-0.03489934280514717,
0.008312921039760113,
-0.015237443149089813,
-0.0009586497326381505,
-0.06408807635307312,
-0.1115536019206047,
-0.015287978574633598,
-0.04786285012960434,
-0.008757156319916248,
-0.013418701477348804,
-0.014739693142473698,
0.009732676669955254,
0.0018651691498234868,
-0.08362554013729095,
-0.021611075848340988,
-0.019472580403089523,
0.005065844859927893,
0.05313858017325401,
-0.04650511592626572,
-0.020848697051405907,
0.001099485089071095,
-0.034659840166568756,
-0.06841795146465302,
0.019119534641504288,
0.01372029073536396,
0.04660249873995781,
-0.02332710474729538,
0.0046416353434324265,
-0.024613263085484505,
-0.036752235144376755,
0.020448986440896988,
0.07218070328235626,
0.023959016427397728,
-0.027549168094992638,
0.06297207623720169,
0.022670365869998932,
-0.014277039095759392,
0.009455740451812744,
-0.052299097180366516,
-0.008593343198299408,
-0.00572065869346261,
-0.013008135370910168,
0.04249332472681999,
-0.014562767930328846,
0.02708475850522518,
0.04287363961338997,
-0.05597928166389465,
-0.003640984883531928,
-0.01963070221245289,
-0.026171386241912842,
-0.06304126977920532,
0.009283236227929592
] |
<p><a href="http://en.wikipedia.org/wiki/Work_%28physics%29">Work</a> is defined as</p>
<p>$$W = \vec{F}\cdot\vec{s}$$</p>
<p>But what what exactly is $\vec{s}$? Is it the displacement of the body on which the force is being applied? Or is it the displacement of the point of application of the force? </p>
<p>If you look at the derivation for the definition of work from kinetic energy (the way many textbooks do it), it would seem to be the former, but I'm not sure since I can think of many examples that contradict the fact.</p>
<p>Or is it something else entirely? </p> | g7798 | [
0.07844126224517822,
0.03177550062537193,
-0.030812526121735573,
-0.008606398478150368,
0.04699962958693504,
0.009076121263206005,
0.02036273665726185,
0.038121361285448074,
-0.0194209273904562,
-0.005010214168578386,
-0.03561748191714287,
-0.024727053940296173,
-0.004171653185039759,
-0.027938449755311012,
0.0022767004556953907,
-0.015714293345808983,
0.008481800556182861,
-0.013709964230656624,
0.01086468156427145,
0.029970986768603325,
0.002964453073218465,
0.02976062521338463,
-0.06094221770763397,
-0.03326037526130676,
0.021991362795233727,
-0.01508670300245285,
0.011147445999085903,
-0.00791252963244915,
-0.027575481683015823,
-0.03431925177574158,
0.02246834896504879,
0.015959318727254868,
0.0505475178360939,
-0.030152833089232445,
-0.02298283390700817,
-0.006994075607508421,
0.03825303539633751,
0.028186289593577385,
0.09133508801460266,
-0.03012925572693348,
-0.06491219997406006,
-0.009709023870527744,
0.01329351682215929,
0.033443331718444824,
0.00916079431772232,
0.0024759273510426283,
-0.08826889842748642,
-0.018394779413938522,
-0.03544043004512787,
-0.01959512010216713,
0.013359563425183296,
0.02349422313272953,
0.009687069803476334,
0.035482075065374374,
0.05296826735138893,
-0.055807434022426605,
0.027023324742913246,
-0.002726351609453559,
0.008585947565734386,
-0.03005291149020195,
0.005378507077693939,
0.03073873184621334,
0.026316730305552483,
-0.012724161148071289,
0.047905098646879196,
-0.05951152741909027,
-0.005841606296598911,
0.028719419613480568,
0.021597089245915413,
-0.0256943516433239,
0.0036472941283136606,
-0.01691947504878044,
0.007038278970867395,
0.009323951788246632,
-0.035844530910253525,
-0.020743627101182938,
0.021199366077780724,
-0.028539668768644333,
0.002519206376746297,
0.010582339949905872,
0.0009166993550024927,
-0.020876286551356316,
-0.012613781727850437,
-0.028345512226223946,
0.08890951424837112,
-0.005552919115871191,
0.010014708153903484,
0.027196237817406654,
0.030501963570713997,
0.02128499746322632,
0.04161558672785759,
0.03142477944493294,
0.0821305513381958,
-0.003833439666777849,
-0.08636259287595749,
-0.06431671977043152,
-0.016124200075864792,
0.0342450812458992,
-0.03232654184103012,
0.02167109213769436,
-0.04981375113129616,
-0.07243523001670837,
-0.0018419910920783877,
-0.03162264823913574,
0.0487527996301651,
-0.03687794879078865,
0.015904296189546585,
-0.037845972925424576,
0.025586191564798355,
-0.0212937630712986,
-0.03515145182609558,
-0.013454198837280273,
-0.0033754319883883,
-0.015951817855238914,
-0.027492903172969818,
-0.05285569280385971,
0.027086589485406876,
-0.024082576856017113,
-0.02549505978822708,
0.031575389206409454,
0.032014183700084686,
-0.00006692752504022792,
-0.005629541352391243,
0.045260027050971985,
-0.03925105929374695,
-0.043967053294181824,
0.014171082526445389,
-0.008694607764482498,
0.02895905263721943,
0.003996134269982576,
0.04353013634681702,
0.025626668706536293,
-0.03206833824515343,
0.017914898693561554,
-0.01654093712568283,
0.007555234245955944,
-0.05363788828253746,
0.0009563473868183792,
-0.0331275649368763,
0.039058927446603775,
0.051993221044540405,
-0.005140542518347502,
0.011696869507431984,
-0.06668965518474579,
-0.05084008350968361,
-0.005201905034482479,
-0.028450319543480873,
-0.03931226581335068,
0.04237887263298035,
-0.033561527729034424,
0.007664050441235304,
0.05106170102953911,
-0.007928350940346718,
-0.12995637953281403,
0.10116949677467346,
-0.019488036632537842,
0.03827116638422012,
0.0329912006855011,
-0.009037178941071033,
0.031793832778930664,
0.07577021420001984,
-0.00027368945302441716,
0.05556582286953926,
0.004150770138949156,
0.007312166504561901,
-0.03218696266412735,
-0.04378405213356018,
-0.042258504778146744,
0.016216618940234184,
0.010127547197043896,
-0.08420819789171219,
-0.035276103764772415,
-0.012982725165784359,
0.05631209537386894,
-0.020374774932861328,
0.0253140889108181,
0.014511683955788612,
0.011773495003581047,
-0.028328625485301018,
0.09237658977508545,
-0.038489241153001785,
-0.03923811390995979,
0.01902781054377556,
-0.05044328048825264,
-0.019514281302690506,
-0.0030242563225328922,
-0.05307323858141899,
-0.03255603089928627,
-0.06439302861690521,
0.012200814671814442,
-0.02636958658695221,
-0.05522538721561432,
0.06445474177598953,
0.010708960704505444,
-0.06275108456611633,
0.006748099345713854,
-0.023292241618037224,
-0.04081200063228607,
0.01399570144712925,
-0.012851206585764885,
0.03077857568860054,
0.034629929810762405,
0.03056771494448185,
0.003588182618841529,
0.028376972302794456,
0.050028201192617416,
-0.012182933278381824,
0.007246879860758781,
-0.020548852160573006,
0.042349301278591156,
0.03953040763735771,
-0.026821373030543327,
-0.001500548212788999,
0.04650229215621948,
-0.039052654057741165,
-0.032701071351766586,
-0.04609033465385437,
-0.00985246803611517,
-0.039435144513845444,
-0.03802081570029259,
-0.042531028389930725,
0.014520428143441677,
0.01745576225221157,
0.031702347099781036,
-0.055821508169174194,
0.03564346581697464,
-0.04767154902219772,
-0.02154013328254223,
0.06341256201267242,
0.03019605576992035,
-0.03866869956254959,
0.04579830542206764,
-0.023317890241742134,
-0.0613161139190197,
0.05560814216732979,
0.05079686641693115,
-0.02144790254533291,
-0.0013535061152651906,
-0.0063812886364758015,
0.05854576453566551,
0.036182936280965805,
-0.09356740862131119,
-0.011770806275308132,
-0.0596037395298481,
0.012465202249586582,
0.02480994537472725,
0.07317730039358139,
-0.010631939396262169,
0.017566613852977753,
-0.04302545636892319,
-0.0052801440469920635,
-0.03963058069348335,
-0.01109180599451065,
0.0216851606965065,
0.051381465047597885,
0.045612234622240067,
-0.03923216462135315,
0.032593484967947006,
-0.07575392723083496,
-0.04433005303144455,
-0.015038869343698025,
0.0013329435605555773,
0.017880111932754517,
0.04075513035058975,
0.024969149380922318,
0.017938930541276932,
-0.02482745796442032,
0.055961139500141144,
0.055310845375061035,
-0.042927782982587814,
0.017131827771663666,
0.05523189902305603,
-0.018213048577308655,
-0.022752976045012474,
-0.004309399053454399,
-0.11170336604118347,
0.029123447835445404,
-0.04490486532449722,
0.029902121052145958,
-0.03883703425526619,
-0.033911142498254776,
0.02343842014670372,
0.009384581819176674,
0.04695765674114227,
0.01857667975127697,
-0.03063485026359558,
-0.0006673747557215393,
-0.025529053062200546,
-0.05836966261267662,
-0.0951094776391983,
-0.017261117696762085,
-0.013030353002250195,
0.016615957021713257,
-0.05727503076195717,
-0.0008657671278342605,
0.04476974904537201,
0.06150456890463829,
-0.051892366260290146,
-0.02860843390226364,
0.05983344092965126,
0.0053253136575222015,
-0.009007617831230164,
-0.012203224934637547,
0.025298871099948883,
0.022946307435631752,
-0.00178372988011688,
0.020249567925930023,
-0.047035399824380875,
-0.04063800349831581,
0.005699038039892912,
-0.015029517002403736,
0.055740948766469955,
0.016132578253746033,
-0.04052002727985382,
-0.09430349618196487,
-0.020439043641090393,
-0.01509957853704691,
-0.047246530652046204,
0.011485098861157894,
-0.009435879997909069,
0.04121162369847298,
-0.0622425451874733,
0.06718669831752777,
0.037921201437711716,
0.044971976429224014,
0.05355212464928627,
-0.041704338043928146,
-0.013364722952246666,
-0.016158433631062508,
-0.04153647646307945,
-0.03549719601869583,
-0.01927218772470951,
-0.044970713555812836,
-0.03856942802667618,
-0.034594178199768066,
-0.0306997112929821,
-0.06449542939662933,
0.02645263634622097,
0.016126807779073715,
0.03978067636489868,
0.002558083040639758,
0.05013422667980194,
-0.013393023051321507,
0.016825590282678604,
0.042660586535930634,
0.022542834281921387,
-0.0006873864331282675,
0.02427482046186924,
0.017601724714040756,
-0.01619105413556099,
0.059043291956186295,
-0.012837542220950127,
-0.006694270763546228,
-0.018239235505461693,
-0.02399796061217785,
-0.025702793151140213,
0.03186408802866936,
0.005341783165931702,
-0.04538652300834656,
-0.012821384705603123,
0.026783322915434837,
0.03503197059035301,
0.027986064553260803,
0.04495834931731224,
-0.03687344491481781,
-0.0064077600836753845,
0.01205484103411436,
0.048042263835668564,
-0.0028980171773582697,
-0.03699776157736778,
0.011095762252807617,
-0.041682835668325424,
0.019779423251748085,
-0.007473885081708431,
0.03784377872943878,
-0.015930097550153732,
0.0227332953363657,
-0.006815450731664896,
-0.03828461095690727,
0.014241636730730534,
0.039583720266819,
0.04271925613284111,
-0.0060924384742975235,
0.016430320218205452,
0.015375262126326561,
-0.0013367070350795984,
-0.09290599822998047,
0.022442013025283813,
0.03873256966471672,
-0.026930782943964005,
-0.008825920522212982,
-0.005280231591314077,
-0.022318048402667046,
0.03106318600475788,
0.046538908034563065,
0.0040776715613901615,
0.022689463570713997,
0.031407345086336136,
0.02463340014219284,
0.0456361249089241,
0.037151869386434555,
0.0279564019292593,
-0.009490997530519962,
-0.011735044419765472,
-0.0038424371741712093,
0.015069575980305672,
0.020181581377983093,
-0.05771881341934204,
-0.013229251839220524,
0.0005465053836815059,
-0.010007400065660477,
-0.08678777515888214,
-0.02329408749938011,
-0.039089400321245193,
0.009943376295268536,
0.001561998506076634,
-0.027318667620420456,
-0.003867459949105978,
0.006936254911124706,
0.08408539742231369,
-0.010982676409184933,
0.03704414144158363,
0.07245688885450363,
0.0061048525385558605,
0.031184755265712738,
0.06637738645076752,
0.03155370429158211,
0.03215755522251129,
0.010681740008294582,
-0.06369263678789139,
0.011062280274927616,
0.02267731912434101,
0.02157599851489067,
0.018061669543385506,
-0.03184536471962929,
0.01870095729827881,
0.027340473607182503,
-0.01298624835908413,
0.011685848236083984,
0.024662960320711136,
0.06133420020341873,
0.02525484189391136,
-0.005120773799717426,
0.021958772093057632,
0.014266007579863071,
0.04386814683675766,
-0.028851116076111794,
-0.04637661203742027,
0.0008743409998714924,
-0.012016457505524158,
-0.06228991225361824,
0.035440586507320404,
-0.03623419255018234,
-0.00881680753082037,
0.024169113487005234,
0.02169659547507763,
0.01552178617566824,
-0.0646698996424675,
-0.02809068374335766,
-0.01616721600294113,
-0.057059451937675476,
-0.043743256479501724,
0.022630754858255386,
-0.0013296408578753471,
0.00013814914564136416,
0.034050438553094864,
-0.013522769324481487,
0.01939336769282818,
-0.09109023213386536,
0.05044569447636604,
-0.01487729325890541,
0.008665518835186958,
0.00046703984844498336,
0.0219900980591774,
0.055979058146476746,
0.030843449756503105,
0.07083079218864441,
0.011716928333044052,
0.03507441654801369,
-0.026064259931445122,
0.03368422016501427,
0.01217629760503769,
0.031099673360586166,
-0.007122336886823177,
0.009846090339124203,
-0.007710614241659641,
-0.003627853700891137,
0.02477368153631687,
0.00813442561775446,
0.026054000481963158,
0.06486596912145615,
0.05245351791381836,
0.005365658085793257,
-0.017757022753357887,
-0.012748011387884617,
0.027010459452867508,
0.042264312505722046,
0.031598761677742004,
0.020479315891861916,
0.027817869558930397,
-0.045835431665182114,
0.014805560931563377,
-0.014393527060747147,
0.013419261202216148,
0.010414494201540947,
0.05916246771812439,
0.050400301814079285,
-0.018486397340893745,
-0.014825467951595783,
0.00974133051931858,
-0.015020678751170635,
0.05596843361854553,
0.013336727395653725,
0.008999938145279884,
0.0023291686084121466,
-0.002019578358158469,
0.0031113135628402233,
-0.03349751979112625,
-0.0014620590955018997,
-0.0422668494284153,
0.01985779218375683,
0.04225418344140053,
0.009302513673901558,
0.00951968040317297,
0.009687799960374832,
0.00987625028938055,
-0.01805991306900978,
-0.0017117863753810525,
-0.04218272119760513,
0.058902520686388016,
0.0023880056105554104,
0.019623171538114548,
0.03750895708799362,
-0.0315871499478817,
-0.05879591777920723,
-0.05130661278963089,
0.03415723145008087,
-0.03620518743991852,
0.052382148802280426,
-0.018442915752530098,
-0.03620054945349693,
-0.05182288959622383,
0.02272682636976242,
0.019625144079327583,
-0.021564248949289322,
-0.004200746770948172,
0.023110071197152138,
-0.00990027654916048,
0.0291132889688015,
-0.08634412288665771,
-0.06402583420276642,
0.06278369575738907,
-0.02563432976603508,
-0.018033580854535103,
0.047564078122377396,
0.010046565905213356,
-0.028016097843647003,
-0.041272956877946854,
-0.022124186158180237,
-0.10784760117530823,
0.0022961932700127363,
0.07464941591024399,
0.001371493679471314,
0.008724558167159557,
0.06051189824938774,
-0.07693183422088623,
0.008068672381341457,
0.07075396925210953,
0.02370833046734333,
0.055991023778915405,
-0.0014359982451424003,
0.04183623194694519,
-0.02728765644133091,
-0.018392935395240784,
0.02914915420114994,
0.00011330629058647901,
0.022054560482501984,
0.004530212376266718,
-0.06633594632148743,
0.0059588016010820866,
0.05334348604083061,
-0.048585716634988785,
0.0003432381490711123,
-0.008968351408839226,
-0.059375517070293427,
0.05392115190625191,
0.005723570007830858,
-0.020080802962183952,
0.03473927080631256,
0.016913600265979767,
0.050206515938043594,
0.014957764185965061,
-0.028778616338968277,
0.06283274292945862,
-0.05049813538789749,
0.006207813508808613,
0.00027765610138885677,
0.022542087361216545,
0.01429007388651371,
0.04717578738927841,
-0.03382592275738716,
0.06220129504799843,
0.04983759671449661,
-0.008020504377782345,
0.02253841981291771,
-0.007089449558407068,
-0.03456437960267067,
0.008099839091300964,
-0.04151742532849312,
0.006318346597254276,
-0.02224692702293396,
0.05131319537758827,
0.02011832408607006,
0.0177360400557518,
-0.011072751134634018,
0.0340251587331295,
-0.02890075370669365,
-0.046140555292367935,
-0.024202456697821617,
-0.0019720366690307856,
-0.023979980498552322,
-0.018698329105973244,
0.047052960842847824,
0.03692979738116264,
-0.01485646702349186,
0.035002779215574265,
-0.04413149878382683,
0.047073688358068466,
0.038681887090206146,
-0.033206406980752945,
0.0010322043672204018,
0.003627524711191654,
-0.017251837998628616,
0.03816596418619156,
-0.03590312972664833,
0.04670017585158348,
-0.02886972762644291,
0.06432041525840759,
0.0770968347787857,
0.030320851132273674,
-0.042112771421670914,
-0.027468618005514145,
0.021136336028575897,
0.00605375599116087,
-0.03926118090748787,
-0.003836976829916239,
-0.0302796121686697,
-0.010156460106372833,
-0.031229257583618164,
0.0001621105329832062,
-0.013564994558691978,
-0.01480012945830822,
-0.029587218537926674,
0.012394599616527557,
-0.018818149343132973,
0.08042272925376892,
-0.03129452094435692,
0.005896708928048611,
-0.055623166263103485,
-0.037607479840517044,
0.0006920398445799947,
-0.010456997901201248,
-0.008585740812122822,
0.026873605325818062,
-0.010444749146699905,
0.08428879827260971,
0.024974456056952477,
-0.004300984088331461,
-0.05355074629187584,
0.005131244193762541,
-0.007430261932313442,
-0.0278112031519413,
-0.0069686719216406345,
-0.009954618290066719,
-0.008854796178638935,
0.034947626292705536,
-0.02985883317887783,
-0.008254681713879108,
-0.004278815817087889,
-0.037627991288900375,
-0.004921420477330685,
0.015894999727606773,
-0.012600546702742577,
-0.06656461209058762,
-0.05940588191151619,
0.003605313366279006,
-0.05075034871697426,
0.03184465691447258,
0.003070421051234007,
0.007851780392229557,
0.026534367352724075,
-0.006243016105145216,
-0.03535771369934082,
0.025907613337039948,
0.027570605278015137,
-0.03866465017199516,
0.0643860474228859,
0.06721559911966324,
0.025111205875873566,
0.03936789929866791,
0.034788500517606735,
-0.030104288831353188,
-0.02696078270673752,
0.002197248162701726,
-0.04228254780173302,
-0.012344266287982464,
-0.01313755102455616,
-0.0076593561097979546,
-0.018211930990219116,
0.011498554609715939,
-0.021291662007570267,
-0.03207781910896301,
0.05613640695810318,
-0.02079137973487377,
0.0008676963043399155,
0.007632470689713955,
-0.04972298443317413,
0.07015517354011536,
0.05123302713036537,
-0.04549148678779602,
0.030691595748066902,
0.05828491598367691,
-0.0518810972571373,
-0.06717177480459213,
0.009118516929447651,
0.007664854638278484,
-0.01877598837018013,
-0.05948398634791374,
0.003097357228398323,
-0.005062543787062168,
-0.04503047093749046,
-0.019882624968886375,
0.007764492183923721,
0.06931085139513016,
-0.04107405245304108,
0.014685571193695068,
0.04083286225795746,
-0.04451454430818558,
-0.0007754658581689,
0.005894866771996021,
-0.034670639783144,
-0.052821386605501175,
-0.06405875831842422,
-0.01940249465405941,
-0.0421416349709034,
-0.009191660210490227,
0.008965052664279938,
0.01556377112865448,
0.047402333468198776,
-0.025376198813319206,
0.032523591071367264,
0.04332824796438217,
-0.012927191331982613,
-0.0009351599146611989,
-0.037611909210681915,
-0.0764746144413948,
-0.0022531398572027683,
0.012971346266567707,
0.04112059995532036,
0.03342072293162346,
-0.023171139881014824,
0.0007523161475546658,
-0.016901373863220215,
-0.037666674703359604,
-0.007944589480757713,
-0.06842363625764847,
0.009232795797288418,
0.02700996585190296
] |
<p>Consider a glass of water and a glass of coffee. Their contents differ by no more than a few grams of particles coming from the roasted and ground coffee, yet the former lets almost all visible light pass through, and the latter blocks most of it.</p>
<p>I am wondering <strong>what are the most efficient ways to turn water opaque by pouring matter in it</strong>, under normal temperature and pressure. By efficient I mean minimising the mass of added matter. By opaque, let's say 99% of daylight is blocked by two inches of liquid.</p>
<p>There is no other reason for my asking than sheer curiosity from the many hours I spend gazing fixedly through the coffee pot.</p> | g7799 | [
0.047032903879880905,
0.031734809279441833,
0.02661367505788803,
-0.025424685329198837,
-0.009143694303929806,
0.013249176554381847,
0.019210511818528175,
-0.024230467155575752,
-0.04927762225270271,
0.023204214870929718,
0.05915592610836029,
-0.017752716317772865,
0.04399674013257027,
0.018359731882810593,
0.0036714498419314623,
0.06405716389417648,
0.04711660370230675,
-0.027797257527709007,
-0.018802646547555923,
0.02261311188340187,
0.030410505831241608,
-0.01844649389386177,
0.048012543469667435,
-0.025464465841650963,
-0.08774533867835999,
-0.01797253079712391,
-0.029163949191570282,
-0.04796195775270462,
0.01408475823700428,
0.0159537885338068,
0.023762894794344902,
-0.00658571207895875,
-0.011412558145821095,
0.002552035730332136,
-0.023328065872192383,
0.04760038107633591,
0.0038889343850314617,
0.022381380200386047,
-0.008792771957814693,
-0.024619359523057938,
-0.04833138361573219,
0.012804568745195866,
-0.04105180874466896,
0.010532583110034466,
-0.032983019948005676,
0.059213750064373016,
-0.0319041907787323,
-0.0350949764251709,
-0.03860153257846832,
-0.09604683518409729,
0.026227246969938278,
-0.0038288517389446497,
0.040144551545381546,
0.04538893327116966,
-0.07094068825244904,
0.04206068813800812,
-0.01201623771339655,
-0.012155117467045784,
0.06616952270269394,
0.002184961922466755,
-0.01025934237986803,
-0.05453909561038017,
-0.03395890071988106,
0.05826851353049278,
-0.020478151738643646,
-0.0035444768145680428,
-0.01917850226163864,
0.01820659451186657,
0.05280110239982605,
0.030578382313251495,
-0.05405108258128166,
-0.01713152788579464,
0.007722001057118177,
-0.06379476934671402,
-0.037884730845689774,
-0.007728841155767441,
-0.00203983997926116,
0.04800207167863846,
0.04352268949151039,
-0.0082471938803792,
-0.04301115870475769,
-0.02184648998081684,
-0.011427927762269974,
-0.052172426134347916,
0.08665395528078079,
0.00708059361204505,
0.00804966315627098,
-0.06634752452373505,
-0.031535468995571136,
-0.012789442203938961,
0.002153409644961357,
-0.054691098630428314,
0.07067536562681198,
0.007608883082866669,
-0.023091107606887817,
0.07652316987514496,
0.02636636421084404,
-0.02736343815922737,
-0.007993418723344803,
0.031540390104055405,
0.038259245455265045,
-0.01957353577017784,
0.036378808319568634,
-0.019798776134848595,
0.0071373931132256985,
-0.028128819540143013,
0.05519154295325279,
0.01422905270010233,
-0.08001190423965454,
-0.004873727913945913,
-0.04047934710979462,
-0.007978766225278378,
-0.05266915634274483,
-0.006556810345500708,
-0.04771475866436958,
-0.08129270374774933,
0.04661881551146507,
0.10001454502344131,
0.017362384125590324,
0.01791577786207199,
0.025948498398065567,
0.10293010622262955,
0.051519524306058884,
0.028463462367653847,
0.03155167028307915,
-0.00244769430719316,
-0.001591291162185371,
-0.015274673700332642,
0.008000658825039864,
-0.04791424795985222,
0.00022541878570336848,
0.04277311637997627,
-0.015637051314115524,
-0.011553436517715454,
0.014063440263271332,
0.04663456976413727,
-0.005405273754149675,
0.004348340909928083,
0.014978673309087753,
-0.049586329609155655,
0.05262147635221481,
-0.009113842621445656,
-0.009904062375426292,
0.05017925798892975,
-0.044932834804058075,
0.01319822482764721,
-0.05518053099513054,
-0.019319944083690643,
0.012203783728182316,
-0.012911549769341946,
0.01149724144488573,
0.022638844326138496,
0.03508497402071953,
0.04239838197827339,
0.026921868324279785,
-0.008875652216374874,
0.0825684666633606,
-0.0667811706662178,
0.031252942979335785,
0.015555045567452908,
0.022210652008652687,
-0.04382769763469696,
-0.03219001367688179,
-0.020892633125185966,
-0.08386442065238953,
0.02165761962532997,
0.006429640576243401,
-0.04299379885196686,
-0.016686871647834778,
-0.05367961898446083,
-0.03810473158955574,
0.034102197736501694,
-0.005362133029848337,
0.06700310856103897,
0.033579397946596146,
0.00004874938167631626,
0.0814911350607872,
-0.0361153669655323,
0.001104891300201416,
0.019808325916528702,
-0.011759323067963123,
-0.004991677589714527,
-0.04274245724081993,
0.016268545761704445,
-0.005057106725871563,
-0.012733540497720242,
0.08560474961996078,
-0.034611862152814865,
-0.0382925309240818,
0.02181101217865944,
-0.010288894176483154,
0.0015682150842621922,
0.0067929369397461414,
0.040642060339450836,
-0.0004818632733076811,
-0.044426508247852325,
0.05129728093743324,
0.047586385160684586,
-0.0456794798374176,
-0.01092679426074028,
-0.06469673663377762,
-0.0015648124972358346,
0.031109357252717018,
0.04039647802710533,
0.017493674531579018,
0.06088406592607498,
0.018361160531640053,
0.05661705881357193,
0.02567395567893982,
0.021519092842936516,
0.021718448027968407,
0.00040732670458965003,
0.07977546006441116,
-0.02900123968720436,
-0.022628340870141983,
0.04844343662261963,
-0.030845437198877335,
-0.02062912844121456,
-0.011438943445682526,
-0.00409083953127265,
0.013144214637577534,
-0.022792639210820198,
-0.04737164080142975,
0.010444354265928268,
-0.006464167032390833,
-0.0010605445131659508,
-0.002543104812502861,
0.015665078535676003,
0.004532504361122847,
0.04508237540721893,
-0.006083976943045855,
0.020813245326280594,
-0.004411060828715563,
-0.02333531342446804,
0.03083937056362629,
0.002896968275308609,
-0.023589590564370155,
0.07209514826536179,
0.035202838480472565,
-0.009672612883150578,
0.021253462880849838,
-0.009402098134160042,
-0.06883488595485687,
-0.04648322984576225,
0.002402592683210969,
-0.009612835012376308,
-0.041399817913770676,
-0.020331712439656258,
0.018172621726989746,
0.026152342557907104,
0.010960687883198261,
-0.009309765882790089,
-0.06629148870706558,
-0.011423810385167599,
-0.04093929007649422,
-0.011204461567103863,
-0.052372731268405914,
0.030542178079485893,
-0.03520013764500618,
-0.022938160225749016,
-0.002731101820245385,
-0.04559396952390671,
0.022446533665060997,
0.017515787854790688,
0.03203972429037094,
0.06582300364971161,
-0.06558191776275635,
-0.007231452967971563,
0.04380647465586662,
0.06216941401362419,
0.01934012584388256,
0.028653061017394066,
0.022401947528123856,
0.029176559299230576,
-0.03718490153551102,
0.015635177493095398,
-0.04867304861545563,
-0.020131738856434822,
0.00799515563994646,
0.02253805100917816,
0.015618975274264812,
-0.030714867636561394,
-0.0373365581035614,
0.05677630752325058,
0.03279195353388786,
-0.0745965763926506,
0.019734783098101616,
0.0265372134745121,
0.044376254081726074,
0.03139219805598259,
0.04103541746735573,
0.051367223262786865,
0.003389174584299326,
0.05092207342386246,
-0.009715758264064789,
-0.0041130841709673405,
0.009262840263545513,
0.012721472419798374,
-0.018757374957203865,
-0.04804150015115738,
0.017399320378899574,
-0.01759372279047966,
-0.021168222650885582,
0.06100183725357056,
-0.06268094480037689,
0.060500092804431915,
0.007990941405296326,
-0.021729595959186554,
-0.057894833385944366,
0.012037244625389576,
0.03491665795445442,
0.03883368894457817,
-0.06449522078037262,
0.04770570993423462,
-0.028167620301246643,
-0.04938938096165657,
-0.03821868449449539,
-0.00947368424385786,
0.005591661669313908,
0.039352476596832275,
0.005898748524487019,
0.029749559238553047,
0.047274474054574966,
-0.04998599737882614,
0.028851626440882683,
0.019611474126577377,
-0.009833401069045067,
-0.04962505027651787,
-0.04803631454706192,
-0.021159576252102852,
0.03543906658887863,
0.05850505083799362,
-0.07074105739593506,
-0.039824098348617554,
-0.04742279648780823,
0.0048850951716303825,
-0.0008079825202003121,
0.0075392937287688255,
0.0018445518799126148,
0.016021938994526863,
0.0008461339166387916,
-0.08057750016450882,
-0.06901396811008453,
-0.01733757182955742,
-0.0028957559261471033,
-0.04982142522931099,
0.0059038433246314526,
-0.03250698000192642,
-0.036173686385154724,
0.0038405675441026688,
0.039947088807821274,
-0.009272504597902298,
0.006927394773811102,
-0.025922775268554688,
0.0022842083126306534,
0.02618969790637493,
0.019445663318037987,
0.042649246752262115,
0.04125526174902916,
-0.023816272616386414,
-0.02319381572306156,
-0.047463223338127136,
0.022901931777596474,
-0.053138986229896545,
-0.046094153076410294,
-0.013001601211726665,
0.034297503530979156,
-0.03755831718444824,
-0.07867465913295746,
0.05038667842745781,
0.008205828256905079,
-0.03199698403477669,
-0.05209954082965851,
0.035061080008745193,
0.006753239315003157,
0.0068880789913237095,
0.02806648425757885,
0.0544995479285717,
-0.00870171282440424,
0.04271402209997177,
-0.007673466578125954,
0.012336164712905884,
0.04212751239538193,
0.0030639073811471462,
-0.020422056317329407,
0.028282443061470985,
-0.023503335192799568,
-0.001978270709514618,
0.05073205754160881,
-0.043578095734119415,
-0.006874220445752144,
0.0020674236584454775,
-0.008172908797860146,
0.025966702029109,
-0.048705898225307465,
-0.028623513877391815,
-0.011402898468077183,
-0.011277366429567337,
0.0063809859566390514,
0.01037381961941719,
0.007130058947950602,
-0.029567312449216843,
0.02358946204185486,
-0.005437921267002821,
-0.009505833499133587,
0.004095882643014193,
-0.005401174537837505,
-0.01815132237970829,
-0.04817585647106171,
-0.0283486507833004,
0.052025023847818375,
-0.01612178608775139,
-0.05205555260181427,
0.02860129624605179,
0.026062361896038055,
-0.05726074427366257,
-0.014449180103838444,
-0.0033591603860259056,
-0.02617182396352291,
-0.012417620979249477,
0.0029598139226436615,
0.015101800672709942,
-0.07124706357717514,
0.020627668127417564,
0.014060448855161667,
0.050619859248399734,
0.014642481692135334,
-0.024141034111380577,
-0.000037621699448209256,
-0.02719433791935444,
0.03975439444184303,
-0.011551975272595882,
-0.017273958772420883,
-0.020968284457921982,
-0.005965525284409523,
0.004613816738128662,
0.004058899823576212,
-0.02620525471866131,
0.01780659705400467,
0.0221041738986969,
-0.045354343950748444,
0.004949614405632019,
0.002241504844278097,
-0.031213948503136635,
-0.0059939194470644,
0.028069159016013145,
0.03881435468792915,
-0.009470338001847267,
0.005596093833446503,
0.007244855631142855,
0.009973629377782345,
0.043464671820402145,
-0.03418518230319023,
-0.010745640844106674,
-0.021116742864251137,
0.059236232191324234,
-0.04839250072836876,
0.0563967265188694,
-0.011791612952947617,
0.03872935473918915,
-0.06592778861522675,
-0.0009509254596196115,
-0.023453956469893456,
0.0511469766497612,
-0.01765984110534191,
-0.0012545670615509152,
-0.041788917034864426,
-0.03389306738972664,
0.021086493507027626,
0.0029388347174972296,
0.008220218122005463,
0.043209902942180634,
0.0416317880153656,
0.06323777139186859,
0.05504944175481796,
0.019920308142900467,
-0.03194468095898628,
0.0418114997446537,
0.04219086840748787,
0.008586086332798004,
-0.010678998194634914,
0.03088325262069702,
0.05346822738647461,
0.06245184689760208,
0.004201862029731274,
0.027238767594099045,
-0.0019893439020961523,
0.034898560494184494,
-0.002670776331797242,
-0.056895140558481216,
-0.03472594916820526,
0.0496421754360199,
-0.015231550671160221,
-0.04298930987715721,
-0.010096431709825993,
-0.004704305436462164,
0.07767567783594131,
-0.0026631217915564775,
0.02908182516694069,
-0.0005655786371789873,
-0.035596657544374466,
-0.04016986861824989,
-0.0055704861879348755,
-0.008449409157037735,
0.038079939782619476,
-0.026338746771216393,
-0.006568020675331354,
-0.033173877745866776,
0.01583852991461754,
0.08876212686300278,
-0.008692084811627865,
-0.026421044021844864,
-0.00181037955917418,
-0.0023710173554718494,
0.022449549287557602,
-0.036169733852148056,
-0.025377698242664337,
0.012009454891085625,
-0.015332050621509552,
-0.06040707230567932,
0.034276168793439865,
-0.03703312203288078,
-0.04940691590309143,
0.06421048194169998,
-0.0025304979644715786,
-0.010996104218065739,
-0.04370969161391258,
-0.03355336934328079,
0.06363064795732498,
-0.041760701686143875,
-0.009476342238485813,
0.026550380513072014,
0.031154815107584,
-0.020223502069711685,
0.002482324605807662,
0.013288173824548721,
0.03165378049015999,
0.03790907561779022,
-0.01104805152863264,
0.030837729573249817,
-0.04439687728881836,
-0.019755279645323753,
0.008953776210546494,
0.0628182515501976,
0.015284872613847256,
-0.04894697666168213,
0.04363865777850151,
-0.040401168167591095,
0.03628566488623619,
0.014846408739686012,
-0.02925051935017109,
0.0333319827914238,
0.06250184029340744,
0.0004884873051196337,
0.06395348161458969,
0.022099466994404793,
0.01665869727730751,
-0.11746734380722046,
0.04847637191414833,
0.03674108162522316,
0.067133828997612,
0.0690680667757988,
0.004121811594814062,
-0.005197256803512573,
-0.00562270125374198,
-0.051739469170570374,
-0.010193637572228909,
-0.0166849996894598,
0.008148224093019962,
0.040001194924116135,
-0.03323004022240639,
0.02942037023603916,
0.003093813778832555,
-0.03335030376911163,
-0.028056209906935692,
0.03259586915373802,
-0.04270191118121147,
0.00034934785799123347,
-0.03939986974000931,
0.024118084460496902,
-0.0223650261759758,
0.008290061727166176,
-0.03442593291401863,
0.013499317690730095,
-0.0025928274262696505,
0.0024646043311804533,
-0.0694749653339386,
0.016211485490202904,
0.02605447731912136,
-0.04021032899618149,
-0.03287835419178009,
-0.01751585118472576,
0.013934766873717308,
-0.04987412318587303,
0.05888283997774124,
-0.032344065606594086,
-0.004310655873268843,
-0.00950855202972889,
-0.060173150151968,
0.04391714558005333,
-0.03216803818941116,
0.032856427133083344,
0.0335383340716362,
-0.0006186909740790725,
-0.0348045788705349,
0.0010861230548471212,
-0.00880633294582367,
-0.012142450548708439,
-0.0038520577363669872,
-0.05423857271671295,
-0.08037522435188293,
0.00016708172915969044,
0.006369923707097769,
-0.0364798977971077,
-0.05685882270336151,
-0.038199204951524734,
-0.023239564150571823,
-0.05449379235506058,
0.0228816419839859,
-0.07970935851335526,
0.014511366374790668,
-0.013640700839459896,
0.06665126979351044,
-0.06515894085168839,
0.0042662485502660275,
-0.010630659759044647,
-0.0026618451811373234,
-0.051956381648778915,
0.08816640079021454,
0.02154519595205784,
0.04108395427465439,
-0.011472508311271667,
0.06443165987730026,
-0.04089198634028435,
-0.012297943234443665,
-0.007762058172374964,
-0.07042286545038223,
0.040820538997650146,
-0.012314721941947937,
0.04088500514626503,
0.0251635629683733,
0.0022815202828496695,
0.02010580711066723,
0.10009409487247467,
0.014604867435991764,
0.039713017642498016,
-0.0038202458526939154,
-0.024283017963171005,
-0.06252779066562653,
-0.018964437767863274,
0.006303600966930389,
-0.05520956218242645,
-0.026767127215862274,
-0.02423507533967495,
-0.06874576210975647,
0.03473692387342453,
0.007569291163235903,
0.028904370963573456,
-0.01893014833331108,
0.001983518013730645,
0.00971410982310772,
0.018780667334794998,
0.006893091835081577,
-0.018679581582546234,
0.04858098551630974,
0.03264916315674782,
0.004735446069389582,
-0.0056704068556427956,
0.0363551527261734,
0.03993700444698334,
0.006164262071251869,
-0.026867995038628578,
-0.08407267183065414,
-0.03829090669751167,
0.05613269656896591,
-0.05486678332090378,
0.04444447532296181,
0.02384522743523121,
0.01578430086374283,
0.007387623190879822,
-0.009005507454276085,
0.008631757460534573,
0.010656068101525307,
-0.034507960081100464,
0.023754587396979332,
-0.0571398101747036,
0.00627104239538312,
0.02854757383465767,
-0.027624478563666344,
-0.02522611804306507,
0.006235337350517511,
-0.013016602955758572,
0.003521983278915286,
0.02326185256242752,
-0.01496073603630066,
0.07975564897060394,
0.023924333974719048,
-0.017941316589713097,
0.10809404402971268,
-0.029852479696273804,
-0.04096299782395363,
-0.03972797095775604,
0.015191614627838135,
-0.037093859165906906,
-0.005061616189777851,
0.018223637714982033,
-0.02571084536612034,
0.008277127519249916,
-0.01687130145728588,
0.012334953062236309,
0.013915492221713066,
0.0017657324206084013,
0.025144781917333603,
-0.07063844799995422,
0.0675855502486229,
0.009810811839997768,
-0.06783124804496765,
0.002791326493024826,
-0.02212066762149334,
0.026924649253487587,
-0.04954138398170471,
-0.004048285540193319,
-0.008335410617291927,
-0.004749889951199293,
-0.033411674201488495,
0.001320420764386654,
0.054982732981443405,
-0.03826421871781349,
-0.037225142121315,
0.00040234799962490797,
0.0010256286477670074,
-0.017747368663549423,
0.014022378250956535,
-0.02592669054865837,
-0.012395180761814117,
-0.03087727352976799,
0.06446249037981033,
-0.03374540060758591,
0.03124227747321129,
0.034726113080978394,
0.00151416368316859,
-0.003261782228946686,
-0.08112752437591553,
-0.013319586403667927,
0.0694340392947197,
-0.01696639694273472,
-0.0072157192043960094,
0.05160389095544815,
-0.011089582927525043,
-0.0512978620827198,
0.031756434589624405,
0.06175243854522705,
-0.010248329490423203,
-0.043906453996896744,
0.009813252836465836,
-0.047287046909332275,
-0.012193702161312103,
-0.013525568880140781,
0.01915086805820465,
-0.016543788835406303,
0.0013226462760940194,
0.043068937957286835,
0.022654322907328606,
0.043406132608652115,
-0.0030836774967610836,
0.011763372458517551,
0.04420457035303116,
-0.028202293440699577
] |
<p>Possibly the most useful thing anyone could tell me about particle physics:</p>
<p>Naively, one could try and make an algebra by enumerating all the types of particles and defining equivalence relationships (some rules), for example</p>
<p>Objects:</p>
<p>object type 1: photon</p>
<p>object type 2: electron</p>
<p>object type 3 ...</p>
<p>object type n</p>
<p>Rules:</p>
<p>rule 1: a photon is equivalent to an electron and a positron</p>
<p>rule 2: a proton is equivalent to three quarks</p>
<p>rule ....</p>
<p>rule n</p>
<p>Then one could study the properties of these relationships as a mathematical structure containing objects that represent particles and rules that define equivalence - i.e. as an algebra. I assume such an algebra would be, if formulated correctly, represented by Feynman diagrams (for some particles at least). Does such an algebra have a name? Is there more than one? Is this at all connected to the idea behind stating that the standard model is U(1) x SU(2) x SU(3)?</p>
<p>By an algebra I understand a closed and consistent collection of mathematical objects and relationships.</p>
<hr>
<p>Thanks for trying to understand what I'm asking, with your input I can aim to make this more comprehensible. So I guess I'm looking for a formal structure which reflects particle reactions which is abstracted away from spatial, temporal and energetic considerations as far as is possible (is it at all possible?).</p> | g7800 | [
0.03526008501648903,
0.02924167551100254,
-0.009046337567269802,
-0.059021301567554474,
0.03986874222755432,
-0.021651044487953186,
-0.011723645962774754,
0.047452811151742935,
-0.012354347854852676,
-0.000979823525995016,
-0.0033786380663514137,
-0.004479311406612396,
0.018832143396139145,
-0.009631263092160225,
-0.01945616491138935,
0.04057251289486885,
0.009029686450958252,
0.001738519174978137,
0.004366719629615545,
-0.00434891739860177,
0.07922649383544922,
0.03075723722577095,
-0.024303574115037918,
-0.0056774369440972805,
-0.0430569164454937,
-0.008359943516552448,
-0.02895011566579342,
-0.06080521270632744,
-0.04015054181218147,
-0.015599239617586136,
0.030227288603782654,
-0.047585807740688324,
0.08126907795667648,
-0.010529767721891403,
-0.030848780646920204,
-0.0976622998714447,
0.03163447603583336,
0.043480321764945984,
-0.0012069748481735587,
0.04515280947089195,
0.02314351685345173,
0.010424366220831871,
-0.045718394219875336,
-0.0006586171803064644,
-0.011297156102955341,
-0.02966299094259739,
-0.024733994156122208,
0.026833046227693558,
0.002971003530547023,
-0.007902396842837334,
0.00039629320963285863,
0.012964721769094467,
0.0329115092754364,
0.015721356496214867,
0.019264912232756615,
0.03991246595978737,
0.034361582249403,
-0.004383419640362263,
0.08992838114500046,
0.01781684346497059,
-0.040239498019218445,
0.03109069913625717,
0.004295173566788435,
0.031032530590891838,
0.097565196454525,
0.049943145364522934,
-0.015821723267436028,
0.03689897432923317,
-0.01029503159224987,
0.017174068838357925,
0.045875489711761475,
-0.029088323935866356,
0.03210350498557091,
-0.009766719304025173,
0.03301163762807846,
-0.009278073906898499,
-0.03450505807995796,
-0.0011110351188108325,
0.038967348635196686,
0.002005440415814519,
-0.04067640379071236,
0.0515204519033432,
0.05162140727043152,
0.019571030512452126,
0.03455961495637894,
-0.03913862630724907,
-0.05347409471869469,
-0.040459439158439636,
-0.029033023864030838,
-0.05560529977083206,
-0.007393022999167442,
-0.010328676551580429,
0.03107893466949463,
-0.005559385288506746,
-0.011527501046657562,
0.002604488516226411,
-0.015950998291373253,
0.044848352670669556,
-0.051312610507011414,
-0.004922925960272551,
-0.06070795655250549,
0.010597702115774155,
0.05224834755063057,
-0.007225971203297377,
-0.009153257124125957,
-0.03093884512782097,
0.013116717338562012,
0.04097101837396622,
0.0053801764734089375,
-0.008134575560688972,
-0.039255112409591675,
0.03365673869848251,
-0.05362190678715706,
0.004122438840568066,
-0.047383200377225876,
-0.04963548853993416,
0.07286790013313293,
-0.03389156237244606,
0.021717768162488937,
0.08263763785362244,
0.014316463842988014,
-0.010751432739198208,
0.009744655340909958,
0.08224023878574371,
-0.060565441846847534,
-0.10555490851402283,
-0.024371743202209473,
0.03902421519160271,
-0.011064507067203522,
-0.009201808832585812,
0.05103273317217827,
-0.05317016318440437,
0.004279023502022028,
0.015645669773221016,
-0.03315683454275131,
0.027996396645903587,
-0.01751529425382614,
-0.015104623511433601,
0.03494379296898842,
-0.0492449551820755,
-0.03563132509589195,
-0.03265583515167236,
-0.030533837154507637,
-0.0346311517059803,
-0.006056348793208599,
-0.016937479376792908,
0.04961639642715454,
-0.04450993612408638,
-0.029369115829467773,
0.050760600715875626,
0.028635984286665916,
0.05356550216674805,
-0.03156682848930359,
-0.03586210310459137,
0.011618547141551971,
-0.014000074937939644,
0.023082150146365166,
0.005665620323270559,
-0.028283298015594482,
-0.04185124859213829,
0.02542494423687458,
-0.010651277378201485,
-0.0023791228886693716,
-0.028585605323314667,
-0.07358852028846741,
-0.045005377382040024,
-0.008609692566096783,
-0.021250372752547264,
0.024728965014219284,
-0.008789288811385632,
-0.036422744393348694,
0.000650981382932514,
-0.05483917519450188,
0.0699373111128807,
0.006703179795295,
0.06496935337781906,
-0.01434460747987032,
0.0002086373424390331,
0.014110487885773182,
-0.003104780102148652,
-0.036983128637075424,
-0.038558706641197205,
0.03608852997422218,
0.019787495955824852,
-0.03227952495217323,
0.003527412423864007,
-0.00494482833892107,
0.056488946080207825,
0.007477595936506987,
0.02471098303794861,
-0.04402628913521767,
-0.023933105170726776,
0.04029794782400131,
0.0039750756695866585,
0.02551991678774357,
0.04110025614500046,
-0.04313302040100098,
-0.019955355674028397,
-0.00740767503157258,
-0.0007070607389323413,
0.026199840009212494,
0.029609067365527153,
0.030419321730732918,
0.045563988387584686,
0.050949860364198685,
0.01058182679116726,
0.01781422831118107,
0.007250169757753611,
0.015556569211184978,
0.0017706358339637518,
0.045878611505031586,
-0.0056070140562951565,
0.046045806258916855,
0.039241623133420944,
-0.035183291882276535,
-0.03900071978569031,
-0.009075653739273548,
-0.013276305980980396,
-0.008590350858867168,
-0.02275768481194973,
-0.04275466874241829,
-0.08558716624975204,
0.049723900854587555,
-0.08376698195934296,
-0.03476889431476593,
0.016383476555347443,
-0.0011046241270378232,
-0.0061016385443508625,
0.00905184168368578,
0.012487051077187061,
-0.07614569365978241,
0.04021429643034935,
-0.03380622714757919,
-0.07590135931968689,
0.06569039821624756,
-0.016619613394141197,
-0.024416999891400337,
0.01642763987183571,
0.05366547405719757,
-0.014902029186487198,
-0.0008631977252662182,
0.013347084634006023,
-0.031179919838905334,
-0.007035899441689253,
0.04017513990402222,
-0.08217490464448929,
0.01599792391061783,
-0.00518909003585577,
-0.018540173768997192,
0.041622478514909744,
-0.0002821030211634934,
-0.027584506198763847,
-0.03263520449399948,
0.002579075051471591,
0.030859701335430145,
-0.0031210999004542828,
-0.015446187928318977,
0.0021431504283100367,
-0.0015338774537667632,
-0.015922876074910164,
0.05227479338645935,
-0.024611065164208412,
-0.018588120117783546,
0.02551700547337532,
-0.01432657428085804,
-0.014366152696311474,
0.011749052442610264,
-0.001059297239407897,
-0.010169742628932,
0.0023068704176694155,
-0.05767476558685303,
-0.018294213339686394,
-0.00659222761169076,
-0.022186651825904846,
-0.0209604911506176,
0.026483723893761635,
-0.011746594682335854,
-0.03103511594235897,
-0.008187881670892239,
-0.0038629674818366766,
0.08785606920719147,
0.007843440398573875,
-0.07292259484529495,
0.0005049488972872496,
0.03826155513525009,
-0.02208179235458374,
0.008094152435660362,
0.018298441544175148,
-0.038558248430490494,
0.016467075794935226,
0.015366584062576294,
-0.023721329867839813,
0.026908447965979576,
0.01971632055938244,
-0.07244762033224106,
-0.008825072087347507,
-0.023804422467947006,
0.009287956170737743,
-0.002544715069234371,
0.08079877495765686,
-0.042246248573064804,
-0.01742878369987011,
0.004769170191138983,
0.0156360175460577,
0.02488401159644127,
0.05252102017402649,
-0.05116594210267067,
-0.02120625041425228,
-0.021481987088918686,
-0.014647046104073524,
-0.04153425991535187,
0.03513091802597046,
0.009312090463936329,
0.01686428301036358,
0.04762424901127815,
0.000355346011929214,
0.0033556956332176924,
0.05960940569639206,
0.03047492355108261,
-0.05719415470957756,
-0.05721957981586456,
-0.01414797268807888,
0.0910211056470871,
-0.039696644991636276,
0.03551309183239937,
0.015513612888753414,
-0.02048092521727085,
0.001239853911101818,
-0.052970536053180695,
-0.025189945474267006,
0.030961191281676292,
-0.0353461392223835,
0.050577834248542786,
0.03303370252251625,
-0.09280560910701752,
-0.04349566251039505,
-0.048625096678733826,
-0.06257964670658112,
0.029038209468126297,
-0.08576291799545288,
0.03586709499359131,
0.00883739348500967,
-0.012134737335145473,
-0.006476374343037605,
-0.002340330509468913,
-0.01890816166996956,
-0.06930984556674957,
0.036789294332265854,
0.033618126064538956,
-0.06188584491610527,
-0.00020999058324377984,
0.051467545330524445,
0.05915558710694313,
0.008256244473159313,
0.009648478589951992,
0.0026076792273670435,
0.04278820380568504,
0.021558107808232307,
0.017241213470697403,
-0.010482579469680786,
-0.03321731090545654,
-0.01733415573835373,
0.04189390689134598,
0.009029601700603962,
-0.0382000207901001,
0.044883210211992264,
-0.043259650468826294,
0.007024112623184919,
0.0345999114215374,
-0.013860142789781094,
0.006397022865712643,
-0.003827678970992565,
-0.049645762890577316,
-0.002125790575519204,
0.0013301259605214,
-0.04531468078494072,
0.036294713616371155,
0.003972661215811968,
-0.03814852237701416,
0.03671840578317642,
0.020217854529619217,
0.06332767754793167,
0.049962084740400314,
0.005142750684171915,
0.05804036557674408,
0.03114793449640274,
-0.014271722175180912,
-0.0089106485247612,
-0.046005215495824814,
0.03580186143517494,
0.008480465039610863,
-0.021430455148220062,
-0.07012668251991272,
0.01413731835782528,
0.03700780123472214,
-0.04502423107624054,
-0.007585700135678053,
-0.04820198938250542,
-0.014454900287091732,
0.006751905661076307,
0.004648661240935326,
-0.018672732636332512,
0.02506641484797001,
0.005024717655032873,
0.005258837714791298,
-0.021683240309357643,
0.056273266673088074,
-0.031132660806179047,
-0.01121017336845398,
0.000443765107775107,
0.022011855617165565,
0.010294423438608646,
0.08869399130344391,
0.0023626042529940605,
-0.002973285736516118,
-0.018948402255773544,
-0.022357357665896416,
-0.01672486774623394,
0.042478296905756,
0.002424132078886032,
0.03748231381177902,
0.04921684041619301,
0.06545897573232651,
-0.011401291005313396,
0.011480274610221386,
0.04832319915294647,
0.02743000164628029,
0.03457950800657272,
-0.0740111917257309,
-0.02536662667989731,
0.013091268949210644,
-0.003079814137890935,
0.009763825684785843,
-0.01318870484828949,
-0.05271882563829422,
-0.015991486608982086,
-0.04723381996154785,
0.06606762111186981,
-0.056854717433452606,
0.036240071058273315,
0.04345784708857536,
0.024152247235178947,
0.04492902755737305,
-0.027046576142311096,
0.0640798807144165,
0.048768769949674606,
-0.02712146006524563,
-0.006965546868741512,
-0.0712624341249466,
-0.02732439525425434,
0.03476659581065178,
0.05296776816248894,
-0.028608819469809532,
-0.025737959891557693,
-0.046699970960617065,
-0.01721728779375553,
0.00812926422804594,
0.009761943481862545,
0.039093978703022,
0.03158905729651451,
-0.08081516623497009,
-0.010583440773189068,
0.044543053954839706,
-0.003307430073618889,
0.007607296574860811,
-0.023439574986696243,
-0.11008518934249878,
0.013663938269019127,
-0.049660731106996536,
-0.0421949103474617,
0.0317109040915966,
-0.03411409631371498,
0.0093366215005517,
-0.040222302079200745,
0.019588543102145195,
-0.012797756120562553,
-0.05070410296320915,
-0.020568298175930977,
0.0004855766019318253,
-0.01588166505098343,
-0.029388392344117165,
0.02708711288869381,
-0.012656268663704395,
-0.0011469365563243628,
0.007510738912969828,
0.035769108682870865,
0.014522274024784565,
0.05739988759160042,
0.016100220382213593,
-0.038068804889917374,
0.008073133416473866,
-0.08804116398096085,
-0.013969252817332745,
0.028298167511820793,
-0.010559380985796452,
-0.029062526300549507,
0.00171697570476681,
-0.0034025355707854033,
0.03863854706287384,
0.026441605761647224,
-0.00721058389171958,
0.022139355540275574,
-0.014951811172068119,
0.01520343217998743,
0.03402896597981453,
-0.0049156504683196545,
0.08334951102733612,
-0.04796659201383591,
-0.02058183029294014,
-0.0324314646422863,
0.04215532913804054,
0.033003658056259155,
-0.04160249978303909,
0.0037654642947018147,
-0.03307878226041794,
0.10186587274074554,
-0.026241017505526543,
0.019959865137934685,
0.012889387086033821,
-0.05062542483210564,
-0.012878519482910633,
-0.026401463896036148,
-0.0037441416643559933,
-0.02112365886569023,
-0.049024105072021484,
-0.0024692299775779247,
-0.05611823499202728,
-0.03386669605970383,
0.0618097260594368,
0.05404002591967583,
0.012709476985037327,
-0.02035662531852722,
-0.005291030742228031,
0.03609198331832886,
-0.07069603353738785,
-0.05195801705121994,
-0.01839747093617916,
0.07240821421146393,
0.07331524789333344,
0.015275327488780022,
0.006331142038106918,
-0.022518975660204887,
0.015564178116619587,
0.014610233716666698,
0.024484287947416306,
0.006567333824932575,
-0.04237489029765129,
0.029733914881944656,
0.028590327128767967,
-0.0004885971429757774,
-0.02601969987154007,
-0.018969083204865456,
0.023940326645970345,
-0.039702158421278,
0.00770782632753253,
0.039693377912044525,
-0.04843245819211006,
-0.0248399805277586,
0.026778927072882652,
0.0137306097894907,
-0.03334272652864456,
0.06294186413288116,
-0.017968427389860153,
-0.026637105271220207,
-0.008453849703073502,
-0.028121434152126312,
-0.03435201942920685,
-0.018696052953600883,
0.05694063380360603,
0.06628012657165527,
0.06915467977523804,
0.02421713061630726,
0.0060744695365428925,
0.02391805872321129,
0.01225958950817585,
-0.03415161743760109,
0.01605338044464588,
-0.03437497094273567,
-0.029715467244386673,
0.0269523486495018,
0.07716485857963562,
0.034304551780223846,
-0.024159472435712814,
-0.005058233626186848,
-0.03979283571243286,
0.04926057904958725,
-0.013391667976975441,
0.02346990443766117,
0.0024124360643327236,
-0.009201103821396828,
-0.027892617508769035,
-0.021082311868667603,
-0.025545652955770493,
-0.022806301712989807,
0.007318870164453983,
0.04785211756825447,
0.09260836988687515,
0.019349398091435432,
0.024497179314494133,
0.008161325938999653,
-0.01715308614075184,
-0.032533157616853714,
-0.03398967534303665,
0.029532911255955696,
0.015407020226120949,
0.1284225583076477,
-0.06477343291044235,
0.017526131123304367,
0.018887421116232872,
0.0028040518518537283,
-0.02033638209104538,
0.006415374111384153,
-0.006694390904158354,
0.017414024099707603,
0.00574254197999835,
-0.09166097640991211,
-0.024389617145061493,
-0.03509180620312691,
-0.04789094254374504,
-0.04314008355140686,
-0.010299909859895706,
0.020780643448233604,
0.0035141953267157078,
-0.03529306873679161,
-0.006751480512320995,
0.017702016979455948,
0.008818495087325573,
0.06858732551336288,
0.04606688767671585,
0.02216337062418461,
-0.019566478207707405,
-0.03789298236370087,
0.008399562910199165,
0.02469358965754509,
0.009389728307723999,
0.015773635357618332,
-0.029339872300624847,
0.0019055826123803854,
0.00530305365100503,
0.04512694478034973,
-0.001848719548434019,
0.024381520226597786,
0.02051679603755474,
0.0377926379442215,
-0.010896368883550167,
-0.0747806578874588,
0.06330755352973938,
-0.009499773383140564,
-0.052433282136917114,
-0.0230929646641016,
0.024972088634967804,
0.02236502803862095,
-0.032781120389699936,
0.019082775339484215,
-0.039366960525512695,
-0.005302318837493658,
0.003625135635957122,
0.0065454826690256596,
0.025536619126796722,
-0.07627607882022858,
0.019130093976855278,
-0.020078390836715698,
0.017937475815415382,
-0.015119288116693497,
-0.03918846696615219,
0.021390948444604874,
0.002303495304659009,
-0.014534085988998413,
0.01993672549724579,
-0.043600231409072876,
-0.016196707263588905,
-0.06677140295505524,
-0.0026402485091239214,
0.018421949818730354,
-0.029039600864052773,
-0.0032045936677604914,
0.011853831820189953,
0.044157154858112335,
-0.016056224703788757,
-0.059303395450115204,
0.02402150258421898,
0.05498676374554634,
-0.022707773372530937,
0.03480010852217674,
0.016726670786738396,
0.03649153560400009,
-0.021764952689409256,
-0.017528919503092766,
-0.024989072233438492,
-0.01167913619428873,
-0.006375054828822613,
-0.028168199583888054,
0.09336135536432266,
-0.11827889829874039,
0.0036091168876737356,
0.015114559791982174,
0.007703497540205717,
0.032575517892837524,
0.037206847220659256,
-0.0013948095729574561,
0.02518906258046627,
0.02352261357009411,
0.001616950612515211,
-0.04777854308485985,
0.022862493991851807,
-0.01633092761039734,
-0.0656905397772789,
0.02616952732205391,
0.0033509391359984875,
-0.008847787976264954,
0.004577829968184233,
0.06279920041561127,
-0.009531283751130104,
0.017112359404563904,
0.014240921474993229,
0.03096705488860607,
-0.01696109212934971,
0.0014262014301493764,
-0.01743694767355919,
0.028193121775984764,
-0.013638431206345558,
0.030370565131306648,
-0.05373693257570267,
-0.056505896151065826,
0.009522699750959873,
0.0010217145318165421,
0.04601245000958443,
-0.017845073714852333,
0.02489352785050869,
0.02085823565721512,
0.00237890868447721,
-0.039640963077545166,
-0.04517005756497383,
0.0995299220085144,
0.011202140711247921,
0.03709976747632027,
-0.006182305980473757,
-0.011419590562582016,
-0.04072718694806099,
0.03915846347808838,
0.00976430531591177,
-0.024961167946457863,
-0.019734075292944908,
-0.03531743586063385,
-0.009238292463123798,
-0.1008104756474495,
-0.021380798891186714,
0.01719379983842373,
0.017786910757422447,
-0.01093296892940998,
-0.06034696474671364,
0.050366733223199844,
-0.020495105534791946,
0.04636964574456215,
0.05856155604124069,
-0.02423720620572567,
0.013456840999424458,
0.01773248240351677,
0.0030842062551528215,
0.025056809186935425,
0.035607900470495224,
0.058475252240896225,
-0.0017977700335904956,
0.004920309875160456,
-0.035958223044872284,
-0.013212294317781925,
-0.020785199478268623,
0.03777698427438736
] |
<p>How broad is the term "String theory"?</p>
<p>Typical <a href="http://en.wikipedia.org/wiki/String_theory" rel="nofollow">brief descriptions of string theory</a> focus on the fact that it describes fundamental particles as being string-like rather than point-like, or, more generally, being at least 1-dimensional.</p>
<p>So is any model in which the fundamental particles are at least 1-dimensional a form of string theory? If not, what are the other requirements?</p>
<p>To put it another way, given a specific model, what factors would you consider when deciding whether that model was a string theory model or not?</p> | g7801 | [
-0.00994542334228754,
0.01284925825893879,
0.003946749493479729,
-0.040950577706098557,
0.02421540580689907,
-0.0071432399563491344,
-0.0061776526272296906,
-0.0377834253013134,
-0.015718860551714897,
-0.016079217195510864,
0.03682193532586098,
0.004426207859069109,
0.04115123301744461,
0.013626798056066036,
-0.008343037217855453,
-0.025318501517176628,
0.0022668014280498028,
-0.018254591152071953,
0.04710709676146507,
0.0000906166824279353,
0.030636027455329895,
0.0026859319768846035,
0.0328536294400692,
-0.029910113662481308,
-0.051017876714468,
0.026588261127471924,
-0.005936863366514444,
-0.03132030740380287,
0.026172613725066185,
-0.0010429498506709933,
0.03677896037697792,
-0.010282117873430252,
0.06779571622610092,
-0.02974296547472477,
-0.003766037756577134,
-0.03065057098865509,
0.0327262319624424,
0.05128376558423042,
0.02905920334160328,
0.026336001232266426,
0.005406457465142012,
-0.009273004718124866,
-0.0444842092692852,
0.02188870683312416,
-0.0030647132080048323,
-0.018335172906517982,
0.026279544457793236,
-0.003230951726436615,
-0.00710276560857892,
0.002830119803547859,
0.013982807286083698,
-0.0023923562839627266,
0.0211830735206604,
0.006435551680624485,
0.01988636516034603,
0.007175522390753031,
-0.00808147806674242,
0.021193644031882286,
0.09194100648164749,
0.016348805278539658,
-0.047197286039590836,
0.1225665733218193,
-0.03758303076028824,
0.026297874748706818,
-0.01952715404331684,
-0.005368439015001059,
-0.004319358617067337,
-0.05586148053407669,
0.05001375451683998,
-0.057359375059604645,
0.04662736877799034,
-0.033172592520713806,
-0.013212261721491814,
-0.025637663900852203,
-0.027721965685486794,
0.01583917811512947,
-0.12078175693750381,
-0.024667521938681602,
-0.03519576042890549,
-0.015220028348267078,
0.009225985035300255,
0.03243742510676384,
-0.004628791473805904,
-0.035599466413259506,
0.06610991060733795,
-0.042577922344207764,
-0.06906625628471375,
-0.0040540243498981,
0.01692088134586811,
0.014524221420288086,
-0.028101947158575058,
0.011821483261883259,
-0.0002757479960564524,
0.013788373209536076,
0.017279839143157005,
-0.015278007835149765,
-0.015095759183168411,
0.020018024370074272,
-0.02199917659163475,
-0.0009565362124703825,
0.00614656787365675,
0.029619164764881134,
0.012931965291500092,
-0.003813402494415641,
0.02824569307267666,
-0.006594422738999128,
0.02442450448870659,
0.0016675154911354184,
0.02814135141670704,
-0.02837255783379078,
-0.047855257987976074,
0.03127909079194069,
-0.03021477535367012,
0.0017940979450941086,
-0.07669511437416077,
0.014003580436110497,
0.013139083050191402,
0.06658788025379181,
0.002883320674300194,
0.04561550170183182,
-0.009446710348129272,
-0.05405774340033531,
0.10668487846851349,
0.02365083433687687,
-0.03421512618660927,
-0.0199449323117733,
-0.008916177786886692,
0.04574686288833618,
-0.03849866986274719,
-0.010488951578736305,
0.01891389861702919,
-0.0036305037792772055,
-0.017688335850834846,
-0.0007698882254771888,
0.04665036126971245,
0.07838509976863861,
-0.02675953134894371,
0.013462109491229057,
0.015499049797654152,
-0.024510741233825684,
-0.0028092232532799244,
-0.0049035814590752125,
-0.02136000245809555,
-0.015010012313723564,
-0.010527408681809902,
0.017486052587628365,
0.01868598349392414,
0.02754516713321209,
-0.02043796516954899,
0.06431851536035538,
-0.008817125111818314,
0.0814061239361763,
0.018650751560926437,
0.0038448080886155367,
0.005124988500028849,
0.038574494421482086,
0.07109062373638153,
0.0033663809299468994,
-0.04665708541870117,
-0.02019958756864071,
0.003046087920665741,
0.0028274080250412226,
0.016210153698921204,
-0.026745423674583435,
-0.056816376745700836,
-0.023850806057453156,
-0.009248499758541584,
-0.03313940390944481,
-0.004404459148645401,
-0.04969367757439613,
-0.0067203473299741745,
0.006671328097581863,
0.02875455468893051,
0.010500308126211166,
-0.010173446498811245,
-0.037502966821193695,
0.010880198329687119,
0.0007019979530014098,
0.035547539591789246,
0.0077551184222102165,
0.0016352914972230792,
-0.04829235374927521,
-0.0029943683184683323,
0.00037543693906627595,
-0.003388312878087163,
0.007462465204298496,
-0.018611274659633636,
0.0064699687063694,
0.035816892981529236,
0.05102746933698654,
-0.01495837140828371,
-0.05162343382835388,
0.020645640790462494,
0.007676076143980026,
0.009562295861542225,
-0.06466792523860931,
0.007073655724525452,
-0.020609157159924507,
-0.00199018488638103,
-0.003945270087569952,
0.019472504034638405,
0.08962804824113846,
0.016429107636213303,
0.035080403089523315,
0.021380377933382988,
-0.003763525979593396,
-0.0238984152674675,
-0.0013771544909104705,
-0.008164777420461178,
-0.01302250474691391,
0.019981300458312035,
-0.020350854843854904,
-0.03898978233337402,
0.031577058136463165,
-0.06232380121946335,
-0.043625470250844955,
-0.03730490058660507,
0.04934253916144371,
-0.038236238062381744,
0.05990161746740341,
0.03413379564881325,
-0.037922728806734085,
0.046239499002695084,
0.01931910775601864,
-0.032517921179533005,
0.03920227289199829,
0.03424534946680069,
0.008301802910864353,
-0.01276834961026907,
0.028086213394999504,
-0.03113267943263054,
-0.07653973251581192,
-0.02621784247457981,
-0.029556507244706154,
0.004329440649598837,
-0.012100915424525738,
-0.020062267780303955,
-0.07713533192873001,
0.0583978109061718,
-0.015002314932644367,
0.013345645740628242,
-0.0090833380818367,
0.028761882334947586,
-0.03502558544278145,
-0.004890764132142067,
-0.06445744633674622,
-0.019467193633317947,
-0.010547655634582043,
-0.02256295457482338,
0.008770501241087914,
-0.02975095435976982,
-0.016191421076655388,
-0.010163608007133007,
-0.006979038007557392,
0.05744900926947594,
-0.013664635829627514,
0.0702057033777237,
0.057323653250932693,
-0.04321642592549324,
-0.03247038647532463,
0.021962972357869148,
-0.067774698138237,
-0.016279803588986397,
0.014748570509254932,
-0.05826422944664955,
0.011673223227262497,
0.02647397294640541,
0.0099348034709692,
-0.045707929879426956,
-0.03552955761551857,
-0.015474650077521801,
0.00666799396276474,
-0.029027681797742844,
-0.0600799061357975,
-0.017203502357006073,
0.03147539123892784,
-0.004861445631831884,
0.026152219623327255,
-0.033701952546834946,
-0.014903804287314415,
0.035072579979896545,
-0.007493939250707626,
-0.03208225965499878,
-0.014280787669122219,
0.02538134716451168,
-0.06067199259996414,
0.009699147194623947,
-0.03731406852602959,
-0.07265996932983398,
0.01749598979949951,
-0.01962142065167427,
0.015633389353752136,
0.02488023415207863,
-0.010542183183133602,
0.020751474425196648,
0.03427154943346977,
0.004582192748785019,
-0.010231474414467812,
0.0130434175953269,
0.07936372607946396,
-0.03459737077355385,
0.03513598069548607,
-0.01685640960931778,
0.052213892340660095,
0.02448863349854946,
0.015080512501299381,
-0.07089313864707947,
-0.02939252369105816,
-0.017250798642635345,
-0.018996963277459145,
-0.03934963047504425,
0.08981606364250183,
0.05983327329158783,
0.04070093855261803,
-0.03928877413272858,
0.013857966288924217,
0.011812914162874222,
0.05805155634880066,
0.020387187600135803,
-0.013814380392432213,
-0.0032725329510867596,
-0.021813221275806427,
0.0756455808877945,
-0.012556763365864754,
-0.0007109891157597303,
0.05953741446137428,
0.008721137419342995,
-0.04741650074720383,
-0.07605859637260437,
-0.03313515707850456,
0.03428485989570618,
-0.08954028785228729,
-0.025722648948431015,
-0.02564268931746483,
-0.04289586469531059,
-0.0331747904419899,
0.017030030488967896,
-0.0464082732796669,
0.05194438621401787,
-0.034425847232341766,
-0.0018706177361309528,
0.014057950116693974,
0.04750565439462662,
-0.009852753952145576,
0.018671225756406784,
-0.023594340309500694,
-0.019623706117272377,
-0.020953096449375153,
0.08393897861242294,
-0.026119746267795563,
0.04336334392428398,
0.0016182006802409887,
0.030577775090932846,
-0.019045816734433174,
0.009046417661011219,
0.014616141095757484,
0.07318922132253647,
0.10209599137306213,
-0.02272580936551094,
0.01953183300793171,
0.04315546154975891,
-0.03180105611681938,
-0.01063621323555708,
0.004314550664275885,
-0.01364864781498909,
0.011636704206466675,
-0.0051215398125350475,
-0.020069660618901253,
0.03845345973968506,
0.012442455627024174,
0.021060146391391754,
-0.0067800250835716724,
-0.02518448606133461,
0.00009210351709043607,
0.03342822566628456,
0.0424891859292984,
0.04081118851900101,
-0.022342665120959282,
-0.022544430568814278,
-0.0048317862674593925,
0.027864504605531693,
0.057769712060689926,
-0.039967384189367294,
0.013643309473991394,
0.0018221888458356261,
-0.002684366889297962,
-0.061442743986845016,
0.006977765820920467,
-0.042478371411561966,
0.02360529825091362,
-0.0011229622177779675,
-0.05755011364817619,
0.002700217068195343,
-0.05591509863734245,
0.011170884594321251,
-0.005112239625304937,
0.00554333021864295,
-0.019538886845111847,
-0.00791426282376051,
0.018107237294316292,
0.049396026879549026,
0.048808760941028595,
-0.008010921999812126,
-0.018305834382772446,
0.03963424265384674,
-0.006114425603300333,
-0.04382096603512764,
-0.01687372475862503,
-0.05762069299817085,
0.004141300916671753,
0.0035302450414747,
0.029611485078930855,
-0.007814852520823479,
0.03278493508696556,
-0.0032203802838921547,
0.005386194214224815,
-0.035338956862688065,
-0.059639234095811844,
-0.0023227068595588207,
0.01377738919109106,
0.00811164453625679,
0.06328009068965912,
-0.03944845870137215,
-0.0169400442391634,
-0.031883593648672104,
0.031317561864852905,
0.007842944003641605,
0.06138007715344429,
-0.06834394484758377,
0.016381826251745224,
0.032864607870578766,
-0.007602289319038391,
-0.03400025889277458,
0.015090896748006344,
-0.05413766950368881,
0.04198182374238968,
-0.07346881181001663,
0.03220289573073387,
0.008066563867032528,
-0.03843816742300987,
0.025888454169034958,
0.0061100018210709095,
0.06826332211494446,
0.00040209360304288566,
0.0047254194505512714,
0.0036194308195263147,
-0.05150578171014786,
0.050116442143917084,
-0.04677426815032959,
0.02000643126666546,
-0.03568568825721741,
0.06296808272600174,
-0.07436522841453552,
-0.0485500693321228,
-0.02713393233716488,
0.0282709039747715,
0.019998200237751007,
0.03478340059518814,
0.014407431706786156,
0.0649019256234169,
-0.028443871065974236,
-0.0037980249617248774,
0.037912629544734955,
0.03913656249642372,
-0.013656075112521648,
-0.015209152363240719,
-0.030476361513137817,
-0.019474366679787636,
-0.008260377682745457,
-0.04806903377175331,
-0.02084815688431263,
-0.019207801669836044,
0.04392730072140694,
-0.03743332251906395,
-0.008142403326928616,
-0.01539598498493433,
-0.027036136016249657,
-0.03993212804198265,
-0.054009005427360535,
-0.008639499545097351,
0.052250828593969345,
-0.04367034509778023,
0.023054854944348335,
0.004762883298099041,
0.0578417107462883,
-0.010498893447220325,
-0.002445848425850272,
0.048843879252672195,
-0.01531559880822897,
0.06014040857553482,
-0.00893864780664444,
0.0018786025466397405,
-0.034985557198524475,
-0.005451679229736328,
-0.03203699737787247,
-0.014240005984902382,
0.0007505582179874182,
-0.05625339597463608,
-0.04065696522593498,
0.009503219276666641,
-0.05959851294755936,
-0.04858280345797539,
0.06955874711275101,
0.015480163507163525,
-0.04615063965320587,
0.02952343039214611,
0.04486291855573654,
-0.06196660175919533,
0.004607450217008591,
-0.04533682391047478,
0.008290684781968594,
-0.0008963336003944278,
-0.06463921815156937,
0.01725813001394272,
0.01530238427221775,
0.03719716519117355,
-0.04296277090907097,
0.01701698824763298,
0.009287750348448753,
-0.0032323303166776896,
-0.02439609356224537,
-0.04295346885919571,
0.060571908950805664,
-0.0006799401598982513,
0.03225170820951462,
0.019000397995114326,
-0.07803138345479965,
-0.013033604249358177,
0.004303000867366791,
0.061172615736722946,
0.04776802659034729,
-0.0042505026794970036,
0.00944623164832592,
0.04626722261309624,
0.007633065339177847,
0.017554981634020805,
0.003167528659105301,
0.05565178766846657,
0.037670377641916275,
-0.013549301773309708,
-0.061296530067920685,
0.07071022689342499,
-0.01680544950067997,
0.022798264399170876,
0.00630349013954401,
0.00041195290395990014,
0.0655275210738182,
0.04566427320241928,
0.044490743428468704,
-0.06775679439306259,
-0.05464807525277138,
0.008569067344069481,
-0.024279747158288956,
-0.026219630613923073,
-0.002309440402314067,
0.015415809117257595,
-0.03514314815402031,
-0.016036376357078552,
0.004235127009451389,
0.025316622108221054,
-0.030602382495999336,
-0.03144506365060806,
0.015192069113254547,
-0.014695730991661549,
-0.008227734826505184,
0.02293400838971138,
-0.03633061796426773,
-0.04683592915534973,
0.05295905843377113,
0.030029481276869774,
-0.007504480890929699,
0.02153930254280567,
-0.01249469630420208,
0.004153309855610132,
-0.023006649687886238,
-0.05824417620897293,
0.024344921112060547,
-0.026799123734235764,
-0.04047270491719246,
0.020630866289138794,
0.019765838980674744,
0.017817005515098572,
0.04580852761864662,
-0.03346840664744377,
-0.03595874458551407,
0.012937134131789207,
0.0023475238122045994,
-0.056713394820690155,
-0.003319485578685999,
0.07528337091207504,
0.0038250091020017862,
0.0010406523942947388,
-0.03554464876651764,
0.030702218413352966,
-0.019526822492480278,
-0.0068464684300124645,
0.02255619689822197,
0.01901382766664028,
0.006444677244871855,
0.03920581936836243,
0.015139902010560036,
0.021315569058060646,
0.001541381236165762,
0.03726429492235184,
0.03934101387858391,
0.11554153263568878,
0.024398447945713997,
0.049234937876462936,
-0.018237542361021042,
-0.025163372978568077,
-0.004018762614578009,
0.02671956457197666,
0.008005400188267231,
0.009351536631584167,
0.005447517614811659,
-0.06531310826539993,
-0.053898684680461884,
-0.04736616089940071,
-0.014410827308893204,
0.0033643164206296206,
0.019072456285357475,
0.023036591708660126,
0.06387190520763397,
0.03705411031842232,
-0.004283546935766935,
0.04556271806359291,
-0.05076111853122711,
0.11739980429410934,
0.05501943454146385,
-0.03102569840848446,
-0.025363938882946968,
-0.04317031428217888,
0.01579800620675087,
0.025643160566687584,
-0.007551329676061869,
-0.008432747796177864,
-0.06210922449827194,
-0.006763978861272335,
-0.05706847831606865,
0.02045907825231552,
-0.02606569230556488,
-0.027478542178869247,
0.09622830152511597,
-0.01208349596709013,
-0.02949051931500435,
-0.04783110320568085,
0.02988688461482525,
-0.007436349522322416,
-0.019815916195511818,
0.0020676879212260246,
-0.0033450559712946415,
-0.004989164881408215,
-0.021547241136431694,
-0.04027852788567543,
0.0833636000752449,
-0.0119432732462883,
0.026859264820814133,
0.04987403005361557,
0.02999521605670452,
-0.023490402847528458,
-0.06205139309167862,
0.012221787124872208,
0.04672614857554436,
-0.0791519433259964,
-0.022845042869448662,
0.08529851585626602,
0.01588086597621441,
-0.10273957252502441,
0.02804204635322094,
0.008637518621981144,
-0.0010807550279423594,
-0.027863476425409317,
0.011974181048572063,
0.01732349582016468,
0.00475159240886569,
-0.03507174178957939,
-0.0437292605638504,
0.026627350598573685,
0.021681495010852814,
-0.0027788863517344,
0.0393497496843338,
0.02754829078912735,
0.022962292656302452,
0.03729045018553734,
-0.03353608027100563,
0.022917307913303375,
0.035783179104328156,
-0.003556357230991125,
0.0016420709434896708,
0.02100376971065998,
0.0027443929575383663,
0.007973910309374332,
0.01661168970167637,
-0.11754150688648224,
0.011113086715340614,
-0.025105878710746765,
0.016969438642263412,
0.04518510773777962,
0.0380086787045002,
0.023444391787052155,
0.010236290283501148,
-0.06750734150409698,
-0.05333145335316658,
0.005760891828685999,
-0.011609571985900402,
-0.03960159793496132,
-0.028302352875471115,
-0.03128166124224663,
-0.0662958100438118,
-0.006864613387733698,
-0.0276234932243824,
0.08097051084041595,
0.011944597586989403,
0.06531494855880737,
0.03685039281845093,
-0.03683391958475113,
-0.018427040427923203,
-0.053823258727788925,
-0.044225942343473434,
-0.04544106125831604,
-0.023524867370724678,
-0.012997361831367016,
0.012972880154848099,
0.021365592256188393,
-0.027776185423135757,
-0.0008643458713777363,
-0.02023075334727764,
-0.07230740040540695,
0.059896714985370636,
0.010137977078557014,
-0.02733735926449299,
0.026072639971971512,
-0.029149789363145828,
0.06674961000680923,
-0.0428546704351902,
0.01913248561322689,
-0.02993043325841427,
0.015453479252755642,
-0.0740780234336853,
-0.0042843869887292385,
0.01527112815529108,
0.06431248039007187,
0.008724579587578773,
-0.015333069488406181,
-0.062460899353027344,
0.06581204384565353,
-0.05150667950510979,
0.02165256254374981,
-0.012576628476381302,
0.027353066951036453,
-0.029792500659823418,
0.011182771995663643,
0.04018126800656319,
0.04268871992826462,
0.05998995527625084,
-0.020489001646637917,
-0.032598789781332016,
0.011022359132766724,
0.003860915545374155,
-0.052980609238147736,
-0.04540124908089638,
0.020963121205568314,
0.0576382651925087,
0.07325831055641174,
-0.02320226840674877,
-0.004466795362532139,
0.006236275192350149,
0.047555457800626755
] |
<p>Can we apply the <a href="http://en.wikipedia.org/wiki/Matter_wave#de_Broglie_relations" rel="nofollow">de Broglie relations</a> to a <a href="http://en.wikipedia.org/wiki/Sound_waves#Physics_of_sound" rel="nofollow">sound waves</a> ?
Is it possible?
if yes how do you do that?
what would be the mass(m) in the equation?</p> | g7802 | [
0.013435962609946728,
-0.012335915118455887,
-0.001640744972974062,
-0.08329566568136215,
0.08769627660512924,
0.0041698128916323185,
0.009110705927014351,
0.016193021088838577,
-0.0432397834956646,
-0.037534985691308975,
-0.022681910544633865,
-0.00972126703709364,
-0.0010598155204206705,
0.04792700707912445,
-0.006184560712426901,
0.0031993528828024864,
0.040229201316833496,
-0.018615320324897766,
0.021415097638964653,
-0.006868193857371807,
0.036119502037763596,
-0.0355801060795784,
-0.0023624312598258257,
-0.06014199182391167,
0.005224786698818207,
0.008241552859544754,
0.01937040127813816,
-0.04026690125465393,
-0.04948129132390022,
-0.009416591376066208,
0.004019709769636393,
-0.00556224025785923,
0.0624588243663311,
0.021495245397090912,
-0.01620093546807766,
-0.01759626530110836,
-0.0043906825594604015,
0.02254466712474823,
0.007696912158280611,
0.014456724748015404,
0.014028958044946194,
0.003964392933994532,
0.01879868283867836,
-0.0044857715256512165,
0.029722344130277634,
0.04011049121618271,
-0.02241840586066246,
-0.04032731056213379,
-0.04590929299592972,
-0.012634576298296452,
-0.007381776347756386,
0.03053424134850502,
0.030708694830536842,
0.05169074982404709,
-0.028152426704764366,
0.05631883069872856,
0.0517430379986763,
-0.019726958125829697,
0.13895288109779358,
0.05244264006614685,
-0.02363484352827072,
-0.014814876019954681,
0.009131663478910923,
0.008328961208462715,
0.057514432817697525,
-0.010354887694120407,
-0.025229861959815025,
-0.031729694455862045,
-0.023359017446637154,
-0.03842949494719505,
0.0703325867652893,
-0.010232471860945225,
-0.008166908286511898,
-0.04888595640659332,
-0.004992691334336996,
0.013359024189412594,
0.005965550895780325,
0.016862688586115837,
-0.011180184781551361,
-0.0006365387816913426,
-0.026667051017284393,
-0.00808457937091589,
0.08467179536819458,
0.019692864269018173,
0.01668567769229412,
-0.07673493027687073,
-0.0013919873163104057,
0.02694818563759327,
0.013991986401379108,
0.03454994037747383,
-0.03557370975613594,
0.0038110686000436544,
0.006216797977685928,
0.024045385420322418,
0.030833914875984192,
-0.03971617668867111,
-0.0475858636200428,
0.010831979103386402,
0.015994679182767868,
-0.021815195679664612,
-0.02397509105503559,
0.007123062387108803,
0.01984192244708538,
-0.015682628378272057,
-0.01120284665375948,
0.027381643652915955,
-0.004418150056153536,
0.0014004337135702372,
-0.04108702391386032,
-0.0049841138534247875,
-0.06176532804965973,
-0.07025999575853348,
-0.020750099793076515,
0.005860510282218456,
-0.07944288849830627,
-0.06040377542376518,
0.009121405892074108,
0.0187099426984787,
-0.07556759566068649,
0.048100054264068604,
-0.004588091745972633,
0.008137480355799198,
-0.026289308443665504,
0.07237227261066437,
-0.046694379299879074,
-0.02760300599038601,
-0.045538149774074554,
0.00609670439735055,
0.11105066537857056,
-0.03053584136068821,
0.016542553901672363,
0.023307079449295998,
0.06571104377508163,
-0.022936340421438217,
-0.016043739393353462,
0.01732759177684784,
0.011908257380127907,
0.0016720021376386285,
-0.037867769598960876,
-0.0007727313204668462,
-0.003846418112516403,
-0.06615796685218811,
0.032041989266872406,
-0.031731344759464264,
-0.08000215888023376,
-0.006855301093310118,
-0.0038249557837843895,
-0.02550411969423294,
0.006159674376249313,
0.08261764794588089,
-0.032767098397016525,
0.0522821769118309,
0.018963424488902092,
0.005356509704142809,
0.0287332646548748,
-0.007046333514153957,
0.021224556490778923,
-0.011203817091882229,
-0.02370091713964939,
-0.05272290110588074,
0.006034105084836483,
-0.0024370963219553232,
-0.000009687692909210455,
0.020491383969783783,
-0.0025806634221225977,
-0.012749400921165943,
0.01809854805469513,
-0.009166335687041283,
-0.022086773067712784,
-0.025955382734537125,
-0.07539650797843933,
0.002997366013005376,
-0.04782985523343086,
0.06882253289222717,
0.03783857449889183,
0.04445183277130127,
0.00630889693275094,
-0.015302546322345734,
0.03705582767724991,
-0.019419154152274132,
-0.001448788563720882,
0.017267584800720215,
0.012837938964366913,
-0.05412888899445534,
-0.001993657788261771,
0.0367899052798748,
0.04455650970339775,
0.0035953850019723177,
-0.017298121005296707,
0.03931089863181114,
-0.08225839585065842,
-0.02613726258277893,
-0.03340914472937584,
0.016234131529927254,
0.0396542102098465,
0.03631972149014473,
-0.0018762837862595916,
-0.014603491872549057,
-0.016676535829901695,
0.03220387548208237,
-0.009533584117889404,
0.03193590044975281,
0.05383996665477753,
-0.0052553568966686726,
0.0911477580666542,
0.008360411040484905,
0.05001244321465492,
-0.0169720109552145,
0.009986838325858116,
-0.032174743711948395,
-0.02074754796922207,
0.003424259601160884,
-0.02643773891031742,
-0.009805276989936829,
-0.09033758193254471,
-0.010816569440066814,
0.028029950335621834,
-0.014772003516554832,
0.0057191671803593636,
0.037821780890226364,
-0.07739545404911041,
0.044664692133665085,
0.03372739255428314,
0.009124543517827988,
0.006179358344525099,
0.006380276754498482,
-0.011430698446929455,
-0.025388818234205246,
-0.061162468045949936,
-0.008904600515961647,
0.048407237976789474,
0.023552466183900833,
0.036653049290180206,
-0.018209004774689674,
0.06037769466638565,
0.08092106133699417,
-0.011838952079415321,
0.008254138752818108,
-0.03697442635893822,
0.06540781259536743,
0.049483854323625565,
-0.0074655055068433285,
-0.049533892422914505,
0.01151875127106905,
-0.026718392968177795,
-0.027687804773449898,
0.04195355251431465,
0.022301316261291504,
0.04216677322983742,
0.013220800086855888,
-0.019862506538629532,
-0.05132999271154404,
-0.003721826244145632,
-0.011126786470413208,
0.07204487174749374,
0.011661909520626068,
-0.0504993237555027,
0.0027182053308933973,
0.012238292954862118,
-0.0007134543848223984,
0.039046987891197205,
-0.03187333792448044,
0.020506571978330612,
0.00040082845953293145,
-0.09743181616067886,
-0.02961685322225094,
-0.05083434656262398,
-0.06688405573368073,
-0.006415530573576689,
0.0008205536869354546,
-0.0064930180087685585,
0.042179059237241745,
0.04468146711587906,
0.035968974232673645,
-0.03788239508867264,
-0.01753576472401619,
-0.0010373760014772415,
-0.00043990122503601015,
0.018855081871151924,
0.010189954191446304,
-0.058545418083667755,
0.058913856744766235,
0.0032887845300137997,
0.003469000803306699,
0.024593574926257133,
-0.04665728658437729,
-0.016354169696569443,
-0.002153232228010893,
0.0438750721514225,
0.03597312793135643,
0.017193084582686424,
0.03150041028857231,
0.035868577659130096,
0.06895938515663147,
-0.029912069439888,
0.05609291046857834,
0.018942099064588547,
-0.013609806075692177,
0.0304916650056839,
0.006998050957918167,
-0.020337728783488274,
0.018983088433742523,
-0.014309843070805073,
-0.04813923314213753,
-0.061385467648506165,
0.012526256032288074,
0.030896443873643875,
-0.027180945500731468,
-0.024487990885972977,
-0.0075425454415380955,
0.04595474526286125,
0.03174641728401184,
0.050141721963882446,
-0.020590869709849358,
-0.010892212390899658,
-0.026473727077245712,
0.04420491307973862,
-0.03911500796675682,
0.045020733028650284,
-0.02278960309922695,
-0.04480094462633133,
-0.04787740483880043,
0.05820077657699585,
-0.06213032081723213,
0.0342838279902935,
0.01580079086124897,
0.0030754469335079193,
0.06149405613541603,
-0.10582122206687927,
-0.043736569583415985,
-0.006207422353327274,
-0.0471528060734272,
-0.01264271792024374,
-0.05377904698252678,
-0.026685697957873344,
-0.004301448352634907,
0.030908742919564247,
-0.019138222560286522,
0.014073893427848816,
0.0613732635974884,
-0.02843593992292881,
-0.03981730341911316,
-0.059612248092889786,
0.031692780554294586,
-0.05516062676906586,
0.0766587108373642,
-0.005866233725100756,
-0.006997651886194944,
0.061897680163383484,
-0.09890341758728027,
-0.0563875176012516,
0.004558755084872246,
0.03526316210627556,
0.01326291635632515,
0.02540266327559948,
-0.01997872069478035,
0.06636277586221695,
0.019342096522450447,
0.044851552695035934,
0.010069113224744797,
-0.05471859127283096,
-0.019794976338744164,
0.02822623960673809,
-0.007824007421731949,
0.010543551295995712,
-0.020823443308472633,
-0.04768568277359009,
0.021772444248199463,
-0.03242480754852295,
0.008038556203246117,
-0.00011083450954174623,
-0.09015427529811859,
0.02168329246342182,
0.007170167751610279,
-0.0049944170750677586,
-0.04512602835893631,
-0.000372579408576712,
-0.022745715454220772,
-0.05327329784631729,
0.05047452449798584,
-0.010984605178236961,
0.03387885540723801,
0.051730312407016754,
-0.044351086020469666,
-0.009460083208978176,
-0.02439003251492977,
-0.03471082076430321,
-0.026179973036050797,
0.01584799773991108,
-0.0261661596596241,
-0.03285548463463783,
-0.022610940039157867,
-0.02685960754752159,
-0.009417903609573841,
0.006807108875364065,
-0.030690902844071388,
-0.014030082151293755,
-0.08849655091762543,
-0.06947249174118042,
0.05492924526333809,
0.00524583924561739,
0.03827769309282303,
0.02662339247763157,
0.018409276381134987,
-0.007596741430461407,
0.03306399658322334,
0.03694290295243263,
-0.03404488041996956,
-0.02599194087088108,
-0.010068248957395554,
-0.04919996112585068,
-0.07053093612194061,
0.021472422406077385,
-0.02425232343375683,
-0.0038267201744019985,
-0.01404721662402153,
0.06333809345960617,
-0.038698047399520874,
-0.028344787657260895,
0.0320725180208683,
-0.010786869563162327,
-0.001704503665678203,
-0.018362510949373245,
-0.01752120815217495,
-0.06311597675085068,
0.030158085748553276,
0.0637655109167099,
-0.059674013406038284,
0.008275479078292847,
-0.010851572267711163,
-0.043371036648750305,
-0.00958289671689272,
0.029733093455433846,
0.0350043848156929,
-0.077103391289711,
0.028200140222907066,
-0.03152042254805565,
0.012104959227144718,
0.03799590468406677,
-0.01588386669754982,
0.01193393487483263,
-0.0034925497602671385,
-0.029568051919341087,
-0.0031376013066619635,
0.012678301893174648,
0.06231062486767769,
-0.004246616270393133,
-0.045926179736852646,
-0.05335133522748947,
-0.037861909717321396,
-0.05400853231549263,
0.026376916095614433,
-0.054237283766269684,
-0.04961802437901497,
0.028773821890354156,
0.045506853610277176,
-0.00465453090146184,
0.03955015167593956,
0.001810824265703559,
-0.015166963450610638,
0.01914757490158081,
-0.01787116564810276,
0.04877656698226929,
-0.0019542279187589884,
0.05880323052406311,
-0.08727888017892838,
-0.0038901735097169876,
-0.02291555516421795,
-0.04450289532542229,
-0.00019841220637317747,
0.03700270503759384,
0.0011401011142879725,
-0.04573274776339531,
0.020979106426239014,
0.0034800691064447165,
-0.0035893863532692194,
-0.029097089543938637,
-0.02623670920729637,
-0.02157972939312458,
-0.049363333731889725,
0.015030378475785255,
0.018737155944108963,
0.028404776006937027,
-0.013619926758110523,
0.01748085953295231,
0.06351086497306824,
-0.01515236310660839,
0.05869198963046074,
-0.03931296989321709,
-0.01538167241960764,
0.025000235065817833,
0.021880125626921654,
-0.039304379373788834,
-0.003987989854067564,
0.022733183577656746,
-0.011581615544855595,
0.030294647440314293,
-0.03682272136211395,
-0.017513442784547806,
-0.013732350431382656,
-0.03326626867055893,
0.01758194901049137,
-0.006622768472880125,
0.01899060048162937,
-0.050605643540620804,
0.04761384800076485,
0.017134591937065125,
0.011845930479466915,
-0.015004166401922703,
0.01990237459540367,
0.06649475544691086,
0.021251101046800613,
0.02036796323955059,
0.034365423023700714,
0.0011888779699802399,
-0.020222119987010956,
-0.03641798347234726,
0.022493179887533188,
0.006319665350019932,
0.010496595874428749,
0.0410621352493763,
-0.06329827755689621,
0.004398914519697428,
-0.00909179262816906,
-0.0498570017516613,
-0.056936778128147125,
-0.028897615149617195,
-0.054451532661914825,
0.0063111144118011,
0.03066413290798664,
-0.023587225005030632,
-0.026958834379911423,
0.0376470722258091,
-0.019565315917134285,
0.035352177917957306,
-0.0516882985830307,
-0.022544963285326958,
0.008300060406327248,
-0.008744150400161743,
0.034453850239515305,
0.017812134698033333,
0.01867743767797947,
0.018164843320846558,
0.0906972885131836,
0.07046234607696533,
0.004222864750772715,
0.027761070057749748,
0.019222084432840347,
-0.003813422517850995,
0.012334293685853481,
-0.07020000368356705,
-0.0203141700476408,
0.004200391937047243,
0.045745112001895905,
0.028699269518256187,
0.008688032627105713,
-0.024827709421515465,
-0.04995911940932274,
-0.02360955998301506,
0.026007160544395447,
0.01689056120812893,
0.03897179290652275,
0.026065392419695854,
0.01825696974992752,
-0.04263918101787567,
-0.010513951070606709,
0.02050122804939747,
-0.00834605097770691,
0.03676288202404976,
-0.004816366359591484,
-0.020300542935729027,
-0.030784592032432556,
-0.048249829560518265,
-0.036921486258506775,
-0.019560182467103004,
0.014982150867581367,
-0.024032268673181534,
-0.05186254158616066,
-0.012978330254554749,
0.012215062975883484,
0.016828611493110657,
-0.020703721791505814,
0.023935459554195404,
0.02528723143041134,
-0.022731859236955643,
-0.007836755365133286,
-0.005305602680891752,
0.009365536272525787,
0.0051726652309298515,
0.006970725487917662,
0.033992618322372437,
-0.02315111644566059,
-0.06980860233306885,
-0.0017587110633030534,
-0.017646418884396553,
-0.012850914150476456,
0.0021651675924658775,
-0.02421528473496437,
0.025467250496149063,
0.04901857674121857,
0.06422120332717896,
0.009227088652551174,
0.035450778901576996,
0.06854613125324249,
-0.013536143116652966,
0.025742169469594955,
-0.06704647094011307,
0.05245605483651161,
-0.018073972314596176,
-0.011734187602996826,
-0.06417040526866913,
-0.02084379270672798,
0.02612648904323578,
-0.02391757443547249,
0.011711479164659977,
0.01138940267264843,
0.011348140425980091,
0.0020465683192014694,
0.0043080998584628105,
-0.014176225289702415,
0.02141115814447403,
-0.01657393015921116,
0.01300875935703516,
-0.016998291015625,
0.0395108126103878,
-0.00832755770534277,
-0.014479621313512325,
-0.018633030354976654,
0.01616709865629673,
0.009940112940967083,
0.05376306176185608,
-0.005898519419133663,
0.020623138174414635,
0.0006679805810563266,
-0.009302058257162571,
0.08054026961326599,
0.041531752794981,
-0.02333994209766388,
0.044157542288303375,
0.05226347595453262,
-0.0501352958381176,
0.06041779741644859,
-0.004458687733858824,
0.06004072725772858,
-0.05818834528326988,
-0.050305578857660294,
0.06399210542440414,
-0.018145859241485596,
-0.1178133636713028,
-0.036791522055864334,
0.005192142445594072,
0.00211114133708179,
-0.0493437685072422,
0.06268022954463959,
-0.029896758496761322,
0.014600425027310848,
0.02287168800830841,
0.032334063202142715,
0.03444904461503029,
0.004448986612260342,
-0.07696016877889633,
-0.01858440227806568,
0.020757829770445824,
-0.020870113745331764,
0.05266852304339409,
0.0637860968708992,
0.03243618458509445,
-0.0241241492331028,
0.01273657288402319,
-0.0022011573892086744,
0.013492240570485592,
-0.021132510155439377,
-0.0321694016456604,
-0.018881382420659065,
-0.04737251624464989,
0.04331883043050766,
0.06064734235405922,
0.027812620624899864,
-0.011328515596687794,
0.024888314306735992,
0.030919354408979416,
-0.033773116767406464,
0.00023068682639859617,
-0.014025040902197361,
-0.007013312075287104,
0.032982248812913895,
0.02085748314857483,
0.042546965181827545,
0.06164124235510826,
0.014937628991901875,
-0.006750420201569796,
0.01097856741398573,
0.04188356176018715,
-0.011700066737830639,
-0.019894428551197052,
-0.043940309435129166,
-0.0016925742384046316,
0.026248078793287277,
0.005246169865131378,
-0.033148393034935,
0.0046276613138616085,
0.015205957926809788,
-0.0333569198846817,
-0.010983463376760483,
-0.01822439208626747,
-0.011654838919639587,
-0.007168050389736891,
-0.01028489414602518,
-0.010612129233777523,
-0.0031116087920963764,
-0.005141487345099449,
0.06439259648323059,
-0.06740544736385345,
0.03133954852819443,
0.09445726871490479,
-0.020546559244394302,
-0.02662079967558384,
0.08270614594221115,
-0.03564910218119621,
-0.014871658757328987,
-0.011393353343009949,
0.030727121978998184,
-0.020485958084464073,
-0.029544169083237648,
0.02033257484436035,
-0.009500071406364441,
-0.03167319297790527,
0.020684875547885895,
-0.019625909626483917,
0.003476593643426895,
-0.054323144257068634,
0.012601162306964397,
0.036158159375190735,
-0.00004536718552117236,
0.014092877507209778,
-0.031957607716321945,
0.06062053516507149,
-0.009783957153558731,
0.017015526071190834,
0.031164485961198807,
0.015127232298254967,
-0.06080703064799309,
0.019921306520700455,
-0.0023759794421494007,
0.0462229959666729,
0.0015105627244338393,
-0.03159613534808159,
0.028444333001971245,
0.061338119208812714,
-0.045351795852184296,
0.02558031864464283,
0.07239915430545807,
-0.011974289081990719,
0.01336559560149908,
0.033528607338666916,
-0.08238445222377777,
0.028579043224453926,
0.037616655230522156,
0.054115425795316696,
-0.004983705934137106,
0.03007361851632595,
0.05270979553461075,
-0.025440523400902748,
0.044210415333509445,
-0.07022292912006378,
-0.045049991458654404,
-0.01308400183916092,
0.01859200932085514
] |
<p>How does the Gordon Decomposition of Dirac Current give rise to spin angular momentum?</p>
<p>I used the Gordon Decomposition to split the Probability Current of the Dirac Field into its orbital current and its spin current. I multiplied the currents by $mc$ to covert them into momentum and then crossed the momentum with position to obtain the orbital angular moment and the spin angular momentum. However the spin angular momentum was twice as large as the accepted value of spin angular momentum. I am stuck on how to get rid of the extra factor of two. </p>
<p>The Gordon Decomposition splits the probability current into two terms
\begin{align}
mc\langle \gamma^{0n} \rangle
=
\langle \gamma^{0} i\hbar \partial^{n} \rangle
+
\tfrac{\hbar}{2}\partial_{j}\langle i\gamma^{0nj} \rangle_{n\neq j}
,
\end{align}
where $\langle \gamma^{0} i\hbar \partial^{n} \rangle$ looks like a orbital momentum current and $\tfrac{\hbar}{2}\partial_{j}\langle i\gamma^{0nj} \rangle_{n\neq j}$ looks like a spin momentum current?</p>
<p>The angular moments of $mc\langle \gamma^{0n} \rangle$ can be computed by crossing then with position to obtain the following:
\begin{align}
mc
\left(
x^m\langle \gamma^{0n} \rangle
-
x^n\langle \gamma^{0m} \rangle
\right)
=
\langle \gamma^{0} i\hbar (x^m\partial^{n}-x^n\partial^{m}) \rangle
+
\tfrac{\hbar}{2}\partial_{j}
\left(
x^m\langle i\gamma^{0nj} \rangle_{n\neq j}
-
x^m\langle i\gamma^{0nj} \rangle_{n\neq j}
\right)
,
\end{align}</p> | g7803 | [
0.012159028090536594,
-0.06946850568056107,
-0.0034722520504146814,
-0.07441757619380951,
0.08126035332679749,
0.0027075002435594797,
0.06649059057235718,
0.04518838971853256,
0.027734631672501564,
0.03251226246356964,
0.0011950409971177578,
-0.03476854786276817,
-0.05853129178285599,
-0.010610354132950306,
0.1297387182712555,
-0.03024027682840824,
0.029240665957331657,
-0.01806180365383625,
0.020133350044488907,
-0.04531149938702583,
-0.023300662636756897,
-0.04006553441286087,
0.03788093850016594,
-0.04323723912239075,
-0.03241570666432381,
-0.0452803373336792,
-0.03162996098399162,
0.012631525285542011,
-0.03391418233513832,
0.06605519354343414,
-0.01820797473192215,
-0.001200962346047163,
0.0034383730962872505,
-0.025163399055600166,
-0.004684194456785917,
0.017267931252717972,
0.04448588192462921,
0.07312235981225967,
0.011553654447197914,
0.01299194898456335,
-0.030451027676463127,
0.01264932006597519,
0.0010066144168376923,
-0.032354071736335754,
-0.0008762352517805994,
-0.015916857868433,
-0.015369814820587635,
0.008552640676498413,
-0.015592068433761597,
-0.025101935490965843,
-0.048404429107904434,
0.031065644696354866,
0.008856578730046749,
-0.0216901283711195,
-0.04105111211538315,
0.0782366469502449,
0.01427497062832117,
-0.01700311340391636,
0.04500443488359451,
0.014336323365569115,
0.024787841364741325,
-0.024384088814258575,
0.009956772439181805,
0.02614438347518444,
0.018450777977705002,
-0.01573428139090538,
-0.021573828533291817,
0.0115446075797081,
-0.008616682142019272,
0.007024023216217756,
-0.00855324137955904,
-0.02672535367310047,
-0.0014388300478458405,
-0.07692880928516388,
-0.047422975301742554,
0.030728019773960114,
0.052931249141693115,
-0.0017087084706872702,
-0.015627065673470497,
-0.011740747839212418,
-0.056957047432661057,
-0.0574745237827301,
0.015867285430431366,
0.015410132706165314,
0.01912802830338478,
-0.006865030620247126,
-0.01425108965486288,
0.033648937940597534,
-0.005902919918298721,
-0.02931906469166279,
0.03844589740037918,
-0.05497150123119354,
0.04577280208468437,
0.01971835270524025,
-0.003700248897075653,
-0.024719294160604477,
-0.06662561744451523,
0.05624905601143837,
-0.025274289771914482,
0.02107337862253189,
0.002776551991701126,
0.01779993250966072,
-0.002185082994401455,
-0.0021084772888571024,
0.010844385251402855,
-0.006098628975450993,
0.004144709091633558,
-0.011542976833879948,
-0.018909478560090065,
0.04247664660215378,
-0.029500870034098625,
-0.024793963879346848,
0.013343814760446548,
-0.017384890466928482,
-0.05142616108059883,
-0.062335848808288574,
0.019883645698428154,
-0.07523398101329803,
0.04345763474702835,
0.031420521438121796,
-0.04238088056445122,
0.024543479084968567,
-0.0027385421562939882,
0.04530761018395424,
0.027141215279698372,
-0.053780000656843185,
-0.006478625815361738,
0.05417422205209732,
0.11682736873626709,
0.006349820643663406,
0.08802969753742218,
-0.036228280514478683,
0.012240874581038952,
0.06848614662885666,
-0.010209338739514351,
0.05651810020208359,
0.012056078761816025,
0.05636783689260483,
-0.029223572462797165,
-0.0021273253951221704,
0.026958374306559563,
-0.0557139553129673,
0.06562989205121994,
-0.048708971589803696,
-0.02212447300553322,
0.015161173418164253,
-0.001400614157319069,
-0.02081194892525673,
-0.0044697355479002,
-0.006908069364726543,
0.04188472777605057,
0.04484761878848076,
-0.03944360464811325,
0.04059489071369171,
0.016245786100625992,
-0.006811481434851885,
0.04868360608816147,
-0.06129765883088112,
0.020259937271475792,
0.05641964450478554,
0.03683999553322792,
-0.013951228931546211,
-0.027273235842585564,
-0.01444967556744814,
-0.055854808539152145,
0.02061668410897255,
0.03264083340764046,
-0.0587555468082428,
-0.03442609682679176,
-0.055566880851984024,
-0.014228668995201588,
0.022182568907737732,
-0.007260365877300501,
0.02446276694536209,
0.03567514196038246,
0.07660394161939621,
-0.027811773121356964,
-0.004657783079892397,
-0.004345924127846956,
0.09443013370037079,
0.0015370884211733937,
0.0783345103263855,
0.07776505500078201,
0.006681450176984072,
0.020778803154826164,
0.01508359331637621,
0.032370276749134064,
0.05458964407444,
0.006859926041215658,
-0.0479980893433094,
-0.0028091606218367815,
0.00035511283203959465,
-0.014789264649152756,
0.014430330134928226,
-0.007600644137710333,
0.025108028203248978,
0.021464070305228233,
-0.06974265724420547,
-0.006004772614687681,
0.08281594514846802,
0.02990921027958393,
0.014216105453670025,
-0.0481550432741642,
0.05093470215797424,
0.02275717630982399,
-0.014491092413663864,
0.032466303557157516,
0.002328599337488413,
0.06528868526220322,
-0.050947438925504684,
0.026065539568662643,
-0.008343913592398167,
-0.04615628719329834,
-0.023245224729180336,
-0.0476362518966198,
-0.03346589207649231,
-0.011136919260025024,
0.026088573038578033,
-0.030861742794513702,
0.0256323404610157,
-0.007443015463650227,
-0.027897385880351067,
0.06372105330228806,
-0.05137357860803604,
-0.026157569140195847,
0.05947984382510185,
-0.0012419149279594421,
-0.0172457005828619,
0.021733205765485764,
0.046507928520441055,
-0.003956649452447891,
-0.0019187105353921652,
-0.018199704587459564,
-0.005030936095863581,
0.0246517825871706,
0.01138396468013525,
-0.028819415718317032,
-0.009872875176370144,
-0.06595265120267868,
0.014345820993185043,
-0.010748605243861675,
0.05533527582883835,
-0.027713946998119354,
-0.026613358408212662,
0.06765905022621155,
0.009484698064625263,
0.06867464631795883,
0.013008627109229565,
-0.009409679099917412,
0.01720818504691124,
0.07133273780345917,
-0.04707907885313034,
-0.061993181705474854,
0.020717209205031395,
-0.04186229407787323,
0.02718427963554859,
-0.020879028365015984,
0.081301249563694,
-0.06852833926677704,
-0.039870936423540115,
0.005569377448409796,
-0.01847427897155285,
0.01865261048078537,
0.02300783433020115,
-0.04602847620844841,
-0.03964153304696083,
-0.010346394032239914,
0.0653400719165802,
0.04690195247530937,
-0.004284105263650417,
-0.008977309800684452,
0.07044295221567154,
-0.013853118754923344,
-0.04068830609321594,
-0.009902618825435638,
-0.005015891510993242,
0.033746618777513504,
-0.020524941384792328,
-0.0264756977558136,
-0.006694581359624863,
-0.04466225579380989,
0.06616434454917908,
-0.015512567013502121,
0.010554930195212364,
0.03444887325167656,
-0.04339039698243141,
0.008881284855306149,
0.014601551927626133,
0.029406476765871048,
-0.0311866644769907,
-0.027698520570993423,
0.06199442595243454,
0.0556756928563118,
-0.04553268104791641,
0.054351452738046646,
-0.034640729427337646,
0.011840603314340115,
-0.02088255248963833,
-0.018824711441993713,
-0.026512734591960907,
-0.022859739139676094,
-0.02496427297592163,
-0.027388256043195724,
0.01807558722794056,
0.01075056754052639,
0.05339427292346954,
-0.0054906210862100124,
-0.010306022129952908,
-0.08064261078834534,
-0.0053243450820446014,
-0.050285689532756805,
0.03851524367928505,
-0.004586101975291967,
-0.01297034602612257,
-0.006262043956667185,
-0.05047706887125969,
-0.033955223858356476,
-0.008347471244633198,
-0.01771080493927002,
0.015622800216078758,
0.008529786951839924,
-0.05626172572374344,
0.006516952067613602,
-0.02244899608194828,
0.04888412356376648,
0.054616834968328476,
-0.0556538961827755,
0.0316496267914772,
-0.034416865557432175,
-0.022298291325569153,
-0.02911371923983097,
0.001703317859210074,
0.02723250538110733,
0.05202007666230202,
-0.06874887645244598,
0.0439428873360157,
-0.0068657491356134415,
0.040123194456100464,
0.0070112403482198715,
-0.057696789503097534,
0.02653767541050911,
-0.013752434402704239,
-0.034917205572128296,
-0.003504575928673148,
-0.009198862127959728,
-0.019601477310061455,
-0.00514675909653306,
0.011379237286746502,
0.02287352830171585,
-0.014377867802977562,
-0.05850251019001007,
-0.009829544462263584,
0.026534659788012505,
0.042665593326091766,
-0.0026671842206269503,
-0.014804321341216564,
-0.029004134237766266,
0.021854950115084648,
0.03931749612092972,
0.037219610065221786,
-0.011539633385837078,
-0.041651830077171326,
0.04046959429979324,
0.0471491664648056,
0.002252036239951849,
-0.03789971023797989,
-0.0392419807612896,
0.044441722333431244,
0.03600563853979111,
-0.029742417857050896,
0.04447058588266373,
-0.03969714790582657,
0.02474372088909149,
-0.03523937612771988,
-0.01328809279948473,
-0.03256122022867203,
0.013617496006190777,
0.012462424114346504,
0.02350347489118576,
0.03707345575094223,
-0.02770783193409443,
0.05180561915040016,
-0.02116183564066887,
0.06285786628723145,
-0.030336473137140274,
0.03606796637177467,
-0.0064154877327382565,
0.017207074910402298,
0.002405813429504633,
0.01144770160317421,
-0.02161928452551365,
-0.0506591871380806,
-0.006821929477155209,
-0.0051564560271799564,
0.0064003001898527145,
-0.08622362464666367,
-0.007212324533611536,
-0.037471190094947815,
-0.04200076684355736,
0.036920126527547836,
-0.015631960704922676,
0.03509650006890297,
0.0005619189469143748,
0.024905476719141006,
0.005931200459599495,
0.07880902290344238,
-0.018410466611385345,
0.00025644287234172225,
0.05907583236694336,
-0.01647811383008957,
0.000013582251085608732,
0.06870067119598389,
0.006075756624341011,
-0.033903710544109344,
0.03094448335468769,
-0.0406138077378273,
0.004898169543594122,
-0.030305571854114532,
-0.013954892754554749,
-0.011982268653810024,
-0.015496891923248768,
0.03362473472952843,
0.011746895499527454,
0.04446316882967949,
-0.011496779508888721,
0.005010891705751419,
0.03521258011460304,
-0.012592935934662819,
-0.005519934464246035,
-0.0455474928021431,
-0.016341613605618477,
0.035103585571050644,
-0.026274196803569794,
0.03211443871259689,
-0.09201880544424057,
0.006619289517402649,
-0.03977454826235771,
-0.02335912548005581,
-0.029349731281399727,
0.04297454282641411,
0.04028365761041641,
-0.04654548689723015,
0.03158998861908913,
-0.010727182030677795,
0.06641556322574615,
0.0050422390922904015,
0.00615919753909111,
-0.040121741592884064,
0.016538817435503006,
0.004895906895399094,
0.009935959242284298,
-0.04645529389381409,
0.018705207854509354,
0.036843083798885345,
-0.006075981073081493,
0.039549894630908966,
-0.08755552768707275,
0.01575332134962082,
-0.023386230692267418,
-0.017939098179340363,
-0.0727829858660698,
-0.021949799731373787,
0.014165254309773445,
-0.045038770884275436,
0.037989914417266846,
0.00861525908112526,
-0.0214224886149168,
-0.047062456607818604,
-0.0011746070813387632,
-0.08670688420534134,
0.0038122248370200396,
-0.035403165966272354,
-0.00835149735212326,
-0.008509786799550056,
-0.02378411404788494,
0.0100795216858387,
-0.028696348890662193,
-0.023017525672912598,
-0.049919482320547104,
0.0010553313186392188,
-0.06271962821483612,
0.006555372383445501,
0.05828853324055672,
-0.005162881221622229,
-0.0034782905131578445,
-0.07344149053096771,
0.014254497364163399,
-0.05202625319361687,
0.001323292963206768,
-0.001778318197466433,
0.017712682485580444,
0.11447661370038986,
-0.0005023024277761579,
-0.018229514360427856,
0.03485993295907974,
0.08170848339796066,
0.017659399658441544,
-0.04147045686841011,
-0.029275650158524513,
0.024115029722452164,
-0.006429740227758884,
-0.01948695257306099,
-0.03145216405391693,
0.04053895175457001,
-0.0519951768219471,
0.07665487378835678,
0.015745684504508972,
0.0010690491180866957,
0.016599223017692566,
0.031115930527448654,
0.011519108898937702,
-0.03356082737445831,
0.029430978000164032,
-0.043255515396595,
0.020705848932266235,
-0.001932355691678822,
0.014563579112291336,
-0.03864172473549843,
-0.02067754790186882,
-0.052392054349184036,
0.017995458096265793,
-0.01165783777832985,
-0.001316371955908835,
-0.015072576701641083,
0.05360851064324379,
-0.06086946651339531,
-0.09126417338848114,
-0.01327693834900856,
0.02953479066491127,
0.052582163363695145,
0.03573547303676605,
-0.01823541335761547,
0.010172274895012379,
-0.0009344254503957927,
-0.01788417063653469,
-0.05539441481232643,
0.02914964035153389,
-0.06323599815368652,
-0.032205332070589066,
0.009311753325164318,
0.007220589555799961,
0.008540527895092964,
0.018479060381650925,
0.040146298706531525,
-0.0491425096988678,
0.012994297780096531,
-0.004447227343916893,
-0.04103890433907509,
0.03621703013777733,
-0.02143922820687294,
0.035652920603752136,
-0.005941053386777639,
0.03794751316308975,
0.0031383156310766935,
0.015191508457064629,
0.008540866896510124,
0.014274438843131065,
-0.006582317408174276,
-0.03274914249777794,
0.01763310469686985,
-0.007269633933901787,
-0.06667023152112961,
0.037302710115909576,
-0.005376230459660292,
-0.008021632209420204,
0.030085330829024315,
-0.018340183421969414,
-0.05257318913936615,
0.01041964627802372,
-0.04289627820253372,
-0.07926763594150543,
-0.006639501545578241,
-0.04917769134044647,
-0.0023100313264876604,
0.009875635616481304,
0.020482441410422325,
0.012670492753386497,
0.0019437954761087894,
-0.03323208913207054,
-0.015429866500198841,
-0.03211618959903717,
0.03421461954712868,
-0.03714072331786156,
0.0006488197832368314,
-0.05187354236841202,
0.05617654323577881,
-0.04528621584177017,
0.0041543361730873585,
0.04317943751811981,
0.017295826226472855,
-0.062223341315984726,
0.04767422005534172,
-0.07200885564088821,
-0.07403784990310669,
-0.014320616610348225,
-0.026363275945186615,
-0.01507190614938736,
-0.02746029943227768,
-0.03139329329133034,
0.015025559812784195,
0.06581196933984756,
0.0041777766309678555,
0.013590308837592602,
0.023242242634296417,
0.046513631939888,
0.05087951943278313,
0.013065002858638763,
-0.03653806075453758,
-0.01601906307041645,
0.007058225572109222,
-0.013159414753317833,
-0.01827426254749298,
-0.018220217898488045,
0.028942346572875977,
0.019796350970864296,
0.010461528785526752,
-0.0016865239012986422,
-0.011933892965316772,
-0.04043196886777878,
-0.015623625367879868,
0.037417665123939514,
0.022269947454333305,
0.015282055363059044,
-0.003919611219316721,
0.032053738832473755,
0.06216759607195854,
0.01787036843597889,
-0.03423832729458809,
0.010589435696601868,
-0.024713806807994843,
0.006380220875144005,
0.006491038482636213,
0.026629691943526268,
0.004187926650047302,
0.031155282631516457,
0.04404580593109131,
-0.018597902730107307,
0.01821500062942505,
0.018382374197244644,
0.04799811542034149,
0.07469215244054794,
0.04518532007932663,
0.02953527309000492,
-0.03390928730368614,
0.026721462607383728,
-0.034449778497219086,
0.0059182471595704556,
0.03202332556247711,
-0.045861661434173584,
0.01901884749531746,
0.03178926184773445,
-0.02603013627231121,
0.015589259564876556,
0.03248266130685806,
-0.03156024217605591,
-0.005210229195654392,
0.03585938736796379,
0.054414693266153336,
0.004600252956151962,
-0.032594118267297745,
-0.04575871303677559,
-0.014632806181907654,
-0.014334401115775108,
-0.06256420165300369,
-0.021825330331921577,
-0.042837876826524734,
-0.05011076107621193,
-0.024302365258336067,
0.04396156594157219,
-0.034168317914009094,
-0.07236594706773758,
-0.011550725437700748,
-0.07584445923566818,
0.002676428994163871,
0.025550590828061104,
-0.009443478658795357,
0.055117540061473846,
-0.01790379174053669,
-0.029059594497084618,
-0.005721060559153557,
-0.02029944211244583,
0.055175475776195526,
-0.0744023472070694,
0.005365552846342325,
0.021578939631581306,
0.04513043165206909,
-0.026894157752394676,
0.047785792499780655,
0.01349937915802002,
0.03681032732129097,
0.017149487510323524,
0.07182388752698898,
0.06453732401132584,
-0.030170325189828873,
-0.018176736310124397,
0.01651259884238243,
-0.018970459699630737,
0.05219235643744469,
0.03863130509853363,
0.007969302125275135,
0.008327886462211609,
0.00404915027320385,
0.049865350127220154,
-0.022044336423277855,
-0.00034617618075571954,
0.023886287584900856,
0.05474679544568062,
-0.0267524104565382,
-0.012874316424131393,
-0.003877887735143304,
0.03361243009567261,
0.016487810760736465,
-0.03795401006937027,
-0.011724792420864105,
-0.038088008761405945,
0.034611012786626816,
0.0010404175845906138,
0.013967965729534626,
0.029468776658177376,
0.005516616627573967,
-0.004734651651233435,
0.02051599882543087,
-0.023640237748622894,
0.02108367532491684,
-0.08148184418678284,
-0.030742567032575607,
-0.01838792860507965,
-0.0022613629698753357,
0.010355113074183464,
0.022672029212117195,
0.005143285263329744,
-0.0241561196744442,
-0.030445348471403122,
0.007423726841807365,
0.021065115928649902,
-0.04463093355298042,
-0.03997694328427315,
-0.08371654897928238,
0.07379812002182007,
-0.026030361652374268,
0.005868338514119387,
-0.05508143827319145,
-0.008683811873197556,
-0.05194668471813202,
-0.022106023505330086,
-0.026784932240843773,
-0.019498532637953758,
0.047506675124168396,
0.0271610114723444,
0.05470533296465874,
0.00901882816106081,
0.04929572343826294,
-0.0035324282944202423,
-0.011721240356564522,
-0.006132312119007111,
0.008923006244003773,
-0.03288968279957771,
0.08982972055673599,
0.0006408861954696476,
0.029825134202837944,
0.012336518615484238,
-0.00028008627123199403,
-0.03582611680030823,
0.03357497230172157,
0.03056563064455986,
-0.022577591240406036,
-0.03845183551311493,
0.024931827560067177
] |
<p>I want to calculate the distance between two objects using an iPhone camera. </p>
<p>Suppose I'm standing with my iPhone 10 feet away from the objects. Now, I want to calculate the distance between those two objects. </p>
<p>Suppose these two objects are on a straight horizontal line. So, how can I calculate the distance between those two points?</p>
<p>I have only the one predefine value like 10 feet or 5 feet/meter which is the distance between camera and the object.</p>
<p>From the above information how can I calculate the distance between two point OR distance of maximum width of screen ? </p>
<p>Reference Android App: <a href="https://play.google.com/store/apps/details?id=kr.sira.speed&hl=en" rel="nofollow">Speed Gun</a></p> | g7804 | [
0.035987842828035355,
-0.03841453790664673,
-0.011431131511926651,
0.06335799396038055,
0.028291698545217514,
0.00915745459496975,
0.019983472302556038,
0.015338601544499397,
-0.03847694396972656,
-0.04983748123049736,
-0.0424579419195652,
-0.015695326030254364,
0.07156860083341599,
0.0029916041530668736,
0.019311955198645592,
-0.0062298281118273735,
0.052032146602869034,
-0.07100318372249603,
0.01169984694570303,
0.013386285863816738,
0.05667693167924881,
0.017548467963933945,
0.0036746386904269457,
-0.051922623068094254,
-0.08054803311824799,
-0.027640433982014656,
-0.002089814515784383,
0.06209099292755127,
-0.07574402540922165,
0.092923603951931,
-0.05446821451187134,
0.08654452115297318,
0.032538868486881256,
0.0038160081021487713,
0.026795830577611923,
-0.007371863350272179,
0.01912188157439232,
0.02617049589753151,
0.029221707955002785,
-0.009566853754222393,
0.027865776792168617,
0.032673850655555725,
0.012721234001219273,
0.0012217952171340585,
0.07266848534345627,
-0.053247611969709396,
-0.025156520307064056,
0.028427237644791603,
0.014076207764446735,
-0.0063875941559672356,
-0.04830947890877724,
0.083741195499897,
0.0010860748589038849,
-0.013005726039409637,
0.014708362519741058,
0.03280499204993248,
0.016519315540790558,
-0.039015814661979675,
0.00688544474542141,
-0.013079768978059292,
0.007012458518147469,
-0.04548660293221474,
-0.0014257464790716767,
0.04222946986556053,
0.05720764398574829,
0.034968115389347076,
-0.05886318162083626,
-0.04829717054963112,
-0.055626031011343,
0.024919556453824043,
0.0008109858608804643,
-0.0675307884812355,
-0.005628173239529133,
-0.0492708683013916,
-0.0772092342376709,
-0.06903918087482452,
0.022952793166041374,
0.01293273363262415,
0.02628559060394764,
0.029127279296517372,
0.032064471393823624,
0.016542773693799973,
0.0019100214121863246,
-0.01116003468632698,
0.0413813479244709,
0.006022183690220118,
0.04402409493923187,
0.039654262363910675,
-0.04274540767073631,
0.02008381113409996,
-0.00047604937572032213,
0.019034728407859802,
0.0770275741815567,
0.02773072011768818,
0.0013829701347276568,
-0.05900667607784271,
-0.013894853182137012,
0.012564478442072868,
0.015480185858905315,
-0.03547655791044235,
-0.03754696622490883,
0.0004134938062634319,
0.09327235072851181,
-0.008572147227823734,
0.019408676773309708,
0.026117676869034767,
0.0622282475233078,
-0.032487161457538605,
-0.05883176997303963,
-0.03468060865998268,
-0.035021375864744186,
-0.04487481340765953,
-0.002988891676068306,
-0.06515306234359741,
-0.0039770398288965225,
-0.04791979491710663,
0.03240770474076271,
0.05521160736680031,
0.06847228109836578,
-0.015676429495215416,
-0.0596645325422287,
0.03810138255357742,
0.01079934649169445,
0.0789259523153305,
-0.013856765814125538,
-0.054635751992464066,
-0.058226704597473145,
-0.0038599788676947355,
0.05546252056956291,
-0.010382447391748428,
-0.005754436366260052,
-0.016026707366108894,
0.01935432292521,
-0.00754204485565424,
-0.07294345647096634,
0.023033507168293,
0.030476359650492668,
0.04112774878740311,
-0.023132670670747757,
0.02416299469769001,
0.0088801309466362,
0.002985283499583602,
-0.03537347540259361,
-0.020278561860322952,
-0.06974278390407562,
0.02065623737871647,
-0.014003408141434193,
-0.00776287168264389,
0.038721200078725815,
0.04013949632644653,
0.07118680328130722,
0.0453190803527832,
-0.024086473509669304,
0.05352417007088661,
0.02570563368499279,
-0.015148421749472618,
-0.05481100454926491,
0.059214554727077484,
0.03584232181310654,
-0.02538192644715309,
0.023375244811177254,
0.02732090838253498,
-0.008416733704507351,
-0.037503067404031754,
-0.0466948002576828,
-0.0275869183242321,
-0.04293122515082359,
-0.02009083889424801,
-0.018736686557531357,
-0.08115283399820328,
-0.04488087445497513,
0.0010595725616440177,
0.06057703122496605,
-0.01840761862695217,
0.0379394106566906,
0.01100927870720625,
-0.017980225384235382,
0.02622891776263714,
-0.04418618977069855,
-0.004360057879239321,
0.0025260229595005512,
-0.025078916922211647,
-0.0049430993385612965,
-0.014136753045022488,
-0.04277649149298668,
0.06495413184165955,
0.02393641136586666,
-0.004729115404188633,
-0.009453443810343742,
-0.005290806293487549,
-0.06344133615493774,
-0.011035728268325329,
0.02984706126153469,
-0.008922701701521873,
-0.017390228807926178,
0.006838963367044926,
0.10727714747190475,
0.03408776596188545,
0.003671108977869153,
0.004413601942360401,
-0.004628557711839676,
0.00949033722281456,
-0.028941283002495766,
0.04130207374691963,
0.029091279953718185,
0.003509638598188758,
0.018007948994636536,
-0.015380077064037323,
-0.037542834877967834,
-0.019267620518803596,
-0.025511713698506355,
0.0030542912427335978,
-0.001415781443938613,
-0.03648460656404495,
0.047596484422683716,
-0.019488302990794182,
0.012003977783024311,
-0.020360242575407028,
-0.08743944019079208,
0.018677636981010437,
0.023250939324498177,
0.012058262713253498,
0.025252509862184525,
-0.011944866739213467,
0.04276784881949425,
-0.03151506558060646,
-0.015796806663274765,
-0.019393587484955788,
-0.05271543934941292,
0.04387325048446655,
0.0011526963207870722,
0.0005421455716714263,
-0.009987822733819485,
0.01725626550614834,
0.030099567025899887,
0.018345173448324203,
-0.016273634508252144,
0.05908603221178055,
-0.009566039778292179,
0.013005408458411694,
0.03740961104631424,
-0.04410380870103836,
0.002309612464159727,
0.034424055367708206,
0.016933172941207886,
-0.058091405779123306,
0.00232663843780756,
0.011535495519638062,
0.0016011374536901712,
0.03174006938934326,
-0.017273105680942535,
0.010158131830394268,
0.014317071996629238,
-0.03757404908537865,
-0.012171071022748947,
-0.043281055986881256,
-0.02038668282330036,
0.003027021186426282,
-0.07658914476633072,
-0.018303295597434044,
-0.032104358077049255,
0.0023961798287928104,
-0.00986451655626297,
-0.009512137621641159,
-0.015590283088386059,
-0.015599063597619534,
-0.06177161633968353,
0.020011279731988907,
0.06046753376722336,
0.001441779313609004,
0.0041869510896503925,
0.02130863070487976,
0.008995000272989273,
-0.023195302113890648,
-0.012855619192123413,
-0.05253094434738159,
0.04310566931962967,
-0.0005273921997286379,
0.029455292969942093,
0.04483645036816597,
0.04254424199461937,
-0.019038867205381393,
-0.09089387208223343,
0.05912761762738228,
0.013429712504148483,
-0.028728611767292023,
0.02668464370071888,
0.05897507816553116,
0.03832976892590523,
-0.02125101163983345,
0.020102404057979584,
0.01844026707112789,
-0.011035973206162453,
-0.021806595847010612,
-0.016373667865991592,
0.007262824103236198,
-0.031166570261120796,
0.0472571887075901,
0.05322163179516792,
-0.009209726005792618,
0.001449043396860361,
0.006264300551265478,
0.018337002024054527,
-0.013169084675610065,
0.04311632364988327,
-0.04006563499569893,
0.014518553391098976,
-0.028797850012779236,
-0.015671266242861748,
-0.04695134609937668,
-0.0012125413632020354,
0.004700204823166132,
-0.025583432987332344,
-0.01933109574019909,
-0.007978429086506367,
-0.02801034227013588,
-0.02074696496129036,
0.016375349834561348,
0.013597892597317696,
0.009103599935770035,
0.005472713615745306,
-0.06981536000967026,
-0.0036710738204419613,
0.042338259518146515,
0.01097253616899252,
0.06331901252269745,
-0.006050843745470047,
0.02197493612766266,
-0.008794870227575302,
0.018543248996138573,
-0.0035993170458823442,
0.033288177102804184,
-0.02834518440067768,
0.005033992230892181,
0.02782442979514599,
-0.0672849789261818,
0.034501057118177414,
-0.023882871493697166,
0.029724666848778725,
0.02355068363249302,
0.026345856487751007,
0.040823593735694885,
-0.04689732566475868,
-0.014817148447036743,
-0.0010281672002747655,
-0.002438948256894946,
0.01694292202591896,
0.03380703553557396,
-0.0030667453538626432,
-0.00572306290268898,
-0.0014728120295330882,
0.009264601394534111,
-0.008543627336621284,
-0.00676713278517127,
0.028912261128425598,
0.09419289976358414,
-0.0657038763165474,
0.018141716718673706,
-0.06359082460403442,
-0.02200903929769993,
0.050818879157304764,
0.03261242434382439,
-0.01326344721019268,
-0.016357650980353355,
-0.021134335547685623,
-0.011706196703016758,
-0.0015555943828076124,
-0.000591353396885097,
0.01691851206123829,
-0.02236931584775448,
0.025500373914837837,
-0.045789480209350586,
0.0030043257866054773,
-0.05265183001756668,
-0.02591019868850708,
0.00654430640861392,
0.04872565343976021,
-0.07271601259708405,
-0.023949040099978447,
0.010419397614896297,
0.01301640272140503,
0.006453246343880892,
0.030352605506777763,
0.018305763602256775,
0.0321541503071785,
-0.054291337728500366,
-0.01864193007349968,
0.00957503542304039,
0.12066365778446198,
-0.006080340128391981,
-0.014924313873052597,
-0.0709000900387764,
-0.04154863953590393,
-0.01207153033465147,
0.005154893733561039,
-0.016162818297743797,
0.010692663490772247,
0.06593429297208786,
-0.029661843553185463,
0.04548830911517143,
0.029731912538409233,
0.03811360523104668,
0.058117445558309555,
0.027566395699977875,
-0.04139212146401405,
-0.03757476434111595,
0.04697898402810097,
0.026299279183149338,
0.008187427185475826,
0.02470879815518856,
0.004781192634254694,
-0.018709968775510788,
0.012133573181927204,
-0.07427451759576797,
0.0268778707832098,
0.02608076110482216,
0.020876243710517883,
0.01910468190908432,
-0.023316457867622375,
-0.022734509781003,
0.006581918802112341,
0.054915186017751694,
-0.018668118864297867,
-0.05718882381916046,
-0.04940992593765259,
0.046001359820365906,
-0.017803238704800606,
-0.0442713163793087,
0.03778715059161186,
0.02748599462211132,
0.05170154571533203,
0.006202590186148882,
-0.0011495451908558607,
0.0065656667575240135,
-0.04284380376338959,
0.05463996157050133,
-0.010601689107716084,
0.010940652340650558,
0.018228432163596153,
-0.0946335718035698,
-0.027196694165468216,
0.029689563438296318,
0.025782467797398567,
0.039552707225084305,
-0.0018572331173345447,
0.02357531152665615,
-0.059348415583372116,
-0.015971079468727112,
-0.05121511220932007,
-0.019775308668613434,
0.007134902290999889,
0.044298116117715836,
-0.008834434673190117,
0.03539182245731354,
-0.04415246099233627,
0.011201197281479836,
-0.03438108414411545,
-0.022823913022875786,
0.05834256857633591,
0.005476190242916346,
-0.007905175909399986,
-0.004047130700200796,
0.0030478828120976686,
-0.012726262211799622,
0.008694970980286598,
0.0021006858441978693,
-0.06498018652200699,
-0.03565211594104767,
0.010616542771458626,
0.03662365674972534,
0.025876928120851517,
0.03427319601178169,
-0.014563532546162605,
0.0018990555545315146,
0.02517656795680523,
0.005455838516354561,
-0.03728940337896347,
-0.004025290720164776,
-0.0021804976277053356,
0.0012838831171393394,
-0.09454138576984406,
0.014356650412082672,
-0.026750411838293076,
-0.022563956677913666,
0.014734095893800259,
-0.011856195516884327,
-0.007985509932041168,
0.06941910088062286,
0.04558776691555977,
-0.006210707128047943,
-0.04319075495004654,
-0.011566692031919956,
-0.032724738121032715,
0.050914257764816284,
-0.016320688650012016,
-0.010120205581188202,
-0.0032088947482407093,
0.0676235482096672,
-0.06003517284989357,
0.017421338707208633,
-0.024733394384384155,
-0.02971196174621582,
0.014917583204805851,
0.024295110255479813,
0.068842314183712,
0.009021819569170475,
-0.026913531124591827,
0.0005987064796499908,
0.016997061669826508,
0.027516724541783333,
0.042986731976270676,
-0.016530636698007584,
0.01985117420554161,
-0.009513231925666332,
-0.0019627464935183525,
-0.012562624178826809,
-0.0024524268228560686,
0.02043982408940792,
-0.015600514598190784,
0.009326820261776447,
0.11782758682966232,
-0.06267214566469193,
-0.00006402729195542634,
-0.01595478132367134,
-0.01162993535399437,
-0.029665345326066017,
-0.03186170756816864,
0.019035683944821358,
0.0183845404535532,
0.02085540071129799,
0.02326171286404133,
0.01548916194587946,
-0.02501070871949196,
-0.06114013493061066,
-0.04980805143713951,
-0.0018419818952679634,
-0.03654751926660538,
-0.03069494292140007,
0.028546296060085297,
-0.022167129442095757,
0.007384628057479858,
-0.02625269442796707,
0.038368597626686096,
0.031046267598867416,
-0.00590299628674984,
-0.04393276572227478,
-0.027178147807717323,
-0.007363383192569017,
0.027713030576705933,
0.02446339838206768,
-0.01922178454697132,
0.052124183624982834,
-0.007017940748482943,
-0.07438627630472183,
0.05371776968240738,
0.014148310758173466,
0.02488464117050171,
-0.022589966654777527,
-0.019961683079600334,
-0.008555134758353233,
0.04560856521129608,
0.029555002227425575,
-0.004163794219493866,
0.00416439026594162,
0.00740580540150404,
-0.06870408356189728,
-0.04194944351911545,
0.03296045586466789,
0.07862554490566254,
0.023072432726621628,
-0.04804668575525284,
-0.00575766758993268,
-0.04538910835981369,
-0.012721381150186062,
0.04987563565373421,
0.013425729237496853,
0.0049767703749239445,
-0.02826014906167984,
-0.07635894417762756,
0.028917351737618446,
-0.03589462488889694,
0.054748084396123886,
-0.012681840918958187,
-0.028061307966709137,
-0.03975126892328262,
0.013530457392334938,
0.02168809063732624,
-0.054576218128204346,
0.059391848742961884,
-0.05278986319899559,
0.04154447093605995,
-0.013286607339978218,
-0.031292933970689774,
-0.08832446485757828,
0.005306940991431475,
-0.025683676823973656,
0.03494546562433243,
0.04018784314393997,
-0.03837069123983383,
0.061432577669620514,
0.004569436423480511,
-0.02209591493010521,
0.026083065196871758,
0.006532433442771435,
-0.05117277801036835,
-0.019982488825917244,
-0.07416103035211563,
0.018545689061284065,
0.06134435161948204,
-0.10177844762802124,
-0.026867525652050972,
0.04344697669148445,
0.005915330722928047,
0.018887916579842567,
-0.03513672575354576,
0.014119375497102737,
0.02782561630010605,
-0.08162327110767365,
-0.03339366242289543,
0.002583675319328904,
-0.03408520668745041,
0.01677015982568264,
0.04371076449751854,
-0.037099238485097885,
0.06003802269697189,
0.004442970734089613,
0.026468969881534576,
0.03654400631785393,
0.03579285368323326,
-0.0020178004633635283,
-0.0005916955415159464,
-0.0561630018055439,
0.03083941712975502,
0.02164009027183056,
-0.0021683142986148596,
0.0628679022192955,
-0.013120153918862343,
0.02509406954050064,
0.011073506437242031,
0.083034448325634,
0.04353205859661102,
-0.016154693439602852,
0.0008450138266198337,
0.032744262367486954,
-0.005511085502803326,
-0.004772052634507418,
-0.014183885417878628,
-0.0012334025232121348,
-0.002647152403369546,
0.025549478828907013,
-0.009937404654920101,
0.010857952758669853,
-0.027055682614445686,
0.0502326674759388,
-0.03734797239303589,
0.032779376953840256,
0.025208694860339165,
-0.04621129482984543,
-0.052451398223638535,
0.032368358224630356,
-0.014184869825839996,
-0.020358817651867867,
-0.007765527814626694,
-0.010348604992032051,
0.008395861834287643,
0.03421866521239281,
-0.02193344756960869,
0.010197356343269348,
-0.07561998814344406,
0.012687796726822853,
-0.04191911965608597,
-0.04180923104286194,
0.002536248415708542,
0.021745998412370682,
0.02818364091217518,
0.057877689599990845,
-0.009295831434428692,
0.0005305273807607591,
-0.057047199457883835,
-0.016716819256544113,
-0.011725678108632565,
0.012771141715347767,
-0.07372021675109863,
-0.032943110913038254,
-0.011743427254259586,
0.007034891750663519,
0.02466694824397564,
-0.027144597843289375,
0.07535706460475922,
-0.061874449253082275,
-0.04024758189916611,
-0.03123304434120655,
0.0023899944499135017,
-0.06690827012062073,
0.02017582766711712,
-0.018055416643619537,
-0.01087938342243433,
0.06013543903827667,
0.02982388250529766,
0.02607148140668869,
0.015419143252074718,
-0.036853160709142685,
0.0305379256606102,
0.036109644919633865,
0.015554139390587807,
-0.029622908681631088,
-0.005841867998242378,
0.013468545861542225,
0.0009110972750931978,
-0.004003772512078285,
-0.021712183952331543,
0.0415201336145401,
-0.014148244634270668,
0.004391773138195276,
-0.07047302275896072,
-0.013481225818395615,
-0.0029292458202689886,
0.03259491175413132,
0.005394982174038887,
0.048871368169784546,
0.0022594451438635588,
-0.044003311544656754,
0.04307453706860542,
-0.07009341567754745,
-0.06146044656634331,
0.045269615948200226,
0.009907829575240612,
-0.025829728692770004,
0.006997718941420317,
-0.030936527997255325,
0.011562025174498558,
0.004929363261908293,
-0.006007309537380934,
-0.040126144886016846,
-0.04112263396382332,
0.017094239592552185,
-0.007605773396790028,
-0.06368052959442139,
-0.012239300645887852,
0.03343070298433304,
0.04722218960523605,
0.023451456800103188,
-0.01822459138929844,
-0.009042231366038322,
0.012663301080465317,
-0.06896572560071945,
0.02512054517865181,
0.08743242174386978,
0.05566135048866272,
-0.019383316859602928,
-0.012922730296850204,
0.05475647747516632,
-0.0024287982378154993,
0.021359479054808617,
0.04235895723104477,
-0.09217749536037445,
0.04435198754072189,
-0.04670793563127518,
0.002643210580572486,
-0.03397507593035698,
0.019940577447414398,
0.01583198457956314,
-0.01683908887207508,
0.010796310380101204,
0.012916458770632744,
-0.05248204246163368,
-0.04534941911697388,
-0.014904617331922054
] |
<p>Much (All?) of quantum theory can be done in separable Hilbert spaces with a countable basis.<br>
How about quantum field theory? Is it “quite happy” (mathematically consistent) if everything is countable, or does it “need” to use an uncountable, continuous space (e.g. rigged Hilbert space) for mathematical consistency, or some other reason?</p> | g7805 | [
0.005782537627965212,
0.04086140915751457,
-0.010168618522584438,
-0.017944946885108948,
-0.011805725283920765,
-0.020490987226366997,
0.009876498021185398,
0.01349894143640995,
0.038296252489089966,
-0.001518825301900506,
-0.04930255934596062,
-0.04487954452633858,
0.002225917764008045,
0.05347581207752228,
-0.05150672420859337,
-0.004647033754736185,
0.031120138242840767,
0.01062779501080513,
-0.01614348031580448,
-0.038625698536634445,
0.003268890781328082,
0.082919642329216,
0.020955683663487434,
-0.05581355467438698,
0.02815585769712925,
0.0025544932577759027,
0.015640709549188614,
-0.07090145349502563,
0.035581719130277634,
0.020585691556334496,
-0.0017848130082711577,
0.014473682269454002,
0.018251225352287292,
-0.06074891239404678,
0.007277620490640402,
-0.020027395337820053,
0.010964084416627884,
0.019013727083802223,
0.07847337424755096,
0.025211377069354057,
0.023403314873576164,
0.006776114460080862,
-0.0327950082719326,
-0.09918839484453201,
-0.015982888638973236,
-0.014295603148639202,
-0.0010469438275322318,
0.0542064867913723,
0.02556406520307064,
0.02751576341688633,
-0.022815704345703125,
0.0026568658649921417,
0.027031267061829567,
0.018093569204211235,
0.06658884137868881,
0.06627010554075241,
0.03702811524271965,
-0.0026563697028905153,
-0.05663463845849037,
-0.0314137227833271,
0.0053704953752458096,
0.011218487285077572,
0.013003412634134293,
-0.006788764148950577,
0.05275692790746689,
0.04279829561710358,
-0.06564301252365112,
-0.010696823708713055,
-0.030083177611231804,
-0.005414694081991911,
0.001822273014113307,
-0.048839595168828964,
0.025330480188131332,
0.009469221346080303,
0.0017333567375317216,
0.03202151134610176,
-0.01045314036309719,
0.011705197393894196,
-0.0001238622353412211,
0.015219871886074543,
-0.030985640361905098,
-0.09946424514055252,
0.010687273927032948,
-0.029416842386126518,
0.0006111376569606364,
-0.03999757021665573,
0.027583489194512367,
-0.01693962886929512,
0.0016593807376921177,
0.06385144591331482,
0.0031216898933053017,
0.02373594045639038,
0.04585162550210953,
0.10573548823595047,
-0.011795085854828358,
-0.008223931305110455,
-0.01796356774866581,
0.005832167807966471,
0.001505750697106123,
-0.023545389994978905,
0.01243315264582634,
0.06631673872470856,
0.033217575401067734,
-0.017484866082668304,
-0.04326370730996132,
0.001798215671442449,
0.00528713408857584,
0.01946099102497101,
0.037576235830783844,
0.06142186000943184,
-0.026509473100304604,
0.021859051659703255,
0.005347919184714556,
-0.002946150489151478,
-0.030342772603034973,
0.03685803711414337,
0.05082518607378006,
-0.041590068489313126,
-0.04174879193305969,
0.04349346086382866,
-0.022868551313877106,
-0.014516910538077354,
0.06712125241756439,
-0.0011224925983697176,
-0.04910128936171532,
0.02694522589445114,
-0.012535679154098034,
0.04489240050315857,
0.025986814871430397,
-0.021659517660737038,
0.023484239354729652,
0.007961309514939785,
0.0022952575236558914,
0.05156493932008743,
-0.023392049595713615,
-0.04425930976867676,
0.026470845565199852,
0.002614307217299938,
0.028513280674815178,
0.030458617955446243,
-0.01786956377327442,
-0.00029586348682641983,
-0.00979198794811964,
-0.0056973714381456375,
0.02688298188149929,
-0.029740631580352783,
0.004166625905781984,
-0.02041870355606079,
0.02049638144671917,
0.057669516652822495,
0.038558509200811386,
0.041319288313388824,
0.0006700069643557072,
-0.024087848141789436,
-0.008385460823774338,
0.009145479649305344,
0.010283932089805603,
-0.038153890520334244,
0.08672619611024857,
-0.01303681917488575,
0.024845385923981667,
0.016139380633831024,
0.02245938964188099,
-0.050988998264074326,
0.007807131391018629,
0.003884402569383383,
-0.02383069507777691,
-0.005997265223413706,
-0.005893774330615997,
-0.027089187875390053,
0.014835200272500515,
0.02655993588268757,
-0.01100979559123516,
-0.012077974155545235,
0.02050459198653698,
0.02443879470229149,
-0.029230138286948204,
0.01191560085862875,
0.005055390764027834,
0.0023069209419190884,
0.021578386425971985,
0.06874709576368332,
-0.007705026771873236,
0.01494783814996481,
-0.024787647649645805,
0.06094176322221756,
0.012834154069423676,
-0.052358388900756836,
-0.05046327784657478,
0.00019110305584035814,
0.03289483115077019,
-0.010978254489600658,
-0.052055202424526215,
0.02844305895268917,
0.05966845154762268,
-0.010140287689864635,
-0.0024193308781832457,
-0.05638797581195831,
-0.010443930514156818,
-0.048898059874773026,
0.029768815264105797,
0.03675936535000801,
-0.032038431614637375,
0.005460796877741814,
0.02665565349161625,
0.01776023395359516,
-0.0012159853940829635,
-0.018606849014759064,
0.0004433723515830934,
-0.013587405905127525,
0.07959184050559998,
-0.009905148297548294,
-0.005744707304984331,
0.024958841502666473,
-0.03071708232164383,
-0.056409042328596115,
-0.02923729456961155,
-0.025436004623770714,
-0.03208334743976593,
0.016170645132660866,
0.02822119928896427,
0.0017143049044534564,
0.004712527152150869,
0.00701259495690465,
0.022635789588093758,
0.011934785172343254,
-0.02637912519276142,
0.020564328879117966,
-0.03066323883831501,
0.05061089247465134,
-0.02358473651111126,
-0.08619969338178635,
-0.014546694234013557,
-0.03514101356267929,
0.029620405286550522,
0.06885094195604324,
-0.0027449114713817835,
0.027647551149129868,
0.05212833732366562,
0.07276201993227005,
0.0707516074180603,
0.016933437436819077,
-0.045832984149456024,
-0.022915303707122803,
-0.0029595966916531324,
0.004620911553502083,
-0.058764614164829254,
0.009738489054143429,
0.010905656963586807,
0.028843645006418228,
-0.07811231911182404,
-0.06237266585230827,
0.016273345798254013,
0.0037925245705991983,
-0.004950269591063261,
0.03359386697411537,
0.04700322821736336,
-0.0013542416272684932,
0.011960770934820175,
0.013393665663897991,
0.03977612033486366,
-0.07241286337375641,
-0.00442667119204998,
0.02486063539981842,
-0.021541055291891098,
0.0024507585912942886,
0.016316857188940048,
0.006619908381253481,
-0.033518966287374496,
-0.010250897146761417,
-0.05844653770327568,
0.02302645519375801,
0.09357529878616333,
0.012563719414174557,
0.02359849028289318,
-0.011819667182862759,
-0.0440259724855423,
-0.0008148097549565136,
0.007039032410830259,
-0.001984354807063937,
0.0036783316172659397,
-0.002052363008260727,
-0.051910895854234695,
-0.016294682398438454,
0.015074457973241806,
-0.07135263830423355,
0.0041049774736166,
-0.01635042019188404,
0.030319694429636,
0.03359071910381317,
0.033281855285167694,
0.016744215041399002,
0.02410168945789337,
0.025555873289704323,
-0.05538073927164078,
-0.003121378133073449,
0.017231428995728493,
-0.049404025077819824,
0.000371861329767853,
0.08042341470718384,
-0.00152225058991462,
0.020913109183311462,
0.005443735513836145,
-0.006999452598392963,
0.030037488788366318,
-0.044111378490924835,
-0.05682595074176788,
0.003126904834061861,
0.01409882865846157,
-0.05889424681663513,
-0.015302262268960476,
0.027348347008228302,
0.04878974333405495,
-0.04678501933813095,
-0.00012482068268582225,
-0.03753890097141266,
0.022923899814486504,
0.001973128877580166,
0.059878505766391754,
-0.07559192180633545,
-0.025197172537446022,
-0.013841495849192142,
0.0443401038646698,
-0.027045946568250656,
0.04207668825984001,
0.08100878447294235,
-0.0220002643764019,
0.012200050055980682,
-0.027925873175263405,
-0.032084301114082336,
0.014131397940218449,
-0.04107747972011566,
0.0542522668838501,
0.0267906803637743,
-0.036149438470602036,
-0.059377532452344894,
-0.006338682025671005,
-0.05631468445062637,
0.03199820592999458,
0.05685901641845703,
-0.05535078048706055,
-0.027534760534763336,
0.032752055674791336,
-0.0047927722334861755,
-0.0071312859654426575,
0.016803549602627754,
0.01652585156261921,
-0.020150620490312576,
0.024864433333277702,
0.011176276952028275,
0.011050647124648094,
-0.0733732208609581,
0.028415994718670845,
-0.014817940071225166,
-0.023190241307020187,
0.012414636090397835,
0.005991462618112564,
0.0382903553545475,
0.029143407940864563,
-0.010085762478411198,
0.028979500755667686,
0.012702617794275284,
0.007358599454164505,
0.008931969292461872,
-0.07526258379220963,
-0.05033322051167488,
-0.01056403387337923,
0.007897048257291317,
0.0031659682281315327,
0.006622530519962311,
-0.02461809292435646,
0.020550891757011414,
-0.028493650257587433,
-0.0013558025239035487,
0.06932280212640762,
-0.006882644258439541,
0.048331037163734436,
-0.030869122594594955,
-0.02872394770383835,
-0.025417054072022438,
0.011870358139276505,
0.05180000141263008,
-0.018689224496483803,
-0.019610963761806488,
-0.020855747163295746,
0.0066055720672011375,
0.004614577628672123,
0.008248482830822468,
-0.024543382227420807,
-0.027875885367393494,
0.021119974553585052,
-0.061275504529476166,
0.023662013933062553,
0.0035353743005543947,
-0.04253498464822769,
-0.026003418490290642,
-0.028521010652184486,
0.002512542065232992,
0.07112342119216919,
0.04343360662460327,
0.021498212590813637,
-0.048162516206502914,
-0.013201448135077953,
-0.02440692111849785,
0.040198419243097305,
-0.026660827919840813,
-0.03147471696138382,
0.008134196512401104,
0.019924748688936234,
-0.07526866346597672,
0.009595487266778946,
0.009325488470494747,
-0.009286420419812202,
-0.04930451512336731,
0.013017325662076473,
0.005815720185637474,
0.00639751460403204,
-0.06396506726741791,
-0.005159943364560604,
-0.04098227620124817,
0.0161028690636158,
0.04626476764678955,
-0.007344699930399656,
-0.012212151661515236,
0.00921038817614317,
-0.015020790509879589,
-0.014246435835957527,
0.041026171296834946,
-0.008017643354833126,
-0.022648153826594353,
0.043230365961790085,
0.06094226986169815,
-0.012554298155009747,
-0.015908049419522285,
-0.059773094952106476,
0.016137253493070602,
-0.11942919343709946,
0.04414289444684982,
0.01604229211807251,
0.010321151465177536,
0.06835655868053436,
-0.02511052042245865,
-0.01359639409929514,
-0.023441070690751076,
-0.027463480830192566,
0.004318268969655037,
-0.06334614753723145,
-0.06267719715833664,
-0.06849008053541183,
-0.04984152317047119,
-0.03297237306833267,
0.04987836256623268,
-0.022430874407291412,
0.03174136206507683,
-0.02427723817527294,
-0.020842159166932106,
-0.009885360486805439,
0.05332478508353233,
0.08297105133533478,
0.02998814731836319,
-0.0350150540471077,
-0.0488489605486393,
0.011531618423759937,
0.060846202075481415,
0.006897750776261091,
0.01767277903854847,
-0.06448838859796524,
-0.0074897692538797855,
-0.03719358891248703,
-0.010622830130159855,
0.08314069360494614,
0.08010603487491608,
0.01709683984518051,
-0.05081013962626457,
-0.020689329132437706,
-0.030790645629167557,
-0.028274934738874435,
-0.0149746248498559,
-0.024652989581227303,
-0.07210902869701385,
0.019702786579728127,
-0.0645630955696106,
0.02741277404129505,
0.02818533219397068,
-0.0037517710588872433,
0.006214608903974295,
0.01764228194952011,
-0.015073739923536777,
-0.04403453320264816,
-0.02007693611085415,
-0.0033876493107527494,
0.005225071217864752,
0.06981959193944931,
0.008664545603096485,
0.009465230628848076,
-0.04096435382962227,
-0.036085858941078186,
-0.07501731812953949,
-0.020348042249679565,
-0.004861252382397652,
0.007130936719477177,
-0.018082458525896072,
0.016583174467086792,
-0.006114012561738491,
-0.03705096244812012,
-0.020164765417575836,
0.05904609337449074,
0.004380620550364256,
-0.010736045427620411,
0.0048009054735302925,
0.03174922987818718,
0.009305999614298344,
-0.023647809401154518,
0.05426657572388649,
0.07600774616003036,
0.012716324999928474,
-0.04694743454456329,
-0.014023320749402046,
-0.04750969633460045,
0.010864070616662502,
0.06097923964262009,
-0.001996943261474371,
0.027124343439936638,
-0.04842093214392662,
0.03623976558446884,
0.03992225602269173,
-0.03496144711971283,
-0.045449480414390564,
0.010781936347484589,
0.03947122395038605,
0.0987662747502327,
0.03033803217113018,
-0.015792829915881157,
-0.02149164490401745,
-0.04876558110117912,
-0.010414430871605873,
-0.00355516467243433,
-0.011377710849046707,
0.014279487542808056,
0.05564913526177406,
-0.01562732830643654,
0.01444217748939991,
0.003327614162117243,
0.017627062276005745,
0.04139970615506172,
-0.024745315313339233,
-0.029645336791872978,
-0.038264498114585876,
0.012149601243436337,
-0.05569424480199814,
-0.09425251185894012,
-0.016480520367622375,
-0.05338253825902939,
-0.011424707248806953,
-0.02046085335314274,
0.053900402039289474,
0.00890408642590046,
0.01662307418882847,
0.02167697250843048,
0.03596736490726471,
-0.00014057695807423443,
-0.007462667766958475,
0.03596093878149986,
-0.08260282129049301,
-0.010094743221998215,
0.045323580503463745,
0.005385440308600664,
-0.024218304082751274,
0.012378967367112637,
0.018356481567025185,
-0.0048643420450389385,
0.06298913806676865,
0.004664007108658552,
0.0427711047232151,
-0.028182776644825935,
0.004446199629455805,
0.04019099846482277,
-0.0061653414741158485,
-0.01309156883507967,
0.028611205518245697,
0.018870379775762558,
-0.012282125651836395,
0.01901116780936718,
-0.10327643156051636,
-0.05077314004302025,
0.02129148319363594,
-0.05037406086921692,
-0.002881233114749193,
0.029303384944796562,
0.031344782561063766,
-0.0740397498011589,
0.0027907390613108873,
-0.0022033900022506714,
-0.031974099576473236,
-0.022410878911614418,
0.01549014262855053,
0.04506922885775566,
-0.01016269437968731,
-0.021979179233312607,
-0.06060822680592537,
-0.0016050315462052822,
-0.005715963430702686,
0.02092786133289337,
0.024280134588479996,
0.013229930773377419,
0.08038651198148727,
-0.034725725650787354,
-0.032548412680625916,
-0.021539613604545593,
0.012869940139353275,
0.003544989973306656,
0.02050284668803215,
0.03615032508969307,
0.016753502190113068,
-0.047220852226018906,
-0.05791084095835686,
-0.01795712299644947,
-0.01702938973903656,
-0.011327420361340046,
0.006376208271831274,
0.004622104577720165,
-0.03675409406423569,
-0.033348891884088516,
0.02050785906612873,
-0.006501348689198494,
0.04964267462491989,
0.039978060871362686,
0.0027710609138011932,
0.05508837848901749,
-0.0319611094892025,
-0.013575512915849686,
0.036401960998773575,
0.05014984682202339,
0.030521512031555176,
-0.01608150079846382,
0.011635987088084221,
-0.08957834541797638,
0.006935705430805683,
-0.027475666254758835,
-0.047360859811306,
-0.046361807733774185,
0.06092564016580582,
0.0928630605340004,
0.007169380784034729,
-0.013962422497570515,
-0.0021915079560130835,
0.09486034512519836,
-0.024975331500172615,
-0.039990637451410294,
-0.015380783937871456,
0.039235200732946396,
0.0014311345294117928,
-0.013447461649775505,
-0.014555869624018669,
-0.06828204542398453,
0.010101553983986378,
-0.004225196782499552,
-0.02704337053000927,
-0.019574040547013283,
-0.011086525395512581,
0.05158234015107155,
0.013030332513153553,
-0.013951393775641918,
-0.02995295263826847,
-0.05825651064515114,
0.0036332698073238134,
-0.021097756922245026,
0.005835601594299078,
-0.005775346886366606,
-0.004913899581879377,
0.06516651809215546,
-0.006440731231123209,
-0.05434876307845116,
0.036781784147024155,
-0.006552314385771751,
-0.014225970022380352,
0.0023157361429184675,
0.07400762289762497,
0.031670063734054565,
0.010812828317284584,
-0.01455236691981554,
0.02982124499976635,
0.024290326982736588,
-0.00237674149684608,
-0.0076304841786623,
0.033632222563028336,
0.03615963086485863,
-0.0021718242205679417,
0.022727007046341896,
-0.02704976126551628,
0.013259626924991608,
-0.023194650188088417,
0.02891361713409424,
-0.05959571525454521,
0.024146167561411858,
0.05364908650517464,
0.045625586062669754,
-0.07108060270547867,
0.05346241965889931,
0.004847711883485317,
0.013766689226031303,
-0.0256800539791584,
-0.0005006584688089788,
-0.06862843036651611,
0.06615252047777176,
-0.014639629982411861,
-0.014430206269025803,
0.0013882315251976252,
-0.0077167353592813015,
0.026216691359877586,
0.03121626377105713,
0.01905604638159275,
-0.010322313755750656,
-0.040805794298648834,
0.00934688188135624,
-0.03659622743725777,
-0.08927397429943085,
0.010886207222938538,
0.03122284822165966,
-0.05547737702727318,
0.053631629794836044,
-0.024375516921281815,
0.00696989893913269,
0.009785215370357037,
0.017070163041353226,
0.021445127204060555,
-0.037778519093990326,
-0.11854483187198639,
0.03551251441240311,
0.0405067503452301,
0.0022959124762564898,
-0.0304261464625597,
0.002035427838563919,
0.02550746314227581,
0.009424528107047081,
0.005684613715857267,
0.0015299082733690739,
-0.008209755644202232,
-0.02674778364598751,
-0.06478843837976456,
0.018044428899884224,
-0.042496126145124435,
0.01664385385811329,
-0.0023637106642127037,
0.010283196344971657,
0.03814270347356796,
-0.09069117903709412,
-0.04199770838022232,
0.04492539167404175,
0.0007333403918892145,
-0.03182854503393173,
-0.042624279856681824,
-0.025375522673130035,
0.047326765954494476,
0.04701435565948486,
-0.06640653312206268,
-0.0022605201229453087,
0.08118435740470886,
0.07733239978551865,
0.04069697484374046,
0.015267540700733662,
-0.005851065739989281,
0.005289129447191954,
-0.014220782555639744,
-0.08971942961215973,
-0.043290432542562485,
0.034888122230768204,
0.031704992055892944
] |
<blockquote>
<p>A sphere of radius $R$ is in contact with a wedge. The point of contact is $\frac{R}{5}$ from the ground as shown in figure. Wedge is moving with velocity $20~\text{m/s}$ towards left then the velocity of the sphere at this instant will be</p>
<p><img src="http://i.stack.imgur.com/8Qubm.png" alt="enter image description here"></p>
</blockquote>
<p><a href="http://www.artofproblemsolving.com/Forum/viewtopic.php?f=513&t=530952" rel="nofollow">http://www.artofproblemsolving.com/Forum/viewtopic.php?f=513&t=530952</a></p>
<p>I have attempted a solution there , however , unable to make any progress . Kindly advice if that is the right path to the solution , if something is there that I am not considering.</p> | g7806 | [
0.0726330578327179,
-0.00199701264500618,
0.017168816179037094,
-0.0019123797537758946,
0.051651883870363235,
-0.014760257676243782,
0.06345100700855255,
-0.017683519050478935,
-0.031217290088534355,
0.0338643416762352,
0.007957159541547298,
0.015821613371372223,
0.006263087969273329,
0.024443065747618675,
0.03769460320472717,
0.020064562559127808,
0.03613186255097389,
-0.007669538259506226,
-0.024674756452441216,
0.01330009289085865,
-0.012846619822084904,
-0.007596621289849281,
0.03520869463682175,
-0.03719223663210869,
-0.02414764277637005,
-0.02442130073904991,
0.03654283657670021,
0.005336096975952387,
-0.07720617204904556,
0.04728526994585991,
0.00922700297087431,
-0.004201698582619429,
-0.013604674488306046,
-0.0534513033926487,
-0.01692214608192444,
-0.01471253577619791,
0.025023512542247772,
-0.01816113479435444,
0.0026631513610482216,
-0.05321194604039192,
0.11009776592254639,
-0.06925520300865173,
0.014544868841767311,
0.007459448650479317,
0.039729371666908264,
-0.010760796256363392,
0.011056818068027496,
0.03123042732477188,
-0.031271375715732574,
0.018874989822506905,
-0.03987366706132889,
0.0531299002468586,
-0.008171789348125458,
-0.028058171272277832,
-0.02226424030959606,
0.0476367324590683,
0.03267277032136917,
-0.013358775526285172,
0.045171987265348434,
0.0068133496679365635,
-0.022512976080179214,
-0.004840356297791004,
-0.03469033166766167,
-0.010680880397558212,
0.03282774239778519,
0.01372518576681614,
-0.05502574145793915,
-0.014886368997395039,
0.03131070360541344,
0.024558182805776596,
-0.009562230668962002,
-0.04993639513850212,
-0.02608438953757286,
-0.05780468508601189,
-0.083198182284832,
0.00926741398870945,
0.044433027505874634,
-0.011505002155900002,
0.023508287966251373,
-0.03411855921149254,
-0.02761695720255375,
0.005984087008982897,
-0.025366319343447685,
-0.012317591346800327,
0.012904351577162743,
-0.014469767920672894,
-0.01739884354174137,
-0.011074819602072239,
-0.058324895799160004,
-0.04480622708797455,
0.037398532032966614,
0.0007590620080009103,
0.03137451410293579,
0.015647077932953835,
-0.017096329480409622,
-0.005576644092798233,
-0.08483078330755234,
0.06425394862890244,
-0.02071073278784752,
0.02571137621998787,
-0.00993760023266077,
-0.04181880131363869,
0.03570765629410744,
-0.0016128093702718616,
-0.014790739864110947,
0.0038018831983208656,
-0.0008120609563775361,
0.04690495878458023,
-0.011585700325667858,
-0.02533542364835739,
0.0064044371247291565,
-0.054905615746974945,
-0.034675996750593185,
-0.03684736415743828,
0.016244884580373764,
-0.07618796080350876,
0.0015384192811325192,
0.05027427524328232,
-0.008203438483178616,
0.022579338401556015,
-0.005508310627192259,
-0.017429538071155548,
-0.03085792250931263,
0.05348876863718033,
-0.007757359649986029,
0.014641646295785904,
0.032217394560575485,
-0.03619900718331337,
0.02748779207468033,
0.03701101616024971,
-0.02350793033838272,
0.004683449398726225,
0.03266119956970215,
0.032943639904260635,
-0.045310258865356445,
0.04387162998318672,
-0.0017905882559716702,
0.0313185416162014,
-0.0026767230592668056,
-0.03172575682401657,
0.0023302657064050436,
-0.03346911817789078,
0.009740788489580154,
-0.012641540728509426,
-0.05864866450428963,
0.0324721522629261,
-0.009336457587778568,
-0.02124813385307789,
0.03561188653111458,
-0.03669796139001846,
-0.030630435794591904,
0.11419987678527832,
-0.024595903232693672,
0.007643881253898144,
0.023412063717842102,
0.018289949744939804,
0.060798514634370804,
-0.00248448527418077,
0.0319032222032547,
-0.01395509298890829,
0.04101502150297165,
-0.02839781530201435,
0.038396403193473816,
-0.0010517843766137958,
-0.05178219825029373,
0.026680974289774895,
0.0037034263368695974,
-0.06564172357320786,
-0.004134169314056635,
-0.07175179570913315,
-0.060149531811475754,
-0.021515801548957825,
0.014429903589189053,
0.04663355275988579,
0.00020558986579999328,
-0.008855768479406834,
0.025905871763825417,
-0.05137166008353233,
-0.016648374497890472,
0.009221883490681648,
0.0039238091558218,
-0.07791081070899963,
0.05349550023674965,
-0.038353677839040756,
-0.016119932755827904,
0.020835882052779198,
0.053426411002874374,
0.025911202654242516,
0.014909069053828716,
-0.03381173685193062,
-0.019603097811341286,
-0.06132890656590462,
-0.04158269241452217,
0.03172130137681961,
0.0032483271788805723,
0.010208499617874622,
0.07838470488786697,
-0.0439581573009491,
-0.028950437903404236,
0.006895469501614571,
-0.0026555131189525127,
0.07698093354701996,
0.011427000164985657,
0.036149099469184875,
-0.0011637000134214759,
0.005819019395858049,
-0.028599126264452934,
-0.024587521329522133,
0.017726833000779152,
0.07789865136146545,
0.05611025542020798,
-0.004940335173159838,
-0.027567120268940926,
0.016052016988396645,
-0.030772527679800987,
0.014941074885427952,
0.01970687136054039,
0.01679074577987194,
-0.02739064022898674,
0.06533940881490707,
-0.053710680454969406,
0.036734066903591156,
0.009290838614106178,
-0.020368102937936783,
-0.013064046390354633,
0.007270761765539646,
-0.024100428447127342,
0.000607346766628325,
-0.017971135675907135,
0.019107533618807793,
-0.02545076236128807,
0.023027703166007996,
0.027535786852240562,
-0.011168941855430603,
0.049805089831352234,
0.017707737162709236,
-0.016930468380451202,
0.0678936317563057,
-0.051083073019981384,
-0.020342422649264336,
-0.002278578467667103,
-0.022979313507676125,
-0.035865556448698044,
-0.033042456954717636,
0.055955540388822556,
-0.024636181071400642,
0.03211335465312004,
0.01774442009627819,
0.001771128154359758,
0.025780420750379562,
0.07190550863742828,
-0.020755507051944733,
-0.022015810012817383,
-0.004577325191348791,
-0.014729083515703678,
0.019118616357445717,
-0.027458522468805313,
0.03636710345745087,
0.025252941995859146,
-0.0785028263926506,
-0.10232575982809067,
-0.039394620805978775,
0.05652335286140442,
-0.0037492699921131134,
-0.08277937024831772,
-0.013905939646065235,
-0.04595273360610008,
0.007703871000558138,
0.026774520054459572,
0.00890957098454237,
-0.03346681594848633,
0.030191807076334953,
0.07748250663280487,
0.03863059729337692,
0.002022825414314866,
-0.0068836696445941925,
0.016516156494617462,
-0.0104066776111722,
-0.023125706240534782,
0.031061140820384026,
-0.008956722915172577,
-0.02947232685983181,
0.010117491707205772,
0.01903323084115982,
0.024151474237442017,
-0.08908220380544662,
0.019287116825580597,
0.0481388233602047,
-0.015094820410013199,
-0.03667594492435455,
-0.02795262262225151,
0.007207597140222788,
0.02832590788602829,
0.04021184891462326,
0.08555947989225388,
0.07173092663288116,
0.025419341400265694,
-0.018202465027570724,
0.01568588614463806,
0.044404610991477966,
0.01481336634606123,
-0.04588447883725166,
-0.011820455081760883,
0.025659795850515366,
0.01074841246008873,
-0.0189933180809021,
0.0035498663783073425,
-0.030587946996092796,
-0.0018036637920886278,
0.0096456753090024,
0.055897459387779236,
0.0322248749434948,
-0.049957118928432465,
-0.02066093496978283,
-0.030845804139971733,
0.006914194207638502,
-0.028853025287389755,
0.03576857969164848,
0.04694341868162155,
0.05576131492853165,
-0.049444448202848434,
-0.019166503101587296,
0.03178194537758827,
0.016245845705270767,
0.022939886897802353,
0.06266564875841141,
-0.04083573445677757,
0.009559301659464836,
-0.03965834155678749,
-0.0038923651445657015,
0.010639614425599575,
0.026879480108618736,
-0.0019903602078557014,
-0.023503100499510765,
-0.04875905066728592,
-0.07904244214296341,
-0.04292724281549454,
0.0591423325240612,
0.04038960114121437,
-0.00924324244260788,
-0.022995132952928543,
-0.064019113779068,
-0.06443674862384796,
-0.03027685172855854,
0.02470862679183483,
0.0549800805747509,
0.019278818741440773,
0.010818565264344215,
0.009992469102144241,
0.03552176430821419,
-0.021258747205138206,
0.015151315368711948,
-0.008001520298421383,
-0.07469166070222855,
0.058720801025629044,
0.0071294717490673065,
0.007046208716928959,
0.047418396919965744,
-0.047590337693691254,
-0.04331253096461296,
-0.03584080934524536,
-0.028418373316526413,
-0.006177717354148626,
0.06083102151751518,
0.006998318247497082,
-0.025357166305184364,
-0.011297382414340973,
0.030687253922224045,
0.023957036435604095,
0.030973011627793312,
0.015204623341560364,
-0.11210181564092636,
0.02226056344807148,
0.020115137100219727,
0.030807634815573692,
0.03607295826077461,
0.0109441252425313,
-0.003979907836765051,
-0.000012122281077608932,
0.057416751980781555,
0.08044270426034927,
0.04554404690861702,
-0.02208034321665764,
-0.012104853056371212,
-0.014416038058698177,
0.04405879229307175,
-0.04629318788647652,
-0.03033447451889515,
0.03655191883444786,
-0.02065243199467659,
0.03491441532969475,
-0.00898931547999382,
0.03900846466422081,
0.011751747690141201,
-0.009792483411729336,
0.03194409981369972,
-0.015853993594646454,
-0.012736708857119083,
-0.04588400200009346,
0.011707539670169353,
0.04407075420022011,
-0.05892820656299591,
-0.03801444545388222,
0.02634798362851143,
-0.002605459885671735,
0.040755826979875565,
0.006371940951794386,
0.01575196534395218,
0.022089147940278053,
-0.024909505620598793,
0.018352368846535683,
0.007916663773357868,
-0.00677980063483119,
-0.043317101895809174,
-0.000003263719236201723,
-0.015935691073536873,
-0.006320517044514418,
0.041440557688474655,
-0.0006884512258693576,
-0.013031335547566414,
-0.05633924901485443,
0.05692886933684349,
0.07789364457130432,
-0.010839372873306274,
0.05494440346956253,
-0.0038535662461072206,
0.04804670810699463,
-0.002603663131594658,
-0.01460887212306261,
0.016395604237914085,
-0.0008422145619988441,
0.012544449418783188,
0.017323177307844162,
0.005329950246959925,
-0.021800395101308823,
0.07075085490942001,
0.01201225258409977,
-0.03528142347931862,
0.016198284924030304,
0.03963856026530266,
-0.0061249700374901295,
0.03146960586309433,
0.007813881151378155,
-0.04216523468494415,
0.03666045144200325,
0.028301533311605453,
-0.0758594200015068,
-0.006108395755290985,
0.01808927208185196,
-0.010970271192491055,
0.04388927295804024,
-0.04475966840982437,
0.011174488812685013,
0.01004177238792181,
-0.057493116706609726,
-0.008367716334760189,
-0.08058734238147736,
0.02079145424067974,
-0.017454633489251137,
-0.01286862138658762,
0.020960412919521332,
0.041787777096033096,
-0.006079531740397215,
-0.00014660003944300115,
-0.014679649844765663,
-0.005429657641798258,
-0.03632740303874016,
0.01396817434579134,
0.014096961356699467,
-0.04078837111592293,
-0.02657201513648033,
-0.029217461124062538,
-0.010270167142152786,
0.05651738494634628,
-0.013748911209404469,
0.07091054320335388,
-0.02803015522658825,
0.011532050557434559,
0.08141465485095978,
-0.032563772052526474,
-0.029770802706480026,
-0.032598547637462616,
-0.008784135803580284,
-0.04670317471027374,
0.024677639827132225,
0.007589808665215969,
-0.01625470444560051,
0.01604142040014267,
0.000016606036297162063,
0.07295728474855423,
0.030476313084363937,
0.011490524746477604,
-0.0634550079703331,
0.01716921664774418,
0.004305535461753607,
0.023980865254998207,
0.03861352801322937,
-0.015230527147650719,
-0.040455032140016556,
0.019787738099694252,
-0.023516185581684113,
-0.08615883439779282,
0.009679541923105717,
-0.0034696285147219896,
0.00015531409007962793,
0.036593060940504074,
0.013953293673694134,
0.04159952700138092,
-0.03318030387163162,
0.00846037082374096,
0.017307216301560402,
-0.014271281659603119,
0.07008933275938034,
-0.03173036500811577,
-0.035422928631305695,
-0.01882191188633442,
0.021932192146778107,
-0.010412122122943401,
-0.04761703684926033,
-0.007040136959403753,
0.038356754928827286,
-0.044177860021591187,
-0.028779417276382446,
-0.04241105169057846,
0.010656125843524933,
0.016974518075585365,
-0.007657231763005257,
-0.014312831684947014,
-0.034391243010759354,
0.033448219299316406,
-0.016860568895936012,
-0.06939768046140671,
0.028149042278528214,
-0.011030216701328754,
-0.012671560049057007,
-0.05014606565237045,
-0.0019003686029464006,
-0.0699571743607521,
0.014069591648876667,
-0.05446777865290642,
-0.048185382038354874,
0.01468371320515871,
-0.0035550121683627367,
-0.022950295358896255,
-0.04024780914187431,
0.052885252982378006,
-0.012525457888841629,
0.017654364928603172,
0.05708552151918411,
0.009760168381035328,
-0.013354523107409477,
0.033575739711523056,
-0.06556504964828491,
-0.06474637985229492,
-0.015530068427324295,
-0.02166079543530941,
-0.01116391085088253,
-0.019860973581671715,
-0.0003304812707938254,
-0.04733024165034294,
0.05585061013698578,
-0.04109906032681465,
-0.019448895007371902,
0.012856032699346542,
-0.03555268049240112,
-0.0656023770570755,
0.026828227564692497,
0.007502720691263676,
0.005234022159129381,
0.011130362749099731,
-0.04205644503235817,
0.025511717423796654,
0.018898138776421547,
0.01152698416262865,
0.008242865093052387,
0.011110077612102032,
0.011143452487885952,
0.0015622923383489251,
-0.002555650658905506,
0.06015225499868393,
-0.04135629162192345,
0.07042499631643295,
0.05607496574521065,
-0.010166812688112259,
0.03327275067567825,
-0.020948264747858047,
-0.05922974646091461,
-0.02741996757686138,
0.03953481838107109,
-0.052490685135126114,
-0.05585870146751404,
0.04086191579699516,
-0.0491231344640255,
0.04329598695039749,
-0.009700003080070019,
-0.06964096426963806,
-0.01569465361535549,
0.008769121952354908,
-0.06136227771639824,
0.06714492291212082,
0.014462093822658062,
-0.05560298636555672,
0.0433712974190712,
-0.02480325661599636,
-0.0362381748855114,
-0.04875261336565018,
0.00968136452138424,
-0.02025800198316574,
-0.00627536978572607,
0.015818461775779724,
-0.008042764849960804,
0.025167157873511314,
0.0700526162981987,
0.053232528269290924,
0.004145965911448002,
0.02536698244512081,
0.004893131088465452,
-0.027712862938642502,
0.00011887336586369202,
-0.14214996993541718,
0.012630967423319817,
0.04250803962349892,
-0.047763925045728683,
-0.07379386574029922,
-0.019001929089426994,
-0.005541485734283924,
-0.03235425427556038,
-0.03347261995077133,
-0.05046787112951279,
0.02629036083817482,
0.03894248232245445,
-0.04467777907848358,
0.024454861879348755,
-0.00951414741575718,
-0.016575708985328674,
0.011216429993510246,
-0.01883414387702942,
0.028109833598136902,
0.04837481677532196,
0.034862715750932693,
0.04152543842792511,
0.026291674003005028,
-0.03630630671977997,
0.015558549202978611,
0.01639997400343418,
-0.027506273239850998,
0.002484457101672888,
0.0016220707911998034,
-0.09671714901924133,
0.01772497035562992,
0.02792503498494625,
-0.00226560584269464,
0.017096225172281265,
0.02551383152604103,
-0.046005070209503174,
-0.00816915463656187,
0.010603347793221474,
0.02286411263048649,
0.015370710752904415,
-0.0001799837191356346,
-0.03726908564567566,
-0.011447358876466751,
-0.03287592530250549,
-0.02385631389915943,
-0.04407325014472008,
0.03856145963072777,
-0.047958992421627045,
0.015628144145011902,
0.008947983384132385,
-0.07612378895282745,
-0.04926016926765442,
-0.014453123323619366,
-0.01708829216659069,
0.026533447206020355,
-0.006909685209393501,
0.038374047726392746,
0.036195989698171616,
0.031235238537192345,
0.030547920614480972,
0.010982074774801731,
0.004820312839001417,
0.001270208740606904,
-0.012105141766369343,
-0.0006659608916379511,
0.0031387540511786938,
0.054390519857406616,
-0.021364718675613403,
0.026580113917589188,
-0.00467432476580143,
0.009046750143170357,
0.038290176540613174,
0.08228825032711029,
-0.01422133669257164,
0.05023486539721489,
-0.009088749997317791,
0.010569675825536251,
0.017656365409493446,
-0.006594259757548571,
-0.025121213868260384,
0.0015667245024815202,
-0.028359858319163322,
-0.006875109393149614,
0.04199182987213135,
0.0027831057086586952,
-0.0009271543240174651,
-0.018007829785346985,
-0.006620614789426327,
-0.00755928223952651,
-0.040338024497032166,
0.023903198540210724,
0.06353685259819031,
0.009688799269497395,
-0.01544063538312912,
-0.006122378632426262,
-0.010686708614230156,
0.05738559365272522,
0.013958388939499855,
0.0814833790063858,
0.03887169808149338,
-0.05608716607093811,
-0.04121965169906616,
-0.029916618019342422,
0.008463039994239807,
-0.08904285728931427,
-0.06861823052167892,
-0.018069330602884293,
0.008574946783483028,
-0.011922293342649937,
0.006251964718103409,
-0.032657623291015625,
0.027097027748823166,
-0.0021197269670665264,
-0.0032542378176003695,
0.029749708250164986,
-0.05869372561573982,
0.010206851176917553,
-0.05725438520312309,
0.003865433856844902,
0.00906804297119379,
0.026544390246272087,
0.0016623750561848283,
-0.009842058643698692,
0.005651604384183884,
0.01693718321621418,
0.03170093148946762,
0.0010763723403215408,
0.04362925514578819,
0.09552334249019623,
0.04101311415433884,
0.00998362060636282,
0.08387605100870132,
0.043273113667964935,
-0.043461717665195465,
-0.01154821366071701,
-0.05460452660918236,
0.022562196478247643,
-0.08582792431116104,
0.04847405105829239,
0.026635251939296722,
-0.03662652522325516,
0.01851356029510498,
-0.04132116213440895,
0.005768060218542814,
0.008737215772271156,
0.0799463614821434,
-0.04428459331393242,
-0.034678176045417786,
0.05253569781780243
] |
<p>Supppose we are given a quantum state that isn't pure state, such that it is a linear combination of the eigenstates of a Hermitian operator $\hat O$.
$$|\psi\rangle=N\sum \alpha_i |i\rangle$$ where $N$ is just a normalization constant.
I just want to make something clear about measuring. If we measure the corresponding eigenvalue of $\hat O$ and find it to be in the $|1\rangle$ state then immediately measure again, would I be right in thinking that the probability of getting the $|2\rangle$ state is $0$?</p>
<p>I think that because I believe the wavefunction collapses to the $|1\rangle$ state upon the first measurement...</p> | g7807 | [
-0.027481375262141228,
0.009251663461327553,
-0.014972164295613766,
-0.00913187675178051,
0.0015299032675102353,
-0.0011062714038416743,
0.05287852883338928,
0.05322945863008499,
0.0340057797729969,
-0.023248324170708656,
-0.017608381807804108,
-0.002639019163325429,
-0.0138023030012846,
0.02872781828045845,
-0.02267458103597164,
-0.034077052026987076,
0.12046497315168381,
-0.016049440950155258,
0.040843863040208817,
-0.028505301102995872,
-0.027126489207148552,
0.0029209291096776724,
0.00640214653685689,
-0.052280787378549576,
0.07214483618736267,
-0.0386502668261528,
0.024617139250040054,
0.024428285658359528,
-0.03630337119102478,
-0.02851700410246849,
0.02557959407567978,
-0.0003415466926526278,
0.03327168896794319,
-0.01305281464010477,
-0.04732801020145416,
0.047679152339696884,
0.05113053321838379,
-0.008468071930110455,
0.03175521269440651,
-0.030087830498814583,
-0.01323261484503746,
-0.0045333122834563255,
0.0331331230700016,
-0.034056443721055984,
0.04597090557217598,
0.01994594745337963,
0.07103234529495239,
0.020361512899398804,
-0.028044164180755615,
0.041734080761671066,
0.022900182753801346,
-0.020001009106636047,
0.055037230253219604,
-0.012728792615234852,
0.0371391586959362,
0.03839362785220146,
-0.04047370329499245,
-0.011432911269366741,
0.029845256358385086,
0.03894764930009842,
0.06028606742620468,
-0.025095075368881226,
0.016522778198122978,
-0.0005814614123664796,
0.015999680384993553,
-0.000207363031222485,
-0.0035580904223024845,
0.032957375049591064,
-0.002357363933697343,
0.016674626618623734,
0.016077090054750443,
-0.08455348014831543,
0.0316881388425827,
-0.02038058638572693,
0.00013316189870238304,
0.01697295904159546,
0.029242977499961853,
-0.028260856866836548,
0.013828204944729805,
0.06855354458093643,
0.011616143397986889,
-0.062324102967977524,
0.026699116453528404,
-0.02316453494131565,
0.014863389544188976,
0.0228887852281332,
-0.006384287495166063,
0.020622672513127327,
-0.02645965851843357,
0.06429024785757065,
0.0036748338025063276,
-0.04073231294751167,
0.06233340501785278,
0.045455534011125565,
-0.02043447643518448,
-0.04193445295095444,
-0.06300272047519684,
0.03235737606883049,
-0.035194579511880875,
0.012316053733229637,
0.010312366299331188,
0.01847957633435726,
-0.02486143633723259,
-0.03634423390030861,
-0.00922116544097662,
0.013938944786787033,
-0.01998220942914486,
-0.02345309965312481,
-0.0007880497723817825,
-0.027821021154522896,
-0.05078665167093277,
0.01792834885418415,
-0.001412134151905775,
-0.04190203920006752,
-0.05056675150990486,
0.005491796415299177,
0.04691927507519722,
-0.0059275818057358265,
-0.02987479232251644,
0.019765188917517662,
0.06392128765583038,
0.0344436913728714,
0.027330627664923668,
0.0672416239976883,
0.004639485850930214,
0.06408770382404327,
-0.05060814693570137,
0.00089475535787642,
0.04736918583512306,
0.055318597704172134,
0.0015639140037819743,
0.036235228180885315,
-0.012979845516383648,
0.021588727831840515,
0.0057388655841350555,
-0.0065582143142819405,
0.02806209959089756,
0.012222064658999443,
-0.0066863372921943665,
0.014735582284629345,
0.004680341575294733,
-0.02624385803937912,
0.03916270285844803,
0.01183741632848978,
0.057212118059396744,
-0.04125864431262016,
0.04796193167567253,
-0.0226927250623703,
0.003263737540692091,
0.03857117146253586,
-0.018726201727986336,
-0.0010616622166708112,
-0.0014217958087101579,
-0.02267398312687874,
0.014616783708333969,
0.022827478125691414,
0.05374618247151375,
-0.013899962417781353,
0.025406548753380775,
0.04027924686670303,
0.021219294518232346,
-0.010964456014335155,
0.02409476414322853,
0.036682553589344025,
-0.00915451068431139,
-0.002329421229660511,
0.020024793222546577,
-0.048247210681438446,
0.01848101057112217,
-0.037086497992277145,
0.066306471824646,
0.027486417442560196,
-0.027742931619286537,
-0.0004826175863854587,
-0.04197027534246445,
0.03210011124610901,
-0.05230192467570305,
-0.020258672535419464,
0.03957070782780647,
-0.01796565018594265,
-0.04359880089759827,
0.04332884028553963,
0.019752658903598785,
-0.036301836371421814,
0.017843345180153847,
-0.03701576218008995,
0.01736500859260559,
0.008975930511951447,
-0.03714066743850708,
0.04928642138838768,
-0.01366026047617197,
0.010157721117138863,
-0.014690128155052662,
-0.018805649131536484,
-0.010580365546047688,
-0.05824721232056618,
0.04934406653046608,
-0.05481911450624466,
-0.03602800890803337,
-0.010145926848053932,
-0.00026026053819805384,
0.021870682016015053,
-0.0046010403893888,
-0.03854240104556084,
-0.05516998469829559,
0.007987943477928638,
0.025572050362825394,
0.010456210933625698,
-0.00834087934345007,
-0.007276794407516718,
0.004166236612945795,
-0.01633419096469879,
-0.0038364320062100887,
-0.010939599014818668,
0.0188290998339653,
0.02040810137987137,
0.08799609541893005,
-0.016644008457660675,
-0.00737955654039979,
-0.0025238848756998777,
-0.03667574003338814,
0.023768695071339607,
0.028740206733345985,
0.01345114503055811,
0.06858844310045242,
0.055964455008506775,
-0.06724144518375397,
0.006099507212638855,
-0.0011672080727294087,
0.008577222004532814,
-0.021111276000738144,
-0.01781381107866764,
-0.009657101705670357,
0.002027775626629591,
0.0031630999874323606,
0.09869454056024551,
0.006964090280234814,
0.020757419988512993,
0.008150983601808548,
-0.006144560407847166,
-0.008190013468265533,
0.024898814037442207,
-0.03897678479552269,
0.004141048528254032,
0.026621662080287933,
0.025770820677280426,
-0.011562266387045383,
0.008205436170101166,
-0.014463502913713455,
0.015601109713315964,
-0.022190788760781288,
0.006170305423438549,
-0.0005428873701021075,
0.027727991342544556,
-0.057544585317373276,
-0.03729155659675598,
0.048003289848566055,
0.010195265524089336,
-0.02413068525493145,
-0.010353266261518002,
0.002643465530127287,
0.04262969642877579,
-0.012900718487799168,
-0.026074610650539398,
-0.03206682577729225,
-0.029655488207936287,
-0.0046804980374872684,
0.0027646878734230995,
-0.038197506219148636,
-0.0038300033193081617,
0.0057255919091403484,
0.047513626515865326,
0.009292811155319214,
0.06939506530761719,
-0.014182411134243011,
-0.05455619469285011,
-0.047895919531583786,
-0.010208150371909142,
0.018123673275113106,
-0.05635960400104523,
-0.10259939730167389,
0.041824813932180405,
-0.038567136973142624,
0.03642246872186661,
0.01201290637254715,
-0.10151524096727371,
0.04650569707155228,
-0.0076519763097167015,
-0.032036419957876205,
0.027086466550827026,
-0.03359570726752281,
-0.00025330917560495436,
-0.013219294138252735,
0.04060681164264679,
-0.022016307339072227,
0.008649715222418308,
0.007453252095729113,
-0.04664666950702667,
0.04519890248775482,
0.13341963291168213,
-0.024492116644978523,
-0.02235334739089012,
-0.03829963505268097,
-0.045576173812150955,
0.022032730281352997,
0.004818865563720465,
-0.0036760426592081785,
-0.047316428273916245,
-0.022866252809762955,
0.007089998107403517,
-0.01887986809015274,
0.00318650109693408,
-0.025261735543608665,
-0.03836767375469208,
0.00042123105959035456,
-0.01292787678539753,
-0.03170401602983475,
0.006845687981694937,
-0.006373681593686342,
0.02855762280523777,
-0.02660675160586834,
-0.043327633291482925,
-0.00177017692476511,
0.01101437583565712,
0.04844750836491585,
-0.035769592970609665,
-0.03636449575424194,
0.0790509358048439,
-0.030028128996491432,
-0.05754557624459267,
0.04879298806190491,
0.006777909118682146,
-0.029979780316352844,
0.00628058984875679,
-0.009952928870916367,
-0.03647427633404732,
-0.022438373416662216,
0.007508790120482445,
0.05435965955257416,
0.02994394116103649,
-0.03133612871170044,
-0.04158606007695198,
-0.01031340193003416,
-0.002068174071609974,
0.03396743908524513,
-0.03595069423317909,
-0.0687229335308075,
0.0035389945842325687,
0.009645530954003334,
-0.025974215939641,
0.0007011809502728283,
0.0016270631458610296,
0.023255765438079834,
-0.02359417825937271,
-0.0006670326110906899,
0.05060339719057083,
0.02472556196153164,
-0.030884431675076485,
0.010404789820313454,
-0.01721552014350891,
0.027975082397460938,
-0.04996001720428467,
-0.021117929369211197,
-0.09409061819314957,
-0.009357083588838577,
-0.007136104628443718,
-0.013086291030049324,
0.050078049302101135,
0.09357050061225891,
0.007927663624286652,
-0.04182872548699379,
0.004240664653480053,
0.012497985735535622,
0.021649470552802086,
0.027427997440099716,
-0.03664679080247879,
0.007577093318104744,
-0.021705862134695053,
-0.004168256651610136,
0.023200951516628265,
0.01706654019653797,
0.004313481040298939,
-0.007750530727207661,
-0.010765420272946358,
0.03188478946685791,
0.04294654726982117,
0.0009536753059364855,
0.03875584900379181,
0.04443579539656639,
-0.054263435304164886,
0.007407479919493198,
-0.08147149533033371,
-0.020531224086880684,
0.0017887927824631333,
0.04721154272556305,
0.04845708981156349,
0.02945065312087536,
-0.043984342366456985,
-0.02478359453380108,
0.06687254458665848,
-0.014261817559599876,
-0.02489146590232849,
0.042011503130197525,
-0.001007331651635468,
-0.025425536558032036,
0.004375779535621405,
0.08223594725131989,
0.06450232863426208,
-0.009869212284684181,
-0.03584401309490204,
-0.043155234307050705,
0.04188431054353714,
0.007815700955688953,
-0.045590031892061234,
0.0252517256885767,
0.022366126999258995,
0.061401281505823135,
-0.046624742448329926,
-0.04227385297417641,
-0.007260218728333712,
-0.021377773955464363,
-0.012901201844215393,
0.03962622210383415,
0.008827111683785915,
-0.029463430866599083,
0.03841520473361015,
0.06743462383747101,
0.024710247293114662,
-0.00869731605052948,
-0.04352560266852379,
0.02484729327261448,
-0.040676604956388474,
0.027218356728553772,
0.031579650938510895,
-0.05714231729507446,
-0.0027159415185451508,
-0.024024255573749542,
-0.005747353658080101,
-0.053542107343673706,
-0.020044656470417976,
-0.018903939053416252,
0.010738007724285126,
-0.048436108976602554,
-0.0028415920678526163,
-0.04273204505443573,
0.0010279356501996517,
0.025374069809913635,
-0.04802459105849266,
0.008418712764978409,
-0.03559659421443939,
-0.019499104470014572,
0.05250322446227074,
-0.02415875345468521,
-0.053794976323843,
-0.021862398833036423,
-0.03413426876068115,
-0.03104853816330433,
0.08558374643325806,
0.029592465609312057,
0.04851143807172775,
0.0054625943303108215,
-0.005667003337293863,
-0.014328516088426113,
-0.053641434758901596,
0.011840111576020718,
-0.03228919953107834,
-0.05066440999507904,
0.055683400481939316,
-0.0589640773832798,
-0.02752731926739216,
0.0236721970140934,
-0.049873534590005875,
0.04625845327973366,
-0.025741687044501305,
-0.05804203450679779,
-0.00734352134168148,
-0.04173446446657181,
-0.0014860600931569934,
-0.005870557390153408,
-0.026931198313832283,
-0.012893293052911758,
-0.03318445384502411,
-0.011701510287821293,
-0.012905309908092022,
0.008394235745072365,
0.011844385415315628,
-0.024517158046364784,
-0.07325521856546402,
-0.0006103268824517727,
-0.0188666433095932,
0.018630821257829666,
0.019610298797488213,
0.07775778323411942,
0.014644739218056202,
0.015954019501805305,
0.006833846215158701,
-0.00933761429041624,
-0.03734574839472771,
-0.025844616815447807,
0.06115540489554405,
-0.03700005263090134,
0.06229608878493309,
-0.02799529954791069,
0.06902004033327103,
-0.016713805496692657,
0.045301489531993866,
0.07492098957300186,
-0.005502074025571346,
0.039988402277231216,
0.03748132288455963,
-0.014687255024909973,
-0.007934450171887875,
-0.007801054511219263,
-0.027435926720499992,
0.031601469963788986,
-0.032717056572437286,
-0.02432047575712204,
0.02976115420460701,
-0.04249733313918114,
-0.02455925941467285,
0.04727710410952568,
0.0075142052955925465,
-0.012052278034389019,
-0.034242622554302216,
-0.007954897359013557,
-0.0015198180917650461,
-0.08090168982744217,
-0.0013316500699147582,
-0.0181049183011055,
0.039406668394804,
0.029263880103826523,
0.05226412042975426,
0.050929926335811615,
-0.020097563043236732,
0.06198166683316231,
-0.022003881633281708,
-0.009674371220171452,
-0.025948822498321533,
0.012044529430568218,
0.03548619523644447,
-0.019952714443206787,
-0.012744667008519173,
0.021207498386502266,
0.06468892097473145,
0.002405171748250723,
0.019738372415304184,
-0.00469067320227623,
-0.021172916516661644,
0.014215019531548023,
-0.05783845856785774,
-0.048834092915058136,
-0.01475999504327774,
-0.09394122660160065,
-0.014066706411540508,
-0.0027013139333575964,
0.0023943802807480097,
0.012361926957964897,
-0.028873462229967117,
-0.07363253086805344,
0.012735662050545216,
0.0864635556936264,
-0.01061152946203947,
0.038835860788822174,
0.056407857686281204,
0.03916306048631668,
-0.020648837089538574,
0.0032519942615181208,
0.023252805694937706,
0.02230922505259514,
0.029026689007878304,
0.000011355645256116986,
0.03489011153578758,
0.017425263300538063,
-0.014320231974124908,
0.0154391685500741,
0.04794778302311897,
-0.057980217039585114,
-0.03076954185962677,
0.03762013837695122,
-0.058447081595659256,
-0.06308460235595703,
-0.0013053620932623744,
0.07990165799856186,
0.017014281824231148,
0.003275063820183277,
0.022283246740698814,
0.008154187351465225,
-0.026676101610064507,
0.01945270411670208,
0.08988586068153381,
-0.013332735747098923,
0.006227567326277494,
-0.012122182175517082,
-0.02861127071082592,
-0.05642959848046303,
0.02484593167901039,
-0.0033154438715428114,
-0.08011343330144882,
-0.014846179634332657,
0.01435989048331976,
0.03865945339202881,
-0.03571305423974991,
0.03478054702281952,
-0.07489760220050812,
-0.045346699655056,
0.09147462248802185,
-0.04275750741362572,
-0.03431551903486252,
-0.024769937619566917,
0.0004060060018673539,
-0.00836512167006731,
-0.032561756670475006,
-0.015027555637061596,
0.007588033564388752,
0.023283228278160095,
-0.032581157982349396,
0.022100234404206276,
0.058604612946510315,
-0.04223442077636719,
0.033245738595724106,
0.09763231873512268,
0.008653818629682064,
0.050652723759412766,
-0.020369062200188637,
0.06678196042776108,
0.0568188801407814,
0.0016267908504232764,
-0.08955729007720947,
0.033112529665231705,
0.009868038818240166,
-0.008887470699846745,
0.0022835528943687677,
-0.008179210126399994,
0.008192844688892365,
-0.03549632430076599,
0.040554143488407135,
-0.007576359435915947,
0.022072676569223404,
0.01859959028661251,
0.039067357778549194,
-0.006829279474914074,
0.09680408239364624,
0.05508153513073921,
0.015575245022773743,
-0.09007630497217178,
0.040695905685424805,
0.021425405517220497,
0.020822038874030113,
-0.0849480926990509,
-0.0019064550288021564,
-0.011573259718716145,
0.023735269904136658,
-0.010661701671779156,
0.003244624938815832,
-0.018736375495791435,
0.02539578080177307,
0.08779542148113251,
0.025728890672326088,
0.007184595335274935,
-0.04699880629777908,
-0.013139279559254646,
-0.06861384212970734,
-0.039581626653671265,
-0.027425389736890793,
-0.004868260119110346,
0.03664228692650795,
-0.03316432237625122,
-0.0828351229429245,
-0.014258041977882385,
-0.10058571398258209,
0.03476053103804588,
-0.05059247091412544,
-0.03991791978478432,
-0.02053002454340458,
0.011285621672868729,
0.03151225671172142,
-0.0011396476766094565,
-0.0179531779140234,
-0.047850314527750015,
-0.01903320662677288,
-0.013659079559147358,
0.00793872494250536,
0.04673701897263527,
0.032892052084207535,
-0.007794168312102556,
0.06915828585624695,
-0.026937568560242653,
-0.0040862904861569405,
-0.016223514452576637,
0.0015595605364069343,
0.0036597978323698044,
-0.00842728279531002,
0.032167933881282806,
-0.018902553245425224,
-0.008396385237574577,
-0.01376187615096569,
0.07446767389774323,
0.03465281054377556,
-0.023181000724434853,
-0.010805509984493256,
-0.012596936896443367,
-0.03498205542564392,
0.0012151835253462195,
-0.005588236730545759,
0.005259467288851738,
-0.045665986835956573,
0.012331698089838028,
-0.06314726918935776,
-0.03176724910736084,
0.003905555233359337,
0.051030341535806656,
-0.019454633817076683,
-0.05053955689072609,
0.02108713798224926,
-0.027940470725297928,
-0.03377360478043556,
-0.054522231221199036,
0.04111696407198906,
0.035499654710292816,
-0.04280242696404457,
-0.023137003183364868,
-0.011235258542001247,
-0.0009086903883144259,
-0.0009099493036046624,
-0.034494124352931976,
-0.017334122210741043,
-0.007776228711009026,
0.07320517301559448,
0.010562952607870102,
-0.021012701094150543,
-0.006200757343322039,
-0.06583545356988907,
-0.043157678097486496,
-0.023396307602524757,
0.003097156761214137,
0.03620363399386406,
0.013348978012800217,
-0.005574306007474661,
-0.035970933735370636,
0.02305547147989273,
-0.05348766967654228,
-0.0271358210593462,
0.011169329285621643,
0.029652995988726616,
0.02804143913090229,
-0.01273792702704668,
-0.019968604668974876,
0.01024012640118599,
0.005285156890749931,
-0.03050738386809826,
-0.019829602912068367,
0.02544904500246048,
-0.00521715497598052,
0.09194424003362656,
0.05922383442521095,
-0.042693328112363815,
0.02659321203827858,
-0.013347925618290901,
-0.004558296408504248,
0.02072843164205551,
0.024639515206217766,
-0.03512886166572571,
-0.08113101869821548,
-0.012105481699109077,
-0.05912976711988449,
-0.06080200523138046,
0.03436891362071037,
-0.004533208440989256
] |
<p>How would the interference pattern look if one source emits blue light and the other source emits red light in Young's double slit experiment?</p> | g7808 | [
-0.043251149356365204,
0.054407998919487,
0.022345753386616707,
-0.016848865896463394,
-0.02875787764787674,
-0.001368822529911995,
-0.00820095930248499,
0.014038728550076485,
0.03336477652192116,
-0.0493294894695282,
0.04609709605574608,
0.050966162234544754,
-0.01412668451666832,
0.02784353494644165,
-0.0352754145860672,
0.012960937805473804,
0.028625110164284706,
-0.00537794129922986,
0.023767825216054916,
0.012888056226074696,
-0.041228387504816055,
0.004257699474692345,
-0.07224788516759872,
-0.0723436027765274,
-0.01147579774260521,
-0.02577602118253708,
-0.031422846019268036,
-0.052213866263628006,
-0.0728469118475914,
-0.023576363921165466,
0.02172248438000679,
-0.07106515020132065,
0.014942826703190804,
-0.002733055502176285,
-0.06747527420520782,
0.013002454303205013,
0.01760876178741455,
0.04217249155044556,
-0.044502142816782,
0.016010792925953865,
-0.008103381842374802,
0.00859725009649992,
-0.011141683906316757,
-0.031196990981698036,
-0.005736226215958595,
-0.014921944588422775,
0.006707469467073679,
-0.01594802737236023,
0.03060459904372692,
-0.01764671504497528,
-0.009454624727368355,
0.06261269003152847,
-0.0027357684448361397,
0.038147058337926865,
0.04756251350045204,
0.07063833624124527,
-0.015472219325602055,
-0.03577025979757309,
0.05320218205451965,
0.006115672178566456,
-0.018234912306070328,
-0.03581621125340462,
-0.012224134057760239,
0.012318543158471584,
-0.021279187873005867,
0.008150437846779823,
-0.009354709647595882,
0.004832988139241934,
0.01137173268944025,
0.039509233087301254,
0.01994217559695244,
-0.052507434040308,
0.027622753754258156,
-0.012491883710026741,
0.03459887206554413,
0.04123367369174957,
0.04859530180692673,
-0.0029569684993475676,
-0.0379050150513649,
0.018337152898311615,
-0.04442446306347847,
-0.02275657467544079,
-0.02749357745051384,
0.0111703434959054,
0.034528136253356934,
0.007021916098892689,
-0.017050202935934067,
-0.015686091035604477,
0.03396198898553848,
-0.001696254126727581,
0.03726417198777199,
-0.025119062513113022,
0.05513812229037285,
-0.02567550539970398,
0.05582164227962494,
0.008202031254768372,
-0.029638484120368958,
0.05695517361164093,
0.03378673270344734,
0.04856443777680397,
-0.025399236008524895,
0.005211302079260349,
-0.017064455896615982,
0.04607740789651871,
-0.010925393551588058,
-0.06140747293829918,
0.0022633338812738657,
0.010798097588121891,
-0.02460295893251896,
-0.016590354964137077,
-0.0408569872379303,
-0.04121619835495949,
-0.027618572115898132,
-0.03509926050901413,
0.022229628637433052,
-0.014736389741301537,
0.023126577958464622,
-0.020958205685019493,
0.03301496431231499,
0.038310956209897995,
0.0358043871819973,
-0.03428836539387703,
-0.03829780966043472,
0.011777316220104694,
0.00755838630720973,
-0.02314116805791855,
-0.008600526489317417,
-0.005412666592746973,
0.036563560366630554,
-0.02117159776389599,
-0.011467981152236462,
-0.006157853174954653,
0.017878402024507523,
0.00557337049394846,
0.07902423292398453,
-0.06773253530263901,
0.06377686560153961,
-0.025449680164456367,
-0.013400210067629814,
-0.013481426984071732,
-0.024377672001719475,
-0.024021517485380173,
-0.0022699758410453796,
-0.007003638427704573,
0.01763707958161831,
-0.011434699408710003,
0.02952495776116848,
-0.00003798692341661081,
0.03225155547261238,
0.021537138149142265,
0.021565217524766922,
0.010634464211761951,
0.02684037946164608,
-0.0009659400675445795,
-0.062170203775167465,
-0.0006746667786501348,
-0.003867614548653364,
-0.029425743967294693,
0.00007352491957135499,
0.0019504466326907277,
0.010670812800526619,
-0.06469141691923141,
0.004776517860591412,
0.0547059029340744,
0.038831472396850586,
-0.010641876608133316,
0.03319690376520157,
-0.07210536301136017,
0.0488676093518734,
-0.01864372007548809,
-0.042371854186058044,
-0.0017490999307483435,
-0.022582121193408966,
0.017533373087644577,
0.03773847967386246,
0.021258292719721794,
-0.021412411704659462,
0.04014919325709343,
0.047964952886104584,
0.047016095370054245,
-0.03919719159603119,
0.006047739647328854,
-0.0728847086429596,
-0.05930658057332039,
0.00046142368228174746,
-0.02358287200331688,
0.0009951189858838916,
-0.11565929651260376,
-0.10229840129613876,
-0.005399918649345636,
0.002407815307378769,
-0.04224173724651337,
-0.0785786435008049,
0.021460531279444695,
-0.008848698809742928,
-0.030907293781638145,
0.02302028052508831,
0.026473429054021835,
0.02233050763607025,
0.059382352977991104,
-0.023006655275821686,
0.028181379660964012,
0.03150931000709534,
-0.01119693461805582,
-0.013370993547141552,
0.07774665206670761,
-0.031232349574565887,
-0.017524253576993942,
-0.029605194926261902,
-0.021679675206542015,
-0.0011919643729925156,
0.04473307356238365,
-0.01675799861550331,
0.0900694727897644,
0.013469817116856575,
0.012272651307284832,
-0.006661716848611832,
-0.015129191800951958,
-0.015208722092211246,
-0.0017392185982316732,
-0.02111108787357807,
0.06049429997801781,
0.03196157142519951,
-0.040618717670440674,
0.012688725255429745,
-0.012883121147751808,
-0.023940231651067734,
0.017233790829777718,
-0.04007639363408089,
0.004907030146569014,
-0.028466353192925453,
-0.01329725980758667,
0.009091746993362904,
-0.0661729946732521,
0.04645804315805435,
0.032420139759778976,
0.009735515341162682,
0.03445490449666977,
-0.027381401509046555,
-0.05784513056278229,
-0.03930627554655075,
-0.015733106061816216,
-0.08245724439620972,
0.05621479079127312,
-0.000041094015614362434,
0.0023855743929743767,
0.04322841390967369,
0.025665823370218277,
-0.019273342564702034,
-0.023322725668549538,
-0.005779361352324486,
0.05344250053167343,
-0.028510807082057,
0.022307876497507095,
-0.034330468624830246,
-0.04512617737054825,
-0.019525958225131035,
0.013736607506871223,
-0.05527766793966293,
-0.06532981991767883,
0.0042020962573587894,
-0.01156525406986475,
0.029499195516109467,
-0.01400325633585453,
0.001910502091050148,
-0.001046338235028088,
0.032104723155498505,
-0.021432414650917053,
0.0007588555454276502,
-0.03105866350233555,
-0.005212026182562113,
0.018809018656611443,
0.01453295350074768,
0.010219239629805088,
0.04067561402916908,
0.02135934866964817,
-0.046866923570632935,
-0.04553557559847832,
0.015843883156776428,
0.010977872647345066,
-0.03295265510678291,
0.03067908249795437,
-0.04107241332530975,
0.04815734177827835,
0.06587036699056625,
-0.03213111311197281,
0.01976691745221615,
0.0571153499186039,
0.002114545088261366,
0.04522893205285072,
-0.07730166614055634,
0.03586806356906891,
-0.0038025013636797667,
0.05208675563335419,
-0.07338391244411469,
-0.01707877404987812,
-0.00010097703489009291,
-0.01240312959998846,
-0.007988507859408855,
-0.040609270334243774,
-0.005327909253537655,
-0.04449090734124184,
-0.027666836977005005,
-0.013971533626317978,
0.031147688627243042,
-0.0832204669713974,
-0.06119726970791817,
0.00384447630494833,
-0.016761794686317444,
0.023570042103528976,
-0.03109508380293846,
0.020213015377521515,
0.009001505561172962,
0.023840250447392464,
-0.00541177811101079,
0.028162535279989243,
-0.013694707304239273,
-0.010900640860199928,
0.022623741999268532,
0.031926270574331284,
0.04063859209418297,
0.019955048337578773,
0.04449689760804176,
0.01587866246700287,
-0.029430247843265533,
-0.041092511266469955,
0.05695845186710358,
-0.004882452543824911,
-0.028171248733997345,
0.020388469099998474,
-0.010743132792413235,
0.023177165538072586,
-0.03949536383152008,
-0.027692701667547226,
0.05712933838367462,
-0.041179902851581573,
0.028156541287899017,
0.02676030620932579,
-0.04931125044822693,
0.06952981650829315,
0.02930578403174877,
-0.019091453403234482,
-0.04269992560148239,
-0.04003380611538887,
-0.03090357780456543,
-0.058446820825338364,
0.0562778040766716,
0.01226732786744833,
0.007595272734761238,
-0.020193738862872124,
0.06741155683994293,
-0.014548874460160732,
0.017360281199216843,
-0.017841419205069542,
-0.029830703511834145,
-0.017905667424201965,
0.020042430609464645,
0.03171081840991974,
0.036329030990600586,
-0.036469265818595886,
-0.0008884380804374814,
-0.023094287142157555,
-0.04071712866425514,
-0.007958710193634033,
-0.0524342805147171,
0.0021478496491909027,
-0.02148681879043579,
-0.0014424043474718928,
-0.005361743271350861,
-0.028061136603355408,
-0.04952342063188553,
0.024646665900945663,
-0.05065498501062393,
-0.02332155406475067,
-0.021255575120449066,
-0.0029489989392459393,
0.04928869754076004,
-0.004994096700102091,
-0.01906304433941841,
0.07301095873117447,
-0.04338338226079941,
0.05356396362185478,
-0.01967359147965908,
0.00708742905408144,
0.0020547709427773952,
0.04999605938792229,
0.021038517355918884,
-0.018132561817765236,
0.010607966221868992,
-0.07818938046693802,
-0.040754284709692,
0.01090230606496334,
-0.07228975743055344,
0.03204957768321037,
0.005026082508265972,
-0.008356194943189621,
0.062372490763664246,
-0.024364424869418144,
-0.010437017306685448,
0.0037782678846269846,
0.014457489363849163,
0.0003333181666675955,
-0.048619307577610016,
-0.04139936342835426,
-0.10131528973579407,
0.04443884640932083,
0.0042501408606767654,
-0.028287094086408615,
0.021556587889790535,
0.07264330238103867,
0.004490850958973169,
-0.01935223676264286,
0.003969498444348574,
-0.057770371437072754,
0.05793200433254242,
-0.0014616394182667136,
0.028908107429742813,
0.04572545737028122,
0.060318298637866974,
0.06244195997714996,
-0.019418837502598763,
0.06199357658624649,
0.008697066456079483,
-0.050227705389261246,
0.006098607089370489,
-0.05164072662591934,
-0.010803072713315487,
-0.0033695315942168236,
-0.002715291688218713,
-0.06391284614801407,
0.0028825588524341583,
0.005604712292551994,
-0.020338596776127815,
0.00018988162628374994,
-0.05936799943447113,
0.04383367300033569,
-0.029080670326948166,
-0.018945323303341866,
0.027682846412062645,
0.07007922232151031,
0.0436396598815918,
-0.05001284182071686,
0.003531293710693717,
-0.023961538448929787,
0.025738496333360672,
0.06868799030780792,
-0.021931307390332222,
-0.04316578805446625,
0.04635060951113701,
-0.010900309309363365,
-0.0565759651362896,
-0.01568681187927723,
-0.009189861826598644,
0.025081763043999672,
-0.011852108873426914,
0.007685921620577574,
-0.051522377878427505,
0.0672350749373436,
0.06448854506015778,
0.08375658094882965,
0.018409334123134613,
0.009077562019228935,
-0.04139937832951546,
0.0003435478138271719,
0.03301309794187546,
-0.03222465142607689,
-0.07419096678495407,
-0.06670042872428894,
-0.043854936957359314,
0.010996110737323761,
-0.04745832458138466,
-0.0015581258339807391,
0.0015776315703988075,
0.04906057193875313,
0.017717234790325165,
-0.006933738477528095,
-0.07710260897874832,
-0.0052578928880393505,
0.03655458614230156,
0.019880829378962517,
-0.030906440690159798,
0.011262616142630577,
0.04538562521338463,
0.030671635642647743,
0.0167466402053833,
-0.007272203452885151,
-0.06249959021806717,
0.07091222703456879,
-0.007780051324516535,
-0.0316951759159565,
-0.015511104837059975,
-0.018355485051870346,
0.0019687043968588114,
0.005720970686525106,
-0.02396344766020775,
0.03241018205881119,
0.06897079944610596,
-0.005878753028810024,
-0.04963722825050354,
0.030905308201909065,
0.007644467521458864,
0.032126229256391525,
0.022795816883444786,
-0.0037491125985980034,
-0.04196683317422867,
0.013187602162361145,
0.024260811507701874,
-0.014402003958821297,
0.0030335402116179466,
0.0361698679625988,
-0.06826689094305038,
-0.03275114297866821,
0.01448168233036995,
-0.03492638096213341,
0.0409347340464592,
0.013198202475905418,
-0.007069294340908527,
0.03488227725028992,
-0.006898027379065752,
-0.07311306893825531,
0.014118853956460953,
0.019328461959958076,
-0.028384387493133545,
0.01566021330654621,
0.0574117936193943,
0.007036074995994568,
-0.0156155526638031,
0.055074941366910934,
-0.028459517285227776,
-0.05534989759325981,
-0.012509163469076157,
0.059256378561258316,
-0.009923025034368038,
0.047746166586875916,
0.015200197696685791,
-0.06149723008275032,
0.054897572845220566,
-0.009657621383666992,
-0.026245059445500374,
0.020061694085597992,
0.03164760395884514,
-0.02285066805779934,
0.05936833843588829,
-0.0021978761069476604,
-0.04033086076378822,
-0.042745258659124374,
0.008464687503874302,
0.012220170348882675,
0.039679042994976044,
0.021427659317851067,
0.05702149495482445,
0.0032507097348570824,
0.03522058203816414,
0.11010024696588516,
-0.004263762384653091,
0.009059162810444832,
0.006583814043551683,
-0.01131253968924284,
0.015455126762390137,
-0.006862381007522345,
0.013943566009402275,
0.005971422418951988,
-0.04742586985230446,
0.03911099582910538,
0.04540208727121353,
0.032383766025304794,
-0.025018839165568352,
-0.04967780411243439,
0.005835434887558222,
-0.020358003675937653,
-0.004218026529997587,
-0.021300364285707474,
-0.028208263218402863,
-0.03141249716281891,
-0.0020140078850090504,
0.050840649753808975,
-0.028737369924783707,
-0.013183066621422768,
-0.034518495202064514,
-0.02223561890423298,
0.03918902948498726,
0.09216073155403137,
-0.027967747300863266,
0.04693765193223953,
0.0038764651399105787,
0.05731896683573723,
-0.022477326914668083,
-0.036498699337244034,
0.025137728080153465,
-0.014255937188863754,
-0.016313694417476654,
-0.05661916732788086,
0.021049080416560173,
-0.03383474797010422,
0.01212852168828249,
-0.0003021916782017797,
-0.045005783438682556,
0.030695848166942596,
-0.022246388718485832,
0.06549927592277527,
-0.009560692124068737,
-0.07591777294874191,
0.039029333740472794,
0.012564357370138168,
0.0355352982878685,
-0.028616096824407578,
0.0191726665943861,
0.009706919081509113,
0.014640631154179573,
0.007794968783855438,
-0.021151183173060417,
-0.0074290004558861256,
-0.034106671810150146,
0.003050917759537697,
-0.01442249957472086,
-0.021893398836255074,
-0.0017702606273815036,
-0.011963182128965855,
0.034708719700574875,
-0.0002017081860685721,
0.0709104984998703,
-0.07070032507181168,
-0.0368766188621521,
-0.07244768738746643,
-0.02580607682466507,
0.041074011474847794,
-0.03201351314783096,
-0.022023485973477364,
0.06060657650232315,
-0.008045114576816559,
0.030952034518122673,
-0.026525428518652916,
0.10920243710279465,
-0.039688590914011,
0.009730802848935127,
0.028858326375484467,
-0.04206804186105728,
0.021653130650520325,
-0.0119723379611969,
0.021355686709284782,
0.09018539637327194,
0.042699117213487625,
0.053286563605070114,
-0.008763721212744713,
0.03391139209270477,
0.029446696862578392,
0.0248933807015419,
-0.013498472049832344,
0.017177967354655266,
0.006685485597699881,
-0.033774860203266144,
-0.015656841918826103,
-0.007344844285398722,
-0.047112882137298584,
0.029383838176727295,
0.012532703578472137,
0.02593410015106201,
0.0581563301384449,
0.05206901952624321,
-0.032374706119298935,
-0.06461883336305618,
0.010756631381809711,
-0.1188981905579567,
-0.0070202709175646305,
0.013329075649380684,
-0.004730296786874533,
0.027337996289134026,
-0.027451161295175552,
-0.06227635219693184,
-0.032145075500011444,
-0.0368240550160408,
-0.0666804388165474,
0.001694252248853445,
0.036504801362752914,
-0.017561031505465508,
-0.050216712057590485,
-0.02016555331647396,
0.02581648901104927,
0.03942476958036423,
-0.036037713289260864,
0.007328166160732508,
-0.00943455658853054,
-0.0117770005017519,
0.06979750096797943,
-0.0010055340826511383,
0.006502245087176561,
0.006019578315317631,
-0.03662572801113129,
0.02206677384674549,
-0.01285147201269865,
0.020645558834075928,
0.027553200721740723,
-0.03518033027648926,
-0.059351786971092224,
-0.01949230767786503,
0.04864155873656273,
0.025065146386623383,
-0.015919774770736694,
0.04910436272621155,
0.03315025195479393,
-0.02055029757320881,
0.0637562945485115,
-0.06416329741477966,
0.03936636075377464,
0.027111371979117393,
0.00685123261064291,
0.044436171650886536,
0.029120104387402534,
0.0017814929597079754,
-0.030690765008330345,
0.0024435613304376602,
0.06836467981338501,
0.015952030196785927,
0.05863653123378754,
-0.027583373710513115,
-0.0074910447001457214,
-0.03655087575316429,
0.020498670637607574,
-0.041580930352211,
0.03464542701840401,
-0.01187864039093256,
0.014567939564585686,
-0.00558917410671711,
0.04785232990980148,
0.02580896019935608,
-0.018097303807735443,
0.05758016183972359,
0.022601302713155746,
-0.01924601010978222,
0.025378232821822166,
-0.0072819506749510765,
-0.03820231929421425,
-0.011510411277413368,
0.02352459914982319,
-0.026098530739545822,
0.028211798518896103,
0.033931273967027664,
0.04937662556767464,
0.01750151999294758,
-0.003875355003401637,
0.029117930680513382,
-0.013992005959153175,
-0.01253889687359333,
-0.04248322919011116,
-0.020291632041335106,
0.012971282005310059,
-0.015801111236214638,
-0.02202346920967102,
0.08796059340238571,
-0.017583299428224564,
0.05211668834090233,
-0.0037812949158251286,
-0.035957131534814835,
0.05948152765631676,
0.10268288105726242,
-0.0252965297549963,
-0.04492734372615814,
-0.0025710314512252808,
-0.024840841069817543,
-0.018671123310923576,
0.016061285510659218,
-0.002707407344132662,
-0.04427266865968704,
-0.003050772938877344,
-0.034167274832725525,
0.020139195024967194,
0.037502240389585495,
-0.0021243852097541094
] |
<p>When are two vectors orthogonal in curved spacetime?</p>
<p>From wikipedia:
<em>"In 2-D or higher-dimensional Euclidean space, two vectors are orthogonal if and only if their dot product is zero, i.e. they make an angle of 90°, or π/2 radians. Hence orthogonality of vectors is an extension of the concept of perpendicular vectors into higher-dimensional spaces."</em> [<a href="http://en.wikipedia.org/wiki/Orthogonality%5d" rel="nofollow">http://en.wikipedia.org/wiki/Orthogonality]</a></p>
<p>How does this generalize for non-Euclidean space?</p>
<p>Is the following true?</p>
<p>Two vectors, $V_1$ and $V_2$, are orthogonal if and only if:
$$G_{MN} V_1^M V_2^N = 0$$
Where $G_{MN}$ is the metric of the space.</p>
<p>P.S.: I used Einstein notation: Summation over $M$,$N$ implied and $M$,$N$ $\in$ $\left\{1, 2, ..., d\right\}$.</p> | g7809 | [
-0.00033876855741254985,
-0.03130273520946503,
0.00122411223128438,
-0.02692103385925293,
-0.01757870614528656,
0.04942317679524422,
0.00832212995737791,
-0.03150784596800804,
-0.01899128407239914,
0.024718470871448517,
0.010286563076078892,
-0.002989589935168624,
0.03476956486701965,
-0.03452930599451065,
-0.052604008466005325,
-0.0250379778444767,
-0.005665990058332682,
0.026935722678899765,
0.002253155689686537,
0.02864866517484188,
0.0008308835094794631,
-0.020078569650650024,
0.0392017737030983,
0.025660518556833267,
0.019439997151494026,
-0.05878397822380066,
0.03169921040534973,
0.002202213741838932,
-0.061982590705156326,
-0.005159761290997267,
0.07505487650632858,
0.00967820081859827,
0.019764520227909088,
0.011865095235407352,
0.0007256786338984966,
-0.007677486166357994,
0.011307936161756516,
-0.04763736203312874,
0.07630867511034012,
-0.01997913420200348,
-0.017965495586395264,
0.02620573528110981,
0.025798067450523376,
0.010624881833791733,
-0.02357243373990059,
-0.039489176124334335,
-0.018618175759911537,
0.07719498872756958,
0.04042064771056175,
-0.0063524977304041386,
-0.03126384690403938,
0.03940604254603386,
0.04278882220387459,
-0.04269672930240631,
-0.03295606002211571,
-0.00936831533908844,
0.020363710820674896,
0.00418056407943368,
0.10307110846042633,
0.04736808314919472,
-0.046695318073034286,
0.004082004074007273,
0.023617789149284363,
0.06913605332374573,
0.017060304060578346,
0.0032999077811837196,
-0.060480501502752304,
-0.010030273348093033,
0.02049049735069275,
-0.005553845781832933,
0.048826564103364944,
-0.027532046660780907,
0.023554727435112,
-0.03459474444389343,
-0.05530112609267235,
0.020951073616743088,
0.05310649052262306,
0.02408464625477791,
-0.05007275566458702,
-0.015365887433290482,
0.00023595994571223855,
-0.018303312361240387,
0.011376556009054184,
0.011116440407931805,
0.06541484594345093,
-0.026401570066809654,
0.00032574290526099503,
-0.021463660523295403,
-0.010912847705185413,
0.03436211869120598,
0.031886402517557144,
-0.019965924322605133,
0.02610224299132824,
0.08017659187316895,
-0.031621649861335754,
-0.035471610724925995,
-0.03944841027259827,
0.00909696239978075,
-0.0007927919505164027,
-0.038341738283634186,
-0.017550528049468994,
0.018551772460341454,
0.04903789609670639,
-0.03742632269859314,
0.05275733768939972,
0.026614848524332047,
0.0497775636613369,
0.029052874073386192,
-0.0439816452562809,
-0.08122511208057404,
-0.06597790122032166,
-0.04172699153423309,
-0.07458170503377914,
-0.049358464777469635,
-0.0215302724391222,
-0.020539769902825356,
0.04030153900384903,
-0.052781637758016586,
-0.006208690349012613,
0.06592001765966415,
0.05931250378489494,
0.0968601182103157,
0.02270444668829441,
0.05661356449127197,
0.020808134227991104,
0.07664097845554352,
0.011727857403457165,
-0.04291408881545067,
0.025479715317487717,
-0.06971099227666855,
0.051724158227443695,
-0.01294082123786211,
0.03816094994544983,
0.017150111496448517,
-0.03223971277475357,
0.026035025715827942,
-0.023519262671470642,
-0.04226383939385414,
-0.003171219490468502,
-0.0079277278855443,
-0.009959552437067032,
-0.011742903850972652,
0.03706737980246544,
-0.04185495898127556,
-0.025478875264525414,
-0.012680446729063988,
0.007624550722539425,
-0.00786814745515585,
0.026377782225608826,
0.0348852276802063,
-0.024174680933356285,
0.05911530926823616,
0.021716007962822914,
-0.07387163490056992,
0.005407616496086121,
0.0019973672460764647,
-0.022965237498283386,
-0.005949427839368582,
0.056700706481933594,
-0.02579483576118946,
0.04789381101727486,
0.05818407982587814,
-0.07105362415313721,
-0.00006379163096426055,
-0.040246546268463135,
0.0007129936711862683,
-0.03708749637007713,
-0.04483354091644287,
0.0052136327140033245,
-0.12522625923156738,
-0.006867874413728714,
0.010426292195916176,
0.058175355195999146,
-0.03391736000776291,
0.01961025781929493,
0.042862534523010254,
-0.002888529794290662,
0.032135143876075745,
-0.037542909383773804,
-0.00977420900017023,
-0.07570447772741318,
0.000785390438977629,
0.002741533564403653,
-0.018802855163812637,
-0.03163822367787361,
0.03368266299366951,
0.0014335291925817728,
0.03556113690137863,
-0.047640763223171234,
0.032486461102962494,
-0.024856746196746826,
0.006300958804786205,
0.004192136228084564,
0.060369379818439484,
-0.019073672592639923,
0.02172432281076908,
0.020628362894058228,
-0.00017593480879440904,
0.03647132217884064,
0.07759235054254532,
-0.02512502856552601,
-0.018520496785640717,
0.013050751760601997,
0.031395893543958664,
0.02495277300477028,
0.015240903943777084,
0.0009608087129890919,
-0.02823948673903942,
0.10117167979478836,
0.012294288724660873,
0.054617516696453094,
-0.044010259211063385,
0.03214935585856438,
-0.006106795277446508,
-0.018087787553668022,
-0.008325371891260147,
0.00062945595709607,
-0.0060022687539458275,
-0.08387758582830429,
0.029278120025992393,
0.06374350935220718,
-0.014952745288610458,
0.007523996755480766,
-0.004022493027150631,
-0.010752021335065365,
-0.03441542759537697,
-0.03760598972439766,
0.012074341997504234,
0.046565547585487366,
-0.0038133515045046806,
0.018990330398082733,
-0.024752382189035416,
-0.027748914435505867,
-0.007010979112237692,
0.006152743939310312,
-0.004894613288342953,
-0.0008152219816111028,
0.03456416726112366,
0.037009257823228836,
0.05973545461893082,
0.044648297131061554,
-0.01916474476456642,
-0.029720986261963844,
0.055628702044487,
0.012381888926029205,
-0.01639082469046116,
0.04586492106318474,
0.015538178384304047,
-0.04054661840200424,
-0.00857474748045206,
-0.03565286472439766,
-0.013052876107394695,
0.009129989892244339,
0.0352378711104393,
0.02628398686647415,
0.0016071498394012451,
-0.017263073474168777,
0.016471967101097107,
-0.11486101150512695,
-0.024281365796923637,
-0.03863891214132309,
-0.04121622443199158,
-0.03608591482043266,
0.01997360773384571,
-0.038176748901605606,
0.027387181296944618,
-0.03935172036290169,
0.062313176691532135,
0.01763739623129368,
0.0438481830060482,
-0.01563950814306736,
0.06854937225580215,
-0.025741109624505043,
-0.034553997218608856,
-0.05316125974059105,
-0.013172285631299019,
-0.010058059357106686,
-0.02022717148065567,
-0.045880354940891266,
-0.023732762783765793,
0.02968496084213257,
0.02779160626232624,
-0.030698135495185852,
-0.002671483438462019,
0.00807151198387146,
-0.02961762063205242,
-0.02688048593699932,
0.04216718673706055,
-0.008703465573489666,
0.023086480796337128,
-0.03248042240738869,
0.06886515766382217,
0.006555295083671808,
-0.07885052263736725,
-0.0015631307614967227,
0.005193559918552637,
-0.0005280756740830839,
0.03415475785732269,
-0.00262486026622355,
0.024454133585095406,
-0.0392727293074131,
-0.03489024564623833,
0.032109253108501434,
-0.05466054752469063,
0.02498706802725792,
-0.058539457619190216,
-0.052494220435619354,
-0.11424772441387177,
-0.03322882950305939,
0.029873328283429146,
0.017241962254047394,
0.01927562989294529,
0.01925276406109333,
0.016601787880063057,
-0.07358178496360779,
0.014246859587728977,
-0.02082665264606476,
-0.060496799647808075,
0.03286939114332199,
0.059894438832998276,
-0.05371136590838432,
0.009478811174631119,
-0.0665898397564888,
0.025521183386445045,
0.04913226142525673,
-0.024001706391572952,
-0.005799942649900913,
-0.00955294445157051,
0.025233572348952293,
0.05504821240901947,
0.012017964385449886,
0.003317298600450158,
-0.007264754734933376,
0.011820363812148571,
-0.017903614789247513,
0.009431018494069576,
0.003761144122108817,
-0.014433154836297035,
0.008871038444340229,
0.04254854843020439,
-0.03186368569731712,
0.02982446737587452,
-0.01951688900589943,
-0.02175816521048546,
-0.013925179839134216,
0.06900393217802048,
0.02552841603755951,
0.07199706137180328,
0.0022106547839939594,
-0.014749852009117603,
0.014026558957993984,
-0.03481340408325195,
0.03427058085799217,
-0.0030842686537653208,
0.027774972841143608,
0.05932628735899925,
0.02440272457897663,
0.055692680180072784,
-0.048702411353588104,
-0.0434652604162693,
0.006137742195278406,
-0.0161395575851202,
-0.016586659476161003,
-0.026875782757997513,
-0.008843787014484406,
-0.010689618065953255,
0.07353134453296661,
-0.03204915672540665,
-0.03751194104552269,
0.01555317547172308,
0.022980673238635063,
-0.011499173007905483,
-0.002335448982194066,
0.06656920164823532,
0.037421684712171555,
-0.02911919727921486,
0.04789239168167114,
-0.021450381726026535,
-0.02884650230407715,
-0.006857432425022125,
0.04568541422486305,
-0.0013388084480538964,
0.03971739113330841,
0.017171161249279976,
-0.031043963506817818,
-0.006797883193939924,
-0.031766053289175034,
-0.00617851410061121,
0.035858165472745895,
-0.051822979003190994,
0.012782985344529152,
0.06998114287853241,
-0.006574470549821854,
-0.0596894808113575,
-0.007583340164273977,
-0.029149478301405907,
0.030595695599913597,
0.06087569519877434,
-0.01951495371758938,
-0.0066246711649000645,
0.015423599630594254,
0.04294518381357193,
0.02889677695930004,
-0.00933760404586792,
0.01680845022201538,
0.04520874097943306,
-0.03565144166350365,
0.02912425436079502,
0.007882754318416119,
-0.02548898011445999,
0.030730191618204117,
0.012618793174624443,
0.01674104668200016,
-0.024420050904154778,
0.08459106832742691,
0.047222621738910675,
0.013611127622425556,
-0.0007623447454534471,
-0.03527671843767166,
0.027652861550450325,
-0.04304026439785957,
0.005457292310893536,
0.01102430373430252,
-0.005985916126519442,
0.045646846294403076,
0.07802612334489822,
0.039014607667922974,
-0.03392159938812256,
0.004380318336188793,
0.012621676549315453,
0.011305507272481918,
0.028276361525058746,
-0.011717128567397594,
0.03773123770952225,
-0.07705138623714447,
0.019491415470838547,
-0.04276956990361214,
0.055402081459760666,
0.04105024039745331,
-0.05591035261750221,
0.0389590747654438,
-0.018667934462428093,
0.014323463663458824,
-0.06190233677625656,
-0.0014024912379682064,
0.06538288295269012,
0.026234423741698265,
-0.05606246367096901,
0.004267737735062838,
0.03131834790110588,
-0.035094745457172394,
0.0027776286005973816,
0.053061343729496,
-0.012185126543045044,
-0.02406628429889679,
-0.0019749989733099937,
-0.04774979129433632,
0.027744758874177933,
-0.03920154646039009,
0.02787899598479271,
-0.06710290908813477,
-0.029584214091300964,
0.01388073805719614,
0.00031875167042016983,
0.0026378831826150417,
0.004006289876997471,
-0.06362142413854599,
-0.0267801396548748,
-0.003462810069322586,
0.04867171123623848,
-0.024619335308670998,
-0.006467926781624556,
-0.039089735597372055,
0.013573015108704567,
-0.04008994996547699,
-0.026676496490836143,
-0.014528161846101284,
-0.019256021827459335,
-0.08286914974451065,
-0.03736518323421478,
-0.05509675294160843,
-0.03879411891102791,
0.03318542614579201,
0.031661588698625565,
0.03693194314837456,
-0.005613396875560284,
0.012046954594552517,
-0.02561037801206112,
0.0455203615128994,
0.009718694724142551,
-0.015332577750086784,
0.026008397340774536,
-0.042287539690732956,
0.04205990955233574,
-0.06416432559490204,
0.0165117010474205,
-0.05231136083602905,
-0.0632166638970375,
-0.05703998729586601,
0.005644868593662977,
-0.03204508498311043,
0.047827333211898804,
0.03251873329281807,
-0.04485652595758438,
-0.006461796350777149,
-0.015456651337444782,
0.07141383737325668,
-0.02314024791121483,
0.0019659572280943394,
0.008766310289502144,
0.026594892144203186,
0.014244353398680687,
-0.023974502459168434,
0.02528221160173416,
0.024088645353913307,
-0.01781843602657318,
0.01545390672981739,
0.0019891306292265654,
0.0007325608166866004,
-0.014683443121612072,
0.006151942070573568,
-0.013321631588041782,
-0.03179096058011055,
-0.054993268102407455,
0.013564580120146275,
0.0013708868063986301,
-0.04148566722869873,
-0.04804567992687225,
0.029265286400914192,
0.08098088204860687,
0.030498240143060684,
0.01114607136696577,
0.016141002997756004,
-0.03618280589580536,
-0.0010773232206702232,
-0.04339783266186714,
-0.010972879827022552,
0.026592731475830078,
0.06917273253202438,
-0.021262986585497856,
-0.0691324770450592,
-0.046163417398929596,
-0.037875089794397354,
0.08572403341531754,
-0.015925636515021324,
0.03175162151455879,
-0.03307562693953514,
0.003878182265907526,
0.026731694117188454,
-0.0028734656516462564,
-0.038080424070358276,
-0.0025999832432717085,
-0.01565920002758503,
-0.03017176128923893,
-0.01445805560797453,
0.008212930522859097,
0.03662371635437012,
0.006091353949159384,
-0.02345801331102848,
0.040811024606227875,
0.07344983518123627,
-0.00029342592461034656,
0.027856310829520226,
-0.030812440440058708,
-0.04778056591749191,
-0.021374497562646866,
0.02553446777164936,
-0.02009795792400837,
0.011286933906376362,
-0.0027909036725759506,
-0.01917180046439171,
0.004615073557943106,
0.052004601806402206,
0.0293237566947937,
-0.003958693705499172,
0.048742566257715225,
-0.02926626242697239,
-0.06314729154109955,
-0.04186825826764107,
0.03914178907871246,
0.0037050668615847826,
0.003270033746957779,
0.033895689994096756,
-0.034947533160448074,
-0.03572813421487808,
0.034528542309999466,
-0.01317332312464714,
0.030230503529310226,
0.031774070113897324,
-0.03315559774637222,
-0.03253782168030739,
0.012677722610533237,
0.0009728353470563889,
0.0013885499211028218,
-0.0420709103345871,
-0.0009062697645276785,
-0.035282932221889496,
0.031624771654605865,
0.016165655106306076,
-0.013319463469088078,
-0.01500642765313387,
0.003174209501594305,
0.04288489371538162,
0.08831481635570526,
-0.007964001968502998,
0.01933770626783371,
-0.09062180668115616,
0.018028920516371727,
0.0066500757820904255,
-0.028148576617240906,
0.03656608983874321,
0.015501665882766247,
-0.033883120864629745,
0.06645392626523972,
0.008323535323143005,
-0.009974745102226734,
-0.0011951109627261758,
-0.01698778197169304,
-0.010906235314905643,
0.015815455466508865,
0.018283933401107788,
0.022649668157100677,
0.02205764688551426,
0.028495006263256073,
-0.019867371767759323,
0.05690735578536987,
-0.011247276328504086,
-0.03981044888496399,
0.03450069576501846,
0.01430696900933981,
-0.013741501607000828,
-0.07737264782190323,
0.02782907895743847,
-0.0197598896920681,
0.04199661687016487,
0.005875396076589823,
-0.028573479503393173,
0.031768716871738434,
0.020717354491353035,
0.03372333571314812,
0.002003544243052602,
0.011708956211805344,
0.025584477931261063,
-0.04675401374697685,
-0.029546858742833138,
-0.0012270007282495499,
-0.005825406406074762,
0.015116389840841293,
-0.06002749130129814,
0.019857769832015038,
0.0660477876663208,
0.0016960172215476632,
-0.024836694821715355,
0.011367334052920341,
-0.0743102952837944,
-0.02170317992568016,
0.017254538834095,
0.04615674912929535,
-0.04459773004055023,
-0.08056670427322388,
-0.021114327013492584,
-0.003379085334017873,
-0.0032598301768302917,
0.014714522287249565,
-0.014610455371439457,
0.008892126381397247,
-0.004212018568068743,
0.012821880169212818,
-0.00792105495929718,
0.007425968069583178,
0.004786151461303234,
-0.010352070443332195,
0.01207810640335083,
0.03765616565942764,
-0.003686068346723914,
-0.03545025736093521,
-0.025331439450383186,
0.0035456286277621984,
-0.05455518886446953,
-0.0009460009750910103,
0.07804365456104279,
-0.01581953465938568,
-0.012765197083353996,
0.005326400510966778,
-0.07472554594278336,
-0.0396743044257164,
0.08040906488895416,
-0.05285803601145744,
-0.028051190078258514,
0.012678385712206364,
-0.049945857375860214,
0.03132983669638634,
-0.0030528120696544647,
-0.01849219761788845,
0.0010477451141923666,
0.027814924716949463,
0.043373625725507736,
0.021894332021474838,
-0.03392881527543068,
-0.022152820602059364,
-0.041650060564279556,
0.0070585752837359905,
-0.03338036686182022,
0.03212212771177292,
0.010395805351436138,
-0.025657499209046364,
0.02783622033894062,
-0.04259123653173447,
0.010044828988611698,
-0.031400345265865326,
0.023236136883497238,
0.0008205014746636152,
0.002677878364920616,
0.019672328606247902,
0.010694785974919796,
-0.05910201370716095,
-0.05414143577218056,
-0.002046533627435565,
0.012320110574364662,
-0.04789525642991066,
-0.06454791128635406,
-0.02170981466770172,
0.0009042474557645619,
-0.0297987200319767,
-0.03170045092701912,
0.013004831038415432,
-0.02459414303302765,
-0.006191774737089872,
0.017651908099651337,
-0.03651270270347595,
0.01987576112151146,
0.042521409690380096,
-0.045010026544332504,
0.05829731747508049,
-0.039181821048259735,
0.026017649099230766,
0.015209056437015533,
-0.02986220084130764,
0.06952747702598572,
0.0051116119138896465,
0.04464985430240631,
-0.003162135137245059,
-0.02632071264088154,
-0.019862474873661995,
-0.0467584989964962,
-0.01706530526280403,
0.010149452835321426,
0.0379752516746521,
-0.023285865783691406,
0.01463595125824213,
-0.04190722480416298,
0.05195341631770134,
0.022597501054406166,
0.027038048952817917,
0.13988615572452545,
-0.019167549908161163,
0.035445258021354675,
0.009982101619243622,
0.07065090537071228,
-0.0028345747850835323,
-0.012625682167708874,
0.008237597532570362,
-0.003974052146077156,
-0.03125273808836937,
-0.0014794982271268964,
-0.029459092766046524,
-0.05785934254527092,
0.03654501587152481
] |
<p>All of my textbooks mention, that entropy-change of all spontaneous physical, and chemical processes is positive, and that such processes need another condition to fulfill- decrease in the net internal-energy of the system, taking part in the process. </p>
<p>I just want to know that what is the reason behind this <strong>tendency</strong> of a system to increase its entropy, and to lose its internal-energy.</p> | g7810 | [
0.00569164426997304,
-0.001714819110929966,
0.00330404588021338,
0.009879698976874352,
0.014629635959863663,
-0.016941960901021957,
-0.030536837875843048,
0.05066277086734772,
-0.04629407450556755,
-0.023788588121533394,
-0.008676552213728428,
0.010161599144339561,
0.016531461849808693,
0.04226978123188019,
-0.021594122052192688,
0.007371305022388697,
0.041774820536375046,
0.0022494231816381216,
0.024385083466768265,
0.02598525583744049,
-0.06882885098457336,
-0.0033361499663442373,
-0.004660175647586584,
-0.05024426057934761,
-0.017909009009599686,
0.007813877426087856,
0.04536450654268265,
-0.012828882783651352,
0.03015414997935295,
-0.0020470779854804277,
0.026001188904047012,
-0.0070644039660692215,
0.024242879822850227,
-0.04761705920100212,
-0.04115815460681915,
-0.0004520525108091533,
0.11616385728120804,
0.010083010420203209,
0.02940009906888008,
-0.004450525622814894,
0.03219820559024811,
-0.03822112828493118,
0.031139012426137924,
-0.038993846625089645,
-0.05076302960515022,
0.0038327581714838743,
-0.0134801110252738,
-0.03693656995892525,
-0.00121471774764359,
-0.06054124981164932,
0.0032463399693369865,
-0.012212091125547886,
0.039477359503507614,
-0.011873285286128521,
0.05401669442653656,
0.0015691292937844992,
-0.035506028681993484,
-0.005049075931310654,
0.020034505054354668,
0.003471527947112918,
0.05182609334588051,
-0.03913143649697304,
0.03223193809390068,
-0.012385784648358822,
0.0386904813349247,
-0.006242789328098297,
-0.007311688736081123,
-0.03411608561873436,
0.03335370868444443,
0.07246450334787369,
-0.04093001037836075,
-0.005554689094424248,
-0.05130743235349655,
-0.00292384740896523,
0.06394211947917938,
-0.03710765019059181,
-0.01766902208328247,
-0.03720204159617424,
0.03175695985555649,
0.0065546841360628605,
-0.021664228290319443,
0.013269017450511456,
0.023239929229021072,
0.0004202636191621423,
-0.0020434362813830376,
0.007189372554421425,
0.03896879777312279,
-0.03208286315202713,
-0.010042810812592506,
0.005167027935385704,
0.01801963895559311,
0.009318123571574688,
0.030259454622864723,
0.033236995339393616,
-0.05928640440106392,
0.02417815290391445,
-0.018933748826384544,
0.04064143821597099,
0.040379032492637634,
0.020863020792603493,
0.0075467610731720924,
-0.09863822162151337,
0.014771449379622936,
0.012675364501774311,
-0.007917795330286026,
-0.03628434240818024,
-0.007566659711301327,
-0.054224058985710144,
-0.012258373200893402,
0.05052858591079712,
0.010799278505146503,
-0.0017806433606892824,
-0.039845824241638184,
-0.05221020057797432,
0.06279854476451874,
0.0013806769857183099,
0.11847694963216782,
-0.029139507561922073,
-0.0045058391988277435,
0.045003827661275864,
-0.027162669226527214,
0.006895164959132671,
-0.01889265887439251,
0.015611859038472176,
-0.024990733712911606,
0.03475422412157059,
0.011237017810344696,
-0.027534019201993942,
0.023401882499456406,
-0.008071647956967354,
0.04091351479291916,
0.01237002294510603,
-0.052936166524887085,
0.011075570248067379,
0.0351736880838871,
0.06449158489704132,
0.010972389951348305,
0.00340059120208025,
0.02866719476878643,
-0.014953488484025002,
0.01415309775620699,
0.029927611351013184,
-0.00820145197212696,
0.004913595039397478,
-0.0024956422857940197,
-0.0072981445118784904,
0.029750069603323936,
0.016127489507198334,
0.029289910569787025,
-0.05457567051053047,
0.004444377031177282,
-0.015047555789351463,
-0.024065714329481125,
-0.08579269796609879,
-0.023152457550168037,
-0.027446357533335686,
-0.001618635724298656,
0.016869597136974335,
-0.013656738214194775,
0.050635937601327896,
0.0331299789249897,
0.012776871211826801,
0.05231807753443718,
0.02598206326365471,
-0.07460932433605194,
0.044709257781505585,
0.020014384761452675,
-0.04674249514937401,
-0.01980295218527317,
-0.029704006388783455,
-0.02924828976392746,
-0.02980453334748745,
-0.008654515258967876,
0.07011421769857407,
0.002542109927162528,
0.02905162051320076,
0.03541741892695427,
0.03828373923897743,
0.03547033295035362,
0.005330109968781471,
-0.0748596340417862,
0.0003853874222841114,
0.045582205057144165,
-0.02812213823199272,
0.035265952348709106,
-0.019231026992201805,
0.011433838866651058,
0.09739075601100922,
-0.1030912846326828,
0.009592155925929546,
-0.0016969642601907253,
-0.02991648204624653,
0.018808355554938316,
-0.030045198276638985,
0.03078201413154602,
-0.025302959606051445,
-0.056201886385679245,
-0.016202958300709724,
-0.039748724550008774,
-0.022620240226387978,
-0.024367641657590866,
-0.0009310681489296257,
-0.027960477396845818,
-0.025469794869422913,
-0.024725567549467087,
0.017288515344262123,
-0.014917831867933273,
0.012434672564268112,
-0.001783581217750907,
-0.012514113448560238,
-0.003273320384323597,
-0.032781004905700684,
-0.07831361889839172,
-0.02801968902349472,
0.035711850970983505,
-0.0016200075624510646,
0.0006615474121645093,
-0.022462336346507072,
0.03869986534118652,
0.030534641817212105,
-0.0041909730061888695,
-0.00908155832439661,
-0.00787232257425785,
0.04702050983905792,
-0.03863964229822159,
0.024456460028886795,
-0.03377559781074524,
-0.04756299778819084,
0.02161416970193386,
-0.009264220483601093,
-0.0435175858438015,
0.05541228875517845,
0.027424326166510582,
0.009553785435855389,
-0.025756819173693657,
0.051957398653030396,
0.002921039704233408,
0.020102521404623985,
0.03492159768939018,
-0.012895921245217323,
-0.047073133289813995,
-0.041988782584667206,
-0.005452502053231001,
0.021286150440573692,
0.01757889986038208,
-0.05627233907580376,
-0.028347698971629143,
-0.07540435343980789,
-0.044122882187366486,
0.0058625927194952965,
0.07303905487060547,
-0.00876765325665474,
0.005843244027346373,
-0.0021199584007263184,
-0.026727620512247086,
0.02743179351091385,
-0.0006162911304272711,
0.06357478350400925,
-0.004336124751716852,
-0.0647706389427185,
-0.014122534543275833,
-0.07220271974802017,
0.01732245832681656,
0.029164453968405724,
-0.03694012388586998,
0.0005862010293640196,
-0.06310836225748062,
-0.019902879372239113,
-0.0006669774302281439,
0.005019025411456823,
0.002958061406388879,
0.06357549875974655,
-0.03704433515667915,
0.05818690359592438,
0.003919542301446199,
0.026828838512301445,
-0.007343715522438288,
0.021382562816143036,
0.0338340625166893,
-0.018219657242298126,
0.00830319244414568,
0.054706793278455734,
-0.021106796339154243,
0.021806322038173676,
-0.005529549904167652,
-0.052237287163734436,
0.027560347691178322,
0.007394316606223583,
-0.038710810244083405,
-0.021519184112548828,
0.004453090485185385,
0.03364468365907669,
0.001855638693086803,
0.016115611419081688,
0.012889182195067406,
0.03854435682296753,
0.03754378855228424,
-0.051999080926179886,
0.005362426396459341,
-0.023412028327584267,
0.011062516830861568,
0.006029474548995495,
-0.027320746332406998,
0.03153805062174797,
0.05633474141359329,
0.08395645767450333,
-0.051482655107975006,
0.00805414654314518,
-0.02482217736542225,
0.01752462610602379,
-0.0349571518599987,
-0.06015447527170181,
-0.026521507650613785,
0.0046056960709393024,
-0.04323240742087364,
0.04835345223546028,
0.008458863943815231,
-0.01009331177920103,
-0.008736420422792435,
-0.02394319698214531,
-0.0001172628763015382,
-0.03087223507463932,
0.01827947050333023,
-0.010610077530145645,
0.025633102282881737,
-0.06406220048666,
-0.030358783900737762,
-0.04871770367026329,
-0.018344219774007797,
-0.040487587451934814,
-0.030948670580983162,
-0.004619891289621592,
0.006394673138856888,
-0.020265687257051468,
-0.051967889070510864,
-0.02855714224278927,
-0.046074673533439636,
-0.02105003036558628,
0.029155965894460678,
0.02232496067881584,
0.04687890782952309,
-0.0029172562062740326,
-0.04360136389732361,
0.021699151024222374,
0.0008379896753467619,
0.025381190702319145,
-0.03724353015422821,
-0.03297879919409752,
0.02109394408762455,
0.018084365874528885,
0.05854402482509613,
-0.0001102772366721183,
0.012008358724415302,
0.028782177716493607,
-0.03471434488892555,
-0.04699556902050972,
-0.0015638129552826285,
0.014174286276102066,
-0.00443488173186779,
-0.02407809905707836,
-0.025709189474582672,
-0.04903971403837204,
0.047968316823244095,
0.01850007474422455,
-0.04413513466715813,
0.051521286368370056,
-0.014534305781126022,
0.06182617321610451,
-0.01678614318370819,
0.008471469394862652,
0.035680826753377914,
0.00398979289457202,
-0.053387586027383804,
-0.013652490451931953,
0.05026194825768471,
-0.01167579460889101,
0.05097740888595581,
0.0653020441532135,
-0.06840335577726364,
0.017568718641996384,
0.12899373471736908,
-0.013763767667114735,
0.011058970354497433,
0.04818899184465408,
0.03677906095981598,
0.0018554499838501215,
-0.04822786897420883,
0.04698203504085541,
-0.028294771909713745,
-0.026785152032971382,
0.0072039407677948475,
0.03627128526568413,
-0.020261498168110847,
-0.02325609140098095,
-0.022805197164416313,
0.004480896517634392,
0.055976931005716324,
-0.00007393117266474292,
0.027240468189120293,
0.055405426770448685,
-0.029119746759533882,
-0.006222858093678951,
-0.021174559369683266,
0.0009230193682014942,
0.014389331452548504,
-0.0176932904869318,
-0.015021729283034801,
-0.012723681516945362,
0.0008090399787761271,
-0.04176041856408119,
0.03883709758520126,
-0.02002318575978279,
-0.0440974235534668,
-0.07731831073760986,
-0.056454990059137344,
-0.02596208080649376,
-0.037378184497356415,
-0.04572027549147606,
0.06510908156633377,
0.009246633388102055,
0.028111519291996956,
0.017531098797917366,
-0.055916666984558105,
0.030208267271518707,
-0.014347482472658157,
0.06940734386444092,
0.047466572374105453,
0.011789807118475437,
0.0210951529443264,
-0.0910039097070694,
-0.005960157141089439,
0.010422084480524063,
-0.005695297848433256,
0.048354510217905045,
-0.0455053485929966,
0.04106127470731735,
-0.020902352407574654,
0.053504813462495804,
-0.041840724647045135,
0.04126529023051262,
0.07549820095300674,
0.051515765488147736,
-0.0035879570059478283,
-0.0624968446791172,
0.046874403953552246,
0.00871060136705637,
0.01656130701303482,
0.03865232318639755,
0.011693951673805714,
-0.0823558121919632,
-0.013606018386781216,
0.052968502044677734,
0.04351324960589409,
-0.007372560445219278,
0.023258434608578682,
-0.027295982465147972,
-0.06282665580511093,
0.033098552376031876,
-0.06514610350131989,
0.04134844243526459,
-0.005335594527423382,
-0.009526565670967102,
0.04248831793665886,
0.0304682906717062,
-0.01672705076634884,
0.014882256276905537,
-0.02451968379318714,
-0.02117556892335415,
0.008137842640280724,
-0.007548913825303316,
0.061323583126068115,
0.028263859450817108,
0.029261093586683273,
0.059918541461229324,
0.003164498368278146,
0.003885766491293907,
-0.03417147323489189,
-0.06492327898740768,
0.013166522607207298,
-0.02241944521665573,
-0.0028153029270470142,
0.0333360880613327,
0.04231243208050728,
0.024583863094449043,
-0.03752945363521576,
-0.04338909685611725,
-0.01316809467971325,
-0.005321086850017309,
0.01700260303914547,
-0.018392853438854218,
0.013076230883598328,
0.07410361617803574,
0.06334521621465683,
-0.0058940378949046135,
-0.022838151082396507,
0.005954411346465349,
-0.007328304927796125,
-0.03566618636250496,
-0.03232147544622421,
0.01654846780002117,
-0.11577139794826508,
-0.031296245753765106,
-0.03033306635916233,
0.015055228024721146,
0.03359868377447128,
-0.032043538987636566,
0.0269777849316597,
-0.024578949436545372,
-0.05853155627846718,
0.03508157655596733,
-0.013957173563539982,
0.025803521275520325,
0.045844029635190964,
0.02141713537275791,
0.03559887781739235,
0.03594723343849182,
0.027070727199316025,
-0.013254859484732151,
-0.016283957287669182,
-0.013201399706304073,
0.03674949333071709,
-0.01273303758352995,
0.05910011753439903,
-0.05776025727391243,
-0.00672577042132616,
0.08827485889196396,
-0.07341128587722778,
0.01586737483739853,
0.023485500365495682,
0.005490852519869804,
-0.01936468668282032,
-0.00477606849744916,
-0.0030543480534106493,
0.024288441985845566,
-0.0365273617208004,
-0.024970537051558495,
-0.022934945300221443,
0.0601753331720829,
-0.04092124477028847,
0.04386681690812111,
0.05997122824192047,
-0.02611798234283924,
-0.04245375841856003,
-0.0007395921857096255,
-0.02524743415415287,
-0.023585237562656403,
-0.05029761418700218,
-0.06106756255030632,
-0.044605132192373276,
0.01725449599325657,
0.006045644637197256,
-0.025455649942159653,
0.042855873703956604,
-0.07167782634496689,
-0.01595037803053856,
-0.01848275400698185,
0.04408252239227295,
0.009258183650672436,
0.027468930929899216,
-0.04716680571436882,
0.014063038863241673,
-0.028210479766130447,
-0.007558561395853758,
0.03951052203774452,
0.056144777685403824,
-0.06556836515665054,
-0.004885835573077202,
0.014712431468069553,
0.02893638052046299,
0.07552380114793777,
0.053886111825704575,
0.0499606728553772,
0.031675174832344055,
-0.0265811737626791,
0.02249443531036377,
0.0018667017575353384,
-0.011260118335485458,
-0.03473067283630371,
-0.002889232011511922,
-0.07728509604930878,
-0.014067099429666996,
-0.04025449976325035,
0.033850912004709244,
-0.05383627489209175,
0.001992611913010478,
0.03181466460227966,
-0.015885930508375168,
0.059552859514951706,
0.042161937803030014,
0.0005377480410970747,
-0.01940864324569702,
0.02966172620654106,
-0.005135579500347376,
-0.03412055969238281,
-0.025380782783031464,
0.015261027961969376,
-0.08251585066318512,
-0.017279157415032387,
0.00944490171968937,
0.020374596118927002,
-0.04981635510921478,
-0.050693925470113754,
0.045593712478876114,
-0.06236607953906059,
-0.005233846604824066,
0.052261460572481155,
0.04756481200456619,
0.006364267785102129,
0.005001257639378309,
0.09037922322750092,
0.017459111288189888,
0.0017594111850485206,
0.04216958209872246,
-0.0431293286383152,
0.04208669438958168,
-0.03998078778386116,
0.008644115179777145,
0.05760236829519272,
-0.022696761414408684,
-0.0422859862446785,
-0.007181847468018532,
-0.006118371617048979,
0.08448613435029984,
0.024141497910022736,
0.007766115944832563,
0.03241879865527153,
-0.038121506571769714,
-0.0009683911921456456,
0.0078846151009202,
0.02199515886604786,
-0.03332257643342018,
0.03502992168068886,
-0.048402924090623856,
-0.004065974615514278,
-0.019510451704263687,
0.007905267179012299,
-0.02616835944354534,
0.011149766854941845,
0.06713680922985077,
-0.04202045872807503,
-0.01946316659450531,
-0.025825755670666695,
0.0003266511776018888,
-0.019244076684117317,
-0.023029355332255363,
0.02400420606136322,
0.011086782440543175,
-0.06511971354484558,
-0.02183687686920166,
-0.012036092579364777,
0.027218356728553772,
-0.0509527325630188,
-0.03659434616565704,
-0.02119516395032406,
0.015908539295196533,
0.06568939238786697,
-0.023267053067684174,
-0.0034961116034537554,
0.04624367505311966,
-0.005454912781715393,
0.019916580989956856,
-0.023865757510066032,
0.04834580421447754,
0.047536931931972504,
0.051722001284360886,
0.09073083102703094,
0.01517103984951973,
-0.03479266166687012,
-0.011498027481138706,
0.008079993538558483,
-0.008878140710294247,
0.02382349595427513,
-0.01881328783929348,
-0.008048010058701038,
-0.02410564199090004,
0.009079987183213234,
0.014390829019248486,
0.00329593475908041,
0.06454537808895111,
-0.04514193907380104,
-0.002837302628904581,
-0.04006059467792511,
0.014905955642461777,
-0.03811698779463768,
-0.0647783949971199,
0.09709305316209793,
-0.08719132095575333,
0.06841109693050385,
0.001105235773138702,
-0.007550664246082306,
-0.053029756993055344,
0.017528297379612923,
-0.028011120855808258,
-0.022263668477535248,
-0.018237018957734108,
0.01759490929543972,
0.012195470742881298,
0.011948909610509872,
0.016556130722165108,
-0.03720550239086151,
0.014213833957910538,
-0.03313218429684639,
-0.01705288700759411,
0.049556996673345566,
0.014835773035883904,
-0.012672046199440956,
-0.009074589237570763,
-0.05593109875917435,
0.014064728282392025,
0.019342031329870224,
-0.03470158949494362,
-0.02838822826743126,
0.062369950115680695,
-0.03147083520889282,
0.05226227641105652,
-0.0035540428943932056,
-0.02117958292365074,
0.0024817304220050573,
-0.016272440552711487,
0.007400172296911478,
-0.003754069097340107,
0.03340531513094902,
-0.09873431921005249,
0.012555615976452827,
-0.06729588657617569,
0.01156020350754261,
0.037966806441545486,
-0.09628979116678238,
0.03168235719203949,
0.02860182709991932,
-0.04939337074756622,
0.006628365255892277,
0.016857976093888283,
-0.0003080727474298328,
-0.051709096878767014,
0.01297658309340477,
0.012195716612040997,
-0.010319914668798447,
0.02093767188489437,
0.03022235818207264,
0.0003704614064190537,
-0.039076004177331924,
0.019995534792542458,
0.03298036754131317,
-0.017402315512299538,
-0.03220488503575325,
0.007054710760712624,
0.050752632319927216,
0.043473031371831894,
-0.036115191876888275,
0.022788483649492264,
-0.03066621907055378,
-0.008353658020496368,
0.001898723072372377,
-0.013964757323265076,
0.002723563462495804,
-0.03875952959060669,
0.019532546401023865,
0.014656678773462772,
0.049068186432123184,
0.0006378254620358348,
0.059189289808273315,
0.010901232250034809,
-0.022806795313954353,
-0.02129426598548889,
-0.05021100491285324,
-0.015777232125401497,
0.01326781790703535
] |
<p>I'm studying some materials on semiconductors, and a section on photoconductivity has left me somewhat confused.</p>
<p>In an extrinsic material, is photoconductivity the result of electrons moving from the valence band to the conduction band, or is it the result of dopant atom ionization? If it is the latter, is the complete ionization assumption invalid for photoconducting devices?</p> | g7811 | [
-0.002019352512434125,
-0.008247250691056252,
-0.008158428594470024,
0.03685889020562172,
0.03207821026444435,
-0.01234541367739439,
0.004608584102243185,
-0.04069652035832405,
0.04915369674563408,
0.01619577966630459,
-0.02248547039926052,
0.03382204473018646,
0.044581856578588486,
-0.03557996079325676,
-0.021287066861987114,
-0.02409505657851696,
0.056820664554834366,
-0.022817151620984077,
0.02077488601207733,
0.02367415465414524,
-0.0014286336954683065,
-0.0017842696979641914,
-0.022098585963249207,
-0.06627880036830902,
0.03115449845790863,
0.05195503681898117,
0.016544412821531296,
-0.0024710448924452066,
-0.03424141928553581,
-0.01342693343758583,
0.0424155555665493,
-0.02571866102516651,
0.03760427609086037,
-0.037572115659713745,
-0.012403585948050022,
-0.02471112087368965,
0.015726009383797646,
-0.008217697031795979,
0.044804394245147705,
0.05600225180387497,
0.032654400914907455,
-0.010134738869965076,
0.008031905628740788,
-0.012427516281604767,
0.02643238939344883,
-0.02696545235812664,
-0.03409044072031975,
0.027693262323737144,
0.020976917818188667,
0.005826755426824093,
0.018525410443544388,
0.029480071738362312,
0.010680384933948517,
0.02296580746769905,
0.020070167258381844,
-0.03562168404459953,
-0.04355016350746155,
0.015616445802152157,
0.07940332591533661,
0.00436166487634182,
0.008338071405887604,
0.0568588562309742,
-0.0013368119252845645,
-0.007351110223680735,
0.0673949345946312,
-0.02879486419260502,
-0.034794971346855164,
0.01811383292078972,
-0.011709118261933327,
-0.01103336364030838,
-0.007766245398670435,
-0.006475913338363171,
-0.027345431968569756,
-0.042259763926267624,
0.030527113005518913,
-0.006009797099977732,
-0.042763497680425644,
-0.07026363164186478,
0.049981337040662766,
0.03518141806125641,
-0.011920939199626446,
-0.12486191093921661,
-0.009564696811139584,
0.013019034639000893,
0.0430409274995327,
-0.06685063987970352,
-0.024317417293787003,
0.013848370872437954,
-0.052163321524858475,
0.023301491513848305,
0.017385033890604973,
-0.07188910245895386,
0.06745632737874985,
-0.033596523106098175,
-0.05938204005360603,
-0.00163081509526819,
0.01895434595644474,
0.0866205245256424,
-0.03653542324900627,
-0.04108447954058647,
-0.0438389889895916,
-0.03803785890340805,
0.009558762423694134,
0.008215458132326603,
0.001022701384499669,
-0.037382420152425766,
-0.018030596897006035,
-0.008028658106923103,
-0.04433180391788483,
0.004305061884224415,
-0.030133182182908058,
-0.011594061739742756,
0.017560677602887154,
-0.011525391601026058,
-0.05966196954250336,
0.09028875827789307,
-0.03484611213207245,
-0.010218843817710876,
0.014309968799352646,
0.024612879380583763,
-0.01055467501282692,
0.05963214486837387,
-0.031806785613298416,
0.06560637056827545,
-0.005039941053837538,
0.04626334458589554,
-0.03210866078734398,
-0.011023478582501411,
-0.060211606323719025,
0.007102704606950283,
-0.030689334496855736,
-0.0001746788911987096,
-0.020192474126815796,
0.05408192425966263,
0.04939315468072891,
-0.03435760363936424,
0.06508535146713257,
-0.020664259791374207,
0.02248886041343212,
-0.02851303108036518,
0.008057965897023678,
-0.00440142722800374,
-0.048792652785778046,
-0.012404737994074821,
0.002808959223330021,
-0.021639663726091385,
-0.036438897252082825,
0.044287726283073425,
0.0513857863843441,
0.010888761840760708,
0.02064114809036255,
0.00831927265971899,
-0.019542116671800613,
-0.06232259050011635,
0.034957267343997955,
-0.040053196251392365,
0.04781816899776459,
-0.06134331598877907,
0.015159481205046177,
0.00498011102899909,
0.02949768304824829,
0.028355084359645844,
-0.044431041926145554,
0.027421684935688972,
0.01022475864738226,
-0.03238961100578308,
-0.019260795786976814,
0.021553074941039085,
-0.04608188942074776,
-0.03709762170910835,
-0.023520389571785927,
0.049782875925302505,
0.004911619238555431,
-0.010165903717279434,
0.014428808353841305,
0.01736948825418949,
0.011595851741731167,
0.023462992161512375,
-0.0026275876443833113,
-0.017636077478528023,
-0.06405140459537506,
0.04157117009162903,
-0.02421651780605316,
-0.040768690407276154,
-0.04324372857809067,
-0.03583068400621414,
-0.047163255512714386,
0.000295427133096382,
-0.026239367201924324,
0.03398844972252846,
-0.023526499047875404,
-0.002654199954122305,
0.02673516981303692,
-0.02607952617108822,
-0.07692325115203857,
-0.035939887166023254,
-0.03585370257496834,
-0.028466328978538513,
-0.013068999163806438,
-0.12288070470094681,
-0.016504688188433647,
0.014309240505099297,
-0.06209959834814072,
0.024420801550149918,
0.0009639532654546201,
0.028793323785066605,
-0.05562127009034157,
-0.035939499735832214,
0.03743574395775795,
0.026028351858258247,
0.027852274477481842,
0.021784985437989235,
0.01753801479935646,
0.06231280788779259,
-0.02284485660493374,
-0.03420101851224899,
0.015040895901620388,
-0.02429194375872612,
0.007886321283876896,
-0.037084151059389114,
-0.042301245033741,
-0.026526417583227158,
0.01671811379492283,
-0.023051219061017036,
-0.0522691085934639,
0.04617748409509659,
0.027121813967823982,
0.055842336267232895,
0.0227335337549448,
0.036264706403017044,
-0.05211659520864487,
0.018587009981274605,
-0.033181436359882355,
-0.003631266299635172,
0.028152067214250565,
0.04493439942598343,
-0.050682682543992996,
-0.0397462397813797,
-0.01229643914848566,
-0.01295811589807272,
-0.0014535033842548728,
-0.04187104105949402,
-0.031742990016937256,
-0.00375158479437232,
0.033866096287965775,
-0.08188753575086594,
-0.01665261946618557,
0.03431101515889168,
-0.02888115867972374,
-0.04864999279379845,
0.042992398142814636,
-0.004250034224241972,
-0.0076941074803471565,
0.04176466539502144,
-0.021482979878783226,
-0.034178659319877625,
-0.02156381867825985,
-0.015357369557023048,
-0.05902854725718498,
-0.0082998126745224,
-0.03845956549048424,
-0.026032252237200737,
-0.027831589803099632,
-0.02707032859325409,
-0.056270502507686615,
0.0024224058724939823,
0.05293353274464607,
-0.030981792137026787,
0.04836394637823105,
-0.011343351565301418,
-0.00247112475335598,
0.06542029976844788,
0.022088011726737022,
0.04088088124990463,
0.06338322162628174,
-0.006525078788399696,
0.011985410936176777,
-0.006263143382966518,
-0.008485213853418827,
-0.05857406556606293,
0.00745161110535264,
0.032192494720220566,
-0.07685171067714691,
-0.02368360012769699,
0.04338386654853821,
-0.04353142902255058,
0.06600706279277802,
-0.04134019836783409,
0.03686968982219696,
0.013943378813564777,
-0.03464071452617645,
0.0020769417751580477,
0.006927884183824062,
0.04894427955150604,
0.053668659180402756,
-0.015308864414691925,
0.08733876794576645,
0.020256906747817993,
-0.00026102879201062024,
0.04248056933283806,
-0.045940954238176346,
0.011099444702267647,
-0.0413057766854763,
0.007874543778598309,
0.01882166974246502,
0.0430007167160511,
0.020364966243505478,
-0.08789399266242981,
-0.02087200991809368,
-0.030557386577129364,
-0.03683386743068695,
0.009998520836234093,
-0.030515335500240326,
0.015672052279114723,
0.016891978681087494,
-0.017465954646468163,
-0.014412865042686462,
0.02483838051557541,
0.04142438992857933,
-0.0109103387221694,
-0.026513705030083656,
0.07226491719484329,
0.024835770949721336,
-0.03017672337591648,
0.03452717885375023,
-0.012424971908330917,
0.0004420338082127273,
-0.02248506434261799,
0.06503874808549881,
-0.002716768067330122,
0.007177330553531647,
0.02933371067047119,
-0.062074482440948486,
0.003070414299145341,
-0.024427663534879684,
-0.058923590928316116,
-0.0068494416773319244,
0.12888802587985992,
0.03241995722055435,
0.01006041094660759,
-0.004916717763990164,
-0.05054258182644844,
-0.063855841755867,
-0.024733925238251686,
0.02979199029505253,
0.025608345866203308,
-0.060313478112220764,
-0.01915702037513256,
-0.011158603243529797,
0.0172716174274683,
0.037011872977018356,
-0.0021096495911478996,
-0.045432716608047485,
0.06589566916227341,
-0.04728352651000023,
0.00023700435122009367,
-0.01741778291761875,
0.0032447027042508125,
-0.06834922730922699,
-0.0018732878379523754,
0.012070383876562119,
-0.024601660668849945,
0.04549596458673477,
-0.01644892990589142,
-0.02667207457125187,
-0.0073456973768770695,
-0.023397544398903847,
0.032290756702423096,
0.05859600007534027,
-0.04896808788180351,
-0.04756324365735054,
-0.01727907359600067,
-0.02639606222510338,
0.015287330374121666,
0.02896706573665142,
-0.011359808966517448,
-0.0013318357523530722,
-0.013206771574914455,
-0.01015322096645832,
0.033761899918317795,
0.014861918054521084,
0.0225138608366251,
0.049260132014751434,
0.028442446142435074,
0.058972638100385666,
0.0027662061620503664,
-0.04408379644155502,
0.05613783374428749,
-0.040636129677295685,
0.0017311305273324251,
-0.04222685098648071,
0.007489299867302179,
-0.013374804519116879,
-0.013220195658504963,
0.015512983314692974,
-0.02559724450111389,
0.006240092683583498,
0.0021957543212920427,
0.09390134364366531,
-0.08052573353052139,
0.012126120738685131,
0.011332483030855656,
0.02185896597802639,
-0.016417087987065315,
0.0008743283106014132,
0.08300791680812836,
0.008050559088587761,
-0.0423487089574337,
-0.01709951087832451,
0.013491632416844368,
-0.04141457751393318,
0.006680853199213743,
-0.030734287574887276,
-0.0201175007969141,
-0.0031203459948301315,
-0.039640072733163834,
-0.01939494162797928,
0.027860265225172043,
-0.04724372923374176,
-0.00856074783951044,
0.05857750028371811,
0.029289191588759422,
0.08678232133388519,
-0.005307673942297697,
0.05844051018357277,
0.14046823978424072,
0.03662766143679619,
-0.01612355373799801,
0.060604192316532135,
-0.024733958765864372,
-0.0206859540194273,
-0.009710385464131832,
0.0033367169089615345,
0.014457005076110363,
-0.07260393351316452,
0.02439342997968197,
-0.022149698808789253,
0.07162395864725113,
0.03865895792841911,
0.04621533304452896,
0.06036531180143356,
0.04369761794805527,
0.031228261068463326,
0.02671637386083603,
0.03079775720834732,
-0.0014544816222041845,
-0.0120773334056139,
0.005635544192045927,
0.06991567462682724,
-0.020767858251929283,
-0.0028797241393476725,
0.02825905755162239,
-0.02816121280193329,
-0.0387284941971302,
-0.04663041606545448,
-0.02341112494468689,
-0.053925465792417526,
-0.01292368397116661,
-0.015508770011365414,
0.059336744248867035,
-0.020531993359327316,
-0.048476122319698334,
-0.014748512767255306,
0.05050577595829964,
0.006596887018531561,
-0.034680966287851334,
0.024911079555749893,
-0.008098654448986053,
-0.056120894849300385,
0.016287479549646378,
-0.0005931060295552015,
0.022821668535470963,
0.06993947923183441,
0.0638771578669548,
0.02078317105770111,
-0.01832914911210537,
0.00016462507483083755,
0.013456569984555244,
-0.010006054304540157,
-0.06448414921760559,
-0.038095831871032715,
0.028906850144267082,
0.012766343541443348,
-0.0014919718960300088,
0.00994294323027134,
0.014413585886359215,
-0.0372530035674572,
0.02454742230474949,
0.011694756336510181,
-0.07774505019187927,
-0.006165702827274799,
-0.07100136578083038,
0.012059048749506474,
-0.025173617526888847,
-0.06290841847658157,
-0.009084062650799751,
0.048983074724674225,
0.06867387890815735,
-0.008212734945118427,
-0.006605292204767466,
-0.005793346557766199,
0.00944136269390583,
0.007066363003104925,
-0.027745848521590233,
0.051417816430330276,
0.0029945513233542442,
-0.018208516761660576,
-0.022515032440423965,
0.007683283649384975,
0.0017937025986611843,
-0.020238347351551056,
-0.016938628628849983,
-0.03315475583076477,
0.00595876295119524,
-0.05033266544342041,
0.02687775529921055,
-0.04713693633675575,
0.01257054228335619,
0.018112724646925926,
-0.01290553156286478,
-0.026746662333607674,
-0.027174565941095352,
-0.01978106051683426,
-0.03028731234371662,
0.06070892512798309,
-0.025491073727607727,
0.02301582507789135,
0.004329117946326733,
0.05820394679903984,
0.04211970418691635,
0.04905393347144127,
0.03661269694566727,
0.02886192500591278,
0.00551203265786171,
-0.025643708184361458,
-0.015124059282243252,
-0.01620287448167801,
0.08622290939092636,
0.029402850195765495,
0.029090343043208122,
-0.032997943460941315,
-0.006737260613590479,
-0.02012527734041214,
0.04585075005888939,
0.048128530383110046,
0.04862571507692337,
-0.06626259535551071,
0.014566311612725258,
-0.01383441686630249,
0.05154228210449219,
0.03993118181824684,
0.029549429193139076,
-0.036249902099370956,
0.0074100070632994175,
0.005602834280580282,
0.017591306939721107,
-0.018818488344550133,
-0.04092898964881897,
0.0002505825541447848,
-0.05897800624370575,
0.027817560359835625,
0.035389043390750885,
0.029327400028705597,
-0.009582169353961945,
0.03869288042187691,
0.018882567062973976,
0.004020532593131065,
-0.039824314415454865,
0.026251908391714096,
-0.021915201097726822,
-0.018406374379992485,
-0.05514928326010704,
0.052407436072826385,
0.005415148567408323,
-0.05000728741288185,
0.004063132684677839,
0.022978534922003746,
-0.0712234228849411,
-0.010817675851285458,
0.0017872160533443093,
-0.036832138895988464,
-0.005631790496408939,
0.00491640530526638,
0.04178756847977638,
0.028173791244626045,
-0.006208580452948809,
0.05043143406510353,
0.0028014436829835176,
0.04365841671824455,
-0.025982141494750977,
-0.024805886670947075,
0.00493781641125679,
-0.031484875828027725,
0.047966472804546356,
-0.0602729432284832,
0.005015213508158922,
0.054691046476364136,
-0.004729618318378925,
0.03441385552287102,
0.022016795352101326,
0.0884731188416481,
0.009816823527216911,
0.03098292089998722,
-0.03198230266571045,
0.04921843856573105,
0.008570029400289059,
0.052756551653146744,
0.007017175201326609,
-0.0018653197912499309,
-0.02744661457836628,
-0.02775506302714348,
-0.030527032911777496,
-0.010662015527486801,
-0.07415872812271118,
0.06170468032360077,
0.014463266357779503,
-0.0068628424778580666,
0.07408840954303741,
-0.010969053953886032,
-0.006070672068744898,
-0.04643576964735985,
-0.0013459709007292986,
0.01210799254477024,
0.007576713804155588,
0.020866379141807556,
0.08434227108955383,
-0.035142987966537476,
0.058177754282951355,
0.05467165261507034,
0.011370901949703693,
-0.03523238003253937,
0.012057040818035603,
0.020917510613799095,
0.0024101908784359694,
0.024678664281964302,
-0.0026590211782604456,
0.05953732877969742,
-0.038035135716199875,
-0.025963634252548218,
0.01160510629415512,
-0.011439044028520584,
0.012181978672742844,
0.015398700721561909,
0.055079247802495956,
-0.03128634765744209,
0.03300001844763756,
0.0031164998654276133,
0.01142081804573536,
-0.03714565932750702,
-0.012648298405110836,
-0.005911447107791901,
-0.019020788371562958,
0.02468263916671276,
0.048362940549850464,
0.023289663717150688,
0.027817916125059128,
-0.005133329425007105,
0.007175502832978964,
-0.009403497911989689,
-0.08423919975757599,
-0.05358482524752617,
-0.02347431145608425,
0.027360593900084496,
0.01883259415626526,
0.013408088125288486,
0.007491433061659336,
0.01042703352868557,
-0.04400884360074997,
-0.04083970934152603,
-0.055626384913921356,
0.003467303467914462,
0.008177654817700386,
0.01168081909418106,
-0.005162857007235289,
0.04805218428373337,
-0.003167667193338275,
-0.024354303255677223,
0.013810493052005768,
-0.04712541401386261,
-0.05552059784531593,
-0.005531804636120796,
0.00902589876204729,
0.072066530585289,
-0.03978145122528076,
-0.06569734215736389,
0.023926906287670135,
-0.07644268125295639,
-0.01619628816843033,
-0.0037877720315009356,
0.06834088265895844,
0.04547421634197235,
0.004330454394221306,
0.01627565175294876,
0.013448689132928848,
0.014957558363676071,
-0.0016897758468985558,
-0.04359424114227295,
0.018588677048683167,
-0.0010449809487909079,
0.005355125293135643,
0.003647832665592432,
0.025711407884955406,
0.036380428820848465,
-0.045369479805231094,
-0.0027403386775404215,
0.027636026963591576,
-0.03232687711715698,
0.01392334420233965,
-0.053484611213207245,
0.005749770440161228,
0.032291483134031296,
-0.008082916028797626,
0.016989903524518013,
-0.027648350223898888,
-0.045423075556755066,
-0.026772119104862213,
0.0025618397630751133,
-0.021634435281157494,
0.0005761042120866477,
0.07624870538711548,
0.009971920400857925,
0.014112584292888641,
-0.008573554456233978,
0.03476506471633911,
-0.04811305180191994,
-0.019166119396686554,
0.04880532622337341,
-0.006309282034635544,
0.01606430485844612,
0.00834562536329031,
-0.01943664252758026,
0.048346441239118576,
-0.005473428871482611,
-0.023888960480690002,
0.010658802464604378,
0.016758350655436516,
0.08721714466810226,
-0.031194506213068962,
0.036769669502973557,
0.0012320787645876408,
-0.02969307079911232,
-0.035010263323783875,
0.039762336760759354,
0.0004581653920467943,
-0.03802408277988434,
-0.008961987681686878,
-0.005765498150140047,
-0.019540004432201385,
0.02930304780602455,
0.03845509514212608,
-0.017542783170938492,
-0.009306919761002064,
0.025944789871573448,
0.014862535521388054,
-0.03968384116888046,
-0.011574730277061462,
0.0003340212278999388,
-0.046228036284446716,
0.0390290804207325,
-0.02797379158437252,
-0.07466314733028412,
0.02759408950805664,
0.01182859018445015,
-0.012343480251729488,
0.04156745970249176,
-0.033386100083589554,
-0.04804343730211258,
-0.04876885935664177
] |
<p>Energy can be built from Lagrangian when considering the symmetry of time $(\frac{\partial L}{\partial t}=0)$. <a href="http://en.wikipedia.org/wiki/Free_energy" rel="nofollow">Free energy</a> is a generalization of energy when the system exchanges heat with the environment. I can't find any sources that building free energy directly from Lagrangian. Is there any way to do that? If it is, what symmetry is it based on?</p> | g7812 | [
0.060609690845012665,
0.020259998738765717,
-0.011636546812951565,
-0.07718195766210556,
-0.03114965930581093,
-0.0214591883122921,
0.0287749245762825,
0.045135557651519775,
-0.08166778832674026,
-0.020375505089759827,
0.0066022975370287895,
0.005251185968518257,
0.05178338289260864,
-0.010198303498327732,
-0.03636892884969711,
0.025964710861444473,
0.03907463327050209,
0.005108856596052647,
0.013100193813443184,
0.052262574434280396,
-0.007220327388495207,
-0.0531904511153698,
0.013347115367650986,
-0.015171765349805355,
0.021962596103549004,
-0.012178785167634487,
0.01573939062654972,
-0.028813274577260017,
-0.041867874562740326,
-0.05874265730381012,
-0.025124914944171906,
0.03152148798108101,
0.040540505200624466,
0.026055393740534782,
-0.06749699264764786,
-0.008244449272751808,
0.007095035631209612,
0.012105841189622879,
0.050916075706481934,
0.02355329506099224,
-0.017144184559583664,
0.01185090746730566,
0.010129626840353012,
0.02957029454410076,
0.022431490942835808,
0.033462103456258774,
-0.02435217797756195,
-0.00018359329260420054,
-0.051969435065984726,
0.01397167332470417,
0.06911559402942657,
0.053366679698228836,
0.0053110988810658455,
-0.07249989360570908,
-0.050845395773649216,
-0.011691628955304623,
0.032139282673597336,
-0.020697155967354774,
0.06659586727619171,
0.020535174757242203,
-0.024618063122034073,
0.011531607247889042,
-0.028428498655557632,
0.03186430782079697,
0.03452903777360916,
-0.003332017455250025,
-0.029240682721138,
-0.012457553297281265,
0.021776309236884117,
0.014730243012309074,
0.036123450845479965,
0.0022244767751544714,
0.00531542906537652,
-0.029862305149435997,
0.003282165387645364,
0.008780903182923794,
-0.0072571211494505405,
0.005677857436239719,
0.011730418540537357,
-0.05833222344517708,
-0.008159623481333256,
0.004885533824563026,
-0.054911497980356216,
0.032381538301706314,
0.09251140058040619,
-0.03710643947124481,
-0.007040491793304682,
0.03367157280445099,
-0.012825720012187958,
0.007845347747206688,
0.02161446027457714,
0.0024166416842490435,
0.0977168083190918,
-0.02574463188648224,
0.024229638278484344,
0.01095400657504797,
-0.013455063104629517,
0.019541408866643906,
-0.037200700491666794,
-0.051186688244342804,
-0.03295141085982323,
-0.004150055814534426,
0.04866646230220795,
-0.02093593217432499,
0.03755232319235802,
-0.033037152141332626,
-0.020376106724143028,
-0.03325130045413971,
-0.018762610852718353,
-0.019769344478845596,
0.07605006545782089,
0.020090162754058838,
0.015158667229115963,
0.004921219777315855,
-0.052461978048086166,
0.00903647392988205,
0.07305949181318283,
-0.07528898864984512,
-0.0012146122753620148,
0.06691999733448029,
0.05196189880371094,
0.019943540915846825,
-0.036514073610305786,
0.027090292423963547,
-0.020675892010331154,
0.05274663120508194,
-0.042199525982141495,
-0.06429532915353775,
-0.012409349903464317,
-0.017267141491174698,
0.03301728144288063,
-0.03049127757549286,
-0.0324932262301445,
0.023990213871002197,
0.025527119636535645,
0.05869583785533905,
-0.029976196587085724,
0.07505162805318832,
0.03258012980222702,
-0.01901189610362053,
-0.022670555859804153,
-0.06295637786388397,
-0.011845587752759457,
0.005770174786448479,
0.03887908533215523,
0.03141394630074501,
-0.04169541969895363,
-0.02847949042916298,
0.03818576782941818,
0.06442231684923172,
-0.03162162005901337,
0.07869534939527512,
0.029832083731889725,
-0.03247489780187607,
0.05742589384317398,
0.007491072174161673,
-0.027558382600545883,
-0.042048268020153046,
0.0184439979493618,
-0.054961394518613815,
0.035366207361221313,
-0.018204160034656525,
0.1212240606546402,
-0.059240225702524185,
-0.018737638369202614,
0.005062302574515343,
0.018153030425310135,
-0.014234776608645916,
-0.02017335034906864,
-0.05045761540532112,
-0.06578419357538223,
0.025535978376865387,
-0.03449266403913498,
0.03625763952732086,
0.0016712496289983392,
0.0172974094748497,
-0.051286205649375916,
-0.0048616728745400906,
0.025482820346951485,
0.011720185168087482,
-0.04711262136697769,
-0.053365107625722885,
0.012908447533845901,
-0.009741160087287426,
0.005053579341620207,
-0.002422848716378212,
0.023875035345554352,
0.03806624189019203,
-0.016026511788368225,
0.03887326270341873,
0.025789586827158928,
0.057862598448991776,
-0.004277716390788555,
0.07183343917131424,
-0.0060042086988687515,
0.012148834764957428,
-0.005788858514279127,
-0.057693466544151306,
-0.015472780913114548,
0.00035002428921870887,
0.02266923524439335,
0.028795024380087852,
0.010339939035475254,
0.036816101521253586,
0.03858814015984535,
0.022384893149137497,
-0.01823718473315239,
-0.0447189062833786,
-0.00381678924895823,
-0.01632869429886341,
0.01080305315554142,
-0.0070718745701014996,
-0.017444323748350143,
-0.02178972028195858,
0.04101383686065674,
-0.030916232615709305,
-0.04074300453066826,
0.016938189044594765,
-0.014624684117734432,
0.007652783300727606,
-0.021253222599625587,
0.05394524335861206,
0.020699406042695045,
-0.016250798478722572,
-0.004179072566330433,
0.039203353226184845,
0.004644402768462896,
-0.023262277245521545,
-0.07071826606988907,
0.00877405982464552,
-0.03920372202992439,
0.02252550795674324,
-0.02959156408905983,
-0.009106927551329136,
0.08569298684597015,
0.014421750791370869,
0.012982378713786602,
0.0200079046189785,
0.01056644506752491,
0.031043600291013718,
0.02927223965525627,
-0.007798598613590002,
-0.025663187727332115,
0.035406485199928284,
0.05488339439034462,
-0.03354225680232048,
0.07053223997354507,
0.04034290462732315,
-0.010922642424702644,
-0.0501992292702198,
0.0036727404221892357,
0.017870239913463593,
-0.06103910878300667,
-0.024494756013154984,
-0.026316387578845024,
-0.05448942258954048,
0.01939544826745987,
0.006403081119060516,
-0.027381714433431625,
-0.07024795562028885,
0.054625701159238815,
-0.020775262266397476,
0.0032463178504258394,
0.02029351145029068,
-0.024002453312277794,
0.020085731521248817,
0.011350126005709171,
-0.08138121664524078,
-0.013060405850410461,
0.028710391372442245,
0.007017843890935183,
0.06531599164009094,
0.0970408245921135,
0.04397911578416824,
-0.04577695578336716,
0.012122024782001972,
0.03732217848300934,
-0.0024988281074911356,
0.03986551985144615,
-0.06290560215711594,
0.01969950646162033,
-0.041978947818279266,
0.022043930366635323,
0.06508835405111313,
0.062062736600637436,
-0.0812804102897644,
0.012732765637338161,
-0.027458008378744125,
-0.02418854646384716,
0.002205674536526203,
0.01062325295060873,
-0.030703533440828323,
-0.021132532507181168,
0.006761699914932251,
-0.06868766248226166,
-0.0056200395338237286,
0.006395456846803427,
-0.03457298129796982,
-0.014141079038381577,
0.04045829176902771,
-0.044862136244773865,
-0.057643890380859375,
-0.011361210606992245,
0.019403288140892982,
-0.014341965317726135,
-0.024270202964544296,
-0.040565989911556244,
-0.032104283571243286,
0.023393429815769196,
-0.01452616136521101,
-0.025665413588285446,
0.003509006928652525,
-0.0018117657164111733,
0.034876421093940735,
-0.025475025177001953,
0.02312125824391842,
-0.051323093473911285,
-0.04936738684773445,
0.04403723031282425,
-0.0756622925400734,
-0.05278376489877701,
-0.028821012005209923,
0.021582363173365593,
0.012675120495259762,
-0.0068736751563847065,
-0.0239491555839777,
0.03239723667502403,
-0.044970229268074036,
-0.017738834023475647,
-0.01039230078458786,
0.014658124186098576,
-0.010708102025091648,
0.04239492490887642,
0.0015948773361742496,
-0.04873014986515045,
-0.04218260198831558,
-0.050472475588321686,
-0.03917664662003517,
0.013905591331422329,
-0.0022293943911790848,
-0.07749354839324951,
0.02054183930158615,
-0.06260688602924347,
0.04883556067943573,
-0.0058192783035337925,
-0.03166576847434044,
-0.049937888979911804,
0.011602860875427723,
0.003188884584233165,
-0.020480679348111153,
0.0034074350260198116,
-0.0153513727709651,
-0.028127389028668404,
0.02831195294857025,
0.016631755977869034,
0.014847352169454098,
0.018681401386857033,
0.010609173215925694,
-0.008881489746272564,
0.05064278095960617,
-0.008343605324625969,
-0.02363993041217327,
0.0762200877070427,
-0.004424183163791895,
-0.004879962187260389,
0.028034860268235207,
-0.02907663956284523,
-0.03085048496723175,
0.015283104032278061,
-0.015420235693454742,
0.05668466538190842,
-0.041845664381980896,
0.004796007182449102,
0.02472520060837269,
0.01782471314072609,
0.03342635557055473,
0.0532200001180172,
0.00787371676415205,
-0.04862546548247337,
0.0038669148925691843,
0.006502176634967327,
-0.048981569707393646,
0.026028994470834732,
0.01103817019611597,
0.057378824800252914,
0.012850794941186905,
-0.08686777949333191,
0.05337180569767952,
-0.041372280567884445,
-0.001682164380326867,
0.039114005863666534,
-0.04040500521659851,
-0.01271857414394617,
0.004719676915556192,
-0.02257223054766655,
0.02883237414062023,
0.03717770054936409,
0.029516270384192467,
-0.00009025834151543677,
0.03672131523489952,
0.02644355781376362,
0.007999378256499767,
0.030547570437192917,
-0.025783611461520195,
0.03894578665494919,
0.03963809460401535,
0.05500481277704239,
-0.02560269460082054,
-0.05562250316143036,
-0.07420852035284042,
-0.005489686969667673,
-0.03570753335952759,
0.05838008224964142,
-0.02031312696635723,
-0.001389630720950663,
-0.06450801342725754,
-0.0005720807239413261,
-0.09129681438207626,
0.04432619363069534,
-0.00982616562396288,
-0.0376422144472599,
-0.06129413843154907,
0.049470506608486176,
0.0038980788085609674,
-0.022622056305408478,
0.09910884499549866,
0.08986536413431168,
-0.04214625805616379,
-0.07394246757030487,
-0.0509086512029171,
0.006215804722160101,
-0.009241905994713306,
-0.01686210371553898,
-0.037963494658470154,
-0.0730069950222969,
-0.01923258975148201,
-0.059708237648010254,
0.04778333380818367,
-0.016901636496186256,
0.07293076813220978,
0.05144843831658363,
0.023909572511911392,
0.04635295271873474,
0.00280008721165359,
0.0013358111027628183,
0.041216641664505005,
-0.0033799640368670225,
-0.07447101175785065,
-0.03589862212538719,
-0.007251498755067587,
0.03908811882138252,
0.024231648072600365,
-0.009359166957437992,
0.026259740814566612,
-0.02680983394384384,
0.005218733102083206,
-0.04509110748767853,
0.012587632052600384,
0.055011216551065445,
0.060680706053972244,
-0.03098016232252121,
-0.0790076032280922,
0.01918373629450798,
-0.03947944939136505,
0.06598725914955139,
-0.011548777110874653,
-0.012671303935348988,
0.012530316598713398,
-0.01451181061565876,
-0.030986789613962173,
0.04244418814778328,
0.02855362370610237,
-0.01517281774431467,
-0.014200092293322086,
0.013622636906802654,
0.003529480891302228,
0.009281138889491558,
-0.03293876349925995,
-0.0017380829667672515,
-0.007059169467538595,
0.0010259925620630383,
-0.013362037017941475,
-0.010158305056393147,
-0.04547937214374542,
0.008236432448029518,
0.04264690354466438,
-0.03264911100268364,
0.016355063766241074,
-0.002245081588625908,
-0.043475668877363205,
-0.01792457513511181,
0.0331273190677166,
0.0001411679550074041,
0.01750960201025009,
0.04169686138629913,
0.06489700824022293,
0.0031136739999055862,
-0.021833866834640503,
0.000026980578695656732,
0.00741971330717206,
-0.048631828278303146,
0.040786564350128174,
0.0033499032724648714,
-0.0021858932450413704,
0.05286761745810509,
0.042198874056339264,
0.08219893276691437,
-0.0043626572005450726,
-0.0541558675467968,
0.012674855999648571,
0.016925401985645294,
-0.03785614296793938,
-0.051988132297992706,
0.029553113505244255,
0.02555367909371853,
-0.04396004229784012,
0.0008894238853827119,
0.0057282354682683945,
-0.03843967989087105,
-0.029450953006744385,
0.020292866975069046,
0.028325006365776062,
0.03152981027960777,
-0.04033239930868149,
-0.0008732892456464469,
0.01123733539134264,
-0.08049304038286209,
-0.04737046733498573,
0.006155902519822121,
0.014382120221853256,
-0.006031307391822338,
0.036864057183265686,
0.02610158361494541,
-0.034093186259269714,
-0.009652209468185902,
-0.005614470690488815,
-0.07791474461555481,
-0.007272731047123671,
0.027894720435142517,
0.011656892485916615,
0.0578932948410511,
-0.09211774915456772,
0.030468162149190903,
-0.012330498546361923,
-0.023855745792388916,
0.007600805722177029,
-0.0553351491689682,
0.04208245128393173,
-0.011331986635923386,
-0.001501463120803237,
-0.01891864649951458,
0.024973006919026375,
0.033068954944610596,
-0.021919943392276764,
0.018331298604607582,
0.003398074069991708,
0.0039551169611513615,
-0.0169711634516716,
-0.08729108422994614,
0.001885338220745325,
0.03391365334391594,
0.03377006575465202,
0.0638178214430809,
-0.0002568961645010859,
-0.00792305450886488,
0.005767509341239929,
-0.008507023565471172,
-0.037830378860235214,
-0.02325502224266529,
0.05598961189389229,
0.04304362088441849,
0.016688110306859016,
-0.0142264598980546,
-0.015581010840833187,
0.04863667115569115,
-0.04719053581357002,
-0.006113394629210234,
-0.09452592581510544,
-0.02819313108921051,
-0.010705030523240566,
-0.056031614542007446,
-0.01622428186237812,
0.01472593192011118,
-0.015289267525076866,
-0.020870286971330643,
0.004043026361614466,
0.031723953783512115,
-0.012663448229432106,
-0.03417717292904854,
0.006601786240935326,
0.005719626322388649,
-0.044054046273231506,
-0.03374064341187477,
0.038421981036663055,
0.053037866950035095,
0.04124846309423447,
-0.05515988543629646,
-0.019803175702691078,
-0.000986583880148828,
0.04916905239224434,
0.00629398925229907,
-0.01143665798008442,
-0.0026898158248513937,
-0.049742523580789566,
-0.006712176371365786,
0.028157221153378487,
-0.02881886065006256,
0.0735231563448906,
-0.010535847395658493,
-0.014677726663649082,
0.015345553867518902,
-0.03352676331996918,
0.0028085126541554928,
-0.0051966262981295586,
-0.0008466584840789437,
-0.019970545545220375,
-0.009058082476258278,
0.011227556504309177,
0.029347028583288193,
0.02624458260834217,
0.044091735035181046,
-0.03923159837722778,
-0.04219149798154831,
-0.03297852724790573,
0.03168321028351784,
0.054065778851509094,
-0.05867438390851021,
0.031673409044742584,
0.05002507194876671,
-0.010902641341090202,
0.03254684433341026,
0.009111208841204643,
-0.03609113022685051,
0.04529258608818054,
-0.030743272975087166,
0.010790095664560795,
-0.047348372638225555,
0.02485043928027153,
0.08870640397071838,
0.040345363318920135,
-0.02207748219370842,
0.03814014792442322,
0.05176698789000511,
0.024201851338148117,
-0.03279236704111099,
0.04808508977293968,
-0.009213767945766449,
0.0013918861513957381,
-0.03539150208234787,
0.001204205909743905,
-0.023966088891029358,
-0.02766585536301136,
-0.011925938539206982,
-0.003040577983483672,
-0.03556092828512192,
-0.007035182323306799,
-0.00894356332719326,
-0.03499908000230789,
0.009896744042634964,
-0.0066642300225794315,
-0.02209041453897953,
0.016020458191633224,
0.04934455454349518,
-0.0385938361287117,
0.038224056363105774,
0.05752208083868027,
-0.004467749502509832,
-0.014104828238487244,
0.06770726293325424,
0.004466842859983444,
-0.05088001489639282,
-0.05886275693774223,
-0.04495421051979065,
0.028359629213809967,
-0.028219575062394142,
-0.006960722152143717,
0.014699499122798443,
0.08828721195459366,
-0.010021957568824291,
0.01021773274987936,
0.018330371007323265,
0.019393587484955788,
-0.037901949137449265,
0.020419228821992874,
-0.014277367852628231,
0.00821939017623663,
0.019421901553869247,
0.028843287378549576,
0.00627484917640686,
0.019120197743177414,
-0.05887888744473457,
0.06734536588191986,
0.015310575254261494,
-0.01947617344558239,
-0.04468322917819023,
-0.008719394914805889,
0.08483089506626129,
-0.0004400547477416694,
-0.005255460739135742,
-0.002469433704391122,
-0.02565666474401951,
-0.03732231259346008,
0.0019272086210548878,
-0.014433811418712139,
-0.02794395200908184,
-0.00572559330612421,
-0.0097348066046834,
-0.020627202466130257,
-0.07091158628463745,
0.005872349254786968,
-0.05592677742242813,
0.04262957349419594,
0.0032351186964660883,
0.024492615833878517,
0.0350269079208374,
0.031336892396211624,
-0.048461273312568665,
0.05572989955544472,
0.022028857842087746,
-0.00845376867800951,
0.004727947060018778,
-0.07201559096574783,
-0.01848318614065647,
-0.057856421917676926,
0.030964946374297142,
0.019147232174873352,
0.02603931911289692,
-0.04515077546238899,
-0.00196830159984529,
0.0006048187497071922,
0.0070637366734445095,
-0.006650252267718315,
0.02123800292611122,
0.015424830839037895,
0.03773839771747589,
-0.02058367431163788,
0.00013342464808374643,
-0.05582354590296745,
0.05287797003984451,
0.055120356380939484,
0.017834920436143875,
-0.01867242343723774,
-0.0019611441530287266,
-0.04089168831706047,
0.0048909904435276985,
0.007196228951215744,
-0.02108178101480007,
0.03829487785696983,
0.05200169235467911,
-0.00300988694652915,
0.019537754356861115,
0.05905820429325104,
0.010154816322028637,
-0.03249984234571457,
0.021951725706458092,
-0.01943179778754711,
0.005414264742285013,
-0.019024794921278954,
0.002687629545107484,
0.044969309121370316,
-0.0003353524662088603,
0.01539431232959032,
0.02487676963210106,
0.018478484824299812,
-0.05115503817796707,
-0.039173923432826996,
0.0284469872713089,
0.016356777399778366
] |
<p>In Synchrotrons I think they use microwaves to accelerate the electrons bundles that fly through-how does putting a microwave through a cavity accelerate an electron? I know that the Electric and Magnetic fields could and do have an effect on the electron, but if the radiation is moving parallel to the electron, wouldn't the force be perpendicular? Also, how exactly does the microwave radiation look in the vacuum chamber? Are the two ends constant nodes? </p> | g439 | [
0.025197133421897888,
0.04783141613006592,
0.016706055030226707,
-0.015340333804488182,
0.056201621890068054,
0.025469204410910606,
-0.02951226383447647,
0.02925756387412548,
-0.035161856561899185,
-0.01149258203804493,
0.033570218831300735,
0.05323446914553642,
0.015560761094093323,
0.036699894815683365,
-0.03173753619194031,
-0.003940201364457607,
0.018048418685793877,
0.024028737097978592,
-0.009790908545255661,
0.010089571587741375,
-0.006306974217295647,
0.02102738432586193,
-0.044069480150938034,
-0.022800279781222343,
-0.029078243300318718,
0.02382737584412098,
0.05283466354012489,
-0.02898372896015644,
0.008703491650521755,
-0.06295697391033173,
0.06962016224861145,
-0.05908552184700966,
0.02095402404665947,
-0.03052666038274765,
-0.00859739724546671,
-0.028635624796152115,
-0.0000926829525269568,
0.04588916897773743,
-0.028943853452801704,
0.025190770626068115,
0.01868823729455471,
-0.07653763890266418,
0.021976735442876816,
0.0038332026451826096,
0.009073328226804733,
0.018196724355220795,
-0.021804828196763992,
-0.009379654191434383,
0.011081816628575325,
-0.005491531919687986,
-0.018773989751935005,
-0.020385976880788803,
0.03013477474451065,
-0.0037221130914986134,
0.010333416052162647,
-0.017029114067554474,
0.02610236033797264,
0.00045458655222319067,
0.13425207138061523,
0.011759733781218529,
-0.010028769262135029,
0.04571262374520302,
0.03543764352798462,
0.00921943224966526,
0.113500215113163,
0.015025131404399872,
-0.03282685577869415,
0.00019245118892285973,
-0.01851535215973854,
0.011057890951633453,
0.0005051297484897077,
-0.031342726200819016,
-0.043209757655858994,
-0.016837649047374725,
0.0023624214809387922,
-0.025412265211343765,
0.027358321473002434,
-0.002306452952325344,
-0.0026030077133327723,
-0.0000883555258042179,
-0.023367613554000854,
-0.028769776225090027,
-0.02100513130426407,
-0.014324469491839409,
0.011784491129219532,
-0.018294671550393105,
0.00026526834699325264,
-0.015560260973870754,
0.04751122370362282,
-0.03212631493806839,
0.007565411273390055,
-0.017888838425278664,
0.024054691195487976,
0.0699508860707283,
-0.021184423938393593,
-0.0448472686111927,
-0.03877032548189163,
0.08847517520189285,
0.017219914123415947,
-0.023406982421875,
0.01572224870324135,
-0.026642555370926857,
0.05742668733000755,
0.014447790570557117,
-0.0007853195420466363,
-0.0435645766556263,
0.017201710492372513,
0.0098644457757473,
0.08880625665187836,
0.013839169405400753,
-0.06431152671575546,
-0.07311026751995087,
-0.018836092203855515,
-0.02555186115205288,
-0.03595990687608719,
-0.025352438911795616,
0.029983719810843468,
0.020244531333446503,
0.04875858873128891,
0.06928754597902298,
0.04151209443807602,
0.03904126212000847,
-0.04962882027029991,
-0.047308120876550674,
-0.02150273136794567,
-0.00992962159216404,
0.038503360003232956,
-0.012451850809156895,
-0.02368951216340065,
-0.013236447237432003,
0.02412509173154831,
-0.017617635428905487,
0.0022358319256454706,
0.04305727407336235,
0.03219430148601532,
-0.014954933896660805,
0.0015063663013279438,
-0.03853818401694298,
0.017615076154470444,
-0.039278388023376465,
-0.020789142698049545,
-0.07274992018938065,
-0.005559490993618965,
-0.03770402446389198,
-0.021249456331133842,
0.003933826927095652,
-0.03370426222681999,
0.03029421530663967,
0.05658387392759323,
0.022055890411138535,
0.022941816598176956,
0.08569396287202835,
0.03501279279589653,
-0.042269203811883926,
0.02838020771741867,
0.004231846891343594,
0.05138952657580376,
-0.019310064613819122,
0.06784335523843765,
0.03486861288547516,
0.022075098007917404,
0.014118693768978119,
0.021509574726223946,
-0.0319373719394207,
-0.044444918632507324,
-0.003822288941591978,
0.005601615644991398,
-0.041294366121292114,
0.06353346258401871,
0.049701590090990067,
-0.0010722845327109098,
0.028987431898713112,
0.01632136106491089,
0.026475025340914726,
-0.021801911294460297,
0.03834298998117447,
0.005465061869472265,
-0.02813381887972355,
0.031916696578264236,
-0.024122051894664764,
-0.0038081530947238207,
-0.034297406673431396,
0.03880680352449417,
0.010343455709517002,
0.0216763187199831,
-0.02588447742164135,
-0.03226158395409584,
0.05304452404379845,
-0.0704418495297432,
0.020076120272278786,
0.02790576033294201,
0.013657431118190289,
0.04858873412013054,
0.05701068043708801,
-0.03416626900434494,
-0.044394589960575104,
-0.028936492279171944,
-0.0331261083483696,
0.046804480254650116,
-0.02517457865178585,
-0.05912768095731735,
0.05967612564563751,
0.08387140929698944,
0.04229455813765526,
0.05489033833146095,
-0.031150948256254196,
-0.04174669831991196,
-0.03337123245000839,
0.05069064721465111,
0.0007467424147762358,
0.02337096445262432,
0.04521705582737923,
0.011525818146765232,
0.0042207748629152775,
-0.02003500610589981,
0.015926972031593323,
-0.06719140708446503,
-0.04730555787682533,
-0.01493225246667862,
0.00013463936920743436,
-0.04050947725772858,
-0.07761412113904953,
0.02940301038324833,
-0.06011461466550827,
-0.039284687489271164,
-0.06855839490890503,
-0.01978123188018799,
-0.05417325347661972,
0.017076293006539345,
0.05525234341621399,
-0.10212154686450958,
0.008888619020581245,
-0.020453790202736855,
-0.04266165569424629,
0.06034146249294281,
-0.025670072063803673,
-0.013258482329547405,
0.05287330970168114,
-0.01549474522471428,
-0.010028216056525707,
0.03380909934639931,
0.0016298505943268538,
0.014513116329908371,
-0.019326142966747284,
0.0013878567842766643,
-0.06148940324783325,
0.07244833558797836,
-0.021416619420051575,
-0.01872440055012703,
-0.03590070828795433,
0.014593890868127346,
-0.05981406196951866,
-0.018043212592601776,
0.05230145901441574,
-0.03396053984761238,
-0.048539821058511734,
-0.05253441631793976,
0.0024760474916547537,
-0.00901398342102766,
-0.02542414702475071,
0.0012980990577489138,
0.0265975221991539,
0.038578733801841736,
0.0336495116353035,
-0.059868521988391876,
0.0013428976526483893,
-0.00477764755487442,
0.04864336550235748,
-0.005739359650760889,
0.006889766547828913,
-0.09268160909414291,
0.04267251864075661,
-0.006359877064824104,
-0.032470740377902985,
0.0009701387607492507,
-0.028105461969971657,
0.05988921597599983,
0.019453328102827072,
0.019592035561800003,
-0.05083869770169258,
-0.04776134341955185,
-0.0033202730119228363,
0.037047918885946274,
0.0022586542181670666,
-0.0210457444190979,
-0.07018639892339706,
-0.03546634316444397,
-0.06584241986274719,
0.0072023626416921616,
0.013517669402062893,
-0.0664067342877388,
-0.01968061923980713,
0.10212961584329605,
0.017071139067411423,
-0.007071787025779486,
0.0028982246294617653,
0.07460217922925949,
-0.035767052322626114,
-0.018818262964487076,
0.01587359420955181,
-0.014092734083533287,
-0.03374340757727623,
-0.038171011954545975,
0.010723852552473545,
-0.005438878666609526,
0.010166704654693604,
-0.06698083132505417,
-0.0206235833466053,
-0.009831958450376987,
0.0370965451002121,
-0.02361335977911949,
0.032033346593379974,
0.003283216618001461,
-0.008202211000025272,
-0.03277263045310974,
-0.044996678829193115,
-0.039351075887680054,
0.00969024933874607,
0.053111087530851364,
0.041743744164705276,
-0.030484026297926903,
-0.019178377464413643,
-0.021356461569666862,
-0.07639257609844208,
0.02735317125916481,
0.07322718948125839,
0.036459729075431824,
-0.03716481104493141,
-0.04496966302394867,
-0.002867907751351595,
0.04424971342086792,
-0.023193592205643654,
-0.06275559961795807,
0.004056139849126339,
0.0006893852259963751,
0.01948733441531658,
-0.056099552661180496,
0.024410169571638107,
-0.019894741475582123,
0.023064063861966133,
0.07104703783988953,
-0.05196058750152588,
-0.03763232007622719,
0.039344169199466705,
0.04844307154417038,
0.06931852549314499,
0.023173894733190536,
-0.04502692446112633,
0.09496257454156876,
-0.06380227953195572,
0.0187494158744812,
-0.014828844927251339,
-0.0028029861859977245,
0.005977537017315626,
-0.01355286967009306,
0.01943061128258705,
0.04128255322575569,
-0.04702330380678177,
0.01865987293422222,
-0.02701706625521183,
0.03758753091096878,
-0.01499585248529911,
0.014785542152822018,
0.0012642097426578403,
-0.04201097413897514,
-0.060376569628715515,
0.0023064494598656893,
0.07057628780603409,
0.05970620736479759,
-0.03593343868851662,
-0.03567380830645561,
0.01451047882437706,
0.02201416902244091,
0.06520013511180878,
0.043923988938331604,
-0.01157020591199398,
-0.0000032038653898780467,
-0.0020873313769698143,
-0.024111978709697723,
-0.004166848957538605,
-0.006671155337244272,
-0.003962387330830097,
-0.0004480610368773341,
0.013259649276733398,
0.03501171991229057,
0.021879475563764572,
-0.027140967547893524,
0.025992222130298615,
-0.028552725911140442,
-0.031359292566776276,
0.029145890846848488,
0.00705762067809701,
-0.0317954458296299,
0.01009812206029892,
-0.05461746081709862,
-0.03239673748612404,
0.0572015643119812,
-0.046395476907491684,
-0.009539666585624218,
0.006327125243842602,
0.03724462538957596,
0.05134515464305878,
-0.01682978868484497,
-0.03732745721936226,
-0.003314554924145341,
0.0495959147810936,
0.011046458035707474,
-0.004555307794362307,
-0.020131900906562805,
-0.024650223553180695,
-0.016002107411623,
0.022251954302191734,
-0.0010018686298280954,
-0.010111093521118164,
0.0007527404231950641,
-0.028454231098294258,
0.010503757745027542,
0.029283244162797928,
0.008163525722920895,
-0.006319526117295027,
-0.00014802040823269635,
0.015772754326462746,
0.012895791791379452,
-0.04545457288622856,
-0.005135647486895323,
0.10551594197750092,
0.04100378230214119,
0.0013679696712642908,
-0.004508504644036293,
-0.028756538406014442,
0.02848518267273903,
0.02661764621734619,
0.027838189154863358,
0.017057744786143303,
0.0028014464769512415,
0.03289397433400154,
-0.01824924163520336,
-0.04121387377381325,
0.020370829850435257,
0.054930876940488815,
0.03542861342430115,
-0.03767503425478935,
0.027214838191866875,
-0.05279005691409111,
-0.03662974387407303,
0.0634482279419899,
-0.04285351186990738,
-0.05025818198919296,
0.033487118780612946,
-0.010351680219173431,
-0.047604575753211975,
0.03476053103804588,
-0.020680507645010948,
-0.05399164929986,
0.02242073230445385,
-0.011951531283557415,
-0.026635127142071724,
-0.008006025105714798,
0.08861721307039261,
0.003786408109590411,
-0.04957904666662216,
-0.027139563113451004,
-0.0057846661657094955,
-0.017234740778803825,
0.014354410581290722,
0.0166061669588089,
0.01098870299756527,
-0.035779085010290146,
-0.04499570652842522,
0.02211950160562992,
0.02509411796927452,
-0.011494796723127365,
-0.009130772203207016,
-0.015417279675602913,
0.02548394352197647,
0.009282736107707024,
-0.014563611708581448,
-0.018779389560222626,
-0.051839303225278854,
0.020171837881207466,
-0.011946460232138634,
-0.030949419364333153,
0.05536569282412529,
-0.041787248104810715,
-0.07067113369703293,
-0.038261011242866516,
-0.03691038116812706,
0.04818120226264,
-0.02406938187777996,
0.019944313913583755,
-0.022566288709640503,
0.005994959734380245,
-0.04095029458403587,
-0.021275155246257782,
-0.004792848601937294,
0.03819777071475983,
0.016213392838835716,
0.014712573029100895,
0.03836346045136452,
0.023691682144999504,
0.019608180969953537,
-0.04628949612379074,
-0.03144680708646774,
-0.028735322877764702,
-0.030970415100455284,
0.0645657479763031,
0.04163682088255882,
-0.02674386464059353,
0.0007534856558777392,
-0.00896143913269043,
0.017906000837683678,
-0.0028156174812465906,
-0.004521452356129885,
0.0216474998742342,
0.03136188164353371,
-0.007711525075137615,
-0.013924899511039257,
0.009478730149567127,
0.00035832307185046375,
0.006446285173296928,
0.023652181029319763,
0.06849531829357147,
0.04508945718407631,
0.008295968174934387,
0.01875784993171692,
-0.00384483952075243,
-0.007321024313569069,
0.07241708040237427,
0.04839182645082474,
0.05199085921049118,
-0.009533124975860119,
0.0007540365331806242,
0.017381124198436737,
0.04442659392952919,
-0.009708700701594353,
-0.04687977209687233,
0.09382595866918564,
-0.006691760383546352,
-0.009095307439565659,
-0.036252256482839584,
-0.024763675406575203,
-0.012584621086716652,
0.02752949297428131,
0.07400607317686081,
-0.048564713448286057,
-0.015082426369190216,
0.01218982134014368,
-0.001068413257598877,
0.0394078865647316,
0.020201507955789566,
-0.061697252094745636,
0.04111370071768761,
0.025621527805924416,
0.072468101978302,
-0.015900911763310432,
0.04364130273461342,
0.0304583627730608,
-0.004979712888598442,
-0.03025904670357704,
-0.061283230781555176,
0.07577872276306152,
0.020616237074136734,
0.020758531987667084,
-0.07519450038671494,
0.04343684762716293,
0.02311008796095848,
0.028407374396920204,
-0.03192899003624916,
0.04982665553689003,
0.004574906080961227,
-0.005851005669683218,
-0.018613040447235107,
-0.027243534103035927,
-0.015673065558075905,
0.030366117134690285,
0.03241436183452606,
-0.0006758381496183574,
0.0313752256333828,
-0.0626959279179573,
0.021756533533334732,
0.032446254044771194,
-0.01709585450589657,
0.025938482955098152,
-0.09707104414701462,
-0.007115120533853769,
0.05049365386366844,
-0.06153888255357742,
0.06927958875894547,
0.12148058414459229,
-0.006512245628982782,
-0.07827123254537582,
-0.03757436200976372,
0.03904326260089874,
-0.00520836329087615,
-0.01968131586909294,
-0.02369547262787819,
-0.013819987885653973,
0.0339706614613533,
-0.016499347984790802,
0.07448509335517883,
-0.00018974866543430835,
-0.015328606590628624,
-0.061074767261743546,
0.04478013142943382,
-0.03188096359372139,
-0.051843687891960144,
0.0038321970496326685,
-0.002573467092588544,
-0.007756861858069897,
0.002199026523157954,
-0.012522435747087002,
-0.010193316265940666,
-0.0316038578748703,
0.020930539816617966,
0.06822393089532852,
0.00012328982120379806,
-0.010048636235296726,
-0.02814110554754734,
-0.00478462316095829,
0.0027034608647227287,
0.010509561747312546,
-0.06274642795324326,
-0.061202771961688995,
0.03705194219946861,
-0.023063817992806435,
-0.0371646024286747,
-0.008979236707091331,
-0.00101703149266541,
0.1092497706413269,
-0.07984739542007446,
0.012474888935685158,
-0.009523129090666771,
0.010361062362790108,
-0.013889651745557785,
-0.013102343305945396,
-0.012469361536204815,
-0.008116432465612888,
-0.016477065160870552,
-0.026549462229013443,
-0.00021572595869656652,
0.0696084126830101,
0.024653930217027664,
-0.02436262182891369,
0.0042904750443995,
-0.021761039271950722,
0.014689726755023003,
-0.006940712686628103,
0.03151595965027809,
0.0370117649435997,
0.024846525862812996,
-0.051491595804691315,
-0.04660557955503464,
-0.013050532899796963,
0.030918648466467857,
0.017881331965327263,
-0.0259165670722723,
0.02494053915143013,
-0.002985169179737568,
-0.027971642091870308,
-0.049802929162979126,
-0.032988034188747406,
0.008273125626146793,
0.04010998085141182,
-0.004198457580059767,
0.0565197579562664,
-0.051860637962818146,
-0.033008329570293427,
0.01474376954138279,
0.014874923974275589,
-0.005466624163091183,
0.005507623311132193,
0.009868988767266273,
0.005368545651435852,
0.029667725786566734,
0.007409957237541676,
-0.024796737357974052,
-0.10505165904760361,
-0.004348688758909702,
-0.035748712718486786,
-0.01671718619763851,
-0.05277903005480766,
-0.0030274461023509502,
0.035138025879859924,
0.00996172521263361,
0.018098337575793266,
0.013193086721003056,
-0.010823694989085197,
0.001815053285099566,
-0.014691224321722984,
-0.05809061601758003,
0.010012669488787651,
-0.06015811115503311,
-0.00889444537460804,
0.025182189419865608,
-0.01666475459933281,
0.008816777728497982,
-0.022953052073717117,
-0.008947350084781647,
-0.023791201412677765,
-0.01956094801425934,
-0.024646257981657982,
0.022300660610198975,
0.03993748873472214,
0.03135034069418907,
0.05094567686319351,
0.028726642951369286,
0.014366544783115387,
-0.04433269798755646,
-0.018434785306453705,
-0.025251466780900955,
-0.032498799264431,
0.05232677236199379,
0.029882708564400673,
-0.010703015141189098,
0.008449911139905453,
0.001460463972762227,
-0.0009912557434290648,
0.0377858430147171,
0.00845327228307724,
-0.05888555198907852,
0.014317955821752548,
0.030200574547052383,
0.04578421637415886,
-0.013985068537294865,
0.046621061861515045,
0.016905104741454124,
-0.003531780792400241,
0.00036497280234470963,
0.006669909227639437,
-0.017964987084269524,
0.029894959181547165,
0.033694300800561905,
-0.01897885650396347,
0.019442729651927948,
-0.01564755290746689,
-0.003542747814208269,
0.03687058016657829,
-0.002277995692566037,
0.016290003433823586,
-0.00275069335475564,
0.022824933752417564,
-0.029169373214244843,
-0.03862807899713516,
-0.031072480604052544,
-0.040431562811136246,
-0.002391406102105975,
-0.031092001125216484,
-0.0046513499692082405,
0.03597955033183098,
0.024274203926324844,
0.007533673662692308,
0.0010258262045681477,
-0.06616334617137909,
0.019658563658595085,
0.017532890662550926,
-0.06363115459680557,
0.03536480292677879,
0.011745321564376354,
0.023806821554899216,
-0.019175777211785316,
0.012421672232449055,
0.006240508984774351,
-0.010685023851692677,
-0.077765554189682,
-0.02050873637199402,
-0.0018872187938541174,
-0.04113788902759552,
-0.0533423125743866
] |
<p>We are taught that the universe began as a singularity - an infinitely small and infinitely dense point. At the beginning of time there was a 'Big Bang' or, more accurately, 'Inflation'.</p>
<p>The main evidence for this is the observation of the red shift of all of the galaxies. This shows us that as time increases, the universe becomes bigger. A logical outcome of this is that going back in time, the universe shrinks. This is then extrapolated back to the beginning of time, where the universe was infinitely small.</p>
<p>However, the only thing that I can see that we know for sure is that the universe used to be smaller. This does not necessarily imply that it used to be infinitely small. How do we know, for example, that the universe doesn't oscillate and that we are in a time where the universe is expanding (and accelerating) and will eventually contract again?</p>
<p>What other evidence is there that suggests we started from an singularity?</p> | g7813 | [
0.06935351341962814,
0.024355916306376457,
0.02907106839120388,
-0.0267120860517025,
0.0006442433223128319,
0.02578713186085224,
0.021941285580396652,
0.04449550062417984,
-0.013329391367733479,
-0.049022503197193146,
0.009734912775456905,
-0.025911172851920128,
0.040572699159383774,
0.05939410626888275,
0.020931093022227287,
-0.039191778749227524,
-0.04712098836898804,
-0.037086162716150284,
-0.019095774739980698,
-0.007483739871531725,
0.024296622723340988,
-0.0024003596045076847,
0.07315077632665634,
-0.06968457251787186,
-0.06148454174399376,
-0.0069925496354699135,
-0.028631621971726418,
0.008371604606509209,
0.049050383269786835,
-0.06800493597984314,
0.029550055041909218,
-0.05239761993288994,
0.04416646435856819,
0.0021173395216464996,
0.0728982612490654,
-0.03174543008208275,
-0.010953666642308235,
-0.01631736569106579,
0.02554495818912983,
-0.03993565961718559,
-0.018318630754947662,
-0.020971199497580528,
-0.007110991980880499,
-0.007075033616274595,
0.03073175624012947,
-0.008534669876098633,
-0.03450894355773926,
0.01787404716014862,
0.052016731351614,
-0.006915396545082331,
-0.06121130660176277,
0.004607346840202808,
0.01670856960117817,
0.030769722536206245,
0.001978823682293296,
0.02046460658311844,
0.037598319351673126,
0.004535368178039789,
0.081978939473629,
0.010657016187906265,
-0.02778361365199089,
0.0006270972080528736,
0.09317417442798615,
0.03603816032409668,
-0.0025455609429627657,
-0.016053207218647003,
0.00011687868391163647,
-0.02254551276564598,
0.0329057015478611,
0.004904847126454115,
0.012400842271745205,
-0.06532775610685349,
0.013406145386397839,
-0.011084877885878086,
-0.013083754107356071,
0.04928130283951759,
0.008031097240746021,
-0.013692393898963928,
-0.02872343361377716,
-0.06576429307460785,
-0.013333210721611977,
-0.03137786313891411,
-0.03951980173587799,
0.028129171580076218,
0.0032938732765614986,
-0.014283779077231884,
-0.058887794613838196,
-0.02025028131902218,
0.0015213857404887676,
-0.005441518500447273,
0.01868119277060032,
0.034809619188308716,
0.04723820462822914,
-0.027616344392299652,
0.06453780084848404,
-0.03717005252838135,
-0.02472563274204731,
0.07329382747411728,
-0.023183777928352356,
0.02425842545926571,
-0.06854931265115738,
-0.000801802845671773,
0.024451157078146935,
-0.045938920229673386,
0.009395222179591656,
0.0010672931093722582,
-0.0348176546394825,
-0.05474640429019928,
-0.012507009319961071,
-0.028959903866052628,
-0.007393126841634512,
-0.052926577627658844,
-0.05941535532474518,
-0.023573193699121475,
-0.030161526054143906,
-0.000059479829360498115,
0.05279027298092842,
0.027490075677633286,
0.05138939246535301,
0.005134525243192911,
-0.04188435524702072,
-0.02886146306991577,
-0.06180460378527641,
0.037498876452445984,
-0.053696271032094955,
-0.0025862252805382013,
-0.01406086515635252,
0.0064178030006587505,
-0.014079015702009201,
0.005648330319672823,
0.032640598714351654,
0.02775706723332405,
-0.05594095587730408,
0.04044331982731819,
0.0460926815867424,
0.030453352257609367,
-0.010565554723143578,
-0.0322372205555439,
0.03300917148590088,
0.083250992000103,
-0.0068576824851334095,
0.008936586789786816,
-0.002937834709882736,
0.013857941143214703,
0.0356927253305912,
0.038055289536714554,
-0.027961965650320053,
-0.015193691477179527,
-0.04572258144617081,
0.024644484743475914,
0.011500425636768341,
0.11965350806713104,
-0.020716628059744835,
-0.012206382118165493,
-0.08320163190364838,
-0.034253060817718506,
-0.0031618718057870865,
-0.03478691354393959,
0.008181738667190075,
-0.03760102391242981,
0.05156984180212021,
-0.04246342182159424,
0.022930769249796867,
0.05009659379720688,
-0.058918412774801254,
0.048052821308374405,
-0.014438936486840248,
-0.013897569850087166,
0.01024600025266409,
0.042476117610931396,
-0.04505821689963341,
-0.02413230761885643,
0.0032655915711075068,
0.019340302795171738,
0.008403245359659195,
0.02574152685701847,
0.04581616446375847,
-0.008704307489097118,
-0.007819403894245625,
-0.011556421406567097,
0.04373850300908089,
-0.040332943201065063,
0.03589553013443947,
0.005756170954555273,
0.05056941881775856,
-0.005419258028268814,
0.0024300303775817156,
0.002299426356330514,
0.008607350289821625,
-0.01601969078183174,
-0.05757789686322212,
-0.06756165623664856,
0.019593866541981697,
-0.025872575119137764,
0.02882944606244564,
-0.04105556011199951,
0.020778248086571693,
0.00004615965372067876,
-0.03353913128376007,
-0.03365505486726761,
0.02703366056084633,
0.029130399227142334,
0.027178321033716202,
0.04678092524409294,
0.01241003442555666,
-0.03816442936658859,
-0.00036850059404969215,
-0.017145264893770218,
0.021589789539575577,
0.03933877497911453,
0.023549828678369522,
-0.047829724848270416,
-0.051230888813734055,
-0.01405487209558487,
-0.008532955311238766,
0.06302113085985184,
-0.05441969633102417,
-0.02164630964398384,
0.011813593097031116,
0.03683818504214287,
-0.026773279532790184,
0.01948125846683979,
0.04975370690226555,
-0.017487907782197,
0.04739101603627205,
0.01443579699844122,
0.01368294470012188,
-0.03417661786079407,
0.0459757000207901,
0.014567242935299873,
-0.1082645058631897,
0.012373347766697407,
-0.03172609582543373,
-0.046425264328718185,
0.02876344695687294,
-0.020227253437042236,
-0.004640435799956322,
-0.0497855618596077,
-0.035501908510923386,
0.05762049928307533,
-0.018100038170814514,
-0.03938210755586624,
-0.03941342234611511,
-0.04305010661482811,
0.03112170659005642,
-0.08255014568567276,
0.040946345776319504,
-0.0944928303360939,
-0.004215720575302839,
0.004894901532679796,
0.029931416735053062,
0.007677028421312571,
0.005088398233056068,
0.006669817958027124,
-0.0027963125612586737,
-0.024765828624367714,
0.04107832536101341,
0.0819263681769371,
-0.010988287627696991,
-0.044394753873348236,
0.06520859897136688,
-0.0026307450607419014,
0.024717209860682487,
0.0532669872045517,
0.007714242674410343,
-0.017590578645467758,
-0.07232461124658585,
-0.04118075966835022,
-0.0446409210562706,
-0.01727050356566906,
0.04165823757648468,
0.029825208708643913,
-0.029748111963272095,
-0.02357705496251583,
0.03771255537867546,
0.02305837906897068,
0.003531885799020529,
0.014328421093523502,
0.060417018830776215,
-0.010104356333613396,
0.0005220002494752407,
0.0627220943570137,
-0.07946925610303879,
-0.002037680009379983,
0.014965470880270004,
0.0020025481935590506,
-0.02521132491528988,
0.0024369985330849886,
0.014395136386156082,
-0.012795363552868366,
0.013800296001136303,
0.020670287311077118,
0.04239426925778389,
0.02817714773118496,
-0.0006359564140439034,
0.012476995587348938,
-0.047310203313827515,
0.007462756708264351,
-0.001386804273352027,
-0.011000462807714939,
0.029000313952565193,
-0.03275231644511223,
-0.006506133824586868,
-0.018950222060084343,
-0.007115003187209368,
0.05641419067978859,
0.02152666263282299,
-0.02798604965209961,
-0.03462788835167885,
-0.06203306093811989,
0.02283777855336666,
0.035012003034353256,
0.010381177999079227,
0.04103221744298935,
-0.044059619307518005,
-0.014157542958855629,
0.011645874939858913,
0.05789787322282791,
0.047029297798871994,
-0.008699772879481316,
0.00104419921990484,
-0.04386969283223152,
-0.025174785405397415,
-0.007980404421687126,
0.05312718078494072,
0.02506454661488533,
-0.05201977491378784,
-0.013479482382535934,
-0.06007276847958565,
0.045671381056308746,
-0.05423588305711746,
-0.05140068009495735,
-0.07392428070306778,
-0.009997665882110596,
-0.04254923015832901,
-0.09421151876449585,
-0.025620291009545326,
0.008318931795656681,
0.024634219706058502,
0.044041261076927185,
0.003902991069480777,
0.023830531165003777,
-0.014804131351411343,
0.019694466143846512,
0.010504781268537045,
0.04490353539586067,
0.02383228950202465,
-0.007844377309083939,
0.03806629404425621,
-0.053241342306137085,
0.0410514734685421,
0.006073521450161934,
0.02770090103149414,
0.009373825043439865,
0.010099715553224087,
0.02357254922389984,
0.05340315401554108,
-0.008806549943983555,
0.06831225007772446,
-0.053917061537504196,
-0.004541483242064714,
-0.061137933284044266,
0.04301600158214569,
0.06791464239358902,
0.01381923072040081,
-0.03283381834626198,
-0.006577565800398588,
-0.0015668036649003625,
0.027440786361694336,
0.006903134286403656,
-0.01627577468752861,
0.0021765173878520727,
-0.012626618146896362,
0.026796428486704826,
0.00023528416932094842,
0.031044725328683853,
0.012499396689236164,
0.07144713401794434,
0.0333825908601284,
0.029878364875912666,
0.04815414547920227,
0.0040816026739776134,
0.037555545568466187,
-0.008655982092022896,
-0.0017324559157714248,
0.016049539670348167,
-0.01192232221364975,
-0.04891681671142578,
-0.01411560457199812,
-0.007859533652663231,
0.061763614416122437,
-0.02205163985490799,
0.015951717272400856,
-0.026382695883512497,
0.046116333454847336,
0.030051659792661667,
0.03803035989403725,
0.0039003363344818354,
0.03812026605010033,
-0.03718918561935425,
-0.01135247852653265,
-0.00443787407130003,
-0.00723479175940156,
-0.013693767599761486,
-0.0028579263016581535,
0.03561997786164284,
0.014898260124027729,
-0.02939787693321705,
0.0036594620905816555,
-0.04661838337779045,
0.016933772712945938,
0.01499710138887167,
-0.0149918207898736,
-0.06637249886989594,
-0.0017967987805604935,
-0.03988330811262131,
0.07415079325437546,
-0.061037663370370865,
0.054582882672548294,
0.03229834511876106,
0.0013148626312613487,
0.0662839487195015,
-0.01610608585178852,
-0.028366707265377045,
-0.008472638204693794,
-0.0017768841935321689,
-0.01869254745543003,
0.014516462571918964,
-0.03086267039179802,
0.03233003616333008,
-0.03229489177465439,
0.017611892893910408,
0.024615677073597908,
0.07507370412349701,
0.008892210200428963,
0.005850236862897873,
0.05061959847807884,
0.035095058381557465,
-0.04372753947973251,
-0.020450856536626816,
0.06141813471913338,
-0.057128872722387314,
-0.009223856963217258,
0.050168514251708984,
-0.01016728300601244,
0.06040908396244049,
-0.04207225516438484,
0.010171704925596714,
-0.020130591467022896,
-0.01514112576842308,
-0.04753531515598297,
0.07042186707258224,
0.004624951630830765,
0.0023401034995913506,
0.01720348186790943,
0.004071490839123726,
-0.002625460969284177,
0.04637704789638519,
-0.03379794582724571,
0.06820320338010788,
-0.046571265906095505,
-0.0038423126097768545,
-0.017613079398870468,
0.07185891270637512,
0.024230966344475746,
-0.022285962477326393,
-0.0433712936937809,
-0.03851821646094322,
0.001807793858461082,
0.03605812042951584,
-0.06455007940530777,
0.041416462510824203,
0.04052852466702461,
0.02314561977982521,
0.0011231874814257026,
-0.04727780446410179,
-0.0019834968261420727,
-0.0712161511182785,
0.02159128524363041,
-0.014148968271911144,
-0.008014504797756672,
-0.018673298880457878,
0.014657934196293354,
-0.03671511262655258,
0.01872837170958519,
0.05826938524842262,
-0.038508087396621704,
0.02345837838947773,
-0.015017648227512836,
0.0014839941868558526,
0.02469869889318943,
-0.02712792344391346,
0.0685829222202301,
0.0031883525662124157,
-0.06001550331711769,
-0.02973886765539646,
0.012865657918155193,
0.023375192657113075,
-0.046577468514442444,
-0.018542295321822166,
-0.0535854697227478,
0.09661762416362762,
-0.00582409230992198,
0.01515630166977644,
-0.008067682385444641,
-0.026005325838923454,
-0.044918108731508255,
-0.0541076734662056,
-0.006792535074055195,
0.010532225482165813,
-0.0016936883330345154,
-0.0003040389565285295,
0.03232312202453613,
-0.007760694250464439,
0.05478232726454735,
-0.034309204667806625,
-0.04566660150885582,
-0.046538401395082474,
0.04770740494132042,
-0.03217153996229172,
-0.07566970586776733,
0.001775078591890633,
0.018126629292964935,
0.016754621639847755,
0.08087971061468124,
0.03737301751971245,
0.05532637611031532,
-0.007410403806716204,
0.0705668032169342,
-0.042643141001462936,
0.08000240474939346,
0.08161807805299759,
-0.01067495159804821,
-0.039690904319286346,
-0.02123907022178173,
0.09216095507144928,
0.016878828406333923,
-0.008673821575939655,
0.02295859344303608,
-0.0726521834731102,
-0.07515694946050644,
0.036460962146520615,
-0.04912256449460983,
0.012476228177547455,
-0.029852576553821564,
0.0437091700732708,
-0.059885118156671524,
0.052447181195020676,
0.06155425310134888,
-0.014729215763509274,
-0.022985640913248062,
0.026997162029147148,
-0.011084625497460365,
0.05122422054409981,
-0.04036174714565277,
0.024003086611628532,
0.05588560551404953,
-0.0026246767956763506,
-0.031403787434101105,
-0.03435468673706055,
-0.003911486826837063,
0.032942891120910645,
-0.03895091265439987,
-0.022131381556391716,
-0.03973150998353958,
-0.053430598229169846,
0.023442579433321953,
-0.060138002038002014,
0.048543889075517654,
0.022837067022919655,
-0.01008070632815361,
0.04201596602797508,
0.08165690302848816,
-0.0068062348291277885,
-0.019861510023474693,
-0.007811118382960558,
-0.0173682551831007,
0.021907029673457146,
-0.05498727411031723,
-0.027528848499059677,
0.0024756030179560184,
0.031618472188711166,
0.07738767564296722,
0.003236361313611269,
-0.0002250269753858447,
0.03778468072414398,
-0.03868643566966057,
-0.01293969713151455,
0.008802485652267933,
0.05315973609685898,
0.05138363316655159,
0.025782467797398567,
-0.016902856528759003,
-0.06696727871894836,
-0.00661706505343318,
-0.03435643017292023,
0.034002408385276794,
-0.03824148327112198,
-0.05717219039797783,
-0.011259304359555244,
-0.038703225553035736,
0.030405722558498383,
0.031078055500984192,
-0.02239701896905899,
0.051533300429582596,
-0.0169709250330925,
0.0019699744880199432,
0.020665230229496956,
0.07934712618589401,
0.0025920113548636436,
0.010274210944771767,
0.012514863163232803,
-0.01862720586359501,
-0.004893601406365633,
0.013661368750035763,
-0.010526840575039387,
0.018092647194862366,
-0.006013024132698774,
0.0078220684081316,
-0.022359807044267654,
0.07906568795442581,
0.024177689105272293,
-0.03368305414915085,
0.029142817482352257,
0.004184139426797628,
0.03472011536359787,
-0.020123640075325966,
0.0027773946058005095,
0.0039033154025673866,
-0.026069236919283867,
-0.019112640991806984,
0.02716323547065258,
-0.02792428992688656,
0.03128891438245773,
-0.05881664529442787,
0.009588371030986309,
0.0004048590490128845,
0.031014787033200264,
-0.027509361505508423,
-0.025805607438087463,
0.020480774343013763,
-0.01852777786552906,
-0.0073906728066504,
0.009746044874191284,
-0.01465526595711708,
0.010468901135027409,
-0.004233672749251127,
0.05133071914315224,
-0.05026949569582939,
-0.020324094220995903,
0.011087595485150814,
-0.010311177000403404,
-0.04790050536394119,
-0.003315649228170514,
-0.051636792719364166,
0.009201111271977425,
-0.006011810153722763,
-0.005241536069661379,
-0.0028309104964137077,
-0.07681003212928772,
-0.0037394713144749403,
-0.0239203292876482,
0.010033555328845978,
-0.020370911806821823,
-0.03028055839240551,
0.017078576609492302,
0.036840952932834625,
-0.02516283094882965,
-0.022707732394337654,
-0.08116310834884644,
0.005337360315024853,
-0.011127998121082783,
-0.04189594089984894,
-0.03484676778316498,
0.0022695325314998627,
-0.008974424563348293,
-0.021606111899018288,
0.00904951710253954,
0.07200784236192703,
0.0637025535106659,
-0.03596298024058342,
0.015911364927887917,
0.03751571476459503,
0.041970591992139816,
0.00024777487851679325,
0.04840819910168648,
-0.03468754515051842,
-0.0005060731200501323,
-0.05505186319351196,
-0.012859649956226349,
-0.04268458113074303,
-0.04358571395277977,
-0.04995162785053253,
0.004323822446167469,
0.00976700522005558,
-0.03767262026667595,
-0.011647793464362621,
0.006298143416643143,
-0.049217648804187775,
-0.04152001440525055,
-0.041521769016981125,
0.019486896693706512,
-0.03492436558008194,
-0.004079094622284174,
0.01667596586048603,
0.009916581213474274,
-0.022265752777457237,
0.02248605154454708,
-0.0397651232779026,
0.018044695258140564,
0.004440074786543846,
-0.009425627067685127,
0.0030151340179145336,
-0.0015063652535900474,
0.023469047620892525,
-0.011023546569049358,
-0.006395370699465275,
-0.021155456081032753,
0.036764636635780334,
-0.016771214082837105,
-0.07907284796237946,
0.02708285115659237,
0.003072901628911495,
-0.0493500679731369,
0.0021189639810472727,
0.017881998792290688,
0.02337503992021084,
-0.0049559082835912704,
-0.013597470708191395,
-0.01844772882759571,
-0.0008261319599114358,
0.012814068235456944,
0.0447358675301075,
0.0025230119936168194,
-0.03324509412050247,
0.039526838809251785,
0.007670726627111435,
0.019232427701354027,
-0.06756778806447983,
-0.022696996107697487,
-0.03459755703806877,
0.017396891489624977,
0.03637399151921272,
0.01964356005191803,
-0.004019276238977909,
-0.057509325444698334,
-0.006787525024265051,
0.03918818384408951,
0.04893914610147476,
-0.08328495174646378,
0.005428850185126066,
0.008353650569915771,
0.04624016955494881,
0.029490014538168907,
-0.05260133743286133,
-0.011008069850504398,
-0.029619012027978897,
0.006667458917945623,
-0.025316936895251274,
-0.03871660307049751,
-0.012319780886173248,
0.03716665506362915,
0.03499029204249382,
0.003712416160851717,
-0.011973796412348747,
-0.026859872043132782,
0.06024203822016716,
-0.03163229301571846
] |
<p>What is the equation for the saddle-like 2d surface (embeded in 3d Euclidean space with cartesian coordinates x, y and z) with constant negative curvature frequently used to illustrate open universe (for example in the following image is taken from Wikipedia)?</p>
<p><img src="http://i.stack.imgur.com/WNUNI.jpg" alt="enter image description here"></p>
<p>Flat universe (zero curvature) is illustrated by a plane, with equation say</p>
<p>$z = 0$</p>
<p>Closed universe (constant positive curvature) is illustrated by a surface of sphere, say</p>
<p>$x^2 + y^2 + z^2 = r$</p> | g7814 | [
0.004642719402909279,
0.01230843085795641,
-0.01657707244157791,
-0.02887716516852379,
-0.018769778311252594,
0.06889582425355911,
-0.01145258266478777,
-0.0843517929315567,
-0.04293094947934151,
-0.04495229572057724,
0.01478875707834959,
0.014432655647397041,
0.10372404754161835,
0.015006301924586296,
0.01682698167860508,
0.04231719300150871,
-0.026885731145739555,
-0.004121528007090092,
-0.014227578416466713,
0.0028740540146827698,
-0.021447153761982918,
-0.04266621917486191,
0.031117478385567665,
-0.035131197422742844,
-0.00660806056112051,
-0.003952148836106062,
0.00017220810696016997,
0.01937895454466343,
-0.010486952029168606,
-0.0566110797226429,
0.023719733580946922,
0.01734951324760914,
0.07174468785524368,
-0.007223374675959349,
-0.04130248352885246,
0.034354716539382935,
0.03465056046843529,
0.029268700629472733,
0.0497027263045311,
-0.03589725121855736,
0.037894632667303085,
0.0011940940748900175,
0.002351401373744011,
0.046433016657829285,
0.05202735215425491,
-0.0344776026904583,
-0.03270428255200386,
0.010143693536520004,
0.029574843123555183,
-0.03197448328137398,
0.009997757151722908,
0.04901144281029701,
0.025476539507508278,
-0.06237337365746498,
-0.0004213323991280049,
0.028708195313811302,
0.017169300466775894,
-0.05358978360891342,
0.03622529283165932,
0.015673838555812836,
-0.047162771224975586,
0.019407479092478752,
0.07753763347864151,
0.0021262457594275475,
0.07510124891996384,
0.03556907922029495,
-0.05161989480257034,
-0.016305871307849884,
0.03407416120171547,
0.028990551829338074,
0.06388525664806366,
-0.006055626552551985,
0.011119702830910683,
-0.04855016618967056,
-0.018370280042290688,
0.05178127810359001,
0.06124285236001015,
-0.021146371960639954,
-0.0585191547870636,
0.014063511975109577,
-0.027991000562906265,
0.06510502099990845,
0.0006464835605584085,
-0.0073894476518034935,
0.07237309217453003,
-0.03289128467440605,
0.008706139400601387,
0.01646127551794052,
-0.04040588438510895,
-0.06481322646141052,
-0.03937486186623573,
0.0035004857927560806,
0.017699776217341423,
-0.04858871549367905,
0.034493718296289444,
-0.013642076402902603,
-0.03517457842826843,
0.03748323395848274,
-0.07778527587652206,
0.005024434067308903,
-0.003771731164306402,
-0.030999692156910896,
0.03309214860200882,
-0.006614599842578173,
0.051491376012563705,
0.011365560814738274,
-0.026989193633198738,
0.019719623029232025,
0.03924668952822685,
-0.03915964066982269,
0.007370953448116779,
0.02535345032811165,
-0.03456968441605568,
-0.014679630286991596,
-0.028028452768921852,
-0.041077621281147,
0.07184498757123947,
-0.05421072617173195,
0.002913265721872449,
0.03077833540737629,
0.03678622469305992,
0.031008675694465637,
-0.019106917083263397,
0.04951984062790871,
-0.009117461740970612,
0.0019783542957156897,
-0.022442612797021866,
-0.05883042886853218,
0.07082861661911011,
-0.012424785643815994,
0.008252783678472042,
-0.007372803520411253,
-0.020680710673332214,
-0.0400376096367836,
-0.05049062520265579,
0.060144178569316864,
-0.01371018961071968,
-0.06820593029260635,
-0.008437307551503181,
0.021757839247584343,
0.011478520929813385,
-0.044170577079057693,
0.003143365029245615,
-0.016974354162812233,
0.0066073895432055,
-0.019537227228283882,
0.021423375234007835,
0.0024254254531115294,
0.016978763043880463,
-0.011670268140733242,
0.006271338555961847,
0.05906461179256439,
-0.006462727207690477,
-0.038437310606241226,
-0.017726650461554527,
0.0018770251190289855,
-0.01304579246789217,
0.0036758147180080414,
0.08483446389436722,
-0.028841586783528328,
0.03632022812962532,
0.0032901454251259565,
-0.021061936393380165,
-0.009856466203927994,
-0.016657056286931038,
0.030115840956568718,
-0.035881392657756805,
-0.07921946048736572,
0.007000110577791929,
0.010692703537642956,
-0.0046736979857087135,
0.010895679704844952,
0.010676558129489422,
0.005560939200222492,
-0.0062101115472614765,
-0.03500344231724739,
-0.003579034237191081,
0.0016966256080195308,
-0.014090217649936676,
0.0059602344408631325,
-0.020137669518589973,
-0.013451171107590199,
0.005840062629431486,
0.04277289658784866,
0.025692541152238846,
-0.006905023939907551,
-0.03825000301003456,
0.016196662560105324,
0.0022895142901688814,
-0.02166825346648693,
-0.011261885985732079,
-0.03908691927790642,
0.06092828884720802,
0.04689629003405571,
0.0028866801876574755,
0.0354527086019516,
0.09526144713163376,
0.006052856799215078,
-0.03908567130565643,
0.0012728332076221704,
0.021797988563776016,
0.05838145315647125,
0.0539473257958889,
0.02726111374795437,
-0.006741880439221859,
-0.06580774486064911,
0.045963093638420105,
-0.04215884953737259,
0.016695775091648102,
0.053042612969875336,
-0.00019281629647593945,
-0.005023033823817968,
0.011020855978131294,
-0.022374238818883896,
-0.0011472925543785095,
0.04913853108882904,
-0.011798235587775707,
-0.016472909599542618,
-0.03145085275173187,
-0.017365463078022003,
0.04764378070831299,
0.03675258532166481,
0.06040310859680176,
-0.053322046995162964,
0.05251386761665344,
0.008181657642126083,
-0.010482474230229855,
0.0025793234817683697,
0.05056685581803322,
0.02698192000389099,
-0.028238391503691673,
-0.08370672911405563,
0.039000384509563446,
-0.009585845284163952,
0.021076222881674767,
-0.04465903714299202,
-0.017751922830939293,
0.048263225704431534,
-0.009821233339607716,
0.035558320581912994,
0.007223926950246096,
0.020543023943901062,
-0.0852622389793396,
0.02953195385634899,
0.03404361382126808,
-0.04695449396967888,
0.01413960661739111,
-0.04317984730005264,
0.01916857436299324,
0.01729641668498516,
0.05392041429877281,
-0.03896046429872513,
-0.007835276424884796,
0.03723333403468132,
0.031742163002491,
-0.005326119251549244,
-0.015224638395011425,
-0.02364521659910679,
-0.05336768180131912,
-0.07172882556915283,
0.028655771166086197,
-0.01645282283425331,
-0.0048524742014706135,
0.041789159178733826,
-0.02842242456972599,
-0.021091917529702187,
-0.03985089808702469,
-0.002690010005608201,
0.016944510862231255,
0.057920459657907486,
0.013639283366501331,
0.01457519643008709,
-0.08972427248954773,
-0.0011925133876502514,
-0.00444241426885128,
-0.03859493136405945,
-0.006941725965589285,
-0.03626750409603119,
-0.08043478429317474,
-0.015116033144295216,
0.044419120997190475,
-0.004435749724507332,
-0.03561555594205856,
0.04085429012775421,
0.007661381736397743,
-0.009240600280463696,
-0.03829415515065193,
-0.0184121523052454,
-0.031985193490982056,
0.04599376767873764,
0.038166508078575134,
0.00016592085012234747,
-0.009896316565573215,
0.01564093865454197,
0.016480710357427597,
0.05569642409682274,
-0.013164754025638103,
0.042312946170568466,
0.0032656192779541016,
0.01540282927453518,
-0.023114578798413277,
-0.007905673235654831,
0.024723080918192863,
-0.05053149163722992,
-0.08477315306663513,
-0.03392655774950981,
0.0834219828248024,
-0.07484589517116547,
-0.0004446408129297197,
-0.03646107017993927,
-0.0685560330748558,
-0.04740382730960846,
0.020312534645199776,
0.019935904070734978,
-0.0021046847105026245,
0.07376950234174728,
-0.06906747817993164,
-0.033469196408987045,
0.0045605492778122425,
0.017187252640724182,
-0.006363753695040941,
-0.02365037240087986,
0.003938088659197092,
0.07507222145795822,
-0.013276290148496628,
0.04357367008924484,
-0.04870804026722908,
0.010363124310970306,
0.006136246491223574,
-0.01564030721783638,
0.038511861115694046,
0.009070196188986301,
0.0020059137605130672,
0.005744109861552715,
0.03853509575128555,
-0.018663765862584114,
-0.006842636503279209,
-0.011971797794103622,
0.07488745450973511,
-0.013220355845987797,
-0.03960014507174492,
0.04072871431708336,
-0.03202880918979645,
-0.039881810545921326,
0.013692975975573063,
0.0251189973205328,
0.01107669435441494,
0.0063307504169642925,
-0.00931060966104269,
-0.04149635136127472,
0.04639437794685364,
0.011502545326948166,
0.04929232597351074,
-0.019795412197709084,
-0.023843880742788315,
0.04594707489013672,
-0.01164354756474495,
-0.02834130823612213,
-0.02159261517226696,
0.014051423408091068,
0.03444685414433479,
-0.04801150783896446,
-0.05559396371245384,
0.008451583795249462,
0.020880773663520813,
-0.060095034539699554,
0.04086463153362274,
-0.021645303815603256,
-0.09063498675823212,
-0.002564517315477133,
0.03546765074133873,
-0.03916268050670624,
-0.022953199222683907,
-0.0069490112364292145,
0.024748699739575386,
0.002533133840188384,
-0.05009647086262703,
0.027632510289549828,
-0.016131186857819557,
0.020046677440404892,
-0.014037523418664932,
0.022399496287107468,
0.05687238276004791,
0.050185348838567734,
-0.03808293491601944,
0.0214936975389719,
-0.045394688844680786,
-0.06819325685501099,
0.022337166592478752,
-0.016331592574715614,
0.04002327471971512,
-0.009948807768523693,
-0.006377681158483028,
-0.01720399037003517,
0.02733134664595127,
-0.045575786381959915,
-0.04561182111501694,
0.002886830596253276,
0.020056193694472313,
0.01765325665473938,
0.029962223023176193,
-0.004670094698667526,
-0.01556247379630804,
0.01930948905646801,
-0.06365294754505157,
-0.02349240332841873,
0.03365138918161392,
-0.0011893071932718158,
0.02491077594459057,
0.01572326384484768,
0.040328145027160645,
0.010551045648753643,
0.014582646079361439,
-0.020258542150259018,
0.09649244695901871,
-0.022804908454418182,
0.06285294890403748,
-0.01859303191304207,
-0.020028525963425636,
0.016918664798140526,
-0.005528229754418135,
0.07929609715938568,
0.032603729516267776,
-0.03115929290652275,
0.026211662217974663,
-0.011424402706325054,
-0.002518674358725548,
0.017783494666218758,
-0.053395938128232956,
-0.021869851276278496,
0.012829163111746311,
0.01594622991979122,
0.00648028589785099,
0.06976289302110672,
-0.06337065249681473,
0.042320698499679565,
-0.003695812774822116,
0.0340542271733284,
-0.0528884083032608,
-0.024926161393523216,
0.02369699813425541,
-0.004228025674819946,
0.0077856252901256084,
-0.032249778509140015,
-0.03507758304476738,
0.06604974716901779,
-0.04286625608801842,
-0.03439776971936226,
0.002789774676784873,
-0.062339428812265396,
-0.032722704112529755,
-0.02435428462922573,
0.049077801406383514,
0.04440688341856003,
-0.019727664068341255,
-0.0065162694081664085,
0.003946769051253796,
0.01210208609700203,
-0.033176351338624954,
0.027116522192955017,
-0.005301312543451786,
0.0026306959334760904,
-0.030572066083550453,
-0.0010294989915564656,
0.04976297542452812,
-0.01832188293337822,
-0.07693428546190262,
-0.01538754627108574,
0.014903252944350243,
0.02545999549329281,
-0.026845373213291168,
0.04886056110262871,
0.033279385417699814,
0.021733345463871956,
-0.04478783532977104,
0.052199095487594604,
-0.022520534694194794,
-0.029189229011535645,
-0.0010041100904345512,
-0.002739307703450322,
0.010569446720182896,
0.015637163072824478,
0.04944482445716858,
-0.006010875571519136,
0.002912556054070592,
0.02035403810441494,
0.014195726253092289,
0.054281096905469894,
-0.03295532241463661,
0.015202749520540237,
0.006048663053661585,
-0.0231039896607399,
0.02184825949370861,
0.026717709377408028,
-0.029274391010403633,
0.003488098504021764,
-0.020280329510569572,
-0.08883305639028549,
0.009801698848605156,
0.038783106952905655,
-0.017022287473082542,
0.004702446050941944,
0.0644831582903862,
0.00046102909254841506,
0.011529085226356983,
0.04473571479320526,
0.03220463916659355,
-0.03728682920336723,
0.06275716423988342,
0.022445300593972206,
0.03906702622771263,
-0.024808896705508232,
0.008595477789640427,
0.035867344588041306,
0.0019688394386321306,
-0.059674013406038284,
-0.007249913178384304,
0.056939747184515,
-0.01657111942768097,
0.03636367619037628,
-0.026560788974165916,
0.04616697132587433,
-0.0019045695662498474,
0.013357988558709621,
0.034013476222753525,
0.001312371576204896,
0.018912190571427345,
0.017451845109462738,
0.06934303045272827,
-0.03654632717370987,
-0.00790693610906601,
-0.004586199298501015,
0.0018270983127877116,
-0.04352802783250809,
0.017770959064364433,
-0.02744259685277939,
0.0170962605625391,
0.09244919568300247,
0.0589023232460022,
-0.020071884617209435,
-0.03260478004813194,
-0.041741836816072464,
0.02266898937523365,
0.03344821557402611,
-0.057576991617679596,
-0.008614236488938332,
-0.006093149073421955,
0.02382138930261135,
0.07182465493679047,
-0.044745538383722305,
-0.00604038592427969,
-0.02198486588895321,
0.034603167325258255,
0.027277372777462006,
-0.06084023788571358,
-0.024722035974264145,
0.04009494185447693,
0.011720765382051468,
-0.06948866695165634,
-0.06875300407409668,
0.019468823447823524,
-0.020724503323435783,
0.004412758629769087,
-0.0047314162366092205,
-0.05962364003062248,
-0.026024984195828438,
0.010800203308463097,
-0.0031736071687191725,
0.08092194050550461,
-0.05807483196258545,
-0.03629699721932411,
-0.015201946720480919,
0.09096809476613998,
0.027503211051225662,
0.039877135306596756,
-0.031758904457092285,
-0.022089790552854538,
-0.0005545119638554752,
-0.05104377865791321,
-0.0076479678973555565,
0.021092142909765244,
-0.015325729735195637,
0.02740473672747612,
-0.03424748778343201,
0.029148723930120468,
0.058350395411252975,
-0.013754384592175484,
-0.03890940919518471,
-0.01056000217795372,
-0.040749892592430115,
0.0468236580491066,
0.04723765701055527,
-0.012718111276626587,
-0.012339431792497635,
0.03722655400633812,
-0.028752736747264862,
-0.040026336908340454,
0.009045647457242012,
-0.07431188225746155,
-0.05439586192369461,
-0.0980982556939125,
-0.012090212665498257,
0.03130335360765457,
0.03127981349825859,
0.0437210276722908,
-0.03009079582989216,
0.00015354654169641435,
-0.016057953238487244,
0.01487534586340189,
0.013784121721982956,
-0.01908222585916519,
0.05508718639612198,
-0.026265066117048264,
0.008940440602600574,
0.003102460177615285,
-0.05632510036230087,
0.00461992435157299,
-0.011615763418376446,
-0.0014725682558491826,
-0.07301321625709534,
-0.03182613477110863,
0.060659173876047134,
0.008348815143108368,
0.0025813058018684387,
0.0035299761220812798,
-0.029995594173669815,
-0.057629264891147614,
0.03423106670379639,
0.027390258386731148,
0.025299914181232452,
-0.009151635691523552,
0.015956075862050056,
0.02869682013988495,
0.021848546341061592,
-0.05582736060023308,
0.014038651250302792,
-0.05017773061990738,
0.041549500077962875,
0.04658595472574234,
0.026910239830613136,
-0.02737032249569893,
0.031636349856853485,
0.02405320666730404,
-0.023893924430012703,
-0.019285138696432114,
-0.020565321668982506,
0.006260185036808252,
-0.048979923129081726,
-0.032372165471315384,
-0.007345834746956825,
0.005472208838909864,
-0.032655417919158936,
0.025644449517130852,
-0.022816695272922516,
-0.012008189223706722,
0.0033667024690657854,
-0.01150292158126831,
0.011833945289254189,
-0.03550918772816658,
-0.05484132096171379,
0.012410898692905903,
0.012068429030478,
-0.011579753831028938,
-0.0049390969797968864,
-0.049392636865377426,
0.058698881417512894,
-0.010619229637086391,
-0.017278701066970825,
0.005776267033070326,
0.01836187019944191,
-0.007141261827200651,
0.04574371501803398,
-0.05092088133096695,
0.001380081637762487,
-0.015095244161784649,
0.010258038528263569,
0.0013988512801006436,
-0.006926375906914473,
0.05603683367371559,
-0.030857201665639877,
0.07380014657974243,
0.035746101289987564,
0.017461486160755157,
-0.0751001313328743,
-0.0534302294254303,
-0.042793434113264084,
0.03544467315077782,
0.00558136124163866,
-0.04416795074939728,
0.005185497459024191,
0.02779000625014305,
0.014871197752654552,
0.004364435561001301,
-0.013531114906072617,
0.023071907460689545,
-0.04494032636284828,
0.006975734140723944,
0.055436596274375916,
0.017659669741988182,
-0.03499908000230789,
0.01767069846391678,
-0.027403609827160835,
-0.0628846064209938,
0.004346777684986591,
-0.007751432713121176,
-0.057908546179533005,
-0.00012996931036468595,
-0.03679949417710304,
0.04901003837585449,
-0.06368580460548401,
-0.003932444844394922,
0.019080648198723793,
-0.030313724651932716,
-0.004075534641742706,
0.003344546305015683,
0.02050183154642582,
0.010710556991398335,
0.0005239659803919494,
0.015720168128609657,
-0.07611662894487381,
-0.050293948501348495,
-0.021169647574424744,
0.03928714990615845,
-0.04349907487630844,
0.010648522526025772,
-0.031416814774274826,
-0.043523069471120834,
-0.04120931029319763,
-0.007765285670757294,
0.029592959210276604,
0.00023945675638969988,
0.042236872017383575,
0.041001975536346436,
0.052093349397182465,
-0.008724027313292027,
0.028139125555753708,
-0.049844320863485336,
0.045814383774995804,
-0.006598383188247681,
-0.00742154847830534,
-0.028491515666246414,
-0.06601714342832565,
0.03756127133965492,
-0.06910792738199234,
0.04004340246319771,
0.03500210866332054,
-0.055326126515865326,
0.0011022016406059265,
0.11406499892473221,
-0.019721554592251778,
0.06418225169181824,
-0.05824560299515724,
0.014901249669492245,
-0.027731437236070633,
0.052322302013635635,
-0.05665522441267967,
0.020893212407827377,
-0.015735391527414322,
0.022098474204540253,
0.009193754754960537,
-0.023555396124720573,
-0.029257752001285553,
-0.026438511908054352,
0.03896142914891243,
-0.005815559532493353,
-0.02210654504597187,
-0.03465816006064415,
0.07178065180778503
] |
<p>In an astronomy forum that I frequent, I have been having a discussion where the state of quantum gravity research came up. I claimed that Loop Quantum Gravity theories couldn't prove GR in the continuum limit, nor could they compute Mercury's perihelion because they didn't have any matter, at this point. Another poster claimed that one of the first things that any gravity scientist checks for the theory is the theory's prediction for the precession of Mercury's perihelion.</p>
<p>Now for cosmological extensions to GR like, MOND, TeVeS or STVG, I can see where this might make sense. But I can't see how this poster's claim holds for quantum-gravity theories that haven't been able to establish that they reproduce GR in the continuum limit and that don't have matter at all.</p>
<p>So I feel like I'm either missing something important about quantum gravity theories, in general, or the poster's comment only applies to cosmological-scale gravity modifications designed as an alternative to dark matter and not quantum gravity theories. Or perhaps a little of each.</p>
<p>How, for instance, would one compute the precession of Mercury's perihelion using CDT, or Rovelli et al.'s spin-foam version of LQG? It may be that the dynamics of any object are implied in the spacetime microstructure, I don't understand the math well enough yet to follow the implications to know if this is true. But how can you compute the orbit of a planet when you require mass and fermions in order to even have the Sun and a planet like Mercury?</p>
<p>I note the very very recent paper of this week, Dec. 21, <a href="http://arxiv.org/abs/1012.4719">http://arxiv.org/abs/1012.4719</a>, where the Marseille LQG group run by Carlo Rovelli claims they can now incorporate Fermions, so my question applies to research prior to this event, not that going forward.</p>
<p>I'm not even close to an expert, so I'm looking for enough information that I'll be able to respond intelligently to the other poster. I'll point them to the answer I received here so perhaps this will help the marketing for this excellent resource.</p> | g7815 | [
-0.020370976999402046,
0.09812359511852264,
0.021062159910798073,
-0.06257656216621399,
0.01598840206861496,
0.05405963584780693,
0.03487373888492584,
-0.005071577616035938,
-0.051771510392427444,
-0.07269828021526337,
0.01692545972764492,
0.00884304754436016,
-0.014710814692080021,
0.020665958523750305,
0.010587906464934349,
-0.0012159493053331971,
0.017406122758984566,
0.02408590540289879,
0.02782701887190342,
-0.02651737630367279,
0.04159412905573845,
-0.049241118133068085,
0.041678495705127716,
-0.04078516736626625,
-0.06718716770410538,
-0.0013506251852959394,
0.012151321396231651,
-0.011151764541864395,
-0.016742752864956856,
0.010231414809823036,
0.025127608329057693,
-0.06613688170909882,
0.018508344888687134,
-0.10056596249341965,
0.007939926348626614,
-0.0011243503540754318,
0.013137182220816612,
0.027311772108078003,
-0.012916439212858677,
0.01811642199754715,
0.03510155901312828,
-0.059786632657051086,
-0.0016681620618328452,
-0.005970457568764687,
0.0016731672221794724,
0.054514478892087936,
0.014740487560629845,
-0.01933261565864086,
0.045699592679739,
0.022380635142326355,
-0.007045390084385872,
0.08044087886810303,
0.069764144718647,
-0.007896492257714272,
-0.004219053778797388,
0.08584039658308029,
0.0033663774374872446,
-0.02049950882792473,
0.029068810865283012,
-0.04329177737236023,
0.046748943626880646,
0.01631629839539528,
0.06454214453697205,
-0.0018208903493359685,
-0.005794943775981665,
0.0436556302011013,
-0.08166161179542542,
-0.03018207848072052,
-0.035294000059366226,
-0.011973192915320396,
0.014031982980668545,
-0.015276804566383362,
-0.015844054520130157,
0.035248901695013046,
-0.01867075450718403,
0.055993977934122086,
-0.007770702242851257,
0.019833620637655258,
0.018470779061317444,
-0.02630271017551422,
0.008583040907979012,
-0.04750366881489754,
-0.047681767493486404,
-0.03004429303109646,
0.06860526651144028,
-0.010894034057855606,
-0.0002840037923306227,
0.03703487291932106,
0.04858498275279999,
0.07481647282838821,
-0.011423164047300816,
-0.07402486354112625,
0.0555058978497982,
-0.01096405740827322,
0.013849020935595036,
0.006210807245224714,
0.0009738708613440394,
0.03521101921796799,
-0.02648051269352436,
0.007639564573764801,
-0.07769141346216202,
0.030109969899058342,
0.01642707921564579,
-0.000859838561154902,
0.006205142475664616,
0.009461033158004284,
-0.005969160236418247,
0.030832448974251747,
0.02674097754061222,
-0.04664621874690056,
-0.06570197641849518,
-0.0009028656058944762,
-0.044715989381074905,
-0.02780788019299507,
-0.04894380271434784,
-0.014096817933022976,
0.11837263405323029,
-0.024057844653725624,
-0.011094659566879272,
0.027693230658769608,
-0.024853317067027092,
-0.003913263790309429,
0.03910428285598755,
0.03437822312116623,
-0.0968468114733696,
-0.004660793114453554,
-0.006835348904132843,
0.03055526129901409,
0.06023170426487923,
0.004621811211109161,
-0.024022288620471954,
0.05211925506591797,
0.007609110325574875,
0.0895693227648735,
0.0008192203240469098,
-0.05101417377591133,
0.010515022091567516,
-0.001929757883772254,
0.006490401923656464,
0.03902061656117439,
-0.015092099085450172,
-0.04177156463265419,
-0.030022457242012024,
-0.012341774068772793,
0.0024503646418452263,
-0.014572332613170147,
0.03404529020190239,
-0.006251772865653038,
0.006062930915504694,
0.014406238682568073,
0.04942314699292183,
0.04188298434019089,
0.044271960854530334,
-0.041481759399175644,
0.05083436146378517,
0.03867429122328758,
0.01017425861209631,
-0.04064982384443283,
-0.0034858393482863903,
0.03489832207560539,
0.03387394919991493,
-0.052931323647499084,
0.009182539768517017,
-0.006098685786128044,
-0.028946025297045708,
0.035229362547397614,
0.00871110800653696,
-0.022476287558674812,
-0.024219470098614693,
-0.01949600875377655,
-0.03188026696443558,
-0.017128266394138336,
-0.00072909687878564,
0.07945425063371658,
0.0055937981233000755,
0.033620886504650116,
0.024384502321481705,
-0.05764814838767052,
-0.028150975704193115,
0.012037689797580242,
-0.005811660550534725,
0.00904247909784317,
-0.02603423036634922,
0.0003431347431614995,
-0.0010803359327837825,
0.03387026861310005,
0.01360822468996048,
-0.027839718386530876,
0.03455207124352455,
0.02652856521308422,
-0.013308157213032246,
0.0580599270761013,
0.05201584845781326,
0.005056360736489296,
-0.011591951362788677,
-0.029851751402020454,
0.02555723488330841,
-0.07136674225330353,
-0.03785406053066254,
0.03176473453640938,
-0.0523497611284256,
0.04682634025812149,
0.005714478436857462,
0.007935925386846066,
0.04289260134100914,
0.004264503251761198,
-0.015635306015610695,
0.03715136647224426,
0.009481876157224178,
-0.005888259969651699,
0.027845632284879684,
-0.0030034007504582405,
0.06838540732860565,
0.03539678826928139,
-0.0377502404153347,
-0.009640772826969624,
0.0043848492205142975,
0.06012449413537979,
0.05387110635638237,
0.0319933220744133,
0.015585681423544884,
0.020204149186611176,
0.0503937229514122,
0.014259526506066322,
0.00015666274703107774,
0.019779689610004425,
-0.005391324404627085,
0.008387856185436249,
-0.03965422511100769,
0.053371332585811615,
-0.010098738595843315,
0.0064210728742182255,
-0.08008018136024475,
-0.020293062552809715,
0.006983854807913303,
0.04805618152022362,
0.018438270315527916,
-0.042775578796863556,
0.04758036136627197,
0.03829417750239372,
0.00631972448900342,
-0.034451138228178024,
-0.021116072311997414,
-0.04318627342581749,
0.06300798058509827,
-0.0384361632168293,
0.013726049102842808,
-0.018907669931650162,
-0.01458839513361454,
0.048450976610183716,
0.04920800030231476,
-0.0018689159769564867,
-0.0410299226641655,
0.010891877114772797,
0.01220416184514761,
0.02217755652964115,
0.0002760440402198583,
0.0013294253731146455,
-0.06523988395929337,
-0.046027619391679764,
0.03475373983383179,
-0.05207481607794762,
-0.00525099178776145,
0.07144604623317719,
-0.033233027905225754,
-0.027123315259814262,
-0.03862187638878822,
0.002606017282232642,
0.0012541033793240786,
-0.07979389280080795,
-0.0076021598652005196,
0.027661552652716637,
0.014064831659197807,
0.05632457509636879,
-0.03801412507891655,
0.04214322566986084,
0.02392427995800972,
0.019578952342271805,
-0.0022518860641866922,
0.009814232587814331,
-0.0398358590900898,
-0.04099775478243828,
-0.04120743274688721,
-0.0124507499858737,
0.024544835090637207,
-0.03778471425175667,
-0.009703870862722397,
0.048973653465509415,
0.0015221006469801068,
0.049770403653383255,
0.017181171104311943,
0.05532146245241165,
0.054885100573301315,
0.06911299377679825,
-0.07821982353925705,
0.06645245105028152,
0.0033813035115599632,
0.011686891317367554,
0.000821729947347194,
0.005113447085022926,
0.0005393846076913178,
0.023586569353938103,
-0.009126962162554264,
0.08720992505550385,
0.052161768078804016,
-0.015498432330787182,
-0.04593602567911148,
-0.02369799092411995,
-0.004405445419251919,
-0.07064774632453918,
0.037065982818603516,
0.023183785378932953,
0.002606285735964775,
-0.009331776760518551,
-0.013420089147984982,
-0.011054957285523415,
0.01313663087785244,
0.01818712241947651,
-0.0012042033486068249,
0.005098662339150906,
-0.019069362431764603,
-0.00559488357976079,
0.017154447734355927,
-0.026103688403964043,
-0.0043005854822695255,
0.047939348965883255,
-0.031099194660782814,
-0.033047545701265335,
0.03279587998986244,
-0.0073468005284667015,
0.048358507454395294,
0.012206466868519783,
0.013160633854568005,
0.033042002469301224,
-0.05421445518732071,
-0.03737332299351692,
0.0429021380841732,
0.03398827463388443,
0.06830150634050369,
0.021796416491270065,
-0.07980397343635559,
-0.016322484239935875,
-0.0036051596980541945,
0.017319317907094955,
0.01686648279428482,
0.019180597737431526,
-0.0031799308490008116,
-0.015169592574238777,
-0.040220871567726135,
-0.005146968178451061,
-0.0163702555000782,
0.0009897386189550161,
-0.009312131442129612,
-0.006050440017133951,
-0.013468723744153976,
0.06440840661525726,
0.04136521741747856,
0.058187998831272125,
0.06420554220676422,
-0.017581772059202194,
-0.03553735837340355,
0.018239568918943405,
-0.0460621640086174,
-0.014936399646103382,
0.08432148396968842,
0.030992761254310608,
0.0010214776266366243,
-0.04062546044588089,
0.004025388974696398,
-0.022966688498854637,
0.030993521213531494,
-0.04617161676287651,
-0.008194568566977978,
0.026688817888498306,
0.08330144733190536,
0.008183610625565052,
0.04745727777481079,
0.022105416283011436,
-0.0027801755350083113,
0.05595608800649643,
0.026010943576693535,
0.04583483561873436,
-0.020767971873283386,
0.03494321554899216,
-0.022589020431041718,
0.01816146820783615,
-0.038139406591653824,
0.00661857845261693,
-0.02856965735554695,
-0.006998779717832804,
-0.029722461476922035,
-0.05018574744462967,
-0.00920000672340393,
-0.03515588119626045,
0.00013158518413547426,
-0.039493098855018616,
-0.01958843134343624,
-0.01147796306759119,
0.08320395648479462,
0.03983303904533386,
0.021102674305438995,
0.027943216264247894,
0.0053904009982943535,
0.016608765348792076,
-0.044012535363435745,
-0.031034016981720924,
0.000668224529363215,
0.009356914088129997,
-0.053838036954402924,
-0.02559692971408367,
0.04153677448630333,
0.03187333792448044,
-0.010479557327926159,
-0.03304043784737587,
0.037950895726680756,
-0.0015439685666933656,
0.022946130484342575,
-0.07050557434558868,
0.03812737017869949,
-0.021864604204893112,
0.02722884900867939,
0.03423185646533966,
0.025597983971238136,
0.00940271932631731,
0.027601949870586395,
0.030899887904524803,
-0.07190077006816864,
-0.005113471299409866,
-0.03370971977710724,
-0.04874283820390701,
0.030494511127471924,
-0.03543941676616669,
-0.010871942155063152,
0.03791214898228645,
-0.024752018973231316,
0.027873748913407326,
-0.06732812523841858,
0.01661795563995838,
-0.030981702730059624,
-0.04015060514211655,
0.0766122117638588,
0.00426888931542635,
-0.0003909508232027292,
0.01786305196583271,
0.006452621426433325,
0.023593325167894363,
-0.0779680460691452,
0.02667365036904812,
0.012959667481482029,
-0.019329676404595375,
-0.04449896514415741,
-0.0553789921104908,
-0.0030251401476562023,
0.0007064964738674462,
-0.056907523423433304,
-0.03282441571354866,
0.012452339753508568,
-0.005996359512209892,
-0.004218677990138531,
-0.008521998301148415,
-0.06334489583969116,
-0.019315341487526894,
-0.018376225605607033,
0.08160317689180374,
0.07634224742650986,
-0.02898525819182396,
-0.04522543400526047,
-0.01942819356918335,
-0.043595414608716965,
-0.05961589515209198,
0.010855638422071934,
-0.006701313890516758,
0.024626944214105606,
-0.048178840428590775,
-0.018506985157728195,
0.021862393245100975,
0.035936497151851654,
-0.04247280955314636,
0.011074120178818703,
-0.011389889754354954,
-0.020008761435747147,
-0.013750530779361725,
0.07040441036224365,
-0.0013093644520267844,
0.00549191003665328,
0.03977515175938606,
-0.04386654123663902,
0.009594425559043884,
-0.055328454822301865,
-0.012829999439418316,
-0.040921300649642944,
-0.00643189949914813,
0.019581299275159836,
0.006353828124701977,
-0.02093985676765442,
0.04953400790691376,
0.05376098304986954,
-0.038487453013658524,
-0.008858882822096348,
-0.04495533928275108,
0.0033903224393725395,
0.045927707105875015,
0.06402138620615005,
-0.03724372014403343,
0.005655554123222828,
0.06945841014385223,
-0.013567526824772358,
-0.05021774023771286,
0.014707549475133419,
0.03176235780119896,
-0.023592844605445862,
0.030033301562070847,
0.0026749337557703257,
-0.007691053673624992,
0.025654098019003868,
-0.038363244384527206,
0.002311763586476445,
-0.02231421321630478,
0.019505616277456284,
-0.05325093865394592,
0.0057871355675160885,
-0.055243805050849915,
0.017528900876641273,
0.013590600341558456,
0.05730678141117096,
-0.017464537173509598,
-0.03263061121106148,
-0.057400915771722794,
0.01972414180636406,
0.0564320832490921,
0.047201890498399734,
-0.020903201773762703,
-0.004432210698723793,
0.005604207515716553,
0.014607846736907959,
-0.03438669070601463,
0.021512756124138832,
0.0542115792632103,
0.022380562499165535,
-0.03872392699122429,
-0.03947867080569267,
0.02640365995466709,
0.004975397605448961,
0.022738007828593254,
0.007298024371266365,
-0.03458485007286072,
-0.012282061390578747,
0.054538141936063766,
0.007792139891535044,
-0.07452559471130371,
-0.08561863005161285,
0.005447449162602425,
0.025438766926527023,
-0.00960446335375309,
-0.051691193133592606,
0.07299420982599258,
-0.017183750867843628,
-0.044933732599020004,
-0.01048211008310318,
0.02143998257815838,
0.03905479982495308,
-0.025897042825818062,
0.04964962974190712,
-0.02223375253379345,
0.011117463931441307,
-0.01680382341146469,
0.020816123113036156,
-0.03367157652974129,
0.035020001232624054,
-0.02669883333146572,
-0.051015615463256836,
-0.009973779320716858,
-0.03650262579321861,
-0.005280748941004276,
0.0032832848373800516,
-0.04015021771192551,
-0.035743411630392075,
-0.05610385909676552,
-0.026431871578097343,
-0.017666462808847427,
0.03219535946846008,
0.006864632945507765,
0.012002706527709961,
-0.011444549076259136,
-0.007425440941005945,
0.03182036057114601,
-0.0249286238104105,
0.01197697501629591,
0.0070936912670731544,
0.011320090852677822,
-0.02837456576526165,
0.03010999783873558,
-0.0418841727077961,
-0.037137795239686966,
-0.02223234437406063,
0.0077917929738759995,
-0.028196383267641068,
-0.038868874311447144,
-0.02905774489045143,
0.029758568853139877,
0.053149912506341934,
-0.047536104917526245,
0.01000792346894741,
0.043864328414201736,
0.03057040460407734,
-0.028557026758790016,
-0.017186490818858147,
0.02156635746359825,
-0.007901263423264027,
0.009116293862462044,
-0.0065236580558121204,
0.006798324640840292,
0.06270059198141098,
0.01580619253218174,
-0.014532283879816532,
0.003154017264023423,
-0.060830533504486084,
-0.02009567990899086,
-0.033275306224823,
0.018101565539836884,
0.0503581240773201,
0.027051473036408424,
0.006889069452881813,
-0.06974036246538162,
-0.009116185829043388,
0.03749145194888115,
0.04520732909440994,
-0.013396980240941048,
0.0832395851612091,
0.027970679104328156,
-0.002161121927201748,
0.058377090841531754,
-0.015192578546702862,
-0.007778350729495287,
0.017086397856473923,
0.02528841234743595,
-0.03811706230044365,
0.011242849752306938,
-0.005394820123910904,
-0.019784310832619667,
-0.005278737284243107,
-0.047981660813093185,
0.019673451781272888,
0.02931080013513565,
-0.040241342037916183,
-0.022467434406280518,
0.04899776354432106,
0.0633930191397667,
0.006670617964118719,
-0.03454962000250816,
0.014602256007492542,
-0.040788374841213226,
0.014757691882550716,
0.036714062094688416,
-0.00463496707379818,
0.0588693767786026,
0.051535751670598984,
0.06751611828804016,
0.0037805757019668818,
-0.03283197432756424,
-0.014592701569199562,
-0.014995655976235867,
0.004410785622894764,
0.027842732146382332,
0.004286398179829121,
0.00776887871325016,
-0.015330699272453785,
-0.03462899103760719,
-0.0020175431855022907,
0.011913027614355087,
0.0023062420077621937,
-0.02971752919256687,
-0.05163805931806564,
-0.03700225055217743,
0.005623208824545145,
-0.019300159066915512,
-0.045812323689460754,
0.027949027717113495,
-0.04663894325494766,
-0.013478193432092667,
-0.040951214730739594,
0.019584083929657936,
-0.04549095779657364,
0.05005262792110443,
0.0074934521690011024,
0.007958672940731049,
-0.013567926362156868,
0.04038074612617493,
-0.046432532370090485,
0.01903017982840538,
-0.017335211858153343,
0.006606068927794695,
-0.00547628290951252,
-0.0049620638601481915,
0.011603699997067451,
0.009144723415374756,
-0.007106272038072348,
0.008611766621470451,
0.027445640414953232,
-0.0018348715966567397,
0.02701644040644169,
-0.05006491765379906,
0.001196707016788423,
0.0014839720679447055,
0.05626634135842323,
-0.007813156582415104,
0.030679261311888695,
-0.04515257850289345,
-0.0695929080247879,
0.023326195776462555,
-0.014295554719865322,
-0.01920820213854313,
-0.04076169803738594,
0.009744795970618725,
0.0038914382457733154,
0.01714952476322651,
-0.05103319138288498,
-0.028663503006100655,
0.003802751423791051,
-0.08397942781448364,
-0.06794674694538116,
-0.04102452099323273,
-0.029124027118086815,
-0.10668990761041641,
-0.045316871255636215,
-0.032576870173215866,
-0.01845923811197281,
-0.025104647502303123,
-0.07614760845899582,
-0.07412059605121613,
0.031992051750421524,
0.0040657115168869495,
-0.05055961385369301,
-0.03304548189043999,
-0.06548662483692169,
0.06896252185106277,
-0.06100325658917427,
-0.09905757755041122,
-0.03106522001326084,
-0.01599287800490856,
0.00371575471945107,
-0.044225890189409256,
0.03463711589574814,
-0.010977149941027164,
0.0765373483300209,
0.02269694209098816,
-0.04279303178191185,
0.00807519443333149,
0.011151853948831558,
-0.01635068655014038,
-0.053278591483831406,
0.0004258583066985011,
0.060839541256427765,
-0.004014645237475634,
0.010339159518480301,
-0.0176498182117939,
-0.05547810345888138,
-0.025237100198864937,
0.03509035333991051,
-0.025672197341918945,
0.019541356712579727,
-0.0012385440059006214,
0.07933232188224792,
0.008139724843204021,
-0.017025666311383247,
-0.013680474832654,
-0.05434947460889816,
-0.007391472812741995
] |
<p>Why in the irradiament mulipoles of Lienard-Wiechert's potential we say that electric quadrupole give a contribute of the same order of the magnetic dipole? How can we see it from their equations? And is there a physical reason for this? Sorry for my trivial question.</p> | g7816 | [
-0.0212204921990633,
0.010451801121234894,
-0.004252714104950428,
-0.01367846131324768,
0.06891091912984848,
0.0339127779006958,
-0.029229143634438515,
-0.026406049728393555,
-0.03249305114150047,
0.022902920842170715,
-0.042873986065387726,
0.007945621386170387,
0.0028568704146891832,
-0.007696450222283602,
-0.014893531799316406,
-0.0347902812063694,
0.015369663946330547,
0.03546407073736191,
0.030622774735093117,
-0.03180438280105591,
-0.027881132438778877,
0.02229963429272175,
-0.053366225212812424,
-0.012970268726348877,
-0.018945975229144096,
0.05418192595243454,
-0.01769806444644928,
-0.022912755608558655,
-0.052153777331113815,
-0.03379538655281067,
0.03041776455938816,
-0.004235276021063328,
0.08241163194179535,
-0.03193948417901993,
-0.02345692180097103,
-0.00458334619179368,
0.013817692175507545,
0.01296471618115902,
0.00038522909744642675,
-0.010092606768012047,
-0.022070011124014854,
-0.0009682601667009294,
0.02649664878845215,
0.02760263904929161,
0.0039005205035209656,
-0.005706374999135733,
-0.030042551457881927,
0.016985861584544182,
-0.010359849780797958,
-0.010902929119765759,
0.03872621804475784,
-0.0072633614763617516,
0.061601512134075165,
-0.019022442400455475,
0.023775653913617134,
0.03133564069867134,
0.00905329454690218,
0.00030610873363912106,
0.022299202159047127,
0.04113785922527313,
-0.0008968889014795423,
0.06233276426792145,
0.06590655446052551,
0.009723189286887646,
0.07383372634649277,
-0.04059514030814171,
-0.030811650678515434,
-0.02626185305416584,
-0.01666037179529667,
0.014026317745447159,
-0.009762506000697613,
-0.03662174195051193,
-0.03384486585855484,
-0.019651325419545174,
0.04041999205946922,
0.022079721093177795,
0.047206200659275055,
0.04912103712558746,
0.025920098647475243,
-0.021243290975689888,
-0.033464472740888596,
0.00083800038555637,
0.0023839245550334454,
0.08311531692743301,
0.06939713656902313,
0.02898564748466015,
0.013078441843390465,
0.018387511372566223,
-0.0180695578455925,
-0.011646061204373837,
0.014546999707818031,
-0.005538035184144974,
0.03213326632976532,
0.013809668831527233,
0.006037253886461258,
-0.04761592298746109,
-0.0014150777133181691,
0.026792239397764206,
-0.023043349385261536,
-0.014158927835524082,
-0.0008462798432447016,
-0.009865919128060341,
0.0043402425944805145,
0.007690178696066141,
-0.007618298754096031,
0.008083960972726345,
-0.004795372020453215,
0.01542271114885807,
0.05167066678404808,
0.06761250644922256,
-0.03144719451665878,
-0.04638103023171425,
-0.02588850073516369,
0.031319621950387955,
-0.0011174469254910946,
0.01044604554772377,
0.02948678657412529,
-0.10504034906625748,
0.00008051969052758068,
0.11615464091300964,
-0.029025154188275337,
0.009820882230997086,
0.04673692584037781,
0.0779491737484932,
0.0053671482019126415,
-0.060172006487846375,
0.053291428834199905,
0.043190233409404755,
0.02991965226829052,
-0.0008789823623374104,
0.004041592124849558,
-0.02931046113371849,
-0.005644547287374735,
0.025887737050652504,
0.04705090820789337,
-0.01901966519653797,
0.021128712221980095,
-0.015374431386590004,
0.00670685525983572,
-0.0006225242395885289,
0.010783668607473373,
-0.01489039696753025,
0.0384225994348526,
-0.07985252887010574,
-0.08630694448947906,
0.01865106262266636,
-0.03373384103178978,
-0.023530323058366776,
0.021819086745381355,
0.03980645537376404,
0.014063768088817596,
0.009745064191520214,
0.018160784617066383,
-0.032902806997299194,
0.03180640563368797,
-0.023150162771344185,
-0.04448562487959862,
-0.02998412773013115,
0.00099663354922086,
0.06491982936859131,
0.015051024965941906,
-0.03108126111328602,
-0.041224125772714615,
0.007397322449833155,
-0.04172160103917122,
0.03948480635881424,
0.06412891298532486,
-0.0425715297460556,
-0.04021232947707176,
-0.02294914424419403,
0.026565730571746826,
-0.0016347226919606328,
0.04920649528503418,
0.014760159887373447,
-0.017781872302293777,
0.07501517981290817,
-0.01235983893275261,
-0.07075518369674683,
0.03925483673810959,
0.046375907957553864,
-0.05369668826460838,
0.04454902559518814,
0.010968727990984917,
-0.01639147661626339,
-0.009374881163239479,
-0.03135314956307411,
-0.01323703397065401,
0.06486576050519943,
-0.054831165820360184,
-0.00852285698056221,
0.008175989612936974,
0.01598263718187809,
-0.003427888499572873,
0.05078626051545143,
0.03535006567835808,
-0.004636263009160757,
-0.051980987191200256,
-0.011364590376615524,
-0.0342765636742115,
0.029298365116119385,
-0.04670735076069832,
-0.010685733519494534,
0.04101103916764259,
-0.018963204696774483,
-0.07400871068239212,
-0.004222366958856583,
0.02562750317156315,
0.008102968335151672,
0.09699513763189316,
-0.0928148403763771,
0.004394622519612312,
-0.017868632450699806,
0.02124531753361225,
-0.017250094562768936,
-0.06279367208480835,
-0.016172917559742928,
0.013993385247886181,
-0.0060875630006194115,
-0.00043787117465399206,
0.036310721188783646,
-0.02578643709421158,
-0.05331268906593323,
0.034267671406269073,
0.007841592654585838,
-0.03360742703080177,
-0.019734887406229973,
-0.024824433028697968,
-0.022610073909163475,
-0.04398491606116295,
0.003924525808542967,
-0.05199561268091202,
-0.0400957316160202,
0.01437884196639061,
0.008372550830245018,
0.013038299046456814,
0.026573240756988525,
-0.06991123408079147,
0.029261387884616852,
-0.018719827756285667,
0.008356279693543911,
0.017857015132904053,
0.008294526487588882,
0.05226052924990654,
0.030150527134537697,
-0.01470408495515585,
0.02972966991364956,
0.0944676548242569,
0.011579755693674088,
-0.044166821986436844,
0.07957299798727036,
0.021843964233994484,
-0.025357026606798172,
-0.012139635160565376,
0.05822930112481117,
-0.059447456151247025,
0.016609732061624527,
-0.008337019011378288,
0.02023141458630562,
-0.00941766332834959,
-0.03466092795133591,
-0.023205986246466637,
0.017093583941459656,
0.03013034723699093,
-0.031204788014292717,
-0.04548526927828789,
0.053951799869537354,
0.0035186465829610825,
0.04113027825951576,
0.041954949498176575,
-0.034690458327531815,
-0.054773714393377304,
0.10528664290904999,
-0.028432108461856842,
0.019014175981283188,
0.0002748382103163749,
-0.043324064463377,
0.07247710227966309,
-0.0008457026560790837,
0.061275236308574677,
-0.01669435389339924,
-0.034782491624355316,
0.02089403197169304,
-0.01688261702656746,
0.004384440835565329,
-0.0299252700060606,
-0.056654706597328186,
-0.0002050265611615032,
-0.018741939216852188,
-0.0167866051197052,
-0.031816523522138596,
-0.03966967761516571,
-0.03192761912941933,
0.05740977078676224,
-0.001495323027484119,
-0.06809695810079575,
-0.05261560156941414,
0.1153859794139862,
0.03177030012011528,
-0.06111845001578331,
-0.013266894966363907,
-0.007485066540539265,
0.037239186465740204,
-0.0012365625007078052,
0.05212608724832535,
0.04525851085782051,
0.08439599722623825,
0.02481035329401493,
-0.001268106047064066,
-0.013905514031648636,
0.015003588050603867,
0.022600140422582626,
0.06394351273775101,
-0.03018951788544655,
-0.015765830874443054,
-0.00023689211229793727,
-0.07153943181037903,
-0.016220584511756897,
0.03653829172253609,
0.027016203850507736,
0.012950378470122814,
-0.0462588332593441,
0.007910124026238918,
-0.03854542225599289,
-0.04146953299641609,
0.03191462531685829,
0.0005086793680675328,
-0.03076784498989582,
-0.01422879472374916,
-0.02283337339758873,
-0.01666690595448017,
-0.0013863156782463193,
-0.012055031955242157,
0.011253710836172104,
0.01083677913993597,
-0.011080712080001831,
-0.032555971294641495,
-0.06916316598653793,
0.015117530710995197,
-0.030345750972628593,
-0.030379943549633026,
0.02280815690755844,
-0.021770162507891655,
-0.09842986613512039,
-0.01019431371241808,
-0.01391586009413004,
0.03085978887975216,
0.009631631895899773,
0.03550951927900314,
-0.007572473026812077,
0.01911051757633686,
0.010493000037968159,
0.02713107503950596,
0.04219963401556015,
0.0757596492767334,
-0.04186520725488663,
-0.01357915811240673,
-0.01798536255955696,
0.009042898193001747,
0.021558240056037903,
0.0037217987701296806,
0.0039949677884578705,
-0.009240609593689442,
0.011963766068220139,
-0.07003890722990036,
-0.014835546724498272,
0.02675609290599823,
-0.01900305412709713,
-0.02879241853952408,
0.04767892509698868,
-0.032690517604351044,
-0.0661703571677208,
0.007446002680808306,
-0.047250159084796906,
-0.02714494802057743,
-0.005715141072869301,
-0.008178627118468285,
-0.04285500943660736,
-0.025086944922804832,
-0.09528994560241699,
-0.04101115092635155,
0.0014829807914793491,
0.05942118540406227,
0.10378187149763107,
0.04602084308862686,
0.02425471320748329,
0.024996355175971985,
-0.08375938981771469,
-0.009306559339165688,
-0.003563492326065898,
-0.07215357571840286,
0.01713399402797222,
-0.032655246555805206,
-0.05494154244661331,
0.00004305805850890465,
-0.01660565659403801,
-0.09085731953382492,
0.058807216584682465,
-0.012242937460541725,
-0.015154828317463398,
0.025688808411359787,
0.035828106105327606,
-0.047528594732284546,
0.0033173246774822474,
-0.01830262318253517,
-0.014569143764674664,
0.01281710434705019,
0.03862166777253151,
-0.026675444096326828,
0.09343869239091873,
-0.043819528073072433,
-0.027756381779909134,
0.0037222278770059347,
0.014937926083803177,
-0.021403761580586433,
0.007117512170225382,
0.013445933349430561,
-0.0021666092798113823,
-0.013096262700855732,
0.022108027711510658,
0.010577203705906868,
0.017756972461938858,
-0.015727678313851357,
0.032864902168512344,
-0.025289611890912056,
-0.01687208190560341,
0.01757853291928768,
0.046105414628982544,
-0.014061134308576584,
-0.016439158469438553,
-0.008925188332796097,
-0.016949813812971115,
0.07686632126569748,
-0.005961183924227953,
-0.011782556772232056,
-0.07109936326742172,
-0.03266036510467529,
-0.05357951670885086,
0.07534592598676682,
-0.017683139070868492,
0.09787720441818237,
0.07663246989250183,
0.029235046356916428,
0.0450964979827404,
-0.015780406072735786,
0.02405225858092308,
0.02756192348897457,
-0.045099809765815735,
-0.014951102435588837,
-0.05244104191660881,
-0.018256889656186104,
0.004785275552421808,
-0.020301060751080513,
0.006799932569265366,
-0.07382778823375702,
0.023883989080786705,
-0.007217906881123781,
0.023427357897162437,
-0.009907581843435764,
0.010674319230020046,
0.017750168219208717,
-0.06268370151519775,
0.02097094990313053,
0.004907544702291489,
-0.009675245732069016,
0.03919753059744835,
-0.004850833211094141,
-0.006578573025763035,
0.015695083886384964,
-0.09766600281000137,
-0.0010181500110775232,
0.024748364463448524,
0.05375543609261513,
0.0026467693969607353,
-0.028502315282821655,
0.020437339320778847,
-0.05066266655921936,
-0.03511358052492142,
-0.03226118162274361,
-0.004692064598202705,
-0.022455668076872826,
-0.0323936827480793,
-0.041696928441524506,
0.02802368439733982,
-0.010332409292459488,
0.011669360101222992,
0.03615498170256615,
-0.007116646971553564,
0.0029762403573840857,
0.011449393816292286,
-0.012219217605888844,
0.012610306963324547,
0.010570473037660122,
0.06590437144041061,
-0.03391877934336662,
-0.00010486758401384577,
0.008096512407064438,
-0.021283000707626343,
0.051347266882658005,
-0.006998704746365547,
0.019017403945326805,
-0.04807524383068085,
-0.008006351999938488,
0.012260074727237225,
0.04304075241088867,
-0.012951909564435482,
0.08552602678537369,
0.05639149621129036,
-0.05657736584544182,
0.015755025669932365,
-0.035750776529312134,
0.002510582795366645,
-0.028140272945165634,
-0.05732414871454239,
0.04293295741081238,
0.011146738193929195,
-0.017286714166402817,
-0.07715152949094772,
0.04342003911733627,
-0.014070217497646809,
-0.06772276014089584,
0.0011630953522399068,
-0.01822471246123314,
0.021977027878165245,
-0.04331261292099953,
0.04940831661224365,
0.004276484251022339,
-0.04771416261792183,
-0.025570666417479515,
0.05888647958636284,
0.02429835870862007,
0.004246981348842382,
0.0499662347137928,
0.04018828272819519,
0.02312355302274227,
0.045978013426065445,
-0.032642662525177,
0.044121962040662766,
-0.03634895384311676,
0.0640399307012558,
0.06694835424423218,
0.0035049347206950188,
-0.0025518774054944515,
0.06541242450475693,
0.045168954879045486,
0.05180768296122551,
-0.02048608474433422,
-0.0096284756436944,
-0.055362600833177567,
-0.01740770787000656,
-0.0510147288441658,
-0.011749323457479477,
0.022648565471172333,
0.040247946977615356,
0.026751574128866196,
-0.048767294734716415,
0.046780019998550415,
-0.02289133332669735,
0.039990611374378204,
-0.022884095087647438,
-0.0025425488129258156,
0.0641787201166153,
-0.02664424106478691,
0.00906422920525074,
-0.018799545243382454,
-0.024278143420815468,
-0.03256813436746597,
-0.00865878164768219,
-0.03357473015785217,
0.05323400720953941,
0.008622064255177975,
0.01765134185552597,
-0.017641669139266014,
0.04987753555178642,
0.03882420063018799,
0.055109456181526184,
0.02036002092063427,
0.02783558890223503,
0.0017771179554983974,
-0.037897370755672455,
-0.02054428681731224,
-0.0036655087023973465,
0.012517477385699749,
0.010106341913342476,
-0.07286649197340012,
-0.0516633503139019,
0.021461866796016693,
-0.07651258260011673,
-0.007114998996257782,
0.01987389661371708,
-0.04972632974386215,
-0.058537643402814865,
-0.018575767055153847,
-0.03211120888590813,
-0.020275723189115524,
-0.004882782697677612,
0.01831706054508686,
-0.025937361642718315,
0.04075824096798897,
-0.014743008650839329,
0.038835786283016205,
0.038583580404520035,
-0.028761161491274834,
-0.010598880238831043,
0.030245298519730568,
0.010525575838983059,
-0.05848342180252075,
0.014369787648320198,
0.028678877279162407,
-0.020759068429470062,
-0.01934574544429779,
0.067352294921875,
0.036604247987270355,
-0.06352425366640091,
-0.034805163741111755,
-0.00635487912222743,
-0.024748647585511208,
-0.06189018487930298,
0.011334775015711784,
-0.07395507395267487,
0.0071675460785627365,
-0.03784216195344925,
-0.031085440889000893,
-0.03722793236374855,
-0.029115665704011917,
0.05082479119300842,
-0.0039294129237532616,
-0.04638347402215004,
0.034892793744802475,
0.04458632320165634,
0.0068845427595078945,
-0.017023056745529175,
0.01925768330693245,
-0.020275553688406944,
0.051067885011434555,
0.03744710609316826,
-0.0060004317201673985,
0.012842157855629921,
-0.05263485386967659,
0.013588201254606247,
0.03949366509914398,
-0.05530589073896408,
-0.01081531960517168,
0.06739407032728195,
-0.011095774360001087,
0.02482805959880352,
-0.01805928163230419,
0.017271999269723892,
0.006558185908943415,
0.034962210804224014,
0.0158474612981081,
0.051482681185007095,
-0.03931330144405365,
0.04612557962536812,
0.004406964872032404,
-0.020063325762748718,
-0.025393623858690262,
-0.019162515178322792,
0.056909795850515366,
0.0388132743537426,
-0.0039179627783596516,
-0.0549364797770977,
-0.013637712225317955,
-0.04610218480229378,
-0.013091214001178741,
-0.009861402213573456,
0.008953480049967766,
0.01830250583589077,
-0.06280552595853806,
-0.004279401618987322,
-0.017211532220244408,
-0.051073379814624786,
-0.0074585904367268085,
0.006804764270782471,
-0.02024245075881481,
-0.052060727030038834,
0.029366306960582733,
0.01634199172258377,
-0.012366208247840405,
0.03529909998178482,
0.011910750530660152,
-0.04416584596037865,
0.030111433938145638,
0.048252612352371216,
-0.040934234857559204,
-0.032339245080947876,
-0.003272115485742688,
-0.014151332899928093,
0.01449256855994463,
-0.0019995621405541897,
-0.016539856791496277,
0.010599943809211254,
-0.003347536316141486,
-0.011340375058352947,
0.010808760300278664,
0.040442466735839844,
0.013471318408846855,
0.007518854457885027,
0.002034911885857582,
0.0342789888381958,
0.025190630927681923,
-0.007352642714977264,
-0.0077864681370556355,
0.021895648911595345,
-0.011201526038348675,
-0.03509627282619476,
-0.012459032237529755,
-0.008522803895175457,
-0.002829210599884391,
-0.04330892488360405,
-0.024729134514927864,
-0.0272951852530241,
0.011270134709775448,
0.04116356372833252,
0.024852270260453224,
0.04701099172234535,
0.02039380371570587,
-0.024743955582380295,
0.050979141145944595,
-0.019176123663783073,
-0.005735374987125397,
0.04120879992842674,
0.03997782617807388,
-0.022427257150411606,
-0.012270750477910042,
-0.04759981483221054,
0.01061201747506857,
0.04517415910959244,
-0.027669604867696762,
0.015983860939741135,
0.026126913726329803,
0.024144066497683525,
-0.002302073407918215,
0.002565088216215372,
0.002693797694519162,
-0.016367819160223007,
-0.023336859419941902,
-0.004531447775661945,
0.07126682996749878,
0.018888071179389954,
0.025373557582497597,
0.009031654335558414,
-0.09010729193687439,
0.008595135994255543,
0.03409477695822716,
-0.04107162728905678,
-0.038623642176389694,
-0.041374921798706055,
0.01935664564371109,
0.03636500611901283,
-0.01873164251446724,
-0.025472356006503105,
-0.07018214464187622,
-0.0018890808569267392,
0.03600000962615013,
0.05762584134936333,
-0.018497420474886894,
-0.026529164984822273,
0.011320063844323158,
0.01803601160645485,
0.032350655645132065,
-0.006019099149852991,
-0.004686249420046806,
-0.034859415143728256,
0.011933623813092709,
0.0014384944224730134,
-0.000293686636723578,
-0.05477265268564224,
0.022958936169743538
] |
<p>Say that the airplane is going in 1000 km/h. On the side of the airplane, there is a 10x10 cm window. How much friction would this window cause. For the sake of the calculation, imagine that the airplane is infinitely long. The window is also perfectly level with the rest of the wall, and there is no turbulence on the side of the plane. The outside air is also standing perfectly still. The airplane is travelling at sea level.</p>
<p>I know it is neglectable compared to the turbulence etc. caused by the form of the airplane, but I really need the answer to the question.</p> | g7817 | [
0.08420606702566147,
0.06027213856577873,
-0.0074291955679655075,
0.024241099134087563,
0.022756531834602356,
-0.0009398586116731167,
0.09787828475236893,
0.05996386334300041,
-0.04683799296617508,
-0.03786924481391907,
-0.03074040450155735,
-0.017607012763619423,
-0.0435880608856678,
0.07753124088048935,
0.041137658059597015,
0.0031199371442198753,
-0.0006621434586122632,
-0.028211599215865135,
-0.008483385667204857,
-0.03271140903234482,
-0.035415541380643845,
-0.027763955295085907,
0.026195716112852097,
-0.014914173632860184,
-0.008423731662333012,
-0.02873326651751995,
-0.06155849248170853,
-0.033449869602918625,
-0.03890920802950859,
0.008020360954105854,
0.05753383785486221,
0.03842343017458916,
-0.0005236889701336622,
-0.08520470559597015,
-0.04305719956755638,
-0.028676612302660942,
0.019742758944630623,
0.018162213265895844,
-0.015161475166678429,
-0.0069680530577898026,
0.008614573627710342,
-0.04566541686654091,
0.007635656278580427,
-0.0001003079887595959,
-0.0037272791378200054,
0.029950836673378944,
-0.018614446744322777,
0.03996701538562775,
0.006303494330495596,
-0.002022405853495002,
-0.009820174425840378,
0.032627321779727936,
0.05206657201051712,
-0.007250053808093071,
-0.05835029482841492,
0.02840510383248329,
0.07097231596708298,
-0.022868948057293892,
0.003478705883026123,
0.07342289388179779,
0.012327194213867188,
-0.02440086007118225,
-0.09913097321987152,
0.01153082400560379,
-0.003065883181989193,
-0.02467595972120762,
-0.049840833991765976,
0.002772008301690221,
0.015403403900563717,
-0.0034388885833323,
0.06916039437055588,
-0.031015919521450996,
0.012779445387423038,
-0.023035908117890358,
-0.11369791626930237,
0.02957618050277233,
-0.021847115829586983,
0.026255760341882706,
0.08961212635040283,
0.03371259197592735,
0.006199299823492765,
-0.000274895312031731,
-0.039613571017980576,
0.005341217387467623,
0.09137219935655594,
0.016882317140698433,
0.04330509155988693,
-0.007955876179039478,
-0.013688924722373486,
-0.01714979112148285,
0.016034599393606186,
-0.04956541955471039,
0.03634557127952576,
-0.017423992976546288,
0.0454043447971344,
-0.01516907848417759,
0.01722649112343788,
0.06708578765392303,
-0.04300684854388237,
0.006841748952865601,
-0.03384416177868843,
-0.040620870888233185,
-0.019880499690771103,
0.022013604640960693,
0.03803359717130661,
-0.054002515971660614,
0.04928438737988472,
0.022121544927358627,
0.019163159653544426,
-0.06125975027680397,
0.0019175703637301922,
0.01569795049726963,
-0.043967925012111664,
0.025649696588516235,
0.03476046025753021,
-0.013992361724376678,
-0.00899600051343441,
0.024203579872846603,
-0.03600608557462692,
0.07296743988990784,
-0.009345241822302341,
0.01440420001745224,
0.011670410633087158,
0.011284693144261837,
0.04784374311566353,
0.002514277119189501,
-0.019016852602362633,
0.06085900589823723,
0.007805359084159136,
-0.025667203590273857,
0.009219327010214329,
0.046173784881830215,
-0.016719546169042587,
-0.008675660938024521,
0.014294284395873547,
0.029566951096057892,
-0.07228721678256989,
0.04180010408163071,
-0.039923399686813354,
0.02719777822494507,
0.0011470706667751074,
-0.0012530010426416993,
0.008594391867518425,
0.005958296824246645,
-0.054374463856220245,
0.004568241070955992,
0.008865873329341412,
0.013973570428788662,
0.02583387680351734,
-0.046633441001176834,
-0.016348717734217644,
0.014033394865691662,
-0.008217469789087772,
-0.02797868102788925,
-0.013052750378847122,
0.020021192729473114,
0.0009076361893676221,
0.002014682861045003,
0.030657198280096054,
0.06580790877342224,
0.04630715399980545,
-0.011623634956777096,
0.08415903151035309,
-0.014795999974012375,
-0.06917917728424072,
0.004010971635580063,
-0.04589118808507919,
0.01410672441124916,
-0.0052039832808077335,
0.01823054440319538,
-0.06116722896695137,
0.045894552022218704,
0.07999471575021744,
0.021742939949035645,
-0.004097211640328169,
0.03447699174284935,
0.04802922159433365,
-0.002064000116661191,
0.0625065416097641,
-0.04108183830976486,
0.014826442115008831,
0.016313055530190468,
0.01943126879632473,
-0.08709871023893356,
-0.002935343887656927,
-0.017953623086214066,
0.011446011252701283,
0.0037857890129089355,
-0.08349621295928955,
0.01668194867670536,
-0.006017056759446859,
-0.00039436077349819243,
-0.01970754936337471,
-0.023898087441921234,
-0.04297472536563873,
-0.019047411158680916,
0.02647755667567253,
-0.01717454008758068,
-0.024435758590698242,
-0.004260794725269079,
-0.038856975734233856,
-0.004296539351344109,
0.08875156193971634,
-0.03027946688234806,
-0.025611311197280884,
0.024758685380220413,
-0.010000411421060562,
-0.0067216502502560616,
-0.010426124557852745,
-0.0207695122808218,
0.012218235060572624,
0.00109872838947922,
-0.012260924093425274,
0.019739491865038872,
0.05925799906253815,
-0.04153243824839592,
-0.004307043273001909,
0.008864720351994038,
-0.03421347215771675,
0.006315398029983044,
0.021743880584836006,
0.009731422178447247,
-0.0027101438026875257,
-0.0032541477121412754,
-0.04784826934337616,
-0.009863175451755524,
-0.068998321890831,
-0.04052787646651268,
-0.010298777371644974,
0.05900425836443901,
-0.007594049442559481,
-0.03434053063392639,
-0.004863454960286617,
0.010380872525274754,
-0.002584286732599139,
0.06722141057252884,
0.02420804463326931,
0.06098015606403351,
0.012606724165380001,
-0.013094218447804451,
0.04207058250904083,
0.03192884474992752,
-0.05164036154747009,
-0.0240019578486681,
0.01059904508292675,
0.0029633601661771536,
-0.045650824904441833,
-0.02147604525089264,
0.004013702739030123,
0.06437648087739944,
0.00908354576677084,
-0.01568702608346939,
0.038949258625507355,
0.03278423100709915,
-0.00974448211491108,
-0.01002733875066042,
-0.019254134967923164,
-0.024458935484290123,
0.042702723294496536,
-0.012410599738359451,
-0.04098762571811676,
0.007615366484969854,
0.002420809119939804,
-0.018379202112555504,
-0.05356720834970474,
0.014343224465847015,
-0.043252527713775635,
0.03367776796221733,
0.03794474899768829,
-0.0028370770160108805,
0.0691303163766861,
0.04047456756234169,
0.030639640986919403,
0.05364209786057472,
0.07686840742826462,
-0.060987990349531174,
0.052548088133335114,
0.02584332786500454,
-0.028713848441839218,
0.005895871669054031,
-0.0054507083259522915,
0.03544674068689346,
-0.04526727646589279,
0.010762279853224754,
0.0291607528924942,
-0.017735907807946205,
0.003841160563752055,
0.1001480370759964,
0.005736821331083775,
0.04148678854107857,
-0.019528832286596298,
0.013389124535024166,
0.08107089251279831,
0.03814441338181496,
0.024124817922711372,
0.05799095332622528,
0.04900353029370308,
-0.045997798442840576,
-0.03202604502439499,
-0.05037091299891472,
0.00230520311743021,
-0.029737040400505066,
0.02612299844622612,
0.03613782674074173,
-0.00041842582868412137,
0.03125183656811714,
-0.022304242476820946,
-0.0645335465669632,
0.007242738269269466,
-0.02096710540354252,
-0.017754876986145973,
0.06107645481824875,
-0.026612576097249985,
-0.0033364850096404552,
-0.04883231222629547,
0.044988274574279785,
0.00659255962818861,
-0.011953992769122124,
0.031303152441978455,
0.042594533413648605,
-0.03357984870672226,
-0.058746643364429474,
0.030607003718614578,
-0.004428810905665159,
0.010617637075483799,
0.0389261320233345,
0.033049002289772034,
-0.01110931672155857,
-0.03353073075413704,
0.015828246250748634,
0.05012210085988045,
0.028225978836417198,
-0.0171829741448164,
-0.03836900740861893,
0.018099775537848473,
0.018308470025658607,
0.010896462947130203,
-0.01760270446538925,
0.0244816392660141,
0.0791226476430893,
-0.006675380282104015,
-0.06385445594787598,
0.004975785501301289,
-0.06026599928736687,
0.004986955784261227,
-0.0021708644926548004,
-0.006432907655835152,
-0.021463556215167046,
-0.0022595967166125774,
-0.0008181832381524146,
0.09965914487838745,
-0.05201749876141548,
-0.03183462470769882,
-0.07192251086235046,
0.013542665168642998,
0.05733776465058327,
-0.019539175555109978,
0.035908568650484085,
-0.038581836968660355,
-0.0059794713743031025,
0.006368231028318405,
-0.02972022257745266,
0.0117196561768651,
0.029088219627738,
-0.01907391846179962,
-0.037542980164289474,
-0.02977657876908779,
0.03393644839525223,
-0.012712201103568077,
-0.039842478930950165,
-0.02197105437517166,
-0.00981470663100481,
-0.048194848001003265,
0.0010078441118821502,
0.04231024533510208,
0.0273115336894989,
0.03755543753504753,
0.010232405737042427,
0.054983094334602356,
0.05029623210430145,
0.039221104234457016,
0.039658427238464355,
-0.04130357503890991,
0.03457530215382576,
0.04766906052827835,
0.02024546079337597,
-0.026682447642087936,
-0.008612055331468582,
0.05226742476224899,
0.005071731749922037,
0.008557239547371864,
-0.03752843663096428,
0.03768525272607803,
0.030279213562607765,
0.00407320074737072,
-0.010685487650334835,
-0.012907174415886402,
0.010697923600673676,
-0.02913881279528141,
0.00834929570555687,
0.1154482364654541,
0.009801029227674007,
-0.028275860473513603,
0.04970388114452362,
0.005896092392504215,
-0.006861564703285694,
0.024834221228957176,
-0.03541974350810051,
-0.009197425097227097,
0.013430172577500343,
0.03192424029111862,
-0.017007119953632355,
-0.05661313608288765,
-0.0675579383969307,
-0.03068828396499157,
0.0683709979057312,
0.007553314324468374,
0.013785039074718952,
0.05722788721323013,
-0.024939265102148056,
-0.022881966084241867,
0.09973622113466263,
-0.028339190408587456,
0.02660292573273182,
0.02010803483426571,
0.03290850669145584,
0.002669484121724963,
0.05615885183215141,
-0.03611238673329353,
-0.06102180853486061,
0.058204710483551025,
0.002132562454789877,
-0.0752352699637413,
0.018234029412269592,
-0.08042161166667938,
0.04351256042718887,
-0.013541939668357372,
0.0164007730782032,
0.00647386722266674,
-0.003628853475674987,
-0.06589863449335098,
0.05410021170973778,
0.03537896275520325,
0.03006419725716114,
-0.033593278378248215,
0.03405044972896576,
-0.0192229263484478,
-0.09372953325510025,
-0.0034075607545673847,
-0.023868726566433907,
-0.042943112552165985,
-0.019539060071110725,
-0.014066686853766441,
0.020279353484511375,
-0.05673275515437126,
0.012977197766304016,
-0.03869416192173958,
-0.02463897317647934,
0.01650891825556755,
0.010954550467431545,
-0.0216426532715559,
0.026906117796897888,
-0.03617033734917641,
0.052276499569416046,
0.006413811352103949,
-0.002360542071983218,
0.012791460379958153,
0.014831895008683205,
-0.08282584697008133,
0.013755482621490955,
0.04384149983525276,
0.0006640198407694697,
-0.0264742411673069,
0.06657206267118454,
0.016894234344363213,
0.010486314073204994,
-0.0014742284547537565,
0.015779415145516396,
0.005553227383643389,
-0.007397627457976341,
0.008941169828176498,
-0.004075800999999046,
0.014602039940655231,
0.02408323995769024,
0.03762218356132507,
-0.04988154396414757,
-0.06240851432085037,
0.004288787487894297,
0.01335261669009924,
-0.0133835319429636,
0.007517100777477026,
0.009141657501459122,
-0.09174921363592148,
-0.0075657726265490055,
-0.015609278343617916,
-0.03573065623641014,
-0.03239089250564575,
-0.03940803185105324,
0.03236404433846474,
-0.01336047612130642,
-0.016520828008651733,
-0.012291238643229008,
0.04192446172237396,
-0.029141433537006378,
-0.007713006343692541,
-0.03501599654555321,
-0.009760448709130287,
-0.03288703411817551,
0.0341004878282547,
0.1183597594499588,
-0.047236211597919464,
-0.012232042849063873,
0.006927771028131247,
-0.033870697021484375,
0.024814438074827194,
-0.05545486882328987,
-0.01477948110550642,
0.01779053546488285,
0.03367595747113228,
0.009809599258005619,
0.04081546142697334,
-0.027515577152371407,
-0.047884125262498856,
-0.006865284405648708,
-0.035728927701711655,
0.030513333156704903,
-0.08578993380069733,
-0.03452574834227562,
-0.008631480857729912,
-0.005800634156912565,
0.024653706699609756,
0.002839142456650734,
-0.013080430217087269,
-0.028796808794140816,
0.010306133888661861,
-0.0025885587092489004,
0.038921210914850235,
-0.05048542842268944,
0.033324189484119415,
0.005414177197962999,
-0.038963090628385544,
0.003002694807946682,
-0.009895974770188332,
0.08061975985765457,
0.020360035821795464,
-0.022764263674616814,
-0.024117516353726387,
0.028688570484519005,
0.009047998115420341,
-0.018936242908239365,
-0.04534050449728966,
0.04034649208188057,
-0.05563006177544594,
0.0007098504574969411,
-0.030020834878087044,
-0.00003816777461906895,
0.00386877846904099,
-0.04418089613318443,
0.042179882526397705,
-0.022431422024965286,
0.07687260210514069,
0.018567658960819244,
0.004164400510489941,
0.019932107999920845,
0.012826371006667614,
-0.013023055158555508,
-0.0008168614003807306,
-0.0012843760196119547,
0.06992822140455246,
0.051029548048973083,
-0.03621255233883858,
0.013069490902125835,
-0.01351157110184431,
0.00797356478869915,
0.09428580105304718,
0.05114704370498657,
0.035348694771528244,
-0.0165670458227396,
-0.05509229749441147,
0.04321518912911415,
-0.02324439212679863,
-0.005103837698698044,
-0.01025727204978466,
-0.029866738244891167,
0.003188526723533869,
-0.011545894667506218,
-0.01688832975924015,
-0.06504537165164948,
0.01853032037615776,
0.019269421696662903,
-0.08847476541996002,
-0.034486718475818634,
-0.013568295165896416,
-0.008725197054445744,
0.016361571848392487,
-0.04826175794005394,
0.01221076026558876,
0.036497101187705994,
-0.023777063935995102,
0.051144059747457504,
0.026910047978162766,
0.03447616100311279,
0.0014077834784984589,
-0.022004714235663414,
-0.015167922712862492,
0.00858931615948677,
0.06921941787004471,
0.02392643317580223,
0.016800863668322563,
0.01707291230559349,
0.020353073254227638,
0.01926785334944725,
0.03024027682840824,
-0.017444223165512085,
-0.10420293360948563,
-0.001273652771487832,
0.0065416558645665646,
-0.05298455059528351,
-0.025797303766012192,
-0.06025412306189537,
-0.009812098927795887,
-0.01026029884815216,
-0.019980859011411667,
-0.041293054819107056,
0.02043081447482109,
0.005140810273587704,
-0.06094382330775261,
0.016101049259305,
0.031328119337558746,
0.02650620974600315,
0.012540974654257298,
-0.020569439977407455,
-0.02575848624110222,
-0.0018669874407351017,
-0.015994591638445854,
-0.015096249990165234,
-0.10309742391109467,
-0.00744986766949296,
0.020982936024665833,
0.041030921041965485,
0.02879999950528145,
-0.0034062389750033617,
-0.011617201380431652,
-0.029763860628008842,
-0.02541409246623516,
-0.0369933620095253,
0.02969950996339321,
-0.021154485642910004,
0.005230305250734091,
-0.06332753598690033,
-0.03303937986493111,
-0.050571948289871216,
-0.01253541000187397,
0.04406094551086426,
0.003401347668841481,
0.02360115759074688,
-0.03321116045117378,
0.009729037992656231,
-0.02522573620080948,
-0.00218765065073967,
0.051896702498197556,
-0.010838356800377369,
-0.025638360530138016,
0.03555044159293175,
-0.026565320789813995,
0.019900549203157425,
0.003969531040638685,
-0.015614036470651627,
0.012035271152853966,
0.00790924672037363,
0.039826005697250366,
-0.05596839636564255,
-0.035088274627923965,
0.004237528890371323,
-0.011375407688319683,
0.04371950402855873,
-0.016913268715143204,
-0.032105494290590286,
0.029623033478856087,
0.02140660025179386,
0.06600791215896606,
-0.009848753921687603,
-0.021148160099983215,
-0.03184434399008751,
0.025856561958789825,
-0.02840256318449974,
0.026330772787332535,
-0.05042776092886925,
0.005029017571359873,
-0.05160585418343544,
-0.020937204360961914,
0.08420705795288086,
0.0008106885943561792,
-0.04858057200908661,
-0.045092806220054626,
0.027580024674534798,
0.0612257719039917,
-0.01869860477745533,
0.0016273332294076681,
0.0007763390312902629,
0.005389383994042873,
0.02319989912211895,
-0.01552529539912939,
-0.006184070836752653,
-0.01874200440943241,
0.023495476692914963,
0.022149916738271713,
0.0021543942857533693,
-0.03391163796186447,
-0.006681345868855715,
-0.003936074208468199,
0.018998997285962105,
0.030868172645568848,
-0.05621322616934776,
-0.012614738196134567,
-0.047788504511117935,
0.023310501128435135,
-0.07167185842990875,
-0.04885158687829971,
0.03290332853794098,
0.02935340255498886,
-0.01436284463852644,
-0.023951968178153038,
-0.08513645827770233,
0.02136380411684513,
0.00197565252892673,
-0.03154030069708824,
-0.04466329514980316,
-0.017950085923075676,
-0.04227360337972641,
0.03285699710249901,
-0.011735617183148861,
0.00860134419053793,
0.020003164187073708,
-0.056652508676052094,
-0.060378141701221466,
0.046783529222011566,
-0.04084938392043114,
0.011980668641626835,
0.013195544481277466,
-0.02435126341879368,
-0.011774306185543537,
0.00180511933285743,
-0.0255331601947546,
-0.02501056343317032,
-0.037708017975091934,
0.026675613597035408,
0.005752480588853359,
-0.0140170156955719,
-0.023249754682183266,
0.0028495562728494406,
0.03337542340159416,
-0.022448906674981117,
0.006798071321099997,
0.055020686239004135,
0.0033238818868994713,
0.007393793668597937,
-0.040231674909591675,
-0.04306034743785858,
-0.02164004184305668,
-0.0319991260766983,
-0.021126464009284973,
0.06721805781126022,
-0.003246571868658066,
0.00949412863701582,
-0.04457259178161621,
0.027632905170321465,
0.005713989492505789
] |
<p>This question is posed in the context of thermodynamics/statistical mechanics. Suppose we define the correlation length as the $\xi$ in the exponential factor $e^{-r/\xi}$ that appears in the correlation function $$C(r) = \langle m(0)m(r) \rangle - \langle m \rangle^2$$ (where $m$ is some relevant order parameter).</p>
<p>Then my question is: how can we, from this mathematical definition, argue the following two physical properties.</p>
<p><strong>Suppose we have our thermodynamic system and we take a chunk out of it with side-length L.</strong></p>
<ol>
<li>If $L > \xi$, the sample has the <strong>same</strong> qualitative behavior as the original sample;</li>
<li>If $L < \xi$, the qualitative behavior is <strong>different</strong>.</li>
</ol>
<p>If one can add extra conditions for these statements to be true, that would be nice/welcome.</p> | g7818 | [
0.07682272791862488,
-0.012045975774526596,
0.0016795048722997308,
-0.06245774030685425,
0.06605682522058487,
-0.002886147005483508,
-0.047321926802396774,
-0.039956968277692795,
-0.014798604883253574,
0.005680996458977461,
0.02314217947423458,
0.010286463424563408,
0.021409736946225166,
-0.00004424888174980879,
0.027022942900657654,
-0.0259384922683239,
0.07599973678588867,
-0.03641146421432495,
0.005438565276563168,
0.03261794149875641,
-0.05171908810734749,
-0.0016182446852326393,
0.008859552443027496,
-0.047003403306007385,
0.03386765345931053,
-0.10151289403438568,
0.0638665109872818,
0.0003148643590975553,
-0.09156941622495651,
-0.008495274931192398,
-0.03491944819688797,
-0.010205314494669437,
0.059018559753894806,
-0.06300925463438034,
-0.04608405381441116,
-0.02411467395722866,
0.06578381359577179,
0.013521290384232998,
0.028052063658833504,
-0.03877042979001999,
0.02120373584330082,
0.0014338591136038303,
0.06734886020421982,
0.0008777670445851982,
0.008544747717678547,
0.025748588144779205,
-0.013247930444777012,
0.04824237525463104,
-0.008800039999186993,
-0.015521942637860775,
-0.038897376507520676,
0.08280521631240845,
0.016878239810466766,
-0.017077377066016197,
0.008905364200472832,
0.0127622215077281,
0.06344680488109589,
0.05578437075018883,
0.01582181826233864,
0.05248377472162247,
0.010802248492836952,
-0.033235520124435425,
-0.006690548732876778,
0.015044148080050945,
0.04638418182730675,
-0.015660589560866356,
-0.01226234994828701,
0.010640790686011314,
-0.015923146158456802,
0.03821364417672157,
0.008232842199504375,
-0.06489887088537216,
-0.024211201816797256,
-0.0037178376223891973,
-0.033750563859939575,
0.015158448368310928,
-0.006052568554878235,
0.04794822633266449,
0.04850504547357559,
-0.00041676382534205914,
-0.08025112003087997,
-0.02262289635837078,
0.03642391040921211,
0.015421212650835514,
0.015358499251306057,
0.032001908868551254,
0.030961541458964348,
-0.005147727206349373,
-0.011951878666877747,
0.05370516702532768,
-0.04261785373091698,
-0.025620248168706894,
0.06120391935110092,
0.09306755661964417,
-0.025937655940651894,
-0.031201792880892754,
-0.009311646223068237,
0.0065385946072638035,
0.000017326397937722504,
0.01637224294245243,
-0.026712382212281227,
0.038529831916093826,
-0.01803080178797245,
-0.030094262212514877,
-0.04204612225294113,
-0.005775164347141981,
0.041336528956890106,
0.01282710675150156,
-0.06699821352958679,
-0.010320057161152363,
-0.022761961445212364,
-0.002428851556032896,
-0.0867716521024704,
-0.002971033798530698,
0.031930986791849136,
-0.027278395369648933,
0.061692945659160614,
-0.04087097570300102,
-0.032876890152692795,
0.028219062834978104,
-0.002684545936062932,
-0.028359007090330124,
0.07824301719665527,
0.03708638623356819,
-0.011510643176734447,
-0.018747320398688316,
0.05894152820110321,
0.024587111547589302,
0.056831832975149155,
-0.03332194685935974,
0.04282005876302719,
0.0007092226296663284,
-0.04646987095475197,
0.013623995706439018,
-0.0009360844269394875,
0.06339081376791,
0.04204992949962616,
0.07851497083902359,
-0.042744800448417664,
0.02111128903925419,
-0.05320614576339722,
-0.04148070514202118,
0.002099479315802455,
-0.003080721478909254,
-0.04274456948041916,
0.03471124544739723,
0.04164983704686165,
-0.03398667648434639,
-0.008991791866719723,
-0.0016342784510925412,
-0.019324496388435364,
0.048005055636167526,
-0.051141634583473206,
-0.02954971231520176,
-0.008624696172773838,
0.05073961988091469,
0.0009328697924502194,
-0.049720145761966705,
-0.006267091259360313,
0.001492440584115684,
-0.029592057690024376,
0.0295706819742918,
0.026331596076488495,
0.07620205730199814,
-0.03438575938344002,
0.02443685010075569,
-0.005868788808584213,
-0.033754702657461166,
-0.037584785372018814,
-0.026477878913283348,
-0.040575236082077026,
0.010162555612623692,
0.026095645502209663,
0.001478971797041595,
-0.02791125699877739,
0.047594763338565826,
0.026085838675498962,
-0.017878828570246696,
0.01709870621562004,
-0.048521488904953,
-0.055701930075883865,
0.06148606911301613,
0.019834134727716446,
0.01686822436749935,
-0.018449636176228523,
-0.015532489866018295,
0.035622935742139816,
0.04933347925543785,
-0.08098154515028,
0.006132178008556366,
-0.04292593523859978,
-0.002730430569499731,
-0.09004587680101395,
0.026557251811027527,
-0.026896817609667778,
-0.06368637830018997,
-0.005091021303087473,
-0.038104426115751266,
-0.02369401790201664,
-0.08913378417491913,
-0.009630955755710602,
0.002757878741249442,
0.05061592161655426,
0.03222551941871643,
0.02236035279929638,
-0.017954370006918907,
-0.06387732923030853,
0.01778331957757473,
-0.01319628395140171,
0.02051880583167076,
0.012050764635205269,
-0.03062089905142784,
-0.04812249913811684,
0.007013316731899977,
0.012975701130926609,
-0.032128676772117615,
-0.01447546761482954,
0.027383027598261833,
-0.005478446837514639,
0.052393630146980286,
-0.04608287289738655,
-0.01745404116809368,
-0.008944578468799591,
-0.014347339048981667,
-0.04042431339621544,
-0.008452232927083969,
-0.04208755120635033,
0.023669900372624397,
-0.031288377940654755,
0.02355431765317917,
-0.04589507728815079,
0.00974186323583126,
0.019832106307148933,
-0.04153308644890785,
0.01252343412488699,
0.020438123494386673,
-0.023730391636490822,
0.0036768177524209023,
0.016200421378016472,
0.05561158061027527,
0.021240506321191788,
0.017088383436203003,
-0.041437339037656784,
0.07508251816034317,
0.035713814198970795,
-0.0377400666475296,
0.05212973803281784,
0.016313446685671806,
0.0003107831871602684,
0.03038196451961994,
-0.02473766915500164,
0.06478659063577652,
-0.013915532268583775,
-0.028494596481323242,
0.008693057112395763,
-0.05002991482615471,
-0.021671799942851067,
0.06004481017589569,
0.004416248295456171,
-0.02488037571310997,
-0.016308216378092766,
-0.011634549126029015,
0.034510087221860886,
-0.0036075471434742212,
-0.009077428840100765,
-0.019522784277796745,
-0.09958148002624512,
0.014073911122977734,
-0.039767827838659286,
-0.016202257946133614,
-0.018302615731954575,
0.03359861299395561,
0.009792298078536987,
0.025402680039405823,
0.005126248579472303,
-0.013958411291241646,
0.0013483460061252117,
-0.032912205904722214,
0.07713503390550613,
-0.03594769164919853,
0.0455729179084301,
0.03090757317841053,
-0.04820188507437706,
0.06834004819393158,
0.08234347403049469,
-0.004603525623679161,
0.05400728061795235,
0.0076403431594371796,
-0.020250525325536728,
0.0030205263756215572,
-0.0493026077747345,
0.036340195685625076,
0.0064771235920488834,
0.03440960496664047,
-0.0146492850035429,
0.010982089675962925,
0.03901152312755585,
-0.058951497077941895,
-0.005339307710528374,
-0.004367162007838488,
0.015032259747385979,
-0.01635121926665306,
-0.032680995762348175,
0.03694644942879677,
0.05146808177232742,
0.04512008652091026,
-0.06558598577976227,
-0.026786554604768753,
0.00633796164765954,
0.015116539783775806,
0.02200411632657051,
0.04665300250053406,
0.04278867691755295,
0.018849456682801247,
-0.03511524572968483,
-0.024313732981681824,
-0.024614673107862473,
0.03302958607673645,
0.014711174182593822,
-0.04626328870654106,
0.015530463308095932,
-0.09223798662424088,
-0.006458485033363104,
-0.0003078964655287564,
0.026679713279008865,
-0.013640180230140686,
-0.0750655084848404,
0.007564424071460962,
-0.02388344518840313,
0.005802023224532604,
-0.01809653639793396,
-0.006343778222799301,
0.03007296286523342,
-0.059163570404052734,
-0.06553373485803604,
0.02889849618077278,
-0.03589169308543205,
-0.0129607068374753,
-0.012100676074624062,
-0.0014822834637016058,
0.018995001912117004,
-0.01247383188456297,
0.02234862744808197,
0.0957932397723198,
-0.06197325885295868,
-0.015606830827891827,
0.0037094191648066044,
0.03325638920068741,
0.05223967880010605,
-0.012005266733467579,
-0.03175688534975052,
-0.023928634822368622,
0.0051781306974589825,
0.03546067699790001,
0.004262892995029688,
0.022948436439037323,
0.05153018981218338,
0.024448756128549576,
0.038894541561603546,
-0.03440682590007782,
0.015544246882200241,
-0.06137413531541824,
0.051297109574079514,
-0.03749769553542137,
-0.028876125812530518,
0.07886362075805664,
-0.009102082811295986,
0.06892918795347214,
0.035319533199071884,
-0.01943015679717064,
0.04541413486003876,
-0.04972083121538162,
-0.004382118582725525,
-0.03246258944272995,
0.003957051318138838,
-0.030558960512280464,
0.027813468128442764,
0.01579604484140873,
-0.027505232021212578,
0.04605894908308983,
0.02903835102915764,
0.00489865941926837,
0.006374699994921684,
0.05232241377234459,
0.009417181834578514,
-0.0578492246568203,
-0.07006525248289108,
-0.016799598932266235,
0.0029108349699527025,
-0.038224682211875916,
-0.013492573983967304,
-0.03559131920337677,
-0.057508956640958786,
0.01272908877581358,
0.005991511978209019,
-0.025456627830863,
0.040961068123579025,
-0.027960024774074554,
0.01707613281905651,
0.04617743566632271,
-0.04688294604420662,
-0.02796129882335663,
0.032092008739709854,
-0.02603122964501381,
-0.026357391849160194,
-0.027076497673988342,
0.01236042845994234,
-0.04630906507372856,
0.006863092537969351,
-0.07376754283905029,
-0.053365062922239304,
-0.06673433631658554,
0.0028843586333096027,
-0.04432572051882744,
-0.038094211369752884,
0.006852274760603905,
0.023746734485030174,
0.004075114615261555,
0.01515217311680317,
-0.015484861098229885,
0.011871181428432465,
-0.01617027074098587,
-0.00446285679936409,
-0.00699090538546443,
-0.03336239606142044,
0.011593814939260483,
0.043940991163253784,
0.004057128448039293,
-0.02185858227312565,
-0.02001175656914711,
0.028537364676594734,
0.0281091146171093,
0.04416603967547417,
0.011185812763869762,
-0.05583173781633377,
0.009956291876733303,
-0.07805101573467255,
0.061902426183223724,
-0.03534022718667984,
0.03932305797934532,
0.005447429604828358,
-0.06574391573667526,
0.027902210131287575,
0.00979671347886324,
-0.001102619105949998,
0.002806935226544738,
0.02761826105415821,
-0.0385625995695591,
-0.05512584373354912,
-0.008036963641643524,
-0.013392120599746704,
0.011745324358344078,
-0.015633897855877876,
-0.05762844532728195,
0.007728442084044218,
-0.046475205570459366,
-0.028023695573210716,
0.009645210579037666,
0.02109534665942192,
-0.01329587958753109,
-0.03866714611649513,
-0.011649963445961475,
0.028973648324608803,
-0.009305142797529697,
-0.04117239639163017,
-0.02062428556382656,
-0.009249514900147915,
0.0013953348388895392,
-0.004960843827575445,
0.05999685078859329,
-0.027437839657068253,
0.0025477258022874594,
0.036436375230550766,
0.018792325630784035,
0.0089688990265131,
-0.040021758526563644,
-0.04450426995754242,
-0.02287236787378788,
-0.013358510099351406,
-0.052527740597724915,
0.020948484539985657,
-0.0013942241203039885,
0.02882363833487034,
-0.004842483904212713,
0.026709934696555138,
-0.06855610013008118,
-0.001360010588541627,
-0.05861153453588486,
-0.00435358751565218,
-0.0030214732978492975,
0.0039211418479681015,
0.024593470618128777,
0.028992198407649994,
0.06434746831655502,
-0.015043378807604313,
-0.014990553259849548,
0.02764112688601017,
0.0033011871855705976,
0.03183577582240105,
-0.026887595653533936,
-0.04062546789646149,
0.05753461644053459,
0.009156428277492523,
0.07875599712133408,
-0.018152516335248947,
0.04190800338983536,
0.02119104191660881,
0.0008136656251735985,
-0.04711807891726494,
-0.01583322510123253,
-0.013024386018514633,
0.06756782531738281,
0.02081478200852871,
-0.008711962029337883,
0.005922519136220217,
0.0360092930495739,
-0.0024975803680717945,
0.0071521843783557415,
-0.015411101281642914,
-0.025131529197096825,
0.05982721596956253,
-0.02242308296263218,
0.02361426316201687,
-0.013643793761730194,
-0.02855077013373375,
0.013735286891460419,
-0.03966867923736572,
-0.05929485335946083,
0.0293281152844429,
0.02385060489177704,
0.02249014377593994,
0.015249397605657578,
-0.01580631546676159,
0.016108542680740356,
-0.020157646387815475,
-0.015789028257131577,
0.014687775634229183,
-0.016500627622008324,
-0.0413789339363575,
-0.015656637027859688,
0.017915481701493263,
0.00901708472520113,
0.02351059392094612,
0.04205285385251045,
-0.0023600009735673666,
0.018351586535573006,
-0.019526556134223938,
-0.059141866862773895,
0.02527197077870369,
-0.025150440633296967,
-0.005693306215107441,
-0.011573596857488155,
-0.006465277634561062,
-0.000815870997030288,
0.04227614775300026,
0.04883008822798729,
0.013200553134083748,
0.006549865938723087,
0.004961030092090368,
0.030136171728372574,
-0.02726985514163971,
-0.016332922503352165,
0.056871287524700165,
0.0038369896356016397,
0.008676717057824135,
-0.06970494240522385,
0.008044760674238205,
-0.025164121761918068,
-0.006929285358637571,
0.07648462057113647,
0.03059232421219349,
0.0017832921585068107,
0.05464663729071617,
0.02866297774016857,
0.015922382473945618,
0.025299180299043655,
-0.015213229693472385,
-0.0015183798968791962,
0.006221608724445105,
-0.025956042110919952,
-0.05508041754364967,
-0.0018733363831415772,
-0.01990179903805256,
-0.025501670315861702,
0.000439412280684337,
0.047969751060009,
0.005155152175575495,
0.006300428416579962,
0.008578022010624409,
-0.034913744777441025,
-0.08867856115102768,
-0.03160451352596283,
-0.05453525856137276,
-0.05249238759279251,
-0.023639829829335213,
0.005394694861024618,
0.01740899682044983,
-0.03208409622311592,
-0.047986339777708054,
0.05109564960002899,
0.030157385393977165,
0.04652553051710129,
0.04349218308925629,
-0.03753918409347534,
-0.012620539404451847,
0.0346452072262764,
-0.01738535799086094,
0.026775678619742393,
0.01369373220950365,
0.01436184998601675,
-0.01691199280321598,
0.009117331355810165,
0.016631178557872772,
-0.00166589324362576,
-0.009505503810942173,
-0.05362223833799362,
-0.003442418994382024,
0.01287657581269741,
-0.012565698474645615,
0.02999073453247547,
0.015256891958415508,
0.013569209724664688,
-0.017021967098116875,
-0.05029774829745293,
0.021773355081677437,
0.06347188353538513,
-0.04587849602103233,
0.0360773503780365,
0.041544631123542786,
-0.05752195790410042,
0.019182195886969566,
0.022020559757947922,
0.026540756225585938,
0.04419693350791931,
-0.0280892513692379,
0.06044613942503929,
-0.073407843708992,
0.01704017072916031,
0.06704851984977722,
0.017696088179945946,
-0.006848067976534367,
0.038498349487781525,
-0.02307944744825363,
-0.013279102742671967,
-0.037956103682518005,
-0.028620490804314613,
0.031966205686330795,
0.018468908965587616,
-0.0882730782032013,
0.018136119470000267,
0.01827741041779518,
0.03795789182186127,
-0.09795724600553513,
0.004318624269217253,
0.004501756746321917,
0.014074829407036304,
0.010399159044027328,
0.02069348841905594,
0.039214782416820526,
-0.04118744656443596,
-0.02191457524895668,
-0.023051539435982704,
-0.010815818794071674,
-0.017377683892846107,
-0.06001034006476402,
0.05745329707860947,
0.02796962298452854,
-0.08015213161706924,
0.02190503291785717,
0.004839184693992138,
0.03741670027375221,
-0.03983430191874504,
0.006647316738963127,
0.0066591426730155945,
-0.00672922795638442,
0.004444113466888666,
0.0364065021276474,
0.010884239338338375,
0.0279336366802454,
0.00907136034220457,
0.033632390201091766,
0.023969918489456177,
0.004432449117302895,
0.004038325510919094,
-0.08419248461723328,
0.03488568961620331,
-0.019689124077558517,
0.028986573219299316,
0.04379403218626976,
-0.006228956859558821,
-0.026524581015110016,
0.019782666116952896,
-0.04716421663761139,
0.04572804644703865,
-0.0009387578465975821,
0.028158996254205704,
0.047061488032341,
-0.006275220308452845,
0.0066507416777312756,
0.06616204231977463,
0.10482970625162125,
0.06389126926660538,
-0.009893505834043026,
0.02521258406341076,
0.03395897150039673,
0.01509882789105177,
0.0330221951007843,
-0.045293547213077545,
-0.07024583965539932,
0.021568283438682556,
0.011283338069915771,
-0.016871420666575432,
0.05526679381728172,
0.025025134906172752,
0.0760219544172287,
-0.020155830308794975,
0.006435979623347521,
-0.015307244844734669,
0.040654391050338745,
-0.009987249039113522,
-0.08065624535083771,
-0.06689292192459106,
-0.05861103534698486,
-0.04477689042687416,
-0.0382029227912426,
-0.033285267651081085,
-0.0023818945046514273,
0.013912132941186428,
-0.035902198404073715,
0.05415957048535347,
0.015216544270515442,
0.013497209176421165,
-0.0036615387070924044,
0.028011789545416832,
-0.007792739197611809,
0.03179055079817772,
-0.0016029971884563565,
0.05689385160803795,
-0.030291683971881866,
0.006254559848457575,
-0.011879203841090202,
-0.020983779802918434,
0.009298546239733696,
-0.03891400992870331,
0.002980694640427828,
-0.09147961437702179,
-0.040231164544820786,
0.05842283368110657,
0.040007997304201126,
-0.002707598265260458,
-0.058991238474845886,
0.03319394960999489,
-0.01344559621065855,
0.06676078587770462,
0.009397726505994797,
0.0005596124683506787,
0.007656781934201717,
0.032049283385276794,
0.0038099545054137707,
0.015302921645343304,
0.02454334869980812,
0.012210222892463207,
-0.04136854037642479,
-0.007769295945763588,
-0.042548298835754395,
0.05189921706914902,
-0.03965843841433525,
0.04401816427707672
] |
<p>Consider a parallel-plate capacitor in free space. A negatively charged point particle with initial velocity $v$ passes through the space between the pair of parallel plates (with an initial path perpendicular to the normal vector of the plates). </p>
<p>The point particle accelerates towards the positively charged plate but passes beyond the edge of the plate. </p>
<p>How is energy conserved, given that the capacitor does work on the particle by accelerating it in the direction towards the negatively charged plate?</p>
<p>EDIT: Was reminded by Art Brown that a negatively charged particle accelerates towards the positive plate.</p> | g7819 | [
0.1139797568321228,
0.06642348319292068,
0.0006509156664833426,
0.0318523608148098,
0.06011340022087097,
0.039966877549886703,
0.023216497153043747,
0.005114399828016758,
-0.0605238638818264,
-0.018513893708586693,
-0.014702674001455307,
0.07759196311235428,
-0.007193084806203842,
0.0023460632655769587,
0.03385477885603905,
0.011341323144733906,
0.09644798189401627,
0.03350101411342621,
0.017107663676142693,
0.07857568562030792,
-0.022981666028499603,
-0.015334626659750938,
-0.02424005977809429,
-0.012211360037326813,
0.008902125991880894,
-0.020681865513324738,
-0.022699538618326187,
-0.07411988824605942,
-0.048284392803907394,
-0.04990897327661514,
0.04466007649898529,
-0.006660195533186197,
0.03823420777916908,
-0.017937328666448593,
-0.016235124319791794,
-0.009094963781535625,
0.07465074211359024,
0.02232959121465683,
0.014327737502753735,
0.010164118371903896,
0.013674168847501278,
-0.029958443716168404,
0.04295678436756134,
-0.02648513950407505,
0.06377367675304413,
-0.013208778575062752,
-0.049304842948913574,
-0.06721140444278717,
-0.053074441850185394,
-0.059341199696063995,
-0.020612206310033798,
0.06831183284521103,
-0.026056518778204918,
0.020467493683099747,
0.011626416817307472,
0.005207263398915529,
-0.010607362724840641,
-0.008740211836993694,
0.05161682888865471,
0.043777476996183395,
-0.022267844527959824,
0.04347333684563637,
0.015711279585957527,
0.020313823595643044,
0.07728002220392227,
-0.03477179631590843,
-0.023550618439912796,
0.020282449200749397,
0.05260616913437843,
0.03628091886639595,
0.03461283817887306,
-0.0333445705473423,
-0.022022590041160583,
-0.041112273931503296,
0.02976527437567711,
-0.004341418389230967,
-0.00792414415627718,
-0.031166499480605125,
0.002738193143159151,
0.0025824527256190777,
-0.1019764393568039,
-0.021248705685138702,
0.019299330189824104,
-0.04249311983585358,
0.01842108741402626,
-0.0012920929584652185,
0.01477422658354044,
-0.009226004593074322,
-0.0878491923213005,
-0.05647663399577141,
0.021362775936722755,
-0.02154507301747799,
0.03844186291098595,
-0.005541385617107153,
-0.017621902748942375,
0.024633249267935753,
-0.0340859554708004,
0.04003087431192398,
0.006980066187679768,
-0.0241946280002594,
0.006774712819606066,
-0.013324418105185032,
0.015411799773573875,
0.010080329142510891,
0.04097823426127434,
0.006962466519325972,
0.06802631169557571,
-0.006387327332049608,
0.03665982186794281,
-0.043911807239055634,
0.045201029628515244,
-0.0940750315785408,
-0.01113327406346798,
-0.0558067262172699,
-0.018384147435426712,
-0.039780449122190475,
0.0942588672041893,
-0.018090957775712013,
0.02198886312544346,
0.06696096807718277,
0.006164266727864742,
0.03486134856939316,
-0.02124851569533348,
0.043410636484622955,
-0.015404490754008293,
0.010979954153299332,
0.03366187959909439,
0.0018892980879172683,
0.011650101281702518,
0.06468848139047623,
0.008826712146401405,
-0.025046823546290398,
-0.005301058292388916,
0.014057140797376633,
-0.04735946282744408,
-0.01755421981215477,
0.008547571487724781,
0.025311516597867012,
0.0382470041513443,
0.010501915588974953,
0.0024978111032396555,
-0.019178016111254692,
-0.0035991370677948,
-0.007286966312676668,
-0.008878924883902073,
-0.006774780340492725,
-0.022469263523817062,
-0.06000196933746338,
0.04981812834739685,
0.040839970111846924,
0.031028911471366882,
0.0891040489077568,
-0.0017192959785461426,
0.01479301042854786,
0.05869659408926964,
-0.0010378677397966385,
0.0965605154633522,
-0.009173248894512653,
0.037670791149139404,
-0.0016933665610849857,
0.06254786252975464,
0.010026946663856506,
0.0009785782312974334,
0.005445457063615322,
-0.04665980488061905,
-0.04725139960646629,
0.02280779741704464,
-0.05122927203774452,
-0.001485454966314137,
0.01013497170060873,
-0.005230790004134178,
-0.0555325448513031,
0.03150181099772453,
0.04177580028772354,
-0.0026646852493286133,
0.009047208353877068,
-0.042807791382074356,
-0.00807182490825653,
-0.019587211310863495,
-0.008179797790944576,
-0.05282578989863396,
-0.05667780339717865,
0.03850719705224037,
-0.0062073515728116035,
0.04826873540878296,
0.03799118846654892,
-0.012884974479675293,
0.0666949450969696,
-0.003159641521051526,
0.007931241765618324,
0.007304028142243624,
-0.008171920664608479,
-0.04263593256473541,
0.008588021621108055,
-0.044011183083057404,
-0.022809593006968498,
0.06482652574777603,
-0.02969919517636299,
0.014597509056329727,
-0.009468837641179562,
-0.010554217733442783,
0.038328006863594055,
0.053947485983371735,
0.05091490224003792,
0.05671925097703934,
-0.06396034359931946,
-0.0002399864315520972,
-0.021585652604699135,
0.028062036260962486,
-0.00791711825877428,
-0.0042073652148246765,
0.05954313650727272,
-0.03172740712761879,
-0.021612385287880898,
0.03398074209690094,
-0.07465645670890808,
-0.04948113113641739,
0.02869202010333538,
-0.04115535318851471,
-0.0026954503264278173,
-0.07383041083812714,
-0.03286554664373398,
0.032781969755887985,
-0.01562698744237423,
-0.048853617161512375,
0.04609447345137596,
-0.0016974577447399497,
-0.03406519070267677,
-0.05546579882502556,
0.03278491273522377,
-0.10304802656173706,
0.04015614092350006,
-0.02729368954896927,
-0.045713309198617935,
0.03663359954953194,
0.023990917950868607,
0.017050713300704956,
0.032458625733852386,
-0.02848043292760849,
0.0038946904242038727,
0.01661236211657524,
-0.0454336553812027,
-0.006619878113269806,
0.027947718277573586,
-0.04137689992785454,
-0.03117123618721962,
0.03257090225815773,
-0.007330054417252541,
-0.043733466416597366,
-0.03834378346800804,
0.05342824384570122,
0.028848031535744667,
0.01098916307091713,
0.026314809918403625,
0.016035960987210274,
-0.02986074984073639,
-0.054688263684511185,
0.01833023503422737,
-0.03661242872476578,
-0.05852898210287094,
0.02749796025454998,
-0.015059509314596653,
-0.07490682601928711,
0.016891518607735634,
0.009411482140421867,
0.028916116803884506,
-0.0059407842345535755,
0.008642368949949741,
0.056897953152656555,
0.006896280683577061,
-0.004145350772887468,
0.0785173624753952,
0.01696973666548729,
0.003478760365396738,
-0.005068533588200808,
-0.04612966999411583,
0.025824489071965218,
-0.04950081184506416,
-0.00043496457510627806,
-0.001865454949438572,
0.01280156522989273,
0.013637775555253029,
-0.03204963356256485,
-0.023399563506245613,
0.017487579956650734,
-0.0559612475335598,
0.02880745381116867,
-0.041836027055978775,
-0.024482078850269318,
-0.011252435855567455,
-0.05035294592380524,
-0.0030471552163362503,
0.04283194616436958,
-0.050450097769498825,
0.09545224159955978,
0.03548915311694145,
0.05175777152180672,
-0.045898668467998505,
-0.0551891066133976,
0.02792968973517418,
-0.013478235341608524,
-0.05101916566491127,
-0.04079883173108101,
0.03384881839156151,
0.05870772898197174,
0.053516145795583725,
-0.04588288441300392,
-0.03542030602693558,
0.0220513753592968,
0.027257606387138367,
-0.0147194629535079,
0.04021758586168289,
-0.024857671931385994,
-0.0016348998760804534,
-0.015299864113330841,
-0.021829398348927498,
-0.01533624529838562,
-0.010461983270943165,
-0.055653464049100876,
0.0017467101570218801,
0.0044546667486429214,
-0.01374080404639244,
0.028072724118828773,
0.04912790283560753,
-0.032220207154750824,
-0.002773866057395935,
-0.03384783864021301,
0.0003132558485958725,
-0.008496399968862534,
0.007745762355625629,
0.013523797504603863,
0.05579632520675659,
0.030511317774653435,
-0.014259112998843193,
0.00246162130497396,
-0.08047515153884888,
-0.004827052354812622,
0.038536570966243744,
0.06339805573225021,
0.0010224217548966408,
0.007508159149438143,
-0.02547161839902401,
-0.045387301594018936,
-0.0461769700050354,
0.005127490498125553,
0.01189885288476944,
0.05093707889318466,
0.0073981983587145805,
0.033131614327430725,
-0.019096018746495247,
0.06353688985109329,
-0.01758970133960247,
0.005543752107769251,
-0.015793129801750183,
-0.062498003244400024,
0.016581475734710693,
-0.014238555915653706,
0.01912158727645874,
-0.052837539464235306,
0.05273081734776497,
-0.010750486515462399,
-0.03105764463543892,
0.01935269497334957,
0.023526575416326523,
-0.008977361023426056,
0.0004746348422486335,
-0.035596784204244614,
0.01248679868876934,
-0.013977495022118092,
-0.03407258912920952,
0.004310494754463434,
-0.04629671201109886,
-0.006219676695764065,
0.05554239824414253,
0.009238721802830696,
-0.016491815447807312,
-0.006581878289580345,
-0.013285734690725803,
-0.0367850735783577,
0.03503861650824547,
0.0031268158927559853,
-0.04851916804909706,
-0.04392147809267044,
-0.02186630293726921,
0.01100066676735878,
0.05648450553417206,
-0.011527557857334614,
0.019660666584968567,
-0.0162158515304327,
-0.020025454461574554,
0.0376371331512928,
-0.04093995690345764,
-0.024705806747078896,
-0.05699304863810539,
0.03968484699726105,
-0.014153572730720043,
-0.0037086515221744776,
-0.007532282266765833,
0.040006622672080994,
-0.006698242854326963,
-0.02046290971338749,
0.03495574742555618,
-0.03882289677858353,
-0.04577656090259552,
-0.00938709732145071,
0.003975562285631895,
0.0009759239619597793,
-0.006401315331459045,
-0.03749570623040199,
0.015430633910000324,
-0.011832313612103462,
-0.0411737859249115,
-0.0515623576939106,
-0.016043471172451973,
-0.04065556451678276,
-0.026348469778895378,
0.006066874135285616,
0.053931962698698044,
0.04352652281522751,
0.020491737872362137,
0.022360749542713165,
-0.013466984033584595,
-0.005658969283103943,
-0.03711800277233124,
0.034111011773347855,
0.08481206744909286,
0.05130160599946976,
0.002157338196411729,
-0.02451949566602707,
-0.016172202304005623,
0.00329027371481061,
0.05090739578008652,
-0.0037157367914915085,
0.027393169701099396,
-0.030257973819971085,
0.0623154491186142,
-0.028051773086190224,
0.029788438230752945,
0.012499876320362091,
0.08265329897403717,
0.059129748493433,
-0.047174837440252304,
0.0003917099966201931,
-0.04725782573223114,
0.009455982595682144,
0.05278928950428963,
-0.012529132887721062,
-0.013948940671980381,
0.007120219059288502,
-0.06401374936103821,
-0.021141985431313515,
0.006877847481518984,
-0.054316598922014236,
-0.0017649070359766483,
0.014719146303832531,
-0.00416282145306468,
-0.0027950257062911987,
0.008845988661050797,
0.03473944962024689,
0.03617881238460541,
-0.03515046089887619,
0.010689972899854183,
0.0014244718477129936,
0.0020680867601186037,
-0.017857318744063377,
0.022134913131594658,
0.008657866157591343,
-0.03620808571577072,
-0.030618395656347275,
0.022830139845609665,
0.041763849556446075,
0.042158342897892,
-0.04371538385748863,
0.0210052952170372,
0.033034857362508774,
-0.025241944938898087,
-0.02494298480451107,
0.017112353816628456,
-0.044245876371860504,
-0.017845330759882927,
-0.0004884466761723161,
0.015999482944607735,
-0.011255260556936264,
-0.027309753000736237,
-0.021882327273488045,
-0.00010142941755475476,
-0.07865595072507858,
0.03694252297282219,
-0.04112311825156212,
-0.026318836957216263,
-0.03634421154856682,
0.041903819888830185,
0.016246750950813293,
0.06109200790524483,
0.04051768407225609,
0.024245047941803932,
-0.012992357835173607,
0.006974407006055117,
-0.016895651817321777,
-0.019312182441353798,
-0.0812535360455513,
-0.07095471769571304,
-0.0019393537659198046,
-0.025284936651587486,
-0.020072946324944496,
0.06764749437570572,
0.060708239674568176,
-0.014164423570036888,
0.00368950585834682,
-0.0013732323423027992,
-0.0228958148509264,
0.018696701154112816,
0.05868305638432503,
-0.00010916748578893021,
0.006511121056973934,
0.006777371279895306,
-0.02627905271947384,
-0.0357777364552021,
-0.0535130612552166,
0.002502559684216976,
0.09074810892343521,
0.016441574320197105,
0.0054716067388653755,
0.04742446169257164,
0.011075099930167198,
0.026171023026108742,
-0.02489078976213932,
0.004907584749162197,
-0.00449187820777297,
0.03711416944861412,
0.05151141807436943,
-0.05147310718894005,
-0.04703628271818161,
0.03287360817193985,
-0.04763833060860634,
-0.031062329187989235,
-0.04370842128992081,
-0.021552985534071922,
0.04105116054415703,
-0.006194370333105326,
-0.04224306717514992,
-0.05029623210430145,
0.055913981050252914,
0.08475189656019211,
-0.04768340662121773,
0.010572768747806549,
-0.061229463666677475,
0.0058546848595142365,
0.011047990061342716,
-0.08765579015016556,
-0.0472547747194767,
-0.035611968487501144,
0.03999136760830879,
-0.01705103926360607,
0.04110798239707947,
-0.018913976848125458,
0.062343522906303406,
-0.03863499313592911,
0.030643483623862267,
-0.06945216655731201,
0.01051678229123354,
-0.02142672799527645,
0.03727574273943901,
0.022844869643449783,
0.028699146583676338,
-0.001792382332496345,
0.06864225119352341,
-0.01100454106926918,
0.05369814485311508,
-0.018892372027039528,
0.008846075274050236,
0.01459792722016573,
-0.019802151247859,
0.014231720007956028,
0.02413896657526493,
0.022429315373301506,
-0.008706152439117432,
0.020322054624557495,
-0.10201666504144669,
0.013701523654162884,
-0.0011427965946495533,
0.031059931963682175,
-0.03353437781333923,
-0.07663439214229584,
-0.023462366312742233,
0.05365448072552681,
0.030027354136109352,
-0.04645927622914314,
0.0843357965350151,
0.003056753659620881,
-0.01551168691366911,
-0.05922488495707512,
0.058473315089941025,
0.00305281113833189,
-0.02202858217060566,
-0.008640766143798828,
-0.016671976074576378,
-0.000934434647206217,
-0.05211522802710533,
0.05021413043141365,
0.011022299528121948,
-0.030570125207304955,
-0.044789496809244156,
-0.06169005483388901,
0.023288948461413383,
-0.04082083702087402,
0.009233484975993633,
0.03063865192234516,
-0.043405164033174515,
0.012367228046059608,
-0.0705699473619461,
0.03489316254854202,
0.05402945354580879,
-0.011398285627365112,
-0.02491180971264839,
0.017360175028443336,
0.015925031155347824,
-0.019650539383292198,
-0.0248597152531147,
0.03933294862508774,
0.04719290882349014,
0.015197383239865303,
-0.05435671657323837,
0.006827651057392359,
0.012659675441682339,
-0.05204448848962784,
0.01115232054144144,
0.030417675152420998,
0.050369780510663986,
0.0037894132547080517,
-0.023535674437880516,
0.05579698458313942,
-0.016781935468316078,
0.03912338614463806,
0.03234678506851196,
0.0029573868960142136,
-0.030964655801653862,
0.028444185853004456,
0.004047771450132132,
-0.02597164921462536,
0.0013308846391737461,
0.025198139250278473,
-0.03383524715900421,
0.03624562919139862,
-0.05640357732772827,
0.03301962837576866,
0.0282791368663311,
0.023730341345071793,
-0.011631108820438385,
-0.0370682068169117,
-0.020656028762459755,
-0.0012193744769319892,
-0.04624152556061745,
0.01720346137881279,
-0.016475388780236244,
0.000850668060593307,
0.03556504845619202,
0.054037146270275116,
-0.0011396413901820779,
0.005908913444727659,
-0.010898669250309467,
-0.05378418788313866,
0.039820123463869095,
0.01626095362007618,
0.018439045175909996,
-0.0005819722427986562,
-0.03135080635547638,
0.005048049613833427,
0.009223691187798977,
-0.03911146521568298,
-0.013362685218453407,
-0.022277122363448143,
-0.06632398068904877,
0.022313781082630157,
0.035284534096717834,
0.02754184417426586,
-0.027631321921944618,
-0.015029381029307842,
-0.01883687451481819,
0.01903577521443367,
0.02871905080974102,
-0.003273031674325466,
-0.000627326313406229,
-0.024652043357491493,
-0.031851738691329956,
0.007288977969437838,
-0.007627155631780624,
-0.0013762599555775523,
0.007793109863996506,
-0.014881439507007599,
-0.03963693231344223,
-0.029953215271234512,
0.08730066567659378,
-0.04686117544770241,
0.01638275757431984,
0.014578130096197128,
0.011869707144796848,
0.02832387574017048,
-0.053785812109708786,
0.030806148424744606,
0.020454607903957367,
-0.033509738743305206,
0.05559082329273224,
0.06827700138092041,
0.009115145541727543,
-0.005300296936184168,
-0.011944261379539967,
-0.09733536094427109,
-0.018530113622546196,
-0.005345485173165798,
-0.005309639498591423,
0.025486066937446594,
0.001195242046378553,
-0.00291987182572484,
0.03844314068555832,
-0.030069060623645782,
-0.018127741292119026,
0.030524009838700294,
-0.0046437205746769905,
0.0344526581466198,
0.01738411746919155,
-0.016679001972079277,
0.00018076506967190653,
-0.04990089312195778,
0.061674490571022034,
-0.024732518941164017,
0.019581705331802368,
0.02589857578277588,
0.01656753569841385,
-0.019207412376999855,
-0.018945055082440376,
0.0195015762001276,
0.012521899305284023,
0.022347871214151382,
-0.0036679354961961508,
-0.0021994002163410187,
0.04015432298183441,
0.014892653562128544,
-0.005109497345983982,
0.004796807654201984,
-0.018232712522149086,
-0.05933774635195732,
0.005265203770250082,
-0.04055672511458397,
-0.05294123291969299,
0.008457504212856293,
0.01013999991118908,
0.02091856114566326,
0.06029767170548439,
-0.026651527732610703,
0.05939488112926483,
-0.04807061702013016,
-0.055448222905397415,
0.013513400219380856,
0.015415051952004433,
-0.052723050117492676,
0.05101658031344414,
0.016690270975232124,
0.0341288223862648,
-0.012781528756022453,
-0.02001224458217621,
-0.018724313005805016,
0.007776434998959303,
-0.056310608983039856,
0.004179096315056086,
-0.054892461746931076,
-0.02443094365298748,
0.011748041026294231
] |
<p>Two open-car trains approach each other at fixed velocities. Each has a radar to see how quickly the other train is approaching, but apart from that the trains have no <em>a priori</em> knowledge of each other.</p>
<p>Each train has engineers on its first and last cars. Each engineer has an atomic clock and a laser for communicating with their partner on the same train. Long before the trains meet, the engineers on each train use their lasers to adjust their relative separations to exactly one kilometer. Using the synchronization procedure first defined by Einstein, the engineers also exchange time data and use it to adjust their atomic clocks until they are precisely synchronized within their shared frame.</p>
<p>The trains meet. The clocks are positioned so that they almost touch as they pass. At the moment of nearest contact, they exchange and record each other's values (timestamps).</p>
<p>Some time later, the clocks on the trailing cars meet and perform the same procedure.</p>
<p>The delay between the leading and trailing data events can now be measured in two ways.</p>
<p>If the two timestamps taken from the first train are compared, the result is the time between the events as measured from the first train. This value is meaningful because the engineers on that train previously synchronized their clocks and stayed within the same frame of reference at all times. If the timestamps from the second train are used, a similar but distinct measurement of the time between the two events can be obtained.</p>
<p>Now, three questions:</p>
<ol>
<li><p>Is there anything wrong or impossible with this experimental setup? If so, what is it?</p></li>
<li><p>If you accept the experiment as realistic and meaningful, will the delays calculated from the perspective of each of the two trains be the same, or different?</p></li>
<li><p>If you answered "different," what is the correct procedure for predicting in advance what the ratio of the two delays will be?</p></li>
</ol>
<hr>
<p><strong>2013-01-10 - The Answer(s!)</strong></p>
<p>I awarded the bounty to @FrankH for pages of excellent and educational work worth of reading by anyone who wants to understand special relativity better.</p>
<p>However, I've also taken the unusual step of re-allocating the <em>answer</em> designation to @MatthewMcIrvin.</p>
<p>There are two reasons: (1) Matthew McIrvin was the first one to spot the importance of the symmetric-velocities frame, which others ended up gravitating (heh!) to; and (2) Matthew's answer is <em>short</em>, which is great for readers in a hurry. FrankH, sorry about the switch, but I didn't realize I could split them before.</p>
<p>So: If you are not overly familiar with special relativity and want to understand the full range of issues, I definitely recommend FrankH's answer. But if you already know SR pretty well and want the key insights quickly, please look at Matthew McIrvin's answer.</p>
<p>I will have more "proximate data exchange" SR questions sometime in the near future. Two frames turns out to be a very special case, but I had to start somewhere.</p>
<hr>
<p>For folks with strong minds, stout hearts, and plenty of time to kill, a much more precise version of the above question is provided below. It requires new notations, alas. </p>
<p>To reduce the growing size of this question, I have deleted all earlier versions of it. You can still find them in the change history.</p>
<hr>
<p><strong>Precise version of the 4-clock conundrum</strong></p>
<p>Please see the first three figures below. They define two new operators, the frame view and clock synchronization operators, that make the problem easier to state precisely:</p>
<hr>
<p><img src="http://i.stack.imgur.com/JTWkQ.png" alt="Setup of the four-clock conundrum using the frame operators"></p>
<hr>
<p><img src="http://i.stack.imgur.com/347QJ.png" alt="Event T1: Leading edge clocks A1 and B1 pass very closely"></p>
<hr>
<p><img src="http://i.stack.imgur.com/EVZtI.png" alt="Event T2: Trailing edge clocks A2 and B2 pass very closely"></p>
<hr>
<p>Note that the four timestamps $\{T_{A1}, T_{B1}, T_{A2}, T_{B2}\}:>\{A,B\}$. That is, the four timestamps are shared and agreed to (with an accuracy of about 1 nanosecond in this case) by observers from <em>both</em> of the interacting frames A or B. Since T1 and T2 are historically recorded local events, this assertion can be further generalized to $\{T1,T2\}:>*$, where $*$ represents all possible frames. (And yes, $:>$ is two eyes looking left, while $<:$ is two eyes looking to the right.)</p>
<p>Using the four shared time stamps, define:</p>
<blockquote>
<p>$T_{\Delta{A}} = T_{A2} - T_{A1}$</p>
<p>$T_{\Delta{B}} = T_{B2} - T_{B1}$</p>
</blockquote>
<p>My main question is this:</p>
<hr>
<blockquote>
<p>Assuming that $T_{\Delta{A}} = f(T_{\Delta{B}})$ exists, what is $f(x)$?</p>
</blockquote>
<hr>
<p><strong>Analysis</strong> (why this problem is difficult)</p>
<p>Based purely on symmetry in the setup, the most obvious answer is $f(x)=x$, that is:</p>
<blockquote>
<p>$T_{\Delta{A}} = T_{\Delta{B}}$</p>
</blockquote>
<p>There are some interesting reasons to be troubled by that seemingly straightforward and even obvious conclusion, not the least of which is that it violates the whole concept of special relativity (the Dingle heresy).</p>
<p>That is, if you assume $f(x)=x$ and follow that line of logic through to its logical conclusion, you quickly end up with time that flows the <em>same</em> for all frames -- that is, no relativity. Such a conclusion is in flat violation of over a century of very detailed experimental evidence, and so is just not supportable.</p>
<p>The following four figures show why it's so hard to assert that $T_{\Delta{A}} = T_{\Delta{B}}$ without violating special relativity.</p>
<hr>
<p><img src="http://i.stack.imgur.com/G59Bl.png" alt="View of Event T1 from Frame A"></p>
<hr>
<p><img src="http://i.stack.imgur.com/j2K87.png" alt="View of Event T2 from Frame A"></p>
<hr>
<p><img src="http://i.stack.imgur.com/IFj5Q.png" alt="View of Event T1 from Frame B"></p>
<hr>
<p><img src="http://i.stack.imgur.com/jmoYk.png" alt="View of Event T2 from Frame B"></p>
<hr>
<p>While the above figures accurately capture the reality of relativistic contraction of both distance and time, the problem in this case is simple: How do you decide which frame to select? The experiment as described can only give one outcome. Which one will it be?</p> | g7820 | [
0.041079916059970856,
0.01325444970279932,
-0.0052430275827646255,
0.00619287695735693,
0.031441520899534225,
-0.02035743184387684,
0.06552433967590332,
0.018830446526408195,
-0.04757169261574745,
-0.008187800645828247,
0.016502872109413147,
-0.014610020443797112,
0.025434326380491257,
-0.023066330701112747,
0.016154447570443153,
0.009882844053208828,
0.13496196269989014,
-0.020199492573738098,
-0.0033851773478090763,
0.03058420680463314,
0.04803164303302765,
0.04449659213423729,
-0.01752563565969467,
-0.049383796751499176,
-0.042202360928058624,
-0.05346187949180603,
0.00048223522026091814,
-0.030627906322479248,
-0.09210807085037231,
-0.03180569037795067,
0.08373057097196579,
-0.020674370229244232,
0.02760857343673706,
-0.029662884771823883,
0.0064194598235189915,
-0.022613782435655594,
0.01091286912560463,
-0.0076403748244047165,
-0.031674910336732864,
0.055784258991479874,
0.08153409510850906,
-0.02291300520300865,
0.015032502822577953,
-0.07482653111219406,
0.07038212567567825,
-0.006466255523264408,
0.011641542427241802,
-0.018528617918491364,
0.022233547642827034,
-0.020647775381803513,
0.010347729548811913,
0.10072986036539078,
0.03061608411371708,
0.0006826622993685305,
0.03683352470397949,
0.06417766958475113,
0.008348374627530575,
0.04037090763449669,
0.04044720530509949,
0.013760235160589218,
0.03540162742137909,
-0.039028484374284744,
0.04893860965967178,
-0.0017092768102884293,
0.08332677185535431,
0.04876697435975075,
0.007482015993446112,
-0.005188797600567341,
0.0313321053981781,
-0.04149246960878372,
-0.01730029284954071,
-0.016159826889634132,
0.0028197274077683687,
-0.0033878798130899668,
-0.014711122028529644,
-0.006213794928044081,
0.02809867076575756,
-0.04334128648042679,
-0.02109679952263832,
0.0680791437625885,
-0.06312117725610733,
-0.04033772274851799,
-0.02730685845017433,
0.03647226095199585,
0.03090280294418335,
0.023794079199433327,
-0.006596664432436228,
0.06769539415836334,
0.027534546330571175,
0.011148150078952312,
0.016969233751296997,
-0.06240994483232498,
0.06382032483816147,
0.010835470631718636,
-0.00004687237742473371,
-0.00882952194660902,
-0.024149298667907715,
0.011936139315366745,
0.06336909532546997,
0.030886324122548103,
-0.019463151693344116,
0.01921248808503151,
-0.03214647248387337,
-0.009819407016038895,
-0.02648445963859558,
-0.05687709152698517,
-0.004631672985851765,
0.026587851345539093,
-0.053247787058353424,
-0.077683225274086,
-0.02797861583530903,
-0.08445420116186142,
-0.002615136792883277,
-0.01942836120724678,
-0.034008197486400604,
-0.028015656396746635,
0.016430683434009552,
-0.03411887213587761,
-0.049944426864385605,
-0.03617372736334801,
-0.006073620170354843,
0.014546536840498447,
0.014938157983124256,
0.02940327860414982,
-0.004157199990004301,
-0.004051136784255505,
-0.023660119622945786,
-0.0029059594962745905,
0.023257896304130554,
-0.01683851331472397,
-0.02608880028128624,
0.05821974202990532,
0.04508156329393387,
0.016251791268587112,
-0.10963471233844757,
-0.002900065155699849,
0.028459062799811363,
-0.01098634209483862,
0.0018137755105271935,
0.003544599050655961,
-0.015685688704252243,
-0.010012354701757431,
-0.03273855894804001,
-0.046181079000234604,
-0.002816693624481559,
0.016911402344703674,
-0.11393190920352936,
0.011994813568890095,
0.009894519113004208,
0.0019396073184907436,
0.0017279746243730187,
0.036247413605451584,
-0.053695667535066605,
0.016527775675058365,
-0.01815391518175602,
-0.004355991259217262,
-0.023974476382136345,
-0.059771422296762466,
-0.018305325880646706,
0.06060245633125305,
0.0937807634472847,
-0.032127104699611664,
-0.010404698550701141,
-0.0244743712246418,
-0.01106761209666729,
0.05070973187685013,
0.01373132225126028,
-0.0269538052380085,
0.06675396859645844,
-0.037413809448480606,
-0.04605453461408615,
-0.027872895821928978,
-0.004877004772424698,
0.007465382106602192,
-0.03520767018198967,
0.0060764821246266365,
0.10035857558250427,
-0.059711944311857224,
0.0052047427743673325,
0.03724803775548935,
0.00907373707741499,
-0.05562008544802666,
-0.011014198884367943,
-0.050281818956136703,
-0.02913621813058853,
-0.05125517398118973,
-0.005260974634438753,
-0.024934226647019386,
-0.04495105892419815,
-0.03478911891579628,
-0.009106958284974098,
-0.03451434522867203,
-0.012581962160766125,
0.027285199612379074,
-0.041999589651823044,
-0.010183344595134258,
-0.038088105618953705,
-0.0038915949407964945,
0.001587500562891364,
0.029637284576892853,
-0.042420290410518646,
-0.007405540440231562,
-0.013102587312459946,
0.051620420068502426,
0.036437295377254486,
0.008770281448960304,
0.014136100187897682,
0.0038424069061875343,
0.0019199897069483995,
0.01957317814230919,
0.001422580680809915,
0.025980841368436813,
0.004882214590907097,
-0.039226800203323364,
-0.009124272502958775,
-0.03566933050751686,
0.06086675077676773,
0.024474672973155975,
-0.033170461654663086,
0.049599554389715195,
0.040153250098228455,
-0.000523831753525883,
0.005251945927739143,
-0.08083286881446838,
-0.02925090305507183,
-0.05287589132785797,
-0.025394674390554428,
-0.05121511220932007,
-0.03719567880034447,
0.013643906451761723,
-0.009596528485417366,
0.08088969439268112,
-0.048631925135850906,
-0.009866312146186829,
0.035150106996297836,
0.013591461814939976,
0.0292690247297287,
0.017883488908410072,
0.05004984885454178,
0.027449144050478935,
0.05688382312655449,
0.007265126798301935,
-0.06027574464678764,
0.03817753493785858,
-0.017658965662121773,
-0.03033420816063881,
0.04016246646642685,
-0.011740045621991158,
0.02064112387597561,
-0.032195694744586945,
-0.010807574726641178,
-0.007166050840169191,
-0.02529887482523918,
-0.029421959072351456,
-0.001709149917587638,
-0.082718625664711,
0.037185441702604294,
0.023580895736813545,
-0.09926096349954605,
-0.02213851734995842,
0.00020028992730658501,
0.016185337677598,
0.03973224759101868,
0.042171772569417953,
-0.022539161145687103,
-0.019320465624332428,
-0.04651916027069092,
0.03707662969827652,
-0.0185136329382658,
-0.06860782206058502,
-0.04590579494833946,
-0.027175316587090492,
-0.003641011891886592,
0.05984799191355705,
-0.020848581567406654,
-0.003141610650345683,
-0.042468804866075516,
-0.03747022524476051,
-0.005686124786734581,
0.06628944724798203,
-0.0011079205432906747,
0.01095596607774496,
-0.02484297566115856,
-0.0521746501326561,
0.051551226526498795,
-0.021167421713471413,
0.01626976765692234,
0.021438654512166977,
0.04620638117194176,
-0.0015996817965060472,
-0.016068415716290474,
0.08756313472986221,
0.06448810547590256,
0.0285784974694252,
-0.04508937895298004,
0.028548896312713623,
-0.007487259805202484,
-0.008386563509702682,
-0.029827307909727097,
-0.04761798307299614,
0.03648126497864723,
-0.015739237889647484,
0.0240829698741436,
0.038610875606536865,
0.03703779727220535,
-0.04078886657953262,
-0.06393588334321976,
-0.006576681975275278,
-0.02131771668791771,
0.004154858645051718,
0.06059480085968971,
-0.02456015720963478,
0.056157439947128296,
-0.054958391934633255,
-0.019173653796315193,
-0.01867220364511013,
-0.001717077218927443,
0.0027122299652546644,
0.003568941028788686,
0.03416899964213371,
0.04064610227942467,
0.0371415913105011,
-0.05065568909049034,
-0.04843414947390556,
0.013307878747582436,
0.003726949915289879,
0.03231881931424141,
0.0004342848842497915,
-0.014755960553884506,
0.014466960914433002,
-0.04459760710597038,
0.02074083313345909,
0.02345576509833336,
-0.0014019040390849113,
0.0346425324678421,
-0.013820506632328033,
0.021118907257914543,
0.017744895070791245,
0.011625358834862709,
0.004962951876223087,
-0.007821283303201199,
-0.01579337753355503,
-0.022145219147205353,
0.013952607288956642,
0.04046564921736717,
0.014408453367650509,
0.052612293511629105,
0.012475996278226376,
-0.02746579237282276,
-0.04735417291522026,
0.03467449173331261,
-0.017080850899219513,
-0.020320462062954903,
0.01396825723350048,
0.0015838216058909893,
0.02969789132475853,
0.0034089575055986643,
0.018325157463550568,
0.024340495467185974,
-0.009506609290838242,
-0.005249229725450277,
0.04072631895542145,
-0.004504865035414696,
0.02702307142317295,
-0.006203868892043829,
-0.009588717482984066,
-0.00932518020272255,
0.00726094376295805,
0.05704927444458008,
-0.036789149045944214,
0.03559170663356781,
-0.009419628418982029,
0.007207007613033056,
-0.015722710639238358,
0.06329787522554398,
-0.0741412341594696,
0.01764693669974804,
0.0013268479378893971,
-0.021499009802937508,
0.05766346678137779,
-0.0004542676033452153,
0.043611835688352585,
-0.03701608628034592,
-0.004105746746063232,
0.09553437680006027,
-0.019840558990836143,
-0.00024183646019082516,
-0.048164092004299164,
-0.061192356050014496,
-0.006089031230658293,
0.013906043022871017,
0.01459110900759697,
-0.05451822280883789,
-0.005538147408515215,
-0.009853404015302658,
-0.022785943001508713,
0.01976901665329933,
0.01961974985897541,
0.009874763898551464,
0.0055377851240336895,
-0.013646220788359642,
0.022790823131799698,
-0.01359820831567049,
-0.020701425150036812,
-0.08837311714887619,
-0.026744436472654343,
-0.03393325209617615,
-0.014806565828621387,
-0.009576317854225636,
0.03102470003068447,
-0.014946553856134415,
0.05482484772801399,
-0.008370622992515564,
-0.04805397614836693,
0.05312390625476837,
0.009246713481843472,
-0.011139013804495335,
-0.0019932317081838846,
0.005601189564913511,
0.009937312453985214,
-0.03460457921028137,
0.06235382333397865,
0.037982333451509476,
-0.10225024819374084,
0.06225734204053879,
0.07579855620861053,
0.020913563668727875,
-0.003709453158080578,
-0.010619351640343666,
-0.025674454867839813,
0.09346649050712585,
0.009405430406332016,
0.02888413891196251,
0.02187875658273697,
-0.02107910066843033,
0.07033505290746689,
0.006800292991101742,
0.011139146983623505,
0.06161044165492058,
0.052542686462402344,
0.014355896972119808,
0.0045802709646523,
0.01546256523579359,
0.025672854855656624,
0.011909738183021545,
0.030518272891640663,
-0.09345506876707077,
-0.06828724592924118,
-0.032934434711933136,
-0.03174431249499321,
0.007811128627508879,
0.03375353664159775,
-0.009747094474732876,
0.04380885884165764,
0.00035509662120603025,
0.00587760703638196,
0.008033457212150097,
0.06260287016630173,
0.027804482728242874,
-0.010262690484523773,
0.011460352689027786,
0.014307727105915546,
0.04528171569108963,
-0.03211607784032822,
0.015630045905709267,
-0.013368579559028149,
-0.04246899485588074,
-0.02095934748649597,
-0.026906978338956833,
-0.0315164215862751,
-0.026285579428076744,
-0.02957083471119404,
0.008013265207409859,
-0.0045808362774550915,
0.0006596884923055768,
-0.00639906944707036,
0.030344374477863312,
-0.0009120861650444567,
0.04151569679379463,
-0.023159395903348923,
-0.03359970822930336,
0.039168890565633774,
0.03228604421019554,
0.054370488971471786,
0.014339161105453968,
0.01889689825475216,
-0.006983779836446047,
-0.011643658392131329,
0.00833477359265089,
-0.054411016404628754,
-0.014924202114343643,
-0.03454987704753876,
0.008384131826460361,
-0.02649267204105854,
-0.011709806509315968,
0.009220095351338387,
0.05083637684583664,
0.018749166280031204,
-0.01120911817997694,
-0.060307711362838745,
-0.05319209024310112,
0.10678719729185104,
0.006786478217691183,
-0.01613394170999527,
-0.020830564200878143,
0.021545346826314926,
-0.0057363808155059814,
0.003330341773107648,
-0.011270328424870968,
0.01960332877933979,
-0.013323094695806503,
0.01742379367351532,
-0.026413731276988983,
-0.052822984755039215,
-0.023892929777503014,
-0.012827880680561066,
0.04654696211218834,
-0.006356487516313791,
0.00026414505555294454,
-0.04415680468082428,
0.008690484799444675,
0.036289509385824203,
0.036745622754096985,
-0.0001255419774679467,
-0.008440140634775162,
-0.012696335092186928,
-0.034572262316942215,
0.0003143096691928804,
-0.015221945941448212,
-0.01864951103925705,
-0.0027978667058050632,
0.00611158600077033,
0.031564049422740936,
-0.0011486689327284694,
0.033860817551612854,
0.007700657472014427,
0.050806544721126556,
-0.04401537775993347,
0.03000801056623459,
0.012794884853065014,
0.011058320291340351,
0.048327360302209854,
0.012522488832473755,
0.07288001477718353,
-0.04123822972178459,
-0.06183464080095291,
-0.03823575749993324,
0.029770953580737114,
0.02876027300953865,
-0.019812416285276413,
-0.044363778084516525,
-0.03501705452799797,
-0.024546992033720016,
0.0005744237569160759,
0.02715502865612507,
0.027304109185934067,
0.058688051998615265,
-0.059096112847328186,
-0.025978265330195427,
0.017858149483799934,
0.014789382927119732,
-0.018693801015615463,
0.04353388398885727,
0.04871964827179909,
0.00953364372253418,
0.0011383012169972062,
-0.05345553904771805,
0.01623784378170967,
-0.007161343935877085,
0.04310845583677292,
0.034585561603307724,
-0.02200174704194069,
-0.002989414846524596,
-0.02290584146976471,
0.015830427408218384,
0.0033817049115896225,
-0.014184960164129734,
-0.01457439549267292,
-0.0558462031185627,
-0.033126119524240494,
-0.03395206481218338,
-0.01984720677137375,
0.006914074532687664,
-0.008442007005214691,
-0.030013369396328926,
0.06964817643165588,
-0.025648724287748337,
-0.000653464172501117,
0.009455140680074692,
-0.04604561626911163,
-0.022814512252807617,
-0.05860655754804611,
0.0016568226274102926,
-0.04719848185777664,
-0.04919614642858505,
-0.026164690032601357,
-0.002802081173285842,
0.05394139140844345,
-0.03632937744259834,
0.10206150263547897,
-0.07340744137763977,
-0.0071674915961921215,
0.05548754706978798,
0.016309678554534912,
-0.006703635677695274,
0.019640769809484482,
-0.029566265642642975,
0.0075835431925952435,
0.04794768989086151,
0.0003903790784534067,
-0.023740744218230247,
0.05134234577417374,
-0.01309701893478632,
0.07141554355621338,
-0.04077591374516487,
0.01687445491552353,
0.002426610793918371,
0.03423980623483658,
-0.008163492195308208,
-0.03097262606024742,
0.06996097415685654,
0.01756010204553604,
0.00029445189284160733,
-0.02691812999546528,
0.003429558826610446,
-0.03892964497208595,
0.0021069408394396305,
-0.05587443709373474,
0.006968248635530472,
0.04529860243201256,
0.009253065101802349,
-0.057845309376716614,
-0.05320723354816437,
0.01260752510279417,
-0.0006657405174337327,
0.02243918552994728,
-0.008219144307076931,
0.07731789350509644,
0.03170434385538101,
0.023776162415742874,
0.036839134991168976,
-0.005104411393404007,
-0.04051811248064041,
0.0013750133803114295,
-0.05147324502468109,
-0.04282741993665695,
0.06176694482564926,
0.02595694176852703,
-0.05292503163218498,
0.01988612860441208,
-0.03185604140162468,
-0.042616743594408035,
-0.04662396013736725,
0.03832455351948738,
-0.025374101474881172,
0.008241374976933002,
0.011300891637802124,
-0.0012758818920701742,
0.05446955934166908,
-0.01865314319729805,
-0.022902822121977806,
-0.026097480207681656,
-0.04430516064167023,
0.009922639466822147,
0.0016800916055217385,
0.026403142139315605,
-0.033210743218660355,
-0.04797995090484619,
-0.007932372391223907,
-0.02279418334364891,
0.01610863022506237,
0.033634085208177567,
0.01150252390652895,
-0.0026084769051522017,
0.06732949614524841,
0.0006491934764198959,
-0.013755870051681995,
0.012997547164559364,
-0.009080157615244389,
-0.021465012803673744,
-0.014575797133147717,
0.007395272143185139,
-0.02088119275867939,
0.020814169198274612,
-0.0017454683547839522,
0.06508234143257141,
-0.024431632831692696,
0.0006266276468522847,
-0.04528602585196495,
-0.04983227699995041,
0.007153040263801813,
0.07384783774614334,
-0.0002545029856264591,
0.03452546149492264,
-0.017015060409903526,
0.0019735670648515224,
0.03691023960709572,
0.05420931801199913,
0.014597883448004723,
0.023297732695937157,
0.00095491943648085,
0.024432078003883362,
0.01307570468634367,
0.07268913835287094,
0.027788693085312843,
0.010998411104083061,
-0.06714700162410736,
-0.014904532581567764,
0.008450252935290337,
-0.00004048028858960606,
-0.025153910741209984,
0.07821720838546753,
0.033306099474430084,
-0.016625648364424706,
-0.00520135834813118,
-0.022121088579297066,
0.006211273837834597,
0.0277843214571476,
0.06548131257295609,
0.011153596453368664,
-0.001725097419694066,
-0.05890912562608719,
-0.030813999474048615,
-0.04212213307619095,
0.03433220088481903,
-0.010310198180377483,
0.03186158463358879,
-0.023966366425156593,
-0.014026815071702003,
-0.07947949320077896,
0.007366437930613756,
-0.010975701734423637,
-0.023316146805882454,
0.07502453774213791,
0.00749262934550643,
0.026750724762678146,
0.009565264917910099,
0.006356220226734877,
-0.04936200752854347,
0.008157521486282349,
-0.00023753615096211433,
-0.11720351129770279,
-0.027176709845662117,
-0.005659820977598429,
-0.005265887826681137,
-0.06385678797960281,
-0.008239900693297386,
0.03562309592962265,
0.003757996018975973,
-0.05116597190499306,
-0.02494708262383938,
0.05371690168976784,
-0.08690783381462097,
0.008096754550933838,
0.055088385939598083,
-0.05407261475920677,
0.03941557928919792,
0.0028032443951815367,
0.006013536360114813,
-0.0005058711394667625,
-0.009027035906910896,
-0.02180766873061657,
-0.034432150423526764,
-0.014532431028783321,
-0.02234618179500103,
0.00017106237646657974,
0.004627347458153963,
-0.015460268594324589
] |
<p>I am studying the history of Modern Physics and Yang-Lee earned their Nobel the next year after the <a href="http://en.wikipedia.org/wiki/Wu_experiment" rel="nofollow">Cobalt experiments</a>. I am familiar with the chronology, but am not clear what those findings meant to the physics community to warrant such recognition for two relatively' unknown physicists.</p>
<p>Other household names had to wait decades for more seemingly significant work.</p>
<p>So can someone clarify what their work meant to the eventual development of the Standard Model?</p> | g7821 | [
0.015148953534662724,
0.0675806999206543,
0.0017562324646860361,
-0.021000705659389496,
0.048719339072704315,
0.053045906126499176,
0.0649651363492012,
0.0257568396627903,
-0.013233330100774765,
-0.030029403045773506,
-0.044305942952632904,
-0.024166777729988098,
0.07410265505313873,
-0.020393867045640945,
0.03792232647538185,
-0.012770305387675762,
0.022050734609365463,
-0.03643770515918732,
-0.00030944059835746884,
-0.01196927297860384,
-0.027808820828795433,
0.018515150994062424,
-0.041217491030693054,
-0.08983822911977768,
-0.061084501445293427,
-0.064531110227108,
-0.06471823900938034,
-0.05203256011009216,
-0.000023030437660054304,
-0.04587347060441971,
0.03337176889181137,
-0.027025926858186722,
0.053803473711013794,
-0.023980630561709404,
0.03937927633523941,
-0.028558077290654182,
0.016494346782565117,
0.01956402137875557,
-0.009622029960155487,
-0.006728308741003275,
-0.02073904499411583,
0.04660750553011894,
0.008856160566210747,
-0.0041638086549937725,
-0.020536979660391808,
-0.0033565028570592403,
-0.03682815656065941,
-0.06478459388017654,
0.0460166335105896,
0.020526569336652756,
0.027845993638038635,
0.03065161220729351,
0.08557561039924622,
0.02385871484875679,
-0.014653668738901615,
-0.016714956611394882,
0.06103779748082161,
-0.05680101364850998,
0.10257197171449661,
0.00944541860371828,
0.024734647944569588,
-0.0014307297533378005,
0.02758845128118992,
-0.03539218008518219,
0.07373299449682236,
0.03283074498176575,
0.015106641687452793,
-0.009715817868709564,
0.07061323523521423,
-0.026450080797076225,
-0.004823803901672363,
-0.04284515604376793,
-0.03226633742451668,
0.010626615025103092,
0.01489974744617939,
0.03601556271314621,
0.021169263869524002,
0.0023157047107815742,
0.02898399904370308,
-0.031394511461257935,
-0.03612896800041199,
0.0077422428876161575,
0.02661866322159767,
0.01322142779827118,
0.04687589406967163,
-0.00978779699653387,
-0.056716930121183395,
0.02714437060058117,
0.05468488484621048,
0.03434125706553459,
-0.014642997644841671,
-0.012263387441635132,
-0.014830907806754112,
-0.025092635303735733,
-0.0095667764544487,
0.01890353485941887,
0.04407881200313568,
0.025281997397542,
-0.0044819144532084465,
0.0909949466586113,
-0.0880969762802124,
-0.004188138991594315,
-0.00665303273126483,
0.010935306549072266,
0.04236597940325737,
0.057799361646175385,
0.021749041974544525,
-0.004251536447554827,
-0.04696796089410782,
-0.017416901886463165,
-0.07038867473602295,
0.05872444435954094,
-0.06620337069034576,
0.004883865360170603,
0.01661037467420101,
0.007063256110996008,
-0.009112001396715641,
-0.04306342825293541,
-0.021697476506233215,
0.03474373742938042,
-0.04747861996293068,
-0.0075505198910832405,
-0.018363216891884804,
0.013459972105920315,
-0.031352750957012177,
0.007828681729733944,
0.03762545436620712,
-0.008909715339541435,
-0.022045208141207695,
-0.05836381018161774,
-0.04089566320180893,
0.03033045120537281,
-0.025963418185710907,
0.06853721290826797,
-0.0172747615724802,
0.005529547110199928,
-0.036250095814466476,
0.04389002546668053,
0.028123022988438606,
-0.01641985774040222,
0.006650058552622795,
-0.021201983094215393,
-0.043141305446624756,
-0.011114233173429966,
0.02049710787832737,
0.029306557029485703,
-0.016379976645112038,
0.02983028069138527,
-0.050297994166612625,
0.06399432569742203,
0.014973239973187447,
0.04544355347752571,
-0.012935264967381954,
-0.025735847651958466,
-0.10995848476886749,
0.015122066251933575,
-0.017734535038471222,
-0.07624700665473938,
-0.02976647950708866,
-0.055890996009111404,
-0.016111290082335472,
-0.03014768473803997,
-0.003958371002227068,
0.013017564080655575,
-0.04668338596820831,
-0.008422435261309147,
0.11660061776638031,
-0.11165393143892288,
-0.014108313247561455,
-0.034092385321855545,
-0.03837106004357338,
0.02805807627737522,
0.024471629410982132,
-0.0034965593367815018,
0.005343643017113209,
0.05377122014760971,
0.019610216841101646,
-0.08828645944595337,
0.023233860731124878,
-0.005243845283985138,
-0.07936237752437592,
-0.01976889930665493,
-0.020595889538526535,
0.024318134412169456,
-0.024718957021832466,
0.0007785458583384752,
-0.06618421524763107,
-0.008305235765874386,
-0.015306858345866203,
0.016587642952799797,
-0.021221961826086044,
-0.07609285414218903,
-0.014869136735796928,
-0.003815829288214445,
-0.04440942034125328,
-0.010478882119059563,
0.008749233558773994,
-0.004573251120746136,
-0.051754727959632874,
-0.03570161387324333,
-0.064092256128788,
0.005169626325368881,
-0.04562575742602348,
-0.020532073453068733,
-0.037134990096092224,
0.043006811290979385,
0.01942666433751583,
-0.05579826980829239,
0.012820576317608356,
-0.046432189643383026,
-0.0453377291560173,
0.0014961287379264832,
0.030823804438114166,
-0.011367658153176308,
0.022569218650460243,
-0.004369744099676609,
-0.0026984678115695715,
-0.010444985702633858,
-0.031825777143239975,
0.01227574236690998,
-0.05578870698809624,
-0.030118636786937714,
0.025476843118667603,
0.013602272607386112,
0.10670267045497894,
0.0037291678600013256,
0.017014171928167343,
-0.028246553614735603,
-0.026371721178293228,
-0.004283352289348841,
-0.05546441301703453,
0.01929803565144539,
-0.06903161853551865,
-0.006265620701014996,
0.03592779114842415,
0.04376419261097908,
-0.014791449531912804,
-0.0382603220641613,
0.04035208746790886,
0.04661132022738457,
-0.00977275613695383,
0.02347472496330738,
-0.02199101634323597,
0.016040470451116562,
-0.006840682588517666,
-0.03875831887125969,
0.033679261803627014,
-0.013813816010951996,
-0.06578612327575684,
-0.005765185225754976,
-0.0023305017966777086,
-0.006281816400587559,
-0.02403484284877777,
-0.018645374104380608,
0.021800439804792404,
0.033569883555173874,
0.043546926230192184,
0.05166136473417282,
-0.06811022758483887,
-0.047977298498153687,
0.02154848910868168,
0.016326064243912697,
0.00671035423874855,
-0.021052418276667595,
0.013794589787721634,
0.013678069226443768,
-0.04744179919362068,
-0.03192484378814697,
-0.007861804217100143,
-0.032264064997434616,
0.013399189338088036,
-0.026598311960697174,
0.031216807663440704,
-0.008910453878343105,
-0.036889463663101196,
0.0068574887700378895,
-0.03306138888001442,
0.0168924480676651,
0.014965115115046501,
-0.04374566301703453,
-0.0814162865281105,
-0.028132552281022072,
-0.041210390627384186,
0.056116119027137756,
-0.03712594881653786,
-0.06104278191924095,
-0.054889317601919174,
-0.03708980232477188,
-0.008576846681535244,
-0.023793576285243034,
-0.05021127313375473,
0.00014836897025816143,
0.048807043582201004,
-0.02179776318371296,
-0.03770844265818596,
0.007649596314877272,
0.01742972806096077,
0.007166046183556318,
-0.005427626892924309,
0.019126441329717636,
0.08475501090288162,
-0.03755263239145279,
-0.003396970685571432,
0.016926990821957588,
0.05923961475491524,
-0.01256691012531519,
-0.023556716740131378,
0.036537054926157,
-0.00270198960788548,
-0.03864671289920807,
0.01290598139166832,
0.028349479660391808,
0.036945123225450516,
0.024095552042126656,
-0.06764165312051773,
-0.010572459548711777,
-0.005042427219450474,
0.011930032633244991,
0.07089905440807343,
-0.025319209322333336,
0.012537738308310509,
-0.0003042189055122435,
-0.01071151066571474,
-0.0416896715760231,
0.01255522295832634,
0.043934259563684464,
0.00277623999863863,
-0.017610516399145126,
0.04736700281500816,
0.005381494760513306,
0.011279054917395115,
-0.01259351335465908,
0.002754215383902192,
-0.0393589586019516,
-0.030001774430274963,
-0.07102552056312561,
0.01727508194744587,
0.045771658420562744,
0.02240990847349167,
0.019517334178090096,
0.023528413847088814,
-0.004796574357897043,
-0.050503503531217575,
0.020233934745192528,
0.05204801633954048,
0.00950632430613041,
-0.018335329368710518,
0.003475405042991042,
-0.03709682077169418,
0.0072462065145373344,
0.07349267601966858,
0.05224376544356346,
-0.05056232213973999,
-0.007426387630403042,
-0.053881749510765076,
0.04359094426035881,
0.002159047406166792,
-0.005911940708756447,
0.00022832363902125508,
-0.035448577255010605,
-0.03342369943857193,
0.01698417402803898,
-0.013627360574901104,
0.042181409895420074,
-0.006413920316845179,
0.06563179939985275,
-0.01633104681968689,
0.017683161422610283,
0.012546321377158165,
-0.05614951625466347,
-0.09764142334461212,
0.06068411096930504,
-0.0020268955267965794,
-0.004719794727861881,
0.010197262279689312,
-0.0436406210064888,
0.047081444412469864,
0.048501916229724884,
-0.05195939168334007,
0.057991135865449905,
-0.02537412755191326,
0.034676048904657364,
-0.013846703805029392,
-0.022137023508548737,
-0.0038026426918804646,
-0.043786030262708664,
-0.042041100561618805,
-0.002706468803808093,
-0.05172188580036163,
-0.06581342965364456,
-0.0032240254804491997,
0.05195923149585724,
-0.023424334824085236,
0.0291097704321146,
-0.016831299290060997,
-0.022502290084958076,
0.014068637043237686,
0.018481310456991196,
0.043335940688848495,
-0.0016012307023629546,
-0.03192076086997986,
0.025441225618124008,
-0.0015801351983100176,
0.04780878499150276,
0.011554088443517685,
0.01421463955193758,
-0.011252976953983307,
-0.03775915876030922,
-0.012994959019124508,
0.03138306364417076,
-0.0441678911447525,
-0.03923286870121956,
-0.006865584757179022,
-0.018974492326378822,
0.024281959980726242,
0.023951219394803047,
0.04506451264023781,
-0.09024468064308167,
-0.023012790828943253,
0.003459695726633072,
0.04011925309896469,
0.04764946922659874,
0.018156057223677635,
-0.018489930778741837,
0.0643266811966896,
0.009397325105965137,
-0.02378539741039276,
0.02581360936164856,
-0.03189414367079735,
-0.0201277919113636,
0.059572841972112656,
0.03609393537044525,
-0.054342884570360184,
0.0007968461723066866,
-0.020763618871569633,
0.011735770851373672,
0.05538339167833328,
0.04006807506084442,
-0.06469845026731491,
0.07152305543422699,
0.10099457949399948,
-0.009755056351423264,
0.04658852145075798,
0.038304563611745834,
0.05285244062542915,
0.05488307401537895,
-0.0058059594593942165,
-0.017976507544517517,
0.0317998006939888,
-0.009149626828730106,
-0.008857772685587406,
0.024465760216116905,
0.01840447261929512,
0.007308162283152342,
0.04179547727108002,
-0.05897517874836922,
0.05491332337260246,
0.0006746979779563844,
0.010594629682600498,
0.05222858488559723,
-0.05953527241945267,
0.0023967961315065622,
-0.01152037549763918,
-0.007922099903225899,
-0.004633283708244562,
-0.010704738087952137,
-0.0502212829887867,
-0.051568008959293365,
-0.06667608767747879,
-0.02545260824263096,
-0.026993876323103905,
-0.011310659348964691,
0.05241550877690315,
0.03745931014418602,
0.019667625427246094,
-0.011031314730644226,
0.018544256687164307,
-0.04936131089925766,
0.027018805965781212,
0.06203743442893028,
0.01025322824716568,
0.045955583453178406,
0.04666381701827049,
0.01100158877670765,
0.06102632358670235,
0.031009254977107048,
-0.06507286429405212,
-0.0006670146249234676,
0.03310806304216385,
-0.010097740218043327,
0.03444182872772217,
-0.018707675859332085,
0.023903431370854378,
0.005485734902322292,
-0.061969075351953506,
0.017194723710417747,
-0.04502783715724945,
-0.010827535763382912,
0.005158304702490568,
0.023133935406804085,
-0.00937744788825512,
0.08509987592697144,
0.02315058559179306,
-0.000187880898010917,
0.025030506774783134,
0.08643472194671631,
0.0016640106914564967,
-0.04395097866654396,
0.0711720734834671,
-0.04046633839607239,
-0.03436846658587456,
0.008113146759569645,
0.032200075685977936,
0.04169948771595955,
0.004118955694139004,
0.011895825155079365,
-0.014187376014888287,
-0.010167565196752548,
-0.04133138805627823,
-0.04804331064224243,
0.0502411313354969,
0.0018565476639196277,
0.043581582605838776,
-0.008294652216136456,
0.012696684338152409,
-0.014230682514607906,
0.0007911521242931485,
0.017903020605444908,
0.03246742859482765,
0.013835940510034561,
0.01528525073081255,
0.00796067900955677,
0.0704953670501709,
0.016356445848941803,
0.04724482446908951,
-0.022977720946073532,
0.01732265204191208,
0.01071700919419527,
0.010205407626926899,
0.008006402291357517,
-0.04479018971323967,
0.030297601595520973,
0.04855046048760414,
0.045464012771844864,
-0.026502462103962898,
-0.005928920116275549,
0.012993584387004375,
-0.018351100385189056,
0.03045281022787094,
-0.05750960856676102,
-0.042489346116781235,
-0.040919166058301926,
0.03332769125699997,
0.06242566183209419,
0.03876379504799843,
0.02764967456459999,
-0.017905626446008682,
-0.008843403309583664,
-0.04477139934897423,
-0.005937478970736265,
0.05283401161432266,
0.020571911707520485,
0.010003538802266121,
0.026164036244153976,
0.025778478011488914,
-0.026338353753089905,
-0.01215248554944992,
-0.05102909356355667,
0.027378572151064873,
0.043946098536252975,
0.0031730292830616236,
0.013172978535294533,
-0.04885832220315933,
-0.03211401775479317,
-0.04523245245218277,
0.0548776350915432,
-0.01963544823229313,
0.032170578837394714,
-0.04086960479617119,
-0.04852955415844917,
0.029260115697979927,
-0.050800468772649765,
-0.012534791603684425,
-0.00882965698838234,
-0.008164545521140099,
0.022149328142404556,
-0.022634251043200493,
-0.011291004717350006,
0.025801820680499077,
0.017593368887901306,
-0.03743289038538933,
-0.04230356961488724,
-0.019295355305075645,
-0.01844775304198265,
-0.05635164678096771,
-0.028682783246040344,
0.040835537016391754,
0.03891558572649956,
-0.011269060894846916,
0.03763503208756447,
-0.022054651752114296,
0.021657947450876236,
0.022483373060822487,
0.005834844894707203,
0.04268065094947815,
0.009675173088908195,
-0.00876237079501152,
-0.007556022610515356,
0.05404725670814514,
0.022528113797307014,
-0.03829546645283699,
0.02003413997590542,
-0.03334585204720497,
0.003449009032920003,
-0.005110575817525387,
-0.04974241554737091,
0.01669939234852791,
0.0542336031794548,
-0.04581752046942711,
0.020278992131352425,
0.038231682032346725,
-0.016306070610880852,
-0.016277967020869255,
0.006522722542285919,
-0.030417291447520256,
0.03445194661617279,
0.027020003646612167,
0.012387078255414963,
0.001869351021014154,
0.03371667116880417,
-0.03670173138380051,
0.03208646550774574,
0.0494190938770771,
0.018763871863484383,
0.002588380128145218,
0.012824923731386662,
0.00574484933167696,
0.008167109452188015,
0.03325987979769707,
-0.017638007178902626,
-0.0010062283836305141,
-0.025607550516724586,
0.03957277908921242,
0.012591620907187462,
-0.014461460523307323,
0.03213852271437645,
0.005145652685314417,
0.05223853886127472,
-0.030856922268867493,
-0.017620772123336792,
-0.019621413201093674,
-0.06538563966751099,
-0.016130084171891212,
0.02502494864165783,
-0.00723964162170887,
0.004769325256347656,
0.05468148738145828,
0.022285250946879387,
0.03600184991955757,
0.005550905596464872,
-0.02773219347000122,
-0.016460014507174492,
-0.006029397249221802,
-0.04312498867511749,
0.0096967201679945,
0.026138633489608765,
-0.024750061333179474,
-0.07337717711925507,
-0.0065795667469501495,
0.031110960990190506,
0.011267668567597866,
-0.004459323361515999,
-0.010357830673456192,
-0.002159732161089778,
-0.010762268677353859,
-0.023716792464256287,
0.0006619821069762111,
-0.0008879298693500459,
-0.021703088656067848,
-0.032805535942316055,
0.002353847958147526,
0.02008347399532795,
0.010635169222950935,
-0.030093546956777573,
-0.0665847435593605,
0.028369106352329254,
-0.01667574979364872,
-0.021902574226260185,
0.03555372729897499,
0.03702522814273834,
-0.01167458388954401,
-0.02809779718518257,
-0.02698931284248829,
-0.011181452311575413,
0.011471560224890709,
0.028293268755078316,
0.035840682685375214,
0.030279124155640602,
0.012772337533533573,
0.040616538375616074,
0.03536863625049591,
-0.0562409982085228,
-0.053878650069236755,
-0.0072618043050169945,
0.02222769521176815,
0.0537072978913784,
-0.0004954125033691525,
-0.04426044225692749,
-0.0011522052809596062,
-0.014427604153752327,
-0.06904202699661255,
0.020326603204011917,
0.07149675488471985,
0.03881178796291351,
0.06586615741252899,
0.04185681790113449,
-0.027110258117318153,
0.00019554102618712932,
0.0183469969779253,
0.07050392031669617,
-0.0221396554261446,
-0.04086769372224808,
-0.002460308838635683,
-0.03398510813713074,
0.000625703192781657,
0.03632594272494316,
-0.05739770829677582,
0.0393124558031559,
-0.00418053800240159,
-0.02384158968925476,
0.02343696728348732,
0.0167777631431818,
-0.032632675021886826,
0.009051603265106678,
-0.013552272692322731,
0.003569394815713167,
0.03867403417825699,
0.006675535347312689,
-0.017353886738419533,
0.00342295179143548,
0.015121905133128166,
-0.0044858879409730434,
-0.003911190200597048,
0.011522007174789906,
-0.056445181369781494,
-0.05174149200320244,
-0.0002352496376261115,
0.04963161423802376,
-0.03401697054505348,
-0.054912008345127106,
-0.0015191243728622794,
0.0559983067214489,
-0.0706310048699379,
0.09756951034069061,
0.06487984210252762,
-0.02819744497537613,
-0.011371219530701637,
0.015394378453493118,
0.046010617166757584,
-0.0069631896913051605,
-0.046635061502456665,
0.04358627647161484,
0.03380601108074188,
0.0271050576120615,
-0.005459193140268326,
-0.0023985672742128372,
0.010934959165751934,
-0.04439122974872589
] |
<p>Suppose I set up the <a href="http://en.wikipedia.org/wiki/Double-slit_experiment" rel="nofollow">double-slit experiment</a> using photons as my particle. Behind the left slit I place a <a href="http://en.wikipedia.org/wiki/Beam_splitter" rel="nofollow">beam splitter</a> that points some of the light off in the direction of a camera (represented as <code>C</code> in the diagram below). We'll say that the beam splitter splits a light beam passing through it into two equal beams. The light that passes through the beam splitter unaffected and the light that passes through the right slit continue on to another camera (represented as <code>CCC</code> in the diagram below). We'll say that camera <code>C</code> is closer to the beam splitter than camera <code>CCC</code> is.</p>
<pre><code> CCC
| |
| |
C-\ |
| |
-----|-|-----
|
|
Laser
</code></pre>
<p>If I fire a single photon through this apparatus, there's about a $1/4$ chance that it will be detected by camera <code>C</code> and about a $3/4$ chance that it will be detected by camera <code>CCC</code>. When the wavefunction reaches camera <code>C</code>, the photon is forced to either be detected by camera <code>C</code> or have the part of the wavefunction leading to camera <code>C</code> disappear.</p>
<p><strong>Question:</strong> In the case that the photon is not detected by camera <code>C</code>, how is the $1/4$ probability from that branch of the wavefunction redistributed to the remaining two branches of the wavefunction, the branch went through the left slit and straight through the beam splitter and the branch that went through the right slit? The first starts with about $1/4$ probability and the second starts with about $1/2$ probability. Does the first get a new probability of $1/3$ and the second a new probability of $2/3$? Does the first get a new probability of $1/2$ while the second keeps its old probability of $1/2$?</p> | g7822 | [
0.01586317829787731,
-0.024635056033730507,
-0.013072872534394264,
0.04476365074515343,
0.044406477361917496,
-0.028001412749290466,
0.05076437070965767,
0.0451434962451458,
0.022481413558125496,
-0.039170701056718826,
-0.046436209231615067,
0.05663850158452988,
0.013611526228487492,
0.013344142585992813,
0.008432529866695404,
0.01698175072669983,
0.10339584201574326,
0.011537635698914528,
0.04128425940871239,
0.07415032386779785,
-0.0450921393930912,
0.03907017782330513,
-0.04578888788819313,
-0.09346239268779755,
-0.003050826257094741,
-0.046063486486673355,
0.01364294532686472,
-0.007832536473870277,
-0.1043819859623909,
0.02943427860736847,
-0.009447146207094193,
0.019198531284928322,
0.0530041940510273,
-0.044940900057554245,
-0.016751855611801147,
0.012952703982591629,
0.06872352212667465,
-0.008430314250290394,
-0.020219536498188972,
0.05203341320157051,
0.010616912506520748,
0.045219291001558304,
-0.017142899334430695,
-0.0653330534696579,
-0.0051857661455869675,
-0.012829878367483616,
0.025397729128599167,
0.016232987865805626,
0.05819074809551239,
-0.05301028490066528,
-0.0011865192791447043,
0.04046972468495369,
-0.011418699286878109,
0.05457824096083641,
0.04919565096497536,
0.04854431748390198,
-0.015338808298110962,
0.018552931025624275,
0.03537891060113907,
-0.015122801065444946,
-0.010360712185502052,
-0.0009000148857012391,
0.029762107878923416,
0.0030754522886127234,
-0.024391699582338333,
0.06219707429409027,
-0.011695570312440395,
-0.0033113614190369844,
0.0017843786627054214,
-0.03190341964364052,
-0.015351255424320698,
-0.02518698200583458,
-0.016503211110830307,
-0.014247622340917587,
-0.0018431475618854165,
-0.05497124418616295,
-0.03257407248020172,
-0.014159594662487507,
-0.03227904066443443,
0.05179711431264877,
-0.04015929251909256,
-0.04580515995621681,
-0.04738061875104904,
0.025157233700156212,
0.017810113728046417,
0.04984644800424576,
-0.005678704474121332,
0.01970590464770794,
-0.005082172341644764,
0.005775940138846636,
0.03995737433433533,
0.013288344256579876,
0.10272926092147827,
0.03294268995523453,
-0.024080881848931313,
0.018565300852060318,
-0.04566983878612518,
0.042612988501787186,
-0.007392661180347204,
-0.0003177097823936492,
0.012224138714373112,
-0.012415622361004353,
0.045333120971918106,
0.05742144212126732,
-0.05813368037343025,
0.03151319921016693,
0.000780874805059284,
-0.02287113107740879,
-0.06334289908409119,
0.030852951109409332,
-0.017015881836414337,
-0.05200424790382385,
-0.02790094166994095,
-0.047519613057374954,
-0.027735985815525055,
-0.02904575504362583,
0.017401104792952538,
-0.0255755502730608,
0.019040049985051155,
-0.007876128889620304,
0.009373950771987438,
0.048079896718263626,
-0.026096900925040245,
0.04047563672065735,
-0.00009831076749833301,
0.020904671400785446,
0.010241162963211536,
0.08356425166130066,
0.056717708706855774,
0.029186170548200607,
-0.024746989831328392,
0.034556347876787186,
-0.0030263683293014765,
0.06767216324806213,
0.005842010956257582,
-0.00660226633772254,
0.07135401666164398,
0.02132422849535942,
0.011264384724199772,
-0.005291393958032131,
0.008031570352613926,
0.01801985502243042,
0.017379043623805046,
-0.011852972209453583,
-0.022611103951931,
0.02700413204729557,
0.009436598978936672,
-0.002401584293693304,
-0.0018242625519633293,
-0.032724399119615555,
0.027172626927495003,
0.0019820297602564096,
-0.06321831792593002,
-0.0030705109238624573,
0.010422603227198124,
-0.025389263406395912,
0.009373665787279606,
-0.010436570271849632,
-0.026561981067061424,
-0.04565965011715889,
0.05497084930539131,
-0.023801885545253754,
0.021944763138890266,
-0.03344248980283737,
-0.0662917047739029,
0.0014237738214433193,
0.04854147508740425,
-0.10271520167589188,
0.0035237146075814962,
-0.06287125498056412,
0.014550392515957355,
-0.010051258839666843,
0.010227312333881855,
-0.031007615849375725,
-0.015809275209903717,
0.07561825960874557,
-0.0001385701325489208,
0.03464002534747124,
-0.01487062405794859,
0.04812692850828171,
-0.06520462781190872,
0.028799617663025856,
-0.003372079925611615,
-0.009869418106973171,
0.002413657493889332,
-0.07027363777160645,
0.0030977874994277954,
-0.005733949597924948,
-0.06715341657400131,
-0.02630484849214554,
-0.04681693762540817,
-0.01335182599723339,
-0.036898769438266754,
0.048363566398620605,
-0.04200347885489464,
-0.016267122700810432,
0.01761132851243019,
-0.0538303405046463,
0.022483602166175842,
0.029291104525327682,
-0.016708755865693092,
0.04873425140976906,
-0.019313599914312363,
0.013995490968227386,
0.03962339460849762,
-0.0060763293877244,
0.004215287044644356,
0.01356676034629345,
-0.06849590688943863,
0.017844241112470627,
-0.010731617920100689,
-0.009731622412800789,
-0.04545481130480766,
0.02563248574733734,
0.03774291276931763,
-0.023597944527864456,
0.05256994441151619,
-0.021362030878663063,
-0.008922727778553963,
-0.04480159282684326,
-0.012631711550056934,
0.009925797581672668,
0.06584865599870682,
-0.035361163318157196,
0.017380015924572945,
0.06426925212144852,
0.005671544931828976,
-0.033016446977853775,
-0.040199991315603256,
0.10934225469827652,
-0.05241348221898079,
-0.005336939822882414,
-0.04155000299215317,
-0.0609646812081337,
0.04216308146715164,
0.016911115497350693,
-0.030669257044792175,
0.035914890468120575,
0.021847190335392952,
-0.0682542696595192,
-0.025290800258517265,
0.003557545365765691,
-0.07024109363555908,
0.01277957670390606,
0.04438447579741478,
-0.06992532312870026,
0.012893950566649437,
-0.004112990107387304,
-0.03254970163106918,
0.0102183036506176,
0.02082427404820919,
-0.03850288316607475,
-0.017412986606359482,
0.03617545962333679,
-0.038042739033699036,
-0.003314596600830555,
0.02688143402338028,
0.05535953491926193,
-0.05943862348794937,
0.01593591831624508,
-0.03335639461874962,
0.004471023567020893,
-0.0012900044675916433,
-0.02347165159881115,
-0.007120135240256786,
-0.01389035303145647,
0.012464781291782856,
-0.01575072854757309,
0.006576947867870331,
-0.03570907935500145,
0.02455187402665615,
0.048155639320611954,
0.03935384005308151,
0.02906615100800991,
0.07117968797683716,
0.053445130586624146,
0.030559422448277473,
-0.048269789665937424,
-0.004766824189573526,
-0.05007131025195122,
-0.019150642678141594,
0.03236011415719986,
-0.03574666380882263,
0.030560771003365517,
0.02025238238275051,
-0.052367743104696274,
0.06400419771671295,
0.0023442176170647144,
-0.006959591526538134,
-0.00607770960777998,
-0.028960438445210457,
0.010315879248082638,
0.03877389058470726,
0.0031081002671271563,
0.031065385788679123,
-0.04345414415001869,
0.013041937723755836,
-0.025627298280596733,
-0.0027890594210475683,
-0.0042309449054300785,
-0.04376678168773651,
-0.01788507215678692,
-0.056251779198646545,
-0.0434926301240921,
0.05772659555077553,
0.015813181176781654,
-0.06843594461679459,
-0.01605166867375374,
0.02420925721526146,
0.021363133564591408,
0.005308920983225107,
0.06009959056973457,
0.0554284006357193,
-0.04622155800461769,
-0.014783667400479317,
-0.05994780361652374,
-0.04471641406416893,
-0.0034229052253067493,
0.0069793895818293095,
0.03276342153549194,
-0.024879127740859985,
0.05086872726678848,
-0.03552379086613655,
-0.015145699493587017,
0.08637852966785431,
-0.01381741464138031,
-0.004188976250588894,
0.02774985134601593,
0.011958640068769455,
0.0057639009319245815,
0.021902872249484062,
0.02733760140836239,
-0.04096371307969093,
0.001218029297888279,
0.04297220706939697,
-0.05021464079618454,
0.014445655979216099,
0.017621325328946114,
0.041225217282772064,
-0.011505382135510445,
0.058837804943323135,
-0.022185461595654488,
-0.03411244973540306,
0.002545023802667856,
0.0368051677942276,
-0.03116319514811039,
0.04876263439655304,
0.04162692651152611,
0.017515014857053757,
0.018230736255645752,
0.010883184149861336,
-0.07194747030735016,
-0.022763080894947052,
0.029426874592900276,
-0.004004350397735834,
0.029597442597150803,
-0.03867819905281067,
-0.004615264944732189,
-0.004306221380829811,
-0.019584881141781807,
-0.007421903777867556,
-0.04462256655097008,
0.03342725336551666,
-0.036357250064611435,
-0.032381702214479446,
-0.022214340046048164,
0.018267156556248665,
0.028481440618634224,
0.015648864209651947,
-0.014236674644052982,
-0.013983326032757759,
-0.029564587399363518,
-0.05713407322764397,
0.035533249378204346,
-0.031141972169280052,
-0.021832577884197235,
0.0603945292532444,
0.003925287630409002,
0.006079911720007658,
0.016517437994480133,
0.006394793279469013,
-0.03002077341079712,
0.08782710134983063,
-0.01758378930389881,
0.00244619557633996,
0.008863535709679127,
0.01215124037116766,
-0.032628241926431656,
0.002943924628198147,
0.011599240824580193,
0.019962551072239876,
-0.018397316336631775,
-0.06342291831970215,
0.029317498207092285,
0.02242106758058071,
-0.018092796206474304,
-0.016292454674839973,
-0.01076660305261612,
-0.042803842574357986,
-0.004079475067555904,
0.0095151262357831,
0.04358382150530815,
0.01145772635936737,
-0.025030434131622314,
-0.018037322908639908,
0.002349382033571601,
0.002254581544548273,
-0.0414888896048069,
-0.02623695321381092,
0.049021705985069275,
0.025987351313233376,
-0.01634342037141323,
-0.03242609649896622,
-0.06758300215005875,
0.05532192438840866,
-0.02589339390397072,
0.07445313036441803,
0.014582616277039051,
-0.01582999899983406,
0.00518755754455924,
-0.00451885350048542,
-0.007524162996560335,
0.035841889679431915,
-0.019181370735168457,
-0.02683752216398716,
0.016635416075587273,
0.027392540127038956,
-0.0068275462836027145,
0.020404327660799026,
-0.029185272753238678,
0.06180214136838913,
0.02488335408270359,
0.024627381935715675,
0.037696722894907,
-0.05639849975705147,
0.05705352500081062,
-0.03795536234974861,
0.009571192786097527,
0.0073037538677453995,
0.07208824157714844,
0.033029988408088684,
-0.05810302123427391,
-0.00012578058522194624,
-0.010754064656794071,
0.026552245020866394,
-0.0203437227755785,
-0.050625089555978775,
-0.04128925874829292,
0.06336187571287155,
-0.06679235398769379,
-0.022001182660460472,
0.041168875992298126,
-0.006084640044718981,
-0.024753522127866745,
0.009942011907696724,
0.008274880237877369,
-0.04608854278922081,
0.01567808724939823,
0.049970753490924835,
0.03476262465119362,
-0.06690480560064316,
-0.0004226029268465936,
0.05095701292157173,
-0.008287006057798862,
0.044034525752067566,
0.005529679823666811,
-0.05038655549287796,
-0.04708097502589226,
-0.021248845383524895,
0.01313689909875393,
0.022281279787421227,
-0.016839947551488876,
0.01888139173388481,
0.04684734717011452,
0.01230582781136036,
-0.02672138810157776,
-0.04152252897620201,
0.031055450439453125,
0.01469652634114027,
-0.007793560158461332,
-0.022107144817709923,
-0.050000403076410294,
0.01677350327372551,
-0.007445790339261293,
0.010932317934930325,
-0.033477745950222015,
-0.006665925029665232,
-0.02605598233640194,
0.02223365008831024,
-0.028425520285964012,
-0.011743636801838875,
-0.011456983163952827,
-0.009668809361755848,
-0.014106055721640587,
0.06369736790657043,
-0.018837163224816322,
0.047233112156391144,
-0.0005628241924569011,
0.027019893750548363,
0.05798948183655739,
-0.03144755959510803,
-0.012472963891923428,
-0.013847418129444122,
0.013137034140527248,
-0.05677977576851845,
0.02643338404595852,
-0.02118431217968464,
-0.019351663067936897,
-0.053502678871154785,
0.02099078893661499,
-0.0360579788684845,
-0.03553829342126846,
-0.016584135591983795,
-0.049308840185403824,
0.06634493917226791,
-0.027806732803583145,
-0.054244264960289,
0.0357251837849617,
-0.006159063428640366,
-0.015593289397656918,
0.07455048710107803,
0.045339640229940414,
0.01970651000738144,
-0.009991908445954323,
0.036971934139728546,
-0.08605914562940598,
-0.08256528526544571,
0.004582706373184919,
-0.010735195130109787,
-0.025082780048251152,
0.01682361215353012,
0.08588369190692902,
0.029220743104815483,
0.051997072994709015,
-0.01787625066936016,
-0.05357207730412483,
0.022665638476610184,
-0.018453324213624,
-0.014881773851811886,
-0.016850948333740234,
0.03978532552719116,
0.006238413508981466,
0.024698037654161453,
0.08518227934837341,
-0.046257276087999344,
-0.02987792156636715,
0.012656031176447868,
-0.043762482702732086,
-0.005643610842525959,
-0.03821663558483124,
0.028568940237164497,
-0.025167517364025116,
-0.03704914450645447,
-0.0392262227833271,
-0.008124449290335178,
-0.0024690853897482157,
0.005581357516348362,
-0.04032689332962036,
0.011811316013336182,
-0.06503532081842422,
0.026984740048646927,
0.01026897318661213,
0.02608412690460682,
0.016555486246943474,
0.0014480652753263712,
-0.017117248848080635,
-0.052622731775045395,
-0.055774617940187454,
-0.009018683806061745,
0.03114526905119419,
-0.006873783655464649,
-0.013631409965455532,
-0.02096615917980671,
0.005399775225669146,
0.01980607956647873,
0.05880779027938843,
-0.003160902764648199,
-0.010034848935902119,
-0.06145496666431427,
-0.004923333413898945,
-0.028646262362599373,
0.0556928887963295,
0.009947187267243862,
-0.02720629796385765,
-0.046230658888816833,
0.06726709008216858,
-0.013861948624253273,
-0.05603933706879616,
0.014668767340481281,
-0.004997709300369024,
0.024813415482640266,
-0.03971882164478302,
-0.003564408514648676,
-0.014945133589208126,
-0.051914770156145096,
0.00824800692498684,
0.028518710285425186,
0.013376428745687008,
-0.009289314039051533,
0.04135890305042267,
0.025940578430891037,
-0.01014008279889822,
0.0530075766146183,
0.007189336232841015,
0.02300499938428402,
0.010656148195266724,
-0.03357971832156181,
0.037094175815582275,
0.02087860368192196,
0.018319258466362953,
0.05051526427268982,
0.012932974845170975,
0.004336153157055378,
-0.01816626638174057,
0.010101988911628723,
-0.014247274026274681,
-0.009484351612627506,
-0.013250824995338917,
0.0023857122287154198,
0.06561849266290665,
0.0356740839779377,
-0.014418353326618671,
-0.0034911383409053087,
0.002046402543783188,
0.04181302338838577,
0.08246628195047379,
-0.022624356672167778,
-0.04622667655348778,
0.03374045714735985,
0.012421894818544388,
-0.010816486552357674,
-0.006762370467185974,
0.006370268762111664,
0.01954738236963749,
0.004145199898630381,
0.0812038853764534,
-0.09395334869623184,
0.0366632379591465,
-0.00021046402980573475,
0.02860483154654503,
0.04650016501545906,
0.05523454397916794,
0.06589934229850769,
-0.008589653298258781,
0.005239836871623993,
0.014764649793505669,
0.036003004759550095,
0.00938513595610857,
-0.03555605188012123,
0.004790861159563065,
-0.0705636665225029,
0.017530666664242744,
-0.009280839934945107,
0.021921206265687943,
0.016538171097636223,
0.049851033836603165,
0.04058994725346565,
0.031212642788887024,
-0.014329232275485992,
-0.04853711649775505,
-0.046970024704933167,
-0.09216026961803436,
-0.07237149775028229,
-0.04401244968175888,
0.026257937774062157,
0.042919691652059555,
0.01441554818302393,
-0.040327928960323334,
-0.08037790656089783,
-0.0221283920109272,
-0.003087650053203106,
-0.010552630759775639,
-0.09775391966104507,
0.022034013643860817,
0.010337690822780132,
-0.010470984503626823,
0.03877554088830948,
0.07962707430124283,
-0.011149642057716846,
-0.033349864184856415,
-0.02560426853597164,
0.032928239554166794,
-0.04054917395114899,
-0.005020200274884701,
-0.017447710037231445,
0.013416202738881111,
-0.02218029461801052,
0.010973198339343071,
0.02480059675872326,
-0.025890743359923363,
-0.01685473509132862,
-0.030697807669639587,
0.040775757282972336,
-0.03626475855708122,
-0.03292999416589737,
0.042905449867248535,
0.05979930981993675,
0.014693942852318287,
0.04658433422446251,
0.03542587533593178,
-0.024387018755078316,
0.03256017342209816,
-0.03512435033917427,
0.037464357912540436,
0.046790849417448044,
-0.019407188519835472,
-0.004441648721694946,
-0.01747320033609867,
0.04834435135126114,
-0.04422140493988991,
-0.018941951915621758,
0.052474237978458405,
-0.02212408371269703,
0.006725446321070194,
-0.06599254906177521,
-0.021916914731264114,
-0.026088986545801163,
0.051467493176460266,
0.0549950934946537,
0.04869633913040161,
-0.021844221279025078,
-0.026804640889167786,
-0.0765145942568779,
0.03351275250315666,
-0.012372041121125221,
-0.0427871011197567,
-0.009776878170669079,
-0.004759201779961586,
0.01880778931081295,
-0.0032696304842829704,
0.012469755485653877,
-0.025022637099027634,
-0.0694049596786499,
-0.032514750957489014,
0.05007045343518257,
0.018677810207009315,
0.05074482411146164,
0.017256328836083412,
-0.03222392126917839,
-0.009691496379673481,
0.004708325490355492,
-0.054532311856746674,
-0.029074205085635185,
-0.04686616733670235,
-0.032966248691082,
-0.006007540971040726,
-0.04309026524424553,
0.009641312062740326,
0.04902523756027222,
0.006203299853950739,
0.009725472889840603,
0.020095547661185265,
-0.013556800782680511,
0.07723169773817062,
0.04324522241950035,
-0.04578770697116852,
-0.02958010509610176,
0.016075341030955315,
-0.0015072458190843463,
-0.03702843561768532,
-0.005475027021020651,
-0.0012183962389826775,
-0.046025387942790985,
-0.047924429178237915,
-0.03958979621529579,
-0.026881031692028046,
-0.008060231804847717,
0.048352714627981186
] |
<p>I have three column data that has time-displacement-force from 1D tensile/compression test. Now I would like to get the standard mechanical properties of the material, like Young modulus, yield stress/strain, strain hardening/softening exponent, Fracture toughness, work done...</p>
<p>Is there algorithms/libraries available that will do it for me or do I have to code them myself? </p> | g7823 | [
0.016938529908657074,
-0.039143916219472885,
-0.021363768726587296,
-0.055010728538036346,
0.003021148033440113,
-0.049529965966939926,
0.013616416603326797,
-0.015991361811757088,
-0.02953512594103813,
0.01763860695064068,
-0.02809351682662964,
-0.016217829659581184,
0.009350218810141087,
-0.055357180535793304,
-0.02331947721540928,
-0.00499306945130229,
0.07531559467315674,
0.002537140855565667,
0.0030718797352164984,
0.08796043694019318,
0.036173027008771896,
0.03671318292617798,
0.00564032094553113,
-0.07097296416759491,
0.011376937851309776,
0.029367242008447647,
-0.045385751873254776,
-0.0018538626609370112,
-0.06411111354827881,
0.057670630514621735,
-0.02235264889895916,
0.010744585655629635,
-0.01097582746297121,
-0.043260760605335236,
0.027075203135609627,
-0.0019496334716677666,
0.022473396733403206,
-0.030192824080586433,
0.06268215924501419,
0.003597838571295142,
-0.04788995906710625,
-0.03434091433882713,
0.011671662330627441,
0.03861089423298836,
0.00047721422743052244,
-0.03236159682273865,
-0.004500493407249451,
-0.0173153318464756,
-0.020568223670125008,
0.012027173303067684,
-0.007478195242583752,
-0.0027810721658170223,
0.049577414989471436,
-0.03274442255496979,
0.005256475880742073,
-0.0020262948237359524,
-0.021960889920592308,
-0.008227836340665817,
0.06853147596120834,
-0.015604839660227299,
-0.012052771635353565,
-0.043162669986486435,
-0.015211308375000954,
-0.030769653618335724,
0.030951155349612236,
0.05225835368037224,
0.0037146832328289747,
-0.024748217314481735,
-0.003725005080923438,
-0.04007532820105553,
-0.000021744155674241483,
0.05153437331318855,
0.039934080094099045,
-0.007337207440286875,
-0.039531778544187546,
-0.003735470585525036,
0.019579634070396423,
-0.017610132694244385,
-0.011142900213599205,
0.00530588673427701,
-0.020633511245250702,
-0.009300468489527702,
0.028601497411727905,
-0.05022108554840088,
0.009975805878639221,
0.0005913027562201023,
0.004867041017860174,
0.031150035560131073,
0.019459670409560204,
0.03796398639678955,
-0.01782444305717945,
-0.0039710854180157185,
0.0017287922091782093,
0.021029381081461906,
0.019343020394444466,
0.01325949840247631,
-0.08492807298898697,
0.0416010282933712,
0.0472901351749897,
-0.0018516118871048093,
0.04620355740189552,
-0.05172758549451828,
0.011944068595767021,
-0.040964990854263306,
-0.0671079233288765,
0.016654524952173233,
0.01774858683347702,
-0.02966184914112091,
-0.026264941319823265,
-0.0030229436233639717,
-0.039393551647663116,
0.04821806401014328,
-0.036598529666662216,
0.02357642352581024,
0.004785331431776285,
-0.05785262957215309,
-0.011097583919763565,
-0.006141889840364456,
-0.06981372088193893,
0.04380347952246666,
0.030166536569595337,
-0.022088440135121346,
0.05005680024623871,
0.027451027184724808,
-0.009385021403431892,
-0.03153917193412781,
0.005016859155148268,
0.03912750631570816,
-0.013203058391809464,
-0.031533654779195786,
-0.002948777051642537,
0.020668871700763702,
-0.02888825349509716,
0.010765144601464272,
-0.03615314140915871,
0.050766777247190475,
-0.00037979197804816067,
0.06098441034555435,
-0.04103626683354378,
0.05587458238005638,
-0.06070858985185623,
0.002656768076121807,
-0.0822303518652916,
-0.006934592500329018,
0.0015545068308711052,
-0.03045361116528511,
-0.06900723278522491,
0.00679432600736618,
0.0275763850659132,
0.051463570445775986,
0.039603736251592636,
0.013600034639239311,
0.07271851599216461,
-0.02245335839688778,
0.030751463025808334,
0.023414092138409615,
0.022972434759140015,
-0.014294043183326721,
-0.011598862707614899,
0.05354158580303192,
-0.010129069909453392,
-0.02963288128376007,
-0.008614950813353062,
0.014966578222811222,
0.027315154671669006,
-0.0005487837479449809,
-0.06790392100811005,
-0.0080259395763278,
0.07125862687826157,
-0.026103170588612556,
-0.017359821125864983,
-0.05304523929953575,
0.04608302190899849,
-0.007724534720182419,
-0.041143905371427536,
0.041029755026102066,
0.014651580713689327,
-0.023556319996714592,
0.049345962703228,
0.04714489355683327,
0.017734959721565247,
0.04914036765694618,
-0.0016870456747710705,
0.009599169716238976,
-0.02448180504143238,
-0.03904425725340843,
-0.0029421341605484486,
-0.0029383525252342224,
-0.051575955003499985,
0.019774913787841797,
-0.06568940728902817,
0.02079162746667862,
0.02953360229730606,
0.007593574933707714,
-0.013916532509028912,
-0.1211291030049324,
-0.03976630046963692,
-0.024062808603048325,
-0.013830188661813736,
-0.06662371754646301,
0.056240782141685486,
0.03454361855983734,
0.03807474672794342,
0.04630894213914871,
-0.005143776535987854,
-0.040472324937582016,
-0.004445502534508705,
0.03387390822172165,
0.016547471284866333,
0.001690307050012052,
-0.032415296882390976,
-0.021610520780086517,
-0.024391844868659973,
0.04828685149550438,
0.021331844851374626,
-0.03105987422168255,
-0.03035914897918701,
-0.03763308748602867,
0.006175468675792217,
-0.016919920220971107,
0.016340693458914757,
0.00495703611522913,
-0.0021219952031970024,
0.009543496184051037,
0.00364258443005383,
-0.03008294478058815,
0.06076277419924736,
0.08848763257265091,
0.024734554812312126,
-0.03328824043273926,
-0.04113806411623955,
-0.012109712697565556,
0.055059242993593216,
-0.02497085928916931,
0.028573136776685715,
0.09348368644714355,
-0.07588626444339752,
0.0009647330734878778,
0.0502777136862278,
0.001729112002067268,
0.006382895167917013,
-0.009175148792564869,
0.01643965020775795,
-0.029148994013667107,
0.03205180913209915,
-0.06364227086305618,
0.032967228442430496,
0.008131190203130245,
0.07870274037122726,
-0.019407691434025764,
0.011765087954699993,
0.027909332886338234,
-0.06771289557218552,
0.0348292738199234,
-0.03338639438152313,
-0.020565666258335114,
0.05868849158287048,
-0.04061778262257576,
-0.01717931590974331,
-0.00702911801636219,
-0.008079417049884796,
0.012152462266385555,
0.03173893317580223,
0.04224017262458801,
-0.015704486519098282,
-0.006437796633690596,
0.02447153627872467,
-0.08272386342287064,
-0.04597872495651245,
0.03616419807076454,
-0.029546676203608513,
-0.02658187970519066,
0.06953348964452744,
0.001574185909703374,
0.044174302369356155,
-0.005797144491225481,
0.0025584627874195576,
0.019299784675240517,
-0.03586871549487114,
-0.03973421826958656,
-0.015450846403837204,
-0.09974787384271622,
0.05095919594168663,
0.020509280264377594,
-0.0019676578231155872,
0.046892207115888596,
-0.016867060214281082,
-0.03343195095658302,
-0.012994838878512383,
0.020206676796078682,
-0.01873115450143814,
0.05291976407170296,
-0.00753913726657629,
0.011125132441520691,
-0.008607135154306889,
-0.023081690073013306,
-0.009268383495509624,
-0.01914340816438198,
-0.015545905567705631,
0.0038518903311342,
-0.06253617256879807,
-0.028276193886995316,
0.04198165610432625,
0.03986719995737076,
-0.001515587093308568,
-0.011386791244149208,
0.02362089604139328,
-0.00699707493185997,
0.02563863806426525,
-0.005518380086869001,
0.006322816479951143,
-0.03337577357888222,
0.0007276805699802935,
-0.009387458674609661,
-0.05574813857674599,
-0.022069979459047318,
0.003249713685363531,
-0.0289666298776865,
0.010444738902151585,
0.017130471765995026,
-0.024658871814608574,
-0.08495692163705826,
0.039877988398075104,
-0.051086679100990295,
-0.01872888393700123,
0.044354986399412155,
-0.032717108726501465,
0.019658276811242104,
0.0009030440705828369,
0.011095685884356499,
0.049350082874298096,
-0.013654735870659351,
0.008696003817021847,
-0.007376637309789658,
-0.01906176283955574,
-0.027778171002864838,
-0.05545186623930931,
-0.01923217438161373,
0.05379568785429001,
-0.036731407046318054,
-0.02183675952255726,
-0.012036686763167381,
-0.02847817726433277,
0.04281613230705261,
-0.04530408978462219,
-0.04032052680850029,
0.0026929560117423534,
-0.01989983767271042,
-0.03174503520131111,
-0.005556755233556032,
0.026301108300685883,
-0.03438283130526543,
0.021348118782043457,
-0.03238451108336449,
0.0460999421775341,
0.06913422048091888,
0.03413238376379013,
-0.029489880427718163,
-0.013224614784121513,
0.012469403445720673,
0.014207875356078148,
-0.019213976338505745,
0.000662653474137187,
0.01472435425966978,
0.007253683637827635,
0.02598719298839569,
0.05177650973200798,
0.09744880348443985,
0.042807143181562424,
-0.002613004529848695,
0.040942538529634476,
-0.03917577490210533,
0.05211887136101723,
0.019902769476175308,
-0.00783626176416874,
-0.027276234701275826,
-0.05473099648952484,
0.001729921204969287,
0.03395805135369301,
0.05249179154634476,
0.04334066063165665,
-0.037119217216968536,
0.03241519257426262,
0.009421834722161293,
-0.023717770352959633,
-0.017341233789920807,
0.008698200806975365,
0.05398876592516899,
0.01012437790632248,
0.00989197101444006,
-0.0007275374955497682,
-0.08449280261993408,
-0.0633285865187645,
-0.009779863990843296,
0.05356983467936516,
-0.04784925654530525,
-0.022340089082717896,
0.0526575893163681,
-0.049020905047655106,
-0.006244023330509663,
-0.054820120334625244,
0.03919459134340286,
0.043291039764881134,
0.04818052798509598,
-0.031090347096323967,
-0.02849697321653366,
-0.03597571328282356,
-0.04523918777704239,
0.013103448785841465,
-0.00045833882177248597,
-0.04301578924059868,
-0.09514336287975311,
0.03802091255784035,
-0.018454786390066147,
-0.014777622185647488,
-0.027425464242696762,
0.05080045387148857,
-0.03415302187204361,
0.011348805390298367,
-0.003583076875656843,
0.02065318077802658,
0.04831720143556595,
0.0005889727617613971,
-0.0026261014863848686,
-0.02455190196633339,
0.02462228760123253,
0.05275982618331909,
-0.050018370151519775,
0.02094503492116928,
-0.009108709171414375,
-0.022511010989546776,
-0.0065609426237642765,
0.019429191946983337,
0.00015211319259833544,
-0.004000661429017782,
0.058153703808784485,
0.05470569059252739,
-0.0038257106207311153,
0.01089076790958643,
-0.04878595098853111,
-0.007793511729687452,
-0.03636624664068222,
0.014814295805990696,
-0.0474398247897625,
-0.014839626848697662,
0.10889045149087906,
-0.0424073301255703,
0.00021531137463171035,
-0.026758380234241486,
0.028491338714957237,
0.00667167641222477,
-0.030461184680461884,
-0.05543101578950882,
0.0003782666753977537,
0.014823229983448982,
0.02379865013062954,
0.07014328986406326,
-0.03262509033083916,
0.049124717712402344,
0.025026071816682816,
-0.01598145067691803,
0.018835149705410004,
-0.05451718345284462,
-0.018612150102853775,
-0.08179246634244919,
0.011768135242164135,
0.00024490198120474815,
0.03337596356868744,
0.06253088265657425,
0.02390642650425434,
0.024017198011279106,
-0.05971671640872955,
0.043983347713947296,
0.019052445888519287,
0.04511847347021103,
0.020782187581062317,
0.001411483739502728,
-0.019333094358444214,
0.0064662741497159,
-0.010396999306976795,
0.032103195786476135,
0.06545668840408325,
0.006463861558586359,
-0.030221451073884964,
0.050147999078035355,
-0.0199600700289011,
-0.026539139449596405,
-0.03752964362502098,
-0.04199998825788498,
0.024728914722800255,
0.03513693809509277,
-0.032330211251974106,
0.058291152119636536,
-0.008479739539325237,
-0.06854123622179031,
-0.022442035377025604,
0.046599190682172775,
0.016048194840550423,
-0.022830532863736153,
-0.009225025773048401,
-0.028575405478477478,
0.0030300889629870653,
-0.004479622468352318,
-0.006351299583911896,
0.005976542364805937,
0.031449440866708755,
0.04971076175570488,
0.014910104684531689,
-0.023855997249484062,
0.026978611946105957,
0.0355025976896286,
-0.009748031385242939,
0.059280138462781906,
0.033468957990407944,
0.04596515744924545,
0.024477021768689156,
0.04744621366262436,
0.04307805374264717,
-0.006427896209061146,
-0.10958300530910492,
0.036389708518981934,
0.03680960834026337,
0.06532351672649384,
0.01447911188006401,
-0.04601213335990906,
0.0009089677478186786,
-0.01161231193691492,
-0.033991340547800064,
0.0165071003139019,
-0.012575976550579071,
-0.03391695022583008,
0.014220256358385086,
-0.02070392109453678,
-0.025297097861766815,
-0.005908967927098274,
-0.017952853813767433,
0.011031868867576122,
-0.017296183854341507,
0.010841503739356995,
-0.0601462684571743,
0.021504294127225876,
0.04524700343608856,
0.02057739347219467,
0.0006548799574375153,
-0.049103911966085434,
-0.02244664542376995,
0.008900715969502926,
-0.034281790256500244,
0.004766899161040783,
-0.031072771176695824,
0.022104252129793167,
0.027808960527181625,
-0.00791595783084631,
-0.03266698122024536,
-0.010013489983975887,
0.08634486049413681,
0.002995702438056469,
-0.06918616592884064,
0.03789621964097023,
0.04384729638695717,
-0.016744673252105713,
0.02967238985002041,
-0.02300647459924221,
-0.008031376637518406,
-0.0060319495387375355,
-0.03614894673228264,
-0.021011268720030785,
0.04136382043361664,
0.06508304178714752,
0.003145385067909956,
-0.0012828137259930372,
-0.05986646190285683,
0.07725164294242859,
-0.0004460811032913625,
0.01110366266220808,
0.02520282194018364,
-0.00870075449347496,
0.011325151659548283,
0.044565778225660324,
-0.07765746861696243,
0.019462499767541885,
-0.03740899637341499,
-0.015384746715426445,
0.08009593188762665,
0.033959437161684036,
0.04630466178059578,
0.009452849626541138,
-0.004859153181314468,
0.004723865073174238,
-0.035319600254297256,
-0.04972972720861435,
0.0006273621111176908,
0.000897045829333365,
-0.06380359083414078,
-0.029512643814086914,
0.019968772307038307,
0.00555776571854949,
0.04413951188325882,
0.09529903531074524,
0.02559347078204155,
-0.01179803628474474,
0.056101780384778976,
0.03249101713299751,
-0.06838831305503845,
-0.0051203262992203236,
-0.016942445188760757,
0.02771485596895218,
-0.019166119396686554,
0.03586401045322418,
-0.01681426540017128,
0.014583002775907516,
0.002662139479070902,
-0.060359079390764236,
0.036506395787000656,
-0.04689362645149231,
-0.051482878625392914,
0.009692149236798286,
-0.013085233978927135,
-0.03198428452014923,
-0.07801589369773865,
0.01343152392655611,
-0.008697142824530602,
0.007454395294189453,
-0.029131339862942696,
-0.0402127280831337,
-0.024771301075816154,
-0.05899796634912491,
0.03735768422484398,
0.01026156172156334,
-0.02147107571363449,
0.05001676082611084,
0.01145304273813963,
0.02604958787560463,
-0.001976638799533248,
-0.03212985396385193,
0.019272591918706894,
-0.02333880215883255,
0.09912849962711334,
0.02905295602977276,
0.01512199454009533,
0.023354027420282364,
-0.03181159496307373,
-0.0017050307942554355,
-0.002183542586863041,
-0.05705529823899269,
-0.028812721371650696,
0.024378661066293716,
0.01622368022799492,
-0.01784597337245941,
0.009646889753639698,
0.056474585086107254,
0.0414380207657814,
0.0247749425470829,
0.046339284628629684,
-0.0018412712961435318,
0.02800850197672844,
0.024226650595664978,
-0.05342846363782883,
0.012001696042716503,
-0.008898359723389149,
-0.023015698418021202,
-0.07313910871744156,
0.009530958719551563,
-0.03709298372268677,
0.0055901953019201756,
0.052830297499895096,
0.01784937083721161,
-0.014565582387149334,
0.04282976686954498,
0.011806657537817955,
0.04504341259598732,
0.010534820146858692,
0.01668970286846161,
0.12530364096164703,
0.030779045075178146,
0.002816846827045083,
-0.029644526541233063,
0.018797483295202255,
-0.042674437165260315,
-0.030847756192088127,
-0.06366868317127228,
0.016688043251633644,
0.01583268493413925,
-0.014577333815395832,
0.009960728697478771,
-0.021486636251211166,
-0.009837441146373749,
-0.0085764704272151,
0.01187499426305294,
0.024552898481488228,
-0.007683797739446163,
-0.006523186340928078,
-0.013843919150531292,
-0.02729441411793232,
-0.019532138481736183,
-0.060494426637887955,
0.030097410082817078,
-0.038056258112192154,
0.022326886653900146,
0.07189326733350754,
0.04445230960845947,
0.01968555338680744,
-0.019297759979963303,
-0.013650706969201565,
-0.03662225976586342,
-0.009926646016538143,
-0.053650740534067154,
-0.026036327704787254,
0.012641812674701214,
0.008451296016573906,
-0.021139811724424362,
-0.00008011589670786634,
-0.028711631894111633,
-0.0854034423828125,
-0.007086306344717741,
0.009356784634292126,
-0.012629127129912376,
-0.02344672940671444,
-0.04353933408856392,
0.028897006064653397,
-0.044923100620508194,
-0.003736383281648159,
0.008014139719307423,
-0.012113851495087147,
0.014178259298205376,
-0.0406159944832325,
-0.07950727641582489,
0.0553811751306057,
-0.04726942256093025,
0.021218683570623398,
0.018390197306871414,
-0.016294287517666817,
0.011887126602232456,
-0.023196959868073463,
0.022651975974440575,
0.05546751618385315,
0.03311442583799362,
0.0069354139268398285,
0.016617529094219208,
0.10284457355737686,
-0.009699271991848946,
0.035936933010816574,
-0.055531591176986694,
-0.0077355364337563515,
0.022481059655547142,
0.022646375000476837,
-0.06490982323884964,
0.08877895027399063,
0.00836483109742403,
-0.02125692553818226,
-0.019285717979073524,
-0.00395780336111784,
0.020523391664028168,
-0.02995239943265915,
-0.07026176899671555,
0.014513975009322166,
0.02172548696398735,
0.013971706852316856,
0.04191543906927109,
-0.05332030728459358,
0.004601868335157633,
0.02910790778696537,
-0.035235289484262466,
-0.0025393895339220762,
-0.024495720863342285,
0.017055269330739975,
-0.029556766152381897,
0.03883647546172142
] |
<p>I've read that all paths inside the EH lead to singularity. ALL paths. Even the ones pointing away from it, right? Because there's NO pointing away from singularity, since ALL paths point to it. </p>
<p>So how could it be at the exact center? Or am I misunderstanding "center" here?</p>
<p><a href="http://physics.stackexchange.com/questions/56906/is-singularity-at-the-exact-centre-of-a-black-hole"></a></p> | g7824 | [
0.0175030454993248,
-0.011255279183387756,
0.021936962381005287,
-0.0022586393170058727,
0.06558592617511749,
0.023623278364539146,
0.02893025055527687,
0.09152790904045105,
0.004762681666761637,
-0.0008606348419561982,
0.001920255832374096,
-0.03590551018714905,
0.06208539009094238,
-0.0228639654815197,
-0.017248766496777534,
-0.024436626583337784,
-0.005098248831927776,
0.042065419256687164,
0.031044287607073784,
-0.011484555900096893,
-0.013882504776120186,
-0.03797472268342972,
0.03120660036802292,
-0.024597615003585815,
0.0013875763397663832,
-0.029279371723532677,
0.07070080190896988,
-0.00569053553044796,
-0.052191704511642456,
-0.006450261455029249,
0.04804649204015732,
0.006677950266748667,
0.05783065780997276,
-0.036278266459703445,
-0.007178816944360733,
0.02518310211598873,
-0.012837870977818966,
0.0235642921179533,
-0.009064079262316227,
0.0625070258975029,
0.010787072591483593,
-0.07780545949935913,
-0.021469464525580406,
-0.03703084588050842,
-0.06397315114736557,
0.034425996243953705,
0.0017731119878590107,
0.00711656641215086,
0.06060737371444702,
0.0021262906957417727,
-0.014362870715558529,
-0.04398369789123535,
0.05424955114722252,
0.04939135164022446,
0.02937859110534191,
0.06506343930959702,
0.032624803483486176,
0.022981515154242516,
0.049026213586330414,
0.04365704208612442,
-0.012229729443788528,
0.013182136230170727,
0.02654510736465454,
0.0503014512360096,
-0.039877068251371384,
-0.040710143744945526,
-0.022732246667146683,
-0.0048282998614013195,
-0.050393927842378616,
-0.013726236298680305,
0.03578663617372513,
-0.06756380200386047,
-0.0052737160585820675,
-0.00260325544513762,
-0.07430878281593323,
0.04217305779457092,
0.04320312663912773,
-0.040912218391895294,
0.06394334882497787,
-0.032829150557518005,
-0.043043844401836395,
-0.016676131635904312,
0.009985728189349174,
0.018445145338773727,
0.030935972929000854,
0.03864779323339462,
-0.007009861525148153,
-0.03005516529083252,
-0.019557150080800056,
-0.01473238505423069,
-0.013029773719608784,
0.051286324858665466,
0.036366529762744904,
0.021192366257309914,
0.009348498657345772,
-0.07871875166893005,
0.00807601772248745,
0.060758184641599655,
0.004269856959581375,
0.009943214245140553,
-0.056713905185461044,
-0.01283170934766531,
0.007058102171868086,
-0.0056852614507079124,
-0.026345986872911453,
-0.011781878769397736,
-0.03601051867008209,
0.03610456734895706,
0.021799540147185326,
0.014957182109355927,
0.0031709743198007345,
-0.02200956828892231,
-0.0462789349257946,
-0.020782411098480225,
-0.013747618533670902,
0.08040716499090195,
0.0945037379860878,
-0.01182167511433363,
0.015486706048250198,
0.010277125984430313,
0.04774630442261696,
-0.03452272713184357,
-0.025612765923142433,
0.0640777200460434,
0.00021511052909772843,
0.008571005426347256,
-0.018254535272717476,
-0.01670496165752411,
-0.012411629781126976,
0.057428814470767975,
-0.0010518399067223072,
-0.020846739411354065,
-0.02917858026921749,
0.0011347674299031496,
0.034577276557683945,
-0.010951770469546318,
0.03695874288678169,
-0.017513008788228035,
0.03263164311647415,
0.004499408416450024,
-0.018041493371129036,
0.017336511984467506,
-0.00303926900960505,
0.028395891189575195,
-0.01963166706264019,
-0.012246771715581417,
0.02486461214721203,
0.022870691493153572,
0.0737532377243042,
0.01682639867067337,
-0.027379730716347694,
0.09286125749349594,
-0.02302655577659607,
0.017479244619607925,
-0.036358047276735306,
-0.02050461806356907,
0.044841863214969635,
0.017285294830799103,
-0.018914449959993362,
-0.010099134407937527,
0.03566524386405945,
-0.006393310613930225,
0.06191358342766762,
0.03638868033885956,
-0.062454864382743835,
-0.003035117406398058,
0.002444383455440402,
-0.05498095229268074,
0.0658990666270256,
0.044383518397808075,
0.0027018750552088022,
0.00820443220436573,
-0.0007472691358998418,
0.07489044964313507,
0.024189405143260956,
-0.005575734656304121,
0.0051768324337899685,
0.029726896435022354,
0.05044930428266525,
-0.016420988366007805,
0.016474559903144836,
0.017110466957092285,
0.024602195248007774,
0.01803593337535858,
-0.042540330439805984,
-0.015046528540551662,
0.03962896019220352,
0.019237129017710686,
0.033824753016233444,
-0.00891356635838747,
-0.0007902977522462606,
-0.0038721379823982716,
-0.026799775660037994,
0.10232371091842651,
0.02171895280480385,
-0.015231676399707794,
-0.012541213072836399,
-0.03843837231397629,
0.016055630519986153,
0.007950429804623127,
0.05024976655840874,
-0.00974125787615776,
-0.021938782185316086,
0.02728882245719433,
0.01885746419429779,
0.03505484387278557,
-0.0036246294621378183,
-0.03459494933485985,
0.00271980301477015,
0.012926522642374039,
0.007664031814783812,
0.03034578263759613,
0.0016144083347171545,
0.0434606596827507,
-0.04761582612991333,
0.017333537340164185,
-0.057744573801755905,
-0.009606930427253246,
-0.007732768077403307,
0.013690214604139328,
-0.0135911600664258,
-0.0060665300115942955,
-0.032516367733478546,
0.0007542199455201626,
0.0033499691635370255,
0.023628124967217445,
-0.009387851692736149,
-0.052600495517253876,
-0.04433954134583473,
-0.026370210573077202,
-0.07177449762821198,
-0.030219385400414467,
-0.016906550154089928,
-0.026864035055041313,
0.039192136377096176,
0.00001791396425687708,
-0.0005233250558376312,
-0.03199026361107826,
-0.004455300979316235,
-0.015453704632818699,
-0.0039972602389752865,
-0.03474496677517891,
0.0156139200553298,
-0.018000848591327667,
0.028521643951535225,
-0.022242767736315727,
0.10919840633869171,
-0.04653961583971977,
-0.05422718822956085,
0.038094229996204376,
0.03480489179491997,
-0.02809729427099228,
-0.022687342017889023,
0.026570932939648628,
-0.019346924498677254,
-0.010448762215673923,
0.028834547847509384,
0.03265445679426193,
-0.04546964541077614,
-0.06438980251550674,
-0.03290296718478203,
-0.0351327545940876,
0.0413149893283844,
0.010029617697000504,
-0.060711104422807693,
0.020110970363020897,
-0.006643732078373432,
-0.060083113610744476,
0.01585034839808941,
-0.008747350424528122,
-0.03546985238790512,
0.11686711013317108,
0.023209653794765472,
0.0395718552172184,
-0.031181903555989265,
0.012075096368789673,
-0.029240014031529427,
0.026832517236471176,
0.057702768594026566,
0.011298947036266327,
-0.0368475541472435,
0.05857829749584198,
-0.04021765664219856,
-0.008403733372688293,
-0.009821626357734203,
0.007339050527662039,
-0.024258246645331383,
0.011991956271231174,
-0.03105960413813591,
0.0007523102685809135,
-0.011308439075946808,
-0.05394851416349411,
0.011178579181432724,
0.03900366649031639,
0.04023367539048195,
0.038815680891275406,
0.022762706503272057,
0.004740281030535698,
-0.03211789205670357,
0.052602723240852356,
0.02695690095424652,
0.006248472258448601,
0.02995159849524498,
0.007778415456414223,
-0.027984874323010445,
0.027552509680390358,
0.028104428201913834,
-0.10103586316108704,
0.0008452050387859344,
-0.020834624767303467,
0.03458624333143234,
-0.013796455226838589,
-0.00119840691331774,
0.02543747052550316,
0.09144137054681778,
-0.011891918256878853,
-0.026546331122517586,
0.002335919067263603,
0.023145586252212524,
-0.017781667411327362,
-0.05997645854949951,
0.036312002688646317,
-0.06753924489021301,
-0.01981087401509285,
0.08176421374082565,
0.013996542431414127,
-0.0032355894800275564,
-0.02049829438328743,
-0.056930843740701675,
-0.02655290812253952,
-0.00621073367074132,
-0.006274046842008829,
-0.054013170301914215,
0.00547599233686924,
-0.040856022387742996,
-0.054511383175849915,
-0.01702660694718361,
0.012349173426628113,
0.03278651088476181,
0.011792237870395184,
-0.005978340748697519,
0.010185843333601952,
0.00947923120111227,
-0.03534611687064171,
0.05027216672897339,
0.009430448524653912,
-0.007628492545336485,
-0.012199277989566326,
0.06516007333993912,
-0.0074552386067807674,
0.010278685949742794,
-0.01098592672497034,
-0.04265037551522255,
-0.011460415087640285,
-0.026673533022403717,
-0.012256074696779251,
0.01446688361465931,
0.007085676304996014,
0.019166171550750732,
0.017056068405508995,
0.010100829415023327,
-0.03283184766769409,
0.04125496745109558,
-0.02042275294661522,
-0.0003036647685803473,
-0.05852322280406952,
0.04811815544962883,
-0.01862039975821972,
0.08036909252405167,
0.003178870538249612,
0.01711050420999527,
0.024882983416318893,
-0.005671427585184574,
-0.02387085184454918,
0.006411128677427769,
-0.045549891889095306,
0.01625901088118553,
0.07076802104711533,
-0.03330807760357857,
0.0369279682636261,
0.02975854091346264,
-0.04499080777168274,
0.006404257845133543,
0.01635243557393551,
0.019477279856801033,
0.047719553112983704,
-0.07131639868021011,
-0.05157368630170822,
0.04107658937573433,
-0.034488607197999954,
0.03319248557090759,
-0.020289113745093346,
0.0512864775955677,
-0.05407463014125824,
-0.023334182798862457,
0.010542194359004498,
0.0038382746279239655,
-0.030270012095570564,
-0.04273291677236557,
0.031427495181560516,
0.04994025081396103,
-0.028146639466285706,
-0.008801263757050037,
0.02270946279168129,
0.014788465574383736,
0.05058832839131355,
0.009134956635534763,
-0.037502992898225784,
0.018420947715640068,
-0.0418168269097805,
0.055417001247406006,
-0.0018790422473102808,
0.02330520562827587,
-0.04542343690991402,
0.07924295961856842,
-0.02006954327225685,
0.021157827228307724,
-0.040099967271089554,
-0.06063459441065788,
-0.055773258209228516,
0.06344136595726013,
-0.09323601424694061,
0.014606761746108532,
-0.055232465267181396,
0.011324174702167511,
0.013288873247802258,
-0.028878450393676758,
0.05831325426697731,
-0.008967921137809753,
0.01528499647974968,
-0.0020371347200125456,
0.02445749193429947,
0.01459509413689375,
0.023862730711698532,
-0.03839297965168953,
0.026692643761634827,
-0.02358827367424965,
-0.03420170769095421,
-0.007403029128909111,
0.01387751940637827,
0.05020816996693611,
0.008918099105358124,
0.023828111588954926,
0.019479170441627502,
-0.014151678420603275,
-0.032725878059864044,
-0.04365629702806473,
-0.00009757689986145124,
-0.02551981620490551,
-0.02571195736527443,
-0.02849225513637066,
-0.0030765903647989035,
-0.04621490463614464,
-0.037349604070186615,
-0.015818316489458084,
-0.017559267580509186,
-0.059531085193157196,
0.0934661477804184,
-0.038007207214832306,
-0.011109870858490467,
-0.08223465830087662,
-0.08750219643115997,
-0.02983311377465725,
0.004085872322320938,
0.06211637705564499,
-0.029566897079348564,
-0.049682531505823135,
-0.020505789667367935,
-0.06415873765945435,
-0.020472463220357895,
0.02776341326534748,
0.04782955348491669,
0.006777102127671242,
-0.013201267458498478,
0.02861863374710083,
0.010042794980108738,
-0.015110401436686516,
-0.04977896437048912,
-0.014594645239412785,
-0.04246072471141815,
-0.024801483377814293,
-0.07479456067085266,
0.0012073871912434697,
0.011617408134043217,
-0.05478502810001373,
0.030649621039628983,
-0.060110028833150864,
0.027903614565730095,
-0.02221154235303402,
0.04521575942635536,
0.00657946802675724,
-0.03975173458456993,
-0.004541613627225161,
-0.06298239529132843,
-0.02470364049077034,
-0.038895055651664734,
-0.025328833609819412,
0.011463741771876812,
0.0014924380229786038,
-0.019681917503476143,
-0.04317111894488335,
0.041433289647102356,
-0.028312448412179947,
0.021442731842398643,
0.01614198461174965,
0.041214071214199066,
0.03612475097179413,
-0.029728613793849945,
-0.004559729248285294,
-0.04242328554391861,
0.009872939437627792,
0.00028198023210279644,
-0.024125944823026657,
0.042406562715768814,
0.04662562534213066,
0.010250281542539597,
-0.01666879653930664,
0.008080089464783669,
0.030025461688637733,
0.04691513627767563,
-0.0031119054183363914,
0.014478732831776142,
0.003999494481831789,
-0.036090172827243805,
-0.007921612821519375,
-0.01228043157607317,
-0.013558936305344105,
0.0005392134771682322,
0.023623308166861534,
0.019613953307271004,
0.006375972647219896,
0.04963904619216919,
0.05203254148364067,
0.0023220465518534184,
-0.017470626160502434,
-0.05285832658410072,
-0.0008703917847014964,
-0.05198485776782036,
0.067498579621315,
-0.025174550712108612,
-0.02464871108531952,
-0.007044860161840916,
-0.03672570735216141,
0.030388694256544113,
-0.028947090730071068,
0.0056219883263111115,
-0.05596087872982025,
-0.013852544128894806,
0.04708688706159592,
-0.022418325766921043,
-0.05704148858785629,
0.040969740599393845,
0.005258895922452211,
0.006774270441383123,
-0.05827489122748375,
0.02507644146680832,
0.026402732357382774,
-0.012598144821822643,
-0.03309769555926323,
-0.07930848747491837,
0.033754896372556686,
-0.022769691422581673,
-0.06535742431879044,
-0.04483192786574364,
-0.006685647647827864,
-0.02117013745009899,
-0.01695070043206215,
0.0027204721700400114,
0.06753922253847122,
0.0038701449520885944,
0.0023874123580753803,
-0.00024545559426769614,
0.0010235566878691316,
0.05471394956111908,
0.008491575717926025,
0.012957648374140263,
-0.01689085178077221,
0.04614134505391121,
-0.05021778494119644,
-0.0063866060227155685,
-0.009045755490660667,
-0.011536897160112858,
0.12194608151912689,
-0.06610176712274551,
0.061763159930706024,
0.04922882840037346,
-0.06401832401752472,
0.03152858465909958,
0.03445086628198624,
0.049473874270915985,
-0.025188403204083443,
0.06146141141653061,
0.01922394335269928,
-0.02268550544977188,
-0.05122438073158264,
-0.016920337453484535,
-0.006768308114260435,
-0.024497609585523605,
-0.03730078414082527,
-0.006481572985649109,
-0.04434613883495331,
0.02481842041015625,
-0.0007409821264445782,
0.01882435381412506,
-0.001010137377306819,
0.0024940376169979572,
0.023390376940369606,
0.012693059630692005,
0.0025888446252793074,
-0.001946761505678296,
0.06943971663713455,
0.055847931653261185,
-0.06002117693424225,
-0.021877504885196686,
-0.04365189000964165,
-0.0006516250432468951,
-0.037113916128873825,
-0.025195883587002754,
0.025795109570026398,
0.005697466898709536,
0.05013500154018402,
0.009725362062454224,
-0.08897881954908371,
-0.001337522640824318,
0.04805038124322891,
0.015485057607293129,
-0.04366570711135864,
0.027185609564185143,
0.034397345036268234,
-0.0452568344771862,
0.026269100606441498,
0.05302984640002251,
-0.04762071743607521,
0.004674605093896389,
0.027202917262911797,
-0.005559547804296017,
0.001523223938420415,
-0.05821114778518677,
-0.010369371622800827,
0.03509039804339409,
0.05108642578125,
-0.007536564487963915,
-0.013800635933876038,
0.05380438268184662,
-0.035169199109077454,
0.0890687108039856,
0.012575754895806313,
0.02052432857453823,
-0.08399194478988647,
0.027810141444206238,
0.030004238709807396,
-0.04784221947193146,
-0.005779084749519825,
-0.0201583169400692,
0.006531017366796732,
-0.02055303007364273,
-0.055945273488759995,
0.004460994154214859,
-0.031865935772657394,
-0.0657716616988182,
0.02640572004020214,
0.059211615473032,
-0.029463930055499077,
-0.023387519642710686,
-0.003955906257033348,
-0.005157738458365202,
0.028243662789463997,
-0.017400206997990608,
-0.02557224966585636,
-0.034505393356084824,
0.02799104154109955,
-0.0008636315469630063,
-0.07938803732395172,
0.004823776893317699,
-0.06438305974006653,
-0.005724791437387466,
-0.0196492001414299,
0.03912811726331711,
-0.043101098388433456,
0.05959358066320419,
0.029024608433246613,
0.0010501234792172909,
0.05357261374592781,
-0.06020813062787056,
0.003984144888818264,
-0.008105961605906487,
-0.0674554705619812,
-0.028126968070864677,
0.0034991330467164516,
-0.059178151190280914,
-0.02136489376425743,
-0.0004415038856677711,
-0.0389157272875309,
-0.04465682432055473,
0.0012408682378008962,
0.003826129948720336,
0.03449151664972305,
0.08785122632980347,
-0.04576750844717026,
-0.0394156351685524,
0.059664156287908554,
-0.023034757003188133,
0.03788077458739281,
0.0286861602216959,
0.010035622864961624,
0.017257260158658028,
0.005865409504622221,
0.020766373723745346,
-0.032307934015989304,
0.058923907577991486,
0.07160914689302444,
0.03791993111371994,
0.018947316333651543,
0.0015484060859307647,
-0.04872556030750275,
0.027135362848639488,
0.02373344637453556,
0.02437274158000946,
-0.024248797446489334,
-0.06577980518341064,
-0.05186530575156212,
0.07610131800174713,
-0.004247910343110561,
0.026366714388132095,
-0.041085757315158844,
0.010755324736237526,
0.01733344979584217,
0.0001554410846438259,
-0.0064326003193855286,
-0.03418135270476341,
0.002342809457331896,
-0.012563493102788925,
0.021632516756653786,
-0.010278893634676933,
-0.02906077541410923,
0.011524675413966179,
-0.03840558975934982,
-0.02281004935503006,
0.017093632370233536,
-0.04422492906451225,
-0.0008629744406789541,
-0.04649346321821213,
-0.009775446727871895,
-0.03480301797389984,
-0.04901197925209999,
-0.03422823175787926,
0.0033576551359146833,
0.012807382270693779,
0.03177637606859207,
0.013343439437448978,
0.030148252844810486,
0.024287503212690353,
0.024114592000842094,
0.006052418611943722,
0.025209587067365646,
-0.061971765011548996,
0.006809499580413103,
-0.02266600728034973,
-0.021882303059101105,
0.05537800490856171,
-0.037470731884241104,
0.0006747280713170767,
0.04969906806945801,
-0.013814669102430344,
0.009717251174151897,
0.014146042056381702,
0.014152668416500092,
0.04064527153968811
] |
<p>From what I've so far understood about light, a photon is emitted somewhere and after some time it's absorbed somewhere else.</p>
<p>Have we had experiments that confirm the path taken or something akin to verifying that photon really do "travel"? If so what are they..</p> | g7825 | [
0.030674228444695473,
0.02671818993985653,
0.026319852098822594,
0.0299861878156662,
0.02461736835539341,
0.010014479979872704,
0.021347906440496445,
0.048355832695961,
0.007229177746921778,
-0.029042934998869896,
0.016139693558216095,
-0.013247472234070301,
0.05052977055311203,
0.003617287613451481,
-0.053740277886390686,
-0.05608038231730461,
0.09595002233982086,
0.0025707141030579805,
0.045594722032547,
0.01748752035200596,
0.010531972162425518,
0.03044544905424118,
0.007218730635941029,
-0.020909756422042847,
-0.06144481897354126,
-0.04093658924102783,
0.04005446285009384,
-0.035069093108177185,
0.00435694819316268,
-0.047232918441295624,
0.020961180329322815,
-0.12543419003486633,
0.05561701953411102,
-0.03347938880324364,
-0.020288119092583656,
-0.05475964769721031,
0.0008698778692632914,
-0.012507529929280281,
0.038276396691799164,
0.02854265086352825,
0.03181243687868118,
0.008143093436956406,
-0.027748480439186096,
0.022899674251675606,
0.06669576466083527,
0.033403180539608,
0.0241076797246933,
-0.027781981974840164,
0.028252393007278442,
-0.003851460525766015,
-0.06909783184528351,
0.021984152495861053,
0.033561404794454575,
0.08849728107452393,
0.05073954537510872,
0.014792541041970253,
-0.009502931497991085,
-0.0008094202494248748,
0.08066661655902863,
-0.0065623740665614605,
-0.03347831591963768,
-0.01964358612895012,
0.022371506318449974,
-0.014126797206699848,
0.02920476347208023,
-0.02232787385582924,
-0.06918523460626602,
-0.03617366775870323,
-0.011906996369361877,
-0.02229829505085945,
0.09449546039104462,
-0.01934395171701908,
-0.019996481016278267,
0.030244503170251846,
0.05301675572991371,
-0.0178179070353508,
0.02657976932823658,
0.019033361226320267,
-0.0275599155575037,
0.03048868104815483,
0.008477166295051575,
-0.04647532105445862,
0.0013379635056480765,
-0.0017705945065245032,
0.04905790463089943,
-0.003199684666469693,
-0.016032857820391655,
0.008358092978596687,
0.040887750685214996,
-0.03952892869710922,
0.04259710758924484,
-0.0006173026049509645,
0.045773398131132126,
0.011574209667742252,
-0.04205670580267906,
-0.004056286532431841,
-0.0032799593172967434,
0.06628014147281647,
-0.009283868595957756,
-0.026673175394535065,
-0.028254177421331406,
0.05533289536833763,
-0.014014583081007004,
0.07500077039003372,
0.03887753188610077,
-0.019009269773960114,
-0.029786167666316032,
-0.02606208436191082,
0.02771991491317749,
-0.01089807040989399,
0.0015425048768520355,
-0.027670614421367645,
0.024023056030273438,
0.022873366251587868,
-0.0035656318068504333,
-0.034682948142290115,
0.005210995674133301,
0.00026627880288287997,
0.03176088631153107,
0.04741779714822769,
0.04510149359703064,
0.045319199562072754,
-0.07390665262937546,
0.018788710236549377,
0.01008995994925499,
-0.0014367192052304745,
-0.009458188898861408,
-0.012349989265203476,
-0.022866908460855484,
0.06699775904417038,
0.023070039227604866,
0.03178710490465164,
-0.032278887927532196,
0.053907498717308044,
0.003871832974255085,
-0.00733113894239068,
0.07779739052057266,
0.001785661792382598,
-0.01267961785197258,
0.008884776383638382,
0.028887681663036346,
-0.020876457914710045,
-0.007945115678012371,
-0.01316097006201744,
0.0204111710190773,
0.05191858112812042,
-0.01597200520336628,
0.03718043863773346,
-0.011057925410568714,
0.039464596658945084,
0.04956917464733124,
0.05026134103536606,
-0.022517669945955276,
-0.041883666068315506,
-0.008816740475594997,
-0.06823200732469559,
0.013271396048367023,
-0.03485054150223732,
-0.018657833337783813,
0.012439421378076077,
0.03155676648020744,
-0.007914330810308456,
0.009126594290137291,
0.001419676817022264,
0.017267920076847076,
-0.03004160337150097,
-0.0026298866141587496,
-0.017677627503871918,
0.012586643919348717,
-0.04532358795404434,
-0.04826411232352257,
0.025364097207784653,
0.004697463475167751,
0.04486694559454918,
-0.024762559682130814,
0.005116443615406752,
-0.010554162785410881,
-0.0207612793892622,
-0.015940263867378235,
-0.018925845623016357,
-0.025201983749866486,
0.03373894840478897,
0.031282197684049606,
-0.04818719998002052,
-0.007281171623617411,
-0.006491581443697214,
-0.06012645363807678,
-0.058953046798706055,
-0.024632956832647324,
-0.03679976984858513,
-0.04157744348049164,
-0.0012102824402973056,
0.02177443355321884,
-0.01783755049109459,
0.005454399157315493,
-0.015842987224459648,
0.008542148396372795,
-0.10188644379377365,
0.0005057375528849661,
0.012507468461990356,
-0.021019406616687775,
0.07585948705673218,
-0.019318969920277596,
-0.014039451256394386,
0.02653481438755989,
0.017013879492878914,
-0.013030853122472763,
-0.027886122465133667,
0.005218488164246082,
-0.00012478143617045134,
0.03858209773898125,
-0.018322674557566643,
0.022776076570153236,
0.027522508054971695,
-0.004375755321234465,
-0.0028808885253965855,
-0.04145197570323944,
0.00051979097770527,
0.03986920416355133,
-0.0406251959502697,
-0.012487491592764854,
0.008487040176987648,
0.007355253212153912,
-0.0179384034126997,
0.008190108463168144,
0.018225718289613724,
-0.0899457186460495,
-0.04208727180957794,
-0.034233178943395615,
0.06813223659992218,
-0.06757239997386932,
-0.011558489874005318,
-0.023653656244277954,
-0.028401069343090057,
0.06987947970628738,
-0.02888910099864006,
-0.04232219234108925,
-0.06911101192235947,
0.07023078948259354,
-0.030613649636507034,
0.0394342802464962,
-0.0254385843873024,
-0.06644974648952484,
0.010255211032927036,
0.020243950188159943,
-0.06049315258860588,
0.016618113964796066,
-0.016751442104578018,
0.04426894709467888,
-0.0160939022898674,
0.053964268416166306,
0.0172843337059021,
0.013878700323402882,
0.007860987447202206,
-0.04074736312031746,
-0.019058674573898315,
-0.011211538687348366,
0.04436742886900902,
-0.048059847205877304,
-0.03395861014723778,
-0.026759197935461998,
-0.00910767912864685,
-0.04884626716375351,
-0.02686542086303234,
0.033358968794345856,
-0.04799028858542442,
-0.02510027214884758,
-0.0006066468777135015,
0.0035624541342258453,
-0.011444180272519588,
0.017413383349776268,
0.0295721385627985,
0.08723190426826477,
-0.016607072204351425,
0.022728756070137024,
0.04339930787682533,
0.04265910014510155,
0.013798072002828121,
0.03929745405912399,
-0.005513635464012623,
-0.0030430040787905455,
-0.023196758702397346,
-0.08675224334001541,
-0.04086440056562424,
0.001633228617720306,
-0.06716474890708923,
0.01965390332043171,
0.0017465281998738647,
0.006702331826090813,
-0.020077185705304146,
0.00012864024029113352,
-0.04486880451440811,
0.04870206490159035,
0.05192481353878975,
-0.0658218115568161,
0.033435236662626266,
0.05879155546426773,
-0.009919765405356884,
0.03387767821550369,
0.010777762159705162,
0.001891448860988021,
-0.031188227236270905,
0.01595362275838852,
-0.010267284698784351,
0.040108561515808105,
0.036641303449869156,
-0.04068344831466675,
-0.058239106088876724,
0.050179798156023026,
0.02614828199148178,
-0.004356793127954006,
0.07759448885917664,
-0.05837033689022064,
0.047407206147909164,
0.0034537469036877155,
-0.005736122373491526,
-0.06132437288761139,
0.0580863356590271,
0.09787919372320175,
0.041829708963632584,
0.04222337156534195,
-0.012087834998965263,
-0.03673061355948448,
-0.004231595899909735,
0.06932209432125092,
-0.043981827795505524,
-0.02974894270300865,
-0.030288461595773697,
-0.0441112294793129,
-0.022520683705806732,
0.010101402178406715,
0.042197175323963165,
-0.04605904594063759,
0.001893513137474656,
0.024850184097886086,
-0.03452305123209953,
-0.029935281723737717,
0.057142190635204315,
0.0254603810608387,
-0.01524396613240242,
0.017406105995178223,
-0.047258809208869934,
0.009481518529355526,
0.06835678964853287,
0.04228987544775009,
-0.011035916395485401,
-0.02306078001856804,
0.004447500221431255,
0.027163390070199966,
-0.040205638855695724,
0.060893140733242035,
-0.006260399241000414,
-0.04182051867246628,
-0.025982780382037163,
-0.017209351062774658,
0.006697152741253376,
0.011006796732544899,
0.04005158320069313,
0.038156695663928986,
-0.03859363868832588,
-0.08014928549528122,
0.05015178024768829,
0.07194472849369049,
-0.039218585938215256,
0.008341006003320217,
0.02192591316998005,
0.02564350701868534,
0.02455919235944748,
0.03394358977675438,
0.01643071323633194,
-0.03647308424115181,
0.028807885944843292,
-0.07442750036716461,
0.043135616928339005,
0.0035100316163152456,
-0.013761047273874283,
0.02207840420305729,
0.029096344485878944,
-0.04093119502067566,
0.057132184505462646,
-0.005728838033974171,
0.05163183808326721,
0.057027120143175125,
-0.01314263604581356,
-0.011905384249985218,
0.0166601724922657,
-0.03705795481801033,
0.012836439535021782,
-0.0005018971278332174,
0.027009544894099236,
-0.01169570442289114,
-0.008973807096481323,
-0.01827976480126381,
-0.012637566775083542,
0.01171624381095171,
-0.042903561145067215,
0.02236853539943695,
-0.00394069729372859,
0.013812855817377567,
-0.05790596082806587,
-9.867910648608813e-7,
-0.0010176175273954868,
0.007596686948090792,
0.013207205571234226,
-0.06205548346042633,
0.0013049732660874724,
0.024038711562752724,
-0.05308536812663078,
-0.02089487388730049,
0.0020511155016720295,
0.0005453583435155451,
-0.0019658806268125772,
-0.023912625387310982,
-0.02750437892973423,
0.009026797488331795,
-0.014480861835181713,
-0.0060782041400671005,
-0.042747169733047485,
-0.018877318128943443,
-0.0036821214016526937,
-0.009965149685740471,
0.030980927869677544,
0.05228545516729355,
0.015739934518933296,
0.018116723746061325,
0.08218629658222198,
0.0013472293503582478,
0.00019502211944200099,
-0.005460713058710098,
-0.037921831011772156,
-0.006189224775880575,
0.00027422094717621803,
-0.0016036065062507987,
0.03512296825647354,
-0.00011232880933675915,
0.0620151124894619,
-0.01726197637617588,
-0.013444805517792702,
0.03884457051753998,
0.031470876187086105,
0.0860733762383461,
0.006832013372331858,
0.0760728120803833,
0.050735119730234146,
0.0019124196842312813,
0.04598958045244217,
-0.02890023961663246,
0.007384955417364836,
0.03560266271233559,
0.007161962334066629,
-0.060911424458026886,
0.044706642627716064,
-0.050957757979631424,
-0.0024645181838423014,
-0.01102329883724451,
0.022849570959806442,
-0.03312183544039726,
0.011857787147164345,
-0.015770239755511284,
0.014133899472653866,
-0.05318797007203102,
-0.0555095411837101,
0.07702435553073883,
-0.00015635053568985313,
-0.011939026415348053,
-0.020094309002161026,
-0.018519680947065353,
-0.006134464871138334,
-0.027452392503619194,
-0.02027609758079052,
-0.045120351016521454,
0.05573325604200363,
0.030109968036413193,
-0.011562235653400421,
0.03739328682422638,
-0.041771840304136276,
-0.0511278361082077,
0.03690933436155319,
-0.05005626007914543,
-0.060821861028671265,
0.008450164459645748,
0.008887164294719696,
-0.01048098225146532,
-0.013423300348222256,
0.010954716242849827,
0.013264941982924938,
-0.08394081145524979,
0.03348784148693085,
0.0038528135046362877,
-0.06988031417131424,
0.04261928051710129,
-0.045716542750597,
-0.0011935231741517782,
-0.06513763964176178,
0.0014904369600117207,
-0.030704651027917862,
-0.03523784503340721,
0.019719665870070457,
-0.008305381052196026,
-0.03948603942990303,
-0.05551987141370773,
0.06254145503044128,
0.041881315410137177,
0.013546696864068508,
0.019589819014072418,
-0.02839699573814869,
-0.008614590391516685,
-0.006183627527207136,
-0.1380615085363388,
-0.020005136728286743,
-0.002724350430071354,
0.00003936559005524032,
-0.0875207707285881,
0.006546305492520332,
0.03813272714614868,
0.004554647020995617,
-0.03234435245394707,
0.05779010429978371,
0.03703732788562775,
-0.033150412142276764,
-0.08045721054077148,
0.027590587735176086,
0.007780115585774183,
-0.014734814874827862,
0.07370167970657349,
0.02763262949883938,
-0.037560708820819855,
-0.010656091384589672,
0.053076568990945816,
-0.04432068392634392,
0.04475007951259613,
-0.023335332050919533,
0.06007752567529678,
0.06472502648830414,
-0.02757895179092884,
-0.06540485471487045,
0.030369680374860764,
-0.032260533422231674,
-0.001321150572039187,
-0.031840477138757706,
-0.0492011234164238,
-0.036922670900821686,
-0.002724867081269622,
0.0560174323618412,
0.029208242893218994,
0.012047413736581802,
-0.017042558640241623,
0.02198169380426407,
0.051445502787828445,
-0.07175719738006592,
0.005666607525199652,
-0.017521873116493225,
-0.02731124311685562,
0.01578742451965809,
0.004535315092653036,
-0.04142012447118759,
-0.016093170270323753,
-0.042649045586586,
0.01341842208057642,
0.028925525024533272,
0.027969013899564743,
0.04960213974118233,
-0.015590392984449863,
-0.05632948502898216,
-0.018546458333730698,
-0.031797491014003754,
0.01367693766951561,
-0.03270280733704567,
-0.0033756005577743053,
0.013541771098971367,
0.0014100458938628435,
0.00823289155960083,
-0.006944663822650909,
0.021489931270480156,
-0.027120554819703102,
-0.026597296819090843,
0.012220329605042934,
-0.006059818901121616,
-0.05653228238224983,
-0.04028886929154396,
0.03473631665110588,
0.0405186228454113,
0.04311874881386757,
-0.023697318509221077,
-0.032403718680143356,
0.04960864409804344,
-0.015316572040319443,
0.01469949260354042,
0.0540456660091877,
-0.01914561353623867,
0.018042996525764465,
0.00047694938257336617,
-0.00953649077564478,
-0.045203544199466705,
-0.0288529209792614,
-0.05985516682267189,
0.01968088187277317,
-0.038356974720954895,
0.024299362674355507,
0.031255971640348434,
-0.043264973908662796,
0.010575659573078156,
0.030181700363755226,
-0.036460984498262405,
0.05150195211172104,
0.01608875021338463,
-0.0279685091227293,
0.03656579181551933,
0.08678673952817917,
-0.008595945313572884,
0.010046498849987984,
0.01206937525421381,
-0.004503188189119101,
0.006935794837772846,
-0.029466189444065094,
-0.07847832143306732,
0.00947196502238512,
0.006647385191172361,
0.06428830325603485,
0.019047284498810768,
0.002094967756420374,
-0.0466158352792263,
-0.025009553879499435,
0.020381562411785126,
0.018378686159849167,
0.09226327389478683,
0.004044982139021158,
0.017735129222273827,
0.024999232962727547,
-0.0008399452781304717,
-0.0017883332911878824,
0.02491588145494461,
-0.003096739063039422,
0.006792777683585882,
-0.026862334460020065,
0.012578372843563557,
-0.02912031300365925,
0.02217600867152214,
-0.0036502929870039225,
0.013043195940554142,
0.010771350003778934,
-0.009895721450448036,
0.0034655409399420023,
-0.031134745106101036,
-0.03314678743481636,
0.07203669100999832,
0.0031456942670047283,
0.010972730815410614,
-0.003041419666260481,
0.02010926976799965,
0.003376786829903722,
-0.04524040222167969,
-0.009497139602899551,
-0.01939329504966736,
-0.008427093736827374,
0.024516409263014793,
-0.05116146430373192,
0.05754124000668526,
-0.04629463329911232,
-0.05686814337968826,
0.010515892878174782,
-0.06591099500656128,
-0.042129434645175934,
0.03679266944527626,
0.003155155573040247,
-0.0024626553058624268,
-0.03302602097392082,
-0.07378088682889938,
-0.01252483855932951,
-0.0023077288642525673,
0.06318005174398422,
-0.02975522167980671,
-0.03884489834308624,
0.056066323071718216,
-0.006631411146372557,
-0.009380057454109192,
-0.019120963290333748,
0.09403733164072037,
-0.03924485296010971,
0.011934727430343628,
-0.04404418542981148,
0.05022626742720604,
0.03572536259889603,
0.0159743744879961,
0.043765079230070114,
0.01705397479236126,
-0.030464187264442444,
-0.03951402008533478,
-0.08397214859724045,
-0.025051299482584,
-0.0033760755322873592,
-0.06398884952068329,
0.022725937888026237,
-0.020306730642914772,
0.051096901297569275,
-0.026243779808282852,
0.02965032495558262,
0.005055497400462627,
-0.026667626574635506,
0.014339126646518707,
-0.09090114384889603,
-0.029015792533755302,
0.035931602120399475,
-0.024106677621603012,
-0.003377095330506563,
-0.0017631755908951163,
-0.06453019380569458,
-0.015230311080813408,
-0.020997099578380585,
0.034093473106622696,
0.008788487873971462,
0.01005441416054964,
-0.01063074916601181,
0.029118984937667847,
0.003454027697443962,
-0.008870705030858517,
-0.01684030517935753,
0.027658339589834213,
0.026274889707565308,
0.010094060562551022,
-0.005462804809212685,
0.00120788614731282,
-0.045799288898706436,
0.015752067789435387,
-0.001065966789610684,
0.020377663895487785,
0.004661092069000006,
-0.005860310047864914,
0.015575592406094074,
-0.052316874265670776,
0.045776743441820145,
0.006012035999447107,
-0.01918368600308895,
-0.0117851123213768,
-0.04684474319219589,
0.020777298137545586,
0.016832292079925537,
-0.005092065315693617,
-0.0049507194198668,
0.026186248287558556,
0.02750096097588539,
-0.07020176947116852,
-0.0016856014262884855,
-0.030849583446979523,
-0.021732287481427193,
-0.034482456743717194,
0.04794950410723686,
0.022619953379034996,
0.021400006487965584,
-0.035734761506319046,
0.0413595475256443,
0.07770411670207977,
0.0058669778518378735,
0.04234238713979721,
-0.010072708129882812,
-0.014696789905428886,
-0.024839576333761215,
-0.01994134858250618,
0.0030192406848073006,
0.041824083775281906,
-0.013731230981647968,
-0.06449372321367264,
0.04980848729610443,
-0.015257677063345909,
-0.01831929385662079,
-0.022834910079836845,
-0.005706092808395624,
-0.0012280357768759131
] |
<p>In <a href="http://youtu.be/QGxNyaXfJsA" rel="nofollow">this youtube video</a> (which is an except from a documentation I believe) a DARPA development for a high-resolution surveillance camera is presented. This question is regarding the optics that are likely to be required to make it work.</p>
<h2>Summary of the specifications given:</h2>
<ul>
<li>$1.8\times10^9$ pixel</li>
<li>covering $35\,km^2$</li>
<li>from an altitude of $5\,km$</li>
<li>using $368$ cellphone camera chips</li>
</ul>
<h2>Some back of the hand calculations:</h2>
<ul>
<li>pixel-equivalent area: $\frac{35\times10^6\,m^2}{1.8\times10^9\,px^2} = 1.94\times10^{-2}\,\frac{m^2}{px^2}$</li>
<li>edge length of pixel-equivalent area: $\sqrt{1.94\times10^{-2}\,\frac{m^2}{px^2}}=1.39\times10^{-1}\,\frac{m}{px}\approx14\,\frac{cm}{px}$</li>
<li>pixel count per chip: $\frac{1.8\times10^9\,px}{368\,chips}\approx5\times10^6\,\frac{px}{chip}$</li>
</ul>
<h2>Optics question</h2>
<p>Cellphone chips have pixel pitches of the order of a few microns. Say they use a typical, decent quality 5 megapixel chip with $2.25\,µm$ pitch.</p>
<p>How are the optics likely to look like to image 15 cm at 5 km distance onto 2.25 µm on the chip within a camera that is at best a meter in diameter?</p>
<p>I am looking for answers beyond "they use a telephoto lens"... Lens focal lengths, combinations and setup for producing the required image is what I am struggling to work out.</p> | g7826 | [
0.027905914932489395,
0.024532871320843697,
-0.009004458785057068,
0.022636307403445244,
0.05242971330881119,
-0.0566585473716259,
-0.01276940107345581,
-0.035073839128017426,
-0.011664269492030144,
-0.030159054324030876,
-0.006886224262416363,
0.04776886850595474,
0.044266004115343094,
0.008123114705085754,
-0.022433515638113022,
0.03536996617913246,
0.05023447796702385,
-0.03675001487135887,
0.004117934498935938,
0.04228625074028969,
-0.00030697783222422004,
-0.0030417984817177057,
-0.018019694834947586,
-0.07757477462291718,
-0.03317362442612648,
-0.020596109330654144,
0.06756814569234848,
-0.013146981596946716,
-0.06045756861567497,
-0.01725137047469616,
0.008056458085775375,
-0.04843762516975403,
-0.009766466915607452,
-0.056551966816186905,
-0.01912129856646061,
0.06865992397069931,
0.04924323037266731,
0.008117341436445713,
-0.01841115392744541,
0.014496142975986004,
-0.03671780973672867,
0.019932253286242485,
-0.006476054433733225,
-0.059328075498342514,
0.015185081399977207,
-0.016264988109469414,
0.02947351150214672,
-0.004195466171950102,
0.03634108975529671,
-0.06487581878900528,
-0.041884895414114,
0.07657834887504578,
-0.008194832131266594,
-0.00835473369807005,
-0.013293368741869926,
0.030320273712277412,
-0.044732317328453064,
0.02447637729346752,
-0.01381013635545969,
0.00980509165674448,
0.0023760448675602674,
-0.003799766069278121,
-0.07648199796676636,
-0.008101897314190865,
0.03760305419564247,
0.02723066322505474,
-0.06842750310897827,
-0.005559161305427551,
-0.016828402876853943,
0.0021357990335673094,
0.030411260202527046,
-0.06361127644777298,
-0.04144705832004547,
0.010784627869725227,
-0.057053182274103165,
-0.03955275937914848,
-0.02347109653055668,
-0.011066541075706482,
-0.01923362724483013,
0.06140774115920067,
0.0004729528445750475,
-0.0028634618502110243,
-0.039808519184589386,
-0.01494735199958086,
0.05207771435379982,
-0.0035997440572828054,
-0.006150403991341591,
-0.009822124615311623,
0.004857550375163555,
0.0348428413271904,
0.06160793453454971,
0.021183975040912628,
0.06419141590595245,
0.016663383692502975,
0.028917133808135986,
-0.026891633868217468,
-0.023109834641218185,
0.03499269485473633,
0.0218193382024765,
-0.01916816085577011,
0.015580142848193645,
0.021813005208969116,
0.013163670897483826,
-0.0035862012300640345,
-0.04946104809641838,
0.02929110825061798,
0.06958623975515366,
0.006328907795250416,
-0.0330563485622406,
0.005365266930311918,
-0.07615689188241959,
0.0032240552827715874,
0.0084227304905653,
-0.06916548311710358,
-0.04240810126066208,
-0.012024136260151863,
0.03136296197772026,
0.07152468711137772,
0.05097373574972153,
0.040878187865018845,
0.03287975862622261,
0.02556375414133072,
0.022097425535321236,
-0.039243344217538834,
-0.002315579680725932,
-0.025596456602215767,
0.024058956652879715,
0.0037356342654675245,
0.016332490369677544,
0.006549112033098936,
0.03453070670366287,
-0.013640628196299076,
-0.04271328076720238,
0.02017359435558319,
0.024193255230784416,
0.02012530155479908,
-0.03579418733716011,
-0.06832443177700043,
-0.000370706693502143,
0.019198821857571602,
-0.015235835686326027,
0.04345716908574104,
0.06093858927488327,
-0.04360787197947502,
-0.06313269585371017,
0.0014298142632469535,
-0.03228330612182617,
-0.039758242666721344,
0.08544290065765381,
-0.0038857441395521164,
0.026138989254832268,
0.011416247114539146,
0.03277440369129181,
0.009140231646597385,
-0.0168752558529377,
0.041509758681058884,
-0.008463791571557522,
0.0541868694126606,
0.000889274466317147,
-0.012128167785704136,
0.024297067895531654,
-0.006218224298208952,
-0.007233769167214632,
0.0268374215811491,
-0.04314422979950905,
-0.021394388750195503,
0.012619785964488983,
-0.03340865671634674,
0.04269810765981674,
-0.004446567036211491,
0.059425171464681625,
-0.010747789405286312,
0.038734398782253265,
-0.004575110040605068,
-0.002252427861094475,
0.037073660641908646,
0.06391599029302597,
0.03649206832051277,
0.012088819406926632,
0.06944626569747925,
-0.02904297411441803,
-0.013273504562675953,
-0.07244159281253815,
-0.017091447487473488,
0.005897685419768095,
-0.017996490001678467,
0.06780854612588882,
-0.05819244682788849,
0.02369707077741623,
0.03187176212668419,
-0.019670628011226654,
-0.004623576533049345,
-0.015450133942067623,
0.03881126269698143,
-0.015789927914738655,
0.01750084012746811,
0.04360176995396614,
-0.05391627177596092,
-0.013047647662460804,
-0.005770402029156685,
-0.011290154419839382,
-0.006346017587929964,
0.005954939406365156,
0.05470903590321541,
0.03329896926879883,
-0.030557792633771896,
-0.008161325007677078,
-0.0054116565734148026,
-0.020656216889619827,
-0.04626137763261795,
-0.03264513239264488,
-0.04626556858420372,
-0.015413818880915642,
-0.016874274238944054,
-0.0032871023286134005,
0.04232339560985565,
-0.004641433712095022,
-0.032980311661958694,
-0.02049654722213745,
-0.015939997509121895,
0.02690758742392063,
0.01455993764102459,
0.0509265661239624,
-0.03345879167318344,
0.019251693040132523,
0.0067205047234892845,
-0.0039481292478740215,
-0.0310341976583004,
0.04749887064099312,
0.015381842851638794,
-0.004502079915255308,
0.033214811235666275,
0.04057687148451805,
-0.09811028093099594,
-0.026353968307375908,
0.026169564574956894,
-0.030011115595698357,
0.041512809693813324,
0.024433506652712822,
0.06429669260978699,
0.006446509156376123,
0.003544844454154372,
-0.05491740256547928,
-0.009027081541717052,
-0.00863268505781889,
0.008716017939150333,
0.00856312271207571,
0.05729007348418236,
-0.018963618203997612,
0.053080808371305466,
0.00532907247543335,
-0.0031137606129050255,
-0.0014179727295413613,
0.0050698695704340935,
-0.05535381659865379,
-0.07060684263706207,
0.045806869864463806,
0.07260945439338684,
-0.02041613683104515,
0.09417026489973068,
-0.0762016698718071,
-0.02977665141224861,
-0.05423077940940857,
-0.056657951325178146,
-0.03868993744254112,
0.013391328044235706,
0.00428486242890358,
-0.01596713624894619,
0.03239651769399643,
0.02922198362648487,
0.046752892434597015,
0.003080361755564809,
0.0650167167186737,
0.017305653542280197,
-0.003941954113543034,
-0.01536554004997015,
-0.014717218466103077,
-0.010092581622302532,
0.017155684530735016,
-0.010723313316702843,
0.04989534616470337,
-0.05755097419023514,
-0.0641888827085495,
0.0923122763633728,
0.006545347161591053,
-0.0009252706659026444,
0.0007510154391638935,
0.030933812260627747,
0.05528939142823219,
-0.015455382876098156,
-0.023512281477451324,
-0.04207160323858261,
0.040262240916490555,
-0.025428038090467453,
0.0007322895107790828,
0.005973017308861017,
0.05474467948079109,
0.0038633986841887236,
0.03311626985669136,
0.051231078803539276,
-0.019938873127102852,
-0.014290706254541874,
0.04738159850239754,
-0.028961356729269028,
0.039883945137262344,
0.018880510702729225,
-0.0302421897649765,
-0.0716494545340538,
-0.026552725583314896,
0.008201263844966888,
0.03639037907123566,
-0.04326914623379707,
-0.05257433280348778,
-0.015811430290341377,
-0.0024088334757834673,
-0.0007293799426406622,
-0.0425114668905735,
0.04912421479821205,
-0.05812304466962814,
0.07503215968608856,
0.014539242722094059,
0.018077827990055084,
-0.04822386056184769,
-0.01234237477183342,
0.029179289937019348,
0.06113759055733681,
0.009158995933830738,
-0.01243487186729908,
0.008180511184036732,
0.022987134754657745,
0.012459484860301018,
0.008306986652314663,
-0.033110957592725754,
-0.043619800359010696,
0.009835654869675636,
-0.010150618851184845,
0.024236567318439484,
0.011439233087003231,
0.062471531331539154,
-0.02694104239344597,
0.019331203773617744,
0.01913628913462162,
-0.07225900143384933,
-0.057414669543504715,
-0.0028852582909166813,
-0.054716285318136215,
-0.039710089564323425,
0.018312465399503708,
-0.01671234518289566,
-0.05843200534582138,
0.026006819680333138,
0.005059573333710432,
0.010197914205491543,
-0.04854957386851311,
0.01640171743929386,
0.061393145471811295,
-0.056598614901304245,
0.050480253994464874,
0.0344095304608345,
-0.037421781569719315,
0.05593707039952278,
0.00808190368115902,
0.01231676060706377,
-0.07238845527172089,
-0.0047782291658222675,
-0.03386547416448593,
-0.025539642199873924,
0.03026009164750576,
0.02259344980120659,
0.007255204953253269,
-0.02233240008354187,
0.0296042338013649,
-0.06586581468582153,
0.010364349000155926,
-0.05025818571448326,
0.06084011495113373,
0.003228310262784362,
-0.03809266909956932,
-0.02101660706102848,
0.000451160449301824,
-0.03661629930138588,
0.05356273427605629,
0.014093050733208656,
-0.006296015810221434,
0.004154707305133343,
-0.029491297900676727,
-0.0018277015769854188,
-0.01540839672088623,
-0.002030288567766547,
-0.027057746425271034,
-0.03192613273859024,
-0.05959409102797508,
-0.000379571778466925,
-0.03298576548695564,
0.028989586979150772,
-0.052905451506376266,
-0.012681680731475353,
0.011777921579778194,
0.03395868092775345,
0.03695123270153999,
0.07632351666688919,
0.048589885234832764,
0.059435948729515076,
0.020177986472845078,
-0.045453883707523346,
-0.048921551555395126,
0.00973140075802803,
0.03082864172756672,
-0.0014044714625924826,
0.030708033591508865,
-0.03372950479388237,
0.06590219587087631,
0.051962897181510925,
-0.06887983530759811,
0.038877032697200775,
0.057381607592105865,
-0.00818908866494894,
-0.010863115079700947,
0.006225632969290018,
0.028513291850686073,
-0.025427715852856636,
0.025362176820635796,
-0.023181263357400894,
-0.03936378285288811,
-0.04669933021068573,
0.06483042985200882,
-0.02564374729990959,
-0.010632738471031189,
0.008273066952824593,
0.014223230071365833,
0.060492560267448425,
0.006278392393141985,
0.046111900359392166,
0.005110040307044983,
-0.00441814586520195,
0.01943555660545826,
0.04059597849845886,
0.028862325474619865,
0.03943134844303131,
-0.010759747587144375,
-0.08150525391101837,
-0.06043735519051552,
0.012231039814651012,
0.019380977377295494,
0.026927389204502106,
0.02294767275452614,
-0.08658646792173386,
0.024350812658667564,
0.028187032788991928,
0.05177640914916992,
0.08442133665084839,
0.04607769474387169,
-0.010741857811808586,
-0.02332877553999424,
-0.002469334052875638,
-0.013935405761003494,
-0.030160581693053246,
-0.0017128709005191922,
0.023633219301700592,
-0.012183715589344501,
-0.011190423741936684,
0.03824736922979355,
-0.030344154685735703,
-0.0038656697142869234,
0.07962451130151749,
0.006775431800633669,
-0.03495100885629654,
0.0009422139846719801,
-0.00803428515791893,
-0.010854010470211506,
-0.06372907757759094,
-0.03908002749085426,
0.02837398275732994,
0.044983718544244766,
-0.04615693539381027,
-0.0032161702401936054,
-0.009265904314815998,
-0.006523262709379196,
0.01981433667242527,
-0.002901406493037939,
-0.016581198200583458,
-0.02946251630783081,
-0.028241511434316635,
0.019998818635940552,
0.037885989993810654,
0.04108195751905441,
-0.02568914368748665,
-0.03290759399533272,
0.037047747522592545,
-0.02736138179898262,
0.0031153245363384485,
0.014590744860470295,
-0.005793980788439512,
-0.00407820288091898,
-0.004577626474201679,
-0.04707680270075798,
0.060445185750722885,
0.010671854950487614,
0.03668717294931412,
0.043067384511232376,
0.08161081373691559,
-0.03315936028957367,
-0.04818769171833992,
-0.021114950999617577,
0.004985199309885502,
0.050619907677173615,
0.041840896010398865,
-0.021672632545232773,
0.041266221553087234,
0.021387683227658272,
-0.023737428709864616,
0.029693128541111946,
0.05147019028663635,
-0.01347128115594387,
-0.04523571953177452,
-0.08040577918291092,
-0.016301220282912254,
0.10799387842416763,
-0.012689992785453796,
-0.013304569758474827,
0.044363293796777725,
-0.08244427293539047,
0.032328907400369644,
0.0658266618847847,
0.04419245198369026,
-0.017057737335562706,
0.01447395421564579,
-0.03183361142873764,
0.014066076837480068,
-0.038655947893857956,
-0.03257758915424347,
0.021662931889295578,
-0.013339127413928509,
-0.020754480734467506,
-0.007800241466611624,
-0.014109069481492043,
0.011185604147613049,
0.02933182194828987,
0.03845779597759247,
-0.02065322920680046,
0.021687433123588562,
0.010659630410373211,
0.017442205920815468,
0.09596368670463562,
0.0018670522840693593,
-0.07315195351839066,
0.07668907940387726,
0.029129451140761375,
0.044054239988327026,
-0.02735758200287819,
0.014607432298362255,
0.01732541434466839,
-0.008253091014921665,
-0.021425439044833183,
-0.015198716893792152,
0.024772334843873978,
0.025466570630669594,
-0.0106362234801054,
-0.002022600034251809,
-0.048942700028419495,
0.0876464769244194,
0.01774980127811432,
-0.06288550794124603,
0.061209652572870255,
0.013387232087552547,
-0.02077747881412506,
0.0287154708057642,
0.06952909380197525,
0.018143340945243835,
-0.007005417253822088,
-0.04815797880291939,
-0.023574549704790115,
-0.03516867756843567,
0.00540602533146739,
0.06075916811823845,
0.018936246633529663,
-0.010384485125541687,
0.04501708969473839,
-0.0252849068492651,
-0.01477301400154829,
-0.0018510047812014818,
0.0036453718785196543,
0.013104608282446861,
0.007627461571246386,
0.000597587029915303,
-0.025085870176553726,
-0.022103283554315567,
-0.0015322034014388919,
0.02334163337945938,
-0.09217644482851028,
-0.01895635947585106,
-0.028484147042036057,
0.05328904464840889,
-0.04985495284199715,
0.019389014691114426,
0.005037450697273016,
0.04018673300743103,
-0.013685076497495174,
-0.006616687867790461,
-0.0024442896246910095,
0.05985851213335991,
-0.014703057706356049,
0.0015361618716269732,
-0.044136278331279755,
-0.03228457272052765,
-0.0024708998389542103,
-0.04818309098482132,
-0.04759927839040756,
0.04174455255270004,
-0.0391199104487896,
0.051180675625801086,
0.038093965500593185,
0.008150381967425346,
-0.0031775482930243015,
-0.02421717904508114,
-0.007002823520451784,
-0.01104022841900587,
-0.012320457957684994,
-0.04757498577237129,
0.01757187955081463,
0.0018531884998083115,
0.01371598057448864,
-0.04035850614309311,
-0.008739393204450607,
-0.022768110036849976,
-0.004738429561257362,
0.10592719912528992,
0.05888858065009117,
0.061465777456760406,
0.06394632160663605,
0.014955650083720684,
-0.02964267134666443,
0.03546636551618576,
-0.04197032004594803,
-0.06200492009520531,
0.07329634577035904,
-0.06857617944478989,
0.02528870664536953,
-0.023174265399575233,
-0.056186698377132416,
0.044153328984975815,
-0.02364230901002884,
0.009163902141153812,
0.011495660990476608,
0.01507666613906622,
0.029553066939115524,
-0.034262288361787796,
0.03171297162771225,
0.017132993787527084,
-0.03610712289810181,
-0.00645131291821599,
-0.038655947893857956,
0.006687297485768795,
0.002417532727122307,
0.0005171203520148993,
0.01611405983567238,
-0.026193706318736076,
-0.032797735184431076,
-0.06081603094935417,
-0.02602383680641651,
-0.005025988910347223,
-0.04559236392378807,
-0.04222333803772926,
-0.02059713937342167,
0.0013116030022501945,
0.0078067295253276825,
-0.00017156901594717056,
-0.02532610483467579,
-0.0864870473742485,
-0.03532599285244942,
0.025163691490888596,
0.0032218305859714746,
-0.066761314868927,
0.02408832684159279,
-0.013222569599747658,
-0.011075209826231003,
-0.04371005296707153,
-0.002872794633731246,
-0.08989233523607254,
0.05231434479355812,
0.003575877984985709,
0.033674634993076324,
0.015641076490283012,
0.004253102466464043,
-0.04912979155778885,
-0.017245803028345108,
-0.0030156231950968504,
-0.03795543685555458,
0.043831564486026764,
-0.058676525950431824,
-0.03063187189400196,
-0.03854585066437721,
0.004936405457556248,
-0.013591380789875984,
-0.02206619828939438,
0.05904345214366913,
0.04126015305519104,
-0.007003935053944588,
-0.0007303958409465849,
0.02159610018134117,
0.060780566185712814,
-0.014355968683958054,
-0.03906356543302536,
-0.02315966971218586,
0.008436789736151695,
0.018741009756922722,
0.038448914885520935,
-0.00027649980620481074,
0.006033605895936489,
0.004232570994645357,
-0.027828196063637733,
0.026493769139051437,
-0.0019174586050212383,
0.01090171653777361,
0.02062283083796501,
-0.05643022060394287,
-0.042148832231760025,
0.0022292397916316986,
-0.04769071564078331,
0.025860678404569626,
-0.019650083035230637,
0.009636152535676956,
0.018050821498036385,
-0.03088080696761608,
-0.0188752431422472,
-0.03797497600317001,
0.003351777559146285,
0.04690397158265114,
0.039870209991931915,
-0.04817918688058853,
-0.03554819896817207,
0.0074614351615309715,
-0.04544848948717117,
-0.034407537430524826,
-0.007047258783131838,
0.0009972612606361508,
0.0012509669177234173,
-0.028717178851366043,
-0.007869793102145195,
-0.005823458544909954,
-0.011527533642947674,
0.002667994238436222,
-0.048380374908447266,
-0.05777217447757721,
-0.00492929806932807,
0.015751227736473083,
-0.009336289018392563,
-0.0000039468268369091675,
0.028668882325291634,
0.02247220277786255,
-0.031885962933301926,
0.0441373847424984,
-0.026448199525475502,
0.05174047499895096,
0.022100983187556267,
-0.04280382767319679,
0.019476281479001045,
-0.001352872932329774,
0.023793255910277367,
-0.06288681924343109,
0.03623063117265701,
-0.03344357758760452,
-0.008005218580365181,
0.02087886817753315,
0.019131427630782127,
-0.0698309913277626,
-0.01947823166847229,
-0.016067972406744957
] |
<p>The potential at the surface of an insulating sphere (radius R) is given by<br>
$$V(R,\theta) = k \cos(3\theta)$$
where $k$ is a constant. Use separation of variables to find the potential inside the sphere (r $\leq$ R) and outside the sphere (r $\geq$ R), and then use your answer to determine the surface charge density $\sigma(\theta)$ on the sphere. Assume there is no charge inside or outside the sphere.</p>
<p>My approach: I will set my reference point at infinity, therefore the potential at infinity is 0, to set that as a boundary condition. Essentially, the approach in finding the surface charge density would be to find the potential function outside the sphere, then integrate that with the surface area. I am following Griffiths for E&M, but he doesn't include a specific example I can refer to for the separation of variables, and how to apply it. I can follow his examples for following potentials pretty easily, but cannot understand the first steps to set up this problem with SOV.</p> | g7827 | [
0.034735873341560364,
0.005076582543551922,
0.006992270238697529,
-0.018219679594039917,
0.011941811069846153,
0.04327769577503204,
0.047899242490530014,
0.01023150235414505,
-0.019200867041945457,
0.045086272060871124,
-0.004652968607842922,
0.012016408145427704,
0.005129878409206867,
0.023012490943074226,
0.012438410893082619,
0.01654396578669548,
-0.04845767095685005,
0.02984444797039032,
0.005326454062014818,
-0.035423554480075836,
0.020271118730306625,
-0.05453043431043625,
0.04468625411391258,
-0.02599121630191803,
-0.013201664201915264,
0.02587893046438694,
-0.0014429938746616244,
0.03087775595486164,
0.030359750613570213,
-0.019814204424619675,
-0.00719559658318758,
0.039688631892204285,
0.019266802817583084,
-0.03668210655450821,
-0.042058736085891724,
0.00990944355726242,
0.03499689698219299,
0.0001004809673759155,
-0.04716871678829193,
-0.0399525910615921,
0.04059996455907822,
-0.054063647985458374,
0.07884329557418823,
-0.005171013064682484,
0.0003755743964575231,
-0.027601877227425575,
-0.00021411872876342386,
0.02524697780609131,
0.01836131513118744,
-0.027800533920526505,
0.04421786963939667,
0.06999652087688446,
-0.012517847120761871,
-0.016222111880779266,
-0.0034090334083884954,
0.012392034754157066,
0.04578055441379547,
-0.032295115292072296,
0.02539033442735672,
0.02996351569890976,
0.016837328672409058,
-0.05630134791135788,
-0.05080030858516693,
-0.002509349025785923,
0.04029175266623497,
0.026740198954939842,
-0.0629352256655693,
-0.017910659313201904,
-0.07176829129457474,
-0.020878763869404793,
0.00038578486419282854,
-0.06374725699424744,
0.012799689546227455,
-0.07357281446456909,
-0.0959373414516449,
0.026479847729206085,
0.03942478820681572,
0.011057798750698566,
0.06002871319651604,
0.02659032866358757,
-0.008675706572830677,
-0.07239209860563278,
0.05000105872750282,
0.02477644756436348,
0.060877397656440735,
-0.006202660501003265,
-0.013370908796787262,
-0.034098248928785324,
-0.05014630779623985,
-0.03526560217142105,
-0.013323942199349403,
0.024335289373993874,
0.014082091860473156,
-0.04048972949385643,
-0.0013066221727058291,
-0.04160919412970543,
0.018656570464372635,
0.019455622881650925,
-0.0013949727872386575,
-0.007318203337490559,
-0.04566824063658714,
-0.01810709945857525,
0.010210081934928894,
0.04258720576763153,
-0.026037292554974556,
0.02024178020656109,
0.028643028810620308,
0.014204530045390129,
0.016830459237098694,
0.0006434998358599842,
-0.01614810898900032,
-0.015263562090694904,
-0.0070541719906032085,
0.03249474987387657,
-0.042793627828359604,
-0.03516251966357231,
0.08849075436592102,
-0.0422046072781086,
-0.01241335179656744,
0.021156447008252144,
-0.04822226241230965,
0.06353241205215454,
0.0132116274908185,
0.03729021176695824,
0.00787919107824564,
0.05198543146252632,
-0.017889896407723427,
0.007926865480840206,
0.04890789836645126,
0.005152000114321709,
0.013113938271999359,
0.02075378969311714,
-0.04088899493217468,
-0.026312295347452164,
-0.005650451872497797,
-0.004372237250208855,
-0.04550151899456978,
0.0007399761234410107,
0.011240746825933456,
0.016228673979640007,
0.0351998545229435,
-0.003964166156947613,
-0.02753637731075287,
-0.008289949968457222,
-0.027908261865377426,
0.04409728944301605,
-0.01682429574429989,
-0.022325294092297554,
-0.03527877852320671,
-0.006005742121487856,
0.020755955949425697,
0.0508611835539341,
0.0031098611652851105,
-0.0067687248811125755,
0.01921761967241764,
-0.02735510841012001,
0.03405236080288887,
0.0023494537454098463,
0.07639011740684509,
-0.01542360894382,
0.014818367548286915,
0.04504112899303436,
0.029462043195962906,
0.013997073285281658,
-0.030855635181069374,
-0.012064321897923946,
-0.007367076817899942,
-0.05183517560362816,
0.0010164894629269838,
-0.09624092280864716,
0.02008558064699173,
-0.001772238058038056,
0.018066728487610817,
0.03731076046824455,
0.003659245790913701,
0.047931134700775146,
-0.028600851073861122,
-0.03835528716444969,
0.03064948134124279,
0.09684651345014572,
0.019392050802707672,
-0.0003736170765478164,
0.05740037560462952,
0.007713078521192074,
0.0015257522463798523,
0.003814038122072816,
0.05392041057348251,
-0.0291096493601799,
-0.023830782622098923,
0.03329862281680107,
-0.053554072976112366,
0.02177153155207634,
-0.01789262145757675,
0.006384420208632946,
-0.0033785784617066383,
0.03217564895749092,
0.10961178690195084,
-0.07219251245260239,
-0.0234666895121336,
-0.03833518922328949,
-0.04370592162013054,
0.04451539367437363,
0.014194740913808346,
0.04378847777843475,
0.024348467588424683,
-0.0017750603146851063,
0.019720545038580894,
-0.07241826504468918,
0.03492949157953262,
0.010300438851118088,
-0.021764593198895454,
-0.04896068200469017,
0.03150850534439087,
-0.0012627370888367295,
-0.008898047730326653,
-0.03517705947160721,
-0.021409926936030388,
0.01167233381420374,
-0.013809608295559883,
0.00157222303096205,
-0.0381094291806221,
0.024295909330248833,
0.023560019209980965,
0.008661416359245777,
-0.011414616368710995,
0.018508439883589745,
0.01937917061150074,
0.010840321891009808,
-0.022512327879667282,
0.013727943412959576,
-0.04456590488553047,
-0.0383610762655735,
0.050085969269275665,
-0.030687114223837852,
-0.02120216004550457,
0.041610945016145706,
-0.0919731929898262,
0.0007230489864014089,
-0.02968810498714447,
-0.05784265324473381,
0.005668953992426395,
-0.018058670684695244,
0.008039667271077633,
0.04800863564014435,
0.03834471479058266,
0.0016217161901295185,
0.03678317368030548,
0.0330951102077961,
-0.011039374396204948,
-0.0025346213951706886,
0.05223057046532631,
0.0272639449685812,
-0.006313246209174395,
-0.018638525158166885,
0.012351129204034805,
-0.04021107405424118,
-0.07692193239927292,
0.004968040157109499,
0.023201270028948784,
-0.0793369710445404,
-0.053615424782037735,
-0.045749735087156296,
0.05538590997457504,
0.016855254769325256,
-0.03968483582139015,
0.025858603417873383,
-0.046986136585474014,
0.021528491750359535,
0.08453147858381271,
0.0036644272040575743,
0.040020786225795746,
0.07303455471992493,
0.07192015647888184,
0.043119966983795166,
0.025951998308300972,
0.010072825476527214,
-0.007133010774850845,
0.030327918007969856,
0.07266507297754288,
-0.011123506352305412,
-0.0017259453888982534,
-0.013627155683934689,
-0.04043968766927719,
0.029693474993109703,
-0.0031210866291075945,
-0.06233826279640198,
0.05494941025972366,
-0.028843458741903305,
0.02327227219939232,
-0.06082283332943916,
0.04552313685417175,
0.016418039798736572,
0.027685068547725677,
0.010569673962891102,
0.0395340770483017,
0.03736824542284012,
-0.013363686390221119,
-0.04422972351312637,
0.0066926791332662106,
0.05143401399254799,
-0.02631795033812523,
-0.006486286409199238,
-0.006030615884810686,
-0.023522349074482918,
0.022806962952017784,
0.013343981467187405,
-0.022001778706908226,
-0.022803816944360733,
0.043948348611593246,
-0.02221222035586834,
0.007971061393618584,
0.04553605616092682,
0.029100870713591576,
-0.019630692899227142,
0.011414751410484314,
0.013706089928746223,
-0.00000914637803361984,
-0.0346142016351223,
0.012643453665077686,
-0.03351416811347008,
-0.050521984696388245,
0.04514949023723602,
0.06262607127428055,
0.008440157398581505,
-0.005051382817327976,
0.057323988527059555,
-0.05508780479431152,
-0.04072349891066551,
-0.04444592818617821,
0.013253786601126194,
-0.0003915492270607501,
0.02501240372657776,
0.05958179756999016,
-0.056565672159194946,
-0.015437745489180088,
-0.009545081295073032,
0.0041769747622311115,
0.0015804674476385117,
0.03877488896250725,
0.021858233958482742,
0.020674696192145348,
-0.07210253179073334,
-0.04085688665509224,
-0.024386150762438774,
-0.05496421828866005,
-0.010392127558588982,
-0.04883335903286934,
0.0370711013674736,
0.0034708494786173105,
-0.035127654671669006,
-0.021719643846154213,
-0.008877932094037533,
0.028910845518112183,
0.02793094329535961,
0.029617611318826675,
-0.018719403073191643,
0.015616039745509624,
0.024752069264650345,
-0.05132671818137169,
-0.013303492218255997,
0.026768628507852554,
-0.028806274756789207,
0.006540084723383188,
-0.03301304206252098,
0.03486413508653641,
-0.06123427674174309,
-0.027797996997833252,
0.036789897829294205,
-0.04727262258529663,
-0.05013316124677658,
0.028656933456659317,
-0.004102109931409359,
-0.008402946405112743,
0.002959686564281583,
0.04736166447401047,
-0.03986393287777901,
-0.041713617742061615,
0.010634412057697773,
0.04705863073468208,
0.012134036049246788,
-0.00392175605520606,
0.022788306698203087,
0.021125417202711105,
-0.00011915645882254466,
0.005463029723614454,
0.042552877217531204,
-0.019765468314290047,
0.02907378412783146,
0.03948784992098808,
-0.041871026158332825,
0.007839610800147057,
-0.0564546212553978,
-0.03258032724261284,
0.02832120656967163,
0.02192607894539833,
-0.014106382615864277,
0.00935907568782568,
-0.030965078622102737,
-0.02883334644138813,
0.006287313532084227,
0.00033720064675435424,
-0.02236318029463291,
0.0016652382910251617,
-0.05269399285316467,
-0.002787758130580187,
-0.014788737520575523,
0.05561792105436325,
-0.05455071106553078,
-0.016000689938664436,
0.0374159999191761,
0.035389382392168045,
-0.08148293942213058,
0.030715879052877426,
-0.04583214595913887,
-0.007754981517791748,
-0.036445796489715576,
0.02278253063559532,
0.015067958272993565,
-0.04213228449225426,
-0.007270074915140867,
-0.04460687190294266,
0.00964618381112814,
0.030132971704006195,
-0.044636569917201996,
0.007471433840692043,
-0.038690511137247086,
0.02866385132074356,
0.00439923582598567,
0.0003877258859574795,
-0.006713794078677893,
-0.07998195290565491,
0.07775592803955078,
-0.049081023782491684,
-0.008582600392401218,
-0.08988407999277115,
0.04901151731610298,
-0.031884804368019104,
-0.056406982243061066,
-0.03562287986278534,
-0.018846947699785233,
0.027055777609348297,
0.029461441561579704,
-0.00689086876809597,
-0.026168622076511383,
0.023989342153072357,
0.04644091799855232,
-0.012062902562320232,
-0.03570609912276268,
0.021158067509531975,
-0.02671642228960991,
-0.02336573228240013,
-0.02694736234843731,
-0.03591543436050415,
0.0021113939583301544,
-0.003588813589885831,
0.006371525581926107,
0.012398487888276577,
-0.01285516656935215,
-0.0046020327135920525,
0.01998187229037285,
0.0564410500228405,
-0.016838232055306435,
-0.046289730817079544,
-0.038331516087055206,
0.007347040809690952,
-0.003038601018488407,
-0.08539941161870956,
0.027146171778440475,
0.015542596578598022,
0.03071536496281624,
-0.023783154785633087,
0.07795587182044983,
0.04710415378212929,
-0.04369162395596504,
0.011499352753162384,
0.013840101659297943,
0.0590091235935688,
0.011713845655322075,
-0.05528215691447258,
-0.0070099737495183945,
-0.02951560914516449,
0.03881404176354408,
0.028094861656427383,
0.07235770672559738,
-0.02231108769774437,
0.035461049526929855,
-0.011570373550057411,
-0.018960142508149147,
-0.06332757323980331,
0.05279187485575676,
0.060445018112659454,
0.02888975292444229,
0.02458801306784153,
0.0618780292570591,
0.027217835187911987,
-0.01936861127614975,
0.06174836680293083,
-0.04897407442331314,
-0.03385547176003456,
0.02018013596534729,
0.00990220531821251,
-0.02857530117034912,
-0.020574895665049553,
0.0623755156993866,
-0.009608488529920578,
-0.0045062885619699955,
0.03467404469847679,
0.019584747031331062,
0.07086338847875595,
0.02843809872865677,
0.03535696491599083,
0.05647146701812744,
0.057391323149204254,
-0.02898174524307251,
-0.0008935504010878503,
-0.024987859651446342,
-0.012973927892744541,
0.03536955639719963,
-0.03290310502052307,
0.018642090260982513,
0.043468497693538666,
0.024616502225399017,
-0.037898145616054535,
-0.037010930478572845,
0.03072599321603775,
-0.0021335240453481674,
-0.011574451811611652,
-0.0537145659327507,
0.03142574056982994,
-0.01232907921075821,
-0.016575302928686142,
-0.016351616010069847,
-0.08161970973014832,
-0.02422492392361164,
0.026381274685263634,
-0.03957131877541542,
-0.04660366475582123,
0.02553948201239109,
0.02390795201063156,
-0.03991895541548729,
-0.0336870513856411,
-0.01622430421411991,
-0.014049196615815163,
-0.009624538943171501,
-0.051787517964839935,
-0.004157232120633125,
-0.04955277964472771,
0.005519108381122351,
0.045449238270521164,
0.015710948035120964,
-0.043538257479667664,
0.01842486672103405,
-0.03476879000663757,
0.008935588411986828,
0.012523049488663673,
-0.00429962994530797,
-0.0050247651524841785,
0.0020403622183948755,
-0.02750118263065815,
0.048904623836278915,
0.005504162050783634,
-0.04886997863650322,
-0.0032642213627696037,
0.0025667801965028048,
-0.031823232769966125,
-0.03301228955388069,
-0.0047523258253932,
-0.04732409492135048,
0.003953428473323584,
0.029306264594197273,
-0.010672428645193577,
-0.022839656099677086,
0.055283352732658386,
-0.011445131152868271,
-0.014386996626853943,
-0.03249335289001465,
-0.013394610024988651,
0.021284814924001694,
0.010278947651386261,
0.014943210408091545,
-0.010053909383714199,
0.05163191631436348,
0.04632456600666046,
-0.02595721185207367,
-0.0018787039443850517,
0.03402402624487877,
-0.013392333872616291,
-0.17004314064979553,
0.022107526659965515,
-0.06555536389350891,
0.056000966578722,
-0.032000940293073654,
0.0010543711250647902,
-0.059446074068546295,
-0.008354843594133854,
-0.02027147449553013,
0.03731287270784378,
0.03105594776570797,
-0.02634241245687008,
0.038238126784563065,
0.01572772115468979,
-0.013564972206950188,
0.02988419122993946,
-0.010648401454091072,
0.06538935005664825,
0.021106984466314316,
0.014161172322928905,
0.006498381495475769,
-0.02794365957379341,
-0.05293916538357735,
-0.0522613599896431,
-0.002293472643941641,
-0.010954529047012329,
-0.027546893805265427,
0.057857248932123184,
0.022160205990076065,
-0.018116243183612823,
0.05936640873551369,
0.02431664429605007,
-0.0206924919039011,
0.009812102653086185,
0.025612886995077133,
-0.01645609550178051,
-0.0021740610245615244,
0.09246231615543365,
-0.0013262606225907803,
-0.0016579459188506007,
-0.009831258095800877,
0.013217323459684849,
0.02332126908004284,
0.0353347584605217,
0.009568488225340843,
0.01027185283601284,
0.005618035793304443,
-0.022531328722834587,
0.06124194338917732,
0.0020845942199230194,
0.009670000523328781,
-0.0027010184712707996,
0.016426529735326767,
-0.04862994700670242,
-0.001146429916843772,
0.05426633730530739,
0.016812074929475784,
-0.04732148349285126,
0.004733295179903507,
0.028804445639252663,
-0.012358210049569607,
-0.04070909693837166,
0.053850654512643814,
0.00726205762475729,
-0.03067360632121563,
-0.03488146513700485,
-0.026511088013648987,
-0.01471896655857563,
0.018063217401504517,
0.016223542392253876,
0.006662607192993164,
0.020883386954665184,
-0.017689114436507225,
-0.048436131328344345,
0.021735336631536484,
-0.03552137315273285,
-0.011971917934715748,
0.006491766311228275,
0.05946718156337738,
-0.04089236631989479,
-0.025779303163290024,
-0.018932243809103966,
-0.07061909884214401,
-0.01827838644385338,
-0.009453638456761837,
-0.04651251807808876,
0.015053145587444305,
-0.013549271039664745,
0.023630043491721153,
0.05271502584218979,
0.07379989326000214,
-0.04008488357067108,
-0.04027561843395233,
0.009256839752197266,
0.009932909160852432,
-0.05313112959265709,
0.0006346995942294598,
0.015399298630654812,
-0.03940418362617493,
-0.0747758001089096,
0.02457357384264469,
0.023764241486787796,
0.10229609906673431,
0.03494076430797577,
0.03952508419752121,
-0.03533075004816055,
0.03445260971784592,
0.016270659863948822,
0.050815656781196594,
0.027991218492388725,
0.02371342107653618,
0.09449872374534607,
0.04401237890124321,
-0.0032687289640307426,
-0.04708794876933098,
0.011559631675481796,
-0.0527774952352047,
-0.008659357205033302,
-0.03010110929608345,
-0.05074974149465561,
-0.00234717084094882,
0.014390234835445881,
0.015098382718861103,
0.006543869152665138,
-0.0074989465065300465,
0.023678304627537727,
0.0007694900850765407,
0.03832763805985451,
0.027592390775680542,
-0.06637050211429596,
0.05007576197385788,
0.02013690024614334,
-0.023229612037539482,
-0.0065058814361691475,
-0.032104671001434326,
0.048290155827999115,
-0.03874770179390907,
-0.008778749965131283,
-0.027779987081885338,
-0.05301254987716675,
-0.0000948142260313034,
0.04693664237856865,
-0.05177609249949455,
-0.03663517162203789,
0.011659001931548119,
-0.012679477222263813,
-0.021731941029429436,
-0.04401625320315361,
-0.020546264946460724,
0.07260530441999435,
-0.041647493839263916,
0.011527245864272118,
-0.0037140988279134035,
0.015035751275718212,
-0.06842276453971863,
0.059822142124176025,
-0.07642081379890442,
-0.002283514244481921,
0.0017577664693817496,
-0.051547594368457794,
0.034805115312337875,
0.08532756567001343,
0.03183005750179291,
0.010294578969478607,
-0.03892737254500389,
-0.04392861947417259,
-0.014548439532518387,
-0.027174538001418114,
-0.04108920320868492,
0.02762598544359207,
0.021459823474287987,
0.03344742953777313,
0.03193501755595207,
-0.03486716002225876,
-0.037953417748212814,
-0.04225877299904823,
0.05738666653633118,
0.02440342679619789,
-0.10148294270038605,
0.03151530399918556,
0.029383903369307518
] |
<p>Let's say I have a projectile being thrown by a player in my 2-D game. I want to work backwards and find the initial velocity to apply to the projectile such that it passes through a target point in space given that the launch point might not be at $y=0$.</p>
<p>Some applications of this would be a basketball shot simulator or a pub darts simulation.</p>
<p>Given:</p>
<ul>
<li>initial or launch angle: $\theta_o$</li>
<li>initial or launch height: $y_o$</li>
<li>target point: ($x_f$, $y_f$)</li>
<li>constant acceleration due to gravity ($g$)</li>
<li>air resistance ignored</li>
</ul>
<p>I need to find:</p>
<ul>
<li>initial launch velocity: $v_o$</li>
</ul>
<p>Here's an image of what I'm talking about.</p>
<p><img src="http://i.stack.imgur.com/uRRkX.png" alt="enter image description here"></p>
<p>I am interested in learning the derivation of the answer not just a formula that I plug-and-chug. Thanks!</p> | g7828 | [
0.031731344759464264,
0.020011715590953827,
-0.0173217561095953,
-0.03258368745446205,
-0.004982596263289452,
0.020368224009871483,
0.023129550740122795,
0.013476438820362091,
-0.048113178461790085,
-0.01059748325496912,
-0.04078620672225952,
0.08824922889471054,
0.03318597003817558,
0.024381594732403755,
0.026503385975956917,
-0.03246438503265381,
0.0599193349480629,
-0.040485233068466187,
0.029303399845957756,
0.03157102316617966,
0.019572369754314423,
-0.039117466658353806,
0.028712132945656776,
-0.010606863535940647,
0.003861016361042857,
-0.027619699016213417,
0.003458276391029358,
0.0039007607847452164,
-0.0797509178519249,
0.012156196869909763,
-0.0015199588378891349,
-0.022203179076313972,
0.02485494129359722,
-0.06563694030046463,
0.023270677775144577,
0.004928098525851965,
-0.02517346292734146,
0.003054959699511528,
-0.030891750007867813,
-0.042712025344371796,
-0.02103058248758316,
-0.04982272535562515,
0.0537712462246418,
0.07972999662160873,
0.05238675698637962,
-0.024223387241363525,
0.009493005461990833,
0.03051363117992878,
-0.02718384563922882,
-0.031071767210960388,
-0.06028861179947853,
0.05024248734116554,
-0.0194950383156538,
-0.09208574891090393,
-0.07910633832216263,
0.048972733318805695,
-0.050081029534339905,
-0.007430315483361483,
0.02273855358362198,
-0.0006745344726368785,
-0.006286425981670618,
0.007236203644424677,
-0.02510095201432705,
-0.04018126055598259,
0.04293734207749367,
-0.0191362127661705,
-0.03546445816755295,
-0.0016470684204250574,
-0.036111198365688324,
-0.024377023801207542,
0.04509297013282776,
-0.03314277157187462,
-0.044543422758579254,
-0.047406360507011414,
-0.0728570744395256,
-0.0183384008705616,
-0.01050575915724039,
-0.015481376089155674,
-0.04155932366847992,
-0.025898320600390434,
-0.05215885490179062,
0.029086271300911903,
0.01660138927400112,
-0.06086788699030876,
0.04975956305861473,
0.013765092007815838,
0.050182271748781204,
0.055260129272937775,
-0.05410315468907356,
-0.04875324293971062,
0.015019458718597889,
0.058842942118644714,
0.010134599171578884,
0.0061334543861448765,
-0.024355299770832062,
-0.01967594027519226,
-0.08484995365142822,
0.06849657744169235,
0.051271483302116394,
0.012367037124931812,
0.00855525303632021,
0.00880362931638956,
0.004623729735612869,
-0.029538314789533615,
-0.003813997143879533,
0.01210132334381342,
0.08679286390542984,
-0.009614499285817146,
-0.01974298618733883,
-0.02341432496905327,
-0.008427558466792107,
-0.05011599883437157,
-0.04094294458627701,
-0.03630821034312248,
-0.011047226376831532,
-0.03614833205938339,
0.08679073303937912,
0.03842246159911156,
0.01092713512480259,
0.056759897619485855,
0.02786688134074211,
0.002152638742700219,
-0.0312734991312027,
0.06263358145952225,
0.005625792779028416,
-0.015400865115225315,
-0.049573276191949844,
-0.023519232869148254,
-0.02614184468984604,
0.04330730065703392,
0.017536118626594543,
-0.009667580015957355,
0.003993549849838018,
0.01329702790826559,
0.001457857433706522,
0.007839708589017391,
0.01823902688920498,
0.015348046086728573,
0.004178586881607771,
0.03602910041809082,
-0.035581592470407486,
-0.03936253488063812,
0.013149195350706577,
-0.031307242810726166,
-0.06838558614253998,
0.0452171266078949,
0.004130184184759855,
0.008731331676244736,
-0.03485778346657753,
0.017823807895183563,
-0.003176294732838869,
0.09632367640733719,
0.016344893723726273,
0.022945556789636612,
-0.00335895293392241,
-0.06971024721860886,
0.035742662847042084,
0.007860954850912094,
0.01800375245511532,
-0.053619448095560074,
0.03781406208872795,
0.015833957120776176,
0.00789284985512495,
0.021137993782758713,
-0.04637633636593819,
0.03399690240621567,
-0.008517538197338581,
-0.010106094181537628,
-0.011416474357247353,
-0.027844132855534554,
-0.03640226647257805,
-0.025318773463368416,
0.01957147754728794,
0.007126093376427889,
-0.017881091684103012,
0.014149541035294533,
0.02571132592856884,
0.02313423343002796,
-0.03423790633678436,
-0.017349496483802795,
0.002993280068039894,
-0.058327604085206985,
0.0009391711791977286,
-0.01448388583958149,
0.013914993032813072,
-0.0180970449000597,
0.05399066209793091,
0.06168798357248306,
0.0008390555158257484,
-0.003995192237198353,
0.022678818553686142,
-0.03664834797382355,
-0.0032897284254431725,
-0.05881384760141373,
-0.026168378069996834,
-0.011227158829569817,
0.09140108525753021,
-0.003679873887449503,
-0.03197210654616356,
0.07368050515651703,
-0.02456352673470974,
0.047827038913965225,
0.03540102019906044,
0.0006291733006946743,
-0.009299565106630325,
-0.02197173237800598,
-0.010089479386806488,
0.011572590097784996,
0.0028670132160186768,
0.055811118334531784,
0.002925422042608261,
-0.010832025669515133,
0.01998610608279705,
0.052416302263736725,
0.06362366676330566,
0.00716338912025094,
-0.034538742154836655,
0.041628722101449966,
-0.07056958973407745,
0.043723512440919876,
-0.008502982556819916,
0.004298901651054621,
0.016026748344302177,
-0.022618863731622696,
-0.044079724699258804,
-0.0015038091223686934,
0.041108138859272,
0.05146823078393936,
0.026130154728889465,
-0.023138336837291718,
-0.005924747791141272,
0.044330764561891556,
-0.0027904005255550146,
-0.03082098811864853,
0.08224625885486603,
-0.010624491609632969,
-0.0174433384090662,
-0.02214590460062027,
0.015451171435415745,
0.026190102100372314,
-0.03006598725914955,
0.0007943160017021,
-0.006419035606086254,
0.015165086835622787,
0.036952972412109375,
-0.08267885446548462,
0.03113904967904091,
0.003010022221133113,
-0.018950723111629486,
-0.02621200680732727,
-0.028896557167172432,
0.02364068292081356,
-0.0495564229786396,
-0.007742700632661581,
-0.0535883903503418,
-0.025622030720114708,
-0.02674270235002041,
0.006074056029319763,
-0.07024025917053223,
-0.05174665153026581,
-0.014229033142328262,
-0.031596843153238297,
-0.014243768528103828,
-0.027148431167006493,
-0.04194215312600136,
0.02197123132646084,
-0.007922841235995293,
-0.0072347018867731094,
-0.001396179897710681,
0.029633207246661186,
-0.07160486280918121,
0.032546065747737885,
0.021184207871556282,
0.019419092684984207,
0.011113046668469906,
-0.021388424560427666,
0.06436074525117874,
-0.02455100789666176,
0.0254618301987648,
0.06492646038532257,
-0.011994230560958385,
-0.053541429340839386,
-0.04671768099069595,
0.04356718435883522,
0.04232506826519966,
-0.058340515941381454,
0.013425870798528194,
0.03423643484711647,
0.010618060827255249,
-0.03402666002511978,
0.0046338834799826145,
0.03979067504405975,
-0.006681427825242281,
0.01524516474455595,
0.035427991300821304,
0.04558991640806198,
0.03479398041963577,
-0.026168715208768845,
0.008203664794564247,
-0.02138160914182663,
0.023338325321674347,
-0.02732631005346775,
0.016342492774128914,
-0.04129662364721298,
-0.04240918904542923,
0.05518028885126114,
-0.029857678338885307,
-0.042595889419317245,
-0.0022220350801944733,
0.0054349759593605995,
0.007496461737900972,
0.0432610958814621,
-0.04762549698352814,
-0.006908144801855087,
-0.03897671401500702,
-0.04773066192865372,
0.02647160179913044,
-0.017273101955652237,
0.0031290394254028797,
0.0179124865680933,
-0.03439588099718094,
-0.07300185412168503,
0.053129374980926514,
0.06711260229349136,
0.004753537010401487,
0.031935084611177444,
0.008664633147418499,
0.024591591209173203,
-0.018844466656446457,
-0.022938700392842293,
0.06294173747301102,
0.0685148686170578,
-0.008761475794017315,
0.004587580915540457,
0.008714362047612667,
-0.039452534168958664,
0.0005610107909888029,
0.01869964599609375,
0.04046516865491867,
0.01988273859024048,
-0.028385745361447334,
-0.00524229696020484,
-0.040157750248909,
-0.01908956468105316,
0.03553769737482071,
-0.04611510410904884,
0.015018665231764317,
0.09953359514474869,
0.008860175497829914,
-0.05653375759720802,
0.04821457341313362,
-0.014037040062248707,
0.003335117595270276,
-0.011735394597053528,
0.001746002002619207,
0.0767640545964241,
0.08989813178777695,
-0.003263999242335558,
-0.03524884209036827,
0.042700354009866714,
-0.03193181753158569,
-0.02206975407898426,
-0.03098243661224842,
0.08151430636644363,
0.028898227959871292,
-0.007033053319901228,
-0.006327094044536352,
0.018693529069423676,
-0.022020796313881874,
0.03233170136809349,
-0.0042261648923158646,
-0.042142994701862335,
0.022082699462771416,
-0.01335602905601263,
-0.005577647127211094,
-0.008445375598967075,
-0.0046092127449810505,
0.036158487200737,
-0.029896428808569908,
0.012070760130882263,
0.05108087509870529,
0.04415209963917732,
0.0024663282092660666,
0.039406709372997284,
-0.0051253121346235275,
0.07069554179906845,
0.012915529310703278,
-0.010471008718013763,
0.06887307018041611,
-0.03297802433371544,
0.054041698575019836,
-0.009365913458168507,
-0.0000747633384889923,
0.021747738122940063,
0.040285464376211166,
0.01785263419151306,
-0.0417771115899086,
-0.04665479063987732,
-0.05747216194868088,
0.009822828695178032,
-0.00829041376709938,
0.02730436809360981,
0.024684039875864983,
0.005528174806386232,
-0.06066885218024254,
-0.010015332140028477,
0.016949918121099472,
-0.015338444150984287,
-0.021608499810099602,
0.021689655259251595,
-0.029363853856921196,
-0.04217662289738655,
-0.001478356309235096,
-0.03579026833176613,
-0.041680507361888885,
-0.027752229943871498,
0.03216211870312691,
0.0389690026640892,
-0.03436599299311638,
0.016912933439016342,
0.04214728623628616,
0.0801900327205658,
0.04077956825494766,
-0.06401445716619492,
0.009028621017932892,
0.0013020924525335431,
0.05492004007101059,
0.03199903294444084,
0.04363931715488434,
-0.019789250567555428,
-0.018004514276981354,
0.013614868745207787,
-0.013673974201083183,
0.06064757704734802,
-0.034529268741607666,
0.0010690155904740095,
0.014761942438781261,
-0.007054300978779793,
0.007813108153641224,
-0.0022445786744356155,
-0.05164872854948044,
-0.026083452627062798,
0.007783419918268919,
-0.015535900369286537,
-0.02135089412331581,
0.0903766080737114,
-0.041496824473142624,
0.0006253705942071974,
-0.021713821217417717,
-0.02439957670867443,
0.01726498268544674,
0.0059288265183568,
-0.011743475683033466,
0.008907821960747242,
-0.06254470348358154,
0.02012663334608078,
-0.009222177788615227,
-0.012364968657493591,
0.005859518889337778,
-0.0016473460709676147,
0.02332237735390663,
0.002788290847092867,
0.004240397363901138,
-0.06468789279460907,
-0.024948349222540855,
-0.02206670679152012,
0.009148387238383293,
-0.010388609953224659,
0.01754925027489662,
-0.01763259992003441,
0.02836097590625286,
0.014150477014482021,
-0.015329243615269661,
0.05355822667479515,
-0.03674965351819992,
0.00695533212274313,
-0.007939920760691166,
0.03017624095082283,
0.06265393644571304,
-0.03372253105044365,
-0.041267335414886475,
-0.013081471435725689,
-0.036096468567848206,
-0.003383991774171591,
-0.022881576791405678,
0.02145402692258358,
-0.003577458206564188,
-0.02089902199804783,
0.02004133351147175,
-0.05100936442613602,
-0.010717340745031834,
-0.015998147428035736,
-0.02563680335879326,
-0.018673090264201164,
-0.03770773857831955,
-0.007436074316501617,
0.011960919015109539,
-0.009637393057346344,
-0.00360970594920218,
-0.004411074332892895,
-0.11063811182975769,
-0.05298783630132675,
0.028956415131688118,
0.028725747019052505,
0.020205238834023476,
-0.0042082215659320354,
0.04356032982468605,
0.021400446072220802,
-0.05147078260779381,
0.006338841747492552,
0.05105089023709297,
0.03082624450325966,
0.032619789242744446,
-0.003894193796440959,
-0.0144544318318367,
-0.015855178236961365,
0.06271886080503464,
0.01487188134342432,
0.0033184390049427748,
-0.02383684366941452,
0.08191714435815811,
-0.026220371946692467,
0.02492433413863182,
0.02390509843826294,
-0.014820857904851437,
0.050524163991212845,
-0.03312725946307182,
-0.014535736292600632,
-0.028173496946692467,
0.053629279136657715,
-0.043347395956516266,
-0.02704370580613613,
-0.07666441053152084,
-0.042165640741586685,
-0.08565160632133484,
0.006935779005289078,
-0.008500071242451668,
-0.018244225531816483,
-0.02951984480023384,
-0.09146703034639359,
-0.07797762751579285,
-0.016843555495142937,
0.022219624370336533,
0.007074111141264439,
-0.047907207161188126,
0.0038965276908129454,
-0.0532805360853672,
0.010142623446881771,
0.025207538157701492,
-0.06507822871208191,
-0.028505830094218254,
0.013323000632226467,
0.0394267663359642,
-0.021298404783010483,
-0.014574873261153698,
0.03270605206489563,
-0.04033556953072548,
0.04156695678830147,
-0.06507137417793274,
-0.013961134478449821,
0.045037541538476944,
-0.024884192273020744,
0.04818611592054367,
0.03791563957929611,
0.008416342549026012,
-0.04403306171298027,
0.037110455334186554,
-0.0044723497703671455,
0.06887117773294449,
0.001120597473345697,
0.001579779083840549,
0.0076081035658717155,
-0.054467108100652695,
-0.003662536386400461,
0.030488990247249603,
0.06786169111728668,
-0.0028200377710163593,
-0.06786835193634033,
-0.04930458217859268,
0.06067813187837601,
-0.013241914100944996,
0.056902334094047546,
0.015236521139740944,
-0.00722131272777915,
-0.020379547029733658,
0.01530340127646923,
-0.015098979696631432,
-0.02397576905786991,
-0.007352693472057581,
-0.05589135363698006,
0.002075212076306343,
0.010301950387656689,
-0.00006370199844241142,
-0.09087952226400375,
-0.060376159846782684,
-0.005912368185818195,
0.00033925732714124024,
-0.023854680359363556,
-0.023747248575091362,
0.04971744492650032,
0.0012699374929070473,
0.02848566137254238,
-0.01621074229478836,
-0.06324689835309982,
0.03543991968035698,
0.021876301616430283,
-0.01709362491965294,
-0.02757493034005165,
0.08576274663209915,
-0.046000611037015915,
-0.013583938591182232,
0.0582120381295681,
0.03357193246483803,
0.08718118071556091,
-0.03501592203974724,
0.031004609540104866,
0.0021061140578240156,
-0.0077034118585288525,
-0.005465701222419739,
-0.016982657834887505,
0.04387671500444412,
0.011452153325080872,
-0.01103831548243761,
0.005452956072986126,
0.07479467988014221,
-0.0018228379776701331,
-0.0497450977563858,
0.020294740796089172,
0.0002677351876627654,
0.0180570799857378,
0.026783039793372154,
-0.03974677622318268,
0.015444387681782246,
0.025701088830828667,
0.03733674809336662,
0.042754173278808594,
0.024078333750367165,
0.09149989485740662,
0.016924066469073296,
0.021035706624388695,
0.01981702260673046,
0.040106043219566345,
-0.013914725743234158,
0.02168421633541584,
-0.04134853184223175,
0.0028809995856136084,
-0.01014895923435688,
-0.012864410877227783,
-0.0592980720102787,
-0.00787531677633524,
-0.011527251452207565,
-0.032723959535360336,
-0.028440983965992928,
-0.00783604010939598,
-0.01838773675262928,
0.04972083494067192,
0.0468461848795414,
0.03855754807591438,
0.01092732697725296,
-0.04665344953536987,
-0.029044652357697487,
-0.041422709822654724,
0.0010374311823397875,
0.007769884541630745,
-0.009808351285755634,
-0.009111633524298668,
-0.007887130603194237,
0.011156030930578709,
0.008739016018807888,
-0.03896387666463852,
0.00443714065477252,
-0.03326791897416115,
-0.05160963535308838,
0.06409058719873428,
-0.016948191449046135,
0.057456083595752716,
-0.02792872115969658,
0.010518070310354233,
-0.019160643219947815,
-0.026459934189915657,
-0.005422832909971476,
0.04133157432079315,
-0.025336135178804398,
-0.015559081919491291,
-0.004179087001830339,
0.034195173531770706,
0.021060915663838387,
-0.02428216114640236,
0.04455612227320671,
-0.030206134542822838,
-0.03598630055785179,
0.04538941755890846,
0.049888234585523605,
-0.04679176211357117,
0.03538127243518829,
-0.007866446860134602,
0.030752597376704216,
0.05614016577601433,
0.017533857375383377,
0.012788872234523296,
0.058312442153692245,
-0.01614280417561531,
0.010530168190598488,
0.027971193194389343,
-0.005134342238306999,
0.011238530278205872,
-0.019894057884812355,
-0.005674487445503473,
-0.04766290262341499,
-0.07545218616724014,
-0.009706578217446804,
0.007141229696571827,
0.035835180431604385,
-0.0116921691223979,
-0.009914777241647243,
0.0241028293967247,
-0.010893517173826694,
0.055182766169309616,
0.0019992452580481768,
-0.03308793529868126,
0.0029807905666530132,
-0.011763635091483593,
0.031003521755337715,
-0.028144946321845055,
0.06367515027523041,
-0.062225066125392914,
-0.04646195471286774,
0.029649628326296806,
-0.010069823823869228,
-0.0218245517462492,
0.0286004189401865,
-0.043981801718473434,
0.01742461510002613,
0.026584303006529808,
-0.02256658487021923,
0.0005088502075523138,
-0.04399789497256279,
-0.0027163021732121706,
0.05541794002056122,
0.028440695255994797,
-0.029821254312992096,
0.02677387185394764,
0.015100983902812004,
-0.031125562265515327,
0.04522690549492836,
-0.029980355873703957,
0.03144761547446251,
0.05710310861468315,
0.05497879907488823,
-0.05074230208992958,
0.1329234093427658,
-0.011036310344934464,
-0.061330851167440414,
0.046771127730607986,
0.03621843829751015,
-0.048737961798906326,
-0.0008150359499268234,
0.029800910502672195,
-0.004311475902795792,
-0.0450420118868351,
-0.06476937234401703,
-0.039674896746873856,
0.013439119793474674,
0.03438713774085045,
0.017052730545401573,
-0.02893807739019394,
-0.030375657603144646,
0.037364568561315536
] |
<p>I once came across the strange, artificial unit "hertz per dioptre", which is dimensionally equivalent to "metres per second". Could this unit, by some stretch of the imagination, be used in some artificial situation where the usage implications of both "hertz" and "dioptre" (frequency of periodic events and refractive power, respectively) would make for the ratio to actually be useful?</p> | g7829 | [
0.006900732405483723,
0.01703648269176483,
0.011234716512262821,
-0.056545279920101166,
-0.01906268298625946,
-0.07007165998220444,
0.023598283529281616,
0.0049879830330610275,
-0.02505166083574295,
0.005657755304127932,
0.03340817987918854,
0.0175942275673151,
0.03554171323776245,
0.02999442256987095,
-0.02509979158639908,
0.02651778794825077,
0.07915739715099335,
0.02853631228208542,
0.02671203948557377,
0.03967040032148361,
0.04555107653141022,
-0.05208843573927879,
-0.03594490885734558,
-0.019264675676822662,
-0.03411354497075081,
0.014859689399600029,
0.017463674768805504,
-0.012776346877217293,
-0.12204740941524506,
-0.02338513918220997,
0.00505245802924037,
-0.040197379887104034,
0.01209951750934124,
-0.049048468470573425,
-0.055259279906749725,
0.033082906156778336,
0.0023542961571365595,
0.009916473180055618,
-0.007338466588407755,
0.03320224955677986,
0.002160828560590744,
0.007990884594619274,
-0.037846360355615616,
0.0038537706714123487,
0.019056646153330803,
0.012469428591430187,
-0.028061451390385628,
0.014845750294625759,
-0.04541502892971039,
-0.009402326308190823,
0.013167356140911579,
0.016806038096547127,
0.08166643977165222,
0.04039532691240311,
0.026382235810160637,
0.022043326869606972,
-0.022949371486902237,
0.005550924688577652,
0.08464960753917694,
0.054821211844682693,
0.03410358354449272,
-0.025136439129710197,
-0.01586337201297283,
0.0012555421562865376,
0.0728486180305481,
0.017719918861985207,
0.027087649330496788,
-0.019586414098739624,
0.004394170828163624,
-0.02724248729646206,
-0.003177434904500842,
-0.06368865072727203,
-0.03103620931506157,
-0.004035784397274256,
-0.02120400220155716,
0.00652807392179966,
-0.03212342783808708,
-0.029879067093133926,
-0.015036380849778652,
0.05442240834236145,
-0.01746237836778164,
-0.006614861078560352,
0.06111103668808937,
-0.007073356769979,
0.08349777013063431,
0.01895776391029358,
0.034834444522857666,
0.003580213524401188,
0.030522361397743225,
0.06489510089159012,
-0.0089548509567976,
-0.026298951357603073,
0.03204410895705223,
-0.007251801434904337,
-0.01920563541352749,
-0.05084136128425598,
-0.024947848170995712,
0.014703022316098213,
0.005199848208576441,
0.026046423241496086,
-0.003940090537071228,
0.014774477109313011,
0.04498026520013809,
0.005776391364634037,
-0.026580605655908585,
0.00996074452996254,
0.020263928920030594,
-0.008413820527493954,
-0.04540592432022095,
-0.06364180147647858,
0.014635694213211536,
-0.011939647607505322,
-0.014544970355927944,
-0.043150242418050766,
-0.024076413363218307,
-0.061154771596193314,
0.03018464334309101,
-0.03753736615180969,
-0.04882783815264702,
0.03966140374541283,
0.04906098544597626,
0.005605557933449745,
-0.020268334075808525,
0.0605660043656826,
-0.04122791066765785,
0.03411116078495979,
-0.03433647006750107,
0.034538835287094116,
0.03742898628115654,
-0.013173938728868961,
-0.009585334919393063,
0.020785018801689148,
-0.031064199283719063,
0.0010583496186882257,
-0.045459747314453125,
0.09237385541200638,
0.07614494860172272,
-0.06560934334993362,
0.011219991371035576,
0.052301689982414246,
0.006344303954392672,
-0.0647842288017273,
0.001373018603771925,
-0.03160395473241806,
-0.07878901809453964,
0.029149740934371948,
-0.019936924800276756,
-0.050201091915369034,
-0.005828064866364002,
0.040041886270046234,
-0.03640245646238327,
0.04532879590988159,
-0.013137872330844402,
-0.023043369874358177,
0.0047424668446183205,
0.036971960216760635,
0.02002379298210144,
0.004449591506272554,
-0.0009219538187608123,
0.05904630199074745,
0.00929347239434719,
-0.016934551298618317,
-0.06278835237026215,
-0.006743780802935362,
-0.05528796464204788,
-0.05713094770908356,
-0.02471511997282505,
-0.012778252363204956,
-0.016753919422626495,
-0.038532599806785583,
-0.005497265607118607,
-0.015137970447540283,
-0.026263106614351273,
0.046553824096918106,
0.011495816521346569,
0.025428403168916702,
0.025886408984661102,
0.010434449650347233,
-0.006393817253410816,
0.0036763735115528107,
-0.05282815545797348,
0.005400988273322582,
0.05998106673359871,
-0.04432808235287666,
-0.019841276109218597,
-0.0024142605252563953,
0.05068381130695343,
-0.018004324287176132,
-0.033867571502923965,
0.06444402039051056,
0.004735665395855904,
-0.019185222685337067,
-0.03103002905845642,
0.07798229902982712,
-0.04983260855078697,
-0.026885125786066055,
0.007090419996529818,
0.04134947806596756,
-0.055540040135383606,
0.052288640290498734,
-0.0016580845694988966,
0.0047098626382648945,
0.022976569831371307,
-0.023390455171465874,
0.05788498744368553,
0.006639768835157156,
-0.005020740441977978,
0.03829557076096535,
0.047770287841558456,
-0.02444966323673725,
0.07195252925157547,
0.008066946640610695,
0.050786092877388,
0.025161856785416603,
-0.04225104674696922,
-0.03171581029891968,
-0.03225500136613846,
-0.026881299912929535,
-0.009671355597674847,
0.028542382642626762,
-0.0328763909637928,
-0.02328425832092762,
0.05222964286804199,
-0.004934054333716631,
-0.023253941908478737,
-0.08968941122293472,
-0.011949475854635239,
-0.02177664078772068,
0.005039773881435394,
0.0040430184453725815,
0.01517702080309391,
-0.0016197896329686046,
0.01944112218916416,
-0.00480751134455204,
0.005177008453756571,
0.042187876999378204,
0.00348577625118196,
0.05606113374233246,
0.009893735870718956,
0.005712280049920082,
0.0602608360350132,
-0.01166335865855217,
-0.017381032928824425,
0.00867149792611599,
-0.06352388858795166,
-0.021992681547999382,
-0.02783023938536644,
0.013425693847239017,
-0.025047194212675095,
0.00574684189632535,
-0.03847341984510422,
-0.021453822031617165,
-0.0006862283335067332,
-0.00618122098967433,
-0.017947282642126083,
0.012244516052305698,
-0.04542969539761543,
0.007110864855349064,
-0.08490317314863205,
0.006519360933452845,
0.012449982576072216,
0.01651647873222828,
0.04719860851764679,
-0.0024109354708343744,
0.02648616023361683,
-0.08796324580907822,
-0.03195834532380104,
0.08190836757421494,
-0.026605091989040375,
0.06672043353319168,
0.04657831788063049,
0.01974339783191681,
-0.007977993227541447,
0.03199271112680435,
-0.045699592679739,
0.0081710834056139,
0.047943130135536194,
-0.08008173853158951,
0.0507575124502182,
-0.05710269883275032,
0.033629536628723145,
-0.008435895666480064,
-0.027044357731938362,
0.005360390059649944,
0.0066522713750600815,
-0.04377535358071327,
0.01080118678510189,
0.10641175508499146,
-0.0134528623893857,
0.015951193869113922,
-0.04679661616683006,
-0.010099798440933228,
0.021427789703011513,
0.0027830679900944233,
-0.015269987285137177,
0.027279537171125412,
0.11180652678012848,
-0.011170828714966774,
0.029757212847471237,
0.014304377138614655,
0.03116033971309662,
-0.033720165491104126,
-0.005618223920464516,
0.04621725156903267,
0.011047672480344772,
0.04884650185704231,
-0.051885221153497696,
-0.029916005209088326,
0.06211944296956062,
-0.028480660170316696,
0.04292086884379387,
0.07010563462972641,
0.02349567599594593,
-0.00013760800356976688,
-0.042201731353998184,
-0.019003715366125107,
0.01716757006943226,
0.017338791862130165,
-0.04019288718700409,
0.057356301695108414,
0.03903665766119957,
-0.02629772759974003,
-0.03286276385188103,
-0.03677969425916672,
0.026550645008683205,
0.06508581340312958,
0.003607264719903469,
0.03531644865870476,
-0.07295776903629303,
0.005269349552690983,
0.021437564864754677,
0.03133073449134827,
0.030219221487641335,
-0.017625974491238594,
-0.034565217792987823,
0.010604098439216614,
-0.01518655102699995,
0.048775382339954376,
0.02215876430273056,
0.018889853730797768,
0.006829230114817619,
0.019814791157841682,
-0.05905262380838394,
-0.038792818784713745,
0.04853060841560364,
-0.01976962946355343,
0.0090538514778018,
0.03766738995909691,
-0.01794407144188881,
-0.035343512892723083,
-0.029572857543826103,
-0.025076650083065033,
0.01987263932824135,
-0.03713604062795639,
0.006654613185673952,
0.05443695932626724,
0.0766180157661438,
0.030397793278098106,
0.019266022369265556,
-0.04101980850100517,
0.045574359595775604,
0.0022805542685091496,
0.02946605533361435,
-0.05297092720866203,
0.01913834922015667,
0.01610698364675045,
0.007133301813155413,
0.08830250799655914,
-0.032473668456077576,
-0.04396797716617584,
0.010940187610685825,
-0.03299405425786972,
-0.051248252391815186,
-0.011101051233708858,
0.04934316501021385,
-0.02177179604768753,
-0.005907795391976833,
-0.012138993479311466,
-0.07386064529418945,
0.04365534335374832,
-0.045559607446193695,
0.06178409978747368,
0.0101584168151021,
0.00586181553080678,
-0.03969857841730118,
-0.04073626920580864,
-0.014096857979893684,
-0.04330836609005928,
0.015155695378780365,
-0.04015081375837326,
0.004333133343607187,
-0.019037993624806404,
-0.03350784629583359,
-0.020228775218129158,
-0.026015933603048325,
-0.022156529128551483,
-0.04424192011356354,
-0.06519293785095215,
0.014851972460746765,
0.023068225011229515,
0.058174315840005875,
-0.03978147357702255,
-0.018203316256403923,
-0.014126807451248169,
-0.0556691512465477,
-0.037642162293195724,
0.037551261484622955,
0.008456684648990631,
0.0010013054125010967,
0.03429911285638809,
-0.03787091746926308,
0.0054802363738417625,
0.026807967573404312,
-0.09923851490020752,
0.01002206839621067,
0.08275321125984192,
0.00834064744412899,
-0.029508104547858238,
0.08776702731847763,
0.068941630423069,
0.01126766111701727,
0.07833126932382584,
-0.006702024023979902,
0.005304845981299877,
-0.020090097561478615,
-0.00375594524666667,
0.07696084678173065,
-0.018897853791713715,
-0.03986424580216408,
-0.039926134049892426,
0.0539444200694561,
0.019340820610523224,
0.017608841881155968,
-0.0007730067009106278,
0.02406563237309456,
-0.003920355811715126,
-0.00024977046996355057,
-0.015871908515691757,
-0.007210445124655962,
0.02256259135901928,
0.04637252166867256,
-0.026979142799973488,
0.0026729656383395195,
-0.0037218062207102776,
0.021391527727246284,
0.03616025671362877,
-0.059878673404455185,
-0.047552019357681274,
-0.032251689583063126,
0.027455726638436317,
0.021724272519350052,
0.044459499418735504,
-0.04066212475299835,
-0.0382506400346756,
-0.01921095699071884,
-0.007116359658539295,
-0.003931862767785788,
-0.05555450916290283,
0.027979645878076553,
0.010359158739447594,
-0.022230444476008415,
0.015557434409856796,
-0.06965690106153488,
0.011171669699251652,
0.013557374477386475,
0.03306576982140541,
-0.024693556129932404,
-0.06526406854391098,
-0.06056146323680878,
-0.021903958171606064,
0.04179130867123604,
-0.05148463696241379,
-0.01544059719890356,
-0.026092587038874626,
0.04441998898983002,
-0.05472599342465401,
-0.02065669558942318,
-0.009300739504396915,
-0.026750124990940094,
0.00881492905318737,
-0.04480881989002228,
-0.02612045593559742,
0.05592253431677818,
-0.0025451157707720995,
-0.03602521866559982,
0.0058228266425430775,
-0.014872491359710693,
0.02493155188858509,
-0.003111670957878232,
-0.04284391179680824,
-0.023247621953487396,
-0.07127048820257187,
0.01340985856950283,
-0.01485730055719614,
0.025643864646553993,
-0.004538900218904018,
0.06824465841054916,
-0.024992376565933228,
-0.008633759804069996,
-0.022350996732711792,
-0.021903077140450478,
-0.02379167638719082,
-0.04278045892715454,
-0.00704372301697731,
0.003076946595683694,
0.00753968907520175,
0.06572499126195908,
-0.0019461754709482193,
-0.027239644899964333,
0.0734885111451149,
0.05972743779420853,
0.0519087053835392,
0.03814792260527611,
0.04943232238292694,
0.0180777870118618,
-0.052851125597953796,
0.02709835022687912,
0.02355225756764412,
-0.013329720124602318,
-0.0008913961937651038,
0.055668555200099945,
0.0176557507365942,
0.027546698227524757,
-0.011091253720223904,
-0.020718703046441078,
0.005772502161562443,
-0.014795388095080853,
0.026933450251817703,
0.015513322316110134,
-0.03693126514554024,
0.04489021375775337,
-0.025648608803749084,
-0.020840240642428398,
-0.07577317208051682,
-0.006299658678472042,
-0.03162970393896103,
-0.016279764473438263,
0.029084445908665657,
0.011020129546523094,
0.006875303108245134,
-0.06076725944876671,
0.027604633942246437,
0.04365093633532524,
-0.0001750806113705039,
0.026520485058426857,
-0.029248995706439018,
-0.0041253999806940556,
-0.010747640393674374,
-0.012535450980067253,
0.013594934716820717,
-0.009610424749553204,
0.05105721578001976,
0.0049480716697871685,
-0.01276357937604189,
0.018879873678088188,
0.016874732449650764,
-0.027580782771110535,
-0.019040614366531372,
-0.032335348427295685,
-0.010388443246483803,
0.020502757281064987,
0.0950499027967453,
0.010410035960376263,
0.06953348964452744,
-0.021801982074975967,
-0.06881915032863617,
0.04718342795968056,
0.020360011607408524,
0.0157620832324028,
-0.0038534451741725206,
-0.028666235506534576,
-0.019321784377098083,
0.04160478338599205,
0.030656464397907257,
0.005477923899888992,
-0.04259591922163963,
-0.0014637219719588757,
-0.0049230968579649925,
0.015996037051081657,
0.015811698511242867,
0.006292520556598902,
-0.016287876293063164,
0.00794918555766344,
0.037053052335977554,
-0.015010757371783257,
-0.002336406847462058,
0.016823168843984604,
-0.0021415064111351967,
-0.039338212460279465,
-0.04398937523365021,
-0.015963345766067505,
-0.013947698287665844,
-0.019112398847937584,
-0.03941323235630989,
-0.005106058437377214,
-0.055433548986911774,
0.007650203071534634,
0.002878419356420636,
-0.038403671234846115,
0.007231753785163164,
0.06981772184371948,
-0.027007224038243294,
0.05497924983501434,
-0.015664150938391685,
0.019776612520217896,
0.021724745631217957,
-0.03884315863251686,
0.015817146748304367,
-0.010646577924489975,
-0.008087944239377975,
0.03118920512497425,
0.02974448911845684,
-0.03345738723874092,
0.04357026517391205,
-0.03765000030398369,
-0.059837281703948975,
0.08237326890230179,
-0.027567006647586823,
0.012752726674079895,
0.05080670490860939,
0.020517699420452118,
-0.08300017565488815,
0.04715204983949661,
-0.06404419988393784,
0.04173998534679413,
0.017956307157874107,
0.009847304783761501,
0.02508542872965336,
0.06898532807826996,
-0.013746311888098717,
-0.026154370978474617,
0.006686184089630842,
-0.003101392649114132,
-0.006490007508546114,
0.011184663511812687,
0.03151280805468559,
-0.06259681284427643,
0.007771946489810944,
0.061403170228004456,
0.01624118909239769,
0.017204364761710167,
-0.017039500176906586,
-0.007290264125913382,
-0.020873358473181725,
0.008171831257641315,
-0.001861788216046989,
0.07966171950101852,
0.024740206077694893,
-0.0008801622898317873,
0.023196754977107048,
-0.0030612563714385033,
-0.0743102952837944,
-0.0014481662074103951,
0.0531131736934185,
-0.021097332239151,
0.03787006810307503,
0.009349287487566471,
0.038139015436172485,
0.025028685107827187,
-0.08630203455686569,
0.0300726480782032,
0.0005546336178667843,
0.02256094105541706,
-0.015291327610611916,
-0.0033781416714191437,
-0.0026466562412679195,
-0.008398841135203838,
-0.050397731363773346,
0.013478082604706287,
-0.07721184939146042,
0.0534168966114521,
-0.016336629167199135,
-0.06016349419951439,
-0.025140270590782166,
0.02920396625995636,
-0.0022038989700376987,
-0.05766932666301727,
-0.030250295996665955,
-0.051394782960414886,
0.007950592786073685,
0.02290777489542961,
-0.012786327861249447,
0.016254035755991936,
-0.04133618250489235,
-0.01696469821035862,
0.0035753967240452766,
-0.04917740449309349,
-0.008731568232178688,
0.07829774171113968,
-0.04014355689287186,
0.004235820844769478,
0.023857785388827324,
0.04244163632392883,
-0.00993876438587904,
-0.0189275573939085,
0.027003196999430656,
0.028941869735717773,
0.023344147950410843,
-0.011180740781128407,
0.012174849398434162,
-0.0036744847893714905,
-0.010693189688026905,
0.018949352204799652,
0.026756346225738525,
0.0356571190059185,
-0.007590566296130419,
0.04059562087059021,
-0.017379719763994217,
-0.018134653568267822,
0.012174948118627071,
0.0028165460098534822,
0.05631326511502266,
0.036987170577049255,
0.008491124957799911,
-0.057567961513996124,
0.004451495595276356,
-0.0508350133895874,
-0.05829551815986633,
-0.0171895083039999,
0.02536923997104168,
-0.028798017650842667,
-0.07497477531433105,
0.02017289772629738,
-0.06671358644962311,
0.002528334269300103,
-0.007850844413042068,
-0.00843172799795866,
-0.011037805117666721,
-0.00143659848254174,
-0.050623245537281036,
0.041909705847501755,
-0.035117555409669876,
-0.03779272362589836,
0.044938065111637115,
-0.019242027774453163,
-0.002219659276306629,
-0.02336794137954712,
0.06718968600034714,
-0.06157642602920532,
0.0733526349067688,
0.013712681829929352,
-0.035740774124860764,
-0.013158522546291351,
-0.019513733685016632,
0.011016125790774822,
-0.006353401113301516,
-0.006964906118810177,
0.02005881257355213,
0.050781864672899246,
-0.0592588447034359,
-0.03737860918045044,
0.0117323137819767,
-0.007909545674920082,
-0.04317677021026611,
0.062415797263383865,
-0.002811113838106394,
0.0343647301197052,
0.007121372502297163,
-0.026257112622261047,
-0.04492361843585968,
0.001499019912444055,
-0.02374909445643425,
-0.015104029327630997,
0.01996695250272751,
-0.004781200550496578,
-0.03700742498040199,
-0.008900659158825874,
0.021840237081050873
] |
<p>I just saw this "<a href="http://www.youtube.com/watch?v=7ctaA2mERzI&feature=player_embedded" rel="nofollow">trick</a>" where a cup of water is turned over onto a table without spilling (using a piece of cardboard. After removing the cardboard from underneath the cup, the person then removes the cup in a particular way (lifts straight up and twists) and lo and behold, the water stays in it's position as if the cup were still there!? (watch the video to fully understand) Is this really possible? If so, and the real question I'm looking to have answered is, how? </p>
<p>After <a href="http://www.b3ta.com/links/592518" rel="nofollow">further research</a> it appears that deionized water is needed as well.</p> | g7830 | [
-0.014925440773367882,
0.018712757155299187,
0.0066030011512339115,
-0.007591267116367817,
-0.0032854233868420124,
-0.006914506666362286,
0.0057142870500683784,
0.04177297279238701,
-0.045302655547857285,
-0.030862903222441673,
-0.01995239593088627,
-0.03653009980916977,
0.00330787873826921,
-0.02530827932059765,
0.014632448554039001,
0.04057686775922775,
0.021185990422964096,
-0.054008763283491135,
-0.011701076291501522,
0.05941702798008919,
0.02696871943771839,
0.016666948795318604,
0.04895099997520447,
-0.05355270951986313,
-0.06576672941446304,
-0.06480172276496887,
-0.02935587614774704,
-0.00942009687423706,
-0.007958449423313141,
0.024740060791373253,
-0.08952175825834274,
0.003359465394169092,
0.021941307932138443,
-0.036045052111148834,
-0.04123023897409439,
0.000046631841541966423,
0.06146060302853584,
-0.043640512973070145,
0.03702296316623688,
-0.0035710346419364214,
-0.0679137334227562,
0.0676354318857193,
-0.0454423613846302,
-0.003326904959976673,
0.0019665563013404608,
0.024888264015316963,
0.0081424405798316,
0.0151004483923316,
-0.061408575624227524,
-0.029313543811440468,
0.029604585841298103,
0.015728434547781944,
0.021755242720246315,
0.04983341321349144,
-0.08965560793876648,
0.009376239031553268,
0.043034832924604416,
0.006770070642232895,
0.07882893085479736,
-0.042382579296827316,
-0.08757738023996353,
0.002967365086078644,
-0.003978155553340912,
0.02828780747950077,
-0.04250740632414818,
0.023003242909908295,
-0.0623449869453907,
0.0047071631997823715,
-0.007850085385143757,
-0.02709444984793663,
0.00021686825493816286,
-0.025530073791742325,
-0.007741428911685944,
0.00013491872232407331,
-0.04855284467339516,
0.03164169564843178,
-0.010706309229135513,
-0.00927741453051567,
0.05253623053431511,
-0.0215558223426342,
-0.04344858601689339,
0.04066915810108185,
-0.0009074801346287131,
0.003841476049274206,
0.02921622060239315,
0.0238706823438406,
0.030682148411870003,
-0.02639603242278099,
-0.0033743393141776323,
0.03544721007347107,
-0.01470938976854086,
-0.033905237913131714,
0.036115862429142,
0.09893341362476349,
0.007822521962225437,
-0.0026273727416992188,
0.016567612066864967,
0.0065136924386024475,
-0.03522835299372673,
0.005125415977090597,
-0.02875848300755024,
-0.022979680448770523,
0.0069262501783668995,
-0.003953104838728905,
0.016770806163549423,
0.029360154643654823,
0.038262028247117996,
0.048416078090667725,
-0.011885766871273518,
-0.02955343760550022,
-0.004459739197045565,
-0.03149750083684921,
-0.025750888511538506,
0.0421241857111454,
0.04295151308178902,
-0.04727029427886009,
-0.04503903165459633,
0.07121093571186066,
0.005344081670045853,
-0.05449691414833069,
0.02221611700952053,
0.05917070060968399,
0.008147134445607662,
0.08199553936719894,
0.02850700542330742,
-0.020053405314683914,
-0.00499068945646286,
0.0034864237532019615,
0.037969525903463364,
0.017164045944809914,
-0.025907324627041817,
0.027092963457107544,
0.02207767590880394,
0.02546626329421997,
0.04247434437274933,
0.054916657507419586,
-0.014241683296859264,
0.030055364593863487,
0.011323116719722748,
-0.051770422607660294,
0.03273676335811615,
0.01129078958183527,
-0.004366396460682154,
0.05943166837096214,
-0.01903885044157505,
-0.016019979491829872,
0.0013137499336153269,
0.059694744646549225,
0.025397874414920807,
-0.03463435545563698,
-0.010053004138171673,
0.008810188621282578,
0.031050782650709152,
-0.011212836019694805,
0.030691271647810936,
0.03329533338546753,
0.022289827466011047,
-0.008062206208705902,
0.0249584149569273,
0.0047368016093969345,
0.04273023456335068,
-0.006267311982810497,
-0.03588410094380379,
0.03294168412685394,
-0.032693907618522644,
-0.009458312764763832,
-0.01753435842692852,
-0.05141455680131912,
-0.012711436487734318,
-0.05123521015048027,
-0.05350795388221741,
-0.03349403291940689,
-0.04559221491217613,
0.030547600239515305,
0.0005262232152745128,
0.013795365579426289,
0.011321594007313251,
0.019102418795228004,
0.024844326078891754,
-0.0038058750797063112,
-0.0028178528882563114,
0.01659742183983326,
0.006588493939489126,
0.008530215360224247,
-0.003295110771432519,
-0.02275828644633293,
0.012332064099609852,
0.038677066564559937,
0.028536811470985413,
-0.035721179097890854,
0.004941500723361969,
-0.01609058305621147,
0.009502842091023922,
0.08084702491760254,
0.03794728219509125,
-0.030342116951942444,
0.034539323300123215,
0.028954917564988136,
0.017537670210003853,
0.004995628260076046,
0.023083046078681946,
-0.09474734216928482,
0.009303092025220394,
-0.022096378728747368,
-0.020363977178931236,
0.004041042644530535,
0.02005252055823803,
-0.04225631058216095,
-0.03139406442642212,
0.015777740627527237,
0.0357472226023674,
0.017424849793314934,
-0.02939062938094139,
-0.04919687658548355,
-0.035482779145240784,
0.03249898552894592,
-0.03125602751970291,
-0.027226820588111877,
-0.03218119964003563,
0.0019122944213449955,
-0.07631804794073105,
0.029649481177330017,
-0.014773835428059101,
0.04173264279961586,
-0.027580315247178078,
-0.036827053874731064,
-0.022720815613865852,
0.030623191967606544,
-0.04840158298611641,
0.02902207523584366,
-0.017033876851201057,
0.011511281132698059,
-0.023968862369656563,
-0.01929525099694729,
0.06612221896648407,
0.012704805471003056,
-0.06240424886345863,
0.11226823925971985,
-0.024868149310350418,
0.02227485179901123,
-0.04090660437941551,
0.003540883306413889,
-0.08563533425331116,
-0.036111705005168915,
0.033422015607357025,
-0.000577480299398303,
-0.000017442960597691126,
-0.0526316799223423,
0.044789429754018784,
0.0012573752319440246,
0.03563172370195389,
-0.037922363728284836,
0.014513373374938965,
-0.03345348685979843,
0.0038868074771016836,
0.007148043718189001,
-0.03403562679886818,
0.05768832936882973,
-0.02556627430021763,
0.02231428772211075,
-0.004742342513054609,
-0.03835330158472061,
0.04638425260782242,
0.0025177402421832085,
0.012181976810097694,
-0.014730418100953102,
-0.046791642904281616,
0.005722536705434322,
0.0034089284017682076,
0.05056067928671837,
-0.005341761279851198,
0.0019590845331549644,
0.030993856489658356,
0.05540080368518829,
-0.030175749212503433,
-0.024830419570207596,
0.0026013890746980906,
-0.011624735780060291,
0.0011382180964574218,
-0.011534427292644978,
0.013599472120404243,
-0.011140565387904644,
-0.07930245995521545,
-0.01882428675889969,
-0.003771255724132061,
0.030846593901515007,
-0.028175003826618195,
-0.04132894054055214,
0.0006353312055580318,
0.026339149102568626,
0.04472104087471962,
-0.03500073775649071,
0.005971694365143776,
0.04318081587553024,
0.007183834444731474,
0.05096378177404404,
-0.016378384083509445,
-0.032498739659786224,
-0.10356561094522476,
-0.0006350210169330239,
-0.026637161150574684,
-0.009499824605882168,
0.013617855496704578,
0.01650024764239788,
0.030537333339452744,
0.04828985780477524,
0.0235365629196167,
-0.0025460876058787107,
0.0029853875748813152,
-0.03377242386341095,
0.040280669927597046,
0.07594335079193115,
-0.10772618651390076,
0.009388301521539688,
-0.009482304565608501,
-0.002295729238539934,
-0.06062597036361694,
0.0013098613126203418,
-0.005786208901554346,
-0.0001385402720188722,
-0.030756277963519096,
0.030762135982513428,
0.009915283881127834,
0.023923305794596672,
0.05004696920514107,
0.0163734033703804,
-0.015844954177737236,
0.012473450042307377,
-0.00411757780238986,
-0.06886458396911621,
0.06984339654445648,
0.021709822118282318,
-0.053407248109579086,
-0.08187958598136902,
-0.021190525963902473,
0.0054636686109006405,
0.0015771733596920967,
0.029420897364616394,
0.07200937718153,
0.03133406862616539,
0.042375754565000534,
-0.027496734634041786,
-0.012479869648814201,
-0.006849345751106739,
-0.008133940398693085,
0.04219873249530792,
0.023146195337176323,
-0.003794496413320303,
-0.03238261863589287,
0.03313527628779411,
0.043018944561481476,
-0.022140471264719963,
-0.048611078411340714,
-0.04086132347583771,
0.015044240280985832,
0.03931877389550209,
-0.006590110715478659,
-0.008044768124818802,
-0.02613736130297184,
-0.040730070322752,
-0.007992471568286419,
-0.03713133931159973,
0.032247621566057205,
-0.005780499428510666,
-0.012153564020991325,
-0.011626910418272018,
0.0158121045678854,
0.007422023452818394,
-0.07983105629682541,
0.05654161795973778,
-0.016471747308969498,
-0.10818759351968765,
-0.051352664828300476,
0.014870783314108849,
-0.030123254284262657,
0.031193379312753677,
0.05154181644320488,
0.045228395611047745,
0.013609695248305798,
0.01970083825290203,
-0.03222116827964783,
0.008829372934997082,
-0.013679957017302513,
-0.023313676938414574,
-0.004131165333092213,
-0.00398497236892581,
0.007094661705195904,
-0.003534117713570595,
0.11086193472146988,
0.003435839433223009,
-0.011371394619345665,
0.06887605786323547,
0.052115920931100845,
0.02888246811926365,
-0.06715983152389526,
0.07796458154916763,
-0.032164473086595535,
0.026271698996424675,
-0.08400092273950577,
-0.01302388310432434,
0.019714675843715668,
0.020261194556951523,
-0.030690651386976242,
-0.012523749843239784,
0.022998804226517677,
-0.009420868009328842,
0.02484162338078022,
-0.026252344250679016,
-0.04564029723405838,
-0.05476684495806694,
0.03713231161236763,
-0.020289655774831772,
-0.05850695073604584,
-0.007179041858762503,
0.012899408116936684,
-0.0006630613934248686,
0.0031418597791343927,
0.03596370294690132,
-0.05219308286905289,
0.02004244364798069,
0.008034627884626389,
-0.01904379017651081,
0.0019501268398016691,
0.05712669715285301,
-0.028795655816793442,
0.004662927705794573,
0.025293687358498573,
-0.0005393288447521627,
0.009551732800900936,
-0.029096638783812523,
-0.008450348861515522,
0.010350889526307583,
0.030564861372113228,
-0.016472503542900085,
-0.006065702065825462,
0.0002423763507977128,
0.015590808354318142,
0.037527330219745636,
-0.012319023720920086,
-0.004111445974558592,
0.020225191488862038,
-0.005749865900725126,
0.018299268558621407,
0.013018785044550896,
0.005665794014930725,
0.010535786859691143,
-0.016976967453956604,
-0.02195630967617035,
0.04884137213230133,
-0.02896505780518055,
-0.030358348041772842,
0.048539645969867706,
-0.009059228003025055,
0.0028996129985898733,
0.005875284317880869,
0.003043432952836156,
-0.0022458534222096205,
-0.010332207195460796,
-0.054474059492349625,
-0.006584877148270607,
-0.027748731896281242,
-0.03741628676652908,
0.025983572006225586,
0.017969580367207527,
0.010995394550263882,
-0.017363443970680237,
-0.0074950228445231915,
-0.048646219074726105,
0.017188917845487595,
0.053428273648023605,
0.012982599437236786,
0.0531446747481823,
0.0026038452051579952,
0.11211451143026352,
0.06252703070640564,
-0.048140447586774826,
0.0020113089121878147,
0.03616645187139511,
0.04554782435297966,
0.0034944794606417418,
0.009904992766678333,
0.03947661444544792,
0.0005667649675160646,
0.03134556859731674,
0.015682708472013474,
-0.002876725047826767,
-0.013687536120414734,
0.052148446440696716,
-0.0032494429033249617,
-0.030958520248532295,
-0.02815568819642067,
-0.026760654523968697,
0.018727267161011696,
-0.049173083156347275,
-0.005986797157675028,
-0.03202718496322632,
-0.0010225088335573673,
-0.03167467564344406,
0.030943289399147034,
0.003400841960683465,
-0.03979838266968727,
-0.008467591367661953,
0.05748285725712776,
-0.051007892936468124,
0.019437434151768684,
-0.04794563725590706,
-0.0032097892835736275,
0.025862079113721848,
-0.034546371549367905,
0.03701997175812721,
0.009684199467301369,
-0.03649859130382538,
-0.018464336171746254,
0.04258427023887634,
0.028084736317396164,
-0.04286891222000122,
0.0021150459069758654,
-0.009628307074308395,
-0.0017054626950994134,
-0.0016593083273619413,
-0.012035981751978397,
-0.007967925630509853,
-0.02338404767215252,
0.0335996150970459,
-0.03912654519081116,
-0.013355690985918045,
-0.030365929007530212,
-0.04776691645383835,
0.05305944010615349,
-0.0035229255445301533,
-0.04279524087905884,
-0.036359015852212906,
0.0007718403358012438,
0.065740667283535,
-0.03878885507583618,
0.011679669842123985,
0.038306768983602524,
0.015228459611535072,
0.0638590082526207,
0.04870323836803436,
0.041569486260414124,
-0.0017591918585821986,
0.01644976995885372,
0.13798044621944427,
-0.03244511038064957,
-0.013091604225337505,
0.0058269621804356575,
0.020786233246326447,
0.03376459702849388,
-0.01677677594125271,
-0.009679734706878662,
0.0791977122426033,
-0.006634111050516367,
0.044526539742946625,
0.013716932386159897,
-0.029500912874937057,
-0.006960200611501932,
-0.06804075092077255,
0.008465486578643322,
-0.06869456171989441,
0.013067827560007572,
0.0016137782949954271,
0.021583275869488716,
0.017818449065089226,
-0.0009742795373313129,
-0.012368747964501381,
-0.019094672054052353,
0.05406026542186737,
0.046973634511232376,
0.003938931971788406,
-0.018611708655953407,
-0.044633425772190094,
0.015869541093707085,
-0.008192162029445171,
-0.02948443591594696,
0.004192701540887356,
-0.0071493941359221935,
-0.0020514964126050472,
0.03419853374361992,
0.010772506706416607,
0.02158954367041588,
0.03434940427541733,
0.04517550393939018,
-0.03592410683631897,
-0.00953283067792654,
0.009505846537649632,
-0.05979777127504349,
0.0228432510048151,
0.03215841203927994,
-0.036502156406641006,
-0.04756181687116623,
-0.02306436002254486,
-0.05422721058130264,
0.022982461377978325,
0.02036689594388008,
-0.0008458335069008172,
-0.00666429428383708,
0.023300793021917343,
-0.01963420957326889,
0.10245129466056824,
-0.07470237463712692,
0.021418802440166473,
0.009355504997074604,
0.020970163866877556,
-0.04429107904434204,
0.017711840569972992,
0.03176746517419815,
0.055511780083179474,
-0.00760352099314332,
-0.07739497721195221,
-0.06041429936885834,
0.02006034553050995,
0.033657368272542953,
-0.07129958271980286,
-0.07173039764165878,
-0.10114345699548721,
-0.012566061690449715,
-0.0034443482290953398,
0.06545887142419815,
-0.05098019912838936,
-0.037935905158519745,
-0.010569574311375618,
-0.01354497391730547,
-0.057586487382650375,
-0.023656679317355156,
0.0002444068668410182,
-0.029339004307985306,
0.00424881000071764,
0.08630181103944778,
0.09553263336420059,
-0.011064632795751095,
-0.04289383068680763,
-0.01067360769957304,
-0.027158435434103012,
-0.01212269626557827,
0.054611675441265106,
-0.0467415377497673,
0.059541817754507065,
0.04213971644639969,
0.023952292278409004,
-0.02961825765669346,
0.040326401591300964,
0.07500509917736053,
0.024522893130779266,
-0.006205112207680941,
0.05913621932268143,
-0.05580460652709007,
-0.008547780103981495,
-0.06847937405109406,
-0.04822525009512901,
0.007541312836110592,
-0.03579826280474663,
-0.04178901016712189,
0.006321595050394535,
-0.02211056463420391,
0.0115591399371624,
-0.048608794808387756,
0.028179505839943886,
-0.09103188663721085,
-0.06913858652114868,
0.04502234235405922,
-0.011352328583598137,
0.01199664082378149,
-0.004389362409710884,
-0.019957659766077995,
-0.003699306631460786,
-0.01736275665462017,
-0.013638664036989212,
-0.00930855143815279,
-0.004469417501240969,
0.01774517446756363,
0.017410695552825928,
-0.0486498661339283,
-0.01762801967561245,
0.08507148921489716,
-0.042364031076431274,
0.10314033925533295,
0.028820645064115524,
0.02423296682536602,
0.029247943311929703,
-0.011019487865269184,
0.007213339675217867,
0.05533236637711525,
-0.029332811012864113,
-0.050858836621046066,
0.023171747103333473,
0.012970520183444023,
0.026480646803975105,
0.009369649924337864,
-0.0008807399426586926,
0.040091097354888916,
0.024736393243074417,
0.002010073745623231,
0.07687477022409439,
0.017317449674010277,
0.0003683941322378814,
0.03916366770863533,
-0.012845157645642757,
-0.0003647729172371328,
-0.036655087023973465,
-0.009303677827119827,
-0.008642618544399738,
-0.013189204968512058,
-0.02091478928923607,
0.011447640135884285,
0.0316736102104187,
-0.05658157169818878,
0.011615296825766563,
0.02183624915778637,
-0.0238777007907629,
-0.016632329672574997,
-0.00627916632220149,
0.00669800816103816,
-0.04529484733939171,
0.08546560257673264,
-0.013786491006612778,
-0.08739382028579712,
0.0010634332429617643,
-0.04165324568748474,
0.027037009596824646,
-0.06910271942615509,
-0.004029515665024519,
-0.036294933408498764,
-0.02585495449602604,
-0.030045295134186745,
0.0358973890542984,
-0.03037719801068306,
-0.0022803042083978653,
-0.05500674247741699,
0.004398730583488941,
-0.014377548359334469,
0.014612150378525257,
-0.0031688862945884466,
-0.025931773707270622,
0.023093227297067642,
-0.02705770917236805,
0.01812152937054634,
-0.0071618943475186825,
-0.0654887780547142,
-0.03044825978577137,
0.032702840864658356,
-0.020118029788136482,
0.000584375869948417,
-0.029671495780348778,
0.0652092769742012,
-0.0292558241635561,
-0.020101644098758698,
0.02059928886592388,
-0.028006793931126595,
-0.031276389956474304,
0.01631573773920536,
0.04955509305000305,
0.003775028046220541,
0.024295249953866005,
0.03371797874569893,
0.016754793003201485,
-0.06562994420528412,
0.016078921034932137,
0.058281730860471725,
-0.018424488604068756,
-0.0027951551601290703,
0.008369878865778446,
0.008028926327824593,
0.014588778838515282,
-0.039903298020362854,
0.0021488212514668703,
0.02117837592959404,
0.024735156446695328
] |
<p>What is the current <strong>record</strong> number of entagled qubits and how has this number been increased? </p>
<p>The latest result on stack exchange, which is 3 years old, reports 14 via
this post: <a href="http://physics.stackexchange.com/q/4226/">How many stabilised qubits have been achieved in Quantum Computing?</a></p>
<p>in accord with this paper: <a href="http://arxiv.org/abs/1009.6126" rel="nofollow">http://arxiv.org/abs/1009.6126</a>?</p>
<p>For the purposes of this post, I'd prefer to leave the D-Wave computers out of the answers. </p> | g7831 | [
-0.007157003507018089,
0.05175573378801346,
-0.005252466071397066,
-0.07367958873510361,
0.049315035343170166,
-0.010132160037755966,
-0.00044783667544834316,
0.02423555590212345,
-0.026459794491529465,
0.008904064074158669,
-0.05069873109459877,
0.0191347636282444,
-0.01600285992026329,
0.019419454038143158,
-0.012301046401262283,
0.016127733513712883,
0.06831896305084229,
0.007700774818658829,
0.057360436767339706,
0.02331264689564705,
0.0008387615089304745,
-0.04003629833459854,
-0.030934028327465057,
-0.029190870001912117,
0.0062135569751262665,
0.0029220073483884335,
-0.009335498325526714,
-0.014896711334586143,
-0.01256533619016409,
0.02942059189081192,
0.06299496442079544,
-0.052132297307252884,
0.04967536777257919,
0.04727907106280327,
-0.0064208535477519035,
-0.05022497475147247,
-0.01607600785791874,
-0.0272903461009264,
0.005912455730140209,
-0.02053120546042919,
0.028830477967858315,
-0.009485134854912758,
-0.0549769289791584,
0.02195696346461773,
-0.057954348623752594,
-0.011333249509334564,
0.03264104574918747,
-0.012236054055392742,
0.005333635490387678,
-0.06170910224318504,
-0.031882233917713165,
0.0003907027712557465,
0.06459438800811768,
0.040522489696741104,
0.0695669874548912,
0.05842236801981926,
-0.053496479988098145,
-0.013583717867732048,
-0.003663415787741542,
0.017490440979599953,
0.006083348765969276,
-0.04309707507491112,
0.022417999804019928,
0.016816554591059685,
0.04184092581272125,
0.028545502573251724,
-0.0405300073325634,
0.031884998083114624,
-0.021967509761452675,
-0.02105981856584549,
-0.01682894676923752,
-0.05463268235325813,
0.01484263502061367,
0.059214960783720016,
0.07062838971614838,
-0.004768992308527231,
0.025112586095929146,
-0.019761301577091217,
-0.01423450093716383,
0.00361933303065598,
-0.01838517375290394,
-0.04430539160966873,
-0.044686783105134964,
-0.04735296219587326,
0.021220726892352104,
-0.026054859161376953,
-0.016209278255701065,
0.005665453616529703,
-0.00900287926197052,
0.06092855706810951,
0.03980891406536102,
0.026560237631201744,
0.02529105544090271,
0.018259599804878235,
-0.03158095106482506,
0.02271050587296486,
0.03570603206753731,
0.014557414688169956,
-0.048112817108631134,
0.03564129397273064,
0.006308858282864094,
-0.051844313740730286,
0.056681077927351,
-0.018904563039541245,
-0.010652432218194008,
0.03729180991649628,
-0.049409836530685425,
-0.06986493617296219,
-0.016788918524980545,
0.039582811295986176,
0.0009023127495311201,
0.03502711281180382,
-0.02211337350308895,
0.048355646431446075,
-0.030858613550662994,
0.056918397545814514,
0.002841984387487173,
-0.020335176959633827,
-0.046501558274030685,
0.045786503702402115,
0.022361261770129204,
0.000890839088242501,
0.05141007900238037,
-0.0010135815246030688,
-0.0007427747477777302,
-0.0007351028616540134,
-0.01792595349252224,
-0.006313761230558157,
0.03225075080990791,
0.04250309243798256,
-0.01403557788580656,
-0.010524432174861431,
0.012151570990681648,
0.009825305081903934,
-0.01651303842663765,
0.03838884085416794,
0.021161723881959915,
0.024376533925533295,
-0.031461432576179504,
-0.009825631976127625,
0.027256136760115623,
-0.05794961005449295,
0.056697241961956024,
0.00511021027341485,
0.0536370724439621,
-0.062290411442518234,
0.04243379458785057,
0.041795287281274796,
-0.013867942616343498,
0.022707568481564522,
0.05789784714579582,
0.009195918217301369,
-0.015720704570412636,
-0.07864073663949966,
-0.0211837999522686,
0.0073145185597240925,
0.0018063461175188422,
-0.006725215818732977,
-0.039606574922800064,
0.07098326832056046,
0.05009683221578598,
-0.00514445174485445,
-0.081285260617733,
-0.026933372020721436,
-0.008398450911045074,
0.022744372487068176,
0.02846614271402359,
-0.045863181352615356,
0.014308826997876167,
0.032963793724775314,
-0.04979855939745903,
-0.006532845087349415,
-0.018248403444886208,
0.005928295664489269,
-0.026033854112029076,
0.012175451032817364,
0.01805580034852028,
-0.019135259091854095,
0.06961408257484436,
-0.006983401253819466,
0.052001792937517166,
-0.004381950479000807,
-0.0018667613621801138,
0.034753214567899704,
0.0018516306299716234,
-0.02196023426949978,
-0.0074241007678210735,
-0.04558466374874115,
0.0041327388025820255,
-0.02985084056854248,
-0.07301011681556702,
-0.028360746800899506,
-0.021295923739671707,
-0.018727988004684448,
-0.017651580274105072,
-0.0007619370007887483,
0.07062758505344391,
0.0012905736221000552,
0.01920727640390396,
-0.007495060097426176,
0.02056933008134365,
0.028187759220600128,
0.010011394508183002,
-0.0418599434196949,
0.04938245937228203,
-0.0008799833594821393,
0.040674544870853424,
-0.0010577685898169875,
0.014170870184898376,
-0.007778930012136698,
-0.03143054619431496,
0.03872363269329071,
-0.004472391214221716,
0.03298048675060272,
0.021471040323376656,
-0.02223397232592106,
0.026215702295303345,
-0.005366217810660601,
0.033209335058927536,
0.014215556904673576,
0.008156759664416313,
0.026883283630013466,
-0.013743046671152115,
0.05066334083676338,
0.0182445477694273,
-0.023723889142274857,
-0.0277166198939085,
0.0026036871131509542,
-0.03036569245159626,
0.017252886667847633,
-0.06692676991224289,
0.04721510037779808,
-0.05849882587790489,
0.00009281731036026031,
0.013945992104709148,
0.026233987882733345,
-0.03050280548632145,
0.019493184983730316,
0.04225347191095352,
0.045748382806777954,
0.06519290804862976,
0.01454926934093237,
-0.03405213728547096,
-0.015395217575132847,
-0.026915647089481354,
-0.005655049812048674,
-0.021909072995185852,
-0.01832651160657406,
0.000258404208580032,
0.018163088709115982,
-0.003199218772351742,
-0.09652996808290482,
-0.016449252143502235,
-0.012639390304684639,
-0.020000066608190536,
0.027511421591043472,
-0.03403099626302719,
0.0017370223067700863,
-0.01163366250693798,
-0.012682948261499405,
0.03138080984354019,
-0.007562596816569567,
0.030145015567541122,
-0.05611782148480415,
0.014934743754565716,
-0.03533400595188141,
0.036990854889154434,
-0.03270886093378067,
0.0011612940579652786,
-0.036473922431468964,
-0.0030657814349979162,
-0.0020946883596479893,
-0.026798123493790627,
-0.003563793608918786,
0.014791707508265972,
-0.030004465952515602,
-0.022419627755880356,
-0.01856539212167263,
-0.002782450057566166,
-0.03933245688676834,
0.009822383522987366,
-0.012485088780522346,
-0.07193061709403992,
0.010778190568089485,
-0.01974586769938469,
-0.02302166260778904,
-0.0002548743213992566,
-0.06792347133159637,
0.035614579916000366,
0.011867565102875233,
0.040860921144485474,
-0.030524736270308495,
0.045896925032138824,
-0.006142809521406889,
-0.03794238716363907,
0.004975087940692902,
-0.050937194377183914,
-0.04759495332837105,
0.04753416031599045,
-0.007924582809209824,
-0.02101951465010643,
-0.022013530135154724,
-0.020092632621526718,
0.016609761863946915,
0.028424186632037163,
-0.020376842468976974,
-0.018262146040797234,
0.03637315332889557,
-0.02170538529753685,
-0.0552402064204216,
0.010654457844793797,
0.03315996378660202,
0.022100109606981277,
-0.013393825851380825,
-0.05878302827477455,
-0.02011312171816826,
0.028189076110720634,
0.05433143302798271,
-0.004199780989438295,
-0.05815252661705017,
0.01581924967467785,
-0.044205669313669205,
0.024546043947339058,
-0.03909936919808388,
0.11997051537036896,
0.015799345448613167,
-0.03768955171108246,
0.020063351839780807,
-0.020864956080913544,
-0.02411133423447609,
-0.041031986474990845,
-0.029442239552736282,
0.062176723033189774,
-0.01429794356226921,
-0.0772022008895874,
-0.036214910447597504,
0.019895227625966072,
-0.09865013509988785,
0.06426121294498444,
0.01977195404469967,
0.024770524352788925,
-0.010421236045658588,
0.014457724057137966,
-0.04225084185600281,
0.046330250799655914,
0.05986449122428894,
-0.006729946006089449,
-0.007100239396095276,
-0.0051001268438994884,
0.00715835252776742,
-0.0017455792985856533,
0.031407300382852554,
0.0031244857236742973,
-0.02702997997403145,
0.04675352945923805,
-0.04585985094308853,
-0.08543713390827179,
0.0703335776925087,
0.014503232203423977,
-0.04750292748212814,
-0.01431366614997387,
0.05575956404209137,
0.07745557278394699,
-0.03790992498397827,
-0.03952930122613907,
-0.03021029196679592,
-0.03445667400956154,
0.027486179023981094,
0.02143712155520916,
-0.029956340789794922,
-0.08179023861885071,
-0.01675988733768463,
-0.004115243908017874,
-0.0412612184882164,
-0.026383930817246437,
-0.02135387994349003,
-0.03066442161798477,
-0.021460069343447685,
0.019213519990444183,
0.028117431327700615,
0.028392843902111053,
0.004748576786369085,
0.0319814570248127,
-0.05752963945269585,
-0.04539138451218605,
-0.0049430085346102715,
-0.030931830406188965,
-0.00542157469317317,
-0.07898522913455963,
-0.03242265433073044,
-0.010029572062194347,
0.0032588245812803507,
-0.0011420022929087281,
-0.056845393031835556,
-0.08857042342424393,
-0.03854687511920929,
-0.011333799920976162,
0.027319107204675674,
0.0039878417737782,
0.06530103087425232,
0.004974787123501301,
-0.0037049828097224236,
-0.015293018892407417,
0.004669775255024433,
0.014022868126630783,
0.008825876750051975,
-0.023782242089509964,
0.00780140794813633,
-0.01110740378499031,
-0.00867651216685772,
0.017914583906531334,
-0.0006224988028407097,
-0.050588708370923996,
-0.07931274175643921,
0.03057192452251911,
0.006347794085741043,
0.02475154958665371,
-0.020475899800658226,
0.01559134665876627,
-0.06490779668092728,
0.03394986316561699,
0.0550430491566658,
0.028259053826332092,
0.048642970621585846,
-0.01960671693086624,
0.019804488867521286,
-0.04574093222618103,
0.0015239297645166516,
0.02790273167192936,
-0.000905354623682797,
0.08055641502141953,
-0.020301559939980507,
0.039454732090234756,
0.034150708466768265,
-0.04119409620761871,
0.005737725645303726,
0.03970473259687424,
0.012759222649037838,
0.05167466402053833,
-0.009939305484294891,
0.10363268107175827,
-0.01906629092991352,
-0.0029137018136680126,
0.014559654518961906,
-0.018867127597332,
0.06443560123443604,
-0.012561646290123463,
0.003788421396166086,
-0.0015328720910474658,
-0.011025342158973217,
0.02175810933113098,
-0.00114799989387393,
-0.006602918729186058,
0.012958488427102566,
-0.001871587592177093,
0.019545001909136772,
-0.0086404113098979,
0.03832777962088585,
0.03289235010743141,
0.016065163537859917,
-0.09589164704084396,
0.011225319467484951,
-0.006523712072521448,
0.038646601140499115,
-0.006211267318576574,
-0.03867293894290924,
-0.03684205934405327,
0.010187600739300251,
-0.043742742389440536,
-0.026832256466150284,
0.020016983151435852,
-0.04286840558052063,
-0.019528962671756744,
-0.03172305226325989,
-0.025240276008844376,
-0.06813441216945648,
-0.00047414202708750963,
-0.032461315393447876,
-0.0030447253957390785,
-0.05011392757296562,
0.03899727389216423,
0.03835355490446091,
0.005736213643103838,
0.03221191093325615,
-0.011672795750200748,
0.016515932977199554,
0.05316123738884926,
-0.07980315387248993,
-0.05677179619669914,
-0.012157509103417397,
0.023574788123369217,
-0.0110416105017066,
0.03209550306200981,
-0.018850931897759438,
-0.005745990201830864,
-0.052069082856178284,
-0.029296936467289925,
-0.05638512596487999,
-0.004634707234799862,
0.0324275828897953,
-0.008596368134021759,
0.050229255110025406,
0.027867048978805542,
-0.007395029067993164,
-0.03566880524158478,
0.05768594518303871,
-0.007175956852734089,
-0.04564680904150009,
-0.042374078184366226,
-0.031207671388983727,
-0.04551529884338379,
0.004160749260336161,
-0.03859902173280716,
-0.042824987322092056,
-0.02506258524954319,
0.040998317301273346,
0.01004062220454216,
-0.006644392851740122,
0.006420318502932787,
-0.011257924139499664,
0.04371480643749237,
0.018210824579000473,
0.04836120456457138,
-0.011660833843052387,
-0.07538846880197525,
-0.046469785273075104,
-0.009422516450285912,
-0.026488857343792915,
0.0508296936750412,
-0.004277360159903765,
0.06398963183164597,
-0.0358704999089241,
-0.01943523809313774,
-0.0008106966270133853,
0.01664130575954914,
0.0007480978965759277,
0.009820759296417236,
0.028163159266114235,
0.007789424620568752,
0.026143750175833702,
-0.010821785777807236,
0.046252500265836716,
-0.015148483216762543,
0.11610178649425507,
0.012359867803752422,
-0.07823877036571503,
-0.019018080085515976,
-0.02659819833934307,
0.011945007368922234,
-0.0024841364938765764,
0.032536379992961884,
0.00228711124509573,
0.014275629073381424,
0.012577426619827747,
0.03406781703233719,
0.027601387351751328,
-0.025089332833886147,
-0.03357263281941414,
-0.007278003729879856,
0.002324915723875165,
-0.026349874213337898,
0.00542109739035368,
0.03546652942895889,
0.044127918779850006,
-0.058439817279577255,
0.0017261140746995807,
-0.04827004298567772,
-0.05931733921170235,
0.025474632158875465,
0.0502360500395298,
0.04527115821838379,
0.05868200957775116,
-0.0018212726572528481,
-0.014375915750861168,
0.05429874360561371,
-0.0075140660628676414,
-0.047592855989933014,
-0.02608894743025303,
-0.011870622634887695,
-0.04180002585053444,
-0.04536724090576172,
0.013143155723810196,
0.0196315236389637,
-0.04353048652410507,
-0.038734205067157745,
0.005551179405301809,
-0.004205434117466211,
0.10306572169065475,
-0.00013816685532219708,
0.01138152927160263,
-0.049817949533462524,
0.051014285534620285,
-0.047680292278528214,
-0.042119190096855164,
-0.005995410494506359,
-0.0205610990524292,
0.04975525662302971,
-0.0012813331559300423,
-0.0457245372235775,
-0.02238919772207737,
-0.03244706243276596,
-0.02513974905014038,
0.05791546776890755,
0.07149618119001389,
0.004143363330513239,
-0.005395652260631323,
0.009694574400782585,
0.015702882781624794,
-0.04868166893720627,
0.037380773574113846,
0.018691865727305412,
-0.06268666684627533,
0.03030385449528694,
0.03878409415483475,
-0.03141293302178383,
-0.1066242903470993,
0.07049228996038437,
-0.001007996266707778,
-0.0330427922308445,
0.07033807784318924,
-0.03690744563937187,
0.0015676068142056465,
-0.07146900147199631,
-0.008660070598125458,
0.028533780947327614,
0.03469404950737953,
0.023679817095398903,
-0.014126542955636978,
0.02137278951704502,
0.0067043425515294075,
0.06394072622060776,
0.011061903089284897,
0.026878660544753075,
-0.004571455996483564,
-0.01257591973990202,
-0.001954645151272416,
-0.06513023376464844,
-0.0020565057639032602,
0.003898239927366376,
-0.03238485008478165,
-0.004619784187525511,
-0.00007714331150054932,
0.051106128841638565,
-0.025040362030267715,
-0.03434661403298378,
0.007035049609839916,
0.05798039585351944,
0.04012028127908707,
-0.005408355034887791,
0.0057042185217142105,
0.03371414169669151,
-0.00182353425770998,
-0.09001509845256805,
0.041095931082963943,
-0.008098656311631203,
0.030811229720711708,
0.010326950810849667,
0.03798016160726547,
0.011345340870320797,
-0.04471372812986374,
0.006445462815463543,
-0.06816233694553375,
-0.0023851878941059113,
0.00734519399702549,
0.05306553468108177,
0.010783126577734947,
0.011589981615543365,
0.013541064225137234,
0.01053821761161089,
-0.054511625319719315,
0.0251311007887125,
-0.023813532665371895,
-0.035104136914014816,
-0.053447168320417404,
0.013524899259209633,
-0.013934703543782234,
0.030008288100361824,
0.016062380746006966,
-0.02744910679757595,
0.007472767494618893,
-0.019488312304019928,
-0.004827182274311781,
-0.01948709599673748,
0.016743576154112816,
0.03531379997730255,
0.06335534900426865,
-0.05789954215288162,
0.004798250738531351,
0.03251070901751518,
0.0003466386697255075,
0.05368795618414879,
0.010701439343392849,
-0.054682470858097076,
0.01100543700158596,
-0.03990921750664711,
0.019884897395968437,
-0.0053735640831291676,
-0.023205460980534554,
0.07569312304258347,
0.015358451753854752,
-0.0016737865516915917,
0.0840340256690979,
0.036862920969724655,
0.1094716265797615,
0.020815672352910042,
0.01969950832426548,
-0.025451557710766792,
-0.034573499113321304,
0.044435013085603714,
0.02189580909907818,
-0.033646419644355774,
-0.02907315269112587,
0.05243522673845291,
-0.01329464465379715,
0.07722053676843643,
0.005620469804853201,
-0.0013281643623486161,
0.0271712988615036,
0.03458976000547409,
0.04031240567564964,
0.04429001361131668,
0.017430122941732407,
-0.05250442028045654,
0.03151288256049156,
-0.02067914791405201,
-0.002068208297714591,
0.09015177935361862,
0.005902303382754326,
0.02190428599715233,
0.027277182787656784,
-0.019627125933766365,
-0.03253774717450142,
-0.06574500352144241,
0.034536268562078476,
-0.03088374249637127,
-0.004114997107535601,
0.06537487357854843,
0.04371225833892822,
-0.048966627568006516,
0.05765089765191078,
-0.016065211966633797,
0.02253420650959015,
-0.027983181178569794,
-0.03913210332393646,
-0.03236719220876694,
-0.048323918133974075,
-0.040847230702638626,
-0.009790516458451748,
0.015287012793123722,
-0.06964144855737686,
0.03369847312569618,
-0.023302551358938217,
-0.009516737423837185,
0.06540200859308243,
-0.000033902382710948586,
-0.028721993789076805,
0.06901489198207855,
-0.039311300963163376,
0.02777181938290596,
0.05302561819553375,
0.04589023441076279,
0.02082129754126072,
0.04399196803569794,
0.014599847607314587,
-0.009362205862998962,
0.011392604559659958,
-0.010422669351100922,
-0.02612454444169998
] |
<p>Okay, here is my understanding. Please correct me if anything here is incorrect. Suppose I have a cube with a side length of ten inches. It has a surface area of 600 square inches, and at an atmospheric pressure of 14.7 pounds per square inch, we can approximate 8800 pounds of air are applied on the cube by the atmosphere. The cube has a volume of 1000 cubic inches of air. But since there is air on the inside of the cube, and the pressure is equal, there pressure is cancelled out.</p>
<p>Now suppose we were to have a bunch of cubes with ten inch sides. We remove 1/2 of the air from the inside of one, and 1/4 of the air from another, and 1/10 from another. How can we calculate the actual pressure of the atmosphere on the cube?</p> | g7832 | [
0.060259051620960236,
-0.0064416006207466125,
0.015169200487434864,
0.015556293539702892,
-0.03698629513382912,
0.012895474210381508,
0.046461690217256546,
0.050095412880182266,
-0.0648341178894043,
0.05032835900783539,
-0.03726305812597275,
0.0022266004234552383,
-0.057535335421562195,
0.01294337585568428,
0.04146793857216835,
0.04857303574681282,
0.009647533297538757,
-0.06494196504354477,
0.036118973046541214,
0.034737955778837204,
0.010768077336251736,
-0.06540562957525253,
-0.0044380659237504005,
-0.06816799193620682,
-0.07465151697397232,
-0.060176316648721695,
0.054066576063632965,
0.01803465560078621,
-0.07006534934043884,
-0.02639029733836651,
-0.04254928603768349,
0.04503561928868294,
0.052179284393787384,
-0.0011604500468820333,
-0.06091374158859253,
0.004258304834365845,
0.04851900041103363,
0.012004675343632698,
0.016283098608255386,
-0.06929387152194977,
0.012858595699071884,
-0.050562676042318344,
0.011204849928617477,
0.01995004154741764,
-0.006497127469629049,
0.01166514866054058,
-0.038888029754161835,
-0.0008160563884302974,
-0.007848271168768406,
-0.017181115224957466,
-0.0068914806470274925,
0.04520813375711441,
-0.003181429347023368,
0.017970114946365356,
-0.08836690336465836,
0.06371919065713882,
0.04895980283617973,
-0.06547755002975464,
0.040396302938461304,
0.022818060591816902,
-0.020988591015338898,
0.030707957223057747,
-0.011733327992260456,
0.04191627353429794,
0.04475943744182587,
0.008198749274015427,
-0.05982086807489395,
0.008802893571555614,
-0.028244225308299065,
0.03958626091480255,
0.04679718613624573,
-0.035266876220703125,
0.028566999360919,
-0.0063133821822702885,
-0.09351997822523117,
0.01869175210595131,
0.011514298617839813,
0.04708535224199295,
0.06893150508403778,
0.052336543798446655,
0.011285045184195042,
-0.056846700608730316,
0.03469721972942352,
-0.02360684424638748,
0.02685699611902237,
-0.045510321855545044,
-0.03310462087392807,
-0.06421617418527603,
-0.09684446454048157,
-0.0012438202975317836,
-0.010904334485530853,
0.010989170521497726,
0.052448347210884094,
0.044580575078725815,
-0.008879018016159534,
-0.021699300035834312,
0.02151995711028576,
-0.0054759434424340725,
-0.005247082561254501,
0.028490033000707626,
-0.03428616002202034,
-0.024863796308636665,
-0.011788229458034039,
0.020938236266374588,
-0.023754794150590897,
-0.04597373679280281,
0.023165766149759293,
0.02668047323822975,
-0.013024741783738136,
0.017191652208566666,
-0.03481672331690788,
-0.022351201623678207,
-0.077091746032238,
0.016521116718649864,
0.022037586197257042,
-0.06304121762514114,
0.04835047572851181,
0.004512172192335129,
-0.03276078402996063,
0.01616106741130352,
0.04436122253537178,
0.06566155701875687,
0.023314910009503365,
-0.006280394736677408,
0.030331823974847794,
-0.01679833233356476,
-0.03210674971342087,
0.037364449352025986,
0.04599420353770256,
-0.04448976367712021,
0.018733134493231773,
-0.0026247273199260235,
-0.023647723719477654,
0.02875947207212448,
-0.01641012355685234,
0.0042852009646594524,
-0.04474204033613205,
0.029684124514460564,
-0.05501103028655052,
-0.024566004052758217,
-0.023834500461816788,
0.05380815267562866,
-0.0032227043993771076,
0.018341118469834328,
0.025003759190440178,
0.0058362726122140884,
-0.03185749053955078,
-0.021247541531920433,
-0.037293691188097,
-0.032417070120573044,
0.026959147304296494,
0.07944919914007187,
0.015274661593139172,
-0.02591400034725666,
-0.06640210002660751,
-0.01878693327307701,
0.0011710678227245808,
-0.026880614459514618,
0.0566333569586277,
0.04569834843277931,
0.052201054990291595,
0.002954561961814761,
0.053667280822992325,
0.05829362943768501,
-0.07933712005615234,
0.057731274515390396,
-0.027014777064323425,
-0.020115507766604424,
-0.01745457388460636,
-0.03156207129359245,
-0.07981550693511963,
0.008809927850961685,
0.025669116526842117,
0.05568810552358627,
-0.015659989789128304,
0.050790999084711075,
0.06833961606025696,
0.036414507776498795,
-0.019433842971920967,
-0.002529062796384096,
0.05218084156513214,
0.02010492980480194,
0.0482325553894043,
-0.02005043625831604,
0.00628478592261672,
0.04127505421638489,
0.05266465246677399,
0.02383871003985405,
-0.01936035417020321,
0.016824238002300262,
-0.011824769899249077,
0.021179817616939545,
0.04586150869727135,
-0.010758373886346817,
-0.004010958131402731,
-0.0062729595229029655,
0.02161281555891037,
-0.042202021926641464,
-0.027815330773591995,
-0.024140769615769386,
-0.02862589806318283,
0.032611727714538574,
0.05328590050339699,
0.009545018896460533,
0.023926323279738426,
-0.008306269533932209,
-0.0027865173760801554,
0.03506302461028099,
0.029041968286037445,
0.009309202432632446,
0.018031077459454536,
0.0018844223814085126,
0.05141201242804527,
0.038615379482507706,
0.021997442469000816,
0.027563966810703278,
-0.054430585354566574,
-0.023231035098433495,
-0.04282461479306221,
0.004895994905382395,
-0.033906489610672,
0.021975897252559662,
-0.05403352528810501,
0.0020627654157578945,
-0.034146375954151154,
-0.002715284237638116,
-0.012943074107170105,
-0.001831035129725933,
0.009945780038833618,
0.03333102539181709,
-0.041605908423662186,
0.008560042828321457,
-0.0056354147382080555,
-0.031214319169521332,
-0.044530171900987625,
0.040441397577524185,
0.01456413697451353,
0.06419061869382858,
-0.007543501444160938,
0.0036223470233380795,
0.03130555525422096,
-0.023799579590559006,
-0.038346998393535614,
0.0009710323065519333,
0.001656416687183082,
0.009784061461687088,
-0.020758677273988724,
-0.008532566949725151,
0.016397124156355858,
-0.004058719612658024,
-0.06656759232282639,
0.03715743497014046,
-0.05083250626921654,
0.029152950271964073,
0.016398858278989792,
0.027916042134165764,
-0.034687504172325134,
-0.030582590028643608,
-0.053326986730098724,
-0.02378172054886818,
-0.012465574778616428,
-0.012115763500332832,
0.029102591797709465,
0.014938218519091606,
-0.04638160765171051,
0.009419641457498074,
-0.07026863843202591,
0.01008635200560093,
0.11060464382171631,
0.062092628329992294,
0.08093351125717163,
0.02027944102883339,
0.012314551509916782,
-0.018625274300575256,
0.021361596882343292,
-0.051649343222379684,
0.026663225144147873,
0.006788649130612612,
0.017743797972798347,
0.02765778824687004,
-0.009589480236172676,
0.04916861653327942,
-0.039369236677885056,
0.017688654363155365,
0.02973472699522972,
-0.050045259296894073,
0.022330936044454575,
0.03461296856403351,
0.0026363360229879618,
-0.00042009761091321707,
0.001406243653036654,
-0.02237928844988346,
0.017607353627681732,
-0.0008366811671294272,
-0.015300240367650986,
0.005064624361693859,
0.02298632822930813,
-0.0034555208403617144,
-0.03432255983352661,
-0.01367991603910923,
-0.01760144904255867,
-0.02228369377553463,
0.03062867559492588,
0.0184449665248394,
0.01119905337691307,
0.07195879518985748,
-0.02971738949418068,
-0.061997249722480774,
0.026062695309519768,
-0.04505234211683273,
0.026032360270619392,
0.08565693348646164,
-0.007761108689010143,
-0.030927812680602074,
-0.0330670103430748,
-0.024606671184301376,
0.04171474650502205,
-0.03787575662136078,
0.015109178610146046,
0.010294314473867416,
-0.025583963841199875,
-0.03913773596286774,
0.0163215734064579,
0.059010498225688934,
0.024230681359767914,
0.016336174681782722,
-0.029464315623044968,
0.055910125374794006,
-0.01866866648197174,
-0.04189722239971161,
-0.02166406251490116,
0.03536267206072807,
-0.05172353610396385,
-0.035103607922792435,
-0.07186892628669739,
-0.000007950829967739992,
-0.0020430749282240868,
0.007935523055493832,
0.020924992859363556,
-0.004807695746421814,
-0.014736462384462357,
-0.023527927696704865,
0.005165561567991972,
-0.034525301307439804,
-0.01801593415439129,
0.04607711359858513,
-0.01020338386297226,
0.008415905758738518,
-0.026107603684067726,
0.019226260483264923,
0.04397325590252876,
-0.014444055035710335,
0.00826968066394329,
-0.05182809382677078,
0.011976711452007294,
0.029585035517811775,
0.03872840851545334,
0.0209138635545969,
-0.00415534432977438,
0.0028408935759216547,
0.0007477631443180144,
-0.032554447650909424,
0.014657066203653812,
0.06497552245855331,
-0.030093267560005188,
-0.04341810941696167,
0.06079980731010437,
0.06331575661897659,
-0.044636376202106476,
-0.04073897376656532,
0.01016337051987648,
-0.023869406431913376,
-0.036180946975946426,
-0.01618962548673153,
0.004696006420999765,
-0.03072104975581169,
-0.019150888547301292,
0.05517198145389557,
0.054743390530347824,
0.03718213737010956,
0.043106842786073685,
0.030123688280582428,
0.012840207666158676,
-0.051152072846889496,
-0.009545940905809402,
0.012879319489002228,
-0.0027626114897429943,
0.021711964160203934,
0.05161432921886444,
-0.02554444782435894,
-0.013272040523588657,
-0.04342477396130562,
-0.07930400222539902,
0.028541188687086105,
-0.01632968708872795,
-0.04638402909040451,
0.012691880576312542,
-0.020587727427482605,
-0.08293160796165466,
-0.026977701112627983,
0.06719622761011124,
0.007917474955320358,
0.06398157775402069,
-0.022900288924574852,
-0.011355098336935043,
0.04805516451597214,
0.017590435221791267,
-0.014709154143929482,
0.03964366018772125,
0.03716899827122688,
0.004681814461946487,
-0.016806619241833687,
-0.0007966174161992967,
-0.06553690135478973,
0.0029468140564858913,
-0.010013178922235966,
0.006103764288127422,
0.037099722772836685,
0.08423313498497009,
0.0022996640764176846,
0.014909782446920872,
0.006289884448051453,
-0.007229135371744633,
0.020222466439008713,
-0.043897949159145355,
0.06697139889001846,
0.011912913993000984,
-0.03559471666812897,
0.006406921893358231,
-0.05215851217508316,
0.004813970532268286,
-0.0021767443977296352,
-0.05183391273021698,
0.02198808267712593,
-0.06905261427164078,
0.009684189222753048,
0.02629457600414753,
-0.016531722620129585,
0.003221274120733142,
0.028535589575767517,
0.015759021043777466,
0.018734073266386986,
0.004826497286558151,
-0.007667000871151686,
0.05700111389160156,
-0.00884250458329916,
0.019666943699121475,
-0.09473889321088791,
-0.007515488658100367,
-0.020300211384892464,
-0.035117097198963165,
-0.006453253328800201,
-0.013357380405068398,
-0.03775598108768463,
-0.04363828897476196,
0.030426058918237686,
-0.014600777998566628,
0.015707530081272125,
0.02907658740878105,
-0.004107716493308544,
-0.06274113804101944,
-0.011896684765815735,
0.031165925785899162,
0.04985147342085838,
-0.04409269616007805,
-0.007908964529633522,
-0.05790199711918831,
0.020844142884016037,
-0.06363076716661453,
-0.03695268556475639,
-0.01654350385069847,
0.001138852909207344,
-0.03264441341161728,
0.089626744389534,
0.056095805019140244,
0.030925126746296883,
-0.01655389741063118,
-0.0042261285707354546,
0.0500711165368557,
-0.024014614522457123,
0.045103926211595535,
-0.014189372770488262,
-0.005087166093289852,
0.05072217434644699,
0.023355260491371155,
-0.040801454335451126,
0.009034130722284317,
-0.03619902580976486,
0.04241614416241646,
0.020383846014738083,
-0.015924904495477676,
0.025243882089853287,
0.012217938899993896,
-0.028765229508280754,
-0.01907532848417759,
-0.042577508836984634,
0.023280898109078407,
-0.04296012222766876,
0.005180584732443094,
0.026398852467536926,
-0.035992443561553955,
-0.016168996691703796,
-0.04470908269286156,
0.0022102307993918657,
-0.03644135221838951,
0.010542362928390503,
0.0022649348247796297,
-0.007383129559457302,
-0.001759510487318039,
0.09517673403024673,
0.008840921334922314,
-0.023424146696925163,
0.06414936482906342,
0.02811790071427822,
0.018564287573099136,
-0.04557417705655098,
-0.01108099240809679,
0.0035194777883589268,
-0.06127554550766945,
0.05078956484794617,
0.07011371850967407,
0.00276616751216352,
0.009295087307691574,
0.0036882832646369934,
-0.005039695184677839,
0.006006143521517515,
-0.05813039839267731,
-0.04543503001332283,
0.024574512615799904,
0.03392143175005913,
-0.11346527189016342,
-0.018945831805467606,
0.0016201435355469584,
-0.025158632546663284,
-0.010009204037487507,
-0.008487897925078869,
-0.01701986975967884,
-0.024707065895199776,
0.12177365273237228,
-0.04932183772325516,
-0.007205014582723379,
-0.020977884531021118,
-0.001293202512897551,
0.06466548144817352,
-0.043477654457092285,
0.007363087963312864,
-0.04422040656208992,
0.005206898786127567,
0.040914494544267654,
0.05715462937951088,
0.015694504603743553,
0.01286454126238823,
-0.007359728682786226,
-0.01592542976140976,
0.05550600215792656,
0.0023414972238242626,
0.028559735044836998,
-0.00021863941219635308,
0.04101856052875519,
-0.008479366078972816,
0.03332716226577759,
-0.0009385308367200196,
0.000021917168851359747,
-0.034401629120111465,
0.012442266568541527,
-0.04802804812788963,
-0.0326051190495491,
0.023614551872015,
-0.031176496297121048,
-0.019114652648568153,
0.008032230660319328,
-0.01942945271730423,
0.0117247449234128,
-0.018502913415431976,
0.030638404190540314,
0.08999525010585785,
0.009321173653006554,
-0.01595854014158249,
0.00472478149458766,
0.07071666419506073,
-0.026332762092351913,
-0.0013029985129833221,
0.013020908460021019,
-0.0735967606306076,
0.016983533278107643,
-0.02095690742135048,
-0.011584637686610222,
-0.027992555871605873,
0.027969596907496452,
0.0009615928865969181,
0.002773490734398365,
-0.01541158463805914,
-0.03443165495991707,
-0.0286438949406147,
-0.05917963758111,
-0.023239756003022194,
0.0059828306548297405,
0.09046566486358643,
0.030649350956082344,
0.031232675537467003,
0.06228110194206238,
0.04703065752983093,
-0.02164832130074501,
-0.08596759289503098,
0.06105608865618706,
-0.031432297080755234,
-0.03004741109907627,
-0.03749103844165802,
0.015694154426455498,
-0.017381256446242332,
-0.04366542398929596,
0.014785481616854668,
0.016619741916656494,
-0.020974159240722656,
0.05593561381101608,
-0.04528449848294258,
-0.01726924441754818,
-0.023954197764396667,
0.012264681980013847,
-0.04289485514163971,
-0.0538257397711277,
-0.012979417107999325,
0.025201763957738876,
-0.06539618223905563,
0.026333296671509743,
-0.01466648280620575,
0.024359868839383125,
-0.00345187122002244,
0.07907568663358688,
0.056458938866853714,
-0.01513149868696928,
0.01740587316453457,
0.017790796235203743,
-0.024565856903791428,
-0.017322726547718048,
0.0833829939365387,
-0.04441984370350838,
0.011513951234519482,
0.0030922426376491785,
0.022519370540976524,
-0.014957636594772339,
-0.015352618880569935,
-0.032043758779764175,
0.06829550117254257,
-0.04411768913269043,
-0.0505392886698246,
0.011284111998975277,
-0.02177155576646328,
0.011337297968566418,
-0.0005240360042080283,
0.012836968526244164,
-0.07197239249944687,
-0.011842452920973301,
0.03470475226640701,
-0.11041568964719772,
0.0063087004236876965,
-0.0353299155831337,
-0.04320681467652321,
-0.013868195936083794,
-0.01609375886619091,
0.0006301334942691028,
-0.05783858895301819,
0.02177821286022663,
0.0578547865152359,
0.00979604758322239,
0.004481700249016285,
0.053466830402612686,
-0.004426775965839624,
0.022681213915348053,
-0.054639317095279694,
-0.032442498952150345,
-0.03987481817603111,
-0.04297586902976036,
0.008348855189979076,
0.007799828425049782,
0.04509919136762619,
0.042352475225925446,
-0.03339207172393799,
-0.010564918629825115,
-0.026941316202282906,
0.008184729143977165,
0.04433051124215126,
-0.05054708570241928,
-0.014141661114990711,
-0.01894470863044262,
-0.006480949465185404,
0.020012080669403076,
0.03746027499437332,
0.02391214109957218,
-0.033983264118433,
0.00321894115768373,
0.028986824676394463,
0.029778068885207176,
0.03327670320868492,
0.0266867745667696,
0.03224961832165718,
0.04469956457614899,
-0.044083140790462494,
-0.011777371168136597,
-0.013651538640260696,
0.020953889936208725,
-0.006026522722095251,
0.0005250211106613278,
-0.05835789069533348,
0.00018184738291893154,
0.005480950698256493,
0.023702897131443024,
0.05822581425309181,
-0.002856050617992878,
-0.005262128543108702,
0.022974470630288124,
-0.022537149488925934,
0.06262597441673279,
-0.009507700800895691,
0.0487326979637146,
-0.0263625830411911,
-0.036854930222034454,
-0.013953045941889286,
0.05073106288909912,
0.003265226958319545,
-0.07686719298362732,
-0.03922128677368164,
-0.023646246641874313,
-0.03255150467157364,
-0.0036113145761191845,
0.02650633081793785,
-0.04360305890440941,
0.008710048161447048,
-0.01038616243749857,
0.018238695338368416,
-0.025688154622912407,
0.034886375069618225,
0.011300360783934593,
0.014630026184022427,
0.008146598003804684,
-0.002924305386841297,
0.009425042197108269,
-0.031286925077438354,
0.01721789501607418,
0.0070869955234229565,
-0.039634834975004196,
-0.01775708980858326,
0.032010067254304886,
-0.02209698036313057,
-0.028088249266147614,
-0.05945907533168793,
-0.0809500515460968,
0.03255685791373253,
0.02543765679001808,
0.009125581942498684,
0.00767524866387248,
-0.0008496177615597844,
-0.008392761461436749,
-0.0015141984913498163,
-0.0292860995978117,
-0.012591944076120853,
-0.017289644107222557,
0.006239716429263353,
0.045112960040569305,
-0.05043398216366768,
-0.0044195144437253475,
0.04753030836582184,
0.015153623186051846,
-0.022986557334661484,
0.025298336520791054,
-0.0005421632085926831,
-0.003394800703972578,
0.01982300542294979
] |
<p>Currently, as described in <a href="http://physics.stackexchange.com/questions/39679/why-cant-collisions-be-elastic">this question</a>, collisions cannot be elastic. However, is there a way to make a collision more elastic?</p>
<p><strong>Background:</strong></p>
<p>We're working on a project right now involving high speed energy transfer to an exercise ball. One of the issues right now is that the exercise ball is going far slower than what basic (e.g. AP Physics AB) calculations say they should be. I know that this is most likely due to the less-than-perfect elasticity of the collision between the ram and the ball. Is there any way to make the collision more elastic?</p> | g7833 | [
0.028023410588502884,
0.02147641032934189,
0.02083035185933113,
-0.0021114875562489033,
0.0661509558558464,
0.04728374257683754,
-0.007141864858567715,
0.023828964680433273,
-0.007899824529886246,
-0.016721025109291077,
0.04663761332631111,
-0.018407616764307022,
0.027213823050260544,
-0.043125830590724945,
-0.008856561034917831,
0.01203533448278904,
0.07417896389961243,
-0.06873921304941177,
0.015994686633348465,
0.058533474802970886,
-0.03003876283764839,
-0.0037647071294486523,
0.018451374024152756,
-0.008469182066619396,
-0.009833311662077904,
0.01449391059577465,
-0.046617720276117325,
-0.011277235113084316,
-0.06321034580469131,
0.026973502710461617,
0.06037041172385216,
-0.039831046015024185,
-0.04096391797065735,
-0.04642121121287346,
-0.023227788507938385,
0.008574365638196468,
0.0015366171719506383,
-0.027224266901612282,
-0.00485451053828001,
0.05676732584834099,
-0.008953019045293331,
-0.0225661788135767,
-0.007093345280736685,
0.005449080839753151,
-0.004732318222522736,
0.007513290271162987,
0.033866818994283676,
0.0016358218854293227,
-0.01303132064640522,
-0.020821906626224518,
-0.05659159645438194,
-0.015639834105968475,
-0.01383515726774931,
-0.0060845473781228065,
0.04697483777999878,
0.008324249647557735,
-0.00724225677549839,
0.07601836323738098,
0.01085644867271185,
-0.0177471861243248,
-0.058323007076978683,
-0.056420207023620605,
0.0329187773168087,
-0.026525180786848068,
0.03137259557843208,
-0.023313239216804504,
-0.04906579107046127,
-0.023413565009832382,
0.02485382929444313,
0.0038336345460265875,
0.06601878255605698,
-0.019245412200689316,
-0.048337046056985855,
-0.01605684868991375,
-0.0031520300544798374,
-0.03824583813548088,
0.01171789038926363,
-0.016283610835671425,
0.04387696459889412,
-0.0013189747696742415,
-0.022616071626544,
0.07595529407262802,
-0.031132960692048073,
-0.09654588997364044,
0.01900634355843067,
0.006822578608989716,
-0.001231267349794507,
0.045067910104990005,
0.018048804253339767,
-0.004047544207423925,
0.05454782769083977,
-0.031136641278862953,
0.06000867486000061,
0.04646940156817436,
-0.060956332832574844,
-0.013107510283589363,
-0.06245075911283493,
0.08126738667488098,
0.009709944948554039,
0.006421050522476435,
0.005466514267027378,
-0.043441809713840485,
0.07749491930007935,
0.01872408390045166,
-0.00934102013707161,
-0.019716961309313774,
-0.018002822995185852,
0.02090121991932392,
-0.009377188980579376,
-0.024236207827925682,
0.025118352845311165,
-0.051051706075668335,
0.005689071957021952,
-0.0430854856967926,
-0.013686183840036392,
-0.013608704321086407,
0.03702341392636299,
0.028772316873073578,
-0.013095397502183914,
0.0831872820854187,
0.043291348963975906,
-0.013760223984718323,
-0.018485862761735916,
0.014956658706068993,
-0.03689025342464447,
-0.04249485582113266,
0.041952263563871384,
-0.011159698478877544,
0.024129344150424004,
-0.010811909101903439,
-0.04861944541335106,
-0.02257819101214409,
0.023710006847977638,
-0.03180891275405884,
-0.00956052727997303,
0.025090565904974937,
0.014639404602348804,
0.0018009712221100926,
-0.01760559156537056,
-0.016172807663679123,
0.009347325190901756,
-0.0008552441722713411,
-0.0056050908751785755,
-0.04030391201376915,
-0.0552532896399498,
0.02116256207227707,
-0.004797955509275198,
0.004258426837623119,
-0.004802040755748749,
0.07380610704421997,
0.029294341802597046,
0.030985815450549126,
0.02170935645699501,
-0.028641952201724052,
0.03296348452568054,
0.020701834931969643,
0.037309274077415466,
0.01714502088725567,
-0.009266436100006104,
0.03716117516160011,
0.03935624659061432,
0.014809719286859035,
-0.04404348507523537,
-0.021628089249134064,
-0.022056547924876213,
0.05781588330864906,
0.009938116185367107,
0.032377053052186966,
0.01752588152885437,
0.01412368007004261,
-0.09139755368232727,
-0.061527904123067856,
0.01339967641979456,
0.011317158117890358,
-0.02308041788637638,
-0.006679480895400047,
0.03105451725423336,
-0.07285146415233612,
-0.03512612357735634,
0.016893574967980385,
-0.02958345040678978,
-0.000764072232414037,
0.002779358299449086,
-0.03943400830030441,
0.0286445003002882,
-0.003984594251960516,
0.004541442729532719,
0.027657736092805862,
-0.021112674847245216,
0.025262799113988876,
-0.030044203624129295,
0.027643484994769096,
-0.0022454033605754375,
-0.05314287170767784,
-0.05023455247282982,
-0.014220470562577248,
0.05647996813058853,
-0.019682155922055244,
-0.02277371473610401,
0.01948852650821209,
0.01666410081088543,
0.08347062021493912,
-0.019737444818019867,
0.040219444781541824,
0.029088443145155907,
-0.024384163320064545,
-0.06171064451336861,
0.01485217735171318,
-0.011221962980926037,
0.02295372076332569,
0.09238476306200027,
0.043160878121852875,
-0.04622168093919754,
0.010219087824225426,
0.012565492652356625,
0.013450643979012966,
-0.026281209662556648,
-0.01088399812579155,
-0.05678178369998932,
0.04136892035603523,
-0.001301331096328795,
-0.01810975931584835,
-0.016537882387638092,
0.013098271563649178,
-0.05149247124791145,
-0.05622163787484169,
0.010780276730656624,
0.0218442864716053,
-0.03717206418514252,
0.004359403159469366,
-0.031164605170488358,
0.07680247724056244,
-0.002077665412798524,
-0.006446256302297115,
0.053774088621139526,
0.03253750875592232,
-0.022615354508161545,
0.06704815477132797,
-0.020510494709014893,
-0.020578844472765923,
0.0829470083117485,
-0.04082709550857544,
-0.004955453798174858,
-0.012360818684101105,
0.013441329821944237,
-0.05047877877950668,
-0.010274026542901993,
-0.033712681382894516,
0.06521201133728027,
0.02213391289114952,
0.05123096704483032,
-0.03907300904393196,
-0.03776637837290764,
-0.05017485097050667,
-0.009072576649487019,
-0.02350103296339512,
-0.0012383058201521635,
0.00988841149955988,
0.02184702455997467,
-0.050913963466882706,
0.04592341557145119,
0.009631742723286152,
0.05524163693189621,
0.0676695704460144,
-0.059108056128025055,
0.03250361606478691,
-0.00367167592048645,
-0.07061582803726196,
-0.07927980273962021,
0.01531585119664669,
-0.10314465314149857,
0.05742901191115379,
0.0044240811839699745,
0.024916138499975204,
0.009320132434368134,
-0.037922319024801254,
-0.0033074740786105394,
-0.005920629948377609,
0.01649392396211624,
-0.013296162709593773,
-0.04598046839237213,
0.024307969957590103,
0.004996730946004391,
-0.04359501972794533,
0.011155731044709682,
-0.04294201359152794,
-0.010667993687093258,
-0.0147806815803051,
-0.0068783629685640335,
0.00489377835765481,
0.017855890095233917,
-0.014751513488590717,
0.00667661102488637,
0.0037824888713657856,
-0.02045225352048874,
0.03921075537800789,
0.017802264541387558,
-0.04918621480464935,
-0.008680013008415699,
0.009947886690497398,
-0.06019230931997299,
0.032412298023700714,
-0.028872741386294365,
0.04952983930706978,
0.0003555262228474021,
0.05144515633583069,
-0.05326694995164871,
-0.022954192012548447,
-0.027902288362383842,
0.029950477182865143,
0.07044561952352524,
0.002889685332775116,
-0.006876882631331682,
0.03286822885274887,
-0.0843520388007164,
-0.008889708667993546,
-0.010169215500354767,
0.025312060490250587,
0.03135274350643158,
-0.018505670130252838,
-0.01764829270541668,
-0.0989377573132515,
0.039749618619680405,
0.011857124976813793,
-0.025434697046875954,
0.0216207392513752,
-0.032896965742111206,
-0.05767449736595154,
-0.020734334364533424,
-0.04411185532808304,
0.00947580486536026,
0.04234153777360916,
0.005747159942984581,
-0.008208690211176872,
-0.08733541518449783,
-0.036612819880247116,
0.013114932924509048,
0.007122407667338848,
0.05831926688551903,
-0.008369093760848045,
0.013470024801790714,
0.023596016690135002,
-0.022452184930443764,
-0.024384863674640656,
-0.0467013381421566,
0.05028420686721802,
0.005214869976043701,
-0.023536937311291695,
0.01150958426296711,
-0.04211091622710228,
0.08217699080705643,
0.011594446375966072,
-0.0011590257054194808,
-0.036013390868902206,
-0.010947568342089653,
-0.02004501409828663,
0.015528329648077488,
0.017633851617574692,
-0.0395699068903923,
0.023970628157258034,
-0.015560547821223736,
-0.009294028393924236,
-0.015820657834410667,
0.03983782231807709,
-0.056282319128513336,
-0.019757775589823723,
-0.058825887739658356,
0.01732962392270565,
0.010416599921882153,
0.05513320490717888,
0.02828773483633995,
-0.0370466448366642,
0.016607118770480156,
0.05051696300506592,
0.06510994583368301,
-0.0160216037184,
0.07718513160943985,
0.047073908150196075,
-0.01291914377361536,
0.0019039639737457037,
0.054775893688201904,
0.03898922726511955,
0.02279278077185154,
0.015440075658261776,
-0.0058725145645439625,
0.019154570996761322,
0.007625465281307697,
-0.012742503546178341,
-0.0027214926667511463,
-0.02243764139711857,
0.045570239424705505,
0.009597127325832844,
-0.02832697704434395,
0.02680475078523159,
-0.0069818939082324505,
-0.013580646365880966,
-0.019976459443569183,
-0.06875879317522049,
-0.09108848869800568,
0.05854367837309837,
-0.03704402968287468,
0.06788407266139984,
-0.061016157269477844,
-0.034938398748636246,
-0.04177987948060036,
-0.010319521650671959,
-0.007976590655744076,
0.018038379028439522,
-0.03412608057260513,
-0.06603922694921494,
-0.0001672975777182728,
-0.060065750032663345,
-0.017644545063376427,
-0.06289973855018616,
-0.056408368051052094,
-0.029706740751862526,
-0.04771861806511879,
0.05222736671566963,
-0.013052500784397125,
0.0006990311667323112,
0.01464735809713602,
0.001266291132196784,
0.011240198276937008,
0.04049395024776459,
0.016157669946551323,
0.08374493569135666,
0.014783785678446293,
-0.04400792717933655,
0.01175723411142826,
0.014583497308194637,
0.012245573103427887,
0.027558039873838425,
-0.0289347805082798,
0.0005053094937466085,
0.02886062115430832,
0.03598707169294357,
0.03677668422460556,
0.009641795419156551,
0.04721860960125923,
-0.004090830683708191,
0.04142417386174202,
-0.0044736373238265514,
0.042421553283929825,
-0.0177414882928133,
0.030682295560836792,
0.027773480862379074,
-0.06012263894081116,
-0.017879895865917206,
-0.05212576687335968,
-0.0035149063915014267,
-0.0059779793955385685,
-0.03732409328222275,
0.0298908818513155,
0.046482183039188385,
-0.058922216296195984,
-0.01595444604754448,
-0.0061346497386693954,
0.027091817930340767,
0.005485546309500933,
0.05210229754447937,
-0.046463511884212494,
0.06321640312671661,
-0.0015798304229974747,
0.011162660084664822,
-0.03478886932134628,
0.025425370782613754,
0.03668360039591789,
-0.04068289324641228,
-0.023450424894690514,
-0.0027133915573358536,
0.0012051716912537813,
0.03508227318525314,
-0.0375242605805397,
0.0414169616997242,
-0.015214151702821255,
0.0005727888783439994,
-0.020317770540714264,
-0.024604877457022667,
0.017732370644807816,
-0.034637466073036194,
-0.0006394963129423559,
0.0000051966985665785614,
-0.02665746584534645,
-0.042644351720809937,
0.01013084314763546,
-0.0064785354770720005,
-0.053896401077508926,
0.01854087971150875,
-0.008189243264496326,
0.001704536029137671,
0.0052647776901721954,
0.025078723207116127,
-0.038779471069574356,
-0.010356038808822632,
0.029030509293079376,
0.0268334299325943,
0.03824882581830025,
-0.0008340142085216939,
-0.03308773785829544,
0.015350441448390484,
-0.029880579560995102,
-0.02590310573577881,
-0.025167671963572502,
-0.025636451318860054,
-0.0015030282083898783,
0.03381303325295448,
0.060335032641887665,
0.02425616793334484,
-0.025639696046710014,
-0.008778956718742847,
-0.017142636701464653,
0.030954552814364433,
0.0013342946767807007,
-0.022408202290534973,
-0.04726031795144081,
0.07728168368339539,
0.04877962917089462,
0.012119953520596027,
-0.007682546507567167,
-0.03336318954825401,
0.05841178074479103,
-0.05871410667896271,
0.060353219509124756,
0.002179588656872511,
-0.08265389502048492,
-0.04786437004804611,
-0.01479647122323513,
-0.0166831836104393,
0.020380329340696335,
0.05755222961306572,
0.05785579979419708,
-0.03293255716562271,
-0.007625078782439232,
-0.01212587021291256,
-0.07440220564603806,
-0.053175657987594604,
-0.028044957667589188,
0.007106454577296972,
-0.03742867335677147,
0.012148620560765266,
0.028009900823235512,
-0.0008426526910625398,
0.03240262717008591,
0.031477298587560654,
0.04357224702835083,
0.008590388111770153,
-0.0488891676068306,
-0.028226319700479507,
0.05540623888373375,
-0.04662755876779556,
0.0019665872678160667,
-0.004633729346096516,
-0.030559271574020386,
-0.022991908714175224,
0.028606507927179337,
0.04502899944782257,
0.018817244097590446,
-0.006910115480422974,
0.0454658567905426,
-0.009732923470437527,
-0.011932759545743465,
-0.029630938544869423,
-0.009472472593188286,
0.014453304931521416,
-0.03150533139705658,
-0.030783014371991158,
-0.011251847259700298,
0.0026006430853158236,
0.05339799448847771,
-0.0024031216744333506,
-0.011156315915286541,
0.07837942987680435,
0.05032392591238022,
0.051965486258268356,
0.03571392595767975,
-0.01939943991601467,
0.012587354518473148,
0.008432818576693535,
-0.03615608438849449,
-0.035121671855449677,
-0.05164264515042305,
0.010533655993640423,
0.017976026982069016,
-0.01800747774541378,
0.006466980557888746,
-0.045591458678245544,
-0.0025118619669228792,
-0.010636437684297562,
0.012306428514420986,
-0.06504330784082413,
-0.004362978041172028,
-0.0016748348716646433,
0.033163778483867645,
-0.054260581731796265,
-0.046022165566682816,
-0.040135178714990616,
-0.029607703909277916,
0.01035265065729618,
-0.03706873208284378,
0.08716386556625366,
0.06316620111465454,
0.016245556995272636,
0.020534412935376167,
0.061893779784440994,
-0.038877516984939575,
0.053704213351011276,
0.005649634171277285,
0.019252700731158257,
0.013687146827578545,
-0.0032426367979496717,
-0.04280313476920128,
-0.0006635098252445459,
0.01838483288884163,
0.09173686802387238,
-0.04541175067424774,
-0.011075573973357677,
-0.03903122618794441,
-0.06313050538301468,
0.02663491852581501,
-0.049994565546512604,
0.007406179327517748,
-0.006668934598565102,
0.01612897589802742,
-0.008238570764660835,
-0.02016299031674862,
-0.030546385794878006,
-0.07296325266361237,
0.11583279073238373,
0.02438059262931347,
-0.037845395505428314,
0.03265450522303581,
-0.00030823348788544536,
-0.028630001470446587,
0.03914841637015343,
0.005887731909751892,
0.11457034200429916,
-0.03428678959608078,
-0.006636831443756819,
-0.013965592719614506,
-0.03625571355223656,
-0.014355149120092392,
0.057240866124629974,
0.006016288883984089,
0.04644818231463432,
-0.04308801889419556,
0.05060697719454765,
0.08219277858734131,
-0.011667058803141117,
-0.006176689639687538,
0.05632345378398895,
0.006997261196374893,
-0.05368702486157417,
-0.04003163054585457,
0.0010015909792855382,
-0.0210488922894001,
0.04387233778834343,
-0.032129231840372086,
0.0013593175681307912,
0.04167312756180763,
-0.007426653057336807,
-0.004395806696265936,
-0.016139810904860497,
0.051899634301662445,
-0.041577573865652084,
0.018181968480348587,
-0.0022429567761719227,
0.004006728995591402,
-0.007422675844281912,
0.011443235911428928,
-0.012182355858385563,
0.03611095994710922,
-0.08126373589038849,
-0.04160314053297043,
-0.038808658719062805,
0.04383770376443863,
-0.03349856287240982,
-0.02801705151796341,
0.02250986360013485,
0.02759358286857605,
0.009431510232388973,
-0.0028226771391928196,
0.018823888152837753,
-0.012323714792728424,
0.06344397366046906,
0.007858139462769032,
0.08549919724464417,
-0.024425726383924484,
0.08172504603862762,
0.02392152138054371,
0.012681304477155209,
-0.013451879844069481,
0.03257672116160393,
-0.00020842914818786085,
0.016070829704403877,
-0.044578760862350464,
-0.020106850191950798,
-0.007923915982246399,
-0.000967258180025965,
0.0001503542298451066,
-0.0033949916251003742,
-0.031248679384589195,
-0.011087518185377121,
0.03930584341287613,
0.00793958455324173,
-0.013206208124756813,
0.06286059319972992,
-0.02641957439482212,
-0.015061047859489918,
-0.040881119668483734,
-0.004793751053512096,
0.03319421410560608,
0.033777013421058655,
-0.025069372728466988,
-0.045966263860464096,
-0.0015856223180890083,
0.0179455503821373,
0.06721621751785278,
-0.022063763812184334,
-0.013287332840263844,
-0.004868946969509125,
-0.006279723718762398,
0.006858030799776316,
-0.038622282445430756,
-0.01057350356131792,
0.006982181686908007,
-0.05709533393383026,
0.03969912230968475,
0.002142614219337702,
-0.03016671910881996,
0.01731977052986622,
0.01623726077377796,
-0.06257974356412888,
0.059025902301073074,
0.021787729114294052,
-0.010059067979454994,
-0.011244288645684719,
-0.0315084382891655,
0.007537893019616604,
-0.05836530029773712,
0.0472998172044754,
0.009961920790374279,
0.010516068898141384,
-0.030996736139059067,
-0.04389350861310959,
0.004161905497312546,
-0.06300541013479233,
0.015903953462839127,
0.06731877475976944,
0.055459100753068924,
-0.01795988529920578,
0.04045488312840462,
-0.010482200421392918,
-0.015763288363814354,
0.06504948437213898,
0.0008640654850751162,
0.004191345069557428,
0.024546803906559944,
0.023854292929172516,
-0.04842400550842285,
-0.029090868309140205,
0.016313692554831505,
0.0790940672159195,
0.012492985464632511,
-0.024493718519806862,
0.0371212512254715,
0.00018895999528467655,
-0.03121059201657772,
-0.027613824233412743
] |
<p>The one-particle states as well as the fields in quantum field theory are regarded as representations of Poincare group, e.g. scalar, spinor, and vector representations. </p>
<p>Is there any systematical procedure that one starts from the Dynkin label for a given representation, to construct a Lagrangian of that field theory? If yes, where can I find that procedure? </p>
<p>I don't care adding interaction by gauge invariance from these Lagrangians will cause non-renormalizability or not. I can live with effective theories. </p> | g7834 | [
-0.02451394312083721,
-0.014336462132632732,
-0.025337086990475655,
-0.10355391353368759,
0.0661102682352066,
-0.030242858454585075,
0.01734595187008381,
0.06781958043575287,
-0.0073326267302036285,
0.0034792108926922083,
-0.003006477141752839,
0.002456729067489505,
0.017905285581946373,
0.06803242117166519,
-0.02364945411682129,
-0.00120499636977911,
0.06513604521751404,
0.05043843388557434,
0.02956799417734146,
-0.06629073619842529,
-0.01881999894976616,
0.010813828557729721,
0.053429942578077316,
-0.015225281938910484,
-0.046467650681734085,
-0.03137889504432678,
0.014335115440189838,
-0.01910777948796749,
0.00144651357550174,
0.003095105057582259,
0.017151497304439545,
0.013522404246032238,
0.0142233707010746,
-0.02525237388908863,
0.0455370731651783,
-0.05028906464576721,
0.052330031991004944,
0.030415281653404236,
0.023355605080723763,
-0.0013200463727116585,
0.01711195334792137,
-0.029417147859930992,
0.04471737891435623,
0.028732391074299812,
-0.06769999861717224,
0.023560985922813416,
-0.002192449290305376,
0.009318079799413681,
-0.04142725467681885,
0.031636957079172134,
0.04535958543419838,
-0.01675369404256344,
0.02020408771932125,
-0.021516313776373863,
-0.004432417917996645,
0.026955774053931236,
-0.026931051164865494,
0.002431167522445321,
0.018779128789901733,
0.010530511848628521,
-0.005400451365858316,
-0.00753825344145298,
-0.02068881131708622,
0.013943593017756939,
0.05387589707970619,
0.0235108844935894,
-0.046505555510520935,
-0.01631367951631546,
-0.03023725561797619,
-0.03233956918120384,
-0.006096396129578352,
-0.047333259135484695,
0.037554625421762466,
-0.02863123081624508,
-0.009200973436236382,
0.04321399703621864,
-0.049717023968696594,
-0.026798749342560768,
0.01603589951992035,
-0.026201527565717697,
-0.015391873195767403,
-0.04705691337585449,
-0.004140208009630442,
-0.04967931658029556,
0.081275075674057,
-0.04022340849041939,
-0.026418473571538925,
0.0077408128418028355,
-0.023988856002688408,
0.015203087590634823,
0.011924882419407368,
0.030440833419561386,
0.034267302602529526,
0.029530838131904602,
-0.026791824027895927,
0.012618039734661579,
-0.013767675496637821,
0.032617177814245224,
-0.060056205838918686,
-0.055527277290821075,
-0.015018758364021778,
0.061011601239442825,
0.006069888360798359,
-0.035820700228214264,
0.0008300481713376939,
0.004812382627278566,
0.00629193801432848,
-0.0403941348195076,
-0.009942550212144852,
0.0015649297274649143,
-0.05399589240550995,
0.05271652340888977,
0.004923433996737003,
-0.0003800459089688957,
-0.020083075389266014,
-0.019612079486250877,
0.07571212202310562,
-0.035481810569763184,
-0.023657381534576416,
0.07057403028011322,
0.0066710347309708595,
0.027389727532863617,
0.06452638655900955,
0.038958948105573654,
0.010363704524934292,
0.03248429298400879,
-0.016651930287480354,
-0.0373578704893589,
-0.007211677730083466,
-0.02865789271891117,
0.04168650880455971,
-0.014816965907812119,
-0.019612856209278107,
0.045534681528806686,
-0.003624552395194769,
0.03596629574894905,
0.031068438664078712,
0.03189010173082352,
0.060796309262514114,
-0.009082137607038021,
-0.02384570986032486,
-0.016833312809467316,
-0.017845317721366882,
-0.023011690005660057,
0.04798948019742966,
-0.028461305424571037,
0.028315387666225433,
-0.06388308852910995,
-0.05141653120517731,
0.04132043942809105,
0.01978910155594349,
0.06334710121154785,
0.04122285917401314,
-0.005696299485862255,
0.08072991669178009,
0.027662545442581177,
0.04097051918506622,
0.01233667228370905,
0.01982874423265457,
-0.013338720425963402,
0.038811538368463516,
-0.0193623099476099,
0.026894493028521538,
0.00681129889562726,
-0.007348911836743355,
-0.002474266104400158,
-0.029768895357847214,
-0.05580815672874451,
0.0062835863791406155,
-0.06298762559890747,
-0.034611355513334274,
0.013297421857714653,
-0.033093761652708054,
0.02002754434943199,
0.02396347187459469,
0.058931685984134674,
-0.10286163538694382,
-0.022027382627129555,
0.006109809037297964,
-0.05029892548918724,
-0.019500505179166794,
-0.03548416495323181,
0.03307651728391647,
-0.015646057203412056,
-0.028572725132107735,
0.035132769495248795,
-0.05916504189372063,
0.07325409352779388,
-0.006129067856818438,
-0.003905301447957754,
0.02267349325120449,
0.06830693781375885,
0.032649487257003784,
0.0073916176334023476,
-0.04907782003283501,
0.004451322834938765,
0.02666119486093521,
-0.07581309229135513,
-0.029271788895130157,
-0.06308843195438385,
0.008496014401316643,
0.0021911286748945713,
-0.00017245595518033952,
0.00999086257070303,
-0.012563303112983704,
-0.03126625716686249,
-0.03966662287712097,
-0.021601621061563492,
0.018694745376706123,
-0.033068712800741196,
-0.007380349561572075,
-0.03694162517786026,
0.024851974099874496,
0.03901362419128418,
-0.028909506276249886,
-0.012451313436031342,
0.023489290848374367,
0.004362952429801226,
-0.04137250781059265,
0.038950733840465546,
-0.05678524076938629,
-0.032171253114938736,
0.06587821990251541,
0.060895539820194244,
-0.023977696895599365,
0.03747408092021942,
-0.009206733666360378,
0.01437495369464159,
-0.06505519896745682,
0.03589153662323952,
-0.0881880521774292,
-0.020979829132556915,
-0.023515112698078156,
-0.07139227539300919,
0.01992328092455864,
-0.012239429168403149,
-0.02761508896946907,
-0.051977433264255524,
0.04315859079360962,
0.026969050988554955,
-0.0551278181374073,
-0.02142327092587948,
0.004397823940962553,
0.03321494162082672,
0.03504372388124466,
0.017945436760783195,
0.012085971422493458,
0.03112979419529438,
-0.038157545030117035,
0.0410262867808342,
-0.06518875062465668,
0.01809454709291458,
-0.07403263449668884,
-0.03970823436975479,
0.025229601189494133,
0.03200474753975868,
0.017272889614105225,
-0.0312720388174057,
0.016460740938782692,
0.008431931026279926,
0.002113418886438012,
-0.04880664870142937,
0.02822883613407612,
0.05186391621828079,
-0.0502464734017849,
0.008984285406768322,
0.017676444724202156,
0.009462197311222553,
-0.041882455348968506,
-0.0024043170269578695,
-0.06752225011587143,
0.03279154747724533,
0.019436748698353767,
-0.053139057010412216,
0.01495138369500637,
-0.0019522270886227489,
0.010148481465876102,
0.025519493967294693,
0.012575981207191944,
-0.045369721949100494,
0.02476758137345314,
-0.057240236550569534,
0.012594729661941528,
-0.04007170721888542,
0.04504883661866188,
-0.06354264169931412,
0.017999470233917236,
-0.004033088218420744,
-0.030011527240276337,
-0.0005048784660175443,
0.04324662685394287,
0.014384285546839237,
-0.0019829156808555126,
-0.02224106714129448,
-0.06116882711648941,
-0.0058419969864189625,
-0.007779387757182121,
0.02695607580244541,
0.033834874629974365,
0.06800097227096558,
-0.029602473601698875,
-0.0566527396440506,
0.006323076784610748,
0.016814522445201874,
0.023856420069932938,
-0.004543480463325977,
-0.06454875320196152,
0.010339874774217606,
-0.007571123074740171,
-0.04140118137001991,
-0.04892316088080406,
-0.0007878043106757104,
-0.007228444330394268,
-0.024817094206809998,
-0.033021800220012665,
-0.01975906454026699,
-0.019627846777439117,
-0.017514944076538086,
0.041414596140384674,
-0.0034120401833206415,
-0.0213780477643013,
-0.004955419339239597,
0.08860724419355392,
0.0001999396044993773,
0.051399387419223785,
0.03831944614648819,
-0.04517378658056259,
0.000099627097370103,
-0.0015256995102390647,
-0.05028032884001732,
0.011209987103939056,
-0.031239928677678108,
0.031036177650094032,
0.01077330019325018,
-0.043263696134090424,
-0.028602348640561104,
-0.08302315324544907,
-0.0703686997294426,
0.034780096262693405,
-0.010619763284921646,
-0.051237206906080246,
-0.06415664404630661,
-0.05448741465806961,
0.03370464965701103,
0.014208827167749405,
-0.027575649321079254,
-0.004684661515057087,
-0.0021468596532940865,
0.02734862081706524,
-0.036858733743429184,
-0.03777061030268669,
0.014171221293509007,
0.03391151875257492,
-0.038671910762786865,
0.005468032322824001,
-0.021837079897522926,
0.07830951362848282,
0.04517688974738121,
-0.013366516679525375,
0.007809008006006479,
0.03830834850668907,
-0.004313967656344175,
0.0024227986577898264,
0.03880714252591133,
-0.0011595621472224593,
0.042796194553375244,
-0.02687457576394081,
-0.017864735797047615,
0.0618487223982811,
0.02850612811744213,
0.029529642313718796,
0.01639118790626526,
0.007277357392013073,
0.018180616199970245,
-0.020385973155498505,
0.015280378051102161,
0.0014365987153723836,
0.005194719415158033,
-0.038314368575811386,
-0.03268614038825035,
-0.03647281974554062,
0.05467076599597931,
0.03352702781558037,
0.04827428236603737,
0.059529803693294525,
0.05207940936088562,
-0.042611055076122284,
0.05839717760682106,
0.01943965256214142,
0.0564725287258625,
-0.04150744900107384,
-0.014559631235897541,
0.028682950884103775,
0.03337911516427994,
0.006029113195836544,
-0.014859790913760662,
0.027015265077352524,
-0.010190791450440884,
-0.02235102467238903,
-0.0023585448507219553,
-0.03394249826669693,
-0.023787109181284904,
0.04358690232038498,
-0.024720393121242523,
0.017408248037099838,
0.00023989257169887424,
0.01947576180100441,
-0.034380968660116196,
-0.014731787145137787,
0.01199879590421915,
-0.004651273135095835,
0.030051512643694878,
0.024707067757844925,
-0.05911629647016525,
-0.04824669659137726,
-0.010269436985254288,
0.0016992657911032438,
-0.0667700543999672,
-0.012735582888126373,
-0.01874145120382309,
0.02705698274075985,
0.050570014864206314,
0.06385977566242218,
0.02262185513973236,
-0.008639045991003513,
0.05126046761870384,
-0.009357220493257046,
0.054088857024908066,
-0.03336126729846001,
-0.023304130882024765,
0.0341184101998806,
-0.03030204214155674,
0.016373416408896446,
-0.0007825485663488507,
-0.09157228469848633,
0.004059311933815479,
-0.0697454884648323,
0.0016726938774809241,
0.06124735251069069,
0.04958518594503403,
0.038388676941394806,
-0.0599253848195076,
0.02385832741856575,
-0.053330451250076294,
-0.051719680428504944,
0.06925047934055328,
-0.011342605575919151,
0.013906579464673996,
-0.04468226060271263,
-0.03735954686999321,
0.014270780608057976,
0.006855564657598734,
-0.042638592422008514,
-0.02610677294433117,
0.017178507521748543,
-0.01598168909549713,
-0.012199493125081062,
0.01521053072065115,
0.0265213530510664,
-0.003291437402367592,
-0.021374495700001717,
0.005767817609012127,
-0.011969341896474361,
0.015908239409327507,
-0.01839982345700264,
-0.027346504852175713,
-0.08764567971229553,
0.09143292158842087,
-0.006672948598861694,
-0.030624380335211754,
0.06457506865262985,
0.005248678848147392,
0.04330696538090706,
-0.0597916878759861,
0.014854668639600277,
-0.012784763239324093,
0.02352195791900158,
-0.01755008101463318,
-0.009394248016178608,
-0.04114160314202309,
0.01905648782849312,
-0.004643185995519161,
-0.030193602666258812,
-0.0035091107711195946,
-0.017721038311719894,
0.007212809752672911,
-0.0017936697695404291,
0.007441812194883823,
-0.06410305947065353,
0.019846122711896896,
-0.033969927579164505,
-0.03154003620147705,
-0.0007989263394847512,
0.008531740866601467,
0.006987408269196749,
0.003742758184671402,
-0.015152698382735252,
-0.02215331606566906,
0.012231334112584591,
-0.02127297967672348,
-0.022733250632882118,
-0.017347605898976326,
0.04909316450357437,
-0.0005934647633694112,
0.02818736620247364,
0.028556080535054207,
0.1166779175400734,
0.024403562769293785,
-0.038144223392009735,
-0.0170939639210701,
0.003422742709517479,
-0.0024192212149500847,
-0.03647290915250778,
-0.0046817283146083355,
0.014900829643011093,
0.007869351655244827,
-0.00573952030390501,
0.050627946853637695,
-0.021664150059223175,
-0.06525895744562149,
0.041679080575704575,
-0.022656554356217384,
0.010752423666417599,
-0.010052484460175037,
-0.016951467841863632,
0.00891182292252779,
-0.07113043963909149,
-0.026027552783489227,
0.035192012786865234,
0.044229745864868164,
0.04485127329826355,
-0.04289308190345764,
0.030998243018984795,
0.012678607366979122,
0.04553074762225151,
-0.06722033768892288,
-0.007834668271243572,
-0.0011490931501612067,
0.040649574249982834,
-0.0022408822551369667,
-0.006749030202627182,
-0.02276521921157837,
0.022911952808499336,
-0.020845260471105576,
0.009432114660739899,
0.03632500767707825,
0.012723146937787533,
0.030966367572546005,
0.012121968902647495,
-0.04310821369290352,
-0.02072204276919365,
0.0053875381126999855,
-0.018509237095713615,
-0.0725332647562027,
-0.02272403985261917,
0.017753731459379196,
0.015061678364872932,
-0.010590110905468464,
0.04226863011717796,
0.08609579503536224,
0.017558831721544266,
-0.039048973470926285,
0.05304701253771782,
-0.044195543974637985,
-0.054727595299482346,
0.06512279063463211,
0.014305018819868565,
-0.07930389791727066,
0.048597998917102814,
0.016739195212721825,
0.009388686157763004,
0.05411134287714958,
0.05069412291049957,
0.005720155779272318,
0.02376808598637581,
-0.009821372106671333,
0.051370684057474136,
-0.01675400696694851,
-0.02624576911330223,
0.04888155311346054,
-0.02567950077354908,
0.01664874516427517,
0.01814647577702999,
-0.05883222818374634,
-0.03982582688331604,
0.026820816099643707,
-0.05653631314635277,
0.00030853081261739135,
-0.027728410437703133,
0.04852350056171417,
0.026410270482301712,
0.001276472001336515,
-0.02743261121213436,
0.022645769640803337,
-0.029147416353225708,
0.03827352821826935,
0.018731197342276573,
-0.05427073314785957,
0.003327681915834546,
0.047899141907691956,
0.043491967022418976,
-0.03816009312868118,
0.027362899854779243,
-0.008397732861340046,
-0.005939066875725985,
0.012134110555052757,
-0.07567930966615677,
0.0008948561153374612,
-0.007652696687728167,
-0.013895483687520027,
0.048135045915842056,
0.012272171676158905,
0.0027591313701123,
-0.0052839466370642185,
0.032795850187540054,
-0.04288750886917114,
0.030871955677866936,
0.0230084378272295,
-0.029686864465475082,
0.021689554676413536,
0.002504681935533881,
0.028600266203284264,
0.0131390281021595,
0.0013409327948465943,
0.006966870743781328,
0.03526269644498825,
-0.028585555031895638,
0.032387878745794296,
0.0388767346739769,
0.004713225178420544,
0.08064116537570953,
0.025889310985803604,
-0.00999283418059349,
0.004583929665386677,
0.03913645073771477,
0.03072209656238556,
-0.04082857444882393,
0.011846129782497883,
0.02149323746562004,
0.018727043643593788,
-0.08308365195989609,
0.06229264289140701,
0.11589669436216354,
-0.018250489607453346,
-0.02916829288005829,
-0.03448246046900749,
0.014996795915067196,
-0.029304102063179016,
-0.01796799898147583,
0.0202505961060524,
0.022719919681549072,
-0.01662934198975563,
-0.023452933877706528,
0.03411220386624336,
-0.004276896361261606,
-0.002413625130429864,
0.0689251571893692,
-0.00697903148829937,
-0.0453459806740284,
-0.021504174917936325,
-0.018706602975726128,
-0.03466321900486946,
0.012800483033061028,
-0.022972239181399345,
0.01967553421854973,
0.015163682401180267,
-0.06895232200622559,
-0.007442103698849678,
0.09005295485258102,
0.01344727911055088,
0.009596736170351505,
-0.06313233822584152,
-0.03230678290128708,
0.0746007040143013,
-0.02435982972383499,
-0.016009848564863205,
-0.018045885488390923,
0.11260952055454254,
-0.005672940518707037,
-0.046466145664453506,
-0.05379388853907585,
0.023660244420170784,
0.019810833036899567,
0.0007859840989112854,
-0.055837180465459824,
-0.027784112840890884,
0.07983260601758957,
0.05102533474564552,
-0.034614063799381256,
-0.005804074462503195,
0.009582368656992912,
-0.05084643512964249,
0.006377936340868473,
0.01033627800643444,
-0.06348594278097153,
-0.009893522597849369,
0.031453657895326614,
0.02070864662528038,
0.011498020961880684,
0.03297626972198486,
-0.005348043981939554,
-0.016665274277329445,
-0.05982230603694916,
0.003299484495073557,
0.00929899699985981,
-0.05171259865164757,
-0.04451341554522514,
-0.0020110453478991985,
-0.0352407842874527,
0.013487489894032478,
-0.0450504906475544,
0.017733706161379814,
0.0003750420000869781,
0.020277466624975204,
-0.019083786755800247,
-0.0022890791296958923,
-0.05192941427230835,
0.029316607862710953,
0.01792314648628235,
0.010757848620414734,
-0.006236579269170761,
0.03817378357052803,
0.022366967052221298,
-0.02119731530547142,
0.046314969658851624,
-0.02309153601527214,
0.013028569519519806,
0.05068559944629669,
0.06593548506498337,
0.034351423382759094,
-0.020107828080654144,
0.02177213504910469,
-0.062307197600603104,
0.06596827507019043,
-0.05200134590268135,
0.018006136640906334,
-0.04322236403822899,
-0.050822120159864426,
0.04623095691204071,
0.03329390287399292,
0.004884900525212288,
-0.056253813207149506,
0.011733372695744038,
0.0009667355916462839,
-0.0009782721754163504,
-0.019017843529582024,
0.01495419256389141,
-0.010664399713277817,
0.0031687477603554726,
-0.04034363105893135,
0.002475566230714321,
0.010423380881547928,
-0.01869741454720497,
0.018147094175219536,
0.029219459742307663,
-0.0064005665481090546,
-0.029843179509043694,
-0.0020390276331454515,
0.11926804482936859,
0.000166921759955585,
0.02134501002728939,
-0.020115869119763374,
0.04090150445699692,
0.041628021746873856,
-0.06429092586040497,
0.03243604302406311,
-0.00495752552524209,
-0.025296473875641823
] |
<p>What's so special about second order equations in classical mechanics? I have a basic understanding of the Lagrangian and Hamiltonian formulations of classical mechanics, so I'm not looking for answers like 'because Newton's second law is a second order ODE' or 'because Euler-Lagrange equations act on a first time derivative of position'. I'm looking for a deeper physical reason - in the same sense that Energy conservation is not fundamental, it results from time translation invariance. I realise two boundary conditions are required to solve for the dynamics of a given system, but I see that more as a result of the equations being second order than the cause of them being second order. Is there a more fundamental organising principle that I am not aware of?</p> | g257 | [
0.08735990524291992,
0.002914721379056573,
0.014555295929312706,
-0.02031458169221878,
0.07446497678756714,
-0.019255658611655235,
0.0319250263273716,
0.012667845003306866,
-0.05643027275800705,
-0.030983297154307365,
0.00685146963223815,
-0.01388737466186285,
-0.01954868622124195,
0.008411695249378681,
-0.02294972538948059,
-0.0285376887768507,
0.020450321957468987,
0.028017578646540642,
0.008302196860313416,
0.025009043514728546,
-0.02833556942641735,
0.027122745290398598,
0.0019027392845600843,
-0.023087596520781517,
-0.024984069168567657,
0.036664705723524094,
0.07656038552522659,
-0.037071552127599716,
0.004734530579298735,
-0.007587878964841366,
-0.000471461215056479,
0.008163517341017723,
0.05431651324033737,
-0.07102153450250626,
0.0008091753115877509,
0.011854881420731544,
-0.004568837583065033,
-0.039944663643836975,
0.05510316416621208,
-0.04623829200863838,
0.022755859419703484,
-0.057886168360710144,
0.02531302347779274,
-0.004493610002100468,
0.032803066074848175,
-0.06539346277713776,
-0.0731247290968895,
-0.062410589307546616,
-0.03961001709103584,
0.0026484294794499874,
0.05354834720492363,
0.019683837890625,
0.06892363727092743,
0.035009294748306274,
-0.005049383733421564,
0.0003847789776045829,
0.03658716008067131,
0.04099456965923309,
0.05664912611246109,
-0.014479764737188816,
0.019872283563017845,
-0.0033977790735661983,
0.006978908088058233,
0.025667235255241394,
0.030826540663838387,
-0.08704963326454163,
-0.01745004393160343,
-0.011707252822816372,
0.03340264782309532,
0.04822123423218727,
-0.01165359653532505,
-0.05796446278691292,
-0.03312966600060463,
-0.0729692280292511,
0.03041168861091137,
-0.004449248779565096,
-0.01914517767727375,
-0.000728875573258847,
0.02385580912232399,
-0.026414671912789345,
-0.04211637005209923,
-0.01824580691754818,
-0.042780160903930664,
0.0485025979578495,
0.05659297853708267,
0.016232049092650414,
-0.003632450010627508,
-0.021481484174728394,
-0.0067573776468634605,
0.010331756435334682,
-0.0044548711739480495,
0.01953129470348358,
0.0532555878162384,
-0.014032742008566856,
-0.046142831444740295,
0.0014303550124168396,
-0.018770424649119377,
0.02405964955687523,
0.0226765014231205,
0.0083318455144763,
-0.02064625173807144,
-0.01591050811111927,
0.03037033975124359,
-0.02181130088865757,
0.03309686854481697,
-0.049480099231004715,
0.06928209215402603,
0.036003392189741135,
-0.01057443581521511,
-0.02310500480234623,
0.03775658458471298,
0.008381587453186512,
0.018637266010046005,
0.03613417223095894,
-0.004323457833379507,
0.06894887238740921,
0.05334516242146492,
0.013632123358547688,
0.0516330786049366,
0.01880832016468048,
-0.01589818112552166,
0.041735418140888214,
0.034987710416316986,
-0.00318281096406281,
-0.037789057940244675,
0.0007783929468132555,
0.04482053592801094,
-0.03470860794186592,
0.005694481078535318,
-0.009347988292574883,
-0.0019483156502246857,
0.036260489374399185,
-0.032515984028577805,
-0.048398151993751526,
-0.003683834569528699,
0.060070522129535675,
0.001445393543690443,
-0.056736260652542114,
0.02870038151741028,
-0.026958854869008064,
-0.007872965186834335,
-0.012593196704983711,
0.031057799234986305,
-0.0438617467880249,
-0.007799907121807337,
0.017691580578684807,
0.01493101380765438,
-0.035609904676675797,
-0.009561752900481224,
0.0038779263850301504,
-0.05463038757443428,
0.03521965444087982,
-0.00010241825657431036,
-0.003486339934170246,
0.0689951553940773,
0.019287819042801857,
-0.037696272134780884,
-0.01610211282968521,
0.002527243923395872,
-0.0008260339382104576,
0.0943426638841629,
0.02843671850860119,
0.006068205460906029,
-0.01096720714122057,
-0.03254345804452896,
0.04187940061092377,
-0.028131913393735886,
-0.08511180430650711,
-0.006231233011931181,
-0.0011309165274724364,
-0.025480130687355995,
0.014738257974386215,
0.0137976398691535,
0.10629632323980331,
-0.003929302096366882,
0.04428701847791672,
0.022092480212450027,
-0.0066245682537555695,
0.05954904854297638,
-0.028070993721485138,
-0.045138221234083176,
-0.010237384587526321,
0.010607476346194744,
-0.02898283861577511,
0.004346583038568497,
0.008716169744729996,
0.007135892752557993,
0.07098540663719177,
-0.06380339711904526,
0.0283033549785614,
0.016416089609265327,
-0.018451331183314323,
0.013783436268568039,
0.008789506740868092,
-0.012268478982150555,
0.07073932886123657,
-0.026911308988928795,
0.022657500579953194,
-0.07299569994211197,
0.06582046300172806,
0.02145545929670334,
0.04514662176370621,
0.023746468126773834,
-0.02657456137239933,
0.002521226182579994,
0.02556423656642437,
-0.009870133362710476,
0.07327615469694138,
-0.003925129305571318,
-0.02949325554072857,
-0.009279083460569382,
-0.06785274296998978,
0.019610481336712837,
0.016441242769360542,
-0.01941775716841221,
-0.07089982181787491,
0.0018206642707809806,
0.017763037234544754,
-0.04781665652990341,
0.011691924184560776,
-0.017223361879587173,
-0.05481474846601486,
0.02591884881258011,
0.005216695833951235,
-0.04127524420619011,
0.009481900371611118,
-0.03681815043091774,
-0.018375206738710403,
-0.03798362985253334,
0.0198258887976408,
-0.03421977162361145,
0.000075216667028144,
0.03227052465081215,
-0.008321797475218773,
0.06263208389282227,
0.03116668574512005,
-0.030474793165922165,
0.003728550625964999,
0.07725457102060318,
0.014277031645178795,
0.04612962156534195,
-0.030220365151762962,
0.020499007776379585,
-0.04318097606301308,
0.05658901110291481,
0.0004509073041845113,
0.06859342753887177,
-0.011314778588712215,
0.0062735071405768394,
-0.005125667434185743,
-0.01823505386710167,
-0.05038830265402794,
-0.04550010710954666,
-0.08224484324455261,
-0.014005864970386028,
-0.04376184567809105,
0.009563945233821869,
0.06903883069753647,
-0.03677603229880333,
-0.05889353156089783,
-0.01858026161789894,
0.012050596065819263,
-0.007461804896593094,
0.03733008727431297,
-0.023617753759026527,
-0.0027182744815945625,
-0.02787475287914276,
0.011356828734278679,
0.023936279118061066,
-0.05180500075221062,
-0.016319649294018745,
0.05086521804332733,
-0.060225896537303925,
0.009493883699178696,
0.005619425792247057,
-0.020265648141503334,
0.016315685585141182,
-0.04301503300666809,
0.017880050465464592,
-0.02579258568584919,
-0.003558941651135683,
-0.04233182966709137,
0.01104555744677782,
0.06521322578191757,
0.058463141322135925,
-0.07301578670740128,
0.00006893283716635779,
-0.012343714945018291,
0.009559571743011475,
-0.025062892585992813,
-0.0027104781474918127,
0.051245637238025665,
-0.017541445791721344,
-0.005292339716106653,
-0.07100141793489456,
0.0015404619043692946,
-0.038874510675668716,
-0.042288195341825485,
-0.032912783324718475,
-0.013093032874166965,
-0.013946225866675377,
-0.015540923923254013,
0.04557765647768974,
0.014523438178002834,
-0.0043034180998802185,
0.055956508964300156,
0.0019178286893293262,
-0.009238822385668755,
-0.02557559683918953,
-0.0069260853342711926,
0.031640131026506424,
0.018178341910243034,
-0.04895598068833351,
-0.016669688746333122,
-0.039422161877155304,
-0.024156004190444946,
0.004083586856722832,
-0.07421675324440002,
0.03571239858865738,
-0.012473422102630138,
-0.024528855457901955,
-0.05334538221359253,
0.04472952336072922,
-0.04064866900444031,
0.02003912813961506,
0.0321890227496624,
-0.0715547576546669,
0.00496767507866025,
-0.006362703628838062,
-0.02273675613105297,
0.022968053817749023,
-0.028074702247977257,
-0.012622986920177937,
-0.007960164919495583,
-0.006275869440287352,
-0.038067352026700974,
-0.047848619520664215,
-0.020479917526245117,
0.01654888316988945,
-0.029622472822666168,
-0.021611683070659637,
0.021822713315486908,
-0.06722550094127655,
0.048287685960531235,
-0.00004658406396629289,
-0.03759588301181793,
-0.003293142421171069,
0.029277656227350235,
-0.02710241638123989,
-0.032281335443258286,
0.035808030515909195,
-0.02938646823167801,
0.017598778009414673,
-0.02295561134815216,
-0.04432111978530884,
0.021201156079769135,
0.0427669882774353,
0.04023172706365585,
0.01829562708735466,
0.013482334092259407,
-0.02941177599132061,
0.028407828882336617,
-0.019167261198163033,
0.029762011021375656,
0.022146891802549362,
0.011164351366460323,
-0.03989569470286369,
-0.04338795319199562,
-0.030403710901737213,
-0.05592270568013191,
0.03479599207639694,
0.03355823829770088,
-0.004753452725708485,
-0.002504157368093729,
0.03705992177128792,
-0.008946683257818222,
0.027276430279016495,
-0.005805211141705513,
-0.024393513798713684,
0.020742636173963547,
0.0013421999756246805,
-0.0013083976227790117,
-0.00607654545456171,
0.03265790268778801,
0.041663672775030136,
0.036942582577466965,
-0.04326982423663139,
-0.022901520133018494,
0.01766345649957657,
0.009121979586780071,
0.0059782592579722404,
-0.00752807455137372,
-0.024745147675275803,
-0.030491868034005165,
0.021957404911518097,
-0.02809590846300125,
0.045084599405527115,
0.00802812073379755,
0.005125991068780422,
-0.03131524845957756,
-0.03092794306576252,
-0.01820935681462288,
-0.0441155880689621,
0.02228826843202114,
0.0363427959382534,
0.005993513856083155,
0.05617162957787514,
-0.029228592291474342,
-0.05195096507668495,
-0.01005710568279028,
0.0032993776258081198,
-0.019673218950629234,
-0.007189953699707985,
-0.04762468487024307,
-0.011129936203360558,
-0.015469325706362724,
-0.007971111685037613,
-0.02079159952700138,
-0.00998569093644619,
0.017414873465895653,
0.052091747522354126,
0.021654099225997925,
-0.006395071744918823,
-0.011395919136703014,
-0.0026396666653454304,
0.09976043552160263,
0.020793942734599113,
-0.052218906581401825,
-0.05166459456086159,
-0.051206883043050766,
-0.002464328659698367,
-0.03278256207704544,
0.034219399094581604,
-0.003507513552904129,
-0.035639017820358276,
0.010926996357738972,
-0.05442046746611595,
0.09077637642621994,
-0.015143473632633686,
0.044707681983709335,
0.05070988088846207,
-0.015452796593308449,
0.02504635602235794,
0.027665533125400543,
0.011991706676781178,
-0.0023342168424278498,
0.025693312287330627,
-0.04940731078386307,
-0.010120624676346779,
-0.046106383204460144,
0.022522790357470512,
0.02605351246893406,
-0.01921200565993786,
-0.008837246336042881,
-0.05595433712005615,
-0.0025400531012564898,
-0.04259881749749184,
-0.05565918609499931,
-0.042616281658411026,
0.03892775997519493,
-0.022160222753882408,
-0.046886492520570755,
-0.010516582988202572,
0.01840207912027836,
0.05285191163420677,
-0.015681089833378792,
-0.03593846410512924,
0.043487340211868286,
-0.074822336435318,
-0.021443109959363937,
0.027627063915133476,
0.03562908619642258,
0.013246091082692146,
-0.060977768152952194,
0.044719941914081573,
-0.003929271828383207,
-0.011876952834427357,
0.024974467232823372,
0.07649149745702744,
-0.04741489142179489,
-0.02489410527050495,
0.010275069624185562,
0.016858981922268867,
0.09456741064786911,
0.004852724727243185,
-0.039448417723178864,
0.025305261835455894,
0.025604967027902603,
0.03267005831003189,
-0.013815304264426231,
0.012541141360998154,
0.060254909098148346,
0.008800536394119263,
0.0017706543439999223,
0.0024785688146948814,
-0.02857024222612381,
0.04840947315096855,
0.0017021048115566373,
0.006386140361428261,
-0.04654921591281891,
-0.10437621176242828,
0.06047520786523819,
0.016223344951868057,
0.007712876424193382,
0.025615354999899864,
0.046725910156965256,
0.04739959537982941,
-0.014649206772446632,
-0.043111108243465424,
0.016445061191916466,
-0.0014006166020408273,
-0.04810177534818649,
-0.0505707822740078,
0.025925686582922935,
-0.0007027048850432038,
-0.014555899426341057,
0.06733417510986328,
0.0005647457437589765,
0.012814431451261044,
0.003736787708476186,
-0.007413179613649845,
-0.00879978109151125,
0.05439447984099388,
0.0021341932006180286,
-0.025549547746777534,
0.047351304441690445,
-0.0492725633084774,
-0.016078725457191467,
0.01470220647752285,
0.056052353233098984,
-0.013875823467969894,
0.03882705792784691,
0.01048724539577961,
-0.026158524677157402,
-0.0525602325797081,
-0.004102316685020924,
-0.021102871745824814,
0.014259552583098412,
0.021556735038757324,
-0.009554639458656311,
-0.024885669350624084,
-0.002619364997372031,
0.009930037893354893,
0.018863163888454437,
0.01987409219145775,
-0.0008517646929249167,
-0.030766082927584648,
-0.018009580671787262,
0.0450013130903244,
-0.014282655902206898,
-0.013056939467787743,
-0.019306404516100883,
-0.031502749770879745,
0.016900839284062386,
-0.0426827147603035,
0.02782679907977581,
-0.00012764052371494472,
-0.0061037577688694,
-0.017991865053772926,
0.040924739092588425,
0.05703635513782501,
0.060310665518045425,
-0.012439640238881111,
0.02702288329601288,
-0.0061479974538087845,
-0.014787433668971062,
0.016969462856650352,
0.029315145686268806,
0.06333499401807785,
0.011777712032198906,
0.016639336943626404,
0.049995306879282,
0.026638397946953773,
0.06098341941833496,
0.04077760875225067,
-0.00596698047593236,
-0.0788746178150177,
-0.05122537538409233,
-0.07155484706163406,
-0.027126142755150795,
-0.008482103236019611,
0.02795049361884594,
0.032407261431217194,
-0.03307013213634491,
-0.043019477277994156,
0.004763469565659761,
-0.00988161563873291,
-0.043518487364053726,
0.04751679673790932,
0.05442102625966072,
0.05650117248296738,
0.00037344248266890645,
-0.014488469809293747,
-0.0412718690931797,
0.0562177374958992,
0.00011855493357870728,
0.09226544201374054,
0.07932676374912262,
-0.005869670771062374,
0.019712021574378014,
0.040504079312086105,
0.01675785891711712,
0.021361643448472023,
0.022435206919908524,
0.048647865653038025,
0.043089576065540314,
0.012437806464731693,
0.03261581063270569,
0.010669196024537086,
0.03536304458975792,
-0.036848779767751694,
-0.022229710593819618,
-0.011059150099754333,
0.0017592536751180887,
-0.0616517998278141,
-0.04680798575282097,
-0.0636262446641922,
0.07993476092815399,
0.03364424407482147,
-0.01050550490617752,
0.007677376735955477,
-0.00920296274125576,
-0.008953001350164413,
0.022920571267604828,
0.019308868795633316,
0.010516644455492496,
-0.058767203241586685,
0.0911506935954094,
0.08945538103580475,
0.020792551338672638,
0.028935452923178673,
0.0031617044005542994,
-0.03609554469585419,
0.03862409666180611,
0.017506590113043785,
-0.022668175399303436,
-0.066712886095047,
-0.008127112872898579,
0.021635357290506363,
0.006993188057094812,
0.0038501406088471413,
0.022053416818380356,
0.0783999115228653,
-0.04459694027900696,
-0.06172360107302666,
0.02755337581038475,
0.0052594877779483795,
0.007318261079490185,
-0.08433748036623001,
-0.03446619585156441,
0.021411610767245293,
-0.023893261328339577,
-0.05028509348630905,
-0.025271840393543243,
-0.003301426535472274,
0.004908801522105932,
-0.029980456456542015,
0.015742547810077667,
0.04269460216164589,
-0.026438573375344276,
-0.027337368577718735,
0.024080127477645874,
-0.02426774799823761,
0.0028698681853711605,
0.019480878487229347,
0.047634270042181015,
-0.00010827140795299783,
-0.053721390664577484,
-0.02589213289320469,
0.022550832480192184,
-0.018691854551434517,
-0.05153180658817291,
-0.02164641208946705,
0.02016231045126915,
0.010379917919635773,
0.04582447558641434,
0.05844596028327942,
-0.003029675455763936,
0.02088458277285099,
-0.018328344449400902,
0.029956137761473656,
0.02258976176381111,
0.02489696815609932,
-0.0351368710398674,
-0.04850216582417488,
0.02691824361681938,
0.03259243443608284,
0.03398316726088524,
-0.05483097583055496,
-0.010695615783333778,
0.011720160953700542,
-0.01743660867214203,
-0.04321938008069992,
-0.025048429146409035,
-0.0433969683945179,
-0.016204338520765305,
0.03530028834939003,
0.06996370851993561,
0.013917378149926662,
-0.054705142974853516,
0.008587079122662544,
-0.08906986564397812,
-0.03412241116166115,
0.01654418557882309,
0.02930968999862671,
0.006965874694287777,
-0.0023941921535879374,
-0.02285347692668438,
-0.07376529276371002,
0.06830480694770813,
-0.04045550525188446,
-0.04078444465994835,
0.04566439613699913,
0.03313196823000908,
0.035115353763103485,
0.0018885203171521425,
-0.060533855110406876,
0.01988336071372032,
-0.05689159408211708,
0.0029101120308041573,
0.056567806750535965,
-0.01361796259880066,
-0.02247408963739872,
-0.09297937899827957,
-0.004428023938089609,
0.019856605678796768,
0.029801996424794197,
-0.05407648906111717,
-0.026483818888664246,
0.010252476669847965,
-0.03342084586620331,
-0.02195753902196884,
0.007549515459686518,
0.09859359264373779,
-0.03821674361824989,
0.00667595025151968,
0.03242136910557747,
-0.028271997347474098,
-0.038125842809677124,
-0.007510048802942038,
0.10607980936765671,
-0.0670817568898201,
-0.02110343985259533,
0.003991713281720877,
-0.005053491797298193,
-0.050743021070957184,
-0.003430906916037202,
-0.023912152275443077,
0.015242855995893478,
0.0024686341639608145,
0.01692250929772854,
0.046283479779958725,
-0.021130569279193878,
0.007467480376362801,
0.0519503653049469,
-0.0739036276936531,
-0.006032763049006462,
0.02048000507056713,
-0.038119010627269745,
0.03411947563290596,
-0.06753623485565186,
-0.0036268921103328466,
0.005031869746744633,
-0.019668374210596085,
-0.02237331122159958,
-0.03874947875738144,
-0.0333714596927166,
0.01652478612959385
] |
<p>I think this is a question about the mathematical axioms of quantum mechanics...</p>
<p>Consider the following operators $\tilde{x}$ and $\tilde{p}$ on Hilbert space $L^2(R)$, defined for fixed $\delta>0$:
$$
(\tilde{x}\psi)(x) = (n+1/2) \delta\ \psi(x)
$$
when $n\delta \leq x <(n+1)\delta$ for some integer $n$; and
$$
(\tilde{p}\psi)(x) = -i \hbar \frac{d\psi}{dx}(x)
$$
when $n\delta < x < (n+1) \delta$, and $(\tilde{p}\psi)(x) = 0$ when $x=n\delta$.</p>
<p>Both these operators are self-adjoint and they commute. Further, $\tilde{p}$ is identical to the usual momentum operator $\hat{p} = -i\hbar \frac{d}{dx}$ on the subspace of $L^2(R)$ on which $\hat{p}$ is defined, and thus has identical spectrum. Finally, by taking $\delta$ small we can make $\tilde{x}$ as close as we like to the usual position operator, $\hat{x}$. Thus naively it looks like $\tilde{x}$ and $\tilde{p}$ represent compatible observables which can be made arbitrarily close to $\hat{x}$ and $\hat{p}$.</p>
<p>I'm pretty sure that I've cheated somewhere, but I can't find anything in the axioms of quantum mechanics that rules out defining observables $\tilde{x}$ and $\tilde{p}$ as above (or at least, the axioms as they are usually presented in under/graduate physics texts). Is there some requirement that observable operators should map $C^\infty$ functions to $C^\infty$ functions? In any case, I'd be grateful if someone could tell me why the above is ruled out.</p>
<p>(As background, I am teaching an undergraduate class on quantum mechanics next semester and I wanted to explain to students that while it's not possible to make exact simultaneous measurement of position and momentum; it is possible to make an approximate simultaneous measurement. In other words, I wanted to find operators which approximate $\hat{x}$ and $\hat{p}$ on 'macroscopic' scales and which commute. This was before I looked in the literature and realised how technical constructing such approximate operators is.)</p> | g7835 | [
-0.022171128541231155,
0.003670735051855445,
-0.019182464107871056,
-0.06809078902006149,
0.023297009989619255,
0.03586830943822861,
0.04729614779353142,
-0.039664339274168015,
-0.06823667883872986,
0.008500694297254086,
-0.0008399125654250383,
0.0013040160993114114,
-0.016972260549664497,
0.012438599020242691,
0.010703160427510738,
-0.03748125955462456,
0.05869800224900246,
-0.007009669207036495,
0.0028860345482826233,
-0.03247129172086716,
-0.017282120883464813,
0.02168787084519863,
0.00659809960052371,
-0.04752793908119202,
-0.013590528629720211,
-0.041897840797901154,
0.0044144741259515285,
-0.0096444021910429,
-0.005734206642955542,
0.007215212564915419,
0.027641693130135536,
0.004734408110380173,
0.04862062633037567,
0.002565366681665182,
-0.01948309689760208,
-0.026813147589564323,
0.08397366106510162,
0.0022096058819442987,
0.05181336775422096,
-0.024312663823366165,
-0.005588337313383818,
-0.08920808136463165,
0.06418438255786896,
-0.04967961087822914,
-0.013442052528262138,
0.019217442721128464,
0.05521243438124657,
-0.0011018628720194101,
0.038747165352106094,
0.04420885443687439,
0.008289303630590439,
0.03288144990801811,
0.07488254457712173,
0.039941076189279556,
0.02795657329261303,
0.051798149943351746,
-0.01877700909972191,
-0.008800695650279522,
0.004780452698469162,
0.018055777996778488,
-0.0058929952792823315,
-0.003646752331405878,
0.04075998067855835,
0.05314074829220772,
0.003939330577850342,
0.01942279189825058,
0.019378304481506348,
0.006125632207840681,
-0.02700209431350231,
-0.035769425332546234,
0.006344590336084366,
-0.024822253733873367,
0.01557410228997469,
0.014990068040788174,
-0.04230457544326782,
0.021660827100276947,
-0.026567667722702026,
-0.04072890430688858,
-0.025253184139728546,
0.03387574851512909,
-0.03718390688300133,
-0.0303847324103117,
0.019019559025764465,
-0.018290748819708824,
0.03591288626194,
0.007510761264711618,
-0.022374853491783142,
-0.008285319432616234,
0.010358604602515697,
0.024007156491279602,
-0.00891320500522852,
-0.045141659677028656,
0.05507398769259453,
0.03837726265192032,
-0.032779090106487274,
-0.01566682569682598,
-0.015623276121914387,
0.05733024701476097,
-0.017060888931155205,
0.011612878181040287,
-0.0011224057525396347,
0.07489462941884995,
-0.022098736837506294,
-0.007368373218923807,
0.0057973978109657764,
-0.015529753640294075,
0.03056202456355095,
-0.03125445544719696,
0.04432336241006851,
0.00207716878503561,
-0.028890494257211685,
0.015949063003063202,
-0.006692172028124332,
-0.0555875338613987,
0.040849469602108,
-0.04768342152237892,
0.022013237699866295,
-0.004867885261774063,
-0.07641460746526718,
0.07738615572452545,
0.03432207927107811,
0.003691594349220395,
0.04700788855552673,
0.07914552092552185,
0.04305340349674225,
0.01600993610918522,
-0.05994969233870506,
-0.0015194303123280406,
0.006389038171619177,
-0.001095696003176272,
0.011972405016422272,
0.023662565276026726,
-0.026887280866503716,
0.04165908321738243,
-0.0438321977853775,
-0.0009551941766403615,
-0.041483134031295776,
-0.025351611897349358,
0.021778294816613197,
-0.05797296017408371,
-0.04142304137349129,
-0.006989256478846073,
-0.01451302319765091,
0.039498068392276764,
0.014793341048061848,
0.006124376785010099,
-0.008455676957964897,
-0.025065237656235695,
0.05218119919300079,
0.028989916667342186,
0.005120056215673685,
0.09298829734325409,
-0.021622389554977417,
0.09069617837667465,
-0.011357622221112251,
0.001789564499631524,
0.032103847712278366,
0.0283175278455019,
-0.002953669521957636,
0.02327180840075016,
0.02036477066576481,
0.0426056794822216,
0.04558144137263298,
-0.014892080798745155,
-0.002267540665343404,
-0.007478212472051382,
0.011356345377862453,
-0.054200585931539536,
-0.015928104519844055,
-0.07255971431732178,
-0.04153740778565407,
-0.011025143787264824,
0.06790203601121902,
-0.03569000959396362,
0.015523381531238556,
0.05098099634051323,
-0.034835461527109146,
-0.03572804108262062,
0.008832760155200958,
0.026226365938782692,
-0.008678946644067764,
0.006805571261793375,
0.007436532527208328,
-0.05235029757022858,
-0.015229274518787861,
0.016102701425552368,
0.03186909854412079,
-0.054083555936813354,
-0.02386242151260376,
0.002003462053835392,
0.02714911662042141,
0.007562483660876751,
0.022868292406201363,
0.06409130990505219,
-0.009324238635599613,
0.028905460610985756,
0.023012785241007805,
-0.048730213195085526,
-0.006699447054415941,
-0.004378913436084986,
0.03807135298848152,
0.027896298095583916,
0.028645794838666916,
0.001700149616226554,
0.0033400615211576223,
0.06565334647893906,
0.00012215848255436867,
-0.017641769722104073,
0.031957097351551056,
0.008375592529773712,
0.0444190576672554,
-0.08911977708339691,
-0.038250770419836044,
-0.012297229841351509,
0.010334938764572144,
-0.008254870772361755,
0.014834584668278694,
-0.011834229342639446,
-0.008988412097096443,
0.0005415635532699525,
0.008995907381176949,
-0.03787310793995857,
0.03367873281240463,
0.007132523227483034,
-0.01847228594124317,
0.04185759648680687,
-0.06010010093450546,
0.0007265839376486838,
-0.03881845623254776,
0.022982778027653694,
-0.0034414161927998066,
0.0004059849597979337,
0.003484737826511264,
0.01274842955172062,
0.01511489599943161,
0.03085283748805523,
0.03291865810751915,
0.02807391621172428,
0.02114010602235794,
0.04741667956113815,
0.06984072178602219,
0.0017552421195432544,
-0.02948988415300846,
0.025769181549549103,
0.04461013525724411,
0.0299825519323349,
0.030855678021907806,
0.037438105791807175,
-0.008931194432079792,
0.04142683371901512,
-0.07284403592348099,
0.011032374575734138,
-0.02107599563896656,
0.005190098192542791,
-0.03479941934347153,
-0.016207002103328705,
0.03705070912837982,
-0.021029654890298843,
-0.02945316955447197,
0.008923364803195,
-0.05085865408182144,
0.021006403490900993,
-0.03921531140804291,
0.04022832587361336,
-0.041658200323581696,
0.0053575304336845875,
-0.028214912861585617,
0.0531703419983387,
0.018382731825113297,
-0.017373308539390564,
0.04246918484568596,
0.02011706307530403,
0.018533827736973763,
0.06862188875675201,
0.006165953353047371,
-0.07921841740608215,
-0.05432960391044617,
-0.10122491419315338,
-0.032655563205480576,
-0.034902773797512054,
-0.05687730759382248,
0.04662620648741722,
-0.06629122793674469,
0.003072261344641447,
0.05023927986621857,
-0.0637529268860817,
0.027083173394203186,
0.023831820115447044,
-0.03303617984056473,
0.014226427301764488,
0.03965483233332634,
-0.02520659938454628,
0.0031179599463939667,
0.03511964902281761,
-0.04874923452734947,
0.019313344731926918,
0.01778624765574932,
-0.006185651291161776,
-0.017676550894975662,
0.07111161202192307,
0.018278002738952637,
0.006211873143911362,
0.028236940503120422,
0.029028495773673058,
0.07605647295713425,
-0.017606345936655998,
-0.07237652689218521,
-0.00823379959911108,
-0.03323083370923996,
0.04341229423880577,
-0.02448885701596737,
0.00890436489135027,
-0.05953012779355049,
-0.05809025466442108,
0.05384848639369011,
-0.03818226978182793,
-0.07196936011314392,
-0.057435546070337296,
-0.047911982983350754,
-0.013387996703386307,
0.00527827488258481,
-0.01790853776037693,
0.009259101934731007,
-0.02562333084642887,
0.06147312745451927,
0.044545892626047134,
-0.06315302103757858,
0.07395122200250626,
-0.017643112689256668,
-0.05443860962986946,
0.025939008221030235,
0.028268026188015938,
0.021609367802739143,
-0.006324585992842913,
-0.04985310509800911,
-0.047472186386585236,
0.03571029007434845,
0.02329447492957115,
0.0410725399851799,
0.027006151154637337,
-0.003653351217508316,
0.01917623169720173,
-0.03536362573504448,
0.024904467165470123,
-0.006909749936312437,
-0.026846664026379585,
0.0009399327682331204,
0.05566601827740669,
-0.008250782266259193,
-0.007895808666944504,
-0.02646949514746666,
0.0005231196410022676,
0.07989107817411423,
-0.018423153087496758,
0.026877770200371742,
0.03797426447272301,
0.03191358596086502,
0.016949225217103958,
0.03717649728059769,
-0.028392836451530457,
0.024265917018055916,
-0.03317439183592796,
0.0014966885792091489,
-0.011403178796172142,
-0.04285944625735283,
-0.021347973495721817,
-0.019338957965373993,
0.00354912132024765,
0.014110558666288853,
-0.0076469494961202145,
-0.016299376264214516,
0.013949451968073845,
-0.0019310167990624905,
-0.04112067073583603,
0.040006764233112335,
-0.056077659130096436,
0.0608992800116539,
-0.06599458307027817,
-0.008622748777270317,
-0.0029676093254238367,
-0.018564725294709206,
0.038911860436201096,
0.030781829729676247,
0.016996683552861214,
0.04903727024793625,
0.02627641148865223,
0.011819977313280106,
-0.004661979153752327,
0.04952714592218399,
-0.03305380046367645,
0.02853422611951828,
-0.08326859772205353,
0.018845228478312492,
0.010109225288033485,
0.04860776290297508,
0.007850310765206814,
0.029135344550013542,
-0.027253879234194756,
-0.004999686032533646,
0.029422035440802574,
-0.027865100651979446,
-0.03032982163131237,
-0.029246307909488678,
0.02094004489481449,
-0.04030998796224594,
-0.029559096321463585,
0.02304508164525032,
0.03877188637852669,
0.03059716522693634,
-0.015824580565094948,
-0.007023519370704889,
0.008043942973017693,
0.0034558342304080725,
0.015031314454972744,
-0.026641566306352615,
0.05021068453788757,
-0.016941092908382416,
-0.022575298324227333,
0.0019503944786265492,
0.00795949436724186,
-0.053130846470594406,
0.08740238845348358,
0.0007253129151649773,
-0.00998021848499775,
-0.00035922115785069764,
0.046601567417383194,
0.049133606255054474,
-0.022454269230365753,
0.009750157594680786,
-0.03017510659992695,
-0.030273767188191414,
0.005486504174768925,
0.014854757115244865,
0.08618102222681046,
-0.017341529950499535,
-0.020676277577877045,
-0.05999341979622841,
0.020521538332104683,
-0.01747230812907219,
0.033955033868551254,
0.021643968299031258,
0.012380319647490978,
-0.04937353730201721,
-0.013316983357071877,
-0.027271844446659088,
0.005052830558270216,
-0.02161305770277977,
-0.05384618788957596,
-0.03038805164396763,
0.026859760284423828,
-0.02932640351355076,
0.02913079410791397,
-0.010344546288251877,
0.009904925711452961,
0.006192119792103767,
-0.057510387152433395,
0.008078241720795631,
0.00777567969635129,
-0.003038005204871297,
-0.04427332431077957,
-0.006281313020735979,
-0.02713196910917759,
0.01818486675620079,
0.025491591542959213,
0.025520475581288338,
0.037459954619407654,
-0.13820402324199677,
0.017565548419952393,
-0.07266067713499069,
-0.08214347809553146,
0.06392896920442581,
0.04234454035758972,
0.031138328835368156,
-0.014883422292768955,
-0.016500750556588173,
-0.02079983614385128,
-0.0027278419584035873,
-0.018643110990524292,
0.04581870138645172,
-0.018166175112128258,
-0.035397011786699295,
0.011044246144592762,
0.005740821361541748,
0.0019396482966840267,
-0.0056637926027178764,
0.017833774909377098,
-0.06049242243170738,
-0.0180641058832407,
0.012883884832262993,
-0.022981807589530945,
0.04450313374400139,
0.07018443197011948,
0.020709652453660965,
-0.0012407853500917554,
0.0014429113361984491,
0.013383585959672928,
-0.051739927381277084,
-0.020143181085586548,
-0.022172898054122925,
0.0048942347057163715,
-0.08133648335933685,
0.002484329743310809,
-0.009941751137375832,
0.009131290018558502,
0.03355284407734871,
-0.015627041459083557,
0.09209921211004257,
0.028366953134536743,
-0.008415746502578259,
0.010729461908340454,
-0.010692763142287731,
0.030489247292280197,
0.020895471796393394,
-0.021705036982893944,
0.033242709934711456,
0.03150037303566933,
-0.0030966189224272966,
-0.014031053520739079,
-0.0786060318350792,
-0.06737814098596573,
0.02913775108754635,
-0.03961591050028801,
0.04520538076758385,
-0.02048499509692192,
0.04631656035780907,
0.024417104199528694,
-0.02906223200261593,
-0.06562578678131104,
-0.07513371109962463,
0.05020979791879654,
0.07663322240114212,
0.016048278659582138,
0.024239961057901382,
-0.05631954222917557,
-0.045330461114645004,
-0.049013927578926086,
-0.018229341134428978,
-0.03198282793164253,
0.003319478128105402,
-0.002396599156782031,
-0.019499771296977997,
-0.05425757169723511,
-0.02377757430076599,
0.0712098553776741,
-0.008375815115869045,
-0.03184173256158829,
0.021186871454119682,
-0.036200787872076035,
-0.018632423132658005,
-0.04747492074966431,
-0.03164829686284065,
-0.014899059198796749,
-0.07203178852796555,
-0.03937573730945587,
0.021834827959537506,
0.03217737749218941,
-0.028574177995324135,
-0.018217355012893677,
-0.02965671382844448,
-0.006286767311394215,
0.04498002678155899,
-0.027457240968942642,
0.02071036398410797,
-0.006687902379781008,
0.008261719718575478,
0.003175819991156459,
-0.03245696425437927,
0.019726969301700592,
0.02941550500690937,
0.041007332503795624,
-0.027597948908805847,
0.03481839969754219,
0.06106574088335037,
0.00884045660495758,
0.01692146062850952,
0.027799544855952263,
0.016227250918745995,
-0.007666850462555885,
-0.007892271503806114,
-0.0024046129547059536,
0.020278779789805412,
0.003027252620086074,
0.007884243503212929,
-0.02579926885664463,
-0.04468630626797676,
0.0777839794754982,
-0.023552630096673965,
-0.03334059566259384,
0.047090448439121246,
0.03290870040655136,
-0.05637700483202934,
-0.022907275706529617,
-0.05130748450756073,
0.011173841543495655,
-0.003530387068167329,
0.026537859812378883,
0.051546789705753326,
-0.03280358761548996,
-0.02581428550183773,
-0.021769661456346512,
0.018268471583724022,
-0.0306157935410738,
0.09902901202440262,
-0.03605562448501587,
-0.034304555505514145,
0.10797624289989471,
-0.03489110246300697,
-0.0021725245751440525,
-0.051468588411808014,
-0.0002909272152464837,
-0.07247935235500336,
0.04011213406920433,
0.01370366383343935,
0.026753073558211327,
-0.050953641533851624,
-0.06879668682813644,
-0.029346443712711334,
0.07366493344306946,
-0.005098022520542145,
0.047039542347192764,
0.06304576247930527,
-0.013234775513410568,
-0.014238026924431324,
-0.006925106514245272,
-0.02632291615009308,
0.037941399961709976,
0.02602846920490265,
0.0627666711807251,
0.006974407006055117,
-0.005686781834810972,
-0.0029842685908079147,
-0.019286533817648888,
0.01475920807570219,
0.00420208927243948,
-0.022871747612953186,
0.02589326910674572,
-0.018419362604618073,
-0.014973167330026627,
-0.0014439906226471066,
0.035625722259283066,
-0.019983943551778793,
0.037038080394268036,
0.026133866980671883,
-0.008195850998163223,
0.005820918828248978,
-0.042263422161340714,
0.013449183665215969,
-0.047497306019067764,
-0.102518729865551,
0.017528865486383438,
0.008667982183396816,
-0.00030610107933171093,
-0.01381629053503275,
0.01726687327027321,
0.008312474936246872,
0.01154820341616869,
0.0339035727083683,
-0.013541814871132374,
-0.020231707021594048,
-0.06876596063375473,
0.011744973249733448,
-0.03121747449040413,
-0.04678880795836449,
-0.01910264976322651,
-0.011824160814285278,
0.08208540827035904,
-0.021148519590497017,
-0.0179792158305645,
-0.046167608350515366,
-0.0016892125131562352,
0.0386338010430336,
-0.03600233048200607,
-0.009042691439390182,
0.02289576083421707,
-0.028698069974780083,
0.02669384889304638,
0.036014072597026825,
0.01582496426999569,
0.00021965977794025093,
-0.02853730134665966,
0.005643201060593128,
0.028329145163297653,
-0.03125789761543274,
0.02548915147781372,
-0.03524148836731911,
0.015611951239407063,
-0.013305915519595146,
-0.014805433340370655,
-0.00888709258288145,
-0.018688930198550224,
-0.010275759734213352,
-0.051472585648298264,
0.000005221989340498112,
-0.00027757760835811496,
0.04570555314421654,
-0.015466870740056038,
0.05548996478319168,
0.0298231840133667,
-0.0137452008202672,
0.018406538292765617,
0.01512459572404623,
-0.054070230573415756,
-0.01975184492766857,
0.007197746075689793,
0.013243542052805424,
0.05787144601345062,
-0.008224769495427608,
-0.06440060585737228,
-0.029116714373230934,
-0.015525109134614468,
0.014886892400681973,
-0.004960775375366211,
0.026345862075686455,
-0.04347529634833336,
0.09794815629720688,
-0.03362523019313812,
-0.07438594102859497,
0.0068038459867239,
0.05590970069169998,
-0.06738831847906113,
0.04425172507762909,
-0.02415255643427372,
0.016122492030262947,
-0.04086746275424957,
-0.032585639506578445,
-0.027711037546396255,
-0.03866799548268318,
-0.05901426076889038,
0.05285526067018509,
0.027353258803486824,
-0.03136679530143738,
-0.031016282737255096,
-0.036425165832042694,
-0.018765058368444443,
-0.06581871211528778,
0.028970003128051758,
0.013060196302831173,
0.04362575337290764,
-0.005416014231741428,
0.0025918344035744667,
-0.013405492529273033,
-0.09010878205299377,
0.0523383803665638,
0.040975477546453476,
0.03387989103794098,
0.007385244593024254,
0.022547312080860138,
-0.002614565659314394,
0.0014736870070919394,
-0.05415903404355049,
-0.02079003117978573,
0.05502137169241905,
-0.039726145565509796,
0.06540649384260178,
0.03173886984586716,
-0.06043447554111481,
0.007219179533421993,
0.04954524710774422,
0.04168516770005226,
0.052144136279821396,
0.00044304816401563585,
-0.004317026119679213,
-0.005107382778078318,
-0.03635706380009651,
-0.05828293040394783,
-0.01410389319062233,
0.0038046594709157944,
0.01879819482564926
] |
<p>I am wondering if there exist closed form-expressions for the time dilation experienced by an observer in different orbits around a Schwarzschild black hole, outside the event horizon, relative to some distant observer sitting fixed relative to the black hole. </p>
<p>I am no expert in GR, but I know these quickly turn into some complicated integrals. Any point in the right direction, even toward an approximate answer, would be much appreciated.</p> | g7836 | [
0.016865886747837067,
0.01192113570868969,
0.010860336944460869,
0.03151393309235573,
-0.028308572247624397,
0.034193817526102066,
0.022115113213658333,
0.00691105704754591,
-0.06473474949598312,
0.020799675956368446,
-0.019230518490076065,
0.035612255334854126,
0.0026715088170021772,
0.0376388244330883,
0.016734452918171883,
-0.012425090186297894,
0.026221299543976784,
-0.03244844079017639,
-0.06891045719385147,
0.012120939791202545,
0.047391463071107864,
-0.023396756500005722,
-0.015199829824268818,
0.042853351682424545,
0.008181179873645306,
-0.011824331246316433,
0.03123212605714798,
0.021229512989521027,
-0.06521381437778473,
-0.038849763572216034,
0.033546082675457,
0.008616307750344276,
-0.002350019058212638,
0.03454804793000221,
0.06781570613384247,
0.029323425143957138,
-0.004596724174916744,
0.01928160898387432,
0.0132930688560009,
0.029312340542674065,
0.03024696744978428,
-0.03670669347047806,
-0.024688182398676872,
0.016673628240823746,
0.05042817071080208,
-0.03900197893381119,
0.023480063304305077,
0.01994207873940468,
0.025891555473208427,
-0.034816231578588486,
-0.022185157984495163,
0.05819866061210632,
0.03939848765730858,
-0.04022833704948425,
0.03231658414006233,
0.044426046311855316,
-0.010934136807918549,
-0.012136446312069893,
-0.024638168513774872,
0.04632510617375374,
-0.0028431883547455072,
-0.07166460901498795,
-0.01652079075574875,
-0.02636224403977394,
0.07537075132131577,
-0.01440947875380516,
-0.028388310223817825,
-0.03569125384092331,
-0.022750528529286385,
0.030746150761842728,
0.007087002974003553,
0.05803091078996658,
-0.06289570778608322,
-0.03706399351358414,
-0.02389199659228325,
0.026003900915384293,
-0.046468570828437805,
0.026674512773752213,
0.015986356884241104,
-0.026391098275780678,
-0.07135118544101715,
0.009697731584310532,
0.021509187296032906,
0.016412869095802307,
0.08489462733268738,
0.0354602113366127,
0.05799826607108116,
0.0300716795027256,
-0.0003690029843710363,
-0.004842404741793871,
0.02799074351787567,
-0.07101526111364365,
0.044244881719350815,
-0.026182811707258224,
0.0091670211404562,
0.051933109760284424,
-0.03093034215271473,
0.04167061299085617,
-0.021551284939050674,
0.04807817190885544,
-0.021775897592306137,
0.03967779129743576,
-0.03121425211429596,
-0.008856459520757198,
0.017951495945453644,
-0.0546702966094017,
-0.07720013707876205,
0.026616910472512245,
0.00044796508154831827,
-0.01092761754989624,
0.038652680814266205,
-0.09403490275144577,
0.02103453502058983,
-0.025742288678884506,
-0.05967143550515175,
-0.04426644369959831,
-0.028534354642033577,
-0.0009746894356794655,
-0.024702472612261772,
0.025664839893579483,
0.010431778617203236,
0.04164212942123413,
0.01255167555063963,
-0.011154036037623882,
0.0175054632127285,
0.013234986923635006,
-0.02041351981461048,
0.0030876018572598696,
-0.037064652889966965,
0.03662842884659767,
0.013780549168586731,
-0.0071299211122095585,
0.07501360774040222,
0.004136355128139257,
-0.07600516080856323,
0.020015137270092964,
0.00897663552314043,
0.009076771326363087,
-0.04545799642801285,
-0.002185956807807088,
0.025227125734090805,
-0.06084727868437767,
-0.02674098312854767,
-0.019981035962700844,
0.02655581198632717,
0.04599697142839432,
-0.052126508206129074,
-0.07486405223608017,
0.01185278408229351,
-0.023280296474695206,
0.005958964582532644,
0.07547818124294281,
-0.00992419570684433,
-0.004370260518044233,
0.019669312983751297,
0.02221326343715191,
-0.055584900081157684,
0.03302387520670891,
-0.02646452561020851,
0.04334746673703194,
0.02340582199394703,
-0.0047759986482560635,
0.011396544985473156,
-0.022741513326764107,
-0.037286870181560516,
0.050676651298999786,
0.030032873153686523,
-0.03046434000134468,
0.049121033400297165,
-0.06755558401346207,
-0.03490602597594261,
0.009141385555267334,
-0.012052866630256176,
-0.0010610626777634025,
-0.0004467198741622269,
0.04722728952765465,
-0.021459635347127914,
-0.02062339521944523,
0.004964618943631649,
0.06867892295122147,
-0.020039726048707962,
-0.012945045717060566,
-0.054985735565423965,
-0.038571637123823166,
0.07565691322088242,
-0.016273407265543938,
0.04917497560381889,
-0.06301174312829971,
-0.041622571647167206,
0.005104638170450926,
-0.0035392327699810266,
-0.02547784522175789,
0.0525071807205677,
0.027841761708259583,
-0.07375913113355637,
0.014063520357012749,
0.055702030658721924,
-0.04381299391388893,
-0.007149275857955217,
0.059816326946020126,
-0.041508130729198456,
0.023271752521395683,
0.03928185626864433,
0.009171553887426853,
0.07708052545785904,
0.06487275660037994,
-0.00045444362331181765,
0.00300574884749949,
0.013248585164546967,
0.006222046446055174,
-0.020568665117025375,
-0.027191419154405594,
0.042867593467235565,
0.0017347241519019008,
-0.019215675070881844,
0.035528529435396194,
0.0012414619559422135,
0.02468438446521759,
0.0317947082221508,
0.0239784587174654,
-0.04584747925400734,
-0.019093217328190804,
-0.019095877185463905,
-0.019132843241095543,
-0.029183540493249893,
0.02131262607872486,
-0.0010254516964778304,
0.034052714705467224,
0.045864786952733994,
0.03494279459118843,
-0.0884343609213829,
0.04826582595705986,
0.02393125742673874,
0.012890960089862347,
0.04246477782726288,
-0.01918914169073105,
0.03983614221215248,
-0.03335944190621376,
0.07148677110671997,
0.024509429931640625,
0.02581394463777542,
0.014820000156760216,
-0.07660084217786789,
-0.004529341123998165,
0.030539019033312798,
0.04161296784877777,
0.022066453471779823,
0.04548861086368561,
0.014372297562658787,
0.024464672431349754,
-0.0354921780526638,
-0.008722648024559021,
0.013403748162090778,
-0.021499518305063248,
-0.015129555948078632,
0.024849751964211464,
-0.010576068423688412,
0.0042229690589010715,
-0.06308125704526901,
-0.04678328335285187,
0.0015235166065394878,
-0.005302052479237318,
0.05115564540028572,
0.03127890080213547,
-0.0423782579600811,
-0.005889368709176779,
-0.009956449270248413,
-0.025774089619517326,
-0.005593619775027037,
0.04621802270412445,
-0.008906643837690353,
0.03349338844418526,
0.02678556740283966,
0.06956755369901657,
-0.00792489480227232,
-0.018829794600605965,
-0.04655316099524498,
0.034357186406850815,
0.04217077046632767,
0.022069916129112244,
-0.0023366310633718967,
-0.02880963869392872,
-0.07601192593574524,
0.014338462613523006,
0.0216215793043375,
-0.06773587316274643,
-0.0031015656422823668,
0.04737696796655655,
-0.006792648229748011,
0.00272068427875638,
0.0012646688846871257,
0.037084225565195084,
0.05241049826145172,
0.10145211964845657,
0.01119984034448862,
0.06554221361875534,
-0.02624855749309063,
-0.0020992294885218143,
-0.01697116531431675,
0.04895150288939476,
-0.028831584379076958,
-0.06777309626340866,
-0.013436436653137207,
0.05061016604304314,
0.01680772565305233,
0.008719162084162235,
-0.005764488596469164,
-0.01863706298172474,
0.012438622303307056,
-0.05201597139239311,
-0.06040491163730621,
-0.034162748605012894,
0.010565775446593761,
-0.043713342398405075,
-0.028389370068907738,
-0.035602569580078125,
-0.021870974451303482,
0.04122842848300934,
-0.014448722824454308,
-0.041520796716213226,
0.004349419381469488,
0.005032726563513279,
-0.02957768365740776,
0.01998903602361679,
-0.010376427322626114,
-0.01670052297413349,
-0.0376804955303669,
-0.01947787031531334,
-0.06519988924264908,
-0.00732406647875905,
-0.03962116315960884,
-0.043456580489873886,
-0.001585303689353168,
-0.0018727160058915615,
-0.009713554754853249,
-0.005476709920912981,
0.009326128289103508,
-0.017386343330144882,
0.053356122225522995,
-0.012853450141847134,
0.03103519231081009,
-0.002171131782233715,
-0.018355345353484154,
0.04780298098921776,
-0.023307841271162033,
-0.01742120459675789,
-0.022264568135142326,
0.004327257163822651,
-0.015402221120893955,
-0.07713603228330612,
-0.0020628427155315876,
0.02173159271478653,
0.011319235898554325,
-0.014581812545657158,
0.038213521242141724,
0.011206619441509247,
0.02206232398748398,
-0.002882635686546564,
0.024594824761152267,
0.015230310149490833,
0.007146297954022884,
0.005362709518522024,
-0.06673084199428558,
-0.006216405425220728,
-0.012602600269019604,
-0.06593737751245499,
0.03268524259328842,
-0.0501435287296772,
0.036192767322063446,
-0.036435503512620926,
0.024774344637989998,
0.011400612071156502,
0.038972657173871994,
-0.003825167892500758,
0.0339895524084568,
-0.05603718012571335,
0.003188349539414048,
0.047661472111940384,
-0.016488730907440186,
-0.01589183136820793,
-0.02536153234541416,
0.04971292242407799,
-0.002192070474848151,
0.0487850084900856,
0.032519180327653885,
-0.025641443207859993,
-0.03345216065645218,
-0.045834142714738846,
0.010415779426693916,
-0.032129161059856415,
0.005176495760679245,
-0.06885217875242233,
-0.01814427226781845,
0.010353134013712406,
0.015946095809340477,
0.015938689932227135,
0.001180725172162056,
-0.025757206603884697,
0.04689682647585869,
0.013574325479567051,
0.054920513182878494,
0.00968942977488041,
0.004442488308995962,
0.02977875806391239,
-0.03304048627614975,
-0.01354304701089859,
0.02900562807917595,
0.06720568984746933,
-0.03537926822900772,
0.014753690920770168,
0.005165931768715382,
-0.03162502497434616,
0.002395861316472292,
-0.017840076237916946,
0.03957119584083557,
0.012275449000298977,
0.0674995630979538,
-0.04701083153486252,
0.02422066032886505,
-0.009415555745363235,
-0.008473903872072697,
0.016558194532990456,
-0.029133368283510208,
0.033258453011512756,
-0.025430038571357727,
0.009380217641592026,
-0.028710059821605682,
0.07684509456157684,
-0.03787035122513771,
0.019413230940699577,
-0.007171256467700005,
-0.010459328070282936,
-0.03389166295528412,
0.037414804100990295,
-0.0840940922498703,
0.052970174700021744,
-0.03255729004740715,
0.03453221917152405,
-0.005768134258687496,
0.04325471445918083,
-0.04677616059780121,
0.03945546969771385,
-0.014525960199534893,
-0.03479854390025139,
0.046897802501916885,
0.04834795743227005,
-0.054801203310489655,
-0.06624121963977814,
-0.007350134197622538,
-0.05298006907105446,
-0.048676300793886185,
0.00017703672347124666,
-0.016207177191972733,
-0.017307789996266365,
0.021889450028538704,
0.016786135733127594,
0.03358390927314758,
0.020717497915029526,
0.032900065183639526,
-0.014532109722495079,
-0.03105894662439823,
-0.029472442343831062,
-0.03883397579193115,
-0.0032239872962236404,
-0.016388921067118645,
0.00778450071811676,
-0.06931822001934052,
0.036326948553323746,
-0.031077712774276733,
0.009049518033862114,
-0.024447068572044373,
0.027561524882912636,
0.06972090154886246,
-0.044810034334659576,
-0.06556282192468643,
0.055741336196660995,
-0.012085448950529099,
-0.05699719861149788,
0.02838338352739811,
-0.03143816068768501,
-0.054551705718040466,
0.012992426753044128,
0.04210973158478737,
0.03289303928613663,
-0.042316459119319916,
-0.0035377098247408867,
-0.017683926969766617,
-0.02175886370241642,
0.002601789077743888,
-0.023628637194633484,
0.032053615897893906,
-0.03002631478011608,
0.007911676540970802,
-0.01668468490242958,
-0.010559050366282463,
0.05702352151274681,
0.022850096225738525,
-0.03946052864193916,
0.06646671891212463,
-0.04151314124464989,
-0.02443242259323597,
0.010641640052199364,
0.012473306618630886,
-0.014745225198566914,
-0.01551733072847128,
0.07112891972064972,
0.013636812567710876,
-0.029209358617663383,
0.08944039791822433,
0.03676914423704147,
0.001958446344360709,
0.04965176433324814,
-0.02176048420369625,
0.03037320077419281,
-0.027237195521593094,
-0.052101895213127136,
0.037192925810813904,
-0.002699497388675809,
-0.02691715955734253,
-0.025735992938280106,
0.014292947016656399,
0.0211808905005455,
0.0071165901608765125,
0.05228300392627716,
0.047631438821554184,
-0.006617829203605652,
-0.03974715247750282,
0.008121836930513382,
-0.003419821383431554,
-0.021323151886463165,
0.04000352323055267,
-0.021286847069859505,
0.02837136946618557,
0.01471159141510725,
0.05044169723987579,
0.020674845203757286,
0.001252638059668243,
0.023976480588316917,
0.010531311854720116,
-0.010047778487205505,
-0.03600390627980232,
0.033198896795511246,
0.03635777533054352,
0.025693045929074287,
-0.027923500165343285,
0.006354366894811392,
-0.08808992803096771,
0.04284985363483429,
0.047245319932699203,
-0.033658090978860855,
-0.045055799186229706,
-0.0029555796645581722,
-0.032135751098394394,
-0.0030540931038558483,
-0.021295787766575813,
0.04998566582798958,
-0.018285905942320824,
-0.02821074239909649,
-0.03392881155014038,
0.00003100692993029952,
0.034288328140974045,
-0.04790032282471657,
-0.02724544331431389,
-0.024609126150608063,
-0.008980234153568745,
-0.05951296538114548,
-0.024924080818891525,
-0.007626112550497055,
0.03504948318004608,
-0.03231805935502052,
-0.01874879002571106,
-0.023603932932019234,
0.01911545731127262,
-0.034377411007881165,
0.01962587796151638,
-0.013709409162402153,
0.01747041940689087,
-0.03332185745239258,
-0.006452243309468031,
0.013653155416250229,
-0.044747933745384216,
-0.03855165094137192,
0.03800436109304428,
-0.06970353424549103,
-0.033717136830091476,
0.040892597287893295,
-0.017608126625418663,
0.01979905180633068,
-0.012874467298388481,
0.01988629437983036,
0.02728782780468464,
-0.02637181617319584,
0.028647437691688538,
-0.03741046413779259,
-0.042029645293951035,
0.055386751890182495,
-0.008536454290151596,
0.020477715879678726,
-0.03768618777394295,
-0.022289931774139404,
-0.05153967812657356,
-0.0077741374261677265,
0.050424378365278244,
0.023768944665789604,
-0.0006896206177771091,
0.026227448135614395,
-0.07151869684457779,
-0.010228689759969711,
0.03281399607658386,
-0.016348278149962425,
0.04787326976656914,
0.03797313570976257,
0.011703704483807087,
0.06117234379053116,
-0.0027874226216226816,
0.02371186390519142,
0.007218122947961092,
0.010009266436100006,
-0.051771752536296844,
-0.05898977071046829,
0.0608074888586998,
0.007552124559879303,
-0.059130579233169556,
-0.02079012058675289,
-0.029248492792248726,
0.04107610881328583,
-0.041325487196445465,
-0.04339318722486496,
-0.008635755628347397,
0.025670012459158897,
0.09610912203788757,
0.043950170278549194,
-0.0010081505170091987,
0.037112727761268616,
0.0269073024392128,
0.060000501573085785,
-0.07421998679637909,
0.03476336970925331,
-0.02689487114548683,
0.02297680638730526,
0.019930653274059296,
-0.020346298813819885,
0.07338313013315201,
-0.005099894944578409,
-0.060260411351919174,
-0.04549837484955788,
0.02850625477731228,
0.035214900970458984,
-0.06807291507720947,
0.009829383343458176,
0.05454941466450691,
-0.062039367854595184,
-0.04161853715777397,
0.014303324744105339,
0.009790532290935516,
-0.06658870726823807,
-0.02200903743505478,
-0.0332588255405426,
0.02154727280139923,
-0.04742778092622757,
0.021872341632843018,
-0.0013275574892759323,
-0.04329381883144379,
0.006111895199865103,
0.019199611619114876,
0.034333549439907074,
-0.0022107542026787996,
-0.05118211358785629,
0.004852193873375654,
-0.0025306602474302053,
0.02616311050951481,
-0.01633266732096672,
-0.09901633113622665,
-0.014395110309123993,
-0.0702805146574974,
-0.004035605117678642,
-0.010923624038696289,
0.06580750644207001,
-0.003999998793005943,
0.0343313068151474,
-0.004207791294902563,
0.01176294032484293,
-0.0456787534058094,
0.046881791204214096,
-0.05298204347491264,
0.020733162760734558,
0.012630771845579147,
0.0028444977942854166,
0.0074529279954731464,
0.06425360590219498,
-0.0017261364264413714,
0.09505385160446167,
-0.0025184873957186937,
-0.050259217619895935,
-0.0036592110991477966,
-0.04721890017390251,
0.05129384994506836,
0.0567467138171196,
0.02483494207262993,
0.00567758921533823,
0.011664082296192646,
0.0021900972351431847,
0.04593946039676666,
-0.015785489231348038,
0.03383613005280495,
-0.033999763429164886,
-0.06719814985990524,
-0.015866899862885475,
-0.021736565977334976,
0.05032490938901901,
0.0356236957013607,
0.00712930504232645,
-0.04605967551469803,
-0.0634545311331749,
-0.00992429256439209,
-0.054494503885507584,
-0.012213596142828465,
0.014572463929653168,
-0.004432111978530884,
-0.054652415215969086,
0.03288664668798447,
0.005961900111287832,
-0.017376236617565155,
-0.03362496197223663,
0.01901875250041485,
-0.018334688618779182,
-0.041844677180051804,
-0.0010212465422227979,
0.03799663484096527,
-0.009400165639817715,
-0.017816390842199326,
0.015949366614222527,
-0.02188309282064438,
0.08577394485473633,
-0.025397086516022682,
0.008880731649696827,
-0.0022739686537534,
-0.039189573377370834,
-0.026871319860219955,
0.058177318423986435,
0.007644823286682367,
-0.08416720479726791,
-0.001816442934796214,
-0.007180654443800449,
0.02999015711247921,
0.00011775736493291333,
0.044061243534088135,
-0.013220333494246006,
0.0624796524643898,
0.007580500561743975,
0.02361920289695263,
0.05004815757274628,
-0.02098194509744644,
-0.022723887115716934,
0.03381400555372238,
-0.06179722771048546,
-0.04747927933931351,
-0.000015665447790524922,
-0.08081961423158646,
0.05181937664747238,
-0.06745615601539612,
0.015317455865442753,
0.016240861266851425,
0.003791799070313573,
-0.009652137756347656,
-0.023103587329387665,
0.061256539076566696,
0.023868903517723083
] |
<p>I am a beginner who is learning QFT. When I was going through the quantisation of Klein-Gordon real-field. I got confused about something:</p>
<p>The solution to Klein-Gordon equations are of the form $ \psi(x^\mu) \sim e^{ik_\mu x^\mu} $. Now the solutions in Peskin and Schroeder have no time dependence. It gives a Fourier transform of this kind:</p>
<p>$$ \psi(\vec x) = \int \frac{d^3p}{(2\pi)^3} \frac{1}{\sqrt{2\omega_p}} \Bigl[a(\vec p) e^{i\vec k. \vec x} + a^\dagger(\vec p) e^{-i\vec k. \vec x} \Bigr] $$</p>
<p>My problem here is, why is the solution is a superposition of $ e^{i\vec k. \vec x} $ and not $ e^{ik_\mu x^\mu} $ ?</p>
<p>[EDIT]</p>
<p>For example in these <a href="http://www.physics.gla.ac.uk/~cwhite/lectures/QFTnotes.pdf">notes</a> in equations 90 and 113 the solutions are superposition of $ e^{ik_\mu x^\mu} $ and I don't where these two things disagree.</p> | g7837 | [
0.021018555387854576,
0.010702626779675484,
-0.011572557501494884,
-0.06965354084968567,
0.06179388612508774,
0.01126137375831604,
0.013960485346615314,
0.02645151875913143,
-0.04447276145219803,
0.010836748406291008,
-0.03324035182595253,
-0.03746912255883217,
-0.02884211391210556,
0.04422157630324364,
-0.04234723374247551,
-0.036931369453668594,
0.07392781227827072,
0.01430272776633501,
-0.01726057194173336,
-0.013234744779765606,
-0.05124717950820923,
0.01806917041540146,
0.0016267700120806694,
-0.04435163736343384,
0.05782070755958557,
-0.06551077961921692,
0.028486669063568115,
-0.016066959127783775,
-0.009349752217531204,
-0.04188133776187897,
-0.007320685312151909,
0.034682389348745346,
0.02493858151137829,
-0.035400766879320145,
0.015307368710637093,
-0.0252066757529974,
0.03518388792872429,
0.009707441553473473,
0.06541957706212997,
-0.03374248743057251,
0.030614279210567474,
0.011944723315536976,
-0.0020531686022877693,
-0.02080359123647213,
-0.027384046465158463,
0.011527176015079021,
-0.006401462014764547,
0.04484942927956581,
-0.030867403373122215,
0.02476719580590725,
0.004251069854944944,
0.06581861525774002,
0.04821065813302994,
-0.048177268356084824,
0.011202998459339142,
0.006764415185898542,
0.055400650948286057,
-0.037020888179540634,
-0.0007753510726615787,
0.04287523403763771,
-0.044933900237083435,
-0.08711815625429153,
0.012721708975732327,
0.026785381138324738,
0.07982698082923889,
-0.033170487731695175,
-0.01702374778687954,
-0.030006168410182,
-0.013420678675174713,
-0.0021354923956096172,
-0.03957211971282959,
-0.05546703189611435,
0.0624382458627224,
0.05232115834951401,
0.018779443576931953,
-0.00761703634634614,
-0.008092455565929413,
-0.037860698997974396,
-0.032687123864889145,
-0.0068991659209132195,
-0.020967574790120125,
0.004250718746334314,
-0.02532222308218479,
-0.005991773214191198,
-0.008010275661945343,
0.014587548561394215,
-0.001177016063593328,
0.03254707157611847,
0.036043666303157806,
0.016087761148810387,
-0.012538151815533638,
0.00019842767505906522,
0.008823388256132603,
0.03434528410434723,
-0.0016596285859122872,
0.0018296971684321761,
-0.047360315918922424,
0.05158640071749687,
-0.007477948907762766,
0.014166727662086487,
-0.03984307870268822,
0.06792805343866348,
-0.005977298133075237,
-0.04192972183227539,
-0.007687887642532587,
-0.02053861878812313,
0.011355140246450901,
0.013429543934762478,
0.04119069501757622,
-0.015276209451258183,
-0.06739216297864914,
-0.0033930924255400896,
-0.054127391427755356,
-0.02657337114214897,
-0.04947987198829651,
-0.03839518502354622,
-0.05937781557440758,
0.023297172039747238,
-0.019762886688113213,
0.029559269547462463,
0.037736810743808746,
-0.03179123252630234,
0.038967330008745193,
-0.006446391809731722,
-0.02302302047610283,
-0.03129412606358528,
-0.02385895699262619,
0.042795535176992416,
0.0508146733045578,
0.008948974311351776,
0.025919489562511444,
-0.01885545253753662,
-0.006368423346430063,
0.057036083191633224,
0.029230806976556778,
0.07309392094612122,
-0.008080164901912212,
0.04525609314441681,
-0.012415901757776737,
0.009776012971997261,
-0.03853145241737366,
-0.044104643166065216,
0.008907822892069817,
0.0002678476448636502,
-0.05127605423331261,
-0.037420984357595444,
0.029880959540605545,
-0.05766899511218071,
-0.0025803381577134132,
0.04137836769223213,
-0.014718602411448956,
0.04715380817651749,
-0.050393231213092804,
0.035201430320739746,
0.011782091110944748,
-0.04089253768324852,
0.02441883087158203,
-0.03190610557794571,
0.008688820526003838,
-0.052159152925014496,
0.015698106959462166,
0.015802161768078804,
0.027945049107074738,
-0.03767558932304382,
-0.015128830447793007,
0.020810771733522415,
0.02181871049106121,
-0.03978006914258003,
-0.025394799187779427,
-0.07015158236026764,
-0.010965852066874504,
0.0247590783983469,
0.05082147568464279,
0.0331588089466095,
0.0033101553563028574,
0.06037179380655289,
0.042442288249731064,
-0.07519076019525528,
0.018545081838965416,
0.025699693709611893,
-0.02922937273979187,
0.03837287425994873,
-0.0030558102298527956,
-0.03979426622390747,
0.020318923518061638,
0.04038672149181366,
-0.00624045031145215,
0.04476558789610863,
-0.04988127201795578,
0.014825575985014439,
-0.0054806796833872795,
0.017726734280586243,
0.028327174484729767,
-0.009972352534532547,
0.014499844051897526,
0.03751342371106148,
0.0008589987410232425,
-0.10168442130088806,
-0.05891723930835724,
0.02657700516283512,
0.011521432548761368,
0.02969302423298359,
0.01836477965116501,
-0.035856977105140686,
0.0485055074095726,
0.010117863304913044,
-0.04535410925745964,
-0.015867365524172783,
0.04846586659550667,
-0.014852107502520084,
0.007673341315239668,
-0.011973332613706589,
-0.044764358550310135,
-0.0029658328276127577,
-0.03449472039937973,
-0.015011264942586422,
0.020938625559210777,
-0.01981721632182598,
-0.04670065641403198,
0.06441156566143036,
0.017351049929857254,
-0.0036490606144070625,
0.050658274441957474,
-0.007964114658534527,
0.0105449128895998,
0.01796109415590763,
-0.013834177516400814,
-0.058142658323049545,
-0.05572158098220825,
0.014713175594806671,
-0.06381537020206451,
-0.04688010737299919,
-0.019118616357445717,
0.0028130800928920507,
0.05738884583115578,
0.027683507651090622,
-0.038364261388778687,
-0.003759965533390641,
0.03275890275835991,
0.07715868204832077,
0.06739732623100281,
0.004562048241496086,
-0.011060452088713646,
-0.036274950951337814,
0.018451234325766563,
-0.009102771990001202,
0.04525225982069969,
-0.008889364078640938,
-0.00300167896784842,
0.0054636141285300255,
-0.014083980582654476,
-0.06759713590145111,
-0.004074500873684883,
-0.036076873540878296,
0.011584784835577011,
-0.0004308264178689569,
0.023545708507299423,
0.027246393263339996,
-0.05355173721909523,
0.0050319586880505085,
-0.003286282066255808,
0.04399329423904419,
0.003992878831923008,
0.02004297636449337,
-0.042627207934856415,
0.005183925852179527,
-0.01209883950650692,
0.09498883783817291,
-0.02250170335173607,
-0.010841519571840763,
-0.012497841380536556,
0.006652018986642361,
-0.0003178856859449297,
0.06859305500984192,
-0.032546814531087875,
-0.07818547636270523,
-0.004225796088576317,
-0.018445929512381554,
0.07628615945577621,
-0.041708845645189285,
-0.029045958071947098,
-0.039548929780721664,
-0.006317558232694864,
-0.018187513574957848,
-0.010045879520475864,
-0.09512476623058319,
-0.0259257759898901,
0.01938443072140217,
0.032649632543325424,
0.03490107133984566,
-0.039915867149829865,
-0.006955259945243597,
-0.01704426109790802,
-0.023122694343328476,
-0.04538090154528618,
0.04462384060025215,
0.013570866547524929,
-0.07399031519889832,
-0.006916542537510395,
0.05227172374725342,
0.001672446494922042,
0.01207795087248087,
0.014431465417146683,
0.03493856266140938,
0.07825940102338791,
-0.03679678961634636,
0.013982666656374931,
-0.07703042030334473,
-0.025673450902104378,
-0.021382223814725876,
-0.005363963078707457,
0.06813561916351318,
-0.009478675201535225,
0.028007280081510544,
-0.03295700624585152,
0.04642440006136894,
-0.008611651137471199,
-0.007289065048098564,
0.01934114471077919,
0.003303732257336378,
-0.013213569298386574,
-0.018694041296839714,
-0.04659327119588852,
0.01760317012667656,
0.035977840423583984,
-0.0007928545819595456,
-0.002362770726904273,
0.018171992152929306,
0.014730177819728851,
-0.02219751663506031,
-0.025883084163069725,
-0.010741915553808212,
0.04489055648446083,
-0.03214222937822342,
-0.051837433129549026,
0.01650473102927208,
-0.06864086538553238,
0.013703613542020321,
-0.02498285472393036,
0.0037754422519356012,
-0.00879550352692604,
-0.03734416887164116,
0.012241200543940067,
0.04693847522139549,
0.020710423588752747,
0.02235463447868824,
-0.0011985055170953274,
0.036885958164930344,
0.01808885857462883,
0.034430332481861115,
-0.0396675169467926,
0.04189106076955795,
0.054725706577301025,
-0.0052273450419306755,
0.009601779282093048,
0.039365846663713455,
-0.004058110527694225,
0.04596611112356186,
0.04337237402796745,
-0.024369023740291595,
0.03461777791380882,
-0.036557119339704514,
-0.014570707455277443,
0.010837693698704243,
0.028323374688625336,
-0.035493411123752594,
0.02868393249809742,
-0.0037056319415569305,
0.001255603739991784,
0.02881038375198841,
0.02521180920302868,
0.07760608941316605,
0.04762009531259537,
-0.01886744424700737,
-0.010098855011165142,
-0.05272868648171425,
-0.039689067751169205,
0.014179859310388565,
0.013348488137125969,
-0.01151982694864273,
-0.0212441124022007,
-0.019724931567907333,
-0.014051283709704876,
-0.007490549236536026,
0.076544851064682,
0.020194055512547493,
-0.006965865381062031,
0.0057416497729718685,
0.016109907999634743,
0.003972981590777636,
0.06537770479917526,
-0.02896719053387642,
-0.02359536848962307,
0.02474452555179596,
-0.013811900280416012,
-0.016326287761330605,
0.05373522639274597,
-0.039418723434209824,
-0.0708000659942627,
-0.01017769891768694,
0.029767310246825218,
-0.010249699465930462,
0.004505207762122154,
-0.015736034139990807,
-0.026889601722359657,
0.00926703680306673,
0.026336733251810074,
-0.03249227628111839,
-0.0010111738229170442,
-0.0420445092022419,
-0.036196209490299225,
0.0012515041744336486,
0.012612473219633102,
-0.0766911581158638,
0.02542920969426632,
-0.019722318276762962,
0.003473506309092045,
-0.0045224945060908794,
-0.04246850684285164,
0.03262059763073921,
0.05935347080230713,
-0.060821808874607086,
-0.0034239166416227818,
0.013991440646350384,
0.01202281005680561,
0.02498496137559414,
0.015458284877240658,
0.04288799315690994,
0.009931270964443684,
0.010837945155799389,
-0.006740627810359001,
0.017573127523064613,
-0.008975816890597343,
0.012563967145979404,
-0.05799606814980507,
0.03109261766076088,
-0.04553608596324921,
0.012894275598227978,
-0.03048168495297432,
0.05715455859899521,
0.05906497314572334,
-0.022034386172890663,
0.002207143697887659,
-0.03951733559370041,
0.01809358038008213,
0.009595369920134544,
-0.06092517822980881,
-0.01852354221045971,
-0.0006010069628246129,
-0.038397036492824554,
0.02290009893476963,
0.028146356344223022,
0.003602835116907954,
-0.007738824468106031,
-0.009019000455737114,
-0.033762142062187195,
0.009915618225932121,
-0.009425459429621696,
0.04435158893465996,
0.03109951876103878,
-0.012441525235772133,
0.004970175679773092,
0.011000894010066986,
0.041507989168167114,
0.04307632893323898,
0.05883236229419708,
-0.0648810863494873,
0.01969780959188938,
-0.039724066853523254,
-0.05681246891617775,
0.011370557360351086,
0.023521188646554947,
0.030398858711123466,
-0.025634754449129105,
0.034456830471754074,
0.07243924587965012,
-0.07333297282457352,
-0.02186558023095131,
-0.021865127608180046,
-0.04121692106127739,
0.023593351244926453,
-0.06612415611743927,
0.028785668313503265,
-0.02884490042924881,
0.006550693418830633,
0.015658177435398102,
-0.005357877817004919,
0.007961052469909191,
-0.017062809318304062,
-0.07460616528987885,
0.04376290738582611,
0.05085259675979614,
0.03305364027619362,
0.01105518452823162,
0.03420757129788399,
0.019953396171331406,
0.010901790112257004,
-0.008888029493391514,
-0.003926425240933895,
0.004654516000300646,
-0.039641253650188446,
0.0018065914046019316,
-0.04011130705475807,
0.005918013863265514,
0.016088422387838364,
0.07753271609544754,
0.0744093731045723,
0.008366134017705917,
0.0106702521443367,
0.045204393565654755,
0.005386790260672569,
-0.0392509400844574,
-0.012346247211098671,
0.0201216172426939,
0.02973688766360283,
-0.01681714691221714,
-0.015422068536281586,
-0.04263037443161011,
-0.010416758246719837,
-0.049690935760736465,
0.04582810029387474,
0.10066624730825424,
-0.0037319555412977934,
0.001580749056302011,
0.08762016892433167,
0.02024928294122219,
-0.028788380324840546,
-0.08421086519956589,
0.07447818666696548,
0.013722721487283707,
0.0506972000002861,
0.011909428052604198,
0.017960410565137863,
0.05567635968327522,
0.06874439120292664,
0.04400220513343811,
0.04762602224946022,
-0.02567868120968342,
0.018784038722515106,
0.006040150765329599,
0.0097862109541893,
-0.013974424451589584,
0.001963420771062374,
0.018159253522753716,
-0.06035240739583969,
0.036500148475170135,
-0.004560502711683512,
0.0008105087908916175,
0.010118351317942142,
-0.02826004847884178,
0.007884755730628967,
-0.049013540148735046,
-0.013807007111608982,
-0.027567626908421516,
-0.0012813707580789924,
0.029697101563215256,
0.013910157606005669,
-0.010068965144455433,
-0.04338571056723595,
-0.017069123685359955,
0.03197139874100685,
-0.00534342834725976,
-0.014913816936314106,
-0.005382861476391554,
0.01372609194368124,
-0.054766811430454254,
0.009983262978494167,
0.00027365918504074216,
0.003824277315288782,
0.03237638995051384,
-0.04058590158820152,
-0.0008461637189611793,
0.005328005645424128,
-0.01922791264951229,
-0.011389343999326229,
0.007618668954819441,
0.00906294770538807,
-0.06013470143079758,
-0.06419790536165237,
0.01666996069252491,
-0.02053212933242321,
0.024834757670760155,
-0.000019236387743148953,
-0.038896579295396805,
-0.01793195866048336,
0.032825153321027756,
-0.020535403862595558,
-0.004447786137461662,
0.09354469180107117,
0.04713289067149162,
-0.03743854910135269,
-0.0016398157458752394,
-0.09007128328084946,
-0.017438607290387154,
0.012362289242446423,
0.006230051163583994,
0.0029289608355611563,
0.002629004418849945,
-0.04367125406861305,
-0.023487895727157593,
0.0285323653370142,
0.02281993441283703,
0.05822879821062088,
-0.012270745821297169,
-0.015051309950649738,
0.015077237971127033,
-0.020748862996697426,
0.057479847222566605,
-0.00880409125238657,
0.09151604771614075,
0.015573812648653984,
-0.0169571191072464,
-0.010419398546218872,
0.03029647469520569,
0.04067946597933769,
-0.03288813680410385,
0.0016986943082883954,
0.03242829442024231,
-0.033026281744241714,
-0.03191063180565834,
0.08348073810338974,
-0.036214228719472885,
-0.013578807935118675,
-0.030520401895046234,
0.010153832845389843,
0.07046721130609512,
0.019454769790172577,
0.010484990663826466,
0.05649581551551819,
0.036012765020132065,
0.014396588318049908,
-0.0035504843108356,
-0.032491326332092285,
-0.0016306914621964097,
-0.03291419520974159,
0.03228425234556198,
-0.11332953721284866,
0.07557062804698944,
-0.015700004994869232,
0.06147167831659317,
-0.008855797350406647,
0.030496783554553986,
0.06077588349580765,
-0.06534784287214279,
-0.030939262360334396,
0.047941818833351135,
-0.0019877320155501366,
0.019420932978391647,
-0.09839196503162384,
0.01719578355550766,
0.04840920493006706,
0.016360944136977196,
-0.02837044559419155,
-0.015081839635968208,
0.020148660987615585,
-0.03358491510152817,
-0.011758016422390938,
0.04714200645685196,
0.012059541419148445,
-0.061898358166217804,
-0.016673041507601738,
-0.01643993891775608,
-0.0915195420384407,
0.03167327493429184,
0.013625300489366055,
0.036802925169467926,
0.06103367358446121,
-0.052066780626773834,
0.04845109581947327,
-0.03215624392032623,
-0.05307340621948242,
-0.010541368275880814,
-0.03944538161158562,
-0.008204127661883831,
0.019900288432836533,
-0.007855771109461784,
0.04174488037824631,
0.02668880484998226,
-0.04031296446919441,
0.011130211874842644,
-0.029758812859654427,
0.039214182645082474,
0.02719680219888687,
-0.03280370682477951,
-0.1043037697672844,
0.006818277295678854,
0.015276323072612286,
-0.039973191916942596,
-0.04889025166630745,
0.0359637476503849,
0.032394926995038986,
0.05586631968617439,
0.004006527364253998,
0.03665075823664665,
-0.019647730514407158,
-0.016979724168777466,
0.006482370663434267,
0.002355345757678151,
0.04264526814222336,
0.028308771550655365,
0.05146390199661255,
-0.043786920607089996,
-0.039714325219392776,
0.018524322658777237,
0.016685370355844498,
0.03388029336929321,
0.0169684998691082,
-0.05234278738498688,
-0.026259442791342735,
-0.007679704111069441,
0.0029939147643744946,
-0.05358516424894333,
0.018287891522049904,
0.06452886760234833,
0.05064218118786812,
-0.028554493561387062,
-0.05631282925605774,
0.039118800312280655,
-0.0001389932440361008,
-0.0479825995862484,
0.006735995411872864,
0.02219044417142868,
0.0022485731169581413,
-0.05633464455604553,
-0.005570583511143923,
-0.008371188305318356,
-0.02942590042948723,
-0.049187999218702316,
-0.028967680409550667,
0.017707152292132378,
-0.0477282740175724,
-0.013181324116885662,
-0.030022239312529564,
-0.004132448695600033,
-0.02057364024221897,
-0.027552109211683273,
-0.020094912499189377,
-0.06530696153640747,
-0.006443664897233248,
-0.03421272337436676,
0.03166725113987923,
-0.030298005789518356,
-0.016542481258511543,
0.027791298925876617,
0.018099835142493248,
0.01201003510504961,
-0.013771088793873787,
-0.00596469733864069,
0.029792435467243195,
-0.03245030716061592,
0.049626875668764114,
0.04013343155384064,
-0.0366414375603199,
0.030127232894301414,
0.050942763686180115,
-0.0558919794857502,
0.005157670006155968,
0.041767287999391556,
0.03691679611802101,
0.030430376529693604,
-0.03358781710267067,
-0.10716597735881805,
-0.0670103132724762,
-0.006774242501705885,
-0.013698034919798374,
-0.0903879776597023,
0.042924199253320694,
0.045884061604738235
] |
<p>Basically how boiling takes place? </p>
<p><em><strong>Also like to know...</em></strong><br>
What makes boiling point alter at various altitudes?<br>
Why bubbles rise through boiling water?</p> | g7838 | [
0.010212336666882038,
-0.003695123828947544,
-0.041893430054187775,
0.09749438613653183,
0.03306673839688301,
0.05741272121667862,
-0.04256492108106613,
0.07892356812953949,
-0.018978452309966087,
-0.02659665048122406,
-0.06412632018327713,
0.05269894376397133,
0.05494169145822525,
0.05089060217142105,
0.02094781957566738,
-0.004369861911982298,
0.0032425655517727137,
-0.03972741588950157,
-0.03773806616663933,
0.00046722020488232374,
0.006209867540746927,
-0.04557821899652481,
0.028642304241657257,
-0.04577704891562462,
-0.05582306161522865,
-0.022015077993273735,
-0.04590668901801109,
0.005793871823698282,
-0.003335042158141732,
0.00740199675783515,
-0.017291275784373283,
0.010180885903537273,
-0.028908120468258858,
-0.0344754233956337,
0.006937267258763313,
-0.11305352300405502,
-0.008424314670264721,
0.0008673533448018134,
-0.010150602087378502,
-0.008640522137284279,
0.05829278379678726,
-0.04441430792212486,
0.04015209898352623,
-0.0034026678185909986,
-0.007067281287163496,
-0.0049490854144096375,
-0.010115105658769608,
0.01501578837633133,
-0.04118333011865616,
0.03179313614964485,
-0.010409664362668991,
0.029900435358285904,
0.015309021808207035,
0.021220814436674118,
0.004523392301052809,
-0.0048215207643806934,
-0.052754197269678116,
0.052812810987234116,
0.08834272623062134,
0.02858823537826538,
-0.005986917298287153,
-0.021721109747886658,
0.06835760176181793,
0.026516595855355263,
0.020222801715135574,
0.0092787966132164,
-0.11027926951646805,
-0.0013732595834881067,
0.04033932089805603,
0.063441202044487,
0.04097416624426842,
-0.07520133256912231,
-0.08729111403226852,
-0.04030207172036171,
-0.09544209390878677,
-0.037538472563028336,
-0.0031178672797977924,
-0.036905042827129364,
-0.00159726501442492,
0.02980012819170952,
0.035132963210344315,
0.007881011813879013,
0.03399667888879776,
-0.0029009785503149033,
-0.03704942762851715,
-0.0434538833796978,
0.018435129895806313,
-0.014578815549612045,
-0.0258321613073349,
-0.02046375535428524,
0.011310292407870293,
0.030586164444684982,
0.07455579191446304,
0.02773475833237171,
0.007521505001932383,
-0.04515322297811508,
-0.008204040117561817,
-0.005022267811000347,
-0.004477822221815586,
0.022829610854387283,
-0.008389410562813282,
-0.005530394148081541,
0.0942886471748352,
0.054782263934612274,
-0.0857691615819931,
0.028288142755627632,
0.03360506892204285,
-0.009005485102534294,
0.0203098114579916,
-0.026747889816761017,
-0.03174823895096779,
-0.014409986324608326,
-0.04959801584482193,
-0.013582281768321991,
0.02755032479763031,
-0.013394414447247982,
-0.005564844235777855,
0.03868606314063072,
-0.0019058032194152474,
0.06693894416093826,
0.03817540034651756,
0.0335402637720108,
-0.004248898010700941,
0.003261274192482233,
-0.003116155741736293,
-0.013938234187662601,
0.06492801755666733,
-0.04886128380894661,
0.009258553385734558,
0.03098468668758869,
0.029149845242500305,
0.023594308644533157,
-0.06692672520875931,
-0.007453927304595709,
0.05522821843624115,
0.029090318828821182,
0.02961014397442341,
0.008172312751412392,
0.030798861756920815,
-0.028470613062381744,
0.017333324998617172,
-0.00021232743165455759,
-0.010634168982505798,
-0.06766026467084885,
0.0222171563655138,
-0.04979817941784859,
0.0015710226725786924,
0.009930192492902279,
-0.011169538833200932,
-0.05207303166389465,
0.01599043980240822,
0.03875776007771492,
0.03345693275332451,
-0.052388422191143036,
0.0674176886677742,
0.04153776541352272,
0.01880166120827198,
-0.000544788024853915,
0.08326251059770584,
0.05391873046755791,
0.04196203872561455,
-0.06719193607568741,
0.004695278592407703,
0.06651892513036728,
-0.09074791520833969,
0.0183260440826416,
-0.014410370960831642,
0.007380322553217411,
0.03437909111380577,
-0.006768548395484686,
-0.02968977391719818,
-0.04808931052684784,
-0.03099537454545498,
0.007449178956449032,
0.02964688092470169,
0.03140141814947128,
0.08481737226247787,
0.01733057014644146,
0.0768999233841896,
-0.0025568369310349226,
-0.02748027630150318,
-0.0018761847168207169,
-0.01691696047782898,
-0.03508811444044113,
0.031935516744852066,
0.030546002089977264,
-0.01577754318714142,
-0.01967562362551689,
-0.035303231328725815,
-0.008551845327019691,
-0.0476350374519825,
-0.06283101439476013,
-0.017582261934876442,
0.009979980066418648,
0.030504830181598663,
-0.1060756966471672,
0.021679840981960297,
-0.01364576630294323,
-0.05555831268429756,
0.05129778012633324,
-0.05242164805531502,
-0.05024326965212822,
0.023881828412413597,
0.010572779923677444,
0.010240456089377403,
0.03744455426931381,
0.011538821272552013,
0.02405734919011593,
-0.02441718429327011,
0.04213828220963478,
-0.013082149438560009,
0.06889533996582031,
0.019273633137345314,
-0.034529637545347214,
-0.029253819957375526,
0.07962372899055481,
-0.0337958000600338,
-0.027362704277038574,
0.03878078609704971,
0.0009966723155230284,
0.02593839541077614,
0.0016322460724040866,
-0.03714838624000549,
0.035048484802246094,
-0.02055368386209011,
-0.030032308772206306,
-0.003266838612034917,
-0.029402462765574455,
0.033060070127248764,
0.0401587039232254,
-0.05576694756746292,
0.009509158320724964,
0.05848058685660362,
0.0056007737293839455,
0.01466299407184124,
0.008114561438560486,
-0.0004684902960434556,
0.01911022700369358,
-0.003682882059365511,
0.010573009960353374,
-0.0006510110106319189,
-0.05175471305847168,
-0.04535006731748581,
0.052878301590681076,
-0.030669741332530975,
-0.007233637850731611,
0.010624261572957039,
-0.011840464547276497,
-0.04033094644546509,
0.014389052987098694,
0.016060102730989456,
-0.009924416430294514,
0.026333900168538094,
0.04470400884747505,
-0.06838551163673401,
-0.044385697692632675,
-0.02544405125081539,
0.005349570885300636,
-0.056628257036209106,
0.014461721293628216,
-0.006064992398023605,
0.05079130828380585,
0.025915196165442467,
-0.04358972609043121,
-0.06531491875648499,
0.007408677600324154,
-0.03823840245604515,
-0.04123764485120773,
0.016379548236727715,
0.02612692303955555,
0.005200613290071487,
0.020858867093920708,
0.007357883732765913,
0.0347704142332077,
-0.03778732568025589,
-0.04423055425286293,
-0.008351216092705727,
0.004420887678861618,
0.023111511021852493,
-0.035879261791706085,
-0.0032965957652777433,
-0.020799849182367325,
-0.0524698905646801,
-0.012864992022514343,
0.02098003402352333,
-0.02306964248418808,
0.020507676526904106,
0.038317061960697174,
0.00534284021705389,
-0.07577281445264816,
0.028921928256750107,
-0.05230029672384262,
0.01591481640934944,
0.02428523823618889,
0.000647872977424413,
0.028000419959425926,
0.0491589717566967,
-0.04058366268873215,
-0.060531049966812134,
-0.014336121268570423,
0.0272170789539814,
-0.049952853471040726,
-0.007047358434647322,
0.016075704246759415,
0.01711723394691944,
0.03912217542529106,
0.006975660566240549,
-0.014227651059627533,
-0.0009532379335723817,
-0.018371105194091797,
-0.006917362101376057,
-0.024063952267169952,
-0.02674155868589878,
0.02671063132584095,
-0.06243070960044861,
0.011680933646857738,
-0.045383911579847336,
0.03790978714823723,
0.08335269242525101,
-0.05554758012294769,
-0.08398056775331497,
-0.045490581542253494,
-0.012866608798503876,
-0.00014676200225949287,
0.008391566574573517,
-0.0007470769924111664,
-0.05288517847657204,
-0.000696090399287641,
-0.02069816179573536,
-0.020680753514170647,
-0.03983410447835922,
0.013966755010187626,
-0.03809240087866783,
-0.040027450770139694,
-0.030731122940778732,
0.005689079873263836,
0.003930195700377226,
0.004535821732133627,
0.0038872743025422096,
-0.003640801412984729,
0.04261920973658562,
-0.003816088428720832,
-0.032792117446660995,
0.017273899167776108,
-0.002872179262340069,
0.025649793446063995,
0.044203538447618484,
-0.057010721415281296,
0.04306785389780998,
0.006582662463188171,
0.0672290176153183,
0.01228424347937107,
0.004336802288889885,
-0.04449177533388138,
0.020749041810631752,
0.008883955888450146,
0.03737897425889969,
0.01960226520895958,
0.00015441159484907985,
-0.04497189074754715,
0.04553869739174843,
-0.01867440715432167,
0.023131825029850006,
0.055314745754003525,
-0.0777878388762474,
0.011035987176001072,
0.017245350405573845,
0.026533503085374832,
-0.02717338129878044,
-0.009759579785168171,
0.04139065742492676,
0.027961915358901024,
-0.05538782849907875,
0.008178530260920525,
0.07340764999389648,
0.03287503868341446,
0.05451292172074318,
0.008854761719703674,
-0.06197357922792435,
0.005248789209872484,
-0.014243636280298233,
-0.03312988579273224,
0.033855315297842026,
-0.02849121019244194,
-0.04526981711387634,
-0.034540608525276184,
-0.0503007136285305,
0.04549630358815193,
0.0024750421289354563,
-0.0888454020023346,
0.03172967955470085,
0.019301151856780052,
0.014655099250376225,
0.008784960955381393,
0.0252971351146698,
0.008806003257632256,
0.0011276953155174851,
0.026276979595422745,
-0.03682895749807358,
0.012802168726921082,
-0.009685143828392029,
-0.023301400244235992,
0.011535647325217724,
0.00303785246796906,
-0.00816707219928503,
-0.016731249168515205,
0.03638371080160141,
-0.01995067484676838,
-0.019464587792754173,
-0.008052533492445946,
0.07847415655851364,
0.03650406375527382,
-0.011903038248419762,
-0.041020467877388,
-0.016540678218007088,
-0.057255882769823074,
0.046166252344846725,
0.05034466087818146,
0.027288220822811127,
-0.05449880659580231,
-0.01837729476392269,
-0.025236258283257484,
0.005330279469490051,
0.0008107826579362154,
0.01733795553445816,
0.0333227664232254,
0.009100677445530891,
-0.021960748359560966,
0.00861086044460535,
-0.012424309737980366,
-0.05579804256558418,
0.0247428510338068,
-0.043116819113492966,
0.012565536424517632,
-0.029873479157686234,
0.022637544199824333,
0.006702075712382793,
0.02715430222451687,
-0.010256806388497353,
0.011624103412032127,
0.0744994580745697,
0.003437203820794821,
-0.0006208503618836403,
-0.016261762008070946,
0.021670026704669,
0.03680858388543129,
0.010726593434810638,
0.032189879566431046,
-0.036406755447387695,
-0.018107915297150612,
-0.055872537195682526,
0.05318591371178627,
0.011397842317819595,
-0.0010389494709670544,
-0.02399064414203167,
-0.011108956299722195,
0.061895158141851425,
0.00032131432089954615,
-0.02408483624458313,
-0.02022351510822773,
-0.01574319414794445,
-0.06917297095060349,
-0.02014419622719288,
0.0011899457313120365,
-0.05638642609119415,
-0.017432304099202156,
-0.026820916682481766,
-0.07421796768903732,
0.016401957720518112,
0.04833639785647392,
0.01561644859611988,
0.029037052765488625,
0.03983990103006363,
0.09500189870595932,
0.07658799737691879,
0.04462745413184166,
0.00038594004581682384,
-0.05948420241475105,
0.03084414079785347,
-0.07018016278743744,
0.021317822858691216,
0.031942278146743774,
0.009707216173410416,
0.04787910357117653,
-0.017507968470454216,
0.03791482001543045,
-0.03927825018763542,
0.026278318837285042,
0.016197243705391884,
0.014447596855461597,
-0.026664603501558304,
0.02263597771525383,
-0.018617283552885056,
0.02812562882900238,
-0.017453784123063087,
-0.04494854435324669,
-0.007218663580715656,
0.04945945367217064,
0.05106312036514282,
-0.0009424473391845822,
-0.036632899194955826,
-0.004906319547444582,
0.022321170195937157,
0.03882680460810661,
0.004657313693314791,
0.009073110297322273,
0.02189970761537552,
-0.005826577544212341,
0.02634379453957081,
0.024888940155506134,
-0.01162610575556755,
0.01211551297456026,
-0.028967585414648056,
0.015727199614048004,
0.08853550255298615,
-0.029978884384036064,
0.0026374266017228365,
-0.00803355872631073,
0.0007930006831884384,
0.016442833468317986,
0.013539189472794533,
-0.005591862369328737,
0.04197758808732033,
0.0737466812133789,
0.022279849275946617,
0.02122088149189949,
-0.06396649777889252,
-0.01471980195492506,
0.07049282640218735,
-0.005763612687587738,
-0.08411454409360886,
0.013359613716602325,
0.07789694517850876,
0.0038802288472652435,
0.012238268740475178,
-0.009711629711091518,
-0.04527870938181877,
-0.00883807148784399,
0.037980761379003525,
0.007738797459751368,
-0.0035395093727856874,
-0.006900765001773834,
-0.03807881847023964,
0.05972107872366905,
0.01985219493508339,
-0.007992013357579708,
-0.06586575508117676,
0.03381647169589996,
0.06571679562330246,
0.042858902364969254,
-0.011833788827061653,
0.021705960854887962,
0.02060859277844429,
0.0024639731273055077,
-0.024001529440283775,
-0.01272424217313528,
0.04401218891143799,
-0.028429029509425163,
0.01723620481789112,
-0.017504582181572914,
0.03058530203998089,
-0.03646890074014664,
0.008062183856964111,
0.01779288798570633,
-0.009153141640126705,
-0.05327623710036278,
-0.029584841802716255,
0.016151675954461098,
0.053128600120544434,
0.030886152759194374,
0.000675673596560955,
0.0058099632151424885,
-0.015923677012324333,
-0.05993478745222092,
0.002511081751435995,
-0.012493258342146873,
-0.031103162094950676,
0.06342770904302597,
-0.004638378974050283,
-0.023697538301348686,
0.00045518967090174556,
0.0401688888669014,
-0.004517340566962957,
0.0020310240797698498,
-0.06816976517438889,
-0.04878870025277138,
-0.03871854767203331,
0.04283548519015312,
0.05522628501057625,
0.03817658871412277,
-0.026809299364686012,
0.014492220245301723,
-0.008812426589429379,
-0.03618917614221573,
0.04386221244931221,
-0.0332862064242363,
-0.031185152009129524,
0.04059349745512009,
-0.01612771674990654,
-0.06395591795444489,
0.04002205654978752,
0.0164343174546957,
0.006569335702806711,
0.009632958099246025,
-0.02195201814174652,
0.003978803753852844,
0.04737479239702225,
0.01767537370324135,
0.0035868820268660784,
0.019522709771990776,
-0.03424381464719772,
0.013203530572354794,
0.047147586941719055,
-0.05207955837249756,
-0.04572588950395584,
-0.013035319745540619,
-0.005717933177947998,
0.0041443663649261,
0.0072496384382247925,
-0.004352165386080742,
-0.0010251119965687394,
-0.017159046605229378,
0.05238157510757446,
-0.0661759078502655,
0.09230931103229523,
-0.030640581622719765,
-0.013560124672949314,
0.02345576323568821,
-0.014578691683709621,
-0.007487144786864519,
0.014219103381037712,
0.00967819057404995,
-0.06763459742069244,
0.014681891538202763,
-0.04986501485109329,
0.030366361141204834,
-0.06071679666638374,
0.011914304457604885,
-0.005979935638606548,
0.045701123774051666,
0.019384758546948433,
0.03125614672899246,
-0.023899998515844345,
0.036565717309713364,
0.004466365557163954,
0.04090208187699318,
-0.0038019916974008083,
-0.043840087950229645,
-0.04535640403628349,
0.01699606142938137,
0.022087784484028816,
-0.059904951602220535,
-0.027270209044218063,
-0.007062637247145176,
0.010442279279232025,
0.026457518339157104,
-0.03268849477171898,
-0.005094836466014385,
-0.0018574055284261703,
-0.02118084765970707,
0.001987224677577615,
0.045802220702171326,
0.02121073566377163,
0.0393819734454155,
0.03149597719311714,
0.004263558890670538,
0.055123213678598404,
-0.039065103977918625,
0.00993350613862276,
0.008450653403997421,
-0.00553569570183754,
-0.014687531627714634,
-0.013992520980536938,
-0.040168385952711105,
0.010996644385159016,
-0.027602573856711388,
-0.02639312483370304,
0.02863922528922558,
0.004783870652318001,
0.034175340086221695,
0.00020405334362294525,
-0.017519988119602203,
0.003006790764629841,
-0.08869554102420807,
-0.015813864767551422,
-0.009933102875947952,
-0.06868565082550049,
0.05964548885822296,
0.03761853650212288,
-0.02935066446661949,
0.015298154205083847,
-0.03154228627681732,
-0.02025553770363331,
-0.012682280503213406,
0.02504880167543888,
0.029219945892691612,
0.016127601265907288,
-0.0678936019539833,
-0.014592002145946026,
-0.035911399871110916,
0.026837682351469994,
-0.040553007274866104,
-0.018587417900562286,
-0.07914453744888306,
-0.011144735850393772,
-0.0037199356593191624,
0.045421261340379715,
0.03494556248188019,
-0.011809454299509525,
-0.006938712205737829,
0.004374632611870766,
0.009471628814935684,
0.05302262306213379,
-0.049969300627708435,
0.011781747452914715,
0.004225162789225578,
-0.030076297000050545,
-0.017276203259825706,
-0.03400333598256111,
-0.0075060660019516945,
0.013204825110733509,
-0.03164445981383324,
-0.005536575336009264,
-0.040118925273418427,
0.022258946672081947,
0.05599544197320938,
0.01860867440700531,
-0.028829025104641914,
-0.021019259467720985,
-0.009951102547347546,
-0.022394156083464622,
-0.0010414605494588614,
0.02311074174940586,
0.004738453309983015,
0.0036004495341330767,
0.03011121042072773,
0.06047602742910385,
-0.009862414561212063,
0.03372063860297203,
-0.02759499102830887,
0.029191678389906883,
0.0759366899728775,
0.040761448442935944,
-0.020849494263529778,
-0.01727265678346157,
-0.06115129590034485,
-0.01912585459649563,
0.043307751417160034,
0.023304523900151253,
-0.04229512810707092,
0.03902779519557953,
0.01264654565602541,
0.0015791854821145535,
0.00045929307816550136,
-0.03766285255551338,
-0.009931324981153011,
-0.06868980824947357,
0.09419433772563934,
0.024266084656119347,
-0.08108208328485489,
-0.049995336681604385,
0.03468521311879158,
-0.001742598949931562,
-0.01619575172662735,
0.017546171322464943,
0.019266005605459213,
-0.05310355871915817,
-0.03780197352170944
] |
<p>I am reading Jan Boer's <a href="http://www-library.desy.de/preparch/desy/proc/proc02-02/Proceedings/pl.6/deboer_pr.pdf" rel="nofollow">review</a> of the AdS/CFT correspondence and I quote from end of page 1, where he is talking about equivalence of (d+1)-dim gravity to d-dim field theory </p>
<p>“If true, it implies [...]. If the degrees of freedom in gravity would be local, one would imagine that one can have arbitrarily large volumes with fixed energy density.[...]”</p>
<p>I don't quite understand that. What does it mean for “degrees of freedom to be local”? And how does that lead to fixed energy-density?</p> | g7839 | [
0.05626301094889641,
0.02832847647368908,
-0.00483782310038805,
-0.05032000690698624,
-0.001975333085283637,
0.031627923250198364,
0.04979761689901352,
0.022967418655753136,
-0.0455901101231575,
-0.028864890336990356,
-0.028524912893772125,
-0.04188216105103493,
0.03806661441922188,
-0.03334977105259895,
-0.015937143936753273,
0.04854537546634674,
0.0009980681352317333,
0.0050171441398561,
-0.005469260271638632,
-0.03163555637001991,
-0.029112422838807106,
-0.01669781468808651,
-0.010700208134949207,
-0.047745272517204285,
0.048888467252254486,
0.016168754547834396,
0.04196765646338463,
-0.027262462303042412,
-0.0391552560031414,
-0.02588624879717827,
0.012687653303146362,
0.03628223389387131,
0.04248293116688728,
-0.04398401826620102,
-0.01983274705708027,
0.008076458238065243,
0.03552646562457085,
0.02021936886012554,
0.0269637331366539,
0.005758531391620636,
-0.03491107374429703,
-0.018732136115431786,
-0.02389249950647354,
-0.024010878056287766,
-0.030766313895583153,
0.03800387308001518,
-0.0021282120142132044,
0.015914665535092354,
0.013249918818473816,
-0.03710925951600075,
-0.03466447442770004,
0.0549267902970314,
0.03797600418329239,
-0.007497464772313833,
-0.009578114375472069,
0.03786774352192879,
0.03042464330792427,
0.045644037425518036,
0.025814395397901535,
-0.00601936737075448,
0.02962677739560604,
-0.004283533897250891,
0.019511152058839798,
0.030515002086758614,
0.019142476841807365,
0.01616932451725006,
-0.024193814024329185,
-0.041821543127298355,
0.028201384469866753,
-0.07869943231344223,
0.006639457773417234,
-0.036042939871549606,
-0.006034261547029018,
-0.009136529639363289,
-0.020885633304715157,
0.0010457959724590182,
0.05022912472486496,
0.01435010228306055,
-0.006835258100181818,
-0.05218855291604996,
-0.07353285700082779,
0.018543239682912827,
0.08565918356180191,
-0.037180714309215546,
0.09463135898113251,
-0.034509751945734024,
0.012135561555624008,
0.014044479466974735,
0.056440457701683044,
0.052527833729982376,
0.02179819345474243,
-0.0020880678202956915,
0.023649031296372414,
0.055599842220544815,
0.00011539042316144332,
-0.03113824501633644,
0.01702895015478134,
0.10542425513267517,
-0.021457206457853317,
-0.03839382529258728,
-0.03243337944149971,
0.04626857489347458,
0.04471343383193016,
0.0673498585820198,
0.014321679249405861,
0.02108452096581459,
-0.0034197422210127115,
0.01933973841369152,
-0.001616565859876573,
-0.0024594315327703953,
-0.05146220698952675,
0.00990272406488657,
-0.012469939887523651,
0.0008479252574034035,
-0.041180215775966644,
-0.02868429198861122,
0.09773596376180649,
-0.012049555778503418,
-0.03979684039950371,
0.02624073065817356,
-0.01715884543955326,
0.010826965793967247,
0.04084968566894531,
0.05980083346366882,
0.004814197309315205,
0.002620106330141425,
0.023785913363099098,
0.01224841084331274,
0.022910743951797485,
0.02035157009959221,
0.060220565646886826,
-0.021851040422916412,
-0.005043711978942156,
0.02780594490468502,
0.017971906810998917,
-0.0028402397874742746,
0.001098482171073556,
-0.01680890843272209,
-0.06470087915658951,
-0.004797359928488731,
-0.030801808461546898,
-0.018057188019156456,
0.014028475619852543,
0.005308531690388918,
0.02346539869904518,
-0.040026500821113586,
-0.01329289935529232,
0.01403798907995224,
0.051098499447107315,
0.022200623527169228,
0.056171614676713943,
0.043940071016550064,
-0.029642244800925255,
-0.10343156009912491,
-0.000589686562307179,
0.00880720466375351,
-0.017130523920059204,
0.03303353860974312,
0.030047796666622162,
-0.031432393938302994,
-0.010137360543012619,
-0.02379576303064823,
0.06763171404600143,
-0.03757195919752121,
0.005627567879855633,
0.04331719130277634,
0.07657898962497711,
-0.04851995036005974,
0.012766052968800068,
-0.054842740297317505,
-0.09214797616004944,
0.001481919432990253,
0.002950470196083188,
0.007540824823081493,
0.012995937839150429,
0.0417238213121891,
-0.0372176319360733,
-0.018718170002102852,
0.003864811733365059,
-0.03869624808430672,
-0.0012503417674452066,
-0.00031064049107953906,
0.014617209322750568,
-0.043057605624198914,
-0.022304551675915718,
0.02746313437819481,
0.036443404853343964,
-0.05095576122403145,
0.014223586767911911,
0.04873864725232124,
-0.05019117891788483,
0.02529766783118248,
-0.03536170348525047,
0.06129930540919304,
0.01115402951836586,
0.0027746199630200863,
0.030299486592411995,
-0.06466945260763168,
-0.03351237252354622,
0.014180661179125309,
-0.006245343945920467,
0.005785890854895115,
0.06855508685112,
-0.026876959949731827,
0.08256345242261887,
0.029071683064103127,
0.010778835043311119,
-0.023327961564064026,
0.08078532665967941,
0.008941450156271458,
0.046771254390478134,
-0.10658977925777435,
-0.0646766722202301,
0.030890535563230515,
-0.0008380073122680187,
0.0340677835047245,
-0.03308112174272537,
-0.006640099920332432,
0.004691691137850285,
-0.019098391756415367,
-0.060943663120269775,
0.018191255629062653,
0.06266972422599792,
0.011309678666293621,
0.00836612656712532,
-0.019457567483186722,
-0.0291979368776083,
-0.022485602647066116,
-0.03037804365158081,
0.0063071902841329575,
-0.037835340946912766,
-0.0008173190290108323,
-0.004761272110044956,
0.0020214023534208536,
0.03944549337029457,
0.0542386993765831,
-0.02226731739938259,
-0.013384933583438396,
0.041649166494607925,
0.005939455237239599,
0.027863839641213417,
0.019782550632953644,
-0.031124481931328773,
0.012365508824586868,
0.0027600019238889217,
0.03634801134467125,
0.07345930486917496,
0.018239060416817665,
-0.01320082601159811,
0.05989022180438042,
0.018991874530911446,
-0.023898057639598846,
0.012700872495770454,
0.054923925548791885,
0.005569372791796923,
0.01840636506676674,
-0.04611988738179207,
-0.019589053466916084,
-0.013078236021101475,
-0.02547711879014969,
0.012064543552696705,
-0.0015554482815787196,
0.00019895278092008084,
-0.003985957708209753,
-0.04654288664460182,
0.024281268939375877,
-0.009361650794744492,
-0.00599563168361783,
0.023723335936665535,
0.02636643499135971,
0.015338947996497154,
0.11313101649284363,
-0.009773907251656055,
0.04391686990857124,
0.0223444364964962,
0.009010818786919117,
0.015770722180604935,
-0.024298835545778275,
0.0014088498428463936,
-0.050725530833005905,
-0.019189298152923584,
0.010965792462229729,
-0.0254092738032341,
0.03719843178987503,
0.0285258200019598,
-0.05265050753951073,
-0.013192635029554367,
-0.019723990932106972,
0.052803803235292435,
-0.021792374551296234,
0.0372125580906868,
0.020119251683354378,
-0.020316671580076218,
0.047935374081134796,
-0.031800027936697006,
0.06359954178333282,
0.0028021533507853746,
0.008636979386210442,
-0.04880933463573456,
-0.005918214563280344,
-0.015263613313436508,
0.00993877649307251,
0.04629414156079292,
-0.024105699732899666,
-0.02220510132610798,
0.05425732210278511,
-0.08366191387176514,
-0.03613412752747536,
-0.06054941192269325,
-0.07576894015073776,
-0.042190905660390854,
-0.010540043003857136,
0.0057828305289149284,
-0.040126267820596695,
-0.04441039636731148,
0.02880757302045822,
0.016731197014451027,
-0.0037467172369360924,
0.031179169192910194,
-0.1072421446442604,
-0.0336516797542572,
-0.027172308415174484,
-0.03038439154624939,
-0.018445387482643127,
0.02063129097223282,
-0.010886571370065212,
-0.0390356071293354,
0.0033266169484704733,
0.0025202478282153606,
0.006617586128413677,
0.046117451041936874,
-0.035428062081336975,
-0.06936751306056976,
0.028818219900131226,
-0.078215591609478,
-0.025021405890583992,
-0.059298254549503326,
0.06179036572575569,
0.07515309005975723,
0.0236000157892704,
-0.03282199800014496,
0.032073013484478,
-0.07145621627569199,
0.03924596309661865,
0.01097348053008318,
0.0951097384095192,
-0.0005958669353276491,
-0.008576016873121262,
0.0006200604257173836,
0.058050088584423065,
0.03985494747757912,
-0.03852030262351036,
0.05488783121109009,
-0.016702432185411453,
-0.011221147142350674,
0.02838999778032303,
0.07442860305309296,
-0.03026970475912094,
0.004530058708041906,
-0.013967576436698437,
0.00510790478438139,
-0.05022520199418068,
0.024778518825769424,
0.02869166061282158,
-0.0551556795835495,
-0.044061824679374695,
-0.03843112289905548,
-0.0387880839407444,
-0.03881799057126045,
0.0011950766202062368,
0.011554456315934658,
-0.10796333104372025,
-0.024737561121582985,
0.06801728159189224,
0.08197802305221558,
-0.01065907534211874,
0.0060179103165864944,
-0.026892082765698433,
-0.04407903552055359,
-0.0004406383086461574,
0.041526537388563156,
0.04869265854358673,
-0.003997097723186016,
-0.0261869877576828,
-0.01719857193529606,
-0.020028233528137207,
-0.03787234053015709,
0.018307991325855255,
0.001998964697122574,
-0.015839995816349983,
-0.0278281532227993,
-0.05528464913368225,
0.0022046712692826986,
0.04278569296002388,
0.047238145023584366,
0.06794950366020203,
-0.00816941075026989,
-0.0034164953976869583,
-0.013313750736415386,
0.02984723635017872,
0.009074649773538113,
0.030995449051260948,
-0.0365561805665493,
-0.046168096363544464,
-0.032503679394721985,
-0.025346389040350914,
0.02057790569961071,
-0.033654194325208664,
0.02914380468428135,
-0.024220895022153854,
0.05304047465324402,
-0.021057717502117157,
0.016869977116584778,
-0.08061377704143524,
-0.0028910429682582617,
0.019507339224219322,
0.00410874467343092,
-0.030787905678153038,
0.08696184307336807,
0.021357782185077667,
0.025384364649653435,
0.07568227499723434,
0.02439972199499607,
-0.045459870249032974,
-0.026243427768349648,
0.08544979244470596,
0.03728949651122093,
-0.00727064348757267,
-0.008596187457442284,
-0.04199940711259842,
-0.013767266646027565,
-0.0204218290746212,
0.060723572969436646,
0.022980034351348877,
-0.06107737123966217,
0.018529662862420082,
-0.022603150457143784,
0.028506506234407425,
-0.027802852913737297,
0.022829970344901085,
0.0017322724452242255,
0.016784127801656723,
0.023340964689850807,
-0.02810118906199932,
0.0031082697678357363,
0.026792610064148903,
-0.00425203051418066,
-0.003668480319902301,
-0.010808069258928299,
-0.005887123290449381,
0.01497966330498457,
0.025729477405548096,
-0.014781681820750237,
-0.0012619908666238189,
0.015580502338707447,
-0.016482830047607422,
-0.05125655606389046,
-0.019265426322817802,
0.030662832781672478,
-0.017450695857405663,
-0.05250526964664459,
-0.019005712121725082,
0.01998704858124256,
0.05584939569234848,
0.009002900682389736,
-0.01802993379533291,
-0.015060598030686378,
-0.043963320553302765,
-0.07382822781801224,
-0.012933950871229172,
0.021116407588124275,
-0.007573083508759737,
-0.03317827358841896,
-0.026023242622613907,
0.01493364293128252,
0.07319507002830505,
0.02201518788933754,
-0.08115476369857788,
-0.010289354249835014,
-0.04708196967840195,
0.006130632478743792,
-0.013490019366145134,
0.02625865302979946,
0.07121065258979797,
-0.01406259834766388,
0.01880542002618313,
-0.03889279440045357,
-0.03891017660498619,
0.02074049413204193,
-0.022635675966739655,
0.0383564829826355,
-0.011140844784677029,
0.0043801055289804935,
0.004530665464699268,
-0.06309143453836441,
0.0451502799987793,
0.003512247931212187,
-0.02288723923265934,
0.03207787126302719,
-0.02336462400853634,
0.006649292539805174,
0.012508255429565907,
0.0164046511054039,
-0.04887659102678299,
-0.001007618149742484,
0.05541728809475899,
0.08817630261182785,
0.017295051366090775,
-0.04994504526257515,
0.016331937164068222,
-0.05333677679300308,
0.02310970053076744,
-0.011501125991344452,
0.08749867975711823,
0.06501686573028564,
-0.06302310526371002,
-0.026056069880723953,
0.00454732496291399,
-0.03144345059990883,
-0.0320686399936676,
0.05477934703230858,
-0.04269599914550781,
0.03562337905168533,
-0.026108568534255028,
0.02358485758304596,
-0.048115942627191544,
-0.052522286772727966,
-0.03643784299492836,
0.05767200514674187,
0.04365389049053192,
-0.05197930708527565,
0.009908818639814854,
0.026809705421328545,
-0.026135988533496857,
-0.08339614421129227,
0.03173992782831192,
-0.04408809542655945,
0.022981079295277596,
-0.0033969138748943806,
0.04582681879401207,
0.017537275329232216,
-0.044459059834480286,
-0.012153240852057934,
0.03365425020456314,
-0.019376181066036224,
-0.029728524386882782,
0.008036518469452858,
-0.0386616475880146,
0.008112055249512196,
0.019222430884838104,
-0.06672403961420059,
-0.022873973473906517,
-0.008837375789880753,
-0.019252728670835495,
-0.0048867384903132915,
-0.041217900812625885,
0.0036659485194832087,
-0.03376442566514015,
-0.0445791631937027,
-0.0031780165154486895,
0.054327305406332016,
0.04849735647439957,
0.01693612150847912,
-0.029727375134825706,
-0.03749241679906845,
-0.02483757771551609,
0.026890015229582787,
-0.016559341922402382,
0.0465678945183754,
-0.008550121448934078,
-0.05028548836708069,
0.008241534233093262,
-0.00568078039214015,
-0.03399985656142235,
0.02074025757610798,
-0.0159898791462183,
0.01564103364944458,
-0.02407684363424778,
-0.027078554034233093,
0.005158138461410999,
0.022231703624129295,
-0.013668294064700603,
0.0022921396885067225,
-0.011433522216975689,
-0.045876484364271164,
0.032457079738378525,
-0.012600480578839779,
-0.0183697659522295,
0.02541510947048664,
-0.06622032076120377,
-0.029241640120744705,
-0.009582285769283772,
-0.003393869148567319,
0.034884076565504074,
-0.06080176681280136,
-0.017882104963064194,
0.029293660074472427,
-0.020119011402130127,
-0.06741879135370255,
-0.016317570582032204,
-0.002859101863577962,
0.07007025182247162,
0.06421730667352676,
-0.01594478078186512,
-0.03237565979361534,
0.002448201645165682,
0.005822114646434784,
-0.0392291322350502,
-0.026545144617557526,
0.05668734386563301,
-0.010809718631207943,
0.01839514635503292,
-0.006601759698241949,
-0.0067219920456409454,
0.0024111750535666943,
0.016989510506391525,
-0.0271269753575325,
-0.03137614205479622,
0.0034696825314313173,
0.011026287451386452,
0.008832777850329876,
-0.023898974061012268,
0.018247829750180244,
-0.04293203353881836,
-0.014394257217645645,
0.056310854852199554,
-0.02313089556992054,
0.008841967210173607,
0.061951104551553726,
0.048708099871873856,
-0.021116485819220543,
0.030456535518169403,
-0.035099130123853683,
-0.009110444225370884,
-0.021274425089359283,
0.028742486611008644,
-0.05580811947584152,
-0.0034786169417202473,
0.02567962557077408,
0.01981499046087265,
-0.03762783110141754,
-0.01840021088719368,
0.004003583919256926,
-0.037547674030065536,
-0.013081452809274197,
0.012346773408353329,
0.017603004351258278,
-0.030132489278912544,
-0.0315149649977684,
-0.013836104422807693,
0.002041119383648038,
-0.0220046266913414,
-0.009321304969489574,
0.033377327024936676,
-0.04248861223459244,
0.04958381876349449,
0.007603941485285759,
0.008646554313600063,
-0.0317559652030468,
-0.07683558762073517,
-0.03769510239362717,
0.024614812806248665,
-0.006501713301986456,
0.042466334998607635,
-0.034710176289081573,
0.019771764054894447,
0.06550049781799316,
-0.0088755302131176,
0.04823838174343109,
-0.03173216059803963,
0.025716867297887802,
-0.010115093551576138,
-0.05941494181752205,
-0.022199898958206177,
-0.030643168836832047,
-0.03691161423921585,
-0.020177125930786133,
0.035584595054388046,
0.03884320333600044,
0.04101613909006119,
0.016377419233322144,
0.0035668392665684223,
0.022265581414103508,
-0.021698439493775368,
-0.0013226834125816822,
0.04268403723835945,
-0.012102452106773853,
-0.0575430653989315,
0.004172188229858875,
0.01688709296286106,
-0.016027506440877914,
-0.029391154646873474,
0.058112140744924545,
0.03644916042685509,
-0.04027876257896423,
0.0011782676447182894,
0.03997744619846344,
0.04537300020456314,
0.05300852656364441,
0.020417992025613785,
0.027913931757211685,
-0.02823745831847191,
-0.07235442101955414,
0.004027316812425852,
0.04344949126243591,
-0.0064245532266795635,
0.004598565865308046,
0.003530054586008191,
-0.04657384380698204,
0.007308365777134895,
0.05172030255198479,
-0.06476876139640808,
0.02168591506779194,
0.024297013878822327,
0.05316872522234917,
-0.0005772534059360623,
-0.0676959902048111,
0.01221498567610979,
0.01336546242237091,
-0.028205646201968193,
0.01428470853716135,
0.0016636060317978263,
0.02499963343143463,
-0.026201045140624046,
0.01365971565246582,
0.007878006435930729,
-0.011010533198714256,
-0.05070522427558899,
0.022934898734092712,
0.034093596041202545,
-0.08616330474615097,
-0.043533626943826675,
0.03059297241270542,
0.02317630499601364,
-0.038972750306129456,
0.01897110976278782,
0.05119824409484863,
-0.04766564816236496,
0.04582654684782028,
0.007552891969680786,
-0.022655492648482323,
-0.017244108021259308,
0.04997283220291138,
0.013206626288592815,
-0.0329122319817543,
-0.010829129256308079,
-0.003934755921363831,
0.027644377201795578,
0.044755659997463226,
-0.051805902272462845,
0.048138707876205444,
-0.015197924338281155,
-0.017821550369262695,
0.0001700652064755559,
0.04027136042714119,
-0.04917098581790924,
0.014736737124621868,
-0.03735260292887688,
0.047899845987558365,
-0.003987740259617567,
-0.0273567084223032,
-0.003278185613453388,
0.06747975200414658,
-0.01839587651193142,
-0.008639122359454632,
-0.0398748442530632,
0.0134764788672328,
0.023171378299593925
] |
<p>Find the <strong>minimum value of the initial velocity</strong> $u$ of the particle such that the particle crosses the wheel of radius $R$.<br>
<img src="http://i.stack.imgur.com/hN0F9.jpg" alt="enter image description here"></p>
<p><strong>Details and assumptions</strong><br>
$R=2m$<br>
$g=9.8m/s^2$<br>
Neglect air resistance.<br>
All surfaces are frictionless.<br>
The value of $\theta$ (angle the projectile makes either with vertical or horizontal), range and $u$ is not known.<br>
Consider the motion in 2-D space only.</p>
<blockquote>
<p>I tried setting the maximum height equal to $2R$ and then finding the corresponding minimum value of $u$, but my answer was incorrect.<br>
Then I tried to set the latus rectum of the parabola (equation of trajectory) equal to $2R$ but that too didn't work.<br>
Can anybody suggest a way to do this question?<br>
Thanks in advance! </p>
</blockquote> | g7840 | [
0.06814085692167282,
0.005987025331705809,
-0.007034610491245985,
0.0689215213060379,
0.026396073400974274,
0.04291808605194092,
0.03558116406202316,
-0.03690139204263687,
-0.0408027321100235,
-0.024895448237657547,
-0.036051079630851746,
0.04284908249974251,
0.06563348323106766,
-0.0026773440185934305,
-0.0005486871232278645,
0.0032831919379532337,
0.03871481865644455,
-0.03196100518107414,
0.041727159172296524,
0.007107504643499851,
-0.00527862599119544,
-0.029242102056741714,
0.006048017181456089,
-0.016242198646068573,
0.010916278697550297,
-0.05849192291498184,
-0.022801298648118973,
0.015588662587106228,
-0.04994886368513107,
0.05577198788523674,
0.013512837700545788,
-0.002799541223794222,
0.01094067469239235,
-0.04188122972846031,
0.007684323936700821,
-0.030231008306145668,
0.01664620265364647,
0.016536036506295204,
-0.03738251328468323,
-0.035824067890644073,
0.0013663222780451179,
-0.044888075441122055,
0.07116465270519257,
0.028766140341758728,
0.030641576275229454,
0.01772073470056057,
0.015173796564340591,
0.01449640654027462,
-0.03330244496464729,
0.008066944777965546,
-0.06546469032764435,
0.022045738995075226,
-0.0336625874042511,
-0.08353141695261002,
-0.044622018933296204,
0.041114673018455505,
-0.007597395684570074,
-0.0273904949426651,
-0.000673354254104197,
0.0480189323425293,
0.004955533426254988,
-0.045700352638959885,
-0.031199203804135323,
-0.029305212199687958,
0.03539111092686653,
-0.012430922128260136,
-0.04158548265695572,
0.03768092766404152,
-0.027437498793005943,
-0.004194059409201145,
0.01755639724433422,
-0.05530077591538429,
0.011207735165953636,
-0.05315972864627838,
-0.08832123875617981,
-0.008755323477089405,
-0.04426833987236023,
0.0030555222183465958,
0.04433133825659752,
-0.004514049738645554,
-0.0617859922349453,
0.05396130308508873,
0.012833422049880028,
-0.039792776107788086,
0.008902106434106827,
-0.02120364084839821,
0.05435173586010933,
0.020008964464068413,
-0.03661540523171425,
-0.012225735001266003,
0.010429847985506058,
0.012865986675024033,
0.006382893770933151,
-0.024248922243714333,
0.021680543199181557,
-0.014466940425336361,
-0.09488903731107712,
0.07196344435214996,
0.030598323792219162,
0.016914406791329384,
0.016268013045191765,
-0.027368515729904175,
0.002861271845176816,
-0.015407711267471313,
0.07052339613437653,
-0.028264477849006653,
0.06183897331357002,
0.010491369292140007,
0.004471160471439362,
-0.04114941135048866,
0.015762386843562126,
-0.10527968406677246,
0.00804364588111639,
-0.06464143842458725,
0.02268551103770733,
0.012743563391268253,
0.06557340919971466,
0.0006779668619856238,
0.004997633397579193,
0.06011028215289116,
-0.008778548799455166,
0.0017702658660709858,
-0.04602692648768425,
0.10204574465751648,
-0.041188232600688934,
-0.03366212919354439,
-0.03515618294477463,
-0.03347816690802574,
-0.006345989182591438,
-0.008734569884836674,
0.017483072355389595,
0.023041557520627975,
0.06600263714790344,
-0.004911205731332302,
-0.019750524312257767,
0.04025107994675636,
0.022869255393743515,
0.017706675454974174,
-0.03571905940771103,
-0.026391558349132538,
-0.01161171868443489,
0.016574274748563766,
0.05471319705247879,
-0.001077236607670784,
-0.06944097578525543,
-0.006693904288113117,
-0.019327569752931595,
-0.006361417472362518,
0.01782710663974285,
0.031015388667583466,
0.0006164021324366331,
0.053095582872629166,
-0.018909815698862076,
0.05414683371782303,
-0.027631031349301338,
-0.05541452020406723,
0.08594382554292679,
0.017116619274020195,
0.0017572848591953516,
0.009265333414077759,
0.03927070274949074,
-0.02321377955377102,
0.0428609661757946,
-0.01445200014859438,
-0.06191042810678482,
0.019388971850275993,
-0.05472221598029137,
-0.009277346543967724,
0.02851272188127041,
-0.05985051020979881,
-0.053759101778268814,
-0.04538131505250931,
0.06374995410442352,
0.014099557884037495,
-0.046426478773355484,
0.011772437021136284,
-0.00037636153865605593,
-0.03053935244679451,
-0.027735721319913864,
0.007752142380923033,
0.004789900965988636,
-0.06391772627830505,
0.04255916550755501,
0.045308005064725876,
0.01837744005024433,
-0.019872130826115608,
0.03538096323609352,
0.021718543022871017,
-0.011471044272184372,
0.012065349146723747,
-0.02257283590734005,
-0.016161346808075905,
0.004138171207159758,
-0.038002632558345795,
-0.008007601834833622,
0.04658060520887375,
0.06874291598796844,
-0.0026590870693325996,
-0.03869299218058586,
-0.029027311131358147,
0.01491712499409914,
0.06836038082838058,
0.04242842644453049,
0.018198287114501,
-0.033596981316804886,
-0.058938778936862946,
0.040465887635946274,
0.062123995274305344,
-0.05293264240026474,
0.03885779157280922,
-0.0064437598921358585,
0.018638500943779945,
-0.022633913904428482,
0.011469828896224499,
-0.036014266312122345,
-0.014242265373468399,
0.017052846029400826,
0.0011232850374653935,
-0.03626143932342529,
0.04645051062107086,
-0.00792750809341669,
0.004294383805245161,
0.026942415162920952,
-0.004831201396882534,
-0.009517073631286621,
0.02470630593597889,
-0.027005068957805634,
-0.010990530252456665,
0.01711767353117466,
0.015232924371957779,
-0.0004035747842863202,
0.024391895160079002,
0.006643413566052914,
-0.04450100660324097,
0.08473901450634003,
0.03074602596461773,
-0.020468013361096382,
0.018762744963169098,
0.03449257090687752,
-0.013288992457091808,
0.05248868837952614,
-0.05427423119544983,
-0.02460082620382309,
-0.028696058318018913,
0.01984519697725773,
-0.009492609649896622,
0.0033492734655737877,
-0.0006922606844455004,
-0.012503651902079582,
-0.02318410389125347,
0.01199228223413229,
-0.022512711584568024,
-0.011573606170713902,
0.005085805896669626,
-0.05026383325457573,
-0.019514909014105797,
-0.06601503491401672,
0.007416334468871355,
-0.03576955944299698,
-0.0729040652513504,
-0.02578587457537651,
-0.006142389960587025,
0.007832052186131477,
0.026120534166693687,
-0.04002728685736656,
0.014143258333206177,
-0.09070286154747009,
-0.0186800304800272,
0.017159201204776764,
-0.00287431082688272,
-0.032246917486190796,
0.04209208860993385,
-0.012693225406110287,
0.047240566462278366,
-0.00923900119960308,
-0.013246229849755764,
-0.0023479920346289873,
0.0010651889024302363,
-0.0030278891790658236,
0.05837715417146683,
0.014604874886572361,
-0.03659677878022194,
-0.014726050198078156,
0.026311254128813744,
0.01199367642402649,
-0.0811208039522171,
0.0025120179634541273,
0.08134599775075912,
-0.007723221555352211,
0.03630241006612778,
0.02553522400557995,
-0.0059837037697434425,
0.041704028844833374,
0.0072692688554525375,
0.021838383749127388,
0.0932968407869339,
0.03418920934200287,
0.04886423796415329,
0.050525739789009094,
-0.02156864106655121,
-0.03134327009320259,
-0.05656228959560394,
-0.04931016266345978,
-0.0221730824559927,
-0.06322526186704636,
0.01272551342844963,
0.005597416777163744,
-0.03539912402629852,
-0.041187088936567307,
0.02599840983748436,
-0.0010858651949092746,
0.03523503988981247,
0.003514479147270322,
-0.012101215310394764,
-0.04259675741195679,
-0.056500960141420364,
-0.040272440761327744,
0.008674398995935917,
-0.022503018379211426,
0.0778500959277153,
0.007488429080694914,
-0.0771496593952179,
-0.004300042986869812,
0.01362780574709177,
-0.015678120777010918,
0.0014855418121442199,
-0.009165480732917786,
0.03685492277145386,
-0.012337678112089634,
-0.03844836726784706,
0.0017483597621321678,
0.1208462193608284,
0.03699494153261185,
0.008010541088879108,
-0.0013778000138700008,
-0.06451409310102463,
0.018692580983042717,
-0.00887299608439207,
0.06625517457723618,
-0.0079707782715559,
-0.05609238147735596,
-0.017400408163666725,
-0.029337983578443527,
-0.0031049877870827913,
0.03516944870352745,
-0.011176902800798416,
0.006255754269659519,
0.014560696668922901,
0.012479351833462715,
-0.023196687921881676,
0.026044877246022224,
-0.003622904187068343,
-0.038443829864263535,
-0.009452896192669868,
0.07519225776195526,
0.06328290700912476,
0.04348181560635567,
0.052212946116924286,
0.0229119174182415,
-0.015220052562654018,
-0.017317790538072586,
-0.037124212831258774,
-0.05720917880535126,
0.059590570628643036,
0.01854509860277176,
-0.049030378460884094,
-0.01651061698794365,
0.01381734386086464,
0.03692619130015373,
0.058108795434236526,
-0.012442205101251602,
-0.06337186694145203,
0.007349600549787283,
0.018274206668138504,
-0.04081370308995247,
0.042204972356557846,
0.008378078229725361,
-0.02861545979976654,
-0.00794462114572525,
0.0018757861107587814,
0.05121853947639465,
0.029956692829728127,
0.009021300822496414,
0.041100285947322845,
0.0015265012625604868,
0.08763737976551056,
-0.06386763602495193,
-0.007585505954921246,
0.048080429434776306,
-0.026312820613384247,
0.018835578113794327,
-0.013532505370676517,
-0.048639100044965744,
-0.02582532912492752,
0.012328154407441616,
-0.03915702924132347,
0.04523620754480362,
-0.032997459173202515,
-0.029783504083752632,
0.017428746446967125,
-0.016747597604990005,
0.04068750888109207,
0.004969150293618441,
0.0037480946630239487,
-0.02452688477933407,
-0.014146430417895317,
0.06427400559186935,
0.03258605673909187,
0.010627374053001404,
-0.013307885266840458,
-0.011792542412877083,
0.0031632876489311457,
-0.011600557714700699,
-0.02157999947667122,
-0.021110564470291138,
0.0071284654550254345,
-0.05245023965835571,
0.03043801710009575,
-0.04931741952896118,
-0.015827257186174393,
-0.005359224043786526,
0.04651396721601486,
0.005791018716990948,
-0.06425867229700089,
-0.048301272094249725,
0.00414656987413764,
0.02023005299270153,
0.04529864713549614,
0.02396577037870884,
0.006683690473437309,
-0.022932983934879303,
0.046606723219156265,
-0.015248319134116173,
0.03484145924448967,
-0.053801488131284714,
0.049637340009212494,
0.024130625650286674,
0.012796602211892605,
0.02190186083316803,
0.013110609725117683,
-0.013378354720771313,
0.010766611434519291,
0.01034034974873066,
-0.02123875916004181,
-0.0017723680939525366,
0.027136601507663727,
0.011001601815223694,
-0.021781673654913902,
0.018249573186039925,
-0.023249592632055283,
0.026306623592972755,
-0.025088107213377953,
-0.0013320654397830367,
0.03894006460905075,
-0.06011081486940384,
-0.02532026171684265,
-0.005309457890689373,
0.021195199340581894,
-0.0008701473125256598,
-0.003833263646811247,
-0.005209635011851788,
0.006165155675262213,
0.005564647726714611,
-0.010611171834170818,
0.007896998897194862,
-0.020665839314460754,
-0.09963449835777283,
0.03195261210203171,
-0.01893175020813942,
-0.026999469846487045,
0.009398802183568478,
0.06296878308057785,
0.012532399967312813,
0.04259849339723587,
-0.07072462141513824,
0.03518019989132881,
0.02164161577820778,
0.011593885719776154,
0.060607973486185074,
-0.0034466260112822056,
-0.041745491325855255,
-0.006470093969255686,
-0.012133478187024593,
0.022678667679429054,
0.02071758545935154,
0.03304791450500488,
-0.05184159427881241,
0.008358095772564411,
0.02051965333521366,
0.022689862176775932,
-0.021836604923009872,
0.055566173046827316,
-0.06318756192922592,
0.0070023974403738976,
-0.007726132869720459,
-0.02087882161140442,
0.00024422560818493366,
-0.01829371601343155,
-0.000974017777480185,
0.011531226336956024,
-0.057951439172029495,
-0.04006510600447655,
0.07729282230138779,
0.0802905410528183,
-0.06422551721334457,
-0.018456345424056053,
0.009537815116345882,
-0.0037616968620568514,
-0.016646144911646843,
0.03050175867974758,
0.052914705127477646,
0.030528245493769646,
0.04293172061443329,
-0.049075741320848465,
-0.0679357722401619,
0.006155526731163263,
0.06140778586268425,
0.06413256376981735,
-0.0002614432305563241,
0.0023298365995287895,
0.0687701553106308,
-0.01604081690311432,
-0.0027107703499495983,
-0.03288205713033676,
0.005093585234135389,
0.013330414891242981,
-0.02326696552336216,
-0.018688620999455452,
-0.017629558220505714,
0.05328526347875595,
-0.009149598889052868,
-0.06393814086914062,
-0.020126650109887123,
0.04780276119709015,
-0.06606176495552063,
-0.05717509612441063,
0.023397279903292656,
-0.02772759087383747,
-0.04438828304409981,
-0.09125202149152756,
-0.06111910939216614,
-0.018489500507712364,
0.026236219331622124,
-0.03518661856651306,
-0.003802489722147584,
0.019761191681027412,
-0.04390363022685051,
0.027514653280377388,
0.008816473186016083,
0.0037844665348529816,
-0.014493216760456562,
0.04148218408226967,
-0.018914563581347466,
-0.03054898977279663,
0.004604801535606384,
0.048855580389499664,
0.028135107830166817,
-0.01617559604346752,
-0.004829983692616224,
-0.022193668410182,
0.03480268642306328,
-0.08722607791423798,
0.04823258891701698,
0.04725642502307892,
-0.02109897881746292,
-0.023882629349827766,
-0.026610976085066795,
0.004887643735855818,
0.06658656150102615,
-0.019006002694368362,
-0.048711519688367844,
-0.000854881014674902,
-0.011196308769285679,
0.03207702189683914,
0.03405718132853508,
0.031109586358070374,
-0.014856322668492794,
-0.007092508487403393,
-0.07891067117452621,
0.0946265384554863,
-0.022107617929577827,
0.016351856291294098,
0.014679264277219772,
0.013864593580365181,
-0.050249338150024414,
0.01730835624039173,
-0.07361546158790588,
0.011401504278182983,
0.024588339030742645,
-0.03966502100229263,
-0.00010532402666285634,
-0.012586995027959347,
-0.05448746681213379,
0.010253789834678173,
-0.016026118770241737,
-0.04068809747695923,
-0.039139654487371445,
-0.016011806204915047,
-0.06601123511791229,
0.043410565704107285,
0.0375291146337986,
0.03294113278388977,
-0.001690573524683714,
0.021797828376293182,
0.026471436023712158,
0.003473355434834957,
-0.01565934158861637,
-0.015863079577684402,
0.03699805960059166,
-0.011167050339281559,
0.013282271102070808,
0.06225544214248657,
0.03593212738633156,
0.07307196408510208,
-0.08119029551744461,
0.013419273309409618,
0.02111206389963627,
-0.0167937483638525,
0.001665956457145512,
-0.05791975557804108,
0.021304897964000702,
0.04248109459877014,
-0.01672186888754368,
-0.0646936371922493,
0.044958505779504776,
-0.07699743658304214,
0.0026437740307301283,
-0.013942649587988853,
0.046600814908742905,
-0.00959057454019785,
0.07874695211648941,
-0.024137092754244804,
0.033811941742897034,
0.019187457859516144,
0.047714486718177795,
0.01233599055558443,
0.0014757767785340548,
0.012490428052842617,
0.00527900829911232,
0.04321812093257904,
0.019535083323717117,
0.026984374970197678,
-0.03159442916512489,
-0.0020257309079170227,
-0.04191798344254494,
-0.0320090614259243,
0.009215056896209717,
0.0006841052090749145,
-0.024055127054452896,
-0.029608916491270065,
0.025478042662143707,
0.012572670355439186,
-0.00036806281423196197,
-0.018048694357275963,
-0.01453360915184021,
-0.03348379582166672,
0.017628800123929977,
0.04910915717482567,
0.02245103195309639,
-0.005184414330869913,
-0.024331334978342056,
-0.026899857446551323,
-0.004141286946833134,
-0.04055717587471008,
-0.03172488138079643,
0.02178480289876461,
-0.05504272133111954,
0.044850412756204605,
0.016008278355002403,
-0.03991043195128441,
-0.015046106651425362,
-0.005890191067010164,
-0.056251708418130875,
0.004506215453147888,
0.012830368243157864,
0.00596207519993186,
0.0013769028009846807,
0.03332299366593361,
-0.029181480407714844,
0.0006136618903838098,
0.04255890101194382,
-0.06411571800708771,
-0.020294761285185814,
-0.015360591001808643,
0.027857119217514992,
0.028733056038618088,
0.021170269697904587,
0.038610104471445084,
0.050337567925453186,
-0.00682406360283494,
-0.0012163280043751001,
0.04564743489027023,
0.0641404390335083,
-0.024306483566761017,
-0.04464944452047348,
-0.008523265831172466,
-0.029713399708271027,
0.05448563024401665,
0.057008400559425354,
-0.01817777007818222,
0.043524447828531265,
0.003617232898250222,
0.0005515593802556396,
0.0301711093634367,
-0.010425401851534843,
0.030980639159679413,
-0.046313244849443436,
0.015569350682199001,
-0.08546116203069687,
-0.013852251693606377,
0.004972310736775398,
0.054356444627046585,
-0.010410907678306103,
-0.0361146442592144,
0.01448301412165165,
0.033697109669446945,
0.020173467695713043,
0.05971368029713631,
0.009800123050808907,
0.014223454520106316,
-0.03131791204214096,
-0.014984370209276676,
0.0003955136053264141,
-0.035462886095047,
-0.019944023340940475,
-0.05362171679735184,
-0.013926994055509567,
-0.02087782882153988,
0.03257074952125549,
-0.0063619790598750114,
0.04910256341099739,
-0.005749877076596022,
0.0019635295029729605,
0.04717898741364479,
-0.04747709259390831,
-0.004452191758900881,
-0.08960447460412979,
0.0027903099544346333,
0.01312998402863741,
0.007696190383285284,
0.009434311650693417,
-0.005029722116887569,
0.01217389851808548,
-0.0013208931777626276,
-0.05388588458299637,
0.01863238774240017,
0.028688307851552963,
0.04674462229013443,
0.03506599739193916,
-0.019168948754668236,
0.03166421130299568,
0.009611131623387337,
-0.04029262438416481,
0.04444117471575737,
0.009276303462684155,
-0.09352234750986099,
0.029763320460915565,
0.0013313817325979471,
-0.030217396095395088,
-0.04141625389456749,
-0.014478853903710842,
-0.021417176350951195,
0.038419246673583984,
0.02518034167587757,
0.0668833926320076,
-0.029924971982836723,
-0.036055244505405426,
0.04146881774067879
] |
<p>Say we have a balloon, negatively charged, the voltage on it is 500 V. Can I measure the charge on it or in other words, the number of excess electrons?</p> | g7841 | [
0.025877388194203377,
0.0210507120937109,
0.008077498525381088,
-0.01282787136733532,
0.0067544011399149895,
0.019465764984488487,
-0.032507602125406265,
0.016214963048696518,
0.0193542018532753,
0.026072846725583076,
-0.07348355650901794,
0.07763214409351349,
-0.05684436485171318,
0.052731890231370926,
0.010011064819991589,
-0.047429926693439484,
0.07479661703109741,
-0.04552115872502327,
0.058731794357299805,
0.025339704006910324,
0.059817176312208176,
-0.04869692400097847,
0.036197226494550705,
0.020447608083486557,
0.00449279323220253,
-0.0390775203704834,
0.0012669120915234089,
0.04853501915931702,
-0.009777403436601162,
-0.003905392484739423,
-0.05217432603240013,
-0.01994900405406952,
-0.016054918989539146,
0.014462504535913467,
-0.034326694905757904,
-0.01818244718015194,
0.037336114794015884,
-0.011184615083038807,
0.023988639935851097,
0.0018545134225860238,
-0.02835278958082199,
-0.00993345770984888,
0.06436462700366974,
-0.018051063641905785,
-0.003914156462997198,
-0.00007201749394880608,
-0.009583539329469204,
0.018447931855916977,
0.04068839177489281,
-0.07513689249753952,
-0.04240082576870918,
-0.009740766137838364,
-0.0420159213244915,
0.015264101326465607,
0.05082768201828003,
-0.022418327629566193,
-0.02929275669157505,
-0.021431496366858482,
0.07692214846611023,
0.05976047366857529,
0.01374929491430521,
-0.002337254583835602,
-0.005262285005301237,
0.02766311913728714,
0.005116153508424759,
0.06006625294685364,
-0.050069183111190796,
-0.022553814575076103,
-0.02624586783349514,
0.04063078761100769,
0.020458372309803963,
-0.061431966722011566,
-0.02477160468697548,
-0.05236198008060455,
-0.002803302137181163,
0.051076505333185196,
0.03679487854242325,
-0.022221341729164124,
0.10606440156698227,
-0.03760313615202904,
-0.004851656965911388,
-0.011817901395261288,
0.034170471131801605,
-0.02243654616177082,
0.08996527642011642,
-0.03982862830162048,
0.014190183952450752,
-0.05031857267022133,
-0.021425332874059677,
-0.015635080635547638,
0.04357362166047096,
-0.021353185176849365,
0.0794694796204567,
0.00799650140106678,
0.023861641064286232,
-0.03208831697702408,
0.00871545821428299,
0.0021603736095130444,
-0.0114824203774333,
-0.012191363610327244,
-0.04605305939912796,
-0.013524644076824188,
-0.0023195315152406693,
-0.026972439140081406,
-0.07628918439149857,
0.0022143027745187283,
-0.036826085299253464,
-0.05526336655020714,
0.0452752448618412,
-0.031509365886449814,
-0.007702053524553776,
-0.08048379421234131,
-0.06224404275417328,
0.0005816942430101335,
-0.02337798662483692,
0.027389435097575188,
0.07491225749254227,
-0.07385674864053726,
-0.09622345864772797,
0.03704230114817619,
0.05625193566083908,
0.041012953966856,
0.04742259904742241,
0.0041464390233159065,
-0.003218924393877387,
0.01798533834517002,
-0.025798846036195755,
0.022568494081497192,
-0.01399867981672287,
0.05781640484929085,
0.009606607258319855,
-0.027916742488741875,
-0.008627654053270817,
-0.019620951265096664,
-0.008188717998564243,
0.025672385469079018,
0.0049804458394646645,
0.029962977394461632,
0.0038718977011740208,
0.042852263897657394,
0.055127669125795364,
-0.0011041065445169806,
0.0018116249702870846,
0.0051731206476688385,
0.02140599489212036,
0.0022292828653007746,
-0.001234585652127862,
0.016743790358304977,
0.03874485567212105,
-0.014022215269505978,
-0.02567373216152191,
-0.018435249105095863,
0.012252595275640488,
-0.06090603023767471,
-0.010288815945386887,
-0.04834313690662384,
0.048686433583498,
0.037051841616630554,
0.029802748933434486,
0.012948115356266499,
-0.012434307485818863,
0.02748994715511799,
-0.00865961704403162,
0.01258817408233881,
0.0031449932139366865,
-0.03523452207446098,
-0.003832570044323802,
-0.0042379614897072315,
-0.03386459872126579,
-0.014315190725028515,
-0.02656278759241104,
-0.002050533425062895,
0.04400694742798805,
-0.07483947277069092,
0.08006352931261063,
0.06012166664004326,
-0.023713024333119392,
-0.015322953462600708,
0.026097724214196205,
0.034719791263341904,
-0.03250936046242714,
-0.009492273442447186,
0.041432324796915054,
0.03447119891643524,
-0.034704528748989105,
0.02186274155974388,
-0.03369928151369095,
0.003027660073712468,
0.00335832592099905,
0.012593351304531097,
0.0191913153976202,
0.033007219433784485,
0.03920205682516098,
-0.0016736371908336878,
0.0010482663055881858,
-0.051433637738227844,
0.008714789524674416,
-0.020812131464481354,
-0.023733919486403465,
-0.016929278150200844,
0.00911764707416296,
-0.03886035084724426,
0.05321621522307396,
0.018165908753871918,
0.028861183673143387,
-0.004324221983551979,
-0.04803080856800079,
-0.09135567396879196,
0.0577579028904438,
0.01917138136923313,
0.02523927390575409,
0.054972920566797256,
-0.013815748505294323,
0.021156836301088333,
-0.03783351927995682,
0.007516191806644201,
0.0314662829041481,
-0.02256060391664505,
0.004995762836188078,
0.011721708811819553,
-0.03933817148208618,
0.02497360296547413,
0.035624563694000244,
0.028659116476774216,
-0.010463451035320759,
0.013012501411139965,
0.059268008917570114,
-0.007430715952068567,
0.025996509939432144,
-0.059730518609285355,
0.011400521732866764,
0.0074572013691067696,
0.009747033007442951,
-0.046051181852817535,
0.00012423731095623225,
0.07027005404233932,
-0.04553098976612091,
0.036963168531656265,
-0.052794381976127625,
-0.032089713960886,
-0.03182705491781235,
-0.015675971284508705,
0.022644560784101486,
0.08261973410844803,
0.006346832495182753,
0.018754595890641212,
-0.054187215864658356,
0.05247942730784416,
0.00403736112639308,
0.03975851461291313,
-0.02307518944144249,
-0.005026813596487045,
-0.0004692095099017024,
0.060576457530260086,
-0.014965572394430637,
-0.0027549341320991516,
-0.042855486273765564,
0.005934552755206823,
-0.012991907075047493,
-0.030499989166855812,
-0.006379533559083939,
0.028503626585006714,
-0.03571106866002083,
0.004464644938707352,
-0.016601037234067917,
-0.051358193159103394,
0.01541225891560316,
-0.011116400361061096,
0.030659399926662445,
0.025290194898843765,
0.059474047273397446,
0.06393980979919434,
-0.02872214838862419,
-0.026731140911579132,
0.014901110902428627,
-0.00890352949500084,
-0.05335951969027519,
-0.00047510149306617677,
0.0692826360464096,
-0.06355778872966766,
-0.003757007885724306,
0.034028779715299606,
-0.006924072280526161,
0.06598746031522751,
-0.02308630757033825,
-0.005511121824383736,
0.016499752178788185,
-0.039976444095373154,
0.0419921800494194,
-0.03212103992700577,
-0.02939077839255333,
-0.002838284242898226,
0.011210897006094456,
-0.02740185149013996,
-0.01072676945477724,
0.045120954513549805,
0.05680394172668457,
-0.008745149709284306,
0.013426434248685837,
-0.005483465734869242,
-0.04495800659060478,
-0.05095308646559715,
-0.0438583567738533,
0.029129959642887115,
0.020985785871744156,
0.015862269327044487,
-0.020984407514333725,
0.013383941724896431,
0.001007228041999042,
-0.01938524842262268,
-0.06336710602045059,
0.017668917775154114,
0.011639934033155441,
0.020724596455693245,
-0.05326996371150017,
0.008767415769398212,
-0.005029831547290087,
0.02269667387008667,
-0.061099905520677567,
-0.01932886615395546,
0.017159126698970795,
-0.025030795484781265,
0.026201259344816208,
0.08483444154262543,
0.023998046293854713,
0.0355403870344162,
0.0036375983618199825,
0.07496564835309982,
0.032895904034376144,
-0.03540662303566933,
0.05343593284487724,
0.01060172077268362,
0.007438332308083773,
-0.015670698136091232,
0.030021876096725464,
-0.03945862501859665,
0.005381045863032341,
0.02741350419819355,
0.01992790400981903,
0.06426910310983658,
-0.017966462299227715,
0.016461312770843506,
-0.09780935943126678,
-0.05394760146737099,
-0.017156166955828667,
-0.0010558776557445526,
-0.06371049582958221,
0.03711317479610443,
0.012882518582046032,
-0.042644064873456955,
0.06574542820453644,
0.0025552441366016865,
0.03257514908909798,
-0.04970995709300041,
0.025347139686346054,
-0.014001197181642056,
0.058808136731386185,
0.008116199634969234,
-0.04429244622588158,
0.017925025895237923,
0.016668999567627907,
-0.020972387865185738,
0.0158150102943182,
-0.0315866693854332,
0.005280132405459881,
-0.028425654396414757,
-0.05117982625961304,
0.08203098177909851,
-0.04399591311812401,
-0.04460371658205986,
-0.028417963534593582,
-0.012412318028509617,
0.012958461418747902,
0.04944181442260742,
0.008498270995914936,
-0.08227416127920151,
0.012624109163880348,
0.005463374312967062,
-0.02060973457992077,
-0.016910530626773834,
0.05477622151374817,
-0.008490248583257198,
0.03905867785215378,
-0.03926973044872284,
0.007918989285826683,
-0.05618502199649811,
-0.04651310667395592,
-0.04233972355723381,
-0.01555186789482832,
-0.09782305359840393,
-0.017569148913025856,
-0.05159077048301697,
-0.04199082404375076,
0.049599580466747284,
-0.0016950872959569097,
-0.018456025049090385,
0.08229774981737137,
-0.015326233580708504,
0.02302662841975689,
0.014194459654390812,
0.031831834465265274,
0.029237253591418266,
0.03808761388063431,
0.00854557380080223,
0.02618766948580742,
0.006431970279663801,
0.10647459328174591,
-0.022211953997612,
0.00764045212417841,
-0.011883717961609364,
-0.021071216091513634,
-0.014572740532457829,
-0.018122335895895958,
-0.02617448940873146,
-0.013106431812047958,
-0.011117956601083279,
0.022333867847919464,
-0.012969153933227062,
0.026185831055045128,
0.021524440497159958,
0.05916004627943039,
0.039180442690849304,
0.0008093999931588769,
-0.035210125148296356,
-0.03920673206448555,
0.07428690791130066,
0.039447519928216934,
0.01556030660867691,
0.030471906065940857,
-0.00523318350315094,
-0.06939427554607391,
0.03869076073169708,
-0.03591212257742882,
0.07524316012859344,
0.016504721716046333,
-0.004628978203982115,
0.004620514344424009,
0.011197739280760288,
-0.012586039490997791,
0.028308182954788208,
0.054839085787534714,
0.022832660004496574,
-0.05808752030134201,
-0.011752508580684662,
-0.03246171772480011,
-0.015359291806817055,
0.022052166983485222,
0.003848473774269223,
-0.032644253224134445,
-0.003233780153095722,
-0.010631222277879715,
-0.01772720366716385,
-0.01999332755804062,
0.004661981016397476,
0.02649414725601673,
-0.021457523107528687,
-0.01539219357073307,
-0.017341308295726776,
-0.040484365075826645,
-0.00534335570409894,
-0.04177642613649368,
0.002944421721622348,
0.022476505488157272,
0.021249672397971153,
-0.015264361165463924,
-0.05416317656636238,
-0.05246540531516075,
-0.04008765146136284,
-0.045792631804943085,
-0.04223090037703514,
-0.030082110315561295,
0.0076623642817139626,
0.026170024648308754,
0.06261274218559265,
-0.012988557107746601,
-0.057344648987054825,
-0.03794519975781441,
0.005966713186353445,
-0.031513575464487076,
-0.05757996812462807,
-0.011645542457699776,
-0.019726507365703583,
-0.07130593061447144,
-0.029446253553032875,
-0.05668606981635094,
0.024653833359479904,
-0.049905821681022644,
-0.003815288422629237,
0.0023974699433892965,
-0.026750219985842705,
0.012498400174081326,
0.05518611893057823,
0.03507614508271217,
0.03791084885597229,
-0.02877526916563511,
-0.011030454188585281,
-0.03376968577504158,
-0.014559783972799778,
0.017684340476989746,
0.052398331463336945,
0.025803353637456894,
0.013562943786382675,
-0.03676080331206322,
0.012123051099479198,
-0.023176157847046852,
0.013262449763715267,
-0.004539838060736656,
-0.05910429731011391,
-0.03868979588150978,
0.04349843040108681,
-0.0634477436542511,
0.05858577787876129,
0.05677803233265877,
0.046510402113199234,
0.0004325295449234545,
0.004959892947226763,
-0.03129206597805023,
-0.02313699945807457,
-0.04763282090425491,
0.01420044619590044,
0.02408953756093979,
-0.039567526429891586,
0.07141292840242386,
0.01270048413425684,
0.053857315331697464,
-0.0689496323466301,
-0.036094434559345245,
-0.03432542085647583,
0.07366029173135757,
0.0014424897963181138,
0.01128633227199316,
-0.022257741540670395,
-0.08491719514131546,
-0.009365184232592583,
-0.04267391189932823,
-0.022235210984945297,
-0.02914009615778923,
0.019535573199391365,
0.0514988973736763,
0.06138967350125313,
0.013670056127011776,
-0.0320206880569458,
0.015563949942588806,
0.07410228252410889,
0.0626349076628685,
-0.0034267562441527843,
-0.08487672358751297,
0.03889414668083191,
0.017971143126487732,
-0.0007616445072926581,
-0.03123374469578266,
0.002051114570349455,
-0.040738463401794434,
0.009479252621531487,
-0.025837978348135948,
0.002822193317115307,
0.0008799316128715873,
-0.011791751720011234,
0.008974525146186352,
0.046804703772068024,
0.032390326261520386,
-0.02626323327422142,
-0.0015817945823073387,
0.03783397749066353,
-0.03846476227045059,
-0.023743167519569397,
-0.009656294248998165,
-0.02418161928653717,
-0.000421011121943593,
-0.012036802247166634,
-0.034914519637823105,
-0.023313749581575394,
-0.026345904916524887,
-0.0288290623575449,
0.015366973355412483,
-0.007801941595971584,
0.023713255301117897,
0.024570509791374207,
0.025413399562239647,
-0.026730583980679512,
-0.0363740548491478,
0.02133150026202202,
0.027616098523139954,
0.017786147072911263,
0.00611668499186635,
0.061715103685855865,
0.03705586493015289,
0.011632202193140984,
-0.06664460897445679,
-0.026160934939980507,
-0.0006439271382987499,
0.00045205617789179087,
-0.000097174801339861,
-0.06879127770662308,
-0.059690989553928375,
-0.0035711326636373997,
-0.045973192900419235,
-0.04093782603740692,
0.03839883580803871,
0.03239847347140312,
0.03150675818324089,
-0.0025127697736024857,
-0.041726697236299515,
-0.032945629209280014,
0.05910411849617958,
0.018494322896003723,
0.02964654564857483,
0.047284096479415894,
-0.027115974575281143,
-0.0390850305557251,
-0.031358614563941956,
0.016591876745224,
0.0018587774829939008,
0.03076130896806717,
0.012787209823727608,
0.010374758392572403,
0.013109046034514904,
-0.02854154258966446,
-0.002702072262763977,
0.02641691453754902,
0.023313656449317932,
-0.0462961420416832,
-0.028416913002729416,
-0.011693127453327179,
0.036471664905548096,
0.0061657968908548355,
0.0536610446870327,
0.02698552794754505,
0.023157775402069092,
0.02255161665380001,
-0.013198061846196651,
0.04308336228132248,
-0.00325936172157526,
0.031706131994724274,
0.0426330491900444,
0.07424260675907135,
0.004317919723689556,
0.006849817931652069,
0.03137148171663284,
0.05000610649585724,
-0.04099097475409508,
0.0407840870320797,
-0.027987491339445114,
0.01868603564798832,
-0.021044641733169556,
-0.05485222861170769,
0.039602071046829224,
0.01475086621940136,
-0.0029107974842190742,
0.001988839590921998,
0.0333394780755043,
0.0196263138204813,
0.006945595610886812,
-0.01622387021780014,
0.00778181804344058,
0.037228506058454514,
0.06298369914293289,
0.04436991363763809,
-0.01747705787420273,
-0.027144981548190117,
0.030443688854575157,
-0.026039930060505867,
-0.013918357901275158,
0.0008073493954725564,
0.022813057526946068,
-0.02791713923215866,
-0.02826010063290596,
-0.04465482011437416,
-0.03367537632584572,
-0.10776879638433456,
0.04258343204855919,
-0.03896298632025719,
-0.052353184670209885,
-0.009022858925163746,
-0.017780082300305367,
-0.048104263842105865,
-0.015877431258559227,
0.09011960029602051,
-0.03302173689007759,
0.015165723860263824,
-0.017806243151426315,
0.03900641202926636,
0.029623957350850105,
0.021764885634183884,
-0.09659019857645035,
-0.03682592511177063,
-0.005291629116982222,
-0.002269426593557,
0.04048222303390503,
-0.004313240293413401,
-0.005126680247485638,
-0.014037529937922955,
0.10135500878095627,
-0.04489533230662346,
0.011971607804298401,
0.007032330147922039,
-0.032159823924303055,
-0.00038223626324906945,
0.013269854709506035,
-0.05689338222146034,
0.015781370922923088,
0.04187517613172531,
-0.0035804680082947016,
-0.018390880897641182,
0.007209925912320614,
0.025353919714689255,
-0.010172081179916859,
-0.0026575939264148474,
-0.06324204802513123,
-0.01933862641453743,
0.0498095378279686,
0.07533640414476395,
-0.005613553803414106,
0.012123439460992813,
0.060645394027233124,
0.0007184072164818645,
-0.018641045317053795,
-0.01351466216146946,
-0.013997667469084263,
-0.003620730945840478,
-0.007522279396653175,
0.03165426477789879,
0.01481671817600727,
-0.08247630298137665,
-0.031353145837783813,
-0.023257622495293617,
0.003935168031603098,
0.07197300344705582,
0.03917438164353371,
0.053716231137514114,
-0.017460644245147705,
-0.015971587970852852,
-0.006980296224355698,
-0.013109130784869194,
-0.03050529956817627,
0.013100098818540573,
0.07650050520896912,
0.004431114532053471,
-0.013980632647871971,
0.03135451674461365,
-0.05328485369682312,
0.008015844970941544,
-0.020882312208414078,
-0.02878553606569767,
-0.02770429104566574,
-0.00865050870925188,
-0.028059935197234154,
0.024268321692943573,
0.052025068551301956,
0.009830986149609089,
0.05309969186782837,
-0.027986669912934303,
0.025856809690594673,
0.04132828116416931,
-0.005873404443264008,
0.003627862548455596,
-0.019057627767324448,
-0.016472110524773598,
-0.03610558807849884,
-0.021377630531787872,
0.005872638430446386,
0.007190142758190632,
-0.015770208090543747,
-0.0003954906715080142,
-0.053335707634687424,
-0.04846864193677902,
-0.005729835946112871,
-0.014291474595665932
] |
<p>Mixing of two different fluids is associated with an increase of entropy. Conversely, separation of two gases must be associated with a decrease of the entropy of the two fluids.</p>
<p>Is there a minimum requirement imposed by this thermodynamic constraint on the minimum energy needed to separate two fluids? </p> | g7842 | [
-0.004922499414533377,
-0.005429151002317667,
0.018336525186896324,
-0.03111306019127369,
-0.022593462839722633,
0.021313613280653954,
-0.07641489058732986,
0.061973679810762405,
-0.05352947860956192,
-0.06922148168087006,
0.0005365273100323975,
-0.05836664140224457,
-0.02285069413483143,
-0.024420589208602905,
0.015230917371809483,
0.029246995225548744,
0.013855193741619587,
-0.00851263478398323,
-0.015171380713582039,
0.044979602098464966,
-0.04011581465601921,
-0.024762960150837898,
0.07797201722860336,
-0.0864911824464798,
0.032820671796798706,
-0.09544102102518082,
-0.024295315146446228,
-0.020920587703585625,
-0.05949579179286957,
0.08425138145685196,
0.05782818794250488,
0.02870318666100502,
0.02198673225939274,
-0.06721875071525574,
-0.012520041316747665,
-0.07212946563959122,
0.05678346008062363,
0.01957772672176361,
-0.018212247639894485,
-0.06180395558476448,
0.04013609513640404,
0.03387698158621788,
-0.019912132993340492,
-0.03679603710770607,
-0.05328374356031418,
-0.03053438849747181,
0.03709417209029198,
-0.028892122209072113,
-0.022824589163064957,
-0.03993963450193405,
0.012240251526236534,
0.0025068430695682764,
-0.04541713744401932,
0.002826299052685499,
-0.03850914165377617,
-0.013159516267478466,
0.009002914652228355,
-0.04161245375871658,
0.005817733705043793,
-0.02135441266000271,
0.011619150638580322,
-0.04772358760237694,
-0.04794492572546005,
0.03098435141146183,
-0.010882293805480003,
-0.0354340597987175,
0.006930843461304903,
-0.09532851725816727,
0.05641740560531616,
0.0059866271913051605,
-0.03634820133447647,
-0.024976706132292747,
0.04505285248160362,
-0.032042041420936584,
0.023063067346811295,
-0.031852975487709045,
0.037966616451740265,
-0.030752845108509064,
0.02072964422404766,
-0.03473949059844017,
0.03489439934492111,
0.0362439826130867,
0.07405105233192444,
-0.030833937227725983,
-0.008315031416714191,
-0.022045115008950233,
-0.0006212486769072711,
-0.037627942860126495,
0.011229473166167736,
0.05390874668955803,
-0.01863391324877739,
-0.02208680659532547,
0.0634407252073288,
-0.022430911660194397,
0.036956071853637695,
0.043624211102724075,
0.00816111359745264,
0.027094736695289612,
-0.016552161425352097,
0.037516262382268906,
-0.025285255163908005,
-0.017563391476869583,
0.04885683208703995,
-0.03970957174897194,
-0.006239901762455702,
-0.010299277491867542,
-0.022933324798941612,
0.04569665342569351,
-0.027628429234027863,
-0.06867977976799011,
-0.02288169041275978,
0.014598146080970764,
-0.04092169925570488,
-0.019617566838860512,
0.019126592203974724,
-0.06242823600769043,
0.02864173986017704,
-0.011444788426160812,
-0.018526915460824966,
-0.004071865230798721,
-0.049898453056812286,
0.03822033852338791,
-0.0061643426306545734,
0.06726258993148804,
0.032947853207588196,
0.0008119705016724765,
0.034265778958797455,
0.0016627005534246564,
0.009730899706482887,
-0.08264223486185074,
0.0764874592423439,
0.0044671837240457535,
0.04217063635587692,
-0.014876370318233967,
-0.02854084223508835,
0.0157160647213459,
-0.009705436415970325,
0.06517261266708374,
-0.0027431203052401543,
-0.017996883019804955,
0.05949670821428299,
0.051093049347400665,
-0.03177420049905777,
0.019128717482089996,
-0.02033987268805504,
-0.01800844445824623,
-0.0060110618360340595,
0.023007191717624664,
-0.033731989562511444,
0.046688374131917953,
-0.011471599340438843,
-0.07272813469171524,
-0.01084850076586008,
0.012390132993459702,
-0.018341122195124626,
-0.005645907483994961,
0.035939112305641174,
-0.03348495811223984,
0.021848037838935852,
-0.037517257034778595,
0.02768165059387684,
0.005344901233911514,
0.07513663917779922,
-0.01796255074441433,
-0.03490554168820381,
0.01972520910203457,
-0.04070456326007843,
-0.028048895299434662,
0.01863250881433487,
-0.0356999970972538,
-0.005473587661981583,
0.007375728338956833,
-0.055952731519937515,
0.054884713143110275,
0.03546418994665146,
0.09140536934137344,
0.023035338148474693,
-0.012791784480214119,
-0.04693012312054634,
-0.006161673925817013,
-0.02995840646326542,
0.03829359635710716,
0.0469156838953495,
-0.03952778875827789,
-0.0020636413246393204,
-0.0006146923988126218,
-0.03862079232931137,
0.0075485967099666595,
-0.10656837373971939,
-0.01668747328221798,
0.01118401624262333,
0.05436672642827034,
-0.000569517957046628,
-0.020168036222457886,
-0.003623858094215393,
-0.007142768241465092,
0.013402885757386684,
-0.018788669258356094,
-0.045986708253622055,
0.012363480404019356,
-0.018985828384757042,
-0.02592613734304905,
0.008327905088663101,
0.019792234525084496,
0.027962423861026764,
0.01848282851278782,
-0.039982110261917114,
0.028871778398752213,
0.012146095745265484,
-0.035516344010829926,
-0.013168226927518845,
-0.05338693782687187,
0.014998180791735649,
-0.033651046454906464,
-0.01842028647661209,
-0.05706958845257759,
0.09285491704940796,
0.035497743636369705,
-0.006404224317520857,
0.012960254214704037,
-0.024623099714517593,
0.03175126761198044,
-0.006370746996253729,
0.011071321554481983,
-0.01441498938947916,
0.023345479741692543,
-0.0026377516333013773,
-0.0003194510063622147,
-0.07129428535699844,
0.0074294391088187695,
-0.012498942203819752,
-0.034101322293281555,
0.03685780614614487,
-0.03642561659216881,
-0.010733568109571934,
0.025614148005843163,
-0.019925028085708618,
0.03469488024711609,
-0.019019896164536476,
0.030466677621006966,
-0.021923821419477463,
-0.04032961279153824,
-0.05811028555035591,
0.11269669979810715,
0.035858724266290665,
0.016677552834153175,
0.001493775867857039,
0.023951148614287376,
-0.025538716465234756,
0.0014705195790156722,
0.016449499875307083,
-0.02544967085123062,
-0.03889055177569389,
-0.014426199719309807,
0.009242184460163116,
0.00022964968229644,
0.03157126531004906,
0.047483790665864944,
-0.06673561036586761,
-0.03414801135659218,
0.01972566731274128,
0.0018271768931299448,
0.013925152830779552,
0.005133653059601784,
-0.0555216446518898,
0.05329916253685951,
-0.021200239658355713,
0.016501471400260925,
0.04474398121237755,
0.0011697476729750633,
0.028355862945318222,
0.042402829974889755,
-0.018117457628250122,
-0.04265204444527626,
0.007162563037127256,
0.01866285502910614,
0.013951980508863926,
-0.02374788373708725,
0.014349580742418766,
-0.02509424276649952,
-0.04390783607959747,
-0.02591370791196823,
-0.03087894432246685,
0.026463700458407402,
-0.03239058703184128,
-0.002819729270413518,
0.0036944695748388767,
0.0058171749114990234,
0.043384939432144165,
0.017641350626945496,
0.01628335751593113,
0.04918939620256424,
0.010246221907436848,
-0.06886519491672516,
0.029738742858171463,
0.012809275649487972,
0.04888418689370155,
-0.03350769728422165,
0.020300032570958138,
0.01468556560575962,
-0.009633246809244156,
-0.0212287288159132,
-0.03677323833107948,
0.021961474791169167,
0.01570364646613598,
-0.03321686014533043,
-0.03669050708413124,
-0.0584329254925251,
-0.025374338030815125,
0.006548187229782343,
-0.019766364246606827,
0.043893877416849136,
0.010507211089134216,
0.049485575407743454,
-0.036928318440914154,
0.0201416015625,
-0.016073351725935936,
-0.02353482134640217,
-0.012715647928416729,
-0.027667516842484474,
0.002801493275910616,
-0.02513561025261879,
0.002937871962785721,
-0.0641888678073883,
0.055084630846977234,
-0.00765757542103529,
-0.04677920415997505,
-0.037289250642061234,
-0.05627348646521568,
0.024663126096129417,
0.02823934331536293,
0.018512709066271782,
0.010963650420308113,
-0.028636714443564415,
-0.040990762412548065,
-0.03860939294099808,
0.001775199081748724,
-0.04318395256996155,
0.024016154929995537,
0.05619075521826744,
0.09050359576940536,
0.032485295087099075,
0.012641055509448051,
0.021498505026102066,
-0.012474823743104935,
0.018914686515927315,
-0.002553455764427781,
0.07151083648204803,
0.050594571977853775,
0.010689083486795425,
0.030533339828252792,
-0.012799642980098724,
-0.010805114172399044,
-0.002626268658787012,
-0.03224971517920494,
-0.03553522005677223,
0.011896640062332153,
-0.01504138670861721,
-0.001096020103432238,
-0.011803332716226578,
-0.012390428222715855,
-0.02547064609825611,
0.016710905358195305,
-0.0003295227943453938,
-0.004583338275551796,
0.018372828140854836,
-0.03093927726149559,
0.009732795879244804,
-0.021780233830213547,
-0.03161131218075752,
-0.023425372317433357,
-0.04201482608914375,
-0.06370957940816879,
0.04101010039448738,
0.034779224544763565,
-0.03758614510297775,
0.10599464923143387,
0.001966293668374419,
0.003318674396723509,
0.011345932260155678,
0.023095615208148956,
-0.036440592259168625,
-0.06390999257564545,
0.03197163715958595,
-0.00013733482046518475,
-0.026829645037651062,
-0.007244976237416267,
0.001687867334112525,
-0.00299907848238945,
-0.05647893622517586,
-0.0022144829854369164,
-0.009863494895398617,
0.010730958543717861,
0.012602292001247406,
0.014225452207028866,
0.03623045235872269,
0.022847333922982216,
0.024438297376036644,
-0.0047601014375686646,
0.11022210121154785,
-0.011319425888359547,
-0.05235875025391579,
-0.013434677384793758,
-0.04319307580590248,
0.0229643601924181,
-0.0293109267950058,
-0.03551509603857994,
-0.005371601786464453,
-0.02480352111160755,
-0.0466022714972496,
0.06091608479619026,
-0.039001185446977615,
-0.018300525844097137,
0.029133228585124016,
-0.00802692212164402,
-0.03216063976287842,
-0.04427691921591759,
-0.015423794277012348,
0.01421458087861538,
0.024736585095524788,
-0.0017660580342635512,
0.0018865803722292185,
-0.04674351587891579,
0.03999869525432587,
-0.05884270370006561,
0.03419363126158714,
0.06251692026853561,
0.015375866554677486,
-0.05177537724375725,
-0.059771958738565445,
-0.0003307775768917054,
0.00460774963721633,
-0.052467238157987595,
0.017624448984861374,
0.02136893756687641,
0.025956975296139717,
0.02444971352815628,
-0.03293127566576004,
0.012250575236976147,
0.005999924149364233,
0.022829212248325348,
0.003721686778590083,
-0.03845435008406639,
0.033402636647224426,
0.0029621869325637817,
0.06279290467500687,
0.03619180619716644,
-0.00207010330632329,
-0.024906087666749954,
-0.015291924588382244,
0.02954760007560253,
0.018651561811566353,
0.04402397945523262,
-0.022734148427844048,
-0.015254751779139042,
-0.0019847298972308636,
-0.002593139884993434,
0.06746361404657364,
-0.01937340572476387,
-0.011818010360002518,
0.026448950171470642,
0.00804444681853056,
0.09625711292028427,
-0.0021789928432554007,
-0.013383892364799976,
-0.015043702907860279,
-0.03152791038155556,
0.05405402556061745,
0.011515147052705288,
-0.013474525883793831,
-0.002556924242526293,
0.06534440815448761,
-0.007661053445190191,
0.09131883084774017,
0.0025337610859423876,
0.0076864250004291534,
0.0022740724962204695,
-0.03303994610905647,
0.033541496843099594,
-0.011090973392128944,
0.04011467099189758,
0.06100928783416748,
0.0416264683008194,
0.08472146093845367,
0.057510145008563995,
-0.008901494555175304,
-0.001177284517325461,
-0.006978369317948818,
0.01161124650388956,
0.022928310558199883,
-0.02545669861137867,
0.11357704550027847,
0.023207293823361397,
0.043469544500112534,
-0.030801504850387573,
-0.024180715903639793,
0.008730254136025906,
-0.05164707824587822,
0.004116205498576164,
0.035220667719841,
-0.05189134553074837,
0.0051751951687037945,
0.039096325635910034,
-0.009527014568448067,
-0.017996804788708687,
-0.03895319625735283,
-0.01907625049352646,
0.008064055815339088,
-0.04233160242438316,
0.11214405298233032,
0.0024725827388465405,
0.002094498835504055,
0.06304268538951874,
-0.00961378775537014,
0.02754920721054077,
-0.0022111160214990377,
0.03675442188978195,
-0.029271285980939865,
-0.016998236998915672,
-0.08823471516370773,
0.06009295955300331,
-0.019761502742767334,
-0.01122303493320942,
-0.017698723822832108,
-0.03311016783118248,
0.054539527744054794,
-0.047308992594480515,
0.03765011578798294,
-0.017679136246442795,
0.030910298228263855,
0.02153818868100643,
0.05597133934497833,
0.0031849194783717394,
0.03873893618583679,
-0.01114535704255104,
-0.035583700984716415,
-0.056736696511507034,
0.040181927382946014,
-0.013139943592250347,
0.01099652610719204,
0.0017322554485872388,
-0.031705163419246674,
-0.03228813409805298,
0.046264734119176865,
0.032621610909700394,
-0.014948015101253986,
-0.04332425817847252,
-0.05836055800318718,
0.01643533632159233,
-0.02469720132648945,
0.021288488060235977,
0.013173922896385193,
-0.009086051024496555,
-0.0024940413422882557,
0.0654149204492569,
-0.03837599605321884,
0.04733302816748619,
0.028430908918380737,
0.002341030165553093,
0.0021131790708750486,
0.017832184210419655,
-0.016065159812569618,
-0.020989298820495605,
0.04726063832640648,
0.01030420046299696,
-0.0938710868358612,
0.029461100697517395,
-0.0002549209166318178,
-0.00474444217979908,
0.06920993328094482,
-0.012065939605236053,
0.002673383569344878,
0.013750642538070679,
0.0014628332573920488,
0.04762018471956253,
-0.03625417873263359,
-0.03313037008047104,
-0.039459358900785446,
-0.06630129367113113,
0.011975488625466824,
-0.06517040729522705,
-0.03694094344973564,
-0.010776308365166187,
-0.029865318909287453,
-0.018241116777062416,
0.03865644708275795,
-0.02911263145506382,
0.0327630341053009,
0.02827940136194229,
-0.014185229316353798,
0.028354577720165253,
-0.08493879437446594,
0.008108486421406269,
-0.030742162838578224,
0.01580001786351204,
-0.010707052424550056,
-0.0007494472665712237,
-0.04502439126372337,
-0.017241712659597397,
0.0453002043068409,
0.01997040957212448,
0.016153473407030106,
0.04012472927570343,
-0.02406025305390358,
-0.04072727635502815,
0.09468928724527359,
0.014821159653365612,
0.044868580996990204,
-0.036574091762304306,
-0.015706682577729225,
-0.027478152886033058,
-0.02268020436167717,
0.04013002663850784,
-0.004509555175900459,
0.0037172220181673765,
0.0328967422246933,
-0.05780691280961037,
0.01801344007253647,
0.0020293775014579296,
-0.036274585872888565,
-0.016213612630963326,
-0.013659215532243252,
0.0035945968702435493,
-0.02772986888885498,
0.02930169180035591,
0.02992083504796028,
-0.059661634266376495,
-0.006413047667592764,
0.004417574964463711,
0.0058031571097671986,
0.06952886283397675,
-0.010746327228844166,
0.030018243938684464,
0.036133795976638794,
-0.007387804798781872,
-0.05641293153166771,
-0.05020841956138611,
0.012682382948696613,
0.037012290209531784,
0.10301361232995987,
0.03734046593308449,
-0.012166453525424004,
0.05140442028641701,
0.07328976690769196,
0.04640866070985794,
0.06658373028039932,
0.021004626527428627,
-0.002834893297404051,
-0.04709726572036743,
0.02314082346856594,
0.022246193140745163,
-0.01575319841504097,
-0.027270948514342308,
-0.025520460680127144,
-0.04178936406970024,
0.0020368359982967377,
-0.06753842532634735,
-0.04825996235013008,
0.04728171229362488,
0.020499104633927345,
0.030613243579864502,
0.010121441446244717,
-0.021980665624141693,
0.06897115707397461,
0.010435876436531544,
0.0725807398557663,
0.01542044896632433,
-0.025396272540092468,
0.03817059099674225,
-0.06065477803349495,
-0.001174828503280878,
-0.03905286639928818,
-0.07090956717729568,
0.01967390440404415,
-0.015394945628941059,
-0.014940962195396423,
-0.017807412892580032,
-0.016812559217214584,
0.08224184811115265,
-0.010875745676457882,
0.012615797109901905,
-0.02282584272325039,
-0.00885977316647768,
-0.044429466128349304,
-0.013399620540440083,
0.048483043909072876,
0.005616799462586641,
-0.043363772332668304,
0.030666949227452278,
0.02871600352227688,
-0.02630099467933178,
0.024569349363446236,
0.019310805946588516,
0.04209686443209648,
-0.07243521511554718,
0.028045285493135452,
0.01630197837948799,
0.02128290943801403,
0.028831524774432182,
0.015491759404540062,
0.03048684075474739,
-0.043552055954933167,
-0.018808655440807343,
0.04563429206609726,
-0.05033060163259506,
0.009718767367303371,
0.04100123792886734,
-0.00130489282310009,
-0.01987670175731182,
-0.002724897814914584,
-0.05215481296181679,
0.010215381160378456,
0.025655308738350868,
0.03313734754920006,
0.014768371358513832,
-0.04899657890200615,
-0.044627051800489426,
0.026580510661005974,
0.032097604125738144,
-0.006204906385391951,
0.038480911403894424,
0.010699921287596226,
-0.00992294680327177,
-0.03162451833486557,
-0.04830778390169144,
-0.022975042462348938,
0.02549283392727375,
-0.05980299785733223,
-0.0016701584681868553,
0.018564673140645027,
-0.03523039445281029,
0.00424408121034503,
-0.0021762545220553875,
-0.01181765366345644,
0.009254495613276958,
-0.0013706499012187123,
0.009898173622786999,
0.005739640910178423,
0.03809940814971924,
0.016423670575022697,
0.002123479498550296,
-0.013679048977792263,
0.03192317113280296,
-0.014135224744677544,
0.030267346650362015,
-0.0647478848695755,
-0.008952494710683823,
0.049467869102954865,
0.05587291345000267,
0.00850591529160738,
-0.03828587010502815,
-0.08604329824447632,
0.0029227815102785826,
0.014827603474259377,
0.0013735517859458923,
-0.024318307638168335,
0.02427377738058567,
0.04196110740303993,
-0.040931586176157,
-0.02505306340754032,
-0.024549026042222977,
0.014429113827645779,
-0.005729364696890116,
0.04340868815779686,
-0.0036809032317250967,
0.03074539266526699,
0.006208248436450958,
0.03470199182629585
] |
<p>Do the laws of physics change anywhere in the universe?Or will they change from place to place in the universe?</p> | g7843 | [
0.005162065848708153,
-0.017356447875499725,
0.011367391794919968,
0.0066807144321501255,
0.04237521439790726,
0.010138807818293571,
-0.036496564745903015,
0.04880881682038307,
-0.0003032361273653805,
-0.005731103476136923,
-0.004833212122321129,
-0.021813463419675827,
-0.036363184452056885,
-0.013043980114161968,
-0.016539316624403,
-0.036458250135183334,
0.049163512885570526,
-0.021582312881946564,
0.02158801443874836,
-0.014253896661102772,
-0.09891199320554733,
-0.03440652787685394,
-0.0030771191231906414,
-0.07372813671827316,
-0.002407679334282875,
-0.013777246698737144,
0.0041317385621368885,
-0.015130652114748955,
-0.05250747501850128,
0.007911170832812786,
-0.017603350803256035,
-0.05892316624522209,
0.05059097707271576,
-0.11640212684869766,
0.029577484354376793,
-0.07496430724859238,
0.004156049340963364,
-0.008590574376285076,
0.05702957883477211,
0.0053664823062717915,
0.03811556100845337,
0.013180739246308804,
-0.03365851566195488,
-0.07074493914842606,
0.07401590794324875,
-0.03117663413286209,
-0.020560385659337044,
-0.004144921433180571,
0.014038186520338058,
0.0011459335219115019,
-0.04181124269962311,
0.001439169980585575,
0.001911683240905404,
0.07131129503250122,
0.019523577764630318,
-0.0000030570181479561143,
0.040476877242326736,
-0.017483316361904144,
0.09122344106435776,
-0.01594342291355133,
0.010472997091710567,
-0.016715772449970245,
0.04034695401787758,
0.004500073846429586,
-0.0010695200180634856,
0.05211285129189491,
-0.036305345594882965,
-0.022400012239813805,
-0.024401478469371796,
-0.0120515963062644,
0.05806894227862358,
-0.012297187931835651,
-0.041280291974544525,
-0.03938119113445282,
0.015260772779583931,
0.02098173461854458,
0.000939207908231765,
0.009470554068684578,
-0.025540705770254135,
0.04348677396774292,
-0.006437635514885187,
0.024146731942892075,
0.04107960686087608,
0.023029647767543793,
0.020512636750936508,
-0.04923807457089424,
0.02086842618882656,
0.05750956013798714,
-0.04134019836783409,
-0.023872166872024536,
-0.015035971999168396,
0.019691942259669304,
0.037882283329963684,
-0.03331201523542404,
-0.0283421091735363,
-0.058658257126808167,
0.025281881913542747,
0.01737995631992817,
0.024298785254359245,
-0.002040890511125326,
-0.0929768979549408,
0.018659986555576324,
0.015606025233864784,
0.03828219324350357,
-0.027983136475086212,
0.00938545074313879,
0.008866623044013977,
-0.017312219366431236,
-0.022174321115016937,
-0.05243903398513794,
-0.005528855603188276,
-0.02448727935552597,
0.0017290972173213959,
0.027729643508791924,
-0.06826061010360718,
-0.016135618090629578,
0.031265974044799805,
-0.02293720655143261,
0.028175780549645424,
0.05217363312840462,
0.04714231938123703,
0.0370490588247776,
0.014947887510061264,
0.016130266711115837,
-0.02236081287264824,
-0.030827105045318604,
-0.060740578919649124,
-0.0136870127171278,
0.01693628542125225,
-0.0032775364816188812,
-0.016473665833473206,
0.009400992654263973,
-0.0711691826581955,
0.014581996016204357,
-0.02528441697359085,
0.03876863047480583,
0.05343995243310928,
-0.003916232381016016,
0.05129695683717728,
-0.015164144337177277,
0.04315042868256569,
-0.017238151282072067,
0.0721360519528389,
-0.014217975549399853,
0.002875743666663766,
-0.050942130386829376,
0.020882409065961838,
0.004998139105737209,
0.037984300404787064,
-0.02670413814485073,
0.027917800471186638,
-0.009687825106084347,
0.005088934674859047,
-0.013556312769651413,
-0.014439712278544903,
0.007262124214321375,
-0.027308795601129532,
0.0987362340092659,
0.02524470165371895,
-0.042465563863515854,
-0.02582469955086708,
-0.06955958902835846,
0.02843140996992588,
-0.008094282820820808,
-0.010194377042353153,
0.01141536794602871,
-0.024991847574710846,
-0.001961728325113654,
-0.0185964684933424,
0.0421675480902195,
-0.07100633531808853,
-0.03480633720755577,
0.0003774812794290483,
0.008910375647246838,
0.00713287852704525,
0.05967163294553757,
-0.05115450546145439,
-0.010943752713501453,
0.005427330266684294,
0.00471506780013442,
0.03205990046262741,
-0.03990017995238304,
0.010199516080319881,
-0.04793860390782356,
-0.001583085861057043,
0.04815921559929848,
-0.06409505009651184,
-0.01747738942503929,
-0.014795263297855854,
-0.062285732477903366,
-0.051693789660930634,
-0.032646603882312775,
-0.040025316178798676,
0.033352382481098175,
0.015058654360473156,
0.007541189435869455,
-0.060816965997219086,
0.009290512651205063,
-0.013526495546102524,
0.011352000758051872,
0.029660316184163094,
0.02965981513261795,
0.018402010202407837,
-0.0023247855715453625,
-0.036185987293720245,
0.014771787449717522,
0.04109925404191017,
0.017562370747327805,
0.011748285964131355,
0.028131680563092232,
0.10688016563653946,
-0.03694528713822365,
0.008420190773904324,
0.016490595415234566,
-0.01881374977529049,
-0.004079256672412157,
-0.012874113395810127,
0.0022007289808243513,
0.024681270122528076,
0.05160163342952728,
0.013667858205735683,
0.021524840965867043,
0.039856038987636566,
-0.005360826384276152,
0.028006304055452347,
-0.044915273785591125,
-0.044687822461128235,
-0.034308068454265594,
0.06191198527812958,
0.012940940447151661,
-0.06559926271438599,
0.016533076763153076,
0.010292952880263329,
0.00020203180611133575,
0.02509855292737484,
0.007758171763271093,
-0.0009352177730761468,
-0.01622987538576126,
0.036966871470212936,
-0.030493728816509247,
-0.028831694275140762,
-0.008805889636278152,
-0.04872780293226242,
0.016487009823322296,
0.061412710696458817,
-0.08538541942834854,
0.05259178206324577,
-0.030835019424557686,
-0.012009603902697563,
0.029361043125391006,
0.08796807378530502,
0.013018586672842503,
-0.011073528788983822,
0.05420813709497452,
-0.03486078232526779,
0.007189299911260605,
0.006940573453903198,
-0.0040757982060313225,
-0.03210457041859627,
-0.04828285053372383,
0.024941522628068924,
-0.016430845484137535,
0.021163417026400566,
0.03208928182721138,
-0.020596738904714584,
0.020663447678089142,
-0.0051894900389015675,
0.04345444217324257,
-0.03393975645303726,
0.02948889508843422,
0.01421855203807354,
0.04938279464840889,
0.010769990272819996,
0.08750876039266586,
0.009885167703032494,
0.01718541607260704,
0.03029012307524681,
-0.03885972499847412,
0.002523750765249133,
-0.01775222085416317,
0.008819609880447388,
0.014200792647898197,
-0.05543242767453194,
-0.04256775230169296,
0.03022429160773754,
-0.05935993045568466,
-0.04060833156108856,
-0.05898093804717064,
-0.04021376743912697,
0.002500987146049738,
0.023365648463368416,
0.04873756691813469,
0.05592293292284012,
0.00861938577145338,
0.02458132430911064,
0.0659630298614502,
-0.010240538977086544,
0.0203970056027174,
-0.04265153035521507,
0.020907554775476456,
0.011551260016858578,
-0.036312077194452286,
-0.013737814500927925,
0.06719568371772766,
0.028939418494701385,
0.09393715113401413,
0.012396564707159996,
0.006399259436875582,
0.10898269712924957,
-0.04326716437935829,
-0.00614587077870965,
0.045743245631456375,
0.03607489541172981,
-0.031270649284124374,
-0.006026803515851498,
0.02678089402616024,
-0.028806393966078758,
0.06260423362255096,
0.053942032158374786,
-0.028606833890080452,
-0.016522467136383057,
0.006738197058439255,
-0.002437958726659417,
-0.019159995019435883,
0.04727839305996895,
0.021608315408229828,
0.015471053309738636,
-0.031582336872816086,
-0.025215545669198036,
-0.029005741700530052,
-0.03779720887541771,
0.03085695207118988,
0.02416829578578472,
-0.04712969809770584,
-0.05348619818687439,
0.00036607537185773253,
-0.001525907777249813,
-0.056196969002485275,
0.03822549805045128,
0.0257047601044178,
0.039461005479097366,
-0.023534489795565605,
-0.005662162788212299,
0.06345097720623016,
0.012955883517861366,
0.06634368002414703,
0.01959642954170704,
-0.019498009234666824,
-0.0005762225482612848,
0.033351246267557144,
0.09105189144611359,
-0.04296606034040451,
-0.022900564596056938,
0.019351938739418983,
-0.03764718025922775,
-0.03455638885498047,
-0.019405296072363853,
-0.013804725371301174,
0.02483179047703743,
-0.03857153654098511,
0.016627492383122444,
-0.07745834439992905,
0.016665196046233177,
-0.024278273805975914,
-0.07736905664205551,
0.05948035046458244,
0.006236778572201729,
-0.05169016867876053,
-0.0050902897492051125,
0.051534321159124374,
-0.0011259993771091104,
-0.004494518972933292,
-0.04420026019215584,
0.02255972847342491,
0.006592956837266684,
0.039250750094652176,
0.04759763181209564,
-0.02935059741139412,
-0.030840467661619186,
0.03567960858345032,
-0.03339406102895737,
0.025332797318696976,
0.01920868642628193,
-0.01963440142571926,
-0.023532843217253685,
0.04928248003125191,
-0.011038570664823055,
-0.05465852841734886,
0.02277788706123829,
-0.005302655044943094,
0.006090987008064985,
-0.024187937378883362,
0.0789799913764,
0.0021401098929345608,
0.07728441059589386,
-0.05310186743736267,
-0.03533206135034561,
0.008800076320767403,
0.014493394643068314,
0.024991964921355247,
0.0039399717934429646,
0.009532105177640915,
-0.0005168243078514934,
-0.009368629194796085,
0.04009551927447319,
0.032736774533987045,
0.024177204817533493,
-0.03614497184753418,
-0.054352473467588425,
-0.026217354461550713,
0.006561263930052519,
0.007809671573340893,
-0.03002888150513172,
-0.03971315175294876,
0.036559779196977615,
0.010602307505905628,
-0.016866208985447884,
-0.062154822051525116,
0.0029077245853841305,
-0.007979962043464184,
0.05555587261915207,
0.03674359992146492,
0.05962745472788811,
-0.02440011128783226,
-0.02615690790116787,
-0.007933614775538445,
-0.004113065544515848,
-0.029907209798693657,
-0.0030887576285749674,
0.05124776065349579,
-0.07315497100353241,
-0.03701215237379074,
0.048743702471256256,
0.04497915506362915,
-0.043567076325416565,
-0.00439524045214057,
-0.019113758578896523,
-0.019204579293727875,
0.0026176280807703733,
-0.006142265163362026,
0.02851073257625103,
-0.02887056954205036,
-0.017847001552581787,
0.03337830305099487,
-0.06361232697963715,
0.09510013461112976,
-0.03054303117096424,
0.0024080323055386543,
0.024048250168561935,
-0.03863561153411865,
-0.06646014004945755,
0.06649670004844666,
-0.02069159224629402,
-0.014936595223844051,
0.030986566096544266,
-0.005966691765934229,
-0.005367136560380459,
-0.0053010424599051476,
0.03082001395523548,
0.0022517829202115536,
-0.08560651540756226,
0.0054946294985711575,
0.0038936310447752476,
0.010456947609782219,
-0.03655127435922623,
0.015773719176650047,
-0.031186319887638092,
-0.03139682486653328,
-0.036245089024305344,
0.010394428856670856,
0.0012621486093848944,
-0.007962876930832863,
0.007151733618229628,
0.0017725665820762515,
0.03852119296789169,
-0.002958538243547082,
0.01701941341161728,
-0.009140918962657452,
-0.012516412883996964,
-0.05105898156762123,
-0.04415171593427658,
0.040075287222862244,
0.025313355028629303,
-0.024520820006728172,
0.003264708211645484,
0.05836900323629379,
-0.017160672694444656,
-0.013569753617048264,
0.03680133447051048,
-0.04817843809723854,
-0.03146970644593239,
-0.007827251218259335,
0.05809352546930313,
0.016138406470417976,
-0.015981459990143776,
-0.016442079097032547,
-0.05638613551855087,
-0.045281071215867996,
0.003525623818859458,
0.030409207567572594,
-0.01785421371459961,
0.061617687344551086,
0.040956050157547,
-0.00464886799454689,
-0.027171561494469643,
-0.0020968839526176453,
-0.011821933090686798,
0.006613275967538357,
-0.007727717515081167,
0.0005180638981983066,
0.0014214374823495746,
0.03465985879302025,
-0.022411910817027092,
0.03605542704463005,
0.05796602740883827,
-0.05006125569343567,
-0.033181723207235336,
0.009375769644975662,
0.0022846751380711794,
-0.035128410905599594,
-0.0235570278018713,
-0.02982173301279545,
0.0945960134267807,
0.01942397467792034,
0.009587734937667847,
0.08447210490703583,
-0.017847172915935516,
-0.01903810352087021,
0.031763989478349686,
0.0010402352781966329,
-0.027699356898665428,
0.03273778036236763,
0.011851108632981777,
-0.024678850546479225,
-0.049612607806921005,
0.01600569114089012,
-0.04613122344017029,
0.005188328213989735,
0.013740398921072483,
0.03432999551296234,
0.02286246232688427,
-0.06515401601791382,
-0.0015366998268291354,
-0.018011821433901787,
-0.013525120913982391,
0.04964723065495491,
-0.06373568624258041,
0.031069070100784302,
0.06872755289077759,
-0.016659175977110863,
-0.03718288615345955,
0.0675063207745552,
-0.035882964730262756,
0.035631198436021805,
-0.0568055622279644,
0.02588493376970291,
0.004364481195807457,
0.014729373157024384,
-0.004770165774971247,
-0.024837302044034004,
0.03643801808357239,
0.08286204934120178,
0.022187892347574234,
-0.019873179495334625,
0.020549392327666283,
-0.06662698835134506,
0.015191311948001385,
-0.06575968861579895,
0.053086817264556885,
0.047617971897125244,
0.058605942875146866,
-0.0069595444947481155,
-0.0785205289721489,
-0.01889915019273758,
0.017416037619113922,
-0.015288330614566803,
-0.05240394547581673,
-0.01603412814438343,
-0.01001907978206873,
-0.006742732599377632,
-0.008027702569961548,
0.02926761656999588,
0.033873964101076126,
-0.013391012325882912,
-0.021068459376692772,
0.053240370005369186,
0.04640163853764534,
0.057845912873744965,
0.04753199964761734,
-0.03873270004987717,
0.00806538388133049,
-0.04815306141972542,
0.016225332394242287,
0.0024847127497196198,
-0.06828782707452774,
0.006406040396541357,
0.018945487216114998,
-0.008944084867835045,
0.022687461227178574,
0.006413199007511139,
-0.007976502180099487,
-0.017692627385258675,
0.019655665382742882,
-0.04087788239121437,
0.026693522930145264,
-0.011317308992147446,
-0.03832234442234039,
-0.007314068265259266,
0.04103437811136246,
-0.007827767170965672,
0.03464728221297264,
-0.016761094331741333,
-0.028063762933015823,
0.037323128432035446,
-0.02124345861375332,
-0.0043210312724113464,
0.013450421392917633,
0.00963420420885086,
0.010949060320854187,
-0.03278050944209099,
0.011267507448792458,
-0.030981484800577164,
-0.0369461327791214,
0.01532752625644207,
-0.03903504088521004,
0.02673640288412571,
-0.029757201671600342,
0.06564547121524811,
0.03248923644423485,
0.016276134178042412,
0.031218644231557846,
0.05223320797085762,
0.0022764375898987055,
0.020912446081638336,
-0.043850477784872055,
0.043532002717256546,
0.0009329732856713235,
-0.004389640875160694,
0.0003600462805479765,
0.0382201187312603,
-0.016969924792647362,
0.0006594973965547979,
0.07035783678293228,
-0.019193651154637337,
0.001183210639283061,
0.030790556222200394,
0.015693819150328636,
-0.04291233420372009,
-0.025110729038715363,
0.0058307945728302,
-0.010645070113241673,
-0.031237347051501274,
-0.0236645694822073,
0.02493605576455593,
-0.003008363302797079,
0.03819569572806358,
-0.03178221359848976,
-0.034015510231256485,
0.0002906723238993436,
-0.10780171304941177,
-0.04655296355485916,
-0.01903502643108368,
-0.03635058552026749,
0.03483119606971741,
-0.0017243112670257688,
0.010743372142314911,
0.07279887795448303,
-0.07769043743610382,
-0.0015697937924414873,
-0.01705356314778328,
0.014320885762572289,
-0.00006110989488661289,
-0.058254729956388474,
0.008845972828567028,
0.0505087785422802,
-0.024829909205436707,
-0.038423024117946625,
0.022330954670906067,
0.012710696086287498,
0.012410051189363003,
0.05975031480193138,
0.04927409067749977,
-0.0033244770020246506,
-0.015368533320724964,
-0.009593016467988491,
0.06031124293804169,
-0.009272641502320766,
-0.05383189767599106,
-0.029502153396606445,
-0.05734533816576004,
0.00996016338467598,
-0.07744331657886505,
0.047714054584503174,
-0.06298528611660004,
0.032605718821287155,
0.008072405122220516,
0.08977678418159485,
0.006956064607948065,
-0.0075558507815003395,
-0.05123308300971985,
-0.0006194886518642306,
-0.021800657734274864,
-0.032899148762226105,
-0.018510714173316956,
-0.014768145978450775,
-0.05223068594932556,
-0.007792013697326183,
-0.017816338688135147,
-0.034514542669057846,
-0.014714380726218224,
-0.012466800399124622,
-0.007287205196917057,
0.04050670564174652,
0.07743464410305023,
0.009065716527402401,
0.03369138389825821,
0.017779778689146042,
-0.04059028625488281,
0.010621476918458939,
0.053401488810777664,
-0.00604039104655385,
0.013336668722331524,
0.01599309593439102,
-0.03140256553888321,
-0.027980603277683258,
0.027715088799595833,
0.02979167178273201,
0.024177828803658485,
-0.04338818043470383,
-0.03467414900660515,
-0.04996022582054138,
0.0071197026409208775,
-0.01827920228242874,
0.032211706042289734,
-0.04783063009381294,
0.039792608469724655,
0.04284420236945152,
-0.029925409704446793,
-0.03218541294336319,
-0.08814168721437454,
-0.014152673073112965,
-0.06805621832609177,
0.0065799374133348465,
0.07585674524307251,
-0.004154770169407129,
-0.031150799244642258,
0.0052762459963560104,
-0.009037749841809273,
0.010772411711513996,
-0.07258761674165726,
-0.016860220581293106,
0.07572102546691895,
0.002931408816948533,
0.04477090761065483,
-0.057905443012714386,
-0.01102844811975956,
0.005323547869920731,
-0.009200804866850376,
-0.016306908801198006,
0.011737857013940811,
0.0214765053242445,
0.019692761823534966,
0.0058591365814208984,
-0.017833584919571877,
-0.0073860809206962585,
-0.023312218487262726,
0.011772913858294487,
0.04885254427790642
] |
<p>A vector field $f^\mu$ is said to be Fermi-Walker transported along a curve $\gamma$ parametrized with $\tau$ if the following holds $$\frac{\mathrm{D}}{\mathrm{d}\tau}f^\mu = -(a^\mu v^\nu - a^\nu v^\mu) f_\nu,$$ where $v^\mu$ is the tangent vector $\gamma$ and $a^\mu$ is its derivative. The uppercase D denotes the covariant derivative. This is the usual transport law for nonrotating tetrads. However, in "Introduction to General Relativity" Lewis Ryder mentions the Fermi transport for which $$\frac{\mathrm{D}}{\mathrm{d}\tau}f^\mu = v^\mu a^\nu f_\nu.$$ What is the significance of this transport? Are there any applications of it?</p> | g7844 | [
-0.010032089427113533,
0.030682925134897232,
-0.005966532044112682,
-0.05532005801796913,
0.0634726956486702,
0.012510870583355427,
0.0461454838514328,
-0.03430962935090065,
-0.045433949679136276,
-0.00532765407115221,
-0.035626597702503204,
-0.03232390433549881,
0.06130054220557213,
0.0008737737662158906,
-0.0013565428089350462,
0.014555036090314388,
0.07433503121137619,
0.02975921891629696,
0.05431891977787018,
-0.03472708910703659,
-0.002507234690710902,
0.021040774881839752,
0.059923380613327026,
0.026599109172821045,
0.04469164460897446,
-0.009392691776156425,
0.020460069179534912,
-0.032915450632572174,
-0.057808347046375275,
-0.04673272743821144,
0.11057908833026886,
-0.03519280627369881,
0.06315439194440842,
-0.05021272599697113,
-0.043019507080316544,
0.0010618512751534581,
0.02002420648932457,
0.012518065050244331,
0.05188155174255371,
0.008704718202352524,
-0.008172865025699139,
-0.04539155587553978,
-0.007466444279998541,
0.019321996718645096,
0.023078666999936104,
0.044245775789022446,
-0.02888043224811554,
-0.0082400506362319,
-0.06496014446020126,
0.05970345437526703,
-0.018910828977823257,
0.017924312502145767,
-0.05001998320221901,
-0.01958264410495758,
-0.04687454178929329,
-0.06507132947444916,
0.005204302258789539,
-0.04011400789022446,
0.030605219304561615,
0.023263974115252495,
-0.011774161830544472,
0.000044130461901659146,
-0.018842756748199463,
-0.020949847996234894,
0.03489481657743454,
-0.04160096123814583,
-0.005360644776374102,
-0.029096288606524467,
0.05593058466911316,
-0.035507719963788986,
0.08693204820156097,
0.016432341188192368,
0.012831251136958599,
-0.03133905678987503,
0.020708128809928894,
0.024332240223884583,
-0.0013113326858729124,
-0.029444729909300804,
-0.0037935173604637384,
-0.07327327877283096,
-0.025186514481902122,
-0.012107493355870247,
-0.015610025264322758,
0.04726916179060936,
0.13047565519809723,
-0.0052702478133141994,
-0.014415206387639046,
0.06397789716720581,
0.03785175085067749,
-0.02894728258252144,
-0.04062359407544136,
-0.05729936808347702,
0.016546426340937614,
-0.020788442343473434,
-0.04014740511775017,
-0.0293163750320673,
-0.06773272156715393,
0.04527093097567558,
-0.0240113977342844,
-0.044598180800676346,
0.020603662356734276,
0.06718003004789352,
0.01750040054321289,
0.05141851678490639,
0.03271985426545143,
-0.010803423821926117,
-0.02656305581331253,
0.021705394610762596,
0.0755123570561409,
0.012492312118411064,
-0.045999009162187576,
0.0052210865542292595,
-0.010205275379121304,
-0.03872743248939514,
0.029929930344223976,
0.011048183776438236,
-0.015815040096640587,
-0.055016834288835526,
-0.012781362980604172,
0.06257332116365433,
-0.02183624543249607,
0.04926997423171997,
-0.004262826405465603,
0.0831538587808609,
-0.04459930956363678,
0.01707710511982441,
-0.03602435439825058,
-0.0043017929419875145,
-0.023183906450867653,
0.022039076313376427,
-0.007863504812121391,
-0.009383498691022396,
0.02638152614235878,
0.05460914224386215,
0.009268448688089848,
0.0022074184380471706,
0.012346133589744568,
0.035768914967775345,
-0.029275400564074516,
0.010282049886882305,
0.039349015802145004,
-0.04581690952181816,
-0.009754934348165989,
0.05593925714492798,
-0.05610872432589531,
0.04053119570016861,
-0.01063468586653471,
-0.04494539275765419,
0.031592465937137604,
-0.013180362060666084,
0.009843907319009304,
0.0798880085349083,
-0.08852994441986084,
0.0032623042352497578,
0.027969608083367348,
-0.06389667093753815,
0.025903793051838875,
-0.04042012616991997,
-0.012045318260788918,
-0.04796098917722702,
0.06169510260224342,
0.00798036064952612,
0.030667802318930626,
-0.030216515064239502,
0.007230339106172323,
-0.008765187114477158,
0.024000467732548714,
0.015630869194865227,
0.009759094566106796,
-0.048871830105781555,
-0.03383336588740349,
0.020410846918821335,
0.053347960114479065,
0.012438920326530933,
-0.019880708307027817,
-0.015800857916474342,
-0.05435526371002197,
-0.01482980977743864,
-0.04254457354545593,
-0.03578304499387741,
-0.020677469670772552,
-0.024457018822431564,
0.03261654078960419,
-0.009983297437429428,
-0.019211718812584877,
-0.07511988282203674,
-0.06512264907360077,
-0.05498969927430153,
-0.05788871645927429,
0.047107305377721786,
0.036630429327487946,
-0.04101753234863281,
0.03796613588929176,
0.05011027306318283,
-0.01961418241262436,
-0.01019494142383337,
0.013472510501742363,
-0.07749176025390625,
-0.01852533593773842,
0.0561438649892807,
-0.018999096006155014,
-0.024706078693270683,
0.01932772994041443,
-0.040549904108047485,
0.030945634469389915,
-0.023937180638313293,
-0.02272050827741623,
0.036390528082847595,
0.04359130933880806,
-0.010793332941830158,
0.07121944427490234,
-0.0658491849899292,
0.06413423269987106,
0.014020397327840328,
-0.050205208361148834,
-0.017051177099347115,
0.03516022115945816,
0.023806961253285408,
-0.024758972227573395,
0.012287139892578125,
0.041065655648708344,
-0.04020208120346069,
0.020619412884116173,
0.039536457508802414,
0.002937308279797435,
0.02034246176481247,
0.02822745032608509,
-0.05152997747063637,
-0.022563312202692032,
0.022643785923719406,
-0.023117603734135628,
-0.008668587543070316,
-0.031462084501981735,
0.037349533289670944,
0.0466875284910202,
-0.019237441942095757,
-0.04123411327600479,
0.0290482509881258,
0.041922055184841156,
0.025791781023144722,
0.0422699898481369,
-0.0237210001796484,
-0.030366860330104828,
-0.056175749748945236,
0.00015703969984315336,
0.056898459792137146,
0.02891591191291809,
-0.008878370746970177,
0.018323460593819618,
-0.034918706864118576,
0.04850490763783455,
-0.028125138953328133,
-0.003222657833248377,
0.0676368698477745,
0.03295910730957985,
0.04904024302959442,
-0.033715710043907166,
0.031117433682084084,
-0.058377865701913834,
-0.014981862157583237,
0.020622823387384415,
-0.02921036072075367,
0.059226617217063904,
-0.028744300827383995,
0.02372227981686592,
0.054549090564250946,
0.021449508145451546,
0.09395568072795868,
-0.02459627203643322,
-0.009813269600272179,
0.0038920275401324034,
0.02586331218481064,
-0.00407368503510952,
0.0035558321978896856,
0.02130165696144104,
-0.04672423377633095,
0.030747001990675926,
0.00136319559533149,
-0.04198208823800087,
-0.050757091492414474,
0.018863730132579803,
-0.034983016550540924,
0.008946908637881279,
0.020667262375354767,
-0.013522549532353878,
-0.043008964508771896,
0.03822619095444679,
0.0027046427130699158,
-0.027263833209872246,
0.03314074128866196,
-0.009883743710815907,
-0.02269039675593376,
0.04219737648963928,
-0.007883480750024319,
0.014270525425672531,
0.04452216625213623,
0.014823406003415585,
0.027139240875840187,
0.018376609310507774,
-0.01050279289484024,
-0.003476344048976898,
-0.022353148087859154,
0.009697148576378822,
-0.056512847542762756,
-0.010121002793312073,
0.013804134912788868,
-0.08020471781492233,
-0.08635897934436798,
-0.06741802394390106,
0.008953164331614971,
-0.009354982525110245,
0.041385892778635025,
-0.0030304582323879004,
-0.016508715227246284,
-0.06203770637512207,
-0.011667560786008835,
-0.00905591994524002,
-0.0030675807502120733,
0.062331706285476685,
0.034510478377342224,
0.011143514886498451,
-0.007780452724546194,
-0.017686722800135612,
-0.012997173704206944,
0.03513564169406891,
0.048811934888362885,
0.009761138819158077,
-0.0002384822873864323,
0.004784470424056053,
-0.031986478716135025,
0.028990350663661957,
0.001485777786001563,
0.05297130346298218,
-0.026914160698652267,
-0.029353303834795952,
-0.04974905773997307,
-0.049981556832790375,
0.0491187684237957,
0.005690437741577625,
-0.034689661115407944,
-0.1157650277018547,
-0.04227707162499428,
-0.028123240917921066,
0.010762249119579792,
0.008586045354604721,
0.022787796333432198,
0.06753025949001312,
0.04955403506755829,
0.0013689937768504024,
0.005638201255351305,
-0.01444156002253294,
-0.051629845052957535,
0.021462172269821167,
0.02351304702460766,
0.008187511004507542,
-0.003554842434823513,
0.004630447831004858,
-0.016724536195397377,
0.03489658236503601,
-0.00016842900367919356,
-0.04254665970802307,
0.01856931298971176,
-0.0380103774368763,
0.07146062701940536,
0.06985771656036377,
0.021978281438350677,
0.007027675863355398,
0.006943871732801199,
0.007857956923544407,
-0.0037695837672799826,
0.03757714107632637,
-0.019063621759414673,
0.04116006940603256,
0.03603149950504303,
-0.009304407984018326,
-0.027291275560855865,
-0.017231449484825134,
0.006133351009339094,
-0.07549554109573364,
0.041957926005125046,
0.026578133925795555,
0.02311740443110466,
0.02577199600636959,
0.028596604242920876,
0.04589680954813957,
0.03192402794957161,
-0.038328494876623154,
-0.0004338126163929701,
0.003404049202799797,
-0.012289989739656448,
-0.005887212231755257,
0.021052170544862747,
0.030684979632496834,
-0.013027128763496876,
0.011761271394789219,
-0.022508999332785606,
0.06740815192461014,
0.030491463840007782,
0.02233080193400383,
-0.029528921470046043,
0.025261273607611656,
0.022603675723075867,
0.010690481401979923,
-0.016445687040686607,
-0.05398879572749138,
0.0008284358773380518,
-0.02556346170604229,
-0.05333681404590607,
-0.03458830714225769,
-0.02615838311612606,
-0.03591805696487427,
0.029107147827744484,
-0.012267964892089367,
-0.048477526754140854,
0.02539609745144844,
0.02520778961479664,
-0.04922797530889511,
0.010107994079589844,
-0.027583377435803413,
0.01103398110717535,
0.06839875876903534,
0.009375969879329205,
0.05189824476838112,
0.006674090400338173,
0.03736129403114319,
0.04807928949594498,
0.03712841868400574,
0.022917337715625763,
0.007981832139194012,
-0.03653516620397568,
-0.05475083738565445,
0.04356776922941208,
-0.07052922248840332,
0.038565494120121,
-0.008842086419463158,
0.05501064658164978,
-0.023807253688573837,
-0.005934524815529585,
0.05498944967985153,
0.044345706701278687,
0.018513357266783714,
-0.04449484124779701,
0.013520847074687481,
0.005720009095966816,
-0.032737184315919876,
0.009505442343652248,
-0.023782866075634956,
-0.020052628591656685,
-0.01655781827867031,
-0.02753327041864395,
0.0020392294973134995,
0.0030843133572489023,
-0.058142129331827164,
0.015795757994055748,
0.058883413672447205,
-0.05947190150618553,
-0.029139168560504913,
-0.035385873168706894,
0.07028885185718536,
-0.02984747290611267,
-0.06540356576442719,
0.045132581144571304,
0.03267151862382889,
0.023893211036920547,
0.006546297110617161,
-0.05703281983733177,
-0.030247021466493607,
0.0023894680198282003,
-0.0008928934694267809,
-0.042068786919116974,
-0.05760161951184273,
-0.011642088182270527,
-0.008543567731976509,
0.010220556519925594,
-0.021344583481550217,
0.022760389372706413,
-0.006604044698178768,
0.02381511591374874,
-0.08531813323497772,
-0.07249598205089569,
0.03935858979821205,
-0.0693669468164444,
0.03662874177098274,
-0.012841330841183662,
-0.025911401957273483,
0.04011248052120209,
-0.03470882400870323,
-0.009283344261348248,
0.0059539321810007095,
-0.03236228972673416,
0.01506826002150774,
0.014355134218931198,
0.028083207085728645,
0.0356624610722065,
-0.029444092884659767,
-0.045204438269138336,
-0.0027424157597124577,
-0.009070334024727345,
0.01823698915541172,
-0.04056829214096069,
-0.010676140896975994,
-0.0007865437655709684,
0.02423115074634552,
-0.0350906178355217,
0.03581943362951279,
0.05668706074357033,
0.06797974556684494,
-0.010139966383576393,
-0.03996015340089798,
0.04096625745296478,
0.038431327790021896,
-0.004003681242465973,
0.026484720408916473,
-0.04727254807949066,
-0.020764974877238274,
0.04856526479125023,
-0.023696446791291237,
-0.018688654527068138,
0.024532126262784004,
-0.06273947656154633,
-0.01605846732854843,
0.05992884933948517,
-0.047388311475515366,
0.007268622983247042,
0.03158864378929138,
-0.02402368374168873,
0.0008363855304196477,
-0.05731862038373947,
-0.027724530547857285,
0.022349931299686432,
0.029157346114516258,
-0.04132212698459625,
0.06016148626804352,
0.020694848150014877,
-0.008947364054620266,
-0.061138756573200226,
0.06790363043546677,
0.006306583061814308,
0.02223462238907814,
0.04833073914051056,
-0.08234244585037231,
-0.07324831187725067,
0.0024051566142588854,
0.04539577662944794,
-0.010094985365867615,
0.01923862285912037,
-0.04626113548874855,
-0.02653748169541359,
0.0020308755338191986,
-0.03100297972559929,
-0.06417623162269592,
-0.04749105125665665,
-0.0063848597928881645,
-0.03238871321082115,
-0.03892211988568306,
0.003842826932668686,
0.01828880049288273,
-0.007954786531627178,
-0.01702411286532879,
-0.022539226338267326,
0.008519832044839859,
-0.04397242143750191,
0.03270429000258446,
0.03432007506489754,
-0.0003208158886991441,
0.0037776976823806763,
-0.027823567390441895,
0.01934277079999447,
0.05418809875845909,
0.023440474644303322,
-0.016819104552268982,
0.040706608444452286,
-0.010720797814428806,
0.06758847832679749,
0.0163467675447464,
-0.012563151307404041,
-0.022779712453484535,
-0.0431840755045414,
-0.04543212056159973,
0.0574641115963459,
0.05186842381954193,
-0.033931441605091095,
-0.02308381162583828,
-0.018051614984869957,
-0.017152298241853714,
0.03474576771259308,
-0.012094801291823387,
-0.032784875482320786,
0.022251702845096588,
-0.04313581809401512,
0.017586201429367065,
0.013039572164416313,
-0.015500469133257866,
-0.00042563321767374873,
0.007694816682487726,
-0.02597852796316147,
-0.03602862358093262,
0.03228813409805298,
-0.0071593355387449265,
0.016040343791246414,
-0.007642366923391819,
0.03385625779628754,
0.009445815347135067,
0.025677267462015152,
0.06012742221355438,
0.0012729251757264137,
0.027878012508153915,
0.039680808782577515,
-0.020740138366818428,
0.019613193348050117,
0.053129587322473526,
0.010188897140324116,
-0.03489694371819496,
0.006779662799090147,
-0.033126454800367355,
-0.009166841395199299,
-0.024450009688735008,
0.04468438774347305,
-0.02764500305056572,
0.004943507257848978,
0.023408815264701843,
0.00955620314925909,
0.012523839250206947,
0.01451002899557352,
0.010655703023076057,
-0.001781703787855804,
-0.026027290150523186,
0.026597773656249046,
0.02715049497783184,
-0.010835666209459305,
-0.013603846542537212,
-0.0034030131064355373,
-0.025885069742798805,
0.005615573842078447,
0.028032952919602394,
0.009210698306560516,
-0.04749612882733345,
0.08551390469074249,
-0.004395313560962677,
0.056562602519989014,
-0.06467276811599731,
0.014717460609972477,
-0.01907474175095558,
-0.0551602765917778,
-0.04437341168522835,
0.07622503489255905,
0.01527875941246748,
0.06684362143278122,
-0.007514841854572296,
-0.012195154093205929,
0.020092176273465157,
0.00893706176429987,
-0.0006062858155928552,
-0.0008839159272611141,
-0.031705647706985474,
-0.008777420967817307,
-0.019834836944937706,
0.08132575452327728,
-0.012997398152947426,
-0.006055046804249287,
-0.010766880586743355,
-0.07982268184423447,
-0.0038637982215732336,
0.03069993294775486,
0.06638003885746002,
0.029816050082445145,
-0.004251331090927124,
0.02101934514939785,
0.036673903465270996,
0.014082890003919601,
-0.019174091517925262,
0.006269034463912249,
-0.01338555384427309,
0.007104749791324139,
0.01628667488694191,
-0.040835000574588776,
-0.02839243970811367,
0.043184809386730194,
0.004647416993975639,
-0.056769710034132004,
-0.015302104875445366,
-0.028151974081993103,
0.04584256559610367,
-0.03478733450174332,
-0.029772276058793068,
0.019667835906147957,
-0.026515275239944458,
-0.06377393752336502,
-0.021917950361967087,
0.009738223627209663,
-0.004735690075904131,
0.02089402638375759,
0.020477594807744026,
0.01576816663146019,
-0.016715552657842636,
-0.02684492990374565,
-0.034684743732213974,
0.08379139006137848,
0.02387930639088154,
-0.004059274215251207,
0.02371428720653057,
-0.014557520858943462,
-0.030880991369485855,
0.025591488927602768,
0.061826229095458984,
0.01382230781018734,
0.006402335129678249,
-0.04212234914302826,
-0.07972652465105057,
-0.0012347560841590166,
-0.007300506345927715,
0.006059921346604824,
0.003670663107186556,
0.08852231502532959,
0.026242034509778023,
0.028432542458176613,
-0.008731631562113762,
0.03239159286022186,
-0.026638289913535118,
-0.013047492131590843,
0.03339632973074913,
-0.014367611147463322,
-0.0013036089949309826,
-0.039506696164608,
0.010325077921152115,
-0.013303308747708797,
-0.042120665311813354,
0.0031654955819249153,
-0.0016335208201780915,
-0.022917404770851135,
-0.025416191667318344,
-0.03447521850466728,
-0.05350066348910332,
0.006347354035824537,
-0.11483200639486313,
0.030096912756562233,
0.02495512180030346,
-0.03776305913925171,
-0.01070934347808361,
0.014039330184459686,
0.05096610262989998,
-0.04558210074901581,
0.011556356213986874,
0.014125034213066101,
-0.055723901838064194,
0.0001983327092602849,
0.028710218146443367,
0.021320270374417305,
-0.05206337943673134,
0.01814606972038746,
-0.007106403820216656,
0.008639075793325901,
-0.020866794511675835,
0.011785674840211868,
0.015719808638095856,
-0.03160392493009567,
0.03817569091916084,
-0.035792071372270584,
0.013093902729451656,
0.017286185175180435,
-0.019074277952313423,
-0.03900105133652687,
0.0032108474988490343,
0.0581703819334507,
-0.03983688727021217,
-0.014646959491074085,
-0.011682006530463696,
0.040941327810287476
] |
<p>Why any fermion can be written as a combination of two Majorana fermions? Is there any physical meaning in it? Why Majorana fermion can be used for topological quantum computation?</p> | g7845 | [
0.03502953052520752,
-0.017248762771487236,
0.01813063956797123,
-0.025623487308621407,
0.06835903972387314,
-0.04891844466328621,
0.01628410443663597,
0.05300687998533249,
-0.015061608515679836,
-0.028780024498701096,
0.011108476668596268,
-0.018834993243217468,
0.08199625462293625,
0.01709097996354103,
-0.01473567821085453,
0.02333047427237034,
-0.019593574106693268,
0.07826907932758331,
0.03540688753128052,
-0.08865118026733398,
-0.018957441672682762,
0.07998771965503693,
0.029601315036416054,
-0.021785356104373932,
-0.018691109493374825,
0.0035709000658243895,
0.022658325731754303,
-0.008587694726884365,
-0.010570530779659748,
-0.023256313055753708,
0.037540968507528305,
-0.07344697415828705,
0.06910282373428345,
-0.0029731467366218567,
-0.027358192950487137,
-0.020431462675333023,
0.026068026199936867,
-0.03385264053940773,
0.03470064699649811,
-0.07122454792261124,
0.02297455258667469,
-0.012275651097297668,
-0.04170636832714081,
-0.07090089470148087,
-0.03613417595624924,
0.036542635411024094,
-0.05459175631403923,
0.033952098339796066,
-0.009979300200939178,
-0.008180282078683376,
0.04580967128276825,
-0.04702004790306091,
0.0027718590572476387,
0.041140396147966385,
0.07785656303167343,
-0.012366094626486301,
0.04777863994240761,
-0.04504811018705368,
0.08035558462142944,
0.03311162441968918,
-0.013008559122681618,
-0.01114967092871666,
-0.0004384279891382903,
0.05221801623702049,
0.05652874708175659,
0.020336614921689034,
-0.013045364990830421,
-0.0038407831452786922,
0.05383769050240517,
0.07344015687704086,
0.019991712644696236,
-0.0617806650698185,
0.043868258595466614,
-0.018478481099009514,
0.06841959804296494,
0.027306435629725456,
-0.012108740396797657,
-0.007356810383498669,
-0.005062232259660959,
0.053949445486068726,
0.001953657018020749,
-0.07768570631742477,
0.01909942552447319,
0.033817194402217865,
0.007395988795906305,
-0.019717209041118622,
-0.03679270297288895,
-0.01922893151640892,
-0.034017615020275116,
0.051576077938079834,
0.021696511656045914,
-0.021739309653639793,
-0.000024233417207142338,
0.016419606283307076,
-0.01687343418598175,
-0.06055322661995888,
-0.04879263415932655,
-0.003999304957687855,
0.014464451931416988,
0.00010331767407478765,
-0.01184081844985485,
0.03739914670586586,
0.04840390011668205,
0.0195364598184824,
0.0013292675139382482,
0.016347825527191162,
-0.001726314309053123,
0.024462005123496056,
-0.03520599752664566,
0.023873301222920418,
-0.02553526498377323,
0.039662446826696396,
0.006003236398100853,
-0.023540114983916283,
0.002023123437538743,
0.04447365924715996,
0.039498310536146164,
-0.06128237769007683,
-0.030831733718514442,
0.02942020818591118,
0.004953853320330381,
-0.04447755962610245,
0.007754697930067778,
0.016690285876393318,
0.007819253951311111,
-0.005269799381494522,
-0.024346353486180305,
0.017484692856669426,
0.04207557067275047,
-0.02248910441994667,
-0.01518984418362379,
-0.053159214556217194,
-0.00447814492508769,
0.0331704318523407,
0.031370509415864944,
0.0032764715142548084,
-0.038134753704071045,
-0.013953883200883865,
0.0291596632450819,
0.007927312515676022,
0.0320562943816185,
-0.0557546466588974,
-0.051333773881196976,
-0.040051139891147614,
-0.0029869209975004196,
-0.02696111984550953,
0.0012925781775265932,
-0.010061084292829037,
0.0030378815717995167,
0.036045562475919724,
-0.02382761240005493,
0.036666158586740494,
-0.008970960974693298,
-0.050960659980773926,
0.03436742722988129,
0.004395213443785906,
0.054741859436035156,
-0.010986260138452053,
-0.00035358130116946995,
0.028062444180250168,
0.035573333501815796,
0.01220033224672079,
0.0027324045076966286,
-0.013371901586651802,
-0.0395168662071228,
0.011013875715434551,
0.021157896146178246,
-0.03601687029004097,
-0.044756222516298294,
-0.027349935844540596,
-0.017452271655201912,
0.03210180997848511,
-0.0567617192864418,
0.03636547178030014,
0.035627782344818115,
0.03310586139559746,
-0.02408466301858425,
0.02916167676448822,
0.02842014469206333,
0.006681600119918585,
-0.009304995648562908,
0.03348194807767868,
-0.03759343549609184,
0.069895438849926,
-0.044509802013635635,
0.008741204626858234,
0.0004524255055002868,
0.08153866976499557,
-0.013822545297443867,
-0.023075662553310394,
0.01747198775410652,
-0.030363161116838455,
0.08783137053251266,
0.06229684129357338,
0.010533498600125313,
-0.025251319631934166,
0.05726051330566406,
-0.0022517109755426645,
-0.08664148300886154,
-0.0002647416549734771,
-0.04329490289092064,
-0.027329053729772568,
0.0369105190038681,
-0.051369164139032364,
0.026957444846630096,
0.057147733867168427,
-0.011210867203772068,
0.0027468905318528414,
0.0019708210602402687,
-0.022537454962730408,
0.026794349774718285,
0.04378584399819374,
0.06270243972539902,
-0.02281205542385578,
0.006772145628929138,
-0.045043203979730606,
-0.017372028902173042,
-0.07855894416570663,
-0.03654434531927109,
0.06488383561372757,
0.01736721768975258,
-0.017063293606042862,
0.023514704778790474,
-0.0034437724389135838,
-0.02839173935353756,
0.03825245052576065,
-0.06811153143644333,
-0.021965479478240013,
-0.02963823452591896,
-0.02774016000330448,
-0.052337851375341415,
-0.04312334209680557,
-0.03517093136906624,
0.03906732052564621,
-0.04317157715559006,
-0.0023071204777806997,
0.00351051427423954,
0.05791597440838814,
0.05569474399089813,
0.04197902977466583,
0.01873433217406273,
-0.057594794780015945,
0.010831591673195362,
0.02013540267944336,
-0.013526762835681438,
-0.0014365140814334154,
0.021711286157369614,
-0.012098410166800022,
-0.02998940274119377,
0.01564398780465126,
-0.015213117934763432,
-0.03901667147874832,
-0.0944734662771225,
0.03391820937395096,
-0.007210122887045145,
-0.018058938905596733,
0.04307851195335388,
-0.03671109676361084,
0.002839285647496581,
-0.039969880133867264,
0.06686628609895706,
-0.040292687714099884,
0.019286274909973145,
0.010006715543568134,
0.03184046223759651,
-0.01702951081097126,
0.008389484137296677,
0.04188040643930435,
0.029984690248966217,
0.05308523401618004,
-0.03794776648283005,
0.03683863580226898,
0.0866360068321228,
-0.04340999200940132,
0.001102471025660634,
-0.0426616370677948,
-0.04127378389239311,
0.026771897450089455,
0.01780260168015957,
-0.033767666667699814,
-0.007820201106369495,
0.06392179429531097,
-0.04329200088977814,
0.07040248066186905,
0.05334877595305443,
-0.026632988825440407,
0.011386936530470848,
0.043966904282569885,
0.035099200904369354,
-0.012780357152223587,
0.027097081765532494,
0.0011588787892833352,
0.03498578444123268,
0.004090069327503443,
0.005042548757046461,
-0.010936805978417397,
-0.032425351440906525,
0.036693137139081955,
-0.017454111948609352,
0.10032641142606735,
0.06266338378190994,
0.016924243420362473,
0.01590152084827423,
-0.015119141899049282,
0.02201264351606369,
0.012955301441252232,
-0.04531839117407799,
0.03738823160529137,
-0.05318387970328331,
-0.05940936505794525,
0.08263856172561646,
0.06537005305290222,
0.04064885154366493,
0.0210249125957489,
-0.02819708362221718,
0.05318751186132431,
-0.04326614737510681,
0.021683182567358017,
-0.020434724166989326,
-0.021123463287949562,
-0.02263966202735901,
0.0059745656326413155,
-0.00466514378786087,
0.01100495271384716,
0.015847856178879738,
0.007474980317056179,
-0.03741837292909622,
0.025148514658212662,
0.030353885143995285,
-0.07273830473423004,
-0.005362336058169603,
-0.005506896413862705,
-0.04098541662096977,
0.029565436765551567,
-0.04054434224963188,
-0.031238745898008347,
-0.03989710286259651,
0.0005311653367243707,
0.010729221627116203,
-0.02977517992258072,
-0.05705585703253746,
-0.028215302154421806,
-0.0476241372525692,
-0.03885599598288536,
0.054379452019929886,
0.012119865044951439,
-0.03198358416557312,
-0.06506017595529556,
-0.012411962263286114,
0.004087361972779036,
-0.021730784326791763,
-0.005041925236582756,
0.05415453389286995,
0.06908614188432693,
-0.03547808155417442,
0.00460453424602747,
-0.014874550513923168,
-0.02337133325636387,
-0.016027092933654785,
0.04812673106789589,
0.06488396227359772,
0.03827142342925072,
-0.04011722654104233,
-0.015199658460915089,
-0.004865435883402824,
-0.02053787186741829,
0.02648879587650299,
0.02559318020939827,
0.009308532811701298,
0.033401139080524445,
-0.032160814851522446,
-0.006727276835590601,
-0.03440112993121147,
-0.04920338839292526,
0.015240184962749481,
0.009777291677892208,
0.0009427631157450378,
-0.025080744177103043,
-0.04130265489220619,
-0.03809935227036476,
0.055165234953165054,
0.005604030564427376,
0.01974925771355629,
0.03273574262857437,
0.03165841102600098,
0.01909177005290985,
-0.08381256461143494,
0.032060809433460236,
0.017505330964922905,
-0.009014544077217579,
-0.03130283206701279,
0.00019548836280591786,
-0.023396721109747887,
-0.017600255087018013,
0.005722008179873228,
0.004229478072375059,
0.02484901435673237,
-0.029513893648982048,
0.0148269422352314,
0.007132676895707846,
-0.06840303540229797,
-0.05390334501862526,
0.009875580668449402,
-0.06352345645427704,
0.006668719928711653,
-0.029617607593536377,
0.014849661849439144,
-0.039116229861974716,
0.057188473641872406,
-0.07143979519605637,
0.02248401567339897,
0.007584163453429937,
-0.003934796899557114,
-0.01143058855086565,
0.00560767063871026,
-0.04335998743772507,
-0.08149378001689911,
-0.05257832631468773,
-0.03337857499718666,
-0.009305596351623535,
0.01856582798063755,
0.005485296715050936,
0.04303555563092232,
0.020723409950733185,
0.0161199402064085,
0.025075096637010574,
0.012302828021347523,
0.017785698175430298,
-0.011579694226384163,
-0.004072471056133509,
0.04231620207428932,
0.08770354092121124,
-0.01747005432844162,
0.0582142099738121,
-0.034159719944000244,
-0.0025844243355095387,
-0.06171400099992752,
0.016513170674443245,
0.07326918095350266,
-0.013585547916591167,
0.04209306091070175,
-0.07657602429389954,
-0.041142579168081284,
-0.0011250533862039447,
-0.007719298359006643,
0.012085852213203907,
-0.0752093642950058,
-0.009351437911391258,
-0.0645814761519432,
0.013621789403259754,
0.021359724923968315,
0.04067518934607506,
0.0057867905125021935,
0.03170556202530861,
0.029565973207354546,
0.01817939430475235,
-0.001563171623274684,
-0.061287254095077515,
-0.012371012009680271,
0.0003483451728243381,
-0.02456524595618248,
-0.017286114394664764,
0.009516232647001743,
0.0055397083051502705,
0.03927098587155342,
0.06040751561522484,
-0.06740894913673401,
-0.0037074389401823282,
0.029032552614808083,
0.009328523650765419,
-0.042375508695840836,
-0.056197211146354675,
-0.025104612112045288,
-0.01945282518863678,
0.04859164357185364,
0.021983178332448006,
-0.03415993973612785,
-0.04344158619642258,
-0.001923608360812068,
-0.03565963730216026,
-0.012211768887937069,
-0.060214124619960785,
0.005205996800214052,
-0.011753182858228683,
-0.04728905111551285,
0.010738400742411613,
-0.058751143515110016,
0.023871352896094322,
0.006451055407524109,
0.02644244022667408,
0.044596731662750244,
-0.017045384272933006,
0.06631201505661011,
0.001576991518959403,
-0.004950805567204952,
-0.009236019104719162,
0.03332410380244255,
0.020530374720692635,
0.009467112831771374,
-0.03600389137864113,
0.0029487379360944033,
-0.023553958162665367,
0.0061793033964931965,
0.01956302858889103,
0.007994411513209343,
0.06194025278091431,
0.05479131266474724,
-0.07539099454879761,
0.005807673092931509,
0.012591439299285412,
0.0546300895512104,
-0.02580120600759983,
-0.017375396564602852,
-0.003442582208663225,
-0.000381964462576434,
0.05280190706253052,
0.06300397217273712,
-0.023669591173529625,
0.005759689956903458,
-0.03760368376970291,
-0.023279638960957527,
0.014862006530165672,
-0.0011333085130900145,
-0.04693005979061127,
0.01749163679778576,
-0.0019210660830140114,
0.005660743918269873,
-0.06353775411844254,
0.041175633668899536,
0.0673147514462471,
-0.03222713619470596,
0.0006674548494629562,
-0.019227618351578712,
-0.0059788827784359455,
-0.036981213837862015,
-0.025813022628426552,
-0.011953627690672874,
-0.03302102908492088,
0.009257498197257519,
-0.000035115794162265956,
-0.0024676411412656307,
0.011265973560512066,
0.016506195068359375,
0.05695214867591858,
0.023808907717466354,
-0.035131338983774185,
0.00645971205085516,
-0.0014362488873302937,
0.015152967534959316,
-0.014921242371201515,
-0.06353528797626495,
0.008511899970471859,
-0.023116661235690117,
-0.10126588493585587,
0.02428044192492962,
0.01601496897637844,
-0.04044391214847565,
0.03294705972075462,
0.005377480760216713,
0.01839512214064598,
0.010606611147522926,
0.01647704653441906,
0.007956607267260551,
0.005717305466532707,
-0.007580021396279335,
-0.017843371257185936,
-0.04410510137677193,
-0.003319769399240613,
0.010144351050257683,
0.01613686792552471,
0.052291739732027054,
0.01279896404594183,
-0.022442270070314407,
0.08628090471029282,
-0.012905342504382133,
-0.0006477334536612034,
0.033882543444633484,
0.023278292268514633,
0.0007564959232695401,
-0.0658549889922142,
0.06199965253472328,
-0.024984322488307953,
0.028007926419377327,
-0.05305223539471626,
0.014854764565825462,
-0.016221418976783752,
-0.038952503353357315,
0.02819252386689186,
0.013700655661523342,
0.03623683750629425,
-0.025344861671328545,
0.009354707784950733,
-0.0695204883813858,
0.0011718780733644962,
0.008063267916440964,
-0.012430462054908276,
-0.005102981347590685,
0.008928573690354824,
-0.08145840466022491,
-0.012541908770799637,
0.011637214571237564,
-0.012374772690236568,
-0.00799481850117445,
0.04954075068235397,
0.03722170367836952,
0.08564954251050949,
-0.027569914236664772,
0.01403451431542635,
-0.0197239238768816,
-0.0031556151807308197,
-0.021492552012205124,
0.00445614755153656,
-0.03303582966327667,
-0.00008050601172726601,
-0.015054607763886452,
-0.06870774179697037,
-0.01245004404336214,
0.006996768526732922,
-0.01206796895712614,
-0.029122857376933098,
0.02823840081691742,
-0.03984193876385689,
-0.03114607185125351,
-0.003639915259554982,
-0.00013620154641103,
0.03061150759458542,
0.0062365722842514515,
0.018415270373225212,
0.0926763266324997,
-0.00572892976924777,
-0.013472300954163074,
0.005091688130050898,
0.06914858520030975,
0.044295504689216614,
-0.021817034110426903,
-0.020883696153759956,
-0.07553146779537201,
-0.01705031283199787,
-0.004123160149902105,
0.0332200713455677,
-0.03735020011663437,
0.047424111515283585,
-0.03619232773780823,
0.040525536984205246,
0.03665924817323685,
0.00791934598237276,
0.0011774069862440228,
-0.025858433917164803,
-0.04673690348863602,
-0.04633354768157005,
0.0005330311832949519,
0.04142380505800247,
0.011977802030742168,
0.014030971564352512,
-0.05773891508579254,
-0.052422042936086655,
-0.05366687476634979,
0.022087926045060158,
-0.050491947680711746,
-0.021781323477625847,
-0.04962890222668648,
0.01631869375705719,
-0.028718531131744385,
-0.04055478051304817,
0.05104227364063263,
0.03388768434524536,
0.008941310457885265,
-0.033531080931425095,
0.024795200675725937,
-0.007252804469317198,
-0.08194799721240997,
-0.002907742280513048,
-0.016029637306928635,
-0.02050938829779625,
-0.012380992993712425,
-0.031879980117082596,
-0.022020898759365082,
-0.046694979071617126,
-0.0035415489692240953,
-0.02680719643831253,
0.038114458322525024,
0.054940469563007355,
0.04882815107703209,
-0.0407780297100544,
-0.006297879386693239,
0.04080849885940552,
0.021540895104408264,
0.06167229264974594,
0.025029202923178673,
0.020041365176439285,
0.06816507130861282,
-0.04863720387220383,
0.04289321228861809,
0.009028837084770203,
-0.055699046701192856,
0.0359986275434494,
-0.03775279223918915,
-0.014765801839530468,
0.007669507060199976,
-0.007576629985123873,
0.04010092467069626,
-0.022520843893289566,
-0.0719171091914177,
0.02373114414513111,
0.04624684900045395,
-0.011516546830534935,
0.06759236752986908,
0.026356961578130722,
-0.011907881125807762,
-0.014295738190412521,
-0.010739144869148731,
0.01833251863718033,
0.012735591270029545,
0.06329914182424545,
-0.07263196259737015,
-0.01967751234769821,
0.026558658108115196,
0.022991133853793144,
0.02036268450319767,
-0.0025066547095775604,
-0.008133157156407833,
-0.04636384919285774,
0.0062270937487483025,
-0.022621773183345795,
-0.1074749156832695,
-0.016769539564847946,
0.0370679534971714,
0.011260694824159145,
0.028479887172579765,
0.08351055532693863,
0.03493696451187134,
0.01784457452595234,
-0.03390452638268471,
0.012338614091277122,
-0.027764851227402687,
0.03947974741458893,
-0.06363736093044281,
0.002360889920964837,
0.016597000882029533,
-0.011958076618611813,
-0.010637106373906136,
0.04329986870288849,
0.00324236205779016,
-0.020253861322999,
-0.015063089318573475,
-0.023623958230018616,
-0.03896968066692352,
0.006874863523989916,
0.06582334637641907,
-0.05306454002857208,
0.02269984781742096,
-0.03997781500220299,
0.004882745910435915,
0.01359652727842331,
-0.007109520956873894,
0.02272525615990162,
-0.004545293748378754,
-0.0004920203355140984,
0.02463245578110218,
-0.0036492228973656893,
0.0364772230386734,
0.04631989449262619,
-0.017959360033273697,
-0.026871027424931526,
-0.002959225559607148,
-0.004465211648494005,
0.00010778411524370313,
-0.012589788995683193
] |
<p>In the case of a complex shape filiform distribution of current, are we allowed to determine the magnetic field created by sections of the distribution and then summing them up, like we do with a discrete distribution of charge when calculating the electric field?</p>
<p>Thank you</p> | g7846 | [
0.02553006447851658,
-0.008159225806593895,
-0.031347449868917465,
-0.054852452129125595,
0.043728332966566086,
-0.042126744985580444,
0.008101538754999638,
0.0077657997608184814,
-0.0026342165656387806,
-0.02381434477865696,
-0.0727478638291359,
-0.003935836721211672,
0.04542146623134613,
-0.014789390377700329,
-0.0055430796928703785,
-0.018453266471624374,
0.006223901640623808,
-0.0004575214406941086,
0.01565088890492916,
0.006129301153123379,
-0.02151983603835106,
-0.0056322310119867325,
0.09736309200525284,
-0.0005873760674148798,
-0.020950496196746826,
0.004175305366516113,
0.021596424281597137,
-0.03664718568325043,
-0.024305518716573715,
-0.02585000731050968,
0.04107285290956497,
0.08744508773088455,
0.0512721948325634,
0.033835235983133316,
-0.05583232268691063,
-0.053927116096019745,
0.01731221377849579,
0.06098384037613869,
0.03847196325659752,
0.027037350460886955,
0.002176017966121435,
0.02882392331957817,
0.03331409767270088,
-0.04481233283877373,
-0.04058656841516495,
-0.003352079540491104,
-0.021717729046940804,
-0.01578969694674015,
-0.04944688826799393,
0.004351109731942415,
-0.07530415803194046,
-0.04712294414639473,
0.046376101672649384,
-0.013582006096839905,
0.0010140703525394201,
-0.013353516347706318,
0.011356500908732414,
-0.05618790164589882,
0.0303021352738142,
0.008648870512843132,
-0.03184432536363602,
0.023220397531986237,
-0.037650056183338165,
0.0546884760260582,
0.018377529457211494,
0.00715139415115118,
-0.06656740605831146,
-0.007807067129760981,
-0.00608427356928587,
-0.0020931323524564505,
-0.0063187796622514725,
-0.030504975467920303,
0.04861990362405777,
-0.042119525372982025,
-0.04457070305943489,
0.019814496859908104,
0.00894697941839695,
0.05240406468510628,
0.03783030062913895,
-0.02332577109336853,
-0.018430577591061592,
0.0119703970849514,
0.04012535884976387,
-0.005793062970042229,
0.001856475486420095,
-0.00740259001031518,
0.035088442265987396,
0.010484416969120502,
0.03077368438243866,
0.06150094047188759,
-0.010045159608125687,
-0.03149307891726494,
0.037940170615911484,
-0.01908649504184723,
-0.019260115921497345,
-0.05913589522242546,
0.007491296622902155,
0.00010703711450332776,
-0.036584850400686264,
0.03376045078039169,
-0.02737244963645935,
0.03470062091946602,
0.001507673179730773,
0.007028419058769941,
-0.02229156158864498,
0.017948897555470467,
-0.031772367656230927,
-0.009028393775224686,
0.02275594137609005,
-0.014966214075684547,
-0.03751811757683754,
-0.05376226454973221,
-0.08057020604610443,
0.05290146544575691,
-0.02271154336631298,
0.010954021476209164,
0.03705905005335808,
-0.04472833126783371,
0.016981732100248337,
0.08527350425720215,
-0.008741114288568497,
-0.08286697417497635,
0.005780666135251522,
0.03340945020318031,
-0.003777808276936412,
0.035872090607881546,
-0.028937391936779022,
0.07208504527807236,
0.05092756822705269,
-0.06239069625735283,
0.03544698655605316,
0.012741721235215664,
0.04192220792174339,
-0.0439516045153141,
0.00022701610578224063,
0.0011272475821897388,
-0.008500400930643082,
-0.002808724995702505,
-0.042528171092271805,
0.03483114391565323,
0.020318321883678436,
-0.02585306577384472,
0.030649852007627487,
-0.0696919783949852,
0.09171585738658905,
-0.002779006026685238,
-0.018778318539261818,
-0.07349349558353424,
0.03882071375846863,
0.012269269675016403,
0.002949956338852644,
-0.014586913399398327,
0.0018600142793729901,
-0.014449111185967922,
0.009511471726000309,
0.001693862141110003,
0.001987548777833581,
0.021329840645194054,
0.013389740139245987,
-0.06293440610170364,
-0.005101123359054327,
-0.03687893599271774,
-0.01618143357336521,
-0.03840640187263489,
0.022587306797504425,
-0.033207006752491,
0.05089142918586731,
0.001426349044777453,
0.010728716850280762,
-0.02779504470527172,
0.06286018341779709,
0.029674256220459938,
0.013911879621446133,
0.04808591306209564,
0.09929600358009338,
0.0009492830140516162,
0.0005478271632455289,
-0.03131711110472679,
0.035887137055397034,
0.007766083814203739,
-0.07255800813436508,
0.04390091076493263,
0.002602251013740897,
0.022657930850982666,
0.02908840961754322,
-0.011672277003526688,
-0.022753916680812836,
0.012963192537426949,
-0.0472099632024765,
0.00020049084560014307,
-0.04538191482424736,
0.022768687456846237,
0.007766598369926214,
0.08976670354604721,
-0.0031983344815671444,
0.007877852767705917,
0.040931932628154755,
0.011520127765834332,
-0.057668253779411316,
0.009308797307312489,
-0.011699384078383446,
0.09508448839187622,
0.0064079430885612965,
-0.016143934801220894,
0.024689385667443275,
0.031934063881635666,
-0.030621666461229324,
-0.03303942829370499,
0.005416561383754015,
0.05171642452478409,
0.005316831637173891,
-0.013493586331605911,
-0.058914560824632645,
0.0257598664611578,
-0.0017410836881026626,
-0.03911448270082474,
-0.023355960845947266,
-0.024959569796919823,
-0.012305347248911858,
-0.01267213374376297,
-0.01922815665602684,
-0.03629028797149658,
0.036226578056812286,
-0.01102385763078928,
-0.034752123057842255,
0.01222355104982853,
0.04798411205410957,
0.013572894036769867,
-0.006487185135483742,
-0.04715164005756378,
-0.0221059862524271,
-0.037689853459596634,
-0.017998434603214264,
-0.031060535460710526,
0.016358891502022743,
-0.018115509301424026,
-0.042293570935726166,
0.0031754630617797375,
-0.00355976028367877,
-0.016637148335576057,
-0.02838108129799366,
-0.017783259972929955,
0.0647306963801384,
-0.014823785051703453,
-0.0072260950691998005,
0.04695276916027069,
0.0581517368555069,
0.014403164386749268,
0.029695112258195877,
-0.00037513719871640205,
0.004455390851944685,
-0.08409993350505829,
0.027776602655649185,
0.043437253683805466,
-0.016484994441270828,
-0.032884631305933,
0.058503832668066025,
0.012635817751288414,
-0.016845231875777245,
-0.0383417010307312,
-0.007495058700442314,
-0.03516625985503197,
-0.018079962581396103,
0.004896457772701979,
-0.04821634292602539,
-0.006156555842608213,
0.04053244739770889,
-0.055388543754816055,
0.010409521870315075,
-0.008044295944273472,
-0.03680368512868881,
0.06886270642280579,
0.006802217569202185,
0.0436556376516819,
0.010376133024692535,
-0.019529007375240326,
0.010595086961984634,
-0.018604999408125877,
0.03489682823419571,
0.039817895740270615,
0.003620641538873315,
-0.033912938088178635,
-0.03663250803947449,
0.02562880888581276,
0.034917380660772324,
-0.029197977855801582,
0.030122267082333565,
-0.04094447195529938,
-0.029608143493533134,
0.059552256017923355,
-0.015170619823038578,
0.01898348517715931,
0.028710128739476204,
-0.008741408586502075,
-0.0541861467063427,
0.01789337396621704,
-0.018641648814082146,
-0.05951206758618355,
0.05637769401073456,
0.006661425810307264,
0.06253734976053238,
-0.014707856811583042,
-0.018415676429867744,
0.0012075335253030062,
0.021879564970731735,
0.054432787001132965,
0.0011366211110725999,
-0.02225475385785103,
0.0351606160402298,
-0.01825920306146145,
-0.04209525138139725,
0.017163777723908424,
0.03507699817419052,
-0.01212269626557827,
-0.027752848342061043,
0.00800385046750307,
0.03649196773767471,
0.0010120597435161471,
0.020206280052661896,
-0.024374302476644516,
-0.03634732589125633,
0.02197379805147648,
-0.032443687319755554,
-0.028759943321347237,
0.03690541535615921,
0.05069589242339134,
-0.03354120999574661,
0.025483978912234306,
0.005620100069791079,
0.0027964541222900152,
-0.008492279797792435,
-0.051660507917404175,
0.003694608574733138,
-0.010623960755765438,
0.009873883798718452,
0.01857890374958515,
-0.011679491959512234,
0.012411942705512047,
0.011039440520107746,
-0.027408378198742867,
-0.0014484801795333624,
0.015738900750875473,
-0.06581620126962662,
-0.1044679507613182,
-0.024551745504140854,
0.03071226179599762,
-0.03915092721581459,
0.010393147356808186,
-0.02375582605600357,
0.004182946868240833,
-0.043460309505462646,
0.024255910888314247,
0.002318689599633217,
0.02443520911037922,
0.012248378247022629,
0.06112755089998245,
0.025124257430434227,
0.017488528043031693,
-0.028036601841449738,
0.015900805592536926,
-0.018640778958797455,
-0.030287569388747215,
0.0008837971836328506,
0.012406652793288231,
0.011270779184997082,
0.01657622680068016,
0.05793822184205055,
0.0695987194776535,
-0.016106627881526947,
-0.04796779900789261,
-0.005608626175671816,
-0.010851407423615456,
0.03258863091468811,
0.04009336978197098,
-0.001364777097478509,
-0.04128231480717659,
-0.027834998443722725,
0.05494797229766846,
-0.03281627222895622,
-0.03653443977236748,
0.025040384382009506,
0.04137146845459938,
0.04876459017395973,
-0.001596079091541469,
-0.00831267237663269,
-0.003880739212036133,
-0.016406003385782242,
0.005147311836481094,
0.011419775895774364,
-0.015175402164459229,
-0.011271207593381405,
-0.02118884027004242,
-0.05599316209554672,
0.0417332760989666,
-0.02056068368256092,
-0.03213445842266083,
-0.0054601458832621574,
-0.0172603540122509,
-0.0009471512166783214,
0.02726110629737377,
0.07080365717411041,
0.0052165198139846325,
-0.019022760912775993,
0.02247549779713154,
0.028276115655899048,
-0.0421864353120327,
0.0004495278117246926,
-0.04145623743534088,
0.055856142193078995,
-0.0566818043589592,
-0.03879483416676521,
-0.0328332744538784,
0.012194998562335968,
-0.0006528848316520452,
0.07906797528266907,
-0.046366266906261444,
0.005769820883870125,
-0.0008773522567935288,
0.05698090419173241,
-0.03440685197710991,
0.028535041958093643,
-0.014173327013850212,
0.022455710917711258,
0.021023767068982124,
-0.06489883363246918,
0.039689864963293076,
0.018341373652219772,
-0.019956514239311218,
0.006559823174029589,
-0.05568879097700119,
-0.06016012281179428,
0.05008956417441368,
-0.03167031705379486,
0.0000982431520242244,
-0.08272815495729446,
-0.01991281844675541,
-0.10039379447698593,
-0.008800040930509567,
-0.020298760384321213,
-0.005359369330108166,
-0.02749904803931713,
0.005002548918128014,
0.045966699719429016,
0.0191296748816967,
0.009681913070380688,
0.024225784465670586,
-0.0513363741338253,
-0.0479520745575428,
-0.01589087024331093,
0.027930840849876404,
-0.011527091264724731,
-0.003747473703697324,
-0.02865278534591198,
0.008333898149430752,
0.052280839532613754,
0.003211175324395299,
0.02362869679927826,
-0.03876837342977524,
0.053114715963602066,
0.03480055555701256,
-0.02430000714957714,
-0.014572784304618835,
-0.01223913673311472,
0.05428284406661987,
0.008628841489553452,
-0.0030352105386555195,
-0.05085131898522377,
-0.02662627026438713,
-0.02067682333290577,
-0.01213432289659977,
0.020972969010472298,
0.06902041286230087,
0.01102706603705883,
-0.057217106223106384,
0.045593541115522385,
-0.028348781168460846,
-0.02991204895079136,
-0.021499553695321083,
-0.09717996418476105,
-0.04849536344408989,
-0.08441930264234543,
-0.01575467921793461,
-0.006965237203985453,
0.003934417385607958,
0.05636512488126755,
-0.0075337546877563,
0.023961352184414864,
-0.014307408593595028,
0.0002530005294829607,
-0.03530127927660942,
0.04458294436335564,
0.06381858885288239,
0.030329331755638123,
0.0010703414445742965,
-0.024436404928565025,
0.0036104440223425627,
0.02426089160144329,
-0.02852480672299862,
-0.05688241496682167,
-0.008792748674750328,
0.0013591962633654475,
0.045396775007247925,
-0.03104110062122345,
0.03070988692343235,
-0.012898662127554417,
0.09264911711215973,
0.01948283426463604,
-0.019417433068156242,
0.004154162481427193,
-0.01936446875333786,
0.040732719004154205,
-0.008897706866264343,
0.040153492242097855,
-0.07125522941350937,
-0.0048501449637115,
-0.003645605407655239,
-0.05903187394142151,
0.007882201112806797,
-0.0057214354164898396,
0.003535814816132188,
0.030589289963245392,
0.03537622466683388,
-0.028805812820792198,
0.008280456997454166,
0.008141866885125637,
-0.0649603009223938,
-0.08346512913703918,
-0.07693715393543243,
0.0758453905582428,
0.040253896266222,
0.05601350963115692,
0.0375487245619297,
-0.05744735524058342,
0.008436008356511593,
-0.027181778103113174,
-0.03670670464634895,
0.04469127207994461,
-0.018774772062897682,
0.035082101821899414,
0.05147205665707588,
0.00747879920527339,
-0.003639607224613428,
0.01590331643819809,
0.015507620759308338,
0.03175584599375725,
-0.04556886851787567,
0.03413614258170128,
0.023096401244401932,
0.015164054930210114,
-0.03921005502343178,
-0.02280304580926895,
0.034432508051395416,
0.01181266363710165,
0.005925362929701805,
-0.004431120119988918,
0.039541952311992645,
-0.04387640208005905,
-0.028621897101402283,
0.0037584546953439713,
0.017701473087072372,
0.009912229143083096,
-0.04574212804436684,
-0.028220919892191887,
-0.022860676050186157,
-0.007593883201479912,
-0.014778927899897099,
-0.004681305959820747,
0.04789842665195465,
0.032897863537073135,
0.03154036030173302,
0.046466778963804245,
-0.04418330639600754,
0.015072508715093136,
-0.022561049088835716,
0.061171453446149826,
-0.03715479001402855,
0.024216527119278908,
-0.0033512809313833714,
-0.009367739781737328,
0.04026740416884422,
0.045104268938302994,
0.011235574260354042,
0.01579924486577511,
0.03943874314427376,
0.061321042478084564,
0.06730452924966812,
-0.03068140149116516,
0.010471767745912075,
-0.013493265956640244,
-0.003471066476777196,
-0.023311980068683624,
-0.008674168027937412,
0.025208061560988426,
-0.020077401772141457,
-0.032926954329013824,
-0.01870056800544262,
0.022902961820364,
0.02437557652592659,
0.002484827069565654,
0.02312355302274227,
0.01483652088791132,
0.0076521458104252815,
-0.0324910432100296,
-0.019931087270379066,
0.03860046714544296,
-0.03417982533574104,
-0.0022846756037324667,
0.025979381054639816,
-0.014936938881874084,
-0.04609411954879761,
0.0539143905043602,
-0.02720416896045208,
-0.059665024280548096,
0.03303245082497597,
0.01735055074095726,
0.01583167165517807,
-0.012682768516242504,
-0.018050994724035263,
0.03627945855259895,
0.028919747099280357,
0.024728404358029366,
-0.01640467531979084,
-0.061641301959753036,
-0.07280651479959488,
-0.018108606338500977,
0.10973110049962997,
0.04210720956325531,
0.03982772305607796,
0.02266952022910118,
0.019791413098573685,
0.0371505506336689,
0.02975691482424736,
-0.054377924650907516,
0.018002113327383995,
0.033474892377853394,
0.06187864765524864,
0.0584876611828804,
-0.015156595967710018,
0.07546216994524002,
0.07597220689058304,
0.01968149095773697,
0.0698496401309967,
0.042403366416692734,
0.02141212299466133,
-0.060345325618982315,
-0.029827939346432686,
0.00927750300616026,
0.02747962810099125,
-0.06075984239578247,
0.03632492199540138,
0.07206191122531891,
0.048919010907411575,
0.009096617810428143,
0.007716533727943897,
-0.014302433468401432,
-0.02661845274269581,
0.028305744752287865,
0.012351847253739834,
-0.022742750123143196,
-0.04579492658376694,
-0.04485994577407837,
0.005711295176297426,
-0.04522272199392319,
-0.09112891554832458,
0.035399530082941055,
0.01812021993100643,
-0.0020768125541508198,
0.011387813836336136,
0.02302190102636814,
-0.042537372559309006,
0.009826689027249813,
-0.036291949450969696,
-0.002285115420818329,
0.05233112722635269,
0.026331577450037003,
-0.03861404210329056,
0.007034588605165482,
0.032597050070762634,
-0.012270774692296982,
-0.013238271698355675,
-0.008123181760311127,
0.006543052848428488,
-0.04388076812028885,
-0.05824755132198334,
-0.037860747426748276,
-0.055488307029008865,
-0.07088445872068405,
-0.053159795701503754,
0.08668822795152664,
0.04538588598370552,
-0.012268688529729843,
0.00020110205514356494,
0.016349103301763535,
-0.04335203021764755,
-0.04691758751869202,
0.021157637238502502,
0.0031765298917889595,
0.025993751361966133,
0.048227109014987946,
0.015080183744430542,
0.03390686213970184,
0.03918732702732086,
0.018077386543154716,
-0.05761938914656639,
0.024631474167108536,
-0.012673626653850079,
-0.004478850867599249,
-0.012961698696017265,
-0.06360262632369995,
-0.02474937215447426,
0.019554631784558296,
0.04564829170703888,
-0.013244302943348885,
0.033590443432331085,
-0.03373264521360397,
0.05559416487812996,
-0.03657858446240425,
0.001305794925428927,
0.017199546098709106,
0.028343653306365013,
-0.03692131116986275,
0.0031573877204209566,
-0.040444426238536835,
-0.02892918698489666,
-0.02190471813082695,
-0.04328817501664162,
-0.018863629549741745,
0.05373416095972061,
0.04068870097398758,
0.0765381008386612,
-0.0009969144593924284,
-0.056959860026836395,
-0.04687563329935074,
0.023193681612610817,
-0.004139458294957876,
-0.00037158752093091607,
-0.03550872579216957,
-0.08435874432325363,
0.07385999709367752,
-0.02911812998354435,
0.024563539773225784,
0.02323836460709572,
-0.014353146776556969,
-0.01789357326924801,
-0.027437476441264153,
0.04513123258948326,
-0.0600832924246788,
0.05996089428663254,
0.01807093806564808,
0.059834450483322144,
-0.05854998528957367,
0.023819854483008385,
-0.05095294862985611,
-0.03524971380829811,
0.06539320945739746,
-0.027179615572094917,
-0.01422920636832714,
-0.0010145656997337937,
0.04644288495182991,
0.020121417939662933,
-0.04551951214671135,
-0.04929126054048538,
-0.027271071448922157,
0.023946190252900124,
-0.02972835674881935,
0.02263335883617401,
0.03406420350074768,
-0.020474977791309357
] |
<p>How can the universe become infinite in spatial extent if it started as a singularity, wouldn't it take infinite time to expand into an infinite universe?</p> | g7847 | [
0.04824680835008621,
0.04230808839201927,
0.005412753205746412,
-0.017760610207915306,
-0.005163934547454119,
0.018802080303430557,
-0.014534350484609604,
0.08031730353832245,
0.0011922905687242746,
-0.04596533253788948,
0.002880570013076067,
-0.04410334303975105,
0.02038564532995224,
0.019060427322983742,
0.009558243677020073,
-0.021533435210585594,
-0.010682140477001667,
-0.015100560151040554,
0.01789955608546734,
0.011183404363691807,
-0.03765678033232689,
-0.00831705704331398,
0.04758347198367119,
-0.024261435493826866,
-0.04870738461613655,
-0.037377070635557175,
0.027801692485809326,
0.0008561774156987667,
-0.003496757475659251,
-0.013707505539059639,
0.05827874317765236,
-0.007122764363884926,
0.0007368414662778378,
0.03878974914550781,
0.03468334674835205,
-0.0048269545659422874,
-0.002772328443825245,
-0.007492911070585251,
0.02287757396697998,
-0.018143463879823685,
-0.06037987768650055,
-0.04497211053967476,
0.00778784416615963,
-0.0367780476808548,
0.0013783688191324472,
0.0030755663756281137,
-0.03247753158211708,
0.04853203147649765,
0.0628233328461647,
-0.07729137688875198,
-0.058712445199489594,
0.002560633234679699,
0.02571420930325985,
0.0017399863572791219,
0.04664842039346695,
0.05495111271739006,
-0.011055445298552513,
-0.025340721011161804,
0.08331027626991272,
0.03131166473031044,
-0.03672574833035469,
-0.0164622962474823,
0.08551818132400513,
0.03630877658724785,
-0.020736584439873695,
-0.031111177057027817,
-0.00743258697912097,
0.01060545165091753,
0.004750168416649103,
0.03434566408395767,
0.041276540607213974,
-0.020306820049881935,
-0.009666617028415203,
0.0036404551938176155,
-0.01687454618513584,
0.06204957142472267,
0.0409921333193779,
0.013669616542756557,
-0.02114132046699524,
0.02139594405889511,
-0.058752045035362244,
0.005527001805603504,
-0.045534465461969376,
-0.0048576705157756805,
0.0043370602652430534,
-0.02834014594554901,
0.030869456008076668,
-0.04774302989244461,
-0.019382640719413757,
0.012724160216748714,
-0.046950776129961014,
0.06180991977453232,
0.02911197580397129,
0.024417949840426445,
-0.025831706821918488,
-0.06521745771169662,
-0.0038519278168678284,
0.08478911221027374,
-0.019040483981370926,
0.012407907284796238,
-0.046036653220653534,
-0.012382152490317822,
0.07642164826393127,
-0.049281347543001175,
-0.006078224629163742,
0.027748670428991318,
-0.007959652692079544,
-0.030184512957930565,
0.029035886749625206,
-0.006340421736240387,
-0.04702024161815643,
-0.054378870874643326,
-0.07538998126983643,
0.0019510829588398337,
-0.030208397656679153,
0.03497267886996269,
0.032794564962387085,
0.027205489575862885,
0.04918501898646355,
0.0037688727024942636,
0.034802209585905075,
0.006673794239759445,
-0.06549057364463806,
0.0429089292883873,
-0.042945608496665955,
0.01109271589666605,
0.034073855727910995,
0.015865903347730637,
0.014487176202237606,
-0.013516138307750225,
0.018556630238890648,
0.0033685308881103992,
-0.031672194600105286,
0.020697075873613358,
0.016819389536976814,
0.006810152903199196,
0.019961003214120865,
-0.05428440123796463,
-0.030642056837677956,
0.08726624399423599,
-0.060676489025354385,
-0.04270283877849579,
0.005913940258324146,
0.006938748061656952,
0.010171951726078987,
0.020384324714541435,
0.03762909024953842,
-0.00025155869661830366,
-0.03042619861662388,
-0.020650340244174004,
-0.016241423785686493,
0.0770481526851654,
0.00034095041337423027,
-0.0013366204220801592,
0.021388990804553032,
0.03335883095860481,
0.036244139075279236,
0.014487543143332005,
0.001784613006748259,
-0.06269178539514542,
0.06576665490865707,
-0.005535317584872246,
-0.036296285688877106,
0.01066646259278059,
-0.07766876369714737,
0.0448940247297287,
0.0044126370921730995,
-0.06227691471576691,
-0.012848648242652416,
-0.020051728934049606,
-0.045182082802057266,
-0.011349553242325783,
-0.007677917368710041,
0.05419200286269188,
0.00813297275453806,
0.03600278124213219,
-0.00872299075126648,
0.02925892174243927,
0.035516221076250076,
0.00006737784133292735,
-0.014353803358972073,
-0.03036973625421524,
-0.00839769747108221,
0.00706267636269331,
0.02550826407968998,
-0.04070480540394783,
-0.015229959972202778,
0.0226325411349535,
-0.0036878057289868593,
0.008251484483480453,
0.07449939846992493,
-0.03023609146475792,
-0.006566285155713558,
0.03741518035531044,
0.003483742941170931,
0.011120748706161976,
0.07345268130302429,
0.0015545255737379193,
-0.057962432503700256,
-0.05575614050030708,
0.021836182102560997,
0.040341299027204514,
-0.0007336877170018852,
0.07688123732805252,
0.012910328805446625,
-0.04688037559390068,
-0.047427620738744736,
0.0016930990386754274,
-0.00392045546323061,
0.027773918583989143,
0.027061255648732185,
-0.06471697986125946,
-0.036964431405067444,
0.03857889771461487,
0.02064155973494053,
0.010486296378076077,
-0.07001768052577972,
0.0076062679290771484,
0.034036729484796524,
0.04270799830555916,
-0.01743452437222004,
0.037177033722400665,
0.029049895703792572,
0.018484322354197502,
0.010285386815667152,
-0.010785908438265324,
-0.025974605232477188,
-0.052071116864681244,
0.03964690864086151,
0.026458101347088814,
-0.08237845450639725,
-0.020136486738920212,
0.012433504685759544,
-0.02568376623094082,
-0.01247036550194025,
0.009639154188334942,
-0.002926145913079381,
0.006010081619024277,
-0.10161640495061874,
-0.00008598100976087153,
0.006728546693921089,
-0.021513773128390312,
0.0009070471860468388,
-0.002324696397408843,
0.003707182127982378,
-0.09349270910024643,
0.07271135598421097,
-0.06872965395450592,
-0.04616923630237579,
0.0173957459628582,
-0.01365610770881176,
-0.011316971853375435,
0.004711759276688099,
0.032454267144203186,
-0.009105325676500797,
-0.055276673287153244,
0.023835856467485428,
0.0884479209780693,
-0.049003370106220245,
-0.08926348388195038,
0.02867066115140915,
-0.01805073581635952,
0.024353619664907455,
0.009835763834416866,
0.0009585479274392128,
0.04239247366786003,
-0.053535960614681244,
0.005402667913585901,
-0.024802422150969505,
0.0005373200983740389,
0.013784835115075111,
0.04583398997783661,
0.024968627840280533,
0.005455147475004196,
-0.0349561832845211,
0.06729977577924728,
-0.0032444808166474104,
-0.011197029612958431,
0.04038926959037781,
-0.01655188389122486,
-0.021678544580936432,
0.05753342807292938,
-0.06595535576343536,
0.03645008057355881,
0.024730022996664047,
-0.05939330905675888,
0.0076147764921188354,
0.0050943451933562756,
-0.027648383751511574,
-0.06220928207039833,
0.02573411352932453,
0.024160131812095642,
0.017415059730410576,
0.03761444613337517,
0.0296456478536129,
0.021700339391827583,
-0.04828057810664177,
0.0032382900826632977,
-0.0001623911812203005,
-0.008219991810619831,
0.005696844309568405,
-0.036389369517564774,
0.03253699094057083,
-0.06748569756746292,
-0.05120096728205681,
0.03795556351542473,
0.029802832752466202,
-0.009427971206605434,
-0.013271921314299107,
-0.04007941484451294,
0.040893103927373886,
0.012818253599107265,
0.00004053243173984811,
0.018478404730558395,
0.022005323320627213,
0.014869348146021366,
0.01484747976064682,
0.024704299867153168,
0.003482031635940075,
-0.008155353367328644,
0.020670322701334953,
-0.0318145789206028,
-0.03068498522043228,
0.022656908258795738,
0.06263457238674164,
0.014949585311114788,
-0.056183841079473495,
-0.04030797630548477,
-0.08658698946237564,
0.043397724628448486,
-0.06691420078277588,
-0.06135648116469383,
-0.021043984219431877,
-0.02768457680940628,
-0.025707611814141273,
-0.0016716583631932735,
-0.04059596359729767,
-0.013203034177422523,
0.033128369599580765,
0.01433180645108223,
0.0006182246725074947,
0.009983859024941921,
-0.02693917788565159,
0.04109056666493416,
0.009335486218333244,
0.04883745312690735,
0.0406416654586792,
-0.0022804168984293938,
0.028901873156428337,
0.03510786592960358,
-0.009126663208007812,
0.023419251665472984,
0.045210063457489014,
0.008125298656523228,
-0.02113007940351963,
0.03485460951924324,
0.017873592674732208,
0.046628065407276154,
0.03601325675845146,
-0.1032646894454956,
0.07542562484741211,
-0.02939767949283123,
0.030865268781781197,
0.033258210867643356,
0.013041285797953606,
0.05192124843597412,
0.04301523417234421,
-0.015839042142033577,
-0.0004897901089861989,
0.05167483165860176,
0.04655883088707924,
-0.054311491549015045,
-0.044965118169784546,
-0.027689624577760696,
0.06876087933778763,
-0.004047004040330648,
-0.010530858300626278,
0.004716326016932726,
0.0199031513184309,
0.022905251011252403,
0.054484304040670395,
-0.03277258947491646,
0.04919905960559845,
0.011802499182522297,
-0.044754501432180405,
0.07890819013118744,
-0.03866758197546005,
-0.07206957787275314,
0.022210413590073586,
-0.0045168050564825535,
0.07803594321012497,
-0.04147450253367424,
0.029903708025813103,
-0.07879841327667236,
0.03888395056128502,
-0.040734387934207916,
-0.006600005552172661,
-0.01751943863928318,
-0.010068816132843494,
-0.003865394974127412,
-0.009425504133105278,
0.011668974533677101,
-0.027648979797959328,
0.017998630180954933,
0.00019722325669135898,
-0.06912931799888611,
0.0333845429122448,
-0.0028041070327162743,
-0.005665098782628775,
-0.01587645336985588,
0.005741058848798275,
0.02144508808851242,
-0.0021377410739660263,
-0.03413543477654457,
0.033507201820611954,
-0.05460934340953827,
0.06544415652751923,
-0.07180305570363998,
0.020391063764691353,
0.01399821788072586,
-0.015315558761358261,
0.0356401763856411,
0.017404744401574135,
0.025051310658454895,
0.05126405134797096,
-0.000011397343769203871,
-0.05733726918697357,
-0.023796988651156425,
-0.016772283241152763,
0.018330933526158333,
-0.008087757043540478,
0.011464394629001617,
0.023046111688017845,
0.05416727438569069,
-0.07861211150884628,
0.024001292884349823,
0.0587153285741806,
0.05158056691288948,
-0.004858258180320263,
0.02376774698495865,
0.0429072268307209,
0.0017689511878415942,
0.022626666352152824,
0.055239688605070114,
0.04585183039307594,
0.048393163830041885,
-0.02124370075762272,
-0.10060127824544907,
0.0013148694997653365,
-0.021237147971987724,
-0.04497212544083595,
0.0695168599486351,
-0.020782435312867165,
-0.021805763244628906,
0.05509199574589729,
-0.04133518412709236,
-0.05331763997673988,
0.044490084052085876,
-0.004237468354403973,
0.013179517351090908,
-0.07103478163480759,
-0.007839404046535492,
-0.09023461490869522,
0.05109464004635811,
0.0244905985891819,
0.015456519089639187,
-0.035705000162124634,
-0.02592414803802967,
-0.060657333582639694,
0.009084203280508518,
-0.03871395066380501,
0.02149619348347187,
0.010136974975466728,
0.023190032690763474,
0.015591705217957497,
-0.03591926023364067,
-0.004996658302843571,
-0.0814618319272995,
-0.0062879957258701324,
-0.03746283799409866,
-0.042088042944669724,
-0.033276624977588654,
0.02891690656542778,
0.0030636980663985014,
0.030156834051012993,
0.09816323220729828,
-0.01120910793542862,
-0.01359762717038393,
0.03617309778928757,
-0.01132181379944086,
-0.018445460125803947,
-0.023654557764530182,
0.03754469007253647,
0.04893992841243744,
0.0012416037498041987,
-0.0030929965432733297,
0.013119698502123356,
-0.023718342185020447,
-0.017130151391029358,
-0.022945962846279144,
-0.013756904751062393,
0.026557497680187225,
-0.006806299090385437,
-0.001138027524575591,
-0.04467446729540825,
0.04105977341532707,
0.015117378905415535,
-0.004362700041383505,
0.0008293160935863853,
-0.01908557116985321,
0.015157610177993774,
0.007368467282503843,
0.020935209468007088,
0.02215559408068657,
0.09587568044662476,
-0.06335834413766861,
-0.032879944890737534,
-0.03903954103589058,
-0.0027845525182783604,
-0.05632014572620392,
-0.023871416226029396,
-0.01643180474638939,
0.01673826575279236,
-0.0024068092461675406,
0.04154011607170105,
0.04270398989319801,
-0.027961764484643936,
-0.05830959603190422,
0.05341809242963791,
0.008276699110865593,
0.05088641121983528,
0.05014960467815399,
-0.02590353414416313,
-0.022546596825122833,
-0.03778311237692833,
-0.01548178680241108,
-0.028986943885684013,
-0.027074988931417465,
0.024120215326547623,
-0.05707959458231926,
-0.025132201611995697,
-0.027776731178164482,
-0.08471880853176117,
0.03243603929877281,
0.035080522298812866,
-0.02118903212249279,
-0.01097046583890915,
0.040039047598838806,
0.044406477361917496,
-0.06130106747150421,
-0.05584093555808067,
0.012218290008604527,
0.03422344848513603,
0.0030926777981221676,
-0.013141181319952011,
0.038141559809446335,
0.017990967258810997,
0.005269911140203476,
-0.07623016834259033,
-0.07967451214790344,
0.041069939732551575,
0.034482862800359726,
-0.013260871171951294,
-0.061399612575769424,
-0.029456280171871185,
-0.020474748685956,
-0.00928016658872366,
-0.018346311524510384,
0.08093960583209991,
0.03782414272427559,
0.009567606262862682,
0.03442944958806038,
0.031271349638700485,
-0.04412943497300148,
0.00035933591425418854,
-0.0011628976790234447,
0.01393655315041542,
-0.001837051589973271,
0.00008925364818423986,
-0.015510836616158485,
-0.0409112349152565,
0.01591131091117859,
0.07749524712562561,
-0.01696576364338398,
-0.0008839850779622793,
0.046654265373945236,
-0.020534437149763107,
0.014350510202348232,
0.08560387790203094,
0.0028438949957489967,
-0.02786760963499546,
0.015281938016414642,
0.07571074366569519,
-0.07061655074357986,
-0.02809126488864422,
0.018343405798077583,
0.008622793480753899,
-0.005907323677092791,
-0.010844327509403229,
-0.02070344239473343,
-0.01901351660490036,
0.057984836399555206,
0.03630465269088745,
0.05149548873305321,
0.005235024727880955,
0.0030040889978408813,
-0.009860588237643242,
-0.013289515860378742,
0.05428336188197136,
0.015565212815999985,
0.00960233062505722,
-0.001751529867760837,
-0.021689144894480705,
-0.013577429577708244,
-0.0010281059658154845,
-0.020235862582921982,
0.05504021421074867,
-0.04251803085207939,
0.05528685078024864,
-0.047465723007917404,
0.06867159903049469,
-0.024312898516654968,
-0.03426298126578331,
0.02612261101603508,
-0.008421455509960651,
0.003768471535295248,
-0.01386923436075449,
0.01990417018532753,
0.029404614120721817,
0.007204896304756403,
0.015546443872153759,
0.02730771154165268,
-0.06553894281387329,
0.02368762716650963,
-0.023508701473474503,
0.01780584268271923,
-0.027784565463662148,
-0.013819432817399502,
0.011053303256630898,
-0.027114953845739365,
0.012757369317114353,
-0.03380177170038223,
0.007438720669597387,
0.01513709593564272,
0.007344731595367193,
0.006018701009452343,
-0.038138289004564285,
0.006287365220487118,
-0.033141400665044785,
-0.04139241203665733,
0.010450641624629498,
-0.00337595259770751,
-0.08747456967830658,
0.048291172832250595,
-0.023754766210913658,
0.005967702250927687,
-0.045714907348155975,
-0.0702156350016594,
-0.006055694539099932,
-0.06614094227552414,
-0.004474542569369078,
0.021997254341840744,
0.005751016549766064,
0.0008018520893529058,
0.0037604919634759426,
0.019652241840958595,
0.08114849776029587,
-0.010872558690607548,
-0.003030607011169195,
-0.06060716137290001,
0.009008952416479588,
0.0020678567234426737,
-0.01630222052335739,
-0.01192341186106205,
0.017780859023332596,
-0.010255461558699608,
-0.04034474119544029,
0.0023846838157624006,
0.06097978353500366,
0.030053479596972466,
-0.003999313339591026,
0.012802055105566978,
0.021156970411539078,
0.018407391384243965,
0.006182258017361164,
-0.0018863838631659746,
0.02173163928091526,
0.004717541392892599,
-0.011462178081274033,
-0.012085155583918095,
-0.03219126537442207,
-0.0334136076271534,
-0.030292721465229988,
0.020559588447213173,
0.06287587434053421,
-0.011822657659649849,
0.02193065732717514,
0.02969544194638729,
0.017943212762475014,
-0.03584000840783119,
-0.05493146553635597,
-0.012776821851730347,
-0.006983379367738962,
-0.048817310482263565,
0.02172793634235859,
-0.045014187693595886,
0.006698387674987316,
0.008313220925629139,
0.0370321087539196,
0.012038386426866055,
0.020346764475107193,
0.03981326147913933,
-0.06815211474895477,
0.02764521725475788,
-0.05382876098155975,
0.006702375132590532,
0.026960991322994232,
-0.02765018306672573,
0.0042943404987454414,
-0.05815093219280243,
-0.039268963038921356,
0.004632954951375723,
0.006815589498728514,
-0.04437953606247902,
-0.048270512372255325,
0.04435737058520317,
0.007426687050610781,
-0.05054290220141411,
-0.0047874730080366135,
-0.01736164279282093,
0.015316370874643326,
0.027677739039063454,
-0.007984759286046028,
-0.01727861352264881,
-0.057309992611408234,
0.03196427598595619,
-0.015721049159765244,
-0.03433826565742493,
-0.017331412062048912,
0.005422273185104132,
-0.05527987703680992,
-0.06506331264972687,
0.041003916412591934,
0.011265266686677933,
0.022282905876636505,
-0.01777712255716324,
-0.031179208308458328,
0.04672682285308838,
0.0344683900475502,
-0.007747238036245108,
-0.013047833926975727,
0.02036983147263527,
0.04519631341099739,
0.023847665637731552,
0.014137323945760727,
0.024523518979549408,
-0.006224171724170446,
-0.018293067812919617,
0.01384243555366993,
-0.0006949990056455135,
0.012116319499909878,
0.03530415892601013,
0.03839677944779396,
-0.010510031133890152,
0.0031757927499711514,
-0.023039186373353004,
-0.02171948179602623,
-0.006505344994366169
] |
<p>Are there any examples of fermionic particles or quasiparticles for which the interaction potential is a globally smooth function? i.e. no singularities or branch points. </p>
<p>As an example, in Flügge's Practical Quantum Mechanics, problem 148 has two repulsive particles on a circle. This is supposed to model the two helium electrons in the ground state. The equation he gives is</p>
<p>$$ -\frac{\hbar^2}{2mr^2}\left(\frac{\partial^2 \psi}{\partial x_1^2}+\frac{\partial^2 \psi}{\partial x_2^2}\right)+V_0\cos(x_1-x_2)\psi=E\psi$$</p>
<p>I don't quite follow why this potential does not have a singularity when $x_2\rightarrow x_1$. Are there other such examples?</p> | g7848 | [
0.06712327897548676,
0.015948481857776642,
0.020747002214193344,
-0.05000223219394684,
0.05444430187344551,
0.029075272381305695,
0.018660379573702812,
0.023135468363761902,
-0.01152937300503254,
0.04051254317164421,
0.006746121682226658,
0.021179961040616035,
-0.01977076195180416,
0.018422435969114304,
-0.021686343476176262,
0.014561103656888008,
0.06966223567724228,
-0.026576656848192215,
0.01542302593588829,
0.027681512758135796,
-0.022140957415103912,
-0.00008228204387705773,
0.05841768532991409,
0.013694500550627708,
0.008635018020868301,
-0.018000803887844086,
0.008680332452058792,
-0.02898668497800827,
-0.023487338796257973,
-0.006722936872392893,
-0.027357444167137146,
0.029449211433529854,
0.036250725388526917,
-0.019147831946611404,
-0.027792248874902725,
0.014706145040690899,
0.057190801948308945,
-0.05258547514677048,
-0.03357943519949913,
-0.049186091870069504,
0.011261961422860622,
0.005331804975867271,
0.030079416930675507,
-0.012653007172048092,
0.015724554657936096,
0.04003169760107994,
0.02446139231324196,
0.02390832081437111,
-0.004263794980943203,
-0.03395406901836395,
0.015339517965912819,
0.0206346046179533,
0.02868761494755745,
-0.03589087352156639,
0.03681689128279686,
0.01621568389236927,
0.08812202513217926,
0.015953771770000458,
0.05357043072581291,
0.030410943552851677,
-0.03788277134299278,
0.00008522321149939671,
0.047352127730846405,
0.03140348196029663,
0.010263487696647644,
-0.016433672979474068,
-0.050676148384809494,
0.018990322947502136,
-0.026705538854002953,
-0.018082167953252792,
-0.0070366510190069675,
-0.026438843458890915,
-0.04832623153924942,
0.03699982911348343,
-0.029275095090270042,
0.021024949848651886,
-0.0224552471190691,
-0.046224355697631836,
0.02081546001136303,
-0.006805908866226673,
-0.06639674305915833,
-0.04333319887518883,
-0.00030843637068755925,
0.02137027308344841,
0.03519188612699509,
-0.0602976456284523,
-0.012361493892967701,
-0.04688428342342377,
-0.024529652670025826,
-0.023305224254727364,
0.015386538580060005,
-0.02817089855670929,
-0.01308938767760992,
-0.006116664968430996,
-0.005241899285465479,
-0.0071350811049342155,
-0.00011987151083303615,
0.062194500118494034,
-0.012236954644322395,
-0.03164409101009369,
-0.0029569463804364204,
0.004693519324064255,
-0.004324553534388542,
0.07232363522052765,
-0.02383401058614254,
-0.02811213582754135,
-0.01990954764187336,
0.0262194462120533,
0.02798520214855671,
0.01381067093461752,
0.013770763762295246,
-0.017784496769309044,
-0.023484406992793083,
0.013857783749699593,
0.014069740660488605,
0.020430542528629303,
0.043776292353868484,
-0.0619974322617054,
-0.02374413050711155,
0.09264782816171646,
0.049573369324207306,
0.0038104457780718803,
0.024814993143081665,
0.024273233488202095,
0.008729742839932442,
0.009375618770718575,
-0.041078832000494,
0.0324598103761673,
0.019583502784371376,
-0.020866917446255684,
0.006346873939037323,
-0.03270528092980385,
-0.012201262637972832,
-0.041673749685287476,
-0.009419872425496578,
0.014569664373993874,
0.02386457473039627,
0.060610175132751465,
0.05036512389779091,
-0.04486945644021034,
0.053393252193927765,
-0.04120592772960663,
0.005616619251668453,
0.0520591139793396,
-0.022503402084112167,
-0.05530599132180214,
0.007759707514196634,
0.0022521924693137407,
-0.013858708553016186,
0.02813193015754223,
0.04361085593700409,
0.042701173573732376,
0.0445338673889637,
0.026217199862003326,
-0.0675673633813858,
0.03426700830459595,
-0.0020827623084187508,
0.003392152488231659,
0.027457445859909058,
-0.01669757068157196,
0.02228507213294506,
-0.032903965562582016,
-0.02737462893128395,
-0.021784953773021698,
0.013361637480556965,
0.04957917705178261,
0.03009684942662716,
-0.07014905661344528,
-0.0030420038383454084,
0.014362800866365433,
-0.033625680953264236,
0.02165217697620392,
-0.0036910041235387325,
0.042143773287534714,
0.0012559023452922702,
-0.0390615351498127,
-0.05416823551058769,
-0.017361251637339592,
0.01638810895383358,
-0.025454213842749596,
-0.008416740223765373,
-0.05479421839118004,
-0.009607343003153801,
-0.028230348601937294,
-0.002383748535066843,
0.0171881802380085,
0.01004075352102518,
0.08305773884057999,
-0.0010915383463725448,
-0.022643234580755234,
0.00827782228589058,
-0.011795002035796642,
-0.007498139515519142,
-0.01847410947084427,
0.021436484530568123,
0.01905464194715023,
0.11516144126653671,
-0.05315248668193817,
0.0028138679917901754,
0.011155468411743641,
-0.025307519361376762,
0.07982450723648071,
0.0449996218085289,
0.02432364411652088,
0.04931914433836937,
-0.035813599824905396,
0.017629949375987053,
-0.010031823068857193,
0.03380795568227768,
-0.028709925711154938,
0.035604327917099,
-0.06263256072998047,
-0.007860149256885052,
0.013362975791096687,
0.004727164749056101,
-0.11722780019044876,
-0.039812032133340836,
-0.002204535063356161,
0.006236211862415075,
-0.015311457216739655,
0.02046908251941204,
0.015687622129917145,
-0.006062601692974567,
0.013844015076756477,
0.04946481063961983,
-0.003869164502248168,
0.013498698361217976,
-0.0026540886610746384,
-0.08281523734331131,
0.05654297024011612,
-0.0888628214597702,
-0.006342355161905289,
-0.0005368537385948002,
-0.06550332903862,
-0.04268910363316536,
0.008783766999840736,
0.007192362565547228,
-0.03659708425402641,
-0.004158826544880867,
-0.055946800857782364,
0.022604092955589294,
-0.0464160330593586,
-0.014715349301695824,
0.0150768356397748,
0.012363200075924397,
-0.006056290119886398,
0.008266451768577099,
0.022719819098711014,
0.03930215537548065,
0.016906876116991043,
-0.0037923164200037718,
-0.03172163665294647,
-0.03799429535865784,
0.05795412138104439,
-0.047714147716760635,
-0.014233817346394062,
0.03321119025349617,
0.024558166041970253,
0.026949265971779823,
-0.06183679401874542,
-0.011732102371752262,
0.03126173093914986,
0.02480054460465908,
0.0555231086909771,
0.004939689766615629,
0.009004826657474041,
0.04470227658748627,
0.0015710056759417057,
0.004160403273999691,
-0.0014410014264285564,
0.02079351246356964,
0.023380780592560768,
0.008245421573519707,
0.053840428590774536,
-0.024755440652370453,
-0.04807206988334656,
-0.018470091745257378,
0.022223398089408875,
0.0051496136002242565,
0.013844599947333336,
-0.04368329793214798,
0.011988756246864796,
0.0009211063152179122,
0.04250812157988548,
0.04393180459737778,
-0.03024001605808735,
0.004780686926096678,
0.024304717779159546,
0.02633163519203663,
-0.00763380853459239,
-0.038125790655612946,
-0.016116265207529068,
0.03828095272183418,
0.013900188729166985,
-0.0005733291036449373,
0.00702716875821352,
-0.008419699966907501,
-0.01966182142496109,
0.033464737236499786,
0.03561447560787201,
0.029841557145118713,
-0.009374191053211689,
-0.03223871812224388,
0.0701717883348465,
0.022588500753045082,
-0.06760299205780029,
0.005269041284918785,
-0.07552191615104675,
-0.023219972848892212,
-0.04870695248246193,
0.03936804085969925,
0.09018563479185104,
-0.018106695264577866,
0.008565790951251984,
-0.015348125249147415,
0.004828509408980608,
0.0014156806282699108,
0.04839475452899933,
0.020670130848884583,
-0.037716902792453766,
0.0006275606574490666,
-0.03975508362054825,
0.013284644111990929,
-0.03180781751871109,
0.07364574074745178,
0.0811125859618187,
-0.06721334904432297,
-0.024403130635619164,
-0.0358990877866745,
0.0011000459780916572,
-0.012899716384708881,
0.011636029928922653,
0.03220157325267792,
-0.025027012452483177,
-0.05037631466984749,
-0.07459410279989243,
0.008414562791585922,
-0.012022027745842934,
0.06996390968561172,
-0.0011180132860317826,
-0.05106755718588829,
0.02427009679377079,
-0.006089310627430677,
-0.018059954047203064,
0.002517676679417491,
-0.004542792681604624,
-0.02999080903828144,
-0.02194211259484291,
0.016364743933081627,
0.026419110596179962,
-0.004597082734107971,
0.022285152226686478,
0.060126230120658875,
-0.023358669131994247,
0.02685788832604885,
-0.0071166809648275375,
-0.007639751769602299,
-0.025734497234225273,
-0.039941322058439255,
-0.004409539978951216,
0.013911861926317215,
0.0038646224420517683,
-0.02110212668776512,
0.049821093678474426,
0.041179556399583817,
-0.07406219094991684,
-0.026646098122000694,
0.034442245960235596,
0.060613952577114105,
-0.00960948970168829,
0.04823177680373192,
0.0100786741822958,
0.04046640172600746,
0.026181956753134727,
0.01888906955718994,
-0.016073018312454224,
-0.011918716132640839,
-0.01960897445678711,
-0.06129498779773712,
-0.05421484634280205,
0.028061171993613243,
-0.04669379070401192,
-0.003067540004849434,
0.03420598804950714,
0.07504929602146149,
0.039034027606248856,
-0.03634124621748924,
0.008381156250834465,
-0.00564532307907939,
0.02096005156636238,
0.09158220887184143,
-0.020749574527144432,
-0.039156753569841385,
0.040608763694763184,
-0.014771982096135616,
0.001173648051917553,
0.04666079208254814,
-0.07874785363674164,
-0.022618835791945457,
0.07538916915655136,
-0.04336071386933327,
-0.045655474066734314,
0.013364240527153015,
-0.055135440081357956,
-0.014990546740591526,
0.004521215800195932,
0.022550541907548904,
-0.0387127511203289,
0.0004659130936488509,
-0.06656169146299362,
0.02877124771475792,
-0.013021498918533325,
0.011028087697923183,
-0.017611270770430565,
-0.01674491912126541,
-0.08036607503890991,
-0.017105557024478912,
-0.028264405205845833,
0.022354980930685997,
-0.08471248298883438,
-0.012022966518998146,
0.0013911445857957006,
-0.009137479588389397,
0.02803812548518181,
0.04090144857764244,
-0.0016365976771339774,
0.017130618914961815,
0.028433356434106827,
-0.015281060710549355,
-0.03967785835266113,
0.023455189540982246,
0.011377185583114624,
0.0005772254662588239,
-0.004221842624247074,
-0.01183128822594881,
0.04152226820588112,
-0.10093007236719131,
-0.07687325775623322,
0.04144453629851341,
0.0832003727555275,
0.03713317587971687,
0.001414260477758944,
0.034502919763326645,
0.04351424053311348,
0.025693360716104507,
0.05068565160036087,
-0.0007754169055260718,
0.014261369593441486,
-0.04962999001145363,
-0.0255119688808918,
-0.010102254338562489,
-0.024789974093437195,
-0.06044702231884003,
-0.015951000154018402,
0.010061909444630146,
-0.04912436380982399,
-0.03558727726340294,
0.0015883410815149546,
0.022304179146885872,
-0.008067687042057514,
-0.005939274560660124,
-0.04320298880338669,
-0.01835557259619236,
0.007136418018490076,
0.001618317561224103,
-0.029605915769934654,
-0.10025490075349808,
0.0354873426258564,
-0.04739600419998169,
-0.07839887589216232,
-0.02394639514386654,
-0.003251565620303154,
0.044752657413482666,
-0.02786530740559101,
0.007779865991324186,
-0.05969950556755066,
-0.016280854120850563,
-0.03414199873805046,
-0.004481767304241657,
-0.05073552951216698,
-0.004167160950601101,
-0.03542949631810188,
0.03846750780940056,
0.02863573655486107,
-0.013969586230814457,
-0.014908596873283386,
0.0049171424470841885,
0.04483538866043091,
-0.027518512681126595,
-0.03079742006957531,
0.024898989126086235,
-0.01695176400244236,
-0.022364092990756035,
0.00912452582269907,
0.05631211772561073,
0.01837029494345188,
0.04387545585632324,
0.028700964525341988,
-0.00501673761755228,
0.05700194463133812,
-0.026672238484025,
-0.043139901012182236,
-0.021243752911686897,
0.04873405396938324,
-0.05098213627934456,
0.12452422827482224,
0.022145982831716537,
-0.08139681816101074,
-0.006157478783279657,
0.03332414850592613,
-0.005922990385442972,
-0.028117813169956207,
0.0616995245218277,
0.034169990569353104,
-0.032015614211559296,
0.040507931262254715,
-0.0401419922709465,
-0.006839273031800985,
-0.04239494726061821,
-0.049689192324876785,
0.0973881259560585,
0.019109072163701057,
-0.008944828063249588,
0.01396763976663351,
0.0970226302742958,
-0.01959533430635929,
0.00015497808635700494,
-0.05170108377933502,
0.0306423157453537,
0.09513798356056213,
0.038795456290245056,
-0.013113983906805515,
-0.054576750844717026,
0.012229721993207932,
0.013125818222761154,
-0.024296794086694717,
-0.024059630930423737,
0.009140824899077415,
0.009955004788935184,
-0.004565531387925148,
0.0009488226496614516,
0.010267551057040691,
-0.012617758475244045,
0.017770543694496155,
-0.03101685270667076,
0.048950228840112686,
0.013218015432357788,
0.02131047658622265,
-0.0016131566371768713,
0.0036498052068054676,
-0.051568932831287384,
-0.03425237908959389,
-0.11090544611215591,
0.02521403320133686,
0.015123061835765839,
-0.00018766407447401434,
0.03395976126194,
-0.009647853672504425,
-0.009111613035202026,
-0.042507898062467575,
0.008440051227807999,
0.0029473095200955868,
0.09489768743515015,
-0.011960070580244064,
-0.008945160545408726,
-0.04936497285962105,
-0.04316287115216255,
-0.008087974973022938,
0.0178433395922184,
-0.011807553470134735,
-0.005477879662066698,
0.05636033043265343,
0.02228355035185814,
-0.00017880930681712925,
0.03777899220585823,
-0.049167752265930176,
-0.037384361028671265,
-0.00294035323895514,
-0.0014063576236367226,
0.041144125163555145,
-0.0018994584679603577,
0.06474827975034714,
0.05117887631058693,
-0.026296397671103477,
-0.008602946065366268,
0.01945323310792446,
-0.01566644012928009,
-0.03777571767568588,
0.0006888036732561886,
0.0569782629609108,
0.007575097493827343,
-0.0038096720818430185,
-0.04975300282239914,
-0.042742207646369934,
0.03152480721473694,
-0.057889532297849655,
-0.0074276309460401535,
-0.053266242146492004,
-0.08668225258588791,
0.020392782986164093,
0.011343244463205338,
0.04604417830705643,
0.008730273693799973,
0.027776755392551422,
0.012606087140738964,
0.015535414218902588,
-0.00543709984049201,
0.05237219110131264,
-0.024117277935147285,
0.038779109716415405,
0.02136061154305935,
0.06212223693728447,
-0.022645307704806328,
-0.05401467904448509,
0.011772694997489452,
-0.061987847089767456,
0.03454531356692314,
0.01892099902033806,
-0.1006285548210144,
-0.03418437018990517,
-0.036453962326049805,
-0.03742431104183197,
0.018627919256687164,
-0.05512841418385506,
0.013875331729650497,
-0.0305260568857193,
-0.061266470700502396,
0.022622501477599144,
0.021283796057105064,
-0.03295488655567169,
0.023917919024825096,
0.006325680762529373,
-0.007703045383095741,
0.0003955023712478578,
-0.059971194714307785,
0.03947388008236885,
-0.043857887387275696,
-0.05213400349020958,
-0.005047273356467485,
0.007600297685712576,
-0.006662973668426275,
0.04848727956414223,
0.017406130209565163,
-0.03286174684762955,
-0.05167574808001518,
0.0013784473994746804,
0.04359223321080208,
0.031580034643411636,
-0.07379505783319473,
0.03904784470796585,
0.03524274751543999,
0.0004703097220044583,
0.01530207134783268,
-0.04147611930966377,
-0.014652331359684467,
-0.00023338386381510645,
-0.023969288915395737,
0.033966951072216034,
0.004019202198833227,
-0.0035843453370034695,
-0.03305156156420708,
0.0005306085222400725,
0.0019731102511286736,
-0.015899935737252235,
0.05522964522242546,
0.04941118508577347,
0.00040799935231916606,
-0.0006814713124185801,
-0.012154198251664639,
-0.02818302810192108,
-0.03165920823812485,
-0.045672714710235596,
-0.038838308304548264,
-0.004515394102782011,
0.023052159696817398,
-0.009987776167690754,
0.028253093361854553,
0.025453485548496246,
0.025232898071408272,
-0.04770771786570549,
0.04017253592610359,
0.04065196216106415,
0.03372464329004288,
-0.010291343554854393,
-0.04434877261519432,
0.016661887988448143,
-0.0007922975346446037,
-0.01628943160176277,
0.007541470229625702,
0.047592222690582275,
0.027318283915519714,
0.01592794619500637,
-0.01927020214498043,
-0.025494573637843132,
-0.03805316984653473,
-0.02459058351814747,
0.013157014735043049,
0.026242811232805252,
0.010786646045744419,
0.019960731267929077,
0.04754260927438736,
0.01888861693441868,
0.005847408436238766,
-0.0392230749130249,
0.03555561229586601,
-0.02704056352376938,
0.007508375681936741,
-0.02865901030600071,
0.0000796449021436274,
-0.028151892125606537,
-0.003945342730730772,
0.06773439049720764,
0.048263952136039734,
0.025760093703866005,
0.014123360626399517,
-0.015353135764598846,
-0.041370078921318054,
0.06532074511051178,
0.11446008831262589,
-0.0007102974923327565,
0.010644230991601944,
-0.023747116327285767,
-0.01452864333987236,
-0.038401197642087936,
-0.0008490734035149217,
-0.05007025599479675,
-0.023771187290549278,
0.009154786355793476,
0.038416486233472824,
0.02602248638868332,
-0.035406652837991714,
0.01709471084177494,
-0.007510149851441383,
0.05559312179684639,
-0.0918775126338005,
-0.032038744539022446,
-0.014838267117738724,
-0.01987667754292488,
-0.01181823294609785,
-0.012595840729773045,
0.004310865420848131,
-0.03157499060034752,
0.03401505947113037,
-0.015718387439846992,
-0.03732937574386597,
-0.02082737721502781,
-0.023852776736021042,
-0.009743482805788517,
0.03751133382320404,
0.04586292803287506,
-0.017257677391171455,
-0.003826824249699712,
0.005925871431827545,
0.050389908254146576,
0.019300095736980438,
-0.045822665095329285,
-0.010081153362989426,
0.054571669548749924,
-0.022845882922410965,
-0.043463271111249924,
-0.022168582305312157,
-0.05203752964735031,
0.01976698823273182,
0.05835515633225441,
0.007060093805193901,
-0.05148704722523689,
-0.03425721079111099,
0.05320407822728157
] |
<p>Is there a way of calculating the mass of a galaxy, or even a nebula from the luminosity? </p>
<p>EDIT </p>
<p>I'm deleting this, and moving the question to Astronomy Stack Exchange - thanks david</p> | g7849 | [
-0.022143958136439323,
-0.04125716909766197,
0.007459679618477821,
-0.10100165754556656,
0.03991743549704552,
-0.009722470305860043,
-0.07899435609579086,
0.023114405572414398,
-0.029236234724521637,
-0.038934968411922455,
0.019026637077331543,
-0.015424440614879131,
0.0746128037571907,
0.02585860714316368,
0.05089395120739937,
0.01115086767822504,
0.04420915246009827,
-0.006180357187986374,
-0.0054730018600821495,
0.04991256818175316,
-0.0042264871299266815,
-0.05332028120756149,
0.012902369722723961,
-0.01695394143462181,
-0.0073443446308374405,
0.03440345451235771,
0.02670922502875328,
0.015410908497869968,
-0.01893993467092514,
-0.03749709203839302,
-0.030574245378375053,
-0.0038735868874937296,
0.024220861494541168,
-0.03984488174319267,
-0.021694784983992577,
0.022476963698863983,
-0.041799046099185944,
0.010745658539235592,
0.023518938571214676,
0.019111959263682365,
0.001704375259578228,
0.004812661092728376,
0.05796605348587036,
0.052840787917375565,
0.00577928964048624,
0.02231326326727867,
0.03145566210150719,
0.007524858228862286,
0.00008392536255996674,
0.03028971143066883,
-0.0519714318215847,
0.046984851360321045,
0.030436981469392776,
0.026268504559993744,
-0.036055516451597214,
0.04433386027812958,
0.0637025535106659,
-0.0822431668639183,
0.06064615398645401,
0.03960460424423218,
-0.051528386771678925,
-0.03470238298177719,
-0.017161322757601738,
-0.033948831260204315,
0.013784502632915974,
0.016308963298797607,
-0.06564386934041977,
-0.013821763917803764,
0.0023141643032431602,
-0.0282283928245306,
0.03766242042183876,
0.04665662720799446,
0.009078171104192734,
-0.043642934411764145,
-0.05483502149581909,
-0.005018497351557016,
-0.022616134956479073,
0.013604333624243736,
-0.062174517661333084,
0.03424112871289253,
-0.001634862506762147,
-0.05348021164536476,
0.01882602833211422,
0.05126373469829559,
-0.02483724057674408,
-0.04663258418440819,
-0.03955067694187164,
-0.024258730933070183,
-0.022090405225753784,
0.020648902282118797,
0.01192315760999918,
0.04380509629845619,
0.022249890491366386,
-0.015430638566613197,
0.031879834830760956,
-0.031222915276885033,
0.016108546406030655,
0.0432758592069149,
-0.04860050231218338,
0.024661622941493988,
-0.030146680772304535,
0.021532751619815826,
-0.0006811529747210443,
0.01786229945719242,
0.017737144604325294,
0.013463577255606651,
-0.01315169595181942,
-0.01667315885424614,
-0.000522841583006084,
0.008062036707997322,
-0.054749466478824615,
-0.04211122542619705,
-0.0014506492298096418,
-0.0032488685101270676,
-0.07659819722175598,
-0.01243710145354271,
0.09520944952964783,
0.026997635141015053,
0.0023481016978621483,
0.052211694419384,
0.05622067302465439,
0.04788370802998543,
-0.011748621240258217,
0.02054045908153057,
0.018916957080364227,
-0.04287339746952057,
-0.005982893519103527,
0.03105664625763893,
-0.015742551535367966,
-0.028039738535881042,
0.016201607882976532,
0.01960994489490986,
0.028640178963541985,
0.009720859117805958,
-0.02415211871266365,
0.0265133548527956,
-0.028519153594970703,
0.0301907230168581,
-0.07433720678091049,
-0.022321296855807304,
0.04094085842370987,
-0.015955792739987373,
0.05424235761165619,
-0.010927081108093262,
-0.011807113885879517,
0.041804421693086624,
-0.03922354057431221,
0.018185647204518318,
0.004338011611253023,
0.03452253341674805,
0.033755093812942505,
0.04513588175177574,
0.01647479087114334,
-0.05871859937906265,
0.03090496174991131,
-0.04613017290830612,
0.012527680955827236,
0.041270822286605835,
-0.041752271354198456,
-0.014647256582975388,
0.018904218450188637,
-0.05263166129589081,
0.055798035115003586,
-0.033367421478033066,
0.005310482811182737,
0.0041228230111300945,
-0.007884759455919266,
-0.01848643086850643,
-0.058139048516750336,
-0.04170786216855049,
-0.038402047008275986,
0.022466495633125305,
0.01015731692314148,
0.02196265198290348,
0.06690278649330139,
0.05437970906496048,
0.04568012058734894,
0.016994213685393333,
-0.011271337978541851,
0.04258080944418907,
0.07147733122110367,
-0.001248080050572753,
0.037426576018333435,
-0.02273475006222725,
-0.0076316362246870995,
-0.08671670407056808,
0.04324807599186897,
-0.019625592976808548,
0.07145462930202484,
0.07582138478755951,
-0.06118585169315338,
0.01786048151552677,
0.08967306464910507,
0.045423172414302826,
0.017463253811001778,
-0.003889927640557289,
0.021671628579497337,
0.021930990740656853,
0.004638035781681538,
0.03407929837703705,
0.0007526007830165327,
0.03984523564577103,
0.01011583674699068,
0.016946516931056976,
0.04404566437005997,
0.010574202053248882,
-0.039269786328077316,
-0.003578954841941595,
0.0024395519867539406,
-0.029545968398451805,
0.01317731011658907,
-0.005488426424562931,
-0.0005773436278104782,
-0.013571702875196934,
-0.011473076418042183,
0.04915719851851463,
-0.04070911183953285,
0.012509092688560486,
0.03030487895011902,
0.010646617971360683,
-0.013464230112731457,
-0.002018882427364588,
0.012136031873524189,
-0.01579308696091175,
0.0031150600407272577,
-0.012594247236847878,
0.03390277549624443,
0.059409238398075104,
-0.026805691421031952,
0.01663011685013771,
-0.033633243292570114,
-0.0279464703053236,
-0.002507873810827732,
0.03115438111126423,
0.08760301768779755,
0.022758224979043007,
-0.00009485454938840121,
-0.02061006799340248,
0.017460690811276436,
0.049297966063022614,
0.05697137862443924,
-0.036223962903022766,
0.005535039119422436,
-0.010386793874204159,
0.0077912709675729275,
-0.07106290012598038,
0.047856174409389496,
0.022710982710123062,
-0.038069043308496475,
0.01674516312777996,
-0.030389217659831047,
-0.0022947227116674185,
0.0008569555357098579,
-0.033511124551296234,
-0.03551677241921425,
-0.017549272626638412,
-0.0352305993437767,
0.016070222482085228,
-0.03460576385259628,
0.03355715796351433,
0.07767300307750702,
-0.05526674538850784,
0.004845090210437775,
-0.04354950785636902,
-0.024047257378697395,
-0.06860220432281494,
-0.02339242585003376,
-0.060507114976644516,
0.020442791283130646,
-0.007839452475309372,
0.01636425405740738,
-0.017248857766389847,
0.033535536378622055,
-0.00395637983456254,
-0.018327701836824417,
0.009240756742656231,
0.028446516022086143,
0.01746179163455963,
0.04207141697406769,
-0.0168539360165596,
0.06191064417362213,
0.0003213983145542443,
-0.1108771562576294,
0.029862500727176666,
0.011766734533011913,
-0.02891852892935276,
-0.013507521711289883,
-0.008725181221961975,
0.05728522315621376,
0.00011531705968081951,
0.04277540743350983,
-0.05417821928858757,
0.011960597708821297,
0.005530000198632479,
-0.02061116136610508,
0.05350559949874878,
0.02716512233018875,
0.08203428238630295,
-0.004539222456514835,
-0.06067734584212303,
0.01274049561470747,
-0.016432953998446465,
0.005125622730702162,
-0.05264166370034218,
0.011358975432813168,
0.05156627669930458,
0.002770013641566038,
0.009905857965350151,
0.05198998004198074,
-0.0853571891784668,
-0.016242068260908127,
0.06651907414197922,
0.02547181397676468,
0.02546464093029499,
0.014156825840473175,
-0.0011075789807364345,
0.011686071753501892,
-0.022829126566648483,
-0.020091308280825615,
-0.01373205054551363,
-0.051920462399721146,
-0.014488663524389267,
0.006166105158627033,
-0.022318260744214058,
0.031226662918925285,
-0.031951840966939926,
-0.009237968362867832,
-0.0035510973539203405,
-0.05325204133987427,
-0.03428211435675621,
-0.011359192430973053,
0.05083190277218819,
-0.06375429034233093,
0.0048762597143650055,
-0.024974456056952477,
0.008830640465021133,
0.07327050715684891,
-0.010085618123412132,
0.07406750321388245,
0.006553349085152149,
-0.050378359854221344,
-0.0027775350026786327,
-0.02857069857418537,
0.021741311997175217,
0.008124427869915962,
0.040997449308633804,
-0.02780480869114399,
-0.05652868375182152,
0.02721538208425045,
-0.05360262840986252,
-0.0033966866321861744,
0.023116419091820717,
-0.00360966008156538,
-0.037715137004852295,
0.04642327129840851,
-0.021566549316048622,
0.012663058936595917,
0.023310808464884758,
0.009692168794572353,
0.0044653830118477345,
0.03000049851834774,
-0.033146318048238754,
0.014023237861692905,
-0.025830553844571114,
0.02337837778031826,
-0.04096877574920654,
0.02016284130513668,
-0.005336306989192963,
0.01742137037217617,
0.019396154209971428,
-0.0010766666382551193,
-0.04917943477630615,
0.007563203573226929,
-0.012358038686215878,
-0.04192943498492241,
-0.0332212820649147,
0.05051605403423309,
0.00016298367700073868,
-0.07723039388656616,
0.02315550670027733,
0.024065503850579262,
0.006962085608392954,
0.0463845431804657,
-0.035086970776319504,
-0.01623232290148735,
-0.021244755014777184,
-0.022883519530296326,
-0.010213594883680344,
0.03704174980521202,
-0.051639001816511154,
0.06267915666103363,
-0.0991993322968483,
-0.029798394069075584,
-0.021244890987873077,
0.0383317656815052,
-0.03174407035112381,
0.04688524454832077,
-0.03189612179994583,
0.05118345469236374,
0.0011607996420934796,
0.028642743825912476,
0.03951491042971611,
0.06038409844040871,
-0.0009678787318989635,
0.01888064108788967,
0.07009474188089371,
0.042077239602804184,
-0.04298682510852814,
-0.010177656076848507,
-0.02217511087656021,
0.0280954260379076,
-0.04291049391031265,
0.051290277391672134,
0.011945925652980804,
0.005007967818528414,
-0.024948282167315483,
0.024551555514335632,
-0.009609842672944069,
-0.001684347866103053,
0.026027319952845573,
-0.04785816743969917,
-0.022977761924266815,
-0.040130797773599625,
-0.037996966391801834,
-0.02977798692882061,
0.04739607498049736,
0.007673829793930054,
-0.013286718167364597,
0.015510264784097672,
-0.00711951544508338,
0.09860356897115707,
0.0060920193791389465,
0.07099026441574097,
0.08624433726072311,
-0.06250374019145966,
0.03125947713851929,
0.029579130932688713,
0.057439789175987244,
0.038856033235788345,
-0.07506730407476425,
0.04216395318508148,
0.021919380873441696,
-0.04143332317471504,
0.04425831884145737,
0.004112597089260817,
0.006997358985245228,
-0.0528741218149662,
-0.004788331221789122,
-0.08453698456287384,
-0.0038558305241167545,
0.02599463053047657,
-0.09074091166257858,
-0.0709378644824028,
-0.02670694701373577,
-0.009888128377497196,
0.0207078754901886,
-0.05116261541843414,
0.07305663824081421,
0.009694521315395832,
0.02651781402528286,
-0.01952623389661312,
0.04891107231378555,
0.05409439653158188,
0.06299333274364471,
0.07133197039365768,
-0.0025310907512903214,
-0.0488986000418663,
-0.05812280625104904,
-0.032403748482465744,
0.004700720775872469,
-0.054887667298316956,
0.018919292837381363,
0.02176072634756565,
-0.01983104832470417,
-0.028546132147312164,
-0.022278429940342903,
-0.04958987236022949,
-0.04028480872511864,
-0.03533770516514778,
0.04013298451900482,
-0.03573637828230858,
0.010372894816100597,
-0.007225438952445984,
-0.018769580870866776,
-0.04156111925840378,
0.08637984842061996,
-0.06441152095794678,
0.008940494619309902,
0.013164307922124863,
-0.05513797700405121,
-0.07360441237688065,
0.00435658311471343,
0.038105517625808716,
-0.04042460024356842,
-0.02161036618053913,
-0.03973491117358208,
-0.011783243156969547,
-0.06554768979549408,
0.0005485278670676053,
0.0012892013182863593,
-0.02183668501675129,
0.04007299989461899,
-0.017764149233698845,
-0.014374333433806896,
0.021298730745911598,
0.020305272191762924,
-0.0048776473850011826,
-0.03101452998816967,
-0.0021660623606294394,
0.029029762372374535,
0.04865102469921112,
0.019697338342666626,
0.03388486057519913,
0.04924488812685013,
0.00041765905916690826,
-0.045999281108379364,
-0.03695106878876686,
0.059448979794979095,
0.06600513309240341,
0.005212211050093174,
-0.04636909440159798,
-0.01890873908996582,
0.03308738395571709,
-0.0016551188891753554,
0.03382689505815506,
-0.018705327063798904,
-0.015148529782891273,
-0.01642642728984356,
0.03086427040398121,
-0.06167718768119812,
0.010015440173447132,
-0.04691498354077339,
-0.007563179358839989,
-0.05028702691197395,
0.011248018592596054,
-0.0009960831375792623,
-0.003183216555044055,
0.021450992673635483,
0.006864727009087801,
0.0198826864361763,
0.029137900099158287,
-0.0030434171203523874,
0.003891255473718047,
0.03781772404909134,
0.05842189863324165,
-0.008688804693520069,
0.010393664240837097,
0.02098216861486435,
0.06798716634511948,
0.01892172545194626,
-0.01761256903409958,
0.0350068174302578,
0.02135911025106907,
0.003313913010060787,
-0.042723532766103745,
0.03124254196882248,
0.014447162859141827,
-0.008135766722261906,
-0.0170200876891613,
-0.007553452625870705,
-0.032054536044597626,
-0.016672993078827858,
0.025951659306883812,
-0.015396807342767715,
-0.01926075853407383,
-0.05429402366280556,
-0.013281642459332943,
-0.10640056431293488,
0.04998821020126343,
-0.03316260874271393,
0.0164483692497015,
0.004026846494525671,
-0.03376782685518265,
-0.02187669463455677,
0.04927689954638481,
-0.012021485716104507,
0.0014052835758775473,
-0.006567825563251972,
0.03539842367172241,
-0.009446228854358196,
0.047814223915338516,
0.01170682068914175,
0.0009589100955054164,
-0.05936772748827934,
-0.0013671463821083307,
0.005502399988472462,
0.005818716250360012,
0.021823305636644363,
-0.03664376959204674,
0.0005977750406600535,
-0.0218497421592474,
-0.013201506808400154,
-0.026830554008483887,
-0.04752087593078613,
-0.0072610690258443356,
-0.034015100449323654,
-0.036008697003126144,
-0.023805612698197365,
-0.011448151431977749,
0.007368510123342276,
0.018434830009937286,
-0.02036355808377266,
0.01750013418495655,
-0.01773596741259098,
0.03240656107664108,
-0.058158956468105316,
-0.060495536774396896,
0.030361689627170563,
0.028286557644605637,
-0.06110827624797821,
0.006961440667510033,
-0.016938474029302597,
-0.006002126261591911,
0.026587484404444695,
-0.01011593732982874,
0.006066028960049152,
-0.0040851766243577,
0.04561221972107887,
-0.02784978412091732,
0.0172958355396986,
0.03641476109623909,
-0.04408548027276993,
-0.0010775250848382711,
-0.07923293113708496,
0.06351207941770554,
0.01819027028977871,
-0.007670534308999777,
-0.021364910528063774,
0.027479877695441246,
-0.0332561656832695,
0.01907285675406456,
0.0063588242046535015,
0.06340918689966202,
-0.01840383931994438,
0.027222607284784317,
-0.009903742000460625,
-0.013808711431920528,
-0.026187265291810036,
0.037003740668296814,
0.019115975126624107,
-0.022133473306894302,
-0.023191865533590317,
0.006358277518302202,
0.07173958420753479,
-0.036814529448747635,
-0.007443369831889868,
-0.008203420788049698,
-0.009729349054396152,
-0.025064600631594658,
-0.01568605564534664,
-0.015731284394860268,
-0.034554965794086456,
-0.0025502394419163465,
0.002732032211497426,
-0.04345610365271568,
0.007916188798844814,
0.028018027544021606,
0.01800726167857647,
-0.04472709447145462,
-0.05005549639463425,
-0.07673045247793198,
-0.02121816948056221,
-0.0007524946122430265,
-0.01890823245048523,
0.032804206013679504,
0.015571735799312592,
0.057913728058338165,
-0.037171684205532074,
-0.018720772117376328,
-0.016942555084824562,
-0.0036569959484040737,
-0.04184601083397865,
-0.09873632341623306,
-0.023309284821152687,
-0.010474123992025852,
-0.03699482977390289,
-0.023048387840390205,
0.004234538413584232,
0.03222154453396797,
-0.018878312781453133,
-0.0649086982011795,
0.05785606428980827,
-0.04668520763516426,
0.06551125645637512,
-0.0016391092212870717,
0.07124622911214828,
-0.028270550072193146,
0.02066526561975479,
0.02784382551908493,
0.004306442569941282,
-0.06391066312789917,
0.0073395101353526115,
0.05829981714487076,
-0.022606464102864265,
-0.059035226702690125,
-0.019092025235295296,
0.02799335867166519,
0.004571966826915741,
0.017666595056653023,
-0.0015167325036600232,
-0.03688887506723404,
-0.006442229263484478,
0.01850419119000435,
-0.03818858414888382,
0.011099343188107014,
-0.011832157149910927,
-0.009284866973757744,
0.07716139405965805,
-0.030092202126979828,
-0.012192842550575733,
0.06090579554438591,
0.029539460316300392,
-0.031182540580630302,
-0.03187128156423569,
0.01246214471757412,
-0.0017639941070228815,
-0.01952071115374565,
0.056195612996816635,
-0.0031643209513276815,
0.02422146126627922,
-0.06352635473012924,
0.009051854722201824,
0.030537929385900497,
-0.015723999589681625,
0.04144475236535072,
0.004186594393104315,
0.0404086597263813,
0.015026330016553402,
0.006755826063454151,
0.009396957233548164,
0.005396001506596804,
0.06288283318281174,
-0.006573352497071028,
-0.03987199813127518,
-0.01855849288403988,
0.007860997691750526,
0.013852507807314396,
-0.06252919882535934,
0.003255900926887989,
0.021465491503477097,
0.03592473641037941,
-0.010716637596487999,
-0.015730086714029312,
-0.06496819108724594,
0.04010738804936409,
-0.03023586794734001,
-0.044982291758060455,
0.050990030169487,
0.056987714022397995,
0.004532133229076862,
-0.0009091878309845924,
0.07534532994031906,
0.04236634448170662,
0.039944954216480255,
-0.01894316077232361,
-0.026696981862187386,
-0.040701981633901596,
-0.012509606778621674,
-0.07028041034936905,
0.01222539134323597,
0.026773523539304733,
-0.010870174504816532,
0.015829818323254585,
0.03407811000943184,
-0.013301811181008816,
-0.04556923359632492,
-0.0007622739067301154,
-0.009898314252495766
] |
<p>My <a href="http://www.cs.berkeley.edu/~vazirani/s07quantum/notes/lecture2.pdf">text shows</a> (sections 0.2 and 0.3) that the joint "state space" of a system composed of two subsystems with $k$ and $l$ "bits of information", respectively, requires $kl$ bits to fully describe it. A critical consequence of this is that the $k+l$ bits in each of the individual subsystems are not sufficient to "span" their joint space, so that there must be states that are "entangled" (formally, cannot be expressed by the tensor product of the states of the subsystems). That much I (<em>think</em>) I understand.</p>
<p>But the text then seems to argue that this is a property that is exclusive to quantum systems. Is that true? Certainly there are classical systems where the state of one subsystem depends on the state of another. Doesn't any joint system that requires conditional probabilities to describe need "extra bits" beyond those necessary to describe the individual subsystems?</p>
<p>Perhaps I'm missing some subtlety about what constitutes a "sub system" or some unstated assumption about how systems are broken into parts. Perhaps a classical system that is "entangled" by conditional probabilities isn't thought of as consisting of valid "subsystems" in the same way that quantum system is.</p>
<p>Is "entanglement" unique to quantum systems? Are conditional probabilities just a kind of "classical entanglement"?</p>
<hr>
<p>Please be pedagogical. This is not meant to be a deep or advanced mathematical question, just a simple conceptual and definitional one. Just imagine I'm having basic probability explained to me (without reference to quantum vs. classical, or even physics). If one struck out all occurrences of the word "quantum" from the linked <a href="http://www.cs.berkeley.edu/~vazirani/s07quantum/notes/lecture2.pdf">text</a> (sections 0.2. and 0.3), wouldn't that be a perfectly valid part of such an explanation?</p> | g7850 | [
-0.0005747623508796096,
0.06723088771104813,
0.0112582016736269,
-0.006824539043009281,
-0.03659804165363312,
0.047945067286491394,
0.013203260488808155,
-0.005271600559353828,
0.0010828502709046006,
-0.04863010719418526,
0.015478882938623428,
-0.013026950880885124,
-0.010019245557487011,
0.013309775851666927,
-0.04768112301826477,
-0.010699777863919735,
0.06328199803829193,
0.03155104070901871,
0.0550510473549366,
0.03669501841068268,
-0.04905815050005913,
0.003313835710287094,
-0.04585111141204834,
0.01711689494550228,
0.0036126552149653435,
-0.035650551319122314,
0.055829863995313644,
-0.026651907712221146,
-0.03349800035357475,
0.00016964905080385506,
-0.0018050034996122122,
-0.04615601897239685,
0.03728175163269043,
-0.049351129680871964,
-0.02941451594233513,
-0.07467301934957504,
0.004561854992061853,
-0.03927135840058327,
-0.035035450011491776,
-0.03615407645702362,
-0.04514175280928612,
0.03356415778398514,
-0.026930678635835648,
-0.05122138932347298,
-0.026001937687397003,
0.009711839258670807,
0.0489996001124382,
0.017190583050251007,
0.01536939013749361,
0.015830492600798607,
-0.0052373381331563,
0.03180937469005585,
0.023683998733758926,
0.04423506185412407,
0.05826443061232567,
0.04114622622728348,
0.03674020245671272,
-0.005307482089847326,
0.0464974008500576,
-0.025495680049061775,
0.034869372844696045,
-0.019533392041921616,
0.017116256058216095,
-0.00594716751947999,
0.020564038306474686,
-0.0017603335436433554,
-0.0005423873662948608,
-0.02656000480055809,
-0.010614484548568726,
0.0022121400106698275,
-0.0020290387328714132,
0.018979458138346672,
0.0028492507990449667,
-0.0101854233071208,
0.047231245785951614,
0.016421327367424965,
0.04289882257580757,
0.04293122887611389,
0.033244144171476364,
0.04361392557621002,
-0.02290603145956993,
-0.05961260572075844,
0.045322395861148834,
-0.016106676310300827,
0.04618772491812706,
0.01663225330412388,
-0.04723214730620384,
-0.06604021787643433,
-0.02031005173921585,
0.05091487616300583,
-0.005219852086156607,
-0.030236834660172462,
0.08973589539527893,
0.012058455497026443,
-0.04254746809601784,
-0.03687824308872223,
-0.051842350512742996,
0.06906202435493469,
0.007464827969670296,
-0.01447827834635973,
-0.03027982823550701,
-0.00836848746985197,
0.04449809715151787,
-0.0465732142329216,
-0.030765781179070473,
-0.004226857330650091,
-0.019505415111780167,
-0.01011049747467041,
0.004716223105788231,
-0.012688182294368744,
-0.027585210278630257,
0.04899849370121956,
-0.010357211343944073,
-0.007543910760432482,
0.008730707690119743,
0.07386353611946106,
0.008753588423132896,
-0.01714189164340496,
-0.01944641023874283,
0.023565078154206276,
-0.03287072479724884,
-0.011026302352547646,
0.052352506667375565,
0.02217083051800728,
-0.08077718317508698,
0.03919703885912895,
0.02125786617398262,
0.002589226933196187,
0.07179761677980423,
0.005765415728092194,
0.00021734557230956852,
0.04216598719358444,
0.03498965501785278,
0.04785085842013359,
0.03058195486664772,
0.043090853840112686,
0.01987268775701523,
-0.0002814575855154544,
-0.026618462055921555,
-0.02368871495127678,
0.013483474031090736,
0.026709383353590965,
-0.05705488473176956,
-0.00419489573687315,
0.03842770308256149,
-0.032694630324840546,
-0.0066113704815506935,
0.005792999640107155,
-0.015886664390563965,
0.05984034016728401,
0.010449491441249847,
0.014773014932870865,
-0.032235145568847656,
-0.024951143190264702,
0.0038107854779809713,
0.07193747907876968,
0.04846030846238136,
-0.007873470894992352,
-0.023545710369944572,
-0.019476184621453285,
0.045997604727745056,
0.06438548862934113,
-0.0014572093496099114,
-0.002258474472910166,
0.009645536541938782,
0.0016699854750186205,
-0.028224121779203415,
-0.04619596526026726,
-0.005630781874060631,
-0.02923140861093998,
-0.030250094830989838,
-0.005720764398574829,
-0.056026261299848557,
0.026302563026547432,
0.041346702724695206,
0.03301365301012993,
0.043556611984968185,
0.011777808889746666,
0.013123671524226665,
-0.011215913109481335,
-0.024238480255007744,
0.03972562402486801,
0.0005313126021064818,
0.019801529124379158,
-0.03558560833334923,
0.01729942299425602,
-0.030639950186014175,
0.07151041179895401,
-0.03521950915455818,
0.0006424690363928676,
-0.03777226433157921,
-0.01623719371855259,
0.02092154137790203,
-0.0031298957765102386,
0.02306123822927475,
0.00408935034647584,
0.006893941201269627,
0.009793590754270554,
-0.006761007476598024,
-0.008806324563920498,
0.04088170826435089,
0.027784280478954315,
0.0025928642135113478,
-0.008225342258810997,
0.03311869874596596,
0.00790146179497242,
-0.08987538516521454,
0.05160217359662056,
-0.02493892051279545,
-0.018505103886127472,
0.003617293434217572,
-0.046856991946697235,
0.009556910954415798,
0.052168071269989014,
0.027858905494213104,
-0.07230840623378754,
0.052099596709012985,
-0.012502674013376236,
-0.028007928282022476,
-0.017037415876984596,
-0.022879263386130333,
-0.024130968376994133,
0.09000109136104584,
0.010754721239209175,
-0.005473440047353506,
0.036167312413454056,
-0.06561775505542755,
-0.02579033188521862,
-0.057575955986976624,
0.07068444043397903,
-0.05046919360756874,
-0.0350397564470768,
-0.003802021499723196,
-0.010405194945633411,
0.038056716322898865,
0.07565250992774963,
0.031125498935580254,
-0.008695550262928009,
0.053460169583559036,
0.023108303546905518,
0.04914263263344765,
-0.03324234485626221,
0.028455764055252075,
0.04260826110839844,
0.006019909866154194,
0.017718691378831863,
0.03855885937809944,
-0.04850276932120323,
-0.051869895309209824,
0.02593119442462921,
-0.0675058364868164,
-0.05705058202147484,
-0.001686116331256926,
-0.04045351594686508,
-0.016003740951418877,
-0.027983296662569046,
0.021258268505334854,
0.022161919623613358,
-0.04210050776600838,
-0.02984415739774704,
-0.02342192828655243,
-0.01911763846874237,
-0.06412588804960251,
-0.00509227067232132,
-0.03847220540046692,
-0.03656632453203201,
0.02582273818552494,
-0.054220572113990784,
-0.01352463848888874,
-0.010831370949745178,
-0.02677121013402939,
0.06291680037975311,
-0.01940957084298134,
0.044897351413965225,
0.054037678986787796,
-0.032364893704652786,
-0.022240007296204567,
0.04291791096329689,
-0.03193776682019234,
-0.009515430778265,
-0.06288260221481323,
0.01962602511048317,
0.022919710725545883,
0.027552427724003792,
-0.01417284645140171,
-0.08984357118606567,
0.05698588863015175,
0.038651224225759506,
0.059791456907987595,
0.06144353002309799,
-0.04483509063720703,
0.01810249127447605,
0.03579704090952873,
0.004827449098229408,
-0.0207669697701931,
-0.0025123918894678354,
-0.010143972933292389,
-0.032160643488168716,
-0.0027064254973083735,
0.034640517085790634,
-0.05424061045050621,
0.04598104953765869,
0.011819462291896343,
0.013662927784025669,
-0.021941980347037315,
-0.01886841282248497,
-0.09604210406541824,
-0.012222747318446636,
-0.03192826360464096,
-0.03265317156910896,
-0.02826438844203949,
0.001178345293737948,
0.04297314211726189,
-0.041132792830467224,
-0.011006114073097706,
-0.023151416331529617,
-0.024857666343450546,
0.017234032973647118,
-0.04904874786734581,
-0.04828602820634842,
-0.02244962751865387,
0.004532782360911369,
-0.04655206948518753,
0.014142905361950397,
0.07261323183774948,
-0.017528099939227104,
-0.060400888323783875,
-0.012486600317060947,
-0.0287210363894701,
0.022472364827990532,
0.028594955801963806,
-0.03385068476200104,
0.03256246820092201,
-0.038837213069200516,
-0.06517040729522705,
-0.07913436740636826,
-0.04650845006108284,
-0.054942015558481216,
-0.011929461732506752,
0.024748222902417183,
0.059357862919569016,
0.014394628815352917,
-0.01244819164276123,
0.06352701783180237,
0.017332827672362328,
0.029405193403363228,
0.001185828703455627,
0.03812868148088455,
0.1181994378566742,
-0.011892206966876984,
-0.02599138207733631,
0.04332788288593292,
0.028669754043221474,
0.014118674211204052,
-0.006547471508383751,
0.08115127682685852,
0.02806658111512661,
0.03936668112874031,
0.04059784859418869,
-0.02503204718232155,
0.062269486486911774,
-0.041492197662591934,
0.0355590283870697,
-0.037767503410577774,
0.0080068688839674,
0.0026103914715349674,
0.03167138248682022,
0.0006703839171677828,
0.0370972640812397,
0.033795010298490524,
-0.028795503079891205,
0.0014612441882491112,
0.011335809715092182,
-0.03537740185856819,
0.06137693673372269,
-0.05349497124552727,
0.0478174053132534,
-0.04420455917716026,
-0.03197186067700386,
-0.02822905033826828,
0.0452364906668663,
0.020166419446468353,
0.06169113889336586,
0.045280810445547104,
0.07636180520057678,
-0.0035132640041410923,
-0.001129242475144565,
0.054766759276390076,
-0.0031412316020578146,
0.05503799393773079,
-0.0008362811640836298,
-0.038912948220968246,
-0.09211885184049606,
-0.04175223037600517,
0.013701817020773888,
0.11124371737241745,
0.043799690902233124,
-0.04845647141337395,
-0.001938238856382668,
-0.031357623636722565,
-0.07732542604207993,
-0.015029096975922585,
0.033258575946092606,
0.02028900757431984,
0.042411014437675476,
-0.016567528247833252,
-0.010882711969316006,
-0.020736437290906906,
-0.007002007216215134,
0.027257082983851433,
0.07232368737459183,
-0.0013337532291188836,
0.0022358621936291456,
0.02340427041053772,
0.011552407406270504,
0.034315142780542374,
0.032631900161504745,
-0.012584450654685497,
0.0037333981599658728,
-0.01099464576691389,
-0.03350371494889259,
0.056525323539972305,
0.002497089561074972,
-0.021483981981873512,
0.021747754886746407,
0.028474798426032066,
0.009902792051434517,
0.007442542351782322,
0.020634127780795097,
-0.039023127406835556,
0.023560060188174248,
0.018970387056469917,
0.00997236929833889,
0.023350993171334267,
-0.04778329282999039,
-0.03949505463242531,
-0.05847126618027687,
0.031042935326695442,
0.015545116737484932,
-0.009474637918174267,
0.050273433327674866,
-0.016381647437810898,
-0.019282642751932144,
0.018224945291876793,
0.020965753123164177,
0.028015900403261185,
-0.007108563091605902,
-0.01628771610558033,
-0.022835809737443924,
-0.06631818413734436,
-0.021178096532821655,
0.06357056647539139,
-0.003114290302619338,
-0.06581790745258331,
-0.014977199956774712,
-0.03204852342605591,
-0.003204550128430128,
0.027747884392738342,
0.010865227319300175,
0.02340167760848999,
-0.006501079071313143,
0.0024130644742399454,
-0.01590503565967083,
0.026485558599233627,
0.020805591717362404,
0.004741141572594643,
-0.06166214868426323,
0.0036506112664937973,
-0.051706597208976746,
-0.01426781713962555,
0.03285406529903412,
-0.0188071820884943,
0.0004949535359628499,
-0.06566206365823746,
0.04508545249700546,
-0.021798627451062202,
-0.028534606099128723,
-0.00795456487685442,
0.019983215257525444,
0.02067183330655098,
0.020877469331026077,
-0.02099120430648327,
-0.003178415587171912,
0.039428893476724625,
0.03125165402889252,
0.03438384830951691,
0.04104069992899895,
-0.030906029045581818,
-0.04059574380517006,
-0.010807373560965061,
0.008275969885289669,
0.0023742530029267073,
0.010562393814325333,
0.04282737895846367,
-0.028239943087100983,
-0.04967884346842766,
-0.004840015433728695,
-0.015926562249660492,
0.019511887803673744,
0.024729859083890915,
-0.030272971838712692,
0.02141350507736206,
0.06600163877010345,
0.026384547352790833,
-0.03519117832183838,
-0.01821986958384514,
0.014582552015781403,
-0.0027390632312744856,
-0.015214812010526657,
-0.010248716920614243,
0.005268903914839029,
0.029063578695058823,
-0.029396533966064453,
-0.0007218830287456512,
-0.002454490168020129,
-0.037946995347738266,
-0.048981111496686935,
-0.015289069153368473,
-0.012303178198635578,
-0.0013605881249532104,
-0.02122192643582821,
-0.021815963089466095,
-0.009897572919726372,
0.0007087873527780175,
-0.04157162085175514,
0.01848195306956768,
-0.10503347963094711,
-0.04782897233963013,
-0.017222771421074867,
0.04353741183876991,
0.07862633466720581,
0.0281110480427742,
-0.005092551466077566,
0.01841099001467228,
-0.019598819315433502,
-0.05938899889588356,
-0.014913732185959816,
0.01605253852903843,
0.012446938082575798,
0.024230098351836205,
-0.02555133029818535,
-0.04009309038519859,
-0.03930530324578285,
0.046670980751514435,
0.011757400818169117,
-0.03854113444685936,
-0.007176986429840326,
-0.046036895364522934,
0.04546453431248665,
-0.04621066525578499,
-0.0034754956141114235,
0.011775260791182518,
0.004927766975015402,
0.009859065525233746,
0.044217027723789215,
0.012171544134616852,
-0.033573634922504425,
0.04979659616947174,
-0.05230838432908058,
0.024080049246549606,
0.04691082984209061,
0.029194772243499756,
0.004969216417521238,
0.05999347195029259,
0.02299807406961918,
-0.03342556953430176,
0.0010629351017996669,
0.007659826427698135,
-0.02655128948390484,
0.08639805763959885,
-0.03409526124596596,
0.015929173678159714,
-0.06053227186203003,
-0.007976544089615345,
-0.019836461171507835,
0.03495928272604942,
-0.04665588214993477,
-0.029600342735648155,
-0.037896011024713516,
0.019109776243567467,
-0.04139167070388794,
0.0073531148955225945,
-0.01848353073000908,
-0.04573453217744827,
-0.06574656069278717,
0.02412872575223446,
-0.051224593073129654,
-0.028164908289909363,
-0.04280440881848335,
0.08239041268825531,
-0.00606865668669343,
0.019074680283665657,
-0.03688542917370796,
-0.017411204054951668,
-0.00045374923502095044,
0.0240780059248209,
0.01616903766989708,
0.08652732521295547,
-0.030385350808501244,
-0.021120911464095116,
-0.02792687714099884,
-0.033115241676568985,
0.04605100303888321,
-0.04097811132669449,
0.025569012388586998,
0.08147144317626953,
0.00982536282390356,
0.004759896546602249,
0.005157047882676125,
0.001658612280152738,
-0.014773856848478317,
-0.025088610127568245,
0.01954600028693676,
0.028267692774534225,
0.024006016552448273,
-0.04282766953110695,
-0.08865413814783096,
-0.022657617926597595,
-0.07019524276256561,
0.011458436027169228,
0.04189499095082283,
-0.00043539004400372505,
0.019790371879935265,
-0.0115113016217947,
0.010161752812564373,
0.053537517786026,
-0.03748514875769615,
0.058770570904016495,
0.017948005348443985,
0.07374585419893265,
0.012440149672329426,
-0.028890831395983696,
0.003852280555292964,
0.06067533418536186,
-0.04637891799211502,
-0.01948394626379013,
-0.05567185580730438,
0.010591144673526287,
0.044520966708660126,
-0.04390157759189606,
0.02462874725461006,
-0.018359016627073288,
0.05305454879999161,
0.028575479984283447,
-0.01626092754304409,
-0.035051748156547546,
0.07568557560443878,
-0.013961703516542912,
-0.02800203301012516,
0.018042081966996193,
-0.046351298689842224,
0.04743603244423866,
-0.044177912175655365,
0.008909528143703938,
0.014275058172643185,
0.00791742093861103,
0.012213547714054585,
0.011154146865010262,
0.06715361773967743,
-0.041784707456827164,
-0.06828383356332779,
-0.012077122926712036,
-0.006383886095136404,
-0.007686890661716461,
-0.01408362202346325,
0.021093932911753654,
0.03297913819551468,
-0.05392390489578247,
-0.07787025719881058,
-0.028362344950437546,
-0.015638817101716995,
-0.015580371953547001,
0.00502073485404253,
0.03752174228429794,
-0.003491015871986747,
-0.012256843037903309,
-0.002668970264494419,
0.021828295662999153,
-0.006943335756659508,
0.001389505690895021,
-0.006891850847750902,
0.04740486666560173,
-0.02549881860613823,
0.06658187508583069,
-0.0014670781092718244,
0.006916822399944067,
0.0033783602993935347,
0.0036416195798665285,
0.00040876292041502893,
-0.013070501387119293,
0.04408646002411842,
-0.03839775547385216,
-0.006102556828409433,
-0.018023457378149033,
0.0019940021447837353,
0.027236809954047203,
0.08754633367061615,
0.02051900513470173,
0.02844243496656418,
-0.02334083802998066,
-0.015110847540199757,
0.056057777255773544,
-0.025500191375613213,
0.045901667326688766,
0.028082409873604774,
-0.025560490787029266,
0.018802735954523087,
-0.04043674096465111,
-0.02652273140847683,
-0.020782392472028732,
-0.01923617720603943,
0.010013056918978691,
-0.04124309867620468,
-0.024874940514564514,
-0.04545309767127037,
-0.03294052183628082,
-0.022596139460802078,
0.031485360115766525,
-0.022415535524487495,
-0.011292664334177971,
0.04594177380204201,
-0.07631668448448181,
-0.038010552525520325,
0.043318308889865875,
-0.032821375876665115,
-0.047707848250865936,
0.05413475260138512,
-0.008072078227996826,
-0.013639487326145172,
0.01189741026610136,
0.014547551050782204,
-0.052194349467754364,
-0.021048394963145256,
0.0640467032790184,
0.011109250597655773,
0.038174182176589966,
-0.0215434730052948,
0.019718028604984283,
-0.027912838384509087,
0.027552949264645576,
-0.012248900718986988,
-0.03872908651828766,
-0.0025682307314127684,
0.005708496551960707,
-0.06737867742776871,
-0.07993139326572418,
-0.020786192268133163,
-0.023922478780150414,
-0.009150227531790733,
0.035370342433452606,
-0.1062854528427124,
-0.05858089402318001,
0.03334091231226921,
0.0014586001634597778,
0.013735465705394745,
0.015978358685970306,
0.04729711264371872,
0.009865225292742252,
0.00297310552559793,
-0.008309607394039631,
-0.010150684043765068,
0.03756305202841759,
-0.0024630846455693245,
-0.03275911137461662,
-0.0382685624063015,
-0.030833682045340538,
0.02343314327299595,
0.02064993418753147
] |
<p>I would like to start off by saying this is not a philosophical question. I have a specific question pertaining to physics after the following explanation and background information, which I felt was necessary to properly formulate my question.</p>
<p>I have done some research on <a href="http://en.wikipedia.org/wiki/Zeno%27s_paradoxes" rel="nofollow">Zeno's Paradoxes</a> as well as some of their modern day mathematical and physical "solutions." I understand that Zeno's dichotomy paradox can be explained mathematically by constructing an argument that makes use of the following infinite series:
$$ \sum_{n=1}^\infty {1 \over 2^n} = 1$$ Because this series converges to $1$, then that implies that if physically traveling from some point A to another point B truly does require an infinite amount of actions in which an object travels ${1 \over 2}$ of the distance, then ${1 \over 4}$ then ${1 \over 8}$ then ${1 \over 16}$ and so on, the sum of those actions would eventually result in traveling the full distance. Mathematically, this makes perfect sense. However, knowing that the mathematics we use to describe the physical world is only a model, adopted when there is sufficient evidence to support it, could it be that the solution gained by the above argument comes to the correct conclusion using the wrong path? Using the infinite series provides a solution to the dichotomy paradox if it does indeed require an infinite amount of actions to move from point A to point B. So, then the question becomes, does it truly take an infinite amount of actions to physically move from one point to another (in which case, I believe the mathematical solution is a perfect model), or are there other phenomena at play that cannot be described in this fashion?</p>
<p>I have one idea pertaining to a quantum mechanical description of the situation that does not disprove, but provides an alternative to the reasoning that it requires an infinite number of actions to move from point A to point B. </p>
<ul>
<li>Suppose we have a box of some macroscopic size (say $1m^3$), and it is in the process of moving with a constant velocity from some point A to another point B. Obviously, the box is made up of atoms, and if we zoom in far enough on the leading face of the box we could see that the motion of said box is really the motion of a very large number of atoms moving in the same direction. According to the uncertainty principle, it is impossible to determine both a particle's momentum and position simultaneously. According to the physics professor who first taught me about this, the reason for this uncertainty does not lie within our measurement methods, but rather, it is an impossibility inherent in the fact that all particles have wavelike characteristics. Thus, their position and momentum are not even clearly defined at a specific moment in time. Could it not be possible then, that if we zoomed in far enough on the leading face of our box, that we would find the face of the box does not have a definite position? If this is true, then wouldn't there be a certain point very close to the destination point, B, where the idea of cutting the remainder of the distance to the destination in half makes no difference to the particles in question? We may say that to complete the trip, we must travel another ${1 \over 2^x}$ portion of the distance we started with, but if the uncertainty in position is larger than this remaining distance, could the particle (and by the same argument, all of the particles that make up the leading face of the box), traverse the final distance to point B without physically having to travel the "infinite" amount of points remaining?</li>
</ul>
<p>Also, I have a second idea that I want to present as an aside, something that I don't believe can be proven as of now, but I wonder if, according to current understanding, it is possible.</p>
<ul>
<li>What if, instead of analyzing the situation at hand through the distance traveled, it was analyzed by analyzing the passage of time. Specifically, if time is quantized, would it resolve the dichotomy paradox in a physical sense? I realize that whether or not time is quantized is up for debate (there is even <a href="http://physics.stackexchange.com/questions/35674/is-time-continuous">this question</a> here at stack exchange that explores the idea), so I am not going to ask if time is quantized. Based off of my understanding, however, there is nothing known as of now that says time cannot be quantized (please correct me if I am wrong). Therefore, if time <em>were</em> quantized then could we not say that for a given constant velocity there is a minimum distance that can be traveled? A distance that corresponds to $\Delta t_{min} * v$? Would this not imply that as our moving box reached a certain distance, $d$ away from point B, and if $d < \Delta t_{min} * v$, the box would physically not be able to travel such a small distance, and in the next moment that the box moved, it would effectively be across the destination point B?</li>
</ul>
<p>All of that being said, here is my specific question: In my above arguments, is any of my logic faulty? Is there any known law that would disprove either of these explanations for Zeno's dichotomy paradox? If so, is there a better way of physically (not mathematically) resolving the paradox?</p> | g7851 | [
-0.005630703177303076,
0.03676624968647957,
-0.017869990319013596,
0.028890304267406464,
0.019149579107761383,
-0.028913693502545357,
0.07494580000638962,
-0.0005282392376102507,
-0.030581042170524597,
-0.018105966970324516,
-0.021289164200425148,
-0.019936734810471535,
0.015593635849654675,
-0.04379090294241905,
-0.04230404272675514,
-0.025359516963362694,
0.04093056917190552,
-0.07299908995628357,
0.038581233471632004,
-0.007032736670225859,
0.06466029584407806,
0.0816086158156395,
0.0036274411249905825,
-0.03179124742746353,
-0.06383638083934784,
-0.043384913355112076,
0.029536385089159012,
0.033855073153972626,
-0.017685342580080032,
0.0005396303604356945,
0.016439169645309448,
-0.0579734668135643,
0.04234636202454567,
-0.01840740442276001,
0.001529388828203082,
-0.013246254064142704,
0.05430314317345619,
-0.01555710006505251,
0.017071964219212532,
0.04793340712785721,
0.05621093139052391,
-0.021364429965615273,
-0.0041540381498634815,
-0.03519521653652191,
-0.05058655887842178,
-0.023825036361813545,
0.004002307076007128,
-0.0010591908358037472,
0.019547222182154655,
-0.006942882668226957,
-0.021440349519252777,
0.04966617748141289,
0.03376757726073265,
0.04685031250119209,
0.016784710809588432,
0.06627005338668823,
0.0750393345952034,
0.016779042780399323,
0.05341990292072296,
0.01773010566830635,
-0.018520165234804153,
-0.002349231392145157,
0.01531381905078888,
-0.010395023971796036,
0.047585710883140564,
-0.048103734850883484,
-0.05371455103158951,
0.01720687374472618,
-0.032915178686380386,
-0.03800124675035477,
0.022557850927114487,
-0.0894569456577301,
-0.021931644529104233,
-0.02087085135281086,
-0.038168903440237045,
0.03355507552623749,
0.024667873978614807,
0.03962470218539238,
0.024026697501540184,
-0.029025709256529808,
-0.06452036648988724,
-0.0006344512803480029,
0.037995729595422745,
-0.05553334206342697,
0.005051620304584503,
-0.0031266892328858376,
-0.0027525885961949825,
-0.02764897234737873,
-0.019268633797764778,
-0.0018659565830603242,
-0.05938639119267464,
-0.006316384766250849,
0.04327826574444771,
0.0252938624471426,
-0.026295093819499016,
0.012901030480861664,
0.0022610039450228214,
0.03564587980508804,
0.006304729264229536,
0.041698478162288666,
-0.028663471341133118,
0.045267872512340546,
0.009365231730043888,
0.04385894536972046,
0.018657034263014793,
-0.013300416991114616,
0.021770749241113663,
0.020223811268806458,
0.014594433829188347,
-0.0060407854616642,
-0.017533039674162865,
-0.03725767880678177,
-0.009380336850881577,
0.006976466625928879,
-0.021592767909169197,
-0.029475007206201553,
-0.015146142803132534,
0.0689600333571434,
0.005696728825569153,
0.05591578036546707,
0.0022980356588959694,
0.04957709461450577,
-0.07400019466876984,
0.024546049535274506,
-0.05249336361885071,
0.0037725521251559258,
-0.01984444633126259,
0.021238815039396286,
-0.015320236794650555,
0.011551358737051487,
0.009845019318163395,
0.02805737406015396,
0.011319173499941826,
0.08496449142694473,
-0.04533928632736206,
-0.008100138045847416,
-0.0016631719190627337,
0.04554218053817749,
-0.012489767745137215,
0.04554876685142517,
0.032475557178258896,
-0.032549746334552765,
-0.008928320370614529,
-0.008056803606450558,
-0.018183734267950058,
0.029542002826929092,
-0.019423726946115494,
-0.026352260261774063,
0.053869929164648056,
-0.01002516783773899,
-0.05336952954530716,
0.08561955392360687,
0.02822679467499256,
0.04974232614040375,
0.01480184867978096,
0.0010546884732320905,
0.017106108367443085,
-0.003032878041267395,
-0.025963876396417618,
-0.02004835568368435,
0.019524721428751945,
0.034717973321676254,
0.012414964847266674,
-0.029272297397255898,
-0.0013515136670321226,
-0.045372124761343,
0.022769106552004814,
-0.024486184120178223,
0.025263682007789612,
-0.052015770226716995,
-0.061390724033117294,
0.017323264852166176,
0.016161158680915833,
-0.0014880638336762786,
0.06410320848226547,
0.03886089101433754,
0.027872612699866295,
0.0033700948115438223,
-0.07059488445520401,
-0.03182617202401161,
-0.006884705740958452,
0.015386738814413548,
0.03530875965952873,
-0.0373862124979496,
-0.008500011637806892,
0.010237685404717922,
-0.020316697657108307,
-0.03760647773742676,
0.009343128651380539,
-0.005357910413295031,
0.019279127940535545,
-0.04877655953168869,
-0.014849621802568436,
-0.017543790861964226,
-0.024879729375243187,
-0.0011083412682637572,
0.06793846935033798,
-0.003057245397940278,
-0.036611005663871765,
-0.020918434485793114,
0.04406164586544037,
0.009090730920433998,
0.04627767950296402,
-0.004329656716436148,
0.018097924068570137,
-0.00099252222571522,
-0.07366053014993668,
0.01968267187476158,
-0.03829498589038849,
0.004349877126514912,
0.01650935597717762,
-0.04666224494576454,
0.000464128446765244,
0.014073626138269901,
-0.05161820352077484,
-0.06221087649464607,
0.03248932957649231,
0.02074465900659561,
-0.0045442706905305386,
0.016044210642576218,
-0.06479732692241669,
-0.024582883343100548,
0.07880276441574097,
-0.004224527161568403,
-0.0169571191072464,
-0.00803343579173088,
0.0019126756815239787,
-0.13052785396575928,
-0.005415397230535746,
0.083231620490551,
-0.0326300710439682,
0.010055525228381157,
0.06764379143714905,
-0.042244892567396164,
0.0678793266415596,
0.00043713964987546206,
-0.006143942940980196,
0.007718678098171949,
0.016854943707585335,
-0.017148621380329132,
0.0741443857550621,
0.002053141128271818,
-0.07305490225553513,
-0.022898182272911072,
0.04191194474697113,
-0.06621772795915604,
-0.03436274081468582,
0.02229432575404644,
0.03537244349718094,
0.027961429208517075,
0.0002979545097332448,
-0.019523393362760544,
0.004662680439651012,
-0.004274118226021528,
0.03306813910603523,
-0.03412958234548569,
0.020417511463165283,
0.05742327868938446,
-0.027614574879407883,
-0.01980031281709671,
0.0040010856464505196,
0.007859894074499607,
-0.011082444339990616,
0.013044902123510838,
-0.035165730863809586,
0.014337687753140926,
-0.06442505866289139,
0.053101006895303726,
-0.05974896252155304,
-0.014354478567838669,
0.005128947086632252,
0.04353300854563713,
0.03824005648493767,
0.06121276319026947,
0.005956276785582304,
0.010647506453096867,
0.04122890532016754,
0.0031027544755488634,
0.04485854133963585,
0.02107127383351326,
-0.00015904626343399286,
-0.010985306464135647,
-0.03439279645681381,
0.008717193268239498,
0.045306961983442307,
-0.007724912371486425,
-0.018522074446082115,
0.04529942199587822,
-0.004140274133533239,
-0.012804125435650349,
0.010590635240077972,
0.02704116888344288,
0.051210056990385056,
0.04406125470995903,
-0.04791465029120445,
0.04798532649874687,
-0.006431854795664549,
-0.06575681269168854,
0.01860637031495571,
-0.06019436568021774,
0.0166168175637722,
-0.059880852699279785,
-0.03347410634160042,
0.021618271246552467,
0.08998475968837738,
0.07018836587667465,
-0.042577099055051804,
0.008521592244505882,
-0.04684048891067505,
0.016900459304451942,
0.027222180739045143,
0.06950913369655609,
0.039608970284461975,
0.04971132054924965,
-0.005962101276963949,
-0.018537482246756554,
0.012658579275012016,
0.036935146898031235,
0.02169661596417427,
-0.04585511237382889,
0.014780615456402302,
-0.010420579463243484,
-0.03613569587469101,
-0.024907661601901054,
0.03669675439596176,
0.009059401229023933,
-0.09947876632213593,
0.04540003836154938,
-0.06387519836425781,
0.029239771887660027,
0.006404362618923187,
-0.005732027348130941,
-0.0216340534389019,
-0.006502507720142603,
-0.02949606440961361,
-0.09025819599628448,
-0.04651781916618347,
0.009554727002978325,
0.0972667708992958,
0.0030651427805423737,
-0.002278560074046254,
-0.004043096210807562,
-0.018026256933808327,
0.06684516370296478,
0.0263458713889122,
0.0029595133382827044,
0.06794813275337219,
0.05815048888325691,
0.03723251819610596,
0.025414252653717995,
0.02298341505229473,
-0.038288604468107224,
-0.07630272209644318,
0.0327129140496254,
0.026367437094449997,
0.05466289445757866,
0.02619364485144615,
0.020270854234695435,
0.013530359603464603,
-0.05310502275824547,
-0.006910428870469332,
0.005729018710553646,
0.054750956594944,
-0.01868954487144947,
0.042149607092142105,
-0.024858353659510612,
-0.03233280032873154,
0.06746067106723785,
0.004364982713013887,
-0.03735627233982086,
-0.03212782368063927,
-0.0245082788169384,
-0.03443736955523491,
0.0015737076755613089,
0.07484949380159378,
-0.07729411125183105,
0.06947653740644455,
0.018144918605685234,
-0.07015057653188705,
0.05850771814584732,
0.09307697415351868,
0.08262669295072556,
0.033224377781152725,
0.0009614133159630001,
0.0008799624629318714,
0.018938355147838593,
-0.051142532378435135,
-0.030062759295105934,
0.01637994311749935,
-0.012685622088611126,
-0.037255629897117615,
-0.008518600836396217,
-0.008179583586752415,
0.0193166546523571,
0.0008715536678209901,
0.005280787590891123,
-0.06061604991555214,
-0.05800313130021095,
-0.019568266347050667,
0.00018138666928280145,
0.040569968521595,
0.0041115619242191315,
-0.013822793960571289,
0.023326396942138672,
0.002880356041714549,
0.014757511205971241,
0.033989887684583664,
0.01660274900496006,
0.03345206379890442,
-0.029391596093773842,
0.044916700571775436,
0.024758154526352882,
0.010737503878772259,
-0.0534575916826725,
-0.021905114874243736,
0.04181942343711853,
-0.04938829317688942,
-0.06884954124689102,
0.009562788531184196,
0.024252908304333687,
-0.01618788205087185,
0.05919681861996651,
0.0249196607619524,
-0.016347777098417282,
-0.022208932787179947,
0.018361367285251617,
0.025564944371581078,
-0.02005276456475258,
-0.006297543179243803,
0.027744246646761894,
0.0037246213760226965,
0.028646063059568405,
0.012997627258300781,
0.08413293957710266,
-0.010031968355178833,
0.03942837938666344,
0.016130877658724785,
0.009404919110238552,
0.00892721302807331,
-0.005403857212513685,
0.06489377468824387,
0.02704116888344288,
-0.004420192912220955,
0.004592875950038433,
-0.016469618305563927,
-0.0035474568139761686,
-0.06545808911323547,
-0.04930036887526512,
-0.03757008910179138,
-0.0499783456325531,
-0.04020374268293381,
0.04833110794425011,
-0.04539074748754501,
-0.0209844708442688,
-0.05424724146723747,
-0.059352897107601166,
-0.025791455060243607,
0.029664283618330956,
-0.003222713014110923,
0.029552053660154343,
-0.05334305390715599,
-0.0023331008851528168,
-0.016322661191225052,
0.07939463108778,
0.0021075063850730658,
-0.04344259947538376,
-0.0014950481709092855,
-0.0073110079392790794,
-0.05430319160223007,
-0.013411246240139008,
-0.03287537023425102,
0.0427062027156353,
0.03276710957288742,
0.04821956902742386,
-0.027852244675159454,
-0.03115127608180046,
-0.013892792165279388,
0.008003835566341877,
-0.0017503427807241678,
-0.018309708684682846,
0.00031227036379277706,
-0.013630161993205547,
0.0457952655851841,
-0.019019033759832382,
-0.006070655304938555,
-0.014443084597587585,
-0.05910511314868927,
-0.01452090498059988,
0.05945010855793953,
0.02748454548418522,
0.04801331087946892,
-0.03751951828598976,
0.01628727652132511,
-0.04202866926789284,
-0.022508813068270683,
-0.008074400015175343,
-0.027402905747294426,
0.0469960942864418,
-0.007970001548528671,
-0.03124878741800785,
0.03386564180254936,
0.027454782277345657,
0.01196567714214325,
-0.026213180273771286,
0.0010059245396405458,
-0.07831165939569473,
0.06355283409357071,
-0.0009808739414438605,
-0.04770011454820633,
0.024656519293785095,
0.02915848419070244,
0.03325716406106949,
-0.03485400974750519,
0.02475993148982525,
0.02181505225598812,
0.007460311986505985,
-0.019041432067751884,
-0.025277411565184593,
-0.05125163495540619,
-0.009342502802610397,
0.050027843564748764,
-0.003525247797369957,
0.05365678668022156,
-0.028697369620203972,
-0.006704665254801512,
0.04479018598794937,
-0.024128541350364685,
-0.039562806487083435,
-0.03048202209174633,
0.06084245443344116,
0.03425068035721779,
0.02749643288552761,
0.015475165098905563,
-0.004058103542774916,
-0.08174746483564377,
0.023505082353949547,
0.03721180558204651,
0.005991179496049881,
-0.0028110116254538298,
0.003603774355724454,
-0.020036064088344574,
-0.06281319260597229,
0.02212933450937271,
0.09090658277273178,
0.011968431062996387,
-0.003162792418152094,
-0.009164372459053993,
-0.010146084241569042,
-0.006344637833535671,
-0.07784730195999146,
-0.021485865116119385,
0.009178990498185158,
-0.07946367561817169,
-0.007299686782062054,
-0.03403119742870331,
-0.00601531146094203,
-0.019246170297265053,
-0.02650795504450798,
-0.011211635544896126,
0.013429193757474422,
0.0137228574603796,
0.03817351162433624,
0.00013050646521151066,
-0.03691652789711952,
0.031517766416072845,
-0.006436801515519619,
0.010090194642543793,
0.016693053767085075,
0.03219941258430481,
0.010614766739308834,
0.015204699710011482,
0.06987185776233673,
0.028922317549586296,
0.04348452389240265,
-0.0053604766726493835,
0.040716953575611115,
-0.011842449195683002,
-0.02276512049138546,
-0.09563056379556656,
-0.018172230571508408,
-0.054225772619247437,
0.03469093143939972,
-0.008178926073014736,
0.006530637852847576,
-0.009702813811600208,
0.054626837372779846,
-0.0678158774971962,
-0.03633671626448631,
0.023852989077568054,
-0.03727542236447334,
0.016305383294820786,
-0.03141364827752113,
0.009236805140972137,
-0.08351655304431915,
-0.037705060094594955,
-0.00032869167625904083,
0.039695318788290024,
-0.0556735098361969,
-0.02829410694539547,
0.044965729117393494,
0.0013047008542343974,
-0.05914031341671944,
-0.01847369410097599,
-0.0037626600824296474,
-0.0426320880651474,
0.01563015952706337,
-0.04382918402552605,
-0.04352540150284767,
-0.006250999867916107,
-0.047662362456321716,
0.023394770920276642,
-0.011177105829119682,
0.006340663880109787,
0.06425677239894867,
0.024502558633685112,
0.015951398760080338,
-0.05819623917341232,
0.0027119277510792017,
-0.05770845338702202,
0.00832081213593483,
0.03830314427614212,
-0.026787588372826576,
-0.045746635645627975,
-0.0014874552143737674,
0.0042275795713067055,
0.013560138642787933,
-0.019828930497169495,
0.03585826978087425,
0.048561036586761475,
0.09191059321165085,
0.013490316458046436,
-0.022232098504900932,
0.022630326449871063,
0.043105367571115494,
-0.04030560329556465,
-0.000032564257708145306,
-0.032781846821308136,
0.006612536497414112,
0.019929319620132446,
-0.04632425308227539,
0.005886361468583345,
-0.01586288772523403,
0.025679439306259155,
0.0222927276045084,
-0.035768523812294006,
-0.03990961238741875,
-0.0021250806748867035,
0.024705510586500168,
-0.05612849444150925,
0.017547212541103363,
0.005106955301016569,
0.04532838985323906,
-0.04622729867696762,
-0.01426150556653738,
-0.04286104440689087,
-0.015575011260807514,
-0.025210192427039146,
0.0031587653793394566,
0.006870431825518608,
-0.10367265343666077,
0.02816006727516651,
-0.057319093495607376,
-0.03283889219164848,
-0.052957139909267426,
-0.029849670827388763,
0.04010093957185745,
0.00992575567215681,
-0.02159353904426098,
-0.011776800267398357,
-0.09133138507604599,
0.01193411834537983,
0.04870402440428734,
-0.008339676074683666,
0.021765029057860374,
-0.001610443228855729,
-0.051660142838954926,
0.008989800699055195,
0.047733161598443985,
0.014926547184586525,
0.0014946945011615753,
0.03184858709573746,
0.01954006962478161,
-0.023729931563138962,
-0.04567858949303627,
-0.02781510539352894,
-0.0035503318067640066,
-0.02931651659309864,
-0.011920217424631119,
-0.0609721913933754,
-0.008294803090393543,
0.03165201097726822,
-0.007644192315638065,
0.038503892719745636,
-0.02404746040701866,
0.03888264298439026,
0.02805400639772415,
0.035588301718235016,
0.04876228794455528,
0.05386928841471672,
-0.017331672832369804,
0.024520717561244965,
0.017355747520923615,
-0.0016679062973707914,
0.0161064974963665,
-0.026635896414518356,
-0.0022379395086318254,
-0.02433173730969429,
0.04483582824468613,
-0.016447408124804497,
-0.0003252743626944721,
0.05146703124046326,
0.030717743560671806,
-0.025854680687189102,
-0.009821038693189621,
0.01886807195842266,
-0.03314198553562164,
-0.00904911756515503,
0.0329047329723835,
0.024593358859419823,
0.02347850799560547,
-0.032715462148189545,
-0.01716812327504158,
-0.03156493604183197,
-0.06329342722892761,
0.017995521426200867,
-0.01395079679787159,
-0.005464341025799513,
-0.05767747759819031,
-0.0626109391450882,
-0.04569649696350098,
0.02079397439956665,
-0.006117298733443022,
-0.028320621699094772,
-0.006416359916329384,
-0.020960433408617973,
0.03404920920729637,
0.01372500415891409,
-0.0348215252161026,
-0.0014825958060100675,
-0.011054109781980515,
-0.001650710473768413,
-0.037331290543079376,
0.0184306763112545,
0.018066948279738426,
-0.005302099976688623,
-0.008619602769613266,
-0.014215156435966492,
0.006689072586596012,
0.033679209649562836,
-0.009141107089817524,
-0.04241267964243889,
0.0350898802280426,
-0.009165585041046143,
0.0397644005715847,
0.002135257702320814,
-0.024139240384101868,
0.022455623373389244,
0.006746824365109205,
0.02318890206515789,
-0.006676411721855402,
-0.04591679945588112,
-0.009067242965102196,
0.0221201591193676,
0.04842346906661987,
-0.0447019562125206,
-0.02948630042374134,
-0.028745941817760468,
-0.01143158134073019
] |
<p>As an assignment for uni I need to figure out an algorithm that explodes a particle of mass $m$, velocity $v$, into $n$ pieces.</p>
<p>For the first part of the assignment, the particle has mass $m$, velocity of $0$, the particle explodes into 6 equal pieces, and is not affected by gravity.</p>
<p>The problem I'm having is, how do I determine 6 equidistant unit vectors in three dimensions?</p>
<p>Assuming I need an initial vector, a unit vector in the direction of $v$ (the initial particle velocity) will do. In the initial case, where $v$ is $(+0, +0, +0)$, let the initial unit vector be in an arbitrary direction.</p>
<p>Also, how do I determine what speed each sub-particle will have? I know that the sum of sub-particle momentum will be equal to the momentum of the initial particle, and because each particle has the same mass they will each have the same speed... Do I need an explosion Force amount or something?</p> | g7852 | [
0.04858289286494255,
0.006000219378620386,
-0.004143248312175274,
0.028304804116487503,
0.029719410464167595,
-0.0021887337788939476,
0.035129934549331665,
0.035689827054739,
-0.0604742206633091,
0.02652481012046337,
-0.01568596623837948,
0.0026961821131408215,
0.010010387748479843,
0.009751410223543644,
-0.026352286338806152,
0.017106888815760612,
0.061014324426651,
-0.013421670533716679,
-0.010985423810780048,
0.07919541001319885,
0.049301911145448685,
0.03979409858584404,
-0.00791469868272543,
0.00621374137699604,
0.054241735488176346,
-0.06405048817396164,
0.001912332372739911,
-0.043231941759586334,
-0.047953732311725616,
0.038867827504873276,
0.018104612827301025,
0.015059382654726505,
0.02808515354990959,
-0.07345280796289444,
-0.0024351258762180805,
-0.0312250517308712,
0.015050617046654224,
-0.005932984873652458,
0.00502769835293293,
-0.011280912905931473,
-0.0016388286603614688,
-0.06301440298557281,
-0.006909993477165699,
0.008377235382795334,
0.030468648299574852,
0.051256462931632996,
0.006215430796146393,
0.002740320051088929,
-0.02734094113111496,
-0.006844950839877129,
-0.053799279034137726,
0.03171851113438606,
-0.004578091204166412,
-0.03904733806848526,
-0.06742528080940247,
0.0658627599477768,
-0.028350871056318283,
-0.014813515357673168,
0.040078870952129364,
0.03784659877419472,
-0.00935664027929306,
-0.00922451727092266,
-0.012427732348442078,
-0.09048540890216827,
0.0008613974787294865,
0.032879702746868134,
-0.023373853415250778,
0.009259170852601528,
-0.017934182658791542,
-0.017099104821681976,
-0.014827616512775421,
-0.023264547809958458,
0.046971216797828674,
-0.027182230725884438,
-0.027191277593374252,
-0.053619954735040665,
-0.013371074572205544,
-0.02778751030564308,
-0.034017413854599,
0.009568698704242706,
-0.0019289265619590878,
0.0317605584859848,
0.06974628567695618,
-0.05085895583033562,
0.027361642569303513,
-0.027403363958001137,
0.00017387239495292306,
0.04625114053487778,
-0.04563203081488609,
-0.04023483768105507,
-0.007820378057658672,
0.036263853311538696,
0.03750324621796608,
0.023250898346304893,
-0.011959230527281761,
-0.05877380073070526,
-0.08320236951112747,
0.05982556566596031,
-0.013927429914474487,
-0.025400545448064804,
0.03217264264822006,
0.041145555675029755,
0.015550949610769749,
-0.08736046403646469,
-0.03335324302315712,
-0.005319131538271904,
0.050562161952257156,
0.024987291544675827,
0.016772879287600517,
-0.04693065211176872,
-0.026915377005934715,
-0.01234755665063858,
-0.03901117667555809,
-0.02842237986624241,
-0.018994998186826706,
0.01592312566936016,
0.07295407354831696,
-0.03120761178433895,
-0.011657817289233208,
0.05954040586948395,
-0.003756972262635827,
-0.008805285207927227,
-0.05765841528773308,
0.036475762724876404,
-0.020234182476997375,
-0.016228828579187393,
-0.04243036359548569,
0.06056226044893265,
0.01691124215722084,
0.03856329992413521,
-0.025181777775287628,
-0.02345815859735012,
0.039221081882715225,
0.022561799734830856,
-0.00569514837116003,
0.035592179745435715,
-0.02077348902821541,
0.04724466800689697,
-0.01477775163948536,
0.06973672658205032,
-0.04063655436038971,
0.053150344640016556,
0.005811299663037062,
0.02626379206776619,
-0.060716137290000916,
-0.004034420475363731,
-0.012472301721572876,
-0.06254471838474274,
-0.030616983771324158,
0.01949414238333702,
-0.012814488261938095,
0.08511518687009811,
0.005547536537051201,
-0.038299672305583954,
0.03420467674732208,
0.011488850228488445,
0.04373481497168541,
-0.010014042258262634,
0.015776919201016426,
-0.04393775016069412,
0.0038886661641299725,
-0.019532721489667892,
-0.020922070369124413,
0.065593421459198,
-0.03897108882665634,
0.002494343789294362,
0.03708559647202492,
-0.05107474699616432,
0.052798233926296234,
-0.02924455516040325,
-0.06332176923751831,
-0.05788290500640869,
0.012302531860768795,
0.03880166634917259,
-0.03699715435504913,
0.004326947499066591,
0.004401038866490126,
-0.03661959618330002,
0.024495545774698257,
0.03557169437408447,
0.0322440080344677,
-0.016897117719054222,
0.04275323078036308,
0.061385150998830795,
-0.021331537514925003,
0.004350331611931324,
0.011075098998844624,
0.08305185288190842,
-0.0017363183433189988,
0.04934261366724968,
0.0019004472997039557,
0.031856436282396317,
-0.02880587801337242,
-0.009595914743840694,
0.00768691673874855,
-0.028927387669682503,
0.0549749881029129,
-0.03963284194469452,
-0.07268114387989044,
0.023623038083314896,
0.023561695590615273,
0.07360513508319855,
0.0024029877968132496,
0.04279907047748566,
0.044292841106653214,
-0.013298471458256245,
-0.0032495190389454365,
0.03104531392455101,
0.0018153685377910733,
0.05696352198719978,
-0.0008908915333449841,
0.0066596996039152145,
0.01393934991210699,
0.035565316677093506,
0.010646558366715908,
0.022681990638375282,
0.04629148915410042,
0.04458020627498627,
0.05200057476758957,
-0.02637951634824276,
-0.017000161111354828,
-0.03827005997300148,
-0.053366728127002716,
-0.0578409768640995,
-0.009915069676935673,
-0.01575346104800701,
-0.029979294165968895,
0.04073106870055199,
-0.008023128844797611,
-0.03467027097940445,
-0.020022274926304817,
0.05593735724687576,
0.06740248203277588,
-0.051861874759197235,
0.05018480122089386,
0.012707509100437164,
0.019669270142912865,
-0.0018514832481741905,
0.026466326788067818,
0.010160772129893303,
0.03392687439918518,
-0.020870335400104523,
-0.016556210815906525,
-0.04811049625277519,
0.036835309118032455,
-0.04908537119626999,
0.057551342993974686,
-0.038548924028873444,
-0.05398780107498169,
0.01644742675125599,
-0.07875370979309082,
0.020240256562829018,
-0.03620496392250061,
0.0020211501978337765,
-0.005850142799317837,
-0.013352316804230213,
-0.03263011947274208,
0.0061114816926419735,
-0.0753403902053833,
-0.03439698368310928,
-0.02794407308101654,
-0.02018563076853752,
0.04420099034905434,
0.043637439608573914,
-0.013785243965685368,
0.002948114648461342,
0.00547725148499012,
-0.0054933540523052216,
-0.039750054478645325,
0.012892886996269226,
-0.0692286267876625,
-0.028298763558268547,
0.021962374448776245,
0.026881124824285507,
-0.04792552441358566,
0.02878713794052601,
0.0390436127781868,
-0.023006729781627655,
-0.025282487273216248,
0.06808602064847946,
-0.04324915632605553,
0.0849711075425148,
-0.07514157891273499,
0.04517757520079613,
0.06481114029884338,
-0.021089253947138786,
0.025618838146328926,
0.06138664484024048,
-0.013949815183877945,
-0.032732125371694565,
0.005380894057452679,
-0.015474662184715271,
0.024327967315912247,
0.01424386166036129,
0.06227843463420868,
0.04529688507318497,
0.025107670575380325,
-0.012636195868253708,
-0.003925742115825415,
-0.043203044682741165,
-0.03091929852962494,
-0.010438147932291031,
0.043880995362997055,
-0.03800470754504204,
0.013331119902431965,
0.006731151137501001,
-0.036925654858350754,
-0.0038336063735187054,
0.040799591690301895,
-0.05834968388080597,
-0.0017648969078436494,
0.07309595495462418,
-0.008288385346531868,
-0.018440833315253258,
-0.025429340079426765,
-0.03155454993247986,
0.028174476698040962,
0.03762471303343773,
-0.05860983207821846,
0.005820750258862972,
-0.0391850620508194,
-0.006045444868505001,
0.10158532112836838,
-0.012755156494677067,
-0.04358420893549919,
0.03665460646152496,
-0.03177401423454285,
-0.005369692109525204,
-0.03209898993372917,
-0.0038007188122719526,
0.017151661217212677,
0.02938724309206009,
0.053696148097515106,
0.042953867465257645,
-0.020818686112761497,
-0.03134895861148834,
0.012808107770979404,
-0.009140717796981335,
0.0335586741566658,
0.02014140784740448,
0.023169882595539093,
-0.02798326313495636,
-0.007336211856454611,
-0.04170245677232742,
-0.03812205418944359,
0.006247296463698149,
0.05999712273478508,
0.015219188295304775,
-0.004312955308705568,
-0.019256606698036194,
0.043082743883132935,
0.010146453976631165,
0.041234008967876434,
-0.006523234769701958,
0.05245838314294815,
0.03316466137766838,
0.037012726068496704,
0.03662719205021858,
-0.005269354674965143,
0.009031758643686771,
-0.019131259992718697,
-0.033111412078142166,
-0.05188623443245888,
0.030683433637022972,
0.03451290354132652,
-0.0042922617867589,
0.0167466439306736,
0.007556637283414602,
-0.0056364391930401325,
0.010651600547134876,
-0.0083143450319767,
-0.059282124042510986,
-0.041296523064374924,
-0.014769758097827435,
-0.053095195442438126,
-0.011041082441806793,
0.024381117895245552,
-0.056525710970163345,
0.006566979922354221,
-0.022069508209824562,
0.028750954195857048,
0.005941865965723991,
0.005971238017082214,
-0.028255274519324303,
-0.000519763445481658,
0.08139011263847351,
-0.016408931463956833,
-0.02148129791021347,
0.014532885514199734,
0.031359393149614334,
0.04206150025129318,
-0.1071891114115715,
-0.07154069095849991,
-0.019334567710757256,
0.0046344720758497715,
-0.008267216384410858,
-0.017448080703616142,
-0.0037700803950428963,
-0.0692567229270935,
0.011659805662930012,
-0.03323524072766304,
-0.02085810899734497,
0.011021708138287067,
-0.024578794836997986,
-0.013364190235733986,
0.011487184092402458,
-0.025254692882299423,
-0.015633048489689827,
0.048283644020557404,
0.06661856919527054,
0.024344302713871002,
-0.005113475024700165,
0.00941791944205761,
-0.018835611641407013,
-0.0034451240207999945,
-0.004609206225723028,
0.004861746449023485,
0.04954393953084946,
0.012992155738174915,
-0.007828589528799057,
0.0745493546128273,
0.022502006962895393,
0.030035922303795815,
-0.06134646758437157,
-0.05730367824435234,
0.006118000950664282,
0.07061976194381714,
0.007448429241776466,
0.03134951740503311,
0.07191353291273117,
-0.023752253502607346,
0.04400872811675072,
-0.02056048810482025,
-0.002176867797970772,
-0.03444140776991844,
-0.010573577135801315,
-0.009730893187224865,
0.027709368616342545,
0.05152962729334831,
0.0445333831012249,
0.050835080444812775,
0.03182269260287285,
-0.048410676419734955,
-0.028281167149543762,
0.06222503259778023,
0.045557957142591476,
-0.028507791459560394,
-0.03204726427793503,
-0.041803453117609024,
-0.012099562212824821,
0.05978482589125633,
0.027220865711569786,
-0.050604309886693954,
-0.05443093553185463,
-0.04091424122452736,
0.022606898099184036,
-0.026490390300750732,
-0.005294135306030512,
0.04744637385010719,
0.042298369109630585,
-0.009184598922729492,
0.004572696052491665,
-0.05094142258167267,
0.02954423800110817,
-0.03621220961213112,
-0.006198110058903694,
-0.04766441136598587,
0.015616063959896564,
-0.01212301291525364,
0.025751451030373573,
0.05912400037050247,
0.007894592359662056,
0.01922237128019333,
0.028694432228803635,
-0.030485522001981735,
0.018529437482357025,
-0.02420373633503914,
0.014593818224966526,
0.02473846822977066,
-0.017770791426301003,
-0.02457852102816105,
-0.05511247366666794,
-0.03048803098499775,
0.02850109525024891,
0.016057277098298073,
0.040408939123153687,
-0.031691692769527435,
0.0017421237425878644,
0.043365076184272766,
-0.032458242028951645,
-0.007076892536133528,
-0.00603068433701992,
-0.04647050052881241,
-0.021653922274708748,
0.012384137138724327,
-0.03311500325798988,
0.03245723992586136,
-0.03874363377690315,
0.010224997997283936,
0.02303897775709629,
-0.035405296832323074,
0.0012251726584509015,
-0.011327022686600685,
0.003959112334996462,
0.023416433483362198,
0.006032254546880722,
0.08578819781541824,
0.051575906574726105,
-0.04201888293027878,
0.022549763321876526,
0.06337950378656387,
0.03470031917095184,
0.057655978947877884,
-0.019956566393375397,
-0.07743660360574722,
-0.013297746889293194,
0.0355294793844223,
0.05629972368478775,
-0.005316528957337141,
-0.021490532904863358,
0.016789132729172707,
0.011127913370728493,
-0.010416148230433464,
-0.037263356149196625,
-0.005594593472778797,
-0.03101484104990959,
-0.06603763997554779,
-0.00713348388671875,
-0.028994157910346985,
0.0489659309387207,
0.03511703386902809,
-0.031241925433278084,
-0.03480018302798271,
-0.03201376646757126,
-0.05635816976428032,
-0.01021946594119072,
0.0040215360932052135,
-0.017368799075484276,
0.01949700154364109,
-0.05724426358938217,
-0.03611721098423004,
-0.06009494513273239,
-0.010500098578631878,
0.054297398775815964,
-0.05187063291668892,
0.016704311594367027,
-0.04515355825424194,
-0.03717289865016937,
-0.015525812283158302,
-0.030751410871744156,
-0.03622943162918091,
0.026711592450737953,
0.04707604646682739,
-0.06238672882318497,
0.003701685229316354,
0.02058466710150242,
-0.04595770314335823,
0.004129411652684212,
-0.032514676451683044,
-0.023093674331903458,
0.032150834798812866,
-0.054848115891218185,
0.01759030483663082,
-0.021753668785095215,
-0.029359810054302216,
-0.059900496155023575,
-0.0023714699782431126,
-0.013693609274923801,
0.0016810301458463073,
0.015203346498310566,
-0.00013854107237420976,
-0.007166879251599312,
-0.0023152013309299946,
-0.01163141243159771,
0.019711535423994064,
0.013503565452992916,
0.033030733466148376,
-0.045771826058626175,
-0.053564611822366714,
0.05586710572242737,
0.06327616423368454,
0.03183106333017349,
0.0007543840329162776,
-0.016192467883229256,
-0.020489269867539406,
0.035273946821689606,
0.01847257651388645,
0.051697988063097,
-0.022799672558903694,
-0.022438254207372665,
0.0164494626224041,
-0.030340081080794334,
-0.06173975020647049,
-0.05516307055950165,
-0.046320706605911255,
0.02676103450357914,
0.005462791305035353,
0.004561938811093569,
-0.01439359039068222,
0.03088577464222908,
0.049038417637348175,
0.03772658482193947,
0.028730779886245728,
0.002727523446083069,
-0.047858886420726776,
0.07234656065702438,
-0.018427113071084023,
-0.018478307873010635,
-0.013466029427945614,
-0.0383407399058342,
0.01068603154271841,
0.011669915169477463,
-0.007469058036804199,
0.04815113916993141,
0.0506853386759758,
-0.0011024930281564593,
0.010659965686500072,
-0.03539922833442688,
0.07611485570669174,
-0.02925788052380085,
0.07338163256645203,
0.005527855828404427,
0.022536883130669594,
-0.06459677964448929,
0.06885647028684616,
0.011174087412655354,
-0.02128473110496998,
0.02012619562447071,
0.035557299852371216,
0.05619928240776062,
0.02352180890738964,
-0.05089998245239258,
-0.012142115272581577,
-0.0027111792005598545,
0.01852409355342388,
0.018142109736800194,
-0.0494404211640358,
0.07569865882396698,
0.016184434294700623,
0.07658545672893524,
0.031354356557130814,
0.001856608665548265,
-0.012971644289791584,
0.020286433398723602,
-0.08442362397909164,
-0.013894431293010712,
0.0814981609582901,
0.025512458756566048,
0.0038205240853130817,
-0.023099316284060478,
-0.024868980050086975,
0.013149190694093704,
-0.0005630151135846972,
0.011728815734386444,
-0.058679383248090744,
0.052091944962739944,
0.011171636171638966,
-0.03451740741729736,
0.054164908826351166,
0.008335812017321587,
-0.024744262918829918,
-0.018018487840890884,
0.01716407760977745,
-0.029770929366350174,
0.005944675765931606,
0.03383227065205574,
0.013271312229335308,
0.012889518402516842,
-0.017506858333945274,
-0.08039343357086182,
-0.011512151919305325,
-0.009720700792968273,
-0.09573353826999664,
0.01475515030324459,
0.005167270544916391,
0.04560612887144089,
-0.017587712034583092,
0.04884408414363861,
0.006836033891886473,
-0.022179340943694115,
0.024642419070005417,
0.06071629375219345,
-0.019487183541059494,
0.03545449301600456,
-0.04306814819574356,
0.042344830930233,
-0.0022973744198679924,
0.043993428349494934,
-0.02398594841361046,
-0.017972424626350403,
-0.031094208359718323,
0.0632111206650734,
0.05459709092974663,
-0.022487452253699303,
-0.011353492736816406,
-0.009982313960790634,
0.011473635211586952,
0.011554948054254055,
0.03871658816933632,
-0.012249546125531197,
-0.015053609386086464,
-0.014903283677995205,
0.05637199431657791,
-0.03706299513578415,
-0.04653496667742729,
-0.007640061434358358,
0.002720699878409505,
0.022577926516532898,
-0.0014712422853335738,
-0.022655479609966278,
-0.0163994412869215,
0.005936049856245518,
-0.02580091543495655,
-0.024418098852038383,
-0.03679436445236206,
-0.01196726318448782,
-0.07639434188604355,
0.013301876373589039,
-0.006520039867609739,
0.016170935705304146,
-0.013910901732742786,
0.012531964108347893,
-0.0429755263030529,
-0.05256112292408943,
-0.023440195247530937,
-0.07460756599903107,
-0.02202959544956684,
0.0780603438615799,
0.025977008044719696,
-0.012889521196484566,
0.006796764209866524,
-0.00436036940664053,
-0.02854698710143566,
0.0745982676744461,
-0.005064467899501324,
-0.0067405011504888535,
0.0201937984675169,
-0.022076213732361794,
-0.01441959198564291,
0.01640784554183483,
-0.044102925807237625,
-0.05214439705014229,
0.015571162104606628,
-0.02778838388621807,
0.0030788173899054527,
-0.05475688353180885,
-0.025692589581012726,
0.030031520873308182,
0.03516337275505066,
-0.035765115171670914,
0.005050482228398323,
-0.03024076111614704,
-0.01683487743139267,
0.041148003190755844,
-0.012099512852728367,
-0.03159189224243164,
0.036450158804655075,
-0.010389876551926136,
-0.03332557529211044,
-0.081577830016613,
-0.010677956975996494,
-0.02566102333366871,
0.014608786441385746,
-0.004601686727255583,
0.04027627035975456,
0.000806299620307982,
-0.025859177112579346,
-0.02956126630306244
] |
<p>I need to calculate the initial velocity required to launch a projectile at a given angle from point A to point B. The only force acting on the projectile after launch will be gravity – zero air resistance. The projectile is launched within a simulated, virtual environment; however, I am asking for help with the physics rather than the simulation itself.</p>
<p>I have had success (with a different equation) when point A and point B are at the same height; however, <strong>once point B is at a different height</strong>, my calculations become less precise – well, wrong in fact.</p>
<p>I researched the following formula for finding the range of a projectile on uneven ground. The parameters are all available to me, except the initial velocity that I need to solve for.</p>
<blockquote>
<p>$d$ : range or distance<br />
$v_i$ : initial velocity<br />
$g$ : gravity<br />
$\theta$ : launch angle<br />
$y_0$ : launch height<br /></p>
</blockquote>
<p>$$d = \frac{v_i \cos\theta}{g}(v{_i} \sin \theta + \sqrt{(v_i \sin\theta)^2 + 2gy_0})$$</p>
<p>I attempted to solve for initial velocity (eq: <strong>A</strong>):</p>
<p>$$v_i = \sqrt{\frac{d^2g}{2\cos\theta^2(y_0+d \tan\theta)}}$$ </p>
<p>Using this equation in my simulation I apply the velocity to a normalised displacement vector and launch the projectile. It gets close to its target but:</p>
<ul>
<li>$x_{final}$ is always correct</li>
<li>$z_{final}$ is always incorrect - it is close to the desired $z$ but always offset by a seemingly proportional amount. </li>
</ul>
<p>I have spent many hours trying to review the equation but I have been unsuccessful. Any advice would be most appreciated:</p>
<ul>
<li>is this the correct equation?</li>
<li>have I solved for $v_i$ correctly? I have looked for an example equation online but I have not found one structured how I need it, i.e. solving for $v_i$</li>
<li>I have spent hours researching online - perhaps I have missed some good (but entry-level) resources. Do you know of any reference material that may help me?</li>
</ul>
<p><strong>Update - I have now named the equation above for referencing below</strong></p>
<p>Following on from the answer by @Pygmalion, which I am still gratefully working to understand:</p>
<p>I agree that your derived equation is equivalent to mine (A). Using yours (@Pygmalion's) in my simulation, I therefore observe the same failures: the projectile always lands short of the target.</p>
<p>I have simplified the simulation keeping the <strong>launch height and target height the same</strong>. I still encounter the same problem with equation A; however, when passing the same parameters to the following equation the projectile always hits the target precisely (eq: <strong>B</strong>):</p>
<p>$$v_i = \sqrt{\frac{dg}{\sin2\theta}}$$</p>
<p>Given the success of equation B when the launch and target heights are the same and the failure of equation A given the same conditions, I question whether equation A is the correct one to solve the problem since I would expect it to work for any combination of launch|target height.</p>
<p>I think the help I need is around why equation B works. Does it cater for conditions that equation A overlooks? If equation A is unsuitable, are you able to recommend an alternative?</p>
<p>In short, the $v_i$ calculated by equation A (in my simulations) is always less than $v_i$ from equation B given the same inputs - the projectile therefore always falls short of its target.</p> | g7853 | [
0.029844943434000015,
0.006142019294202328,
-0.014436617493629456,
0.023558707907795906,
0.024018654599785805,
0.08817394077777863,
0.0320025272667408,
-0.009013631381094456,
-0.06506603211164474,
0.026495859026908875,
-0.03215448185801506,
0.07223360985517502,
0.010314184240996838,
-0.017200959846377373,
0.012231368571519852,
0.010414570569992065,
0.08958648145198822,
-0.03960596024990082,
0.02610819973051548,
0.010177990421652794,
-0.005985481198877096,
-0.022185374051332474,
-0.01079663634300232,
-0.02439071424305439,
-0.049909137189388275,
-0.057997170835733414,
-0.010193192400038242,
-0.013337196782231331,
-0.08972486108541489,
0.028391461819410324,
-0.05292164161801338,
0.015827743336558342,
0.036546267569065094,
-0.04892801493406296,
-0.032148391008377075,
0.013746656477451324,
-0.025157488882541656,
0.018457552418112755,
-0.04785223677754402,
-0.0496649369597435,
0.007855263538658619,
-0.027478305622935295,
0.007586579769849777,
0.015336267650127411,
0.02748611569404602,
-0.004280576948076487,
-0.027718909084796906,
-0.005902858916670084,
-0.021568885073065758,
0.0025659187231212854,
-0.0552089586853981,
0.04874666407704353,
-0.016414668411016464,
-0.1013522744178772,
-0.0514821894466877,
0.05820845067501068,
0.003950407728552818,
0.00828221533447504,
0.010707956738770008,
0.003600423689931631,
0.04009704664349556,
-0.0024146593641489744,
-0.025940753519535065,
-0.03371826559305191,
0.016263114288449287,
-0.028758278116583824,
-0.020795125514268875,
-0.023842543363571167,
-0.06337165087461472,
-0.009143459610641003,
-0.016740145161747932,
-0.04596426337957382,
-0.03835110366344452,
-0.0458831824362278,
-0.029373954981565475,
-0.01098053902387619,
0.025926223024725914,
-0.042375754565000534,
-0.007118996698409319,
0.004788792692124844,
-0.031279563903808594,
0.042267218232154846,
0.03169897571206093,
-0.026428624987602234,
-0.007112559862434864,
-0.04343489930033684,
0.0036933368537575006,
0.057251591235399246,
-0.020245324820280075,
-0.00546862231567502,
0.03571736440062523,
0.050791945308446884,
-0.02617993950843811,
0.018868008628487587,
-0.06584284454584122,
-0.029538191854953766,
-0.08917748928070068,
0.07747109234333038,
0.05704905465245247,
0.021404752507805824,
0.01960299164056778,
0.0027565844357013702,
0.04490090161561966,
-0.022495843470096588,
-0.0013485447270795703,
-0.006242229137569666,
0.09854580461978912,
0.028462378308176994,
0.011709827929735184,
-0.030355297029018402,
-0.036124855279922485,
-0.06864967197179794,
-0.043276187032461166,
-0.08187144249677658,
-0.027725815773010254,
-0.028070013970136642,
0.047515954822301865,
0.02180797979235649,
0.007368452847003937,
0.05041434243321419,
-0.019589750096201897,
0.012736981734633446,
0.011653576977550983,
0.05645681545138359,
-0.0591280572116375,
-0.0945725068449974,
-0.03762151300907135,
-0.05153442546725273,
-0.0033388719893991947,
0.021938111633062363,
-0.006757355760782957,
-0.04876188933849335,
-0.016379965469241142,
0.012752832844853401,
-0.009445954114198685,
-0.023246731609106064,
0.057707853615283966,
-0.010069615207612514,
0.014473114162683487,
0.024668386206030846,
-0.033699266612529755,
0.02273663505911827,
0.008084254339337349,
-0.036653392016887665,
-0.0591936893761158,
0.022649627178907394,
0.022503720596432686,
-0.008081424981355667,
-0.022497979924082756,
-0.004821403417736292,
-0.011857366189360619,
0.09446575492620468,
0.009230438619852066,
0.023490501567721367,
-0.013996245339512825,
-0.0478186160326004,
0.0684875100851059,
0.017571138218045235,
0.02412288822233677,
-0.024888623505830765,
0.06622016429901123,
-0.025524955242872238,
0.011779366992413998,
-0.001118615735322237,
-0.04688248783349991,
0.04212125390768051,
-0.009141719900071621,
-0.050753042101860046,
-0.0035971757024526596,
-0.04778663441538811,
-0.04976474493741989,
-0.03123907744884491,
0.0340755358338356,
0.017300548031926155,
-0.03921622410416603,
-0.0007182331755757332,
0.06744328886270523,
-0.016630403697490692,
-0.03708091750741005,
-0.02092924900352955,
0.044075120240449905,
-0.04171380773186684,
0.0157889686524868,
-0.029323475435376167,
-0.02340664528310299,
-0.013733931817114353,
0.0576465018093586,
0.03255424648523331,
0.04000062867999077,
-0.05229586362838745,
-0.03631104901432991,
0.03868670389056206,
-0.024587219581007957,
-0.036247655749320984,
-0.047606438398361206,
0.014642222784459591,
0.08323493599891663,
-0.018266359344124794,
-0.03506040945649147,
0.05404643714427948,
-0.028270093724131584,
0.051798321306705475,
0.05910542607307434,
0.02222348377108574,
-0.015615884214639664,
-0.016453716903924942,
0.03264162316918373,
-0.020815366879105568,
-0.006430370733141899,
0.05976327136158943,
0.004484329838305712,
0.017473924905061722,
0.017778972163796425,
0.06658242642879486,
0.02854573167860508,
-0.016022946685552597,
-0.004781351424753666,
0.016797779127955437,
-0.040274929255247116,
0.041478775441646576,
-0.00042845873394981027,
0.004981469828635454,
0.0067158043384552,
-0.04190216585993767,
-0.015349110588431358,
-0.006517699453979731,
0.013570229522883892,
-0.011452565900981426,
0.013968468643724918,
-0.04687587171792984,
0.06957926601171494,
0.04089242219924927,
0.020520148798823357,
-0.0678892508149147,
0.0723290741443634,
0.01814194954931736,
-0.008399609476327896,
-0.03346448764204979,
0.0470045730471611,
-0.009801775217056274,
-0.0029803805518895388,
-0.05798906087875366,
-0.012138450518250465,
0.02175304852426052,
0.02884092554450035,
-0.04743911325931549,
0.036089811474084854,
-0.009679134003818035,
-0.004190397914499044,
-0.02296363189816475,
-0.04869476705789566,
0.021436717361211777,
-0.03968844190239906,
-0.011038949713110924,
-0.0405893437564373,
-0.020122507587075233,
0.02351611852645874,
-0.018295565620064735,
-0.022089801728725433,
-0.053372595459222794,
-0.06406079977750778,
-0.03673935309052467,
-0.00963263213634491,
0.03294496238231659,
-0.05328362062573433,
0.08393783122301102,
-0.05549708008766174,
0.021866586059331894,
0.007607315666973591,
-0.004942001774907112,
-0.05707191675901413,
0.027987755835056305,
0.02591402642428875,
0.042961589992046356,
0.0003664267424028367,
0.01579943671822548,
-0.025897962972521782,
-0.00947477575391531,
0.043223462998867035,
0.09206003695726395,
-0.011002381332218647,
-0.0014878035290166736,
-0.015955915674567223,
-0.003130561439320445,
0.07179732620716095,
-0.04076552763581276,
0.04010504111647606,
0.04540054127573967,
0.011553417891263962,
-0.04597482085227966,
0.023176059126853943,
0.003246319480240345,
0.0054411506280303,
0.00545272184535861,
-0.024051111191511154,
0.0718085765838623,
-0.020354896783828735,
-0.013753465376794338,
0.0548386387526989,
-0.02024349384009838,
-0.0014521905686706305,
0.021681111305952072,
-0.006138619501143694,
0.013186710886657238,
-0.03544004634022713,
0.013326043263077736,
0.01941179856657982,
-0.03585831820964813,
-0.028456270694732666,
0.02162512205541134,
-0.00019514728046488017,
0.014242610894143581,
-0.018120748922228813,
-0.025781478732824326,
-0.03954844921827316,
-0.04462619870901108,
0.018410274758934975,
-0.005373782012611628,
-0.06542002409696579,
0.048934612423181534,
-0.021163031458854675,
-0.03979038447141647,
0.0020541909616440535,
0.04543648287653923,
-0.021843165159225464,
0.058759063482284546,
0.003036088775843382,
0.07005610316991806,
-0.037135541439056396,
0.020161084830760956,
0.03870350494980812,
0.0798138678073883,
0.009278655983507633,
-0.008704477921128273,
-0.01217664498835802,
-0.03662031143903732,
0.012367007322609425,
0.03669733926653862,
0.06925952434539795,
0.02316446602344513,
-0.00022813644318375736,
0.0018314460758119822,
-0.05223200097680092,
-0.02635771967470646,
0.01350757572799921,
-0.015627065673470497,
0.025680921971797943,
0.05037221312522888,
-0.0317993201315403,
-0.03372367471456528,
0.06359799951314926,
-0.005749173928052187,
-0.01610276661813259,
-0.01881917007267475,
0.020838556811213493,
0.07787921279668808,
0.07181081920862198,
-0.01648086868226528,
-0.010018670931458473,
0.03847547620534897,
0.0012664241949096322,
-0.012103819288313389,
0.0036961191799491644,
0.07554306834936142,
-0.004389062058180571,
-0.037693995982408524,
-0.04672820493578911,
-0.008145710453391075,
-0.010065264068543911,
0.01838005520403385,
0.03955484554171562,
-0.05182567238807678,
0.0030158571898937225,
-0.04588936269283295,
-0.0011442776303738356,
-0.01801389828324318,
0.015429596416652203,
-0.013289500027894974,
-0.04211962968111038,
0.022398777306079865,
0.05611760541796684,
-0.004821829032152891,
-0.01793791726231575,
0.03594497591257095,
0.01357909757643938,
0.05117715522646904,
-0.014834540896117687,
-0.005377694498747587,
0.08306729793548584,
-0.015276770107448101,
-0.001296649337746203,
-0.018812736496329308,
-0.009918468073010445,
0.06969542801380157,
0.05221139267086983,
0.06127091124653816,
-0.01899162121117115,
-0.003048158250749111,
-0.05200447887182236,
0.03452952206134796,
0.0005985440220683813,
-0.01616663485765457,
0.012994974851608276,
0.03347032889723778,
-0.059591151773929596,
-0.03569949045777321,
0.009618139825761318,
0.0019196332432329655,
-0.059926535934209824,
0.01996258646249771,
0.00780412508174777,
-0.011371452361345291,
-0.020818687975406647,
-0.05297889932990074,
-0.006563359871506691,
-0.04818292334675789,
-0.023327304050326347,
0.009601140394806862,
-0.0187048502266407,
-0.025719448924064636,
0.04945722594857216,
0.07061927020549774,
0.04480506479740143,
-0.07224728912115097,
0.10123427212238312,
-0.016271183267235756,
0.009093351662158966,
0.03516111895442009,
0.06609268486499786,
0.013693124987185001,
0.001969503704458475,
0.022191520780324936,
0.008707191795110703,
0.008557797409594059,
-0.015379267744719982,
0.04869740456342697,
0.02936885505914688,
-0.016108551993966103,
0.04875567555427551,
0.0538860484957695,
0.014348104596138,
0.022514821961522102,
0.006552769336849451,
-0.028792111203074455,
0.019082533195614815,
0.03874636068940163,
-0.035932108759880066,
0.005068034864962101,
0.0019740990828722715,
-0.002709167543798685,
0.03738715872168541,
-0.013706404715776443,
0.0367702841758728,
-0.023877441883087158,
-0.09066207706928253,
0.010464844293892384,
-0.008912789635360241,
0.03087732568383217,
-0.012415705248713493,
-0.01669185794889927,
0.021604016423225403,
0.0117558054625988,
0.0013314597308635712,
-0.01674632355570793,
-0.026056798174977303,
-0.03887751325964928,
0.00846794806420803,
0.01373337022960186,
-0.02973020076751709,
-0.04944325238466263,
0.00961028691381216,
-0.006442933343350887,
0.04030609503388405,
0.020536772906780243,
-0.054741859436035156,
0.031359802931547165,
0.0005981905851513147,
0.02373575232923031,
0.056362003087997437,
-0.0668979287147522,
-0.04409310221672058,
-0.003025616751983762,
-0.0214073583483696,
0.045256804674863815,
-0.026652783155441284,
-0.0065489960834383965,
0.0057461760006845,
-0.04058435931801796,
0.049379706382751465,
0.005611112806946039,
0.035294558852910995,
-0.019501909613609314,
-0.05437561497092247,
-0.04168861731886864,
0.021380022168159485,
0.02339828759431839,
0.019530290737748146,
0.05414634197950363,
0.0001921195798786357,
0.025156697258353233,
-0.018680976703763008,
-0.029695527628064156,
-0.006624660920351744,
0.009017753414809704,
-0.022505538538098335,
0.02029416151344776,
0.04959484189748764,
0.009150163270533085,
-0.06429072469472885,
0.03343462944030762,
0.025617696344852448,
0.014956632629036903,
0.07705627381801605,
0.004082426894456148,
-0.005813585128635168,
-0.014764739200472832,
0.048330068588256836,
0.012164323590695858,
-0.032109662890434265,
-0.07514750957489014,
0.08610840141773224,
-0.054977916181087494,
0.01806764490902424,
-0.010539723560214043,
0.046757496893405914,
0.020017363131046295,
-0.02215644344687462,
-0.021626541391015053,
-0.05426808074116707,
0.05906674265861511,
-0.02244223654270172,
0.004099695011973381,
-0.10193433612585068,
-0.012013271450996399,
-0.06758173555135727,
-0.022034641355276108,
-0.043149080127477646,
-0.0375211127102375,
0.00883439276367426,
-0.09890798479318619,
-0.07654370367527008,
-0.00959254615008831,
0.006563405506312847,
0.05342666432261467,
-0.047912243753671646,
0.020794564858078957,
-0.047791171818971634,
-0.028825758025050163,
0.0560283325612545,
-0.052903253585100174,
-0.05358258634805679,
-0.0023171950597316027,
-0.001151354401372373,
0.006821330636739731,
-0.02265673689544201,
0.028944961726665497,
-0.038188386708498,
0.0261717289686203,
-0.040271904319524765,
-0.03286690264940262,
0.045991890132427216,
-0.00764604564756155,
-0.0029583307914435863,
0.031189190223813057,
-0.01261222455650568,
-0.014041057787835598,
0.016627727076411247,
-0.002771194325760007,
0.03343359753489494,
-0.03709457069635391,
-0.02061568945646286,
0.0021821914706379175,
-0.03225856274366379,
-0.04298356920480728,
0.04560929536819458,
0.054853711277246475,
-0.02725164033472538,
-0.04861368611454964,
-0.0180892962962389,
0.03643203154206276,
-0.0335894450545311,
0.03026445582509041,
0.031110486015677452,
-0.010347780771553516,
-0.06572680920362473,
0.018521808087825775,
-0.056216608732938766,
-0.041891880333423615,
-0.008727257139980793,
-0.06675460934638977,
0.009520748630166054,
-0.00690982211381197,
-0.024797365069389343,
-0.04367785528302193,
-0.06854173541069031,
-0.05406143143773079,
0.06066279113292694,
0.0007207366870716214,
-0.05603083223104477,
0.03602798283100128,
0.049245256930589676,
0.00849630031734705,
0.01516572292894125,
-0.014396453276276588,
0.013443933799862862,
0.014271032996475697,
-0.0064198910258710384,
0.0066271573305130005,
0.05192883685231209,
-0.01475377008318901,
-0.002346297027543187,
0.08143090456724167,
0.04250284284353256,
0.04967872053384781,
-0.03950553014874458,
-0.009928128682076931,
0.01166863925755024,
0.019335096701979637,
-0.015179512090981007,
-0.0008459914824925363,
0.02677379548549652,
0.019834207370877266,
0.009935460053384304,
-0.035049792379140854,
0.027764400467276573,
0.02117597870528698,
0.014926206320524216,
0.026923062279820442,
-0.01553532388061285,
0.006867654155939817,
0.02975483238697052,
-0.03120322898030281,
-0.014349602162837982,
0.02820855937898159,
0.020412227138876915,
0.06678121536970139,
0.02804417721927166,
0.06917976588010788,
-0.03258528560400009,
-0.00037462578620761633,
0.0018531676614657044,
0.0293883066624403,
0.000702624034602195,
0.03693947568535805,
-0.0463130883872509,
0.03283322975039482,
-0.01592116802930832,
-0.020903589203953743,
-0.0288985725492239,
0.029628096148371696,
0.02819989062845707,
-0.060798123478889465,
-0.036460183560848236,
0.021690310910344124,
-0.022056397050619125,
0.028855282813310623,
-0.02676081471145153,
-0.043465521186590195,
-0.005284854676574469,
-0.011508487164974213,
-0.050275176763534546,
-0.03463122248649597,
0.020503519102931023,
0.0007860652985982597,
-0.03382010757923126,
0.06490743160247803,
-0.00359172560274601,
0.028252167627215385,
0.016713734716176987,
-0.012722810730338097,
0.01075541041791439,
-0.009275844320654869,
-0.0355224646627903,
-0.006783324293792248,
-0.01936471275985241,
0.03486579284071922,
-0.0223690215498209,
0.037358175963163376,
-0.032919447869062424,
-0.01417494472116232,
0.0024002580903470516,
0.01727522909641266,
-0.023683670908212662,
0.011049189604818821,
0.022228572517633438,
0.0311298631131649,
0.01279852632433176,
0.03142819181084633,
0.003450807649642229,
-0.003318236907944083,
-0.029696758836507797,
-0.014943367801606655,
0.026530586183071136,
0.0006628874689340591,
0.031919240951538086,
-0.026726195588707924,
0.023984553292393684,
0.05412368103861809,
0.03626476600766182,
0.010984688997268677,
0.0590502955019474,
0.004359331447631121,
0.003670506179332733,
0.019050346687436104,
0.006804050877690315,
0.03110319748520851,
0.01534130610525608,
0.04958060011267662,
-0.023213138803839684,
-0.026004694402217865,
0.03544166311621666,
-0.003660992719233036,
0.04058251902461052,
0.018911464139819145,
0.0013233813224360347,
-0.000763093528803438,
-0.017416341230273247,
0.027823196724057198,
-0.005753591191023588,
-0.016910608857870102,
-0.028250455856323242,
0.006631562486290932,
0.050505463033914566,
-0.038331951946020126,
0.0508488230407238,
-0.03975814953446388,
-0.04189760237932205,
0.02468271180987358,
0.04777133837342262,
-0.026884840801358223,
-0.02374829724431038,
-0.07307465374469757,
0.012564939446747303,
0.061877354979515076,
-0.019694052636623383,
-0.018762659281492233,
0.017020558938384056,
-0.04150444641709328,
0.027305399999022484,
0.02813318371772766,
-0.019563036039471626,
0.0403253398835659,
-0.025298384949564934,
0.0031989479903131723,
-0.016377875581383705,
0.017478538677096367,
0.0486140102148056,
0.041810065507888794,
0.00910892616957426,
-0.05233136937022209,
0.07481247931718826,
0.031159652397036552,
-0.049317117780447006,
0.059123847633600235,
0.014580516144633293,
-0.09064650535583496,
-0.008412313647568226,
0.015271688811480999,
0.00823912862688303,
-0.044977784156799316,
-0.06278624385595322,
-0.024259598925709724,
0.0038806491065770388,
-0.008363327011466026,
0.008150234818458557,
0.007653637323528528,
-0.03577433526515961,
0.012156792916357517
] |
<p>I've been reading 'How the Hippies saved Physics', which describes a design for a superluminal communication device, of which the crucial part was a laser which duplicated an incoming photon many times. The reason this won't work is what is now known as the no-cloning theorem - a quantum state can't be duplicated in this way. It may appear that a laser can do this, but it can't.</p>
<p>The thing is that I have vague memories of reading that when the laser was first talked about, it was claimed that quantum theory forbade such a device. What I'd like to know is whether there were such claims, and if so were they based on the idea that a laser would duplicate a quantum state.</p> | g7854 | [
0.0007408406818285584,
0.029719535261392593,
0.0253484845161438,
-0.00663805054500699,
-0.02826491929590702,
0.012017871253192425,
0.009231006726622581,
0.003164992667734623,
-0.0016321911243721843,
-0.031983643770217896,
-0.036596912890672684,
0.005078983027487993,
-0.007632412947714329,
-0.010354675352573395,
-0.031060438603162766,
-0.014016928151249886,
0.07321898639202118,
-0.01091063767671585,
0.062388826161623,
0.0440557561814785,
-0.03812667354941368,
0.03642687574028969,
-0.009165738709270954,
-0.09793202579021454,
-0.05850638076663017,
-0.02964900992810726,
-0.0015689689898863435,
-0.05857318639755249,
-0.061272669583559036,
-0.06989505887031555,
0.06745791435241699,
-0.05593064799904823,
0.015158201567828655,
-0.04972976818680763,
0.03529568016529083,
-0.01990843005478382,
-0.013268515467643738,
-0.010759107768535614,
-0.027173615992069244,
0.05193169414997101,
-0.032343991100788116,
-0.008532577194273472,
0.001682663569226861,
-0.053712185472249985,
0.025221966207027435,
0.011747948825359344,
0.029877271503210068,
-0.007295351941138506,
0.05020998418331146,
-0.02693028934299946,
0.02229321002960205,
0.030104590579867363,
-0.009977586567401886,
-0.023028356954455376,
0.08008017390966415,
0.00627715652808547,
-0.042604781687259674,
0.03446287289261818,
0.047667838633060455,
0.0009044867474585772,
-0.022535109892487526,
-0.006342961918562651,
-0.013460507616400719,
0.019390998408198357,
0.06641270965337753,
-0.0036780203226953745,
-0.00047369670937769115,
0.006695289630442858,
-0.009355737827718258,
0.02366548404097557,
0.012125356122851372,
0.0031349598430097103,
-0.027044987305998802,
-0.04925516992807388,
0.0624920055270195,
0.033132366836071014,
-0.029319126158952713,
0.004691010806709528,
0.0283436868339777,
0.03985001891851425,
-0.047906242311000824,
-0.04706564173102379,
0.027678731828927994,
0.02207568660378456,
0.020338134840130806,
0.022326139733195305,
-0.038580864667892456,
0.018193643540143967,
-0.0005836209165863693,
0.0030996191781014204,
0.01928778365254402,
-0.01462238747626543,
0.06723103672266006,
0.0008022238034754992,
0.010869331657886505,
-0.03839026391506195,
0.02608390897512436,
-0.015250565484166145,
-0.03594567999243736,
-0.003791248658671975,
-0.010100167244672775,
-0.02339089661836624,
0.053896769881248474,
0.0023691251408308744,
-0.011271581053733826,
0.02857629954814911,
0.022038305178284645,
0.00454994710162282,
-0.017357636243104935,
0.005523717030882835,
-0.012833650223910809,
-0.0333188995718956,
-0.029263600707054138,
-0.02737262286245823,
-0.018743496388196945,
0.03172038495540619,
0.07174867391586304,
0.0009970151586458087,
0.0029928237199783325,
-0.020834362134337425,
0.032164666801691055,
0.009039141237735748,
-0.045914530754089355,
-0.008982166647911072,
-0.009113705717027187,
0.01289591658860445,
-0.0005302042700350285,
-0.003791250055655837,
-0.0083216093480587,
0.004363290499895811,
-0.0352383516728878,
-0.001281894277781248,
-0.016958223655819893,
0.055850058794021606,
-0.02734878472983837,
-0.005683829542249441,
0.05942423641681671,
-0.03876154497265816,
0.04520786181092262,
-0.034849561750888824,
0.01614292338490486,
-0.03443368896842003,
-0.0030173317063599825,
0.014108794741332531,
0.05074508488178253,
-0.0047360253520309925,
0.02447199448943138,
-0.004006591625511646,
-0.011976716108620167,
0.040906842797994614,
0.02667219005525112,
0.026602791622281075,
-0.005134132225066423,
-0.04358409717679024,
-0.015151801519095898,
0.026764556765556335,
0.04920518025755882,
-0.025574492290616035,
0.014970130287110806,
-0.0018643962685018778,
0.01376430131494999,
0.007144503761082888,
0.02926257811486721,
-0.021107830107212067,
-0.03868740051984787,
0.006177506409585476,
0.03454429656267166,
-0.0497206449508667,
-0.029161108657717705,
0.050703030079603195,
-0.02325388416647911,
0.048707012087106705,
-0.0025121551007032394,
0.026457328349351883,
0.019071588292717934,
0.03608473017811775,
-0.011106559075415134,
-0.06126962974667549,
-0.02781227044761181,
-0.04154573380947113,
-0.0887322649359703,
-0.0009904990438371897,
-0.04315220192074776,
-0.005837992765009403,
-0.008503924123942852,
0.04493596404790878,
-0.035610735416412354,
-0.013478138484060764,
-0.002620099810883403,
-0.00855272263288498,
-0.06215091794729233,
0.012914290651679039,
0.0024051577784121037,
-0.053755052387714386,
0.005972723476588726,
-0.04186811298131943,
0.01958387903869152,
-0.01842299848794937,
0.009078387171030045,
0.02772308699786663,
-0.019891897216439247,
0.05829807370901108,
-0.02178528532385826,
-0.03850017860531807,
-0.02668645791709423,
-0.038026243448257446,
-0.03492246940732002,
0.0006445752806030214,
0.008175273425877094,
0.00466232979670167,
0.04341953247785568,
0.0340353399515152,
0.024795081466436386,
-0.01861805096268654,
0.03147769719362259,
-0.04286498203873634,
0.016433799639344215,
-0.015950964763760567,
0.030390208587050438,
-0.01333176251500845,
0.0006296439096331596,
0.051001325249671936,
0.0897856280207634,
-0.024745160713791847,
0.053016964346170425,
0.05455552786588669,
-0.012276124209165573,
-0.015595912002027035,
-0.009894090704619884,
0.010222875513136387,
-0.05326533317565918,
-0.040520645678043365,
-0.049374718219041824,
-0.04857086390256882,
0.04300310090184212,
0.08299765735864639,
-0.006066567730158567,
0.03287476673722267,
0.004236244596540928,
0.040766000747680664,
0.03723221272230148,
0.017779601737856865,
-0.04710599407553673,
-0.017302921041846275,
-0.01414862647652626,
-0.10329096764326096,
-0.00957503356039524,
-0.028724627569317818,
0.030327342450618744,
-0.011896182782948017,
-0.0012995494762435555,
-0.0638488233089447,
-0.02270594611763954,
0.021449444815516472,
0.019253304228186607,
0.015900613740086555,
0.05604240670800209,
0.003478030441328883,
-0.07505279034376144,
-0.012446611188352108,
0.007132973987609148,
0.007442308124154806,
0.02493039146065712,
-0.06959128379821777,
-0.05213252454996109,
-0.024497058242559433,
-0.008118663914501667,
-0.03694038465619087,
0.0035912615712732077,
-0.0006971786497160792,
-0.023554310202598572,
0.05442279577255249,
-0.021082419902086258,
0.027119863778352737,
0.012787642888724804,
0.004063015338033438,
-0.02205248549580574,
0.00778197543695569,
0.04011443257331848,
-0.0015317293582484126,
-0.0021635196171700954,
0.0034760066773742437,
-0.04984649643301964,
-0.005072786472737789,
0.05022851750254631,
-0.07501955330371857,
0.027657827362418175,
-0.00017526716692373157,
0.013684502802789211,
0.022149765864014626,
-0.005379884038120508,
-0.010142325423657894,
-0.015551330521702766,
0.017130142077803612,
-0.017358558252453804,
0.011716876178979874,
-0.0015681650256738067,
0.018567876890301704,
-0.024090679362416267,
0.041506748646497726,
0.00677235284820199,
0.0014002214884385467,
0.01390212494879961,
0.006626068148761988,
0.022878892719745636,
0.015591831877827644,
-0.05388713255524635,
0.005509363021701574,
0.034966833889484406,
0.010609597899019718,
-0.024596938863396645,
0.08365511894226074,
-0.009824535809457302,
0.010485491715371609,
-0.00047714589163661003,
-0.0007546964916400611,
0.06727321445941925,
0.03828764334321022,
0.08614921569824219,
0.009819994680583477,
-0.06773754954338074,
0.02127705328166485,
0.0173477903008461,
-0.04484762251377106,
0.0232863612473011,
0.06281524896621704,
-0.0621909499168396,
0.07057623565196991,
0.0213522519916296,
0.017727261409163475,
-0.0007624339195899665,
0.008923439309000969,
-0.03611167147755623,
-0.04001240059733391,
-0.02195749245584011,
-0.0674147680401802,
-0.06099574267864227,
0.008520363830029964,
0.04353154078125954,
0.06791792064905167,
0.020412618294358253,
0.019082024693489075,
-0.03712857887148857,
0.0022425083443522453,
0.04028937593102455,
0.06253982335329056,
-0.01764550432562828,
0.010273909196257591,
0.026221895590424538,
-0.002524313982576132,
0.08400633931159973,
-0.008169004693627357,
-0.013983817771077156,
0.02596186101436615,
0.025060035288333893,
0.05244910344481468,
0.026513805612921715,
-0.001468474860303104,
0.020916836336255074,
0.000005060135208623251,
-0.008729609660804272,
-0.022916827350854874,
0.07342706620693207,
-0.040734533220529556,
0.059900492429733276,
0.02839938923716545,
-0.006867669057101011,
0.015353446826338768,
0.05757199600338936,
0.017682278528809547,
-0.0059568011201918125,
-0.03824876993894577,
-0.0350581593811512,
-0.017122972756624222,
-0.01726057194173336,
0.04963025078177452,
0.052742645144462585,
-0.01883404329419136,
-0.0640534907579422,
0.05474462732672691,
0.045621760189533234,
0.005671998020261526,
-0.01578485779464245,
0.003375104395672679,
0.013554547913372517,
-0.0006843867595307529,
-0.012951883487403393,
-0.01695268787443638,
0.0002487107994966209,
-0.01120162382721901,
0.015284785069525242,
-0.006238148547708988,
-0.051196299493312836,
-0.05040013790130615,
0.010657637380063534,
0.06946998089551926,
-0.0051424214616417885,
-0.09467865526676178,
0.051704082638025284,
-0.03216473013162613,
0.0585276260972023,
0.022109759971499443,
0.017293227836489677,
-0.023972531780600548,
-0.07759086787700653,
-0.060916151851415634,
0.05727534368634224,
0.022273549810051918,
-0.01189395785331726,
-0.014404873363673687,
-0.019754422828555107,
0.07512788474559784,
-0.023802317678928375,
-0.02516733482480049,
0.02056877315044403,
-0.02062895894050598,
0.0031240861862897873,
-0.016555985435843468,
-0.015896253287792206,
0.0658368468284607,
-0.017992807552218437,
0.04207108914852142,
0.011855770833790302,
0.005734022241085768,
0.018643606454133987,
0.00300021143630147,
-0.011008216999471188,
-0.030102623626589775,
-0.012598582543432713,
-0.016102895140647888,
0.06362718343734741,
0.0013658824609592557,
0.007795115001499653,
0.015264752320945263,
0.04319986328482628,
-0.05142594128847122,
-0.015327815897762775,
0.033408842980861664,
-0.0007766867056488991,
0.03784849867224693,
0.07027313858270645,
-0.04969403147697449,
0.05946760252118111,
0.036986518651247025,
-0.0010202658595517278,
0.0662732943892479,
-0.04864329844713211,
0.02384643256664276,
-0.027033889666199684,
-0.001982803689315915,
0.014258339069783688,
0.012344472110271454,
0.009363173507153988,
-0.021364495158195496,
-0.018349384889006615,
-0.03156931698322296,
-0.04575815796852112,
0.03819959610700607,
0.03518307954072952,
0.0719718262553215,
-0.04343399778008461,
0.04384269937872887,
0.06842170655727386,
0.009376532398164272,
0.04011005908250809,
0.02313080243766308,
-0.04796124994754791,
0.011297836899757385,
-0.06648662686347961,
-0.08746599406003952,
-0.015105485916137695,
0.021733928471803665,
0.03575510159134865,
0.07360398769378662,
-0.01207626610994339,
-0.1104809120297432,
0.01177260372787714,
0.02132696472108364,
0.0031225597485899925,
0.0015647702384740114,
0.027804307639598846,
0.00812623929232359,
0.01844932697713375,
-0.05655577406287193,
0.03844667971134186,
-0.023843416944146156,
-0.06517564505338669,
0.00149058538954705,
-0.02724798582494259,
-0.04026016220450401,
0.002135196002200246,
-0.035102296620607376,
0.01985280029475689,
-0.0023470779415220022,
0.00260694557800889,
-0.039890747517347336,
0.012332645244896412,
-0.01832352578639984,
-0.014144863933324814,
0.04221317544579506,
-0.07945442199707031,
0.044477351009845734,
0.009480965323746204,
-0.044548407196998596,
0.008699514903128147,
0.003422196488827467,
0.010353224352002144,
0.0306987501680851,
-0.045308373868465424,
0.003856938099488616,
-0.07044060528278351,
-0.01891488954424858,
-0.08208552747964859,
0.0028959696646779776,
0.0201131422072649,
-0.008977578021585941,
-0.05003849044442177,
-0.0027480379212647676,
0.006046870723366737,
-0.009976989589631557,
-0.038207557052373886,
-0.008944282308220863,
0.03694711625576019,
0.07031206041574478,
0.02446443773806095,
0.011134717613458633,
-0.005577416159212589,
0.018411805853247643,
-0.04168529435992241,
0.026697048917412758,
0.015946239233016968,
0.0278167761862278,
0.02444348856806755,
-0.001937692053616047,
-0.0260763056576252,
-0.021952060982584953,
0.026350000873208046,
0.030904093757271767,
-0.00884340051561594,
0.002670735353603959,
-0.009678835980594158,
-0.04007156193256378,
-0.00476760184392333,
0.08030208945274353,
-0.005137717351317406,
0.02093665674328804,
-0.035116080194711685,
0.007055297028273344,
0.005563889630138874,
-0.05136244744062424,
-0.031046466901898384,
0.0021859887056052685,
-0.009537376463413239,
0.004895757883787155,
0.027002034708857536,
-0.03044983558356762,
-0.02156800590455532,
0.020828068256378174,
0.028743566945195198,
0.0009401430143043399,
-0.014793765731155872,
0.05721984803676605,
0.015934903174638748,
0.04122352600097656,
0.009605488739907742,
0.01544701773673296,
-0.031955819576978683,
-0.04553117975592613,
0.012759633362293243,
0.024511897936463356,
-0.006347386632114649,
0.04602617397904396,
-0.1016513779759407,
-0.0047647119499742985,
-0.00575260492041707,
-0.03051804192364216,
0.03574537858366966,
-0.05669662356376648,
-0.056837502866983414,
-0.03433914855122566,
0.0009595069568604231,
0.04795307666063309,
0.032184939831495285,
-0.03448819741606712,
-0.009408731944859028,
0.008963175117969513,
-0.03967529162764549,
0.050762202590703964,
-0.033502619713544846,
0.04381255805492401,
-0.051957108080387115,
0.013341672718524933,
-0.0622967854142189,
0.010121729224920273,
-0.035124991089105606,
-0.025417860597372055,
-0.03431679680943489,
-0.002511231927201152,
-0.004789292346686125,
-0.010565675795078278,
0.01708241179585457,
-0.06051159277558327,
-0.01737022213637829,
-0.045060548931360245,
-0.03815002366900444,
0.09174589067697525,
-0.02794606052339077,
-0.003800861304625869,
0.022758040577173233,
-0.018944118171930313,
-0.04426516219973564,
-0.01228269375860691,
0.00296437693759799,
-0.03309900686144829,
-0.010527127422392368,
-0.015487453900277615,
-0.00975485797971487,
0.01648070476949215,
-0.05879708379507065,
0.008481372147798538,
0.10640589147806168,
-0.01237213984131813,
-0.027415094897150993,
0.03381640464067459,
-0.00916109886020422,
0.054777055978775024,
-0.009875173680484295,
0.020910173654556274,
0.08082184940576553,
0.06573694944381714,
-0.010763122700154781,
-0.05475812777876854,
-0.03219465911388397,
0.04222862794995308,
0.011020220816135406,
0.08055700361728668,
-0.04661324992775917,
-0.035323869436979294,
0.001361270435154438,
-0.039363253861665726,
-0.011251856572926044,
0.009252835996448994,
0.09074553102254868,
0.028646541759371758,
0.006615149322897196,
0.05558577552437782,
-0.014945980161428452,
0.02594302035868168,
-0.009135622531175613,
-0.010015002451837063,
-0.05163507163524628,
-0.031834326684474945,
-0.0817316398024559,
0.05690764635801315,
-0.000570562609937042,
0.04653773829340935,
0.03747496008872986,
0.05354265123605728,
-0.047649431973695755,
-0.04831419140100479,
-0.021089790388941765,
-0.04797714948654175,
0.029847556725144386,
-0.06579383462667465,
-0.007535445969551802,
0.036334533244371414,
0.06613105535507202,
-0.023941421881318092,
0.00614536739885807,
-0.011164022609591484,
0.009900284931063652,
-0.04145439341664314,
-0.040212832391262054,
-0.02141616679728031,
-0.02726881019771099,
-0.04017837345600128,
0.0389944352209568,
0.060392312705516815,
-0.010786598548293114,
-0.025028139352798462,
-0.07839827239513397,
0.022097203880548477,
0.01976786181330681,
-0.04719667136669159,
-0.06974627077579498,
0.004984328057616949,
-0.03859711065888405,
0.025397466495633125,
-0.0026868670247495174,
-0.04800717160105705,
-0.02515992894768715,
-0.07386545091867447,
0.0480346716940403,
0.021403728052973747,
-0.0017195538384839892,
0.00821276567876339,
0.028360877186059952,
0.045610181987285614,
-0.01769726164638996,
0.039470113813877106,
-0.025561459362506866,
0.010057576932013035,
-0.08072414249181747,
0.025571072474122047,
0.03990590199828148,
0.034814029932022095,
-0.005446859169751406,
0.021213846281170845,
0.0008992080111056566,
0.006505504250526428,
-0.035866208374500275,
0.0337337851524353,
-0.006961744744330645,
-0.00018929365614894778,
0.06924903392791748,
-0.04530242085456848,
-0.025482239201664925,
0.01650277152657509,
0.06655120849609375,
-0.037332113832235336,
0.015084028244018555,
0.0344308577477932,
-0.03209082409739494,
-0.007867451757192612,
0.011110605672001839,
0.01996554248034954,
0.020725101232528687,
0.04897866025567055,
-0.06005431339144707,
0.007942214608192444,
0.02800518460571766,
0.011213324964046478,
-0.041681353002786636,
-0.007835768163204193,
-0.020583052188158035,
0.0031338606495410204,
0.005376783665269613,
0.04746822640299797,
-0.01066326629370451,
-0.024945644661784172,
-0.027078310027718544,
-0.012621937319636345,
-0.008616333827376366,
-0.06695790588855743,
0.015716100111603737,
-0.019025733694434166,
-0.08495061099529266,
-0.039153825491666794,
-0.004648738075047731,
0.005150009412318468,
-0.023262515664100647,
0.022135844454169273,
-0.025387760251760483,
0.035727307200431824,
0.12318598479032516,
0.000986147322691977,
0.023954330012202263,
0.06074649840593338,
0.06783459335565567,
-0.03374829515814781,
-0.0239116158336401,
-0.006440302357077599,
-0.009221324697136879,
-0.04603225737810135,
-0.0495789460837841,
-0.03862689435482025,
-0.005497381556779146,
-0.011061262339353561
] |
<p>I have a question to ask about the operationalist view of space-time. I am a mathematician who happens to be interested in physics, so if anyone thinks that my question is a silly or vague one, please feel free to close it.</p>
<p>Many physics textbooks that discuss Special Relativity mention that one way of setting up a coordinate system in flat Minkowski space is to imagine that there is an infinite grid of meter rules that pervades the universe, with synchronized clocks located at each node of the grid. In order to obtain more precise measurements of space-time events, one simply divides the grid into more nodes. I feel that this presents problems, because what does it mean to say that ‘all the clocks are synchronized’? Any act of moving a clock from a starting point to its designated node is sure to involve some acceleration, and this is going to upset any synchronization attempt. Also, such a description is not satisfactory because it is impossible to deal with an infinite number of meter rules and clocks.</p>
<p>Things are made worse in curved space-time because of the further effect of gravitational time-dilation. Hence, I believe that the only logically consistent way to perform measurements of space-time events is to use a single atomic clock carried by a single observer and to use the world-lines of photons emitted by a light source carried by the observer to ‘carve out’ a local-coordinate system. The exact description of how this can be done is beyond me, so I would like to gather some useful information from anyone in the community. Thank you very much!</p> | g7855 | [
0.029847120866179466,
0.05587288737297058,
-0.0086143109947443,
-0.045178357511758804,
0.015524245798587799,
0.0003909301885869354,
0.0034155766479671,
0.02974582649767399,
-0.003920596092939377,
0.0014823325909674168,
-0.0023380250204354525,
-0.015566290356218815,
0.024108242243528366,
0.024852635338902473,
-0.01652926206588745,
-0.013610475696623325,
0.05153699964284897,
0.03218181058764458,
-0.012584758922457695,
-0.004684466868638992,
0.08756764233112335,
0.029788313433527946,
0.04716099798679352,
-0.0686149075627327,
0.013277411460876465,
0.014352265745401382,
0.06182670593261719,
-0.06496188044548035,
-0.058301571756601334,
-0.05060948058962822,
0.038724713027477264,
-0.034828875213861465,
-0.0050598192028701305,
-0.005600597709417343,
0.043405383825302124,
-0.06517025828361511,
-0.009068732149899006,
-0.010336712934076786,
0.006363272666931152,
0.03433224931359291,
-0.022612914443016052,
0.01304700132459402,
-0.007277104537934065,
-0.08970200270414352,
0.04996980354189873,
-0.006252731196582317,
-0.004012171644717455,
0.0336252897977829,
0.067365862429142,
0.018984787166118622,
-0.04836946353316307,
-0.027072811499238014,
-0.019320448860526085,
0.0021192370913922787,
-0.0012808166211470962,
0.052866071462631226,
0.041992902755737305,
-0.0053244116716086864,
0.08434701710939407,
0.06426610052585602,
-0.004748388659209013,
-0.058402903378009796,
0.03350924700498581,
-0.017600830644369125,
0.028564639389514923,
0.06487474590539932,
-0.026331791654229164,
-0.04100719094276428,
0.038416098803281784,
0.019349364563822746,
-0.0025130955036729574,
-0.0440603606402874,
0.008084503002464771,
-0.04249091446399689,
-0.027777042239904404,
0.0719662457704544,
-0.024219032377004623,
-0.0006243225070647895,
0.028752965852618217,
0.01021350733935833,
-0.04323713853955269,
-0.003852125024423003,
0.017231246456503868,
0.023759327828884125,
0.04209202527999878,
-0.025149326771497726,
0.013582272455096245,
-0.02945808507502079,
-0.027720818296074867,
0.052788298577070236,
0.05337786301970482,
-0.008928020484745502,
0.07139215618371964,
-0.007940779440104961,
-0.09563018381595612,
0.009779413230717182,
-0.025723980739712715,
0.0161946602165699,
0.032182641327381134,
0.023709995672106743,
-0.032918695360422134,
-0.02275119349360466,
-0.05448712781071663,
0.009110924787819386,
0.013576950877904892,
-0.027565360069274902,
-0.029659172520041466,
0.012065589427947998,
0.018207145854830742,
-0.030676331371068954,
-0.0305587537586689,
-0.03731922805309296,
-0.0233635064214468,
-0.043750688433647156,
-0.07030023634433746,
-0.01830294169485569,
0.07288357615470886,
-0.0018943423638120294,
-0.02288420870900154,
0.016696937382221222,
-0.026665879413485527,
0.03876109421253204,
-0.01262887567281723,
0.031797971576452255,
-0.022901305928826332,
-0.02343507669866085,
-0.02525760978460312,
0.0406610481441021,
0.0036782643292099237,
0.014469563029706478,
0.0027366303838789463,
0.037856318056583405,
-0.07726273685693741,
0.018950169906020164,
-0.07865715771913528,
-0.02022676356136799,
0.01637749932706356,
-0.03902444988489151,
0.01669291965663433,
-0.005520468112081289,
-0.009548833593726158,
-0.03242421895265579,
-0.001128254341892898,
-0.07547663897275925,
-0.005894758738577366,
0.009447586722671986,
-0.018850648775696754,
-0.0027639728505164385,
0.012354517355561256,
-0.00902104377746582,
-0.05507134273648262,
0.07606302946805954,
-0.0051444643177092075,
-0.05104583874344826,
-0.03395221009850502,
0.011212280951440334,
0.012314063496887684,
-0.026910698041319847,
-0.0020570396445691586,
-0.000935884250793606,
0.08442919701337814,
-0.026314524933695793,
0.0002912441559601575,
-0.03715098649263382,
-0.0554657019674778,
-0.0008630997035652399,
-0.0296697486191988,
-0.06370387226343155,
0.05287908762693405,
-0.06917987763881683,
-0.08035116642713547,
-0.04794689640402794,
0.009628256782889366,
0.006235022563487291,
-0.025314245373010635,
0.07880224287509918,
0.03858886659145355,
0.03000492975115776,
-0.011503786779940128,
-0.006119484547525644,
0.015824556350708008,
-0.051242895424366,
0.015288932248950005,
-0.05807684734463692,
-0.022862037643790245,
-0.00988970696926117,
-0.0017406216356903315,
-0.054204151034355164,
-0.025575553998351097,
-0.005512599367648363,
0.038376741111278534,
-0.03404125198721886,
0.047605425119400024,
0.05895545706152916,
0.021016277372837067,
0.051752109080553055,
0.01856204867362976,
0.024703335016965866,
-0.0008543137228116393,
0.025834355503320694,
-0.0038724986370652914,
-0.008273197337985039,
0.005274208262562752,
0.004128977656364441,
0.0902116447687149,
-0.0018955814884975553,
-0.03569219261407852,
0.021629955619573593,
-0.014226921834051609,
0.05631018429994583,
0.07619403302669525,
0.01646113581955433,
0.038492824882268906,
-0.03457123041152954,
-0.06544383615255356,
-0.014442541636526585,
-0.02837860770523548,
0.00869452953338623,
0.027736060321331024,
0.03853300213813782,
-0.03369118273258209,
-0.0005807786947116256,
0.015360658057034016,
-0.0072287702932953835,
0.045126281678676605,
-0.026994740590453148,
-0.008088740520179272,
-0.043404072523117065,
0.015020354650914669,
-0.041159581393003464,
-0.04443269595503807,
0.02635311335325241,
-0.031072676181793213,
-0.0038639227859675884,
0.06854083389043808,
0.06840256601572037,
0.004594509955495596,
0.02669728733599186,
0.026593051850795746,
0.009988728910684586,
-0.014578703790903091,
-0.03949257731437683,
-0.010748766362667084,
-0.021336553618311882,
0.03825734183192253,
-0.062109630554914474,
0.013803438283503056,
-0.0035317365545779467,
-0.02758839912712574,
-0.040603622794151306,
-0.002463679062202573,
-0.05642574280500412,
-0.027420058846473694,
-0.062408335506916046,
-0.007924607023596764,
-0.04138216748833656,
0.04677483066916466,
0.07263551652431488,
-0.13542452454566956,
-0.03853481262922287,
0.004697195719927549,
-0.05086769908666611,
-0.010151052847504616,
0.03511301800608635,
0.04142206534743309,
-0.04039875045418739,
-0.05709662660956383,
0.05690491572022438,
-0.018719496205449104,
0.02886662818491459,
-0.024747828021645546,
0.011967139318585396,
-0.01944921538233757,
0.0559183731675148,
-0.053874578326940536,
0.019706454128026962,
0.0001645606243982911,
-0.004678741563111544,
0.044170450419187546,
0.017220815643668175,
-0.003540380159392953,
-0.01116463728249073,
-0.08438719063997269,
-0.028146477416157722,
0.03375780209898949,
-0.005676803644746542,
-0.02663472108542919,
0.011956240981817245,
0.004023923072963953,
0.01962297596037388,
-0.0031245993450284004,
0.021279174834489822,
-0.020145073533058167,
-0.014730420894920826,
-0.05958487093448639,
0.054107632488012314,
-0.03423814848065376,
-0.013836667872965336,
0.025415122509002686,
0.023729419335722923,
0.009971680119633675,
0.004031727556139231,
0.016102703288197517,
0.0030656056478619576,
-0.003914116881787777,
0.002440981101244688,
-0.03357825055718422,
-0.056797511875629425,
-0.0050001563504338264,
-0.02094336599111557,
0.04421022906899452,
0.03522840514779091,
0.0070199319161474705,
-0.004749101120978594,
0.017659081146121025,
0.03248308226466179,
-0.023473788052797318,
0.021189767867326736,
-0.03342200070619583,
0.017773866653442383,
0.006344083230942488,
0.08356891572475433,
-0.045165397226810455,
-0.020297357812523842,
0.040422894060611725,
0.022091617807745934,
0.04035024344921112,
0.00044736411655321717,
-0.07322518527507782,
0.047373756766319275,
-0.0016140782972797751,
0.005607506260275841,
-0.002287827664986253,
0.04994582384824753,
-0.006677156314253807,
-0.0006262010429054499,
-0.029653968289494514,
-0.013476209715008736,
-0.01179764699190855,
0.006461514160037041,
0.0015394305810332298,
0.007227557711303234,
-0.057979851961135864,
0.011086824350059032,
0.003947827965021133,
0.045317478477954865,
0.01036713644862175,
0.011785092763602734,
-0.03654852136969566,
-0.026638047769665718,
0.05180095508694649,
-0.04000931605696678,
-0.0019501616479828954,
-0.028796156868338585,
-0.0007607422885484993,
0.04902457073330879,
0.05738474056124687,
0.04866766929626465,
0.008972826413810253,
-0.037472814321517944,
-0.011787015944719315,
0.05264164134860039,
0.01849830150604248,
0.016450315713882446,
0.012935162521898746,
0.022363875061273575,
-0.005076497793197632,
0.016889194026589394,
0.024433793500065804,
-0.05192387476563454,
0.04676104336977005,
-0.013017337769269943,
-0.002703998005017638,
0.009368142113089561,
0.03379158675670624,
-0.08281183987855911,
0.005537912715226412,
0.012673170305788517,
0.011025353334844112,
0.03218402341008186,
0.00011221732711419463,
0.03399824723601341,
0.010459339246153831,
0.00004330539013608359,
0.06533019244670868,
0.03543195500969887,
0.020110640674829483,
-0.0363183431327343,
-0.012226276099681854,
-0.05006827414035797,
0.08450030535459518,
-0.0785122662782669,
-0.011735296808183193,
-0.02738839201629162,
0.023554014042019844,
-0.007071441970765591,
-0.012912065722048283,
-0.0022589329164475203,
0.02613556757569313,
0.018060581758618355,
0.06014372780919075,
0.017495417967438698,
0.007588918320834637,
-0.04798123985528946,
-0.024285167455673218,
0.03604522719979286,
-0.010118165984749794,
-0.03497118502855301,
0.005870424676686525,
0.01018822193145752,
0.007248024456202984,
0.018443120643496513,
0.002606971887871623,
-0.0742596909403801,
0.06326786428689957,
0.007640352938324213,
0.03757278621196747,
0.004507372621446848,
0.028899148106575012,
0.019674845039844513,
-0.010760457254946232,
0.08310683816671371,
0.015706229954957962,
-0.05218060687184334,
-0.0025794091634452343,
0.060848839581012726,
-0.0005737289320677519,
-0.02389785274863243,
-0.01481034979224205,
-0.016392245888710022,
0.048539601266384125,
-0.00986223854124546,
0.04546646773815155,
0.0539957657456398,
-0.04159677028656006,
-0.034630607813596725,
0.045943647623062134,
0.05021052062511444,
0.0025443558115512133,
0.07520322501659393,
0.05271380767226219,
-0.016683971509337425,
0.021134596318006516,
0.009232972748577595,
-0.0426771380007267,
0.040150776505470276,
-0.06327126175165176,
-0.08006057888269424,
-0.03665735945105553,
-0.00354110449552536,
0.011281125247478485,
0.04561154171824455,
-0.006439626216888428,
0.003725154558196664,
-0.025854283943772316,
0.04390152171254158,
-0.041906099766492844,
0.052046068012714386,
0.034987837076187134,
0.02318578213453293,
-0.023925043642520905,
-0.05675985664129257,
-0.01838725619018078,
0.04924939200282097,
0.040194835513830185,
0.032732006162405014,
-0.038232602179050446,
-0.008913982659578323,
-0.11530576646327972,
-0.022857150062918663,
0.05789531394839287,
0.029425717890262604,
0.006406904198229313,
-0.01893441192805767,
0.012211036868393421,
0.04781617224216461,
-0.045626528561115265,
0.00871983915567398,
-0.007881538942456245,
-0.04289938881993294,
-0.047948770225048065,
-0.00812345091253519,
0.004506752360612154,
-0.012938433326780796,
-0.016119273379445076,
0.012936873361468315,
0.026719868183135986,
-0.029777050018310547,
0.04040404036641121,
-0.004955601412802935,
0.003936863970011473,
-0.010001673363149166,
0.033295486122369766,
-0.024499040096998215,
0.010885627940297127,
0.026527391746640205,
0.03421450033783913,
-0.03358752653002739,
0.05007946118712425,
-0.04178614169359207,
-0.027690177783370018,
0.058938998728990555,
-0.02555139921605587,
-0.06594536453485489,
-0.0321316234767437,
-0.0029158045072108507,
-0.006160601042211056,
0.007964164018630981,
-0.0777394026517868,
0.07442164421081543,
0.005776188801974058,
0.06816335767507553,
-0.022519579157233238,
0.03599155694246292,
0.031200844794511795,
-0.06792046129703522,
-0.010278461501002312,
-0.0770718976855278,
-0.05563857778906822,
-0.07227684557437897,
-0.03706656023859978,
0.06487049162387848,
0.0432090125977993,
-0.01660730130970478,
0.01993023231625557,
0.014994646422564983,
-0.023750506341457367,
0.02478155866265297,
0.012867985293269157,
-0.06614549458026886,
0.016174228861927986,
0.0029825111851096153,
-0.021243896335363388,
0.016488894820213318,
0.006630205549299717,
-0.02732737734913826,
0.02309265173971653,
0.07786564528942108,
0.10323740541934967,
0.009313647635281086,
-0.009579436853528023,
-0.02400921657681465,
0.024569205939769745,
0.012215683236718178,
-0.05007355287671089,
-0.014258099719882011,
-0.04255888983607292,
0.033736031502485275,
0.03839616850018501,
-0.0027914801612496376,
-0.06816887110471725,
0.04119400307536125,
0.004538241308182478,
0.0049370103515684605,
-0.03435838222503662,
0.06851162016391754,
0.02010062336921692,
0.014069169759750366,
-0.06567308306694031,
-0.004628440365195274,
0.025681469589471817,
0.04627741128206253,
0.0009934789268299937,
-0.026358921080827713,
-0.014961792156100273,
-0.030795134603977203,
0.006952429655939341,
-0.045372262597084045,
0.054487552493810654,
0.027530347928404808,
-0.0019249424804002047,
-0.03579513356089592,
0.017616579309105873,
0.026029769331216812,
-0.030366022139787674,
-0.013919943012297153,
-0.004236024338752031,
0.0011540655978024006,
-0.04749586060643196,
0.02398943342268467,
-0.04126942157745361,
0.01856214739382267,
0.003958347253501415,
-0.026062894612550735,
-0.01004366297274828,
0.018988674506545067,
0.0036969510838389397,
-0.011558257043361664,
-0.018288344144821167,
-0.019584687426686287,
0.031175851821899414,
-0.0034484146162867546,
0.004608467686921358,
0.017252599820494652,
-0.07345142960548401,
0.040102794766426086,
0.004701175261288881,
0.005090214777737856,
-0.0033629643730819225,
0.025739602744579315,
-0.014416608028113842,
-0.03402121737599373,
0.009727884083986282,
-0.009567109867930412,
0.019995583221316338,
0.06927772611379623,
-0.07278095930814743,
-0.004884043708443642,
0.07026410102844238,
-0.012774389237165451,
0.0025537179317325354,
0.012792441993951797,
-0.039240118116140366,
0.06598266214132309,
-0.00965317152440548,
-0.026280805468559265,
0.0037016519345343113,
-0.01708749681711197,
-0.0071945530362427235,
-0.022971557453274727,
0.08770392835140228,
0.033639319241046906,
-0.019278302788734436,
0.0022197251673787832,
-0.01770872063934803,
-0.037118203938007355,
0.03779158741235733,
-0.050548020750284195,
0.023146167397499084,
-0.0031639826484024525,
-0.017307931557297707,
-0.021176792681217194,
0.008722512051463127,
0.035130977630615234,
0.01939406618475914,
0.027050675824284554,
-0.023299766704440117,
0.01572548598051071,
0.011167970485985279,
0.006892723497003317,
0.006005265284329653,
0.020402561873197556,
0.045595910400152206,
-0.004325516056269407,
-0.049130700528621674,
-0.022936932742595673,
0.041385967284440994,
0.011821473948657513,
-0.026438452303409576,
0.037288129329681396,
-0.028272371739149094,
-0.06323191523551941,
-0.026911456137895584,
0.04408526420593262,
-0.025294315069913864,
-0.0028845341876149178,
-0.012294470332562923,
0.021457910537719727,
0.010313360020518303,
-0.0853082686662674,
-0.025719832628965378,
0.0014339258195832372,
-0.04620800539851189,
-0.0157150998711586,
-0.028518307954072952,
0.006505119148641825,
-0.0015144619392231107,
0.012927034869790077,
-0.04063437506556511,
-0.06622165441513062,
-0.02127922885119915,
-0.003958870191127062,
-0.02542273700237274,
-0.0362982451915741,
0.056702621281147,
-0.008215910755097866,
-0.04916501045227051,
0.028873350471258163,
-0.04097725823521614,
0.002105756662786007,
-0.016536347568035126,
0.0357825830578804,
0.001987550873309374,
0.01940757967531681,
-0.012231290340423584,
0.0843387171626091,
0.03308418020606041,
-0.005155313294380903,
-0.01695534773170948,
-0.05564313381910324,
0.020832441747188568,
0.0445614792406559,
-0.0008711558184586465,
-0.03999674320220947,
0.0012179962359368801,
0.00223599118180573,
0.07364179939031601,
0.009689496830105782,
-0.02890988439321518,
-0.015532011166214943,
0.03997218236327171,
-0.03468141704797745,
0.005701079964637756,
0.012839904054999352,
0.048184171319007874,
0.016908904537558556,
-0.013705720193684101,
-0.019216591492295265,
0.022691894322633743,
0.01837177202105522,
0.017178209498524666,
0.01994704082608223,
-0.024366842582821846,
-0.014466061256825924,
-0.0022625576239079237,
-0.042005255818367004,
-0.03862161189317703,
-0.015018980018794537,
0.032088521867990494,
-0.000790501362644136,
-0.022000271826982498,
-0.001911238068714738,
0.019805321469902992,
-0.048484962433576584,
0.02726963721215725,
0.053908560425043106,
0.031462643295526505,
-0.047025952488183975,
0.008322895504534245,
-0.0818578451871872,
0.03782963007688522,
-0.036233559250831604,
-0.0381341427564621,
0.07887644320726395,
0.0036350868176668882,
-0.02735099568963051,
0.004257168620824814,
-0.033888280391693115,
-0.030473319813609123,
-0.00725123006850481,
0.0035463334061205387,
-0.06052068620920181,
-0.037748318165540695,
-0.02074924297630787,
0.014449536800384521,
-0.02598559483885765,
0.0032851973082870245,
0.013666445389389992,
0.004847400356084108,
-0.013959996402263641,
0.013277887366712093,
0.07746803760528564,
-0.0285134669393301,
-0.02180470898747444,
0.019481008872389793,
-0.05187314748764038,
0.06479444354772568,
-0.014214696362614632,
0.03658601641654968,
0.025544889271259308,
0.015642555430531502,
0.0588507317006588,
0.01171246636658907,
-0.017342830076813698,
-0.0538729727268219,
-0.015621519647538662,
0.05157347396016121,
0.018508249893784523
] |
<p>I have a small RC-controlled toy helicopter with removable tail rotor. </p>
<p>Suppose I remove the tail rotor, hold the tail with my hand, start the rotor until it moves with constant angular velocity and then let it go. Suppose that the heli remains on the floor all the time.</p>
<p>Then the body of the helicopter begins to turn into the opposite direction of the rotor. </p>
<p>My problem is to explain this in terms of angular momentum. At first this seemed to contradict angular momentum conservation because I assumed that the helicopter is a closed system and there is no external torque, but the rotor keeps the same angular velocity while the body starts to turn into the other direction. </p>
<p>My second thought was that I have to take the air into account. If I do that it seems plausible to me to explain it as follows:</p>
<p>The rotor transfers angular momentum from to the surrounding air. However to keep it running at constant angular velocity, the motor has to transfer angular momentum to the rotor, which is only possible if the body of the helicopter gets the same amount of angular momentum as goes to the rotor, but into the opposite direction. </p>
<p>But then I thought, the body should turn faster and faster to infinity which obviously doesn't happen. So I guessed I should also take the friction with the floor into account where the angular momentum of the body is transferred to.</p>
<p>This leads me to the following three questions:</p>
<ol>
<li><p>Is my reasoning described above correct or I am completely wrong?</p></li>
<li><p>If I would do the experiment on an almost frictionless turntable (which I don't have available at the moment), would the body of the helicopter indeed become faster and faster almost to infinity?</p></li>
<li><p>If I would do the same thing in a vacuum, what would happen? I guess (see my first thought above), that the body wouldn't turn at all. Is that correct?</p></li>
</ol>
<p>So it would be great if someone could clarify this in terms of angular momentum.</p>
<p>Since the same problem should occur in real helicopters, I guess that there should be some detailed literature about it's physics, but I didn't find any resources about this. So if you have any references for more details or further reading on this problem, it would be also great if you could post it.</p> | g7856 | [
0.06030320003628731,
-0.008758055977523327,
0.01463448815047741,
0.033061906695365906,
0.08786015957593918,
0.014238694682717323,
0.047918595373630524,
0.03278988227248192,
-0.005881286691874266,
0.0057962690480053425,
-0.0469890758395195,
-0.032167479395866394,
-0.010710932314395905,
0.04523073881864548,
0.07294485718011856,
0.006145463325083256,
0.03272209316492081,
-0.023019809275865555,
0.007083500735461712,
0.006033468991518021,
0.06616338342428207,
0.012174638919532299,
-0.0679999589920044,
-0.013456489890813828,
-0.015316125936806202,
-0.03779854625463486,
-0.05919516086578369,
0.000995338661596179,
-0.001927704201079905,
-0.04662448540329933,
-0.010759202763438225,
0.02752857096493244,
-0.011635849252343178,
0.005487585905939341,
-0.02137490175664425,
0.003681468777358532,
0.031380705535411835,
0.007126668468117714,
0.0054245260544121265,
-0.02332218736410141,
0.03131664916872978,
0.00894591398537159,
-0.014620142988860607,
0.004547264892607927,
0.01380200870335102,
-0.017407512292265892,
-0.014044739305973053,
0.025616062805056572,
-0.028113631531596184,
0.01180068589746952,
-0.016921846196055412,
0.0038487864658236504,
0.027188394218683243,
0.034096527844667435,
0.007576875854283571,
0.012257739901542664,
0.044519659131765366,
-0.04718513414263725,
0.0062209609895944595,
-0.01359222736209631,
-0.06037098914384842,
-0.01039821282029152,
-0.012450337409973145,
-0.004244283307343721,
0.026680290699005127,
-0.041267283260822296,
-0.015486389398574829,
-0.015593639574944973,
0.04999434947967529,
0.035000838339328766,
0.04492783918976784,
-0.042230356484651566,
0.0323936864733696,
-0.02125283144414425,
-0.06639780104160309,
-0.007223867811262608,
-0.0069020334631204605,
-0.05212626978754997,
0.0654035210609436,
0.02273787371814251,
-0.08053579181432724,
0.02139686420559883,
-0.008702925406396389,
-0.009652547538280487,
0.045964017510414124,
0.02995927445590496,
-0.006966112181544304,
-0.03768037259578705,
-0.03919193893671036,
-0.013979678973555565,
0.07278270274400711,
-0.006192117929458618,
0.04777394235134125,
-0.0030766171403229237,
-0.025306841358542442,
-0.02076738141477108,
-0.03671141341328621,
0.09502331912517548,
-0.005943102762103081,
0.02743595838546753,
0.004028524737805128,
-0.0011056369403377175,
-0.0016519407508894801,
-0.017119087278842926,
0.007875862531363964,
0.012565414421260357,
0.014811473898589611,
0.015442997217178345,
-0.028050333261489868,
0.0282011516392231,
0.03349735587835312,
-0.08492951840162277,
-0.032492876052856445,
-0.02334434539079666,
-0.01803121156990528,
-0.06449037790298462,
0.03144959732890129,
-0.014824040234088898,
0.017073364928364754,
0.014927679672837257,
-0.024310367181897163,
-0.00737784942612052,
-0.040016058832407,
0.025772834196686745,
0.03446270152926445,
-0.04489336535334587,
-0.010747252963483334,
0.03821785748004913,
0.04294084012508392,
0.04309805855154991,
-0.03616296499967575,
-0.036758631467819214,
0.02026788890361786,
0.031060069799423218,
0.044720638543367386,
-0.010784836485981941,
-0.020079435780644417,
-0.013086844235658646,
0.023341357707977295,
-0.013390119187533855,
0.03705979511141777,
0.02855282463133335,
-0.003526952350512147,
-0.0007673487416468561,
0.0000014691424894408556,
0.05352753400802612,
0.018977558240294456,
0.020093603059649467,
0.06465136259794235,
-0.03299343213438988,
0.035832975059747696,
0.05301815643906593,
-0.01792951114475727,
0.00967832189053297,
0.022478407248854637,
0.037467245012521744,
0.036661963909864426,
0.005048563703894615,
0.038212649524211884,
0.01904582418501377,
0.06144193187355995,
-0.01562146469950676,
-0.00862340722233057,
-0.008100113831460476,
-0.0841313973069191,
0.024125728756189346,
-0.08483762294054031,
-0.04605790972709656,
-0.025161808356642723,
-0.0261080265045166,
-0.08230271190404892,
0.018466362729668617,
0.054688919335603714,
0.04880059137940407,
0.06664862483739853,
0.0032679878640919924,
0.01883697137236595,
0.012029843404889107,
-0.034403279423713684,
0.0010876035084947944,
-0.000148296938277781,
0.022814137861132622,
0.028846323490142822,
0.045391906052827835,
0.059134144335985184,
0.035552941262722015,
0.013042671605944633,
0.06582200527191162,
-0.08303861320018768,
-0.07431761920452118,
-0.002461029915139079,
-0.0007845706422813237,
-0.022334367036819458,
0.02160349115729332,
-0.040314458310604095,
0.027813715860247612,
-0.023189602419734,
-0.022065987810492516,
-0.008907380513846874,
0.013733095489442348,
0.039333779364824295,
-0.016564009711146355,
0.05399753898382187,
-0.0018242460209876299,
0.024145545437932014,
-0.06068933382630348,
-0.003704654984176159,
-0.021906215697526932,
0.0586596317589283,
-0.019100012257695198,
0.06994199752807617,
0.049165721982717514,
-0.043788228183984756,
0.046920549124479294,
-0.00016467535169795156,
0.01626014895737171,
0.006152831483632326,
0.01364566944539547,
-0.043789055198431015,
-0.019130367785692215,
0.03496212139725685,
-0.041072845458984375,
-0.018141916021704674,
-0.02697150781750679,
-0.05611782893538475,
0.01101723127067089,
-0.01409235130995512,
-0.01885758526623249,
-0.034458987414836884,
0.05628763511776924,
-0.023902252316474915,
-0.01828060857951641,
0.013889255933463573,
-0.048850204795598984,
0.029046358540654182,
-0.007592375855892897,
-0.00437969621270895,
0.061738841235637665,
-0.013019619509577751,
-0.015343496575951576,
0.009233295917510986,
0.02479230985045433,
-0.03511375933885574,
-0.050287436693906784,
0.013716570101678371,
-0.06367725133895874,
0.009334013797342777,
-0.04452185332775116,
0.017192799597978592,
0.005377060733735561,
-0.015254141762852669,
0.051029253751039505,
0.0033934179227799177,
0.014284458011388779,
-0.001127042225562036,
-0.05393092334270477,
-0.03160013258457184,
0.027283379808068275,
-0.008778844960033894,
-0.026432432234287262,
-0.007596983108669519,
0.034145791083574295,
0.004762670956552029,
0.07511068880558014,
-0.101265087723732,
0.009801666252315044,
-0.03765358403325081,
0.0381331592798233,
0.03655468672513962,
-0.006607978139072657,
-0.02477368526160717,
0.050538357347249985,
-0.006613664794713259,
0.06578043848276138,
0.0018833454232662916,
-0.024303684011101723,
0.05000585317611694,
-0.021886341273784637,
-0.038086846470832825,
0.0468343161046505,
-0.0360686257481575,
0.03991866111755371,
-0.04662497714161873,
0.01875089295208454,
0.02727614715695381,
0.0006720019737258554,
-0.02995453029870987,
0.0019667786546051502,
-0.08851949125528336,
0.019546614959836006,
-0.08720625191926956,
0.04946189746260643,
0.06623034924268723,
-0.010397473350167274,
0.10374390333890915,
0.06990015506744385,
0.04791231453418732,
-0.038315583020448685,
-0.024693509563803673,
0.059969257563352585,
0.01836695335805416,
-0.017078639939427376,
-0.008571648970246315,
0.014598233625292778,
0.0167764350771904,
0.029828950762748718,
-0.022859446704387665,
0.006004725582897663,
-0.014223539270460606,
0.08173026889562607,
-0.019734026864171028,
-0.020558154210448265,
-0.03260338306427002,
-0.05198347568511963,
-0.013161267153918743,
-0.020764121785759926,
-0.03770511597394943,
-0.014963421039283276,
-0.024348650127649307,
0.012587795034050941,
-0.030333474278450012,
-0.01831982098519802,
0.024544045329093933,
0.02353491447865963,
0.07837215065956116,
0.05413622036576271,
-0.059151556342840195,
0.038920119404792786,
-0.003764552529901266,
-0.08033551275730133,
0.033852845430374146,
0.058145105838775635,
-0.009554140269756317,
-0.06387250870466232,
-0.06220197305083275,
-0.026423713192343712,
-0.03317029029130936,
0.03297843411564827,
0.025091730058193207,
-0.018535751849412918,
0.04668925702571869,
-0.07949461787939072,
-0.022819383069872856,
0.0014369614655151963,
-0.047058604657649994,
0.03420357406139374,
0.022278353571891785,
-0.000517705047968775,
-0.017014481127262115,
-0.018722346052527428,
0.03907182440161705,
-0.01631319336593151,
0.03195137530565262,
-0.00615226523950696,
0.025748170912265778,
0.028557956218719482,
-0.005906255915760994,
0.039818644523620605,
0.0013015390140935779,
-0.014987178146839142,
-0.010949278250336647,
-0.05939282104372978,
0.02605360373854637,
0.00948082935065031,
-0.048185188323259354,
-0.030820662155747414,
-0.02644830383360386,
-0.018868597224354744,
-0.0020609425846487284,
0.003416245337575674,
-0.03198040649294853,
0.025105591863393784,
-0.055729031562805176,
-0.01366986520588398,
-0.03099057823419571,
-0.01742434687912464,
0.05066283792257309,
0.04540019482374191,
-0.05326203629374504,
0.015934571623802185,
0.013620751909911633,
0.023376772180199623,
-0.041451964527368546,
0.03653731942176819,
-0.03640851378440857,
0.06439820677042007,
0.015213262289762497,
0.06033850833773613,
-0.0018711265875026584,
0.011677458882331848,
0.036984629929065704,
-0.03807348012924194,
0.058843325823545456,
-0.03712509572505951,
0.06910847127437592,
-0.0132253123447299,
-0.025221263989806175,
-0.08588644117116928,
-0.009456734172999859,
-0.00009911909728543833,
0.02669331431388855,
-0.007989262230694294,
-0.015884729102253914,
0.014473466202616692,
-0.04226498305797577,
0.07014238834381104,
0.01629829593002796,
0.013178563676774502,
-0.013940053060650826,
0.027374984696507454,
0.006057735998183489,
0.002724591176956892,
-0.018810242414474487,
-0.04033610597252846,
-0.030290985479950905,
-0.007432151585817337,
-0.04194038733839989,
0.019932297989726067,
0.006561584305018187,
0.05384200066328049,
-0.056632328778505325,
0.04005655273795128,
-0.010207335464656353,
-0.015189362689852715,
0.0447063185274601,
-0.014704437926411629,
0.01345134899020195,
0.017788441851735115,
-0.020678363740444183,
-0.05413209646940231,
0.03190947324037552,
0.0051839170046150684,
-0.018702751025557518,
0.019312569871544838,
-0.11284619569778442,
0.06758233159780502,
-0.030018078163266182,
0.024379828944802284,
0.01654302515089512,
0.01661941036581993,
0.039785027503967285,
0.05034549534320831,
0.008383515290915966,
0.010585672222077847,
-0.07748869806528091,
0.049845218658447266,
-0.030005551874637604,
-0.061043646186590195,
0.023302115499973297,
-0.07296901941299438,
-0.08140228688716888,
0.05750716105103493,
-0.01385045237839222,
-0.020709261298179626,
-0.036484502255916595,
-0.029790474101901054,
-0.008228280581533909,
-0.007776452694088221,
-0.02359837293624878,
-0.02778531424701214,
-0.046943262219429016,
0.011342624202370644,
0.03224780410528183,
-0.003157047089189291,
0.018100906163454056,
0.018778663128614426,
-0.01651087775826454,
-0.04439651221036911,
0.012441909871995449,
0.0008387562702409923,
-0.005956739187240601,
0.006565402261912823,
0.05874583497643471,
0.06814716011285782,
-0.020692899823188782,
0.042984019964933395,
0.0206166859716177,
0.02245333418250084,
0.019071727991104126,
-0.046953000128269196,
-0.032059669494628906,
-0.019868290051817894,
0.004028751514852047,
-0.0045000226236879826,
-0.009562971070408821,
-0.05078522488474846,
-0.0420982800424099,
-0.003953602630645037,
0.07249663025140762,
-0.021733803674578667,
0.018708519637584686,
0.027782421559095383,
-0.03943230211734772,
-0.010352592915296555,
0.04775568097829819,
0.03238627687096596,
0.004764993209391832,
-0.031419724225997925,
-0.05968708172440529,
-0.036606837064027786,
-0.03902739658951759,
-0.040560752153396606,
-0.02212991751730442,
0.02799907885491848,
-0.03824419155716896,
0.019693242385983467,
0.017866315320134163,
-0.003152735298499465,
-0.019987428560853004,
0.05925126373767853,
-0.018858760595321655,
0.06485352665185928,
-0.007008856628090143,
-0.030033813789486885,
-0.011603538878262043,
0.007532438263297081,
-0.03723720461130142,
0.037489235401153564,
0.009733091108500957,
0.015972109511494637,
-0.015753578394651413,
0.002512548351660371,
-0.005581611301749945,
-0.03886484354734421,
-0.03191429004073143,
0.009778367355465889,
-0.0401734858751297,
-0.021557925269007683,
-0.07545662671327591,
0.051346711814403534,
0.016696186736226082,
-0.03324630856513977,
0.03860817477107048,
0.05085476487874985,
-0.04602448269724846,
0.003874245099723339,
0.005656255874782801,
-0.04896518215537071,
0.018862105906009674,
-0.0050282240845263,
-0.000034042685001622885,
-0.028755730018019676,
-0.0326840914785862,
0.09672997146844864,
-0.033858802169561386,
-0.009799966588616371,
-0.040100179612636566,
-0.04367993026971817,
0.029572144150733948,
-0.049969084560871124,
-0.06355324387550354,
0.037695616483688354,
-0.033807169646024704,
0.010673020035028458,
-0.03196125477552414,
-0.012243472971022129,
-0.03415476903319359,
-0.003890358842909336,
-0.04877706989645958,
-0.020818406715989113,
0.03523629158735275,
0.0089450404047966,
0.034711744636297226,
-0.005894939415156841,
-0.005931707564741373,
0.005063769407570362,
0.0034625886473804712,
-0.06809069216251373,
0.05286275967955589,
0.013975625857710838,
-0.0379825159907341,
0.008927588351070881,
0.025186363607645035,
0.00573723204433918,
0.03134458139538765,
0.04802175983786583,
0.011205763556063175,
0.031105469912290573,
-0.02291332185268402,
0.04986255615949631,
-0.00038998614763841033,
-0.000052193568990333006,
0.04761255905032158,
-0.020157119259238243,
-0.0027661193162202835,
0.02857506461441517,
-0.039952438324689865,
-0.008971120230853558,
0.031060397624969482,
-0.02950604446232319,
-0.04281792417168617,
0.02709302119910717,
-0.03149283677339554,
-0.05724896863102913,
0.004875842481851578,
0.023482130840420723,
-0.0036972227972000837,
0.0036851062905043364,
-0.02433602325618267,
-0.050151288509368896,
0.004239566158503294,
-0.046586669981479645,
0.02021992951631546,
0.0006222318625077605,
-0.02841835841536522,
0.03710956871509552,
0.05057554692029953,
0.03286220505833626,
0.05773554742336273,
-0.003070703474804759,
-0.05488624423742294,
0.028261516243219376,
0.02749834954738617,
-0.009727291762828827,
-0.016230544075369835,
0.07449313253164291,
0.023641381412744522,
-0.005920554045587778,
0.012035801075398922,
-0.003968642093241215,
0.07996919006109238,
0.0073667485266923904,
-0.013108517043292522,
-0.007589041255414486,
0.0350397489964962,
-0.016192961484193802,
-0.0387391522526741,
0.027482185512781143,
0.023803962394595146,
0.04284186661243439,
0.017622172832489014,
-0.030561577528715134,
-0.057538241147994995,
0.041064999997615814,
-0.0033926262985914946,
0.04773109033703804,
-0.015237174928188324,
0.016424207016825676,
0.06320477277040482,
0.045432645827531815,
0.010701622813940048,
0.0606175921857357,
-0.04357030987739563,
0.044108305126428604,
-0.0026005699764937162,
-0.027335677295923233,
0.05939065292477608,
-0.022429704666137695,
-0.011541919782757759,
0.003640336450189352,
-0.03631841763854027,
-0.0027361572720110416,
-0.023667993023991585,
-0.00312557234428823,
-0.0009303765255026519,
-0.014673618599772453,
-0.017477931454777718,
-0.017061525955796242,
-0.002783267991617322,
0.007878482341766357,
-0.01043914444744587,
-0.02033701352775097,
-0.03683168441057205,
0.01837419532239437,
-0.041105177253484726,
-0.005761304870247841,
-0.014712819829583168,
-0.025713438168168068,
0.06557364016771317,
0.010548756457865238,
0.018861591815948486,
-0.017887696623802185,
-0.0489734411239624,
-0.03259588032960892,
-0.024440227076411247,
0.041272372007369995,
0.01781448908150196,
-0.033180367201566696,
0.005486401729285717,
0.0524931363761425,
-0.051206979900598526,
0.05114004760980606,
-0.024381471797823906,
0.05015170946717262,
-0.03419484198093414,
-0.003682031761854887,
-0.07612589746713638,
0.059189822524785995,
0.0006027889903634787,
-0.09491408616304398,
-0.020977741107344627,
0.09213142096996307,
-0.014076335355639458,
0.0016668286407366395,
-0.005681003909558058,
0.03927760571241379,
0.06170188635587692,
0.030106276273727417,
-0.0277663953602314,
0.007860172539949417,
0.023599276319146156,
-0.011791301891207695,
0.050114113837480545,
0.03907764330506325,
0.03350791335105896,
0.02969970926642418,
0.026064850389957428,
0.02342761680483818,
-0.031438421458005905,
0.05895582213997841,
0.017147064208984375,
-0.017256485298275948,
-0.014549990184605122,
0.0016798444557935,
-0.04846121370792389,
-0.004296322353184223,
-0.014168653637170792,
-0.03248501569032669,
-0.0012604417279362679,
-0.006607546471059322,
-0.029474161565303802,
-0.009177261032164097,
-0.04135866463184357,
0.017770249396562576,
-0.002043838845565915,
-0.06398890167474747,
-0.07078863680362701,
-0.042382001876831055,
0.0035048408899456263,
-0.003194682067260146,
-0.030112745240330696,
-0.010268808342516422,
-0.03412231430411339,
-0.025973360985517502,
-0.0260318536311388,
-0.007015594746917486,
-0.007507123053073883,
-0.030697964131832123,
-0.07381800562143326,
-0.027267368510365486,
-0.05466553196310997,
-0.015954267233610153,
0.05000067129731178,
-0.005888605490326881,
-0.00891764648258686,
0.031180808320641518,
0.03280217573046684,
0.05231010541319847,
-0.009400272741913795,
0.042280279099941254,
0.02436288818717003,
0.07415589690208435,
-0.03791331872344017,
0.02723166160285473,
0.03463122993707657,
-0.04090598598122597,
-0.04021131619811058,
0.042114149779081345,
-0.0038750937674194574,
-0.0018422564025968313,
-0.061479248106479645,
0.04681884124875069,
-0.008792671374976635,
-0.030972953885793686,
0.006023393012583256,
-0.08288194239139557,
-0.03936075046658516,
0.05402546748518944
] |
<p>A function $f(ax)$ that satisfies
$$
f(ax)=a^\Delta f(x)\,\,\, (\Delta \in R)
$$
is said to be <em>scale invariant</em>. The most general function $f(x)$ that satisfies the previous condition is of the form
$$
f(x)=C x^{\Delta}
$$
If we consider the set of distributions, namely the set of all $f(x)$ such that $\int f(x)dx=1$, is it possible to <a href="http://math.stackexchange.com/questions/140962/scale-invariance-of-power-law-distribution">prove</a> that the only distribution that is invariant under <em>scale transformation</em> is
$$
f(x)=C x^{-1}.
$$
This means that in general I can build a generic distribution as a power law that still satisfies the scale invariance properties $f(ax)=a^\Delta f(x)$, but this generic distribution will not be invariant under scale transformations.
So, what is the physical meaning of the scale invariance property in a generic power law distribution? </p>
<p><strong>First Edit:</strong> For a distribution $f$, if I perform a change of variables, I must preserve the probability, namely
$$
|f(x)dx|=|g(y)dy|,
$$
so that the new distribution $g$ will be given by $f(x)|\frac{dx}{dy}|=g(y)$.
If a distribution is invariant under change of variables, I must have
$$
g(y)=f(y).
$$
Replacing $x$ with $ax$ and using the invariance of the distribution $f(x)$ under this transformation, I have $f(x)=C x^{-1}$. </p> | g7857 | [
0.0077052065171301365,
-0.01278560608625412,
-0.021962082013487816,
-0.04990347847342491,
0.02623804286122322,
0.04338991641998291,
-0.04269276559352875,
0.014685181900858879,
-0.08681419491767883,
0.03505931794643402,
-0.008797450922429562,
0.018679510802030563,
0.012928587384521961,
-0.04318699240684509,
-0.02359292283654213,
0.03377833962440491,
0.05190874636173248,
-0.03414756804704666,
0.06047602742910385,
-0.012839770875871181,
-0.048356298357248306,
-0.009887289255857468,
-0.002083492698147893,
-0.015482437796890736,
0.029398027807474136,
-0.025821717455983162,
0.0012484012404456735,
0.003781081410124898,
-0.02496378682553768,
-0.00602624099701643,
0.0025010753888636827,
0.023158643394708633,
0.0859028697013855,
-0.04441167786717415,
-0.0016241263365373015,
-0.006803473457694054,
0.03225261718034744,
0.06980478763580322,
0.08567763864994049,
0.05376559495925903,
-0.06318442523479462,
0.08914144337177277,
0.004008627962321043,
-0.016122760251164436,
-0.02425217628479004,
0.04277186840772629,
-0.028211524710059166,
0.010914124548435211,
-0.015501496382057667,
-0.010478324256837368,
-0.01725868508219719,
0.03809289634227753,
0.06296233087778091,
-0.01750342547893524,
-0.06267376244068146,
0.0022343595046550035,
0.08476541191339493,
0.04269896820187569,
0.04049175977706909,
-0.0014929929748177528,
0.02242167480289936,
-0.03101218491792679,
0.024212254211306572,
-0.0046086981892585754,
0.02562141977250576,
-0.0261447262018919,
-0.023521285504102707,
0.004067718982696533,
0.0015539531596004963,
-0.0017754191067069769,
-0.031241223216056824,
-0.0017356732860207558,
0.02912457101047039,
-0.004671191330999136,
-0.012586484663188457,
-0.06842978298664093,
0.035059623420238495,
0.034741323441267014,
-0.031560640782117844,
-0.03878631070256233,
-0.04514118283987045,
0.04240816459059715,
0.039728015661239624,
0.030993802472949028,
-0.012907063588500023,
-0.0009772444609552622,
0.042153142392635345,
0.02911091223359108,
0.015053343959152699,
0.07965748012065887,
0.02867032401263714,
-0.041842296719551086,
0.005463223438709974,
0.02100403979420662,
-0.00906887836754322,
-0.03985614329576492,
0.003867601277306676,
0.06684455275535583,
-0.06139909103512764,
-0.03747544810175896,
-0.013750807382166386,
0.015214866027235985,
-0.039475005120038986,
0.024732695892453194,
-0.038594216108322144,
0.010834035463631153,
0.076645627617836,
-0.0035333356354385614,
0.05436791852116585,
-0.010143816471099854,
0.0018107143696397543,
-0.01304025761783123,
0.0426650308072567,
-0.035276297479867935,
0.0016319372225552797,
-0.054546330124139786,
0.015368400141596794,
-0.03516635671257973,
0.026084646582603455,
0.007909371517598629,
0.03471919521689415,
-0.04858691990375519,
-0.011413549073040485,
0.04321024939417839,
-0.02214355580508709,
0.025434862822294235,
0.0029389895498752594,
0.04107191786170006,
-0.01447377260774374,
-0.06192179396748543,
0.04664086550474167,
-0.01568932645022869,
-0.044810011982917786,
-0.01655501127243042,
0.061824068427085876,
0.019532660022377968,
0.05392353609204292,
0.008823026902973652,
0.006297951098531485,
0.007474840618669987,
-0.04720926657319069,
0.03709941729903221,
0.04686106741428375,
-0.010725910775363445,
0.011740199290215969,
0.03981846198439598,
-0.006248914636671543,
-0.01597338728606701,
0.04850459098815918,
-0.016878435388207436,
-0.02023710496723652,
0.1008480116724968,
-0.04696265980601311,
-0.04141492024064064,
-0.001379490946419537,
0.009554625488817692,
-0.044769927859306335,
0.05195893347263336,
0.004269104450941086,
0.008821803145110607,
0.02086206153035164,
0.031019041314721107,
-0.02523297816514969,
-0.038148827850818634,
0.018826037645339966,
-0.04052409902215004,
-0.014789845794439316,
0.008017727173864841,
-0.01894504390656948,
-0.030694622546434402,
-0.05386461690068245,
0.04669372737407684,
0.025187071412801743,
-0.0006001145229674876,
-0.017970679327845573,
-0.005156564526259899,
0.02080591209232807,
0.013754045590758324,
0.03146414831280708,
-0.036182109266519547,
-0.05090126395225525,
0.0056551555171608925,
-0.0038064608816057444,
-0.06742670387029648,
0.007385512348264456,
0.010541839525103569,
0.05068890377879143,
-0.021934639662504196,
-0.02736438810825348,
0.014555826783180237,
-0.0244244746863842,
-0.005549935158342123,
0.011221763677895069,
0.060982149094343185,
-0.010215381160378456,
-0.07701816409826279,
0.019407939165830612,
-0.009445729665458202,
-0.042203158140182495,
0.007168223615735769,
0.028869271278381348,
0.044876642525196075,
0.010222035460174084,
-0.027147261425852776,
-0.018507327884435654,
0.01620890200138092,
-0.035613421350717545,
-0.047352392226457596,
0.018623538315296173,
0.03058789111673832,
0.013373426161706448,
-0.08797768503427505,
-0.011024982668459415,
-0.053311463445425034,
0.017019476741552353,
0.017011579126119614,
-0.048103347420692444,
-0.028729410842061043,
-0.05916834995150566,
0.0030336417257785797,
-0.002259222324937582,
-0.0634021982550621,
-0.02835468389093876,
0.07405027747154236,
-0.018925156444311142,
0.002927818102762103,
-0.04017174243927002,
-0.01068184059113264,
0.06249567121267319,
0.004666833207011223,
-0.04476995766162872,
0.03928988054394722,
-0.010478810407221317,
-0.010350044816732407,
-0.04588857665657997,
0.03410104289650917,
-0.031052468344569206,
0.05160936713218689,
0.06759125739336014,
0.018293607980012894,
-0.015111628919839859,
-0.05667630955576897,
0.016736317425966263,
-0.023780306801199913,
0.062260884791612625,
0.054454486817121506,
0.041222698986530304,
0.01603764295578003,
0.05406304821372032,
0.02980140596628189,
-0.03239128366112709,
-0.016753846779465675,
0.04561754688620567,
0.008759698830544949,
0.019666677340865135,
-0.0432305783033371,
0.07993566244840622,
-0.018722865730524063,
-0.01648886688053608,
0.033287163823843,
-0.012115348130464554,
0.014811278320848942,
0.021932316944003105,
-0.006189462263137102,
-0.06924498081207275,
0.0325431264936924,
0.028176605701446533,
0.01501266285777092,
-0.013439016416668892,
-0.009895571507513523,
-0.005939966067671776,
0.05804803594946861,
-0.0055851140059530735,
0.06372931599617004,
0.00010890081466641277,
0.01529029943048954,
0.004654656630009413,
-0.07767316699028015,
-0.00617526238784194,
-0.0018392885103821754,
0.003190051531419158,
-0.013070467859506607,
-0.09606052190065384,
-0.025389479473233223,
0.024724261835217476,
-0.033605463802814484,
-0.008205832913517952,
-0.0553453266620636,
-0.04739267751574516,
0.08752863854169846,
0.01407722756266594,
0.003150439588353038,
-0.006451440043747425,
-0.027827957645058632,
-0.05857598036527634,
-0.032130058854818344,
-0.02825879119336605,
-0.09425731003284454,
0.03519206494092941,
-0.022691959515213966,
0.007542621809989214,
-0.053769100457429886,
-0.03252861276268959,
-0.019596727564930916,
0.10069803893566132,
0.0737512931227684,
-0.019954942166805267,
0.020556464791297913,
-0.016867918893694878,
0.05678298696875572,
-0.004037744831293821,
0.03463953360915184,
-0.040541235357522964,
-0.009864225052297115,
0.01805381290614605,
-0.00656159920617938,
0.02269722893834114,
-0.0006718254880979657,
-0.012609422206878662,
-0.06415468454360962,
0.021031618118286133,
-0.061119966208934784,
0.05566835775971413,
-0.021080510690808296,
0.017852768301963806,
-0.00413642730563879,
-0.05136428028345108,
0.016781238839030266,
-0.0006077663856558502,
0.008413047529757023,
-0.0065769897773861885,
0.017704183235764503,
0.02462606504559517,
-0.0034773405641317368,
-0.055620912462472916,
-0.00989740900695324,
-0.048036735504865646,
-0.007607751991599798,
0.04426101967692375,
0.019183991476893425,
0.03676671162247658,
-0.04703562334179878,
-0.0746363177895546,
0.032557349652051926,
-0.03908123821020126,
0.01118506956845522,
0.02397957444190979,
-0.0011263188207522035,
0.0487767830491066,
0.023044312372803688,
0.0441935732960701,
-0.03935239836573601,
0.0719599798321724,
-0.037384696304798126,
0.04783410578966141,
0.006596950814127922,
0.07440272718667984,
-0.06789953261613846,
-0.025840289890766144,
-0.02586100436747074,
0.015954086557030678,
-0.05166807025671005,
-0.0007947141421027482,
0.04069878160953522,
-0.020030301064252853,
0.07509595900774002,
-0.006979914847761393,
-0.0019380954327061772,
0.0027099556755274534,
0.019239723682403564,
0.017187656834721565,
0.015889789909124374,
0.028232578188180923,
0.024662751704454422,
0.0036089427303522825,
-0.011878455989062786,
0.007130529265850782,
0.06425338238477707,
-0.008629836142063141,
0.004691402427852154,
0.03950020670890808,
0.04056321457028389,
0.0340433232486248,
-0.019879888743162155,
0.015401738695800304,
0.002396871568635106,
-0.05929739773273468,
-0.0018229400739073753,
0.03151137754321098,
-0.017709603533148766,
-0.0064510442316532135,
-0.0022784157190471888,
-0.034630607813596725,
0.03965211659669876,
-0.010728688910603523,
-0.027335455641150475,
-0.025081690400838852,
-0.020641589537262917,
-0.029437344521284103,
0.015265163965523243,
-0.028484029695391655,
0.009332340210676193,
0.0020355461165308952,
-0.01196278166025877,
0.044271767139434814,
-0.030802223831415176,
0.015832632780075073,
-0.029801679775118828,
0.0013590926537290215,
-0.02195727452635765,
0.018637295812368393,
-0.009455762803554535,
0.007752739358693361,
-0.05483478680253029,
-0.03346135839819908,
0.03297293931245804,
-0.028403766453266144,
-0.02935316227376461,
0.006802725605666637,
-0.022885410115122795,
0.006557478569447994,
-0.002275157021358609,
0.03944704681634903,
0.02666209265589714,
-0.024135522544384003,
0.060596566647291183,
0.04891234636306763,
-0.022665301337838173,
0.05980052053928375,
0.014519689604640007,
-0.012250388972461224,
0.012472378090023994,
0.021359292790293694,
0.0011860613012686372,
-0.029316991567611694,
-0.02549140155315399,
-0.05977010726928711,
0.0018928495701402426,
-0.051817089319229126,
0.0110027389600873,
0.03080654703080654,
0.020570257678627968,
0.0010788990184664726,
-0.02408602461218834,
-0.060304321348667145,
0.018348636105656624,
-0.010376784019172192,
-0.00018448139599058777,
-0.014126276597380638,
0.027710657566785812,
0.00460821483284235,
0.009621826000511646,
-0.0068197790533304214,
-0.04394177719950676,
0.00986399780958891,
-0.06390634924173355,
0.03180091828107834,
-0.00000187500972970156,
0.0688285306096077,
-0.0019049517577514052,
-0.02592097595334053,
-0.012215220369398594,
-0.04221316799521446,
-0.00443592295050621,
0.021379290148615837,
-0.00006691752787446603,
-0.04730347916483879,
0.018442729488015175,
-0.010451867245137691,
0.04579541087150574,
0.059334445744752884,
-0.01474516000598669,
-0.03420928120613098,
0.0022513025905936956,
0.05881432071328163,
0.04635901749134064,
0.03011571615934372,
-0.03735379874706268,
0.04828885570168495,
-0.022602679207921028,
-0.006409523542970419,
0.014847450889647007,
0.027023103088140488,
0.010060419328510761,
-0.0015699873911216855,
-0.01255149208009243,
-0.01638520136475563,
-0.025886498391628265,
-0.003002977930009365,
-0.030817102640867233,
-0.007010388653725386,
0.019983256235718727,
0.060074158012866974,
0.024491429328918457,
0.024756062775850296,
0.011460144072771072,
-0.019077973440289497,
-0.07018927484750748,
-0.005501630716025829,
-0.057462070137262344,
-0.026318617165088654,
-0.0016850297106429935,
0.06971640139818192,
-0.004302555229514837,
0.007300538942217827,
0.012686588801443577,
0.012682046741247177,
0.051042258739471436,
0.007213493809103966,
0.0453181117773056,
-0.005519401282072067,
0.010320932604372501,
-0.018133336678147316,
-0.0055388035252690315,
-0.00543553102761507,
-0.032603491097688675,
-0.039720404893159866,
0.044024284929037094,
0.004514654166996479,
-0.11066380888223648,
0.04439191892743111,
-0.041168369352817535,
0.01757846772670746,
-0.03886864706873894,
-0.015333251096308231,
0.02592751383781433,
-0.027049899101257324,
-0.05618709325790405,
-0.02065891958773136,
0.06145358458161354,
0.03274828568100929,
-0.008406237699091434,
-0.03238997980952263,
-0.02164417691528797,
-0.04301605746150017,
-0.023924870416522026,
0.00029048972646705806,
0.041784632951021194,
-0.0035485057160258293,
0.015272651799023151,
-0.00804985873401165,
0.01012519933283329,
0.013545975089073181,
-0.057186052203178406,
-0.0768563523888588,
-0.0269315205514431,
-0.03914221003651619,
-0.032601866871118546,
-0.01642676815390587,
-0.00033000385155901313,
0.05027280002832413,
-0.015857430174946785,
-0.008682494051754475,
-0.008418276906013489,
-0.035544417798519135,
0.06067178025841713,
0.05860093608498573,
-0.005891756620258093,
0.0659937784075737,
-0.037171464413404465,
0.03164535388350487,
0.0032407869584858418,
0.011449904181063175,
-0.04996678605675697,
-0.007861295714974403,
-0.08750288933515549,
0.05729236453771591,
-0.012992145493626595,
0.015431675128638744,
0.08915414661169052,
-0.00529064517468214,
0.06440822780132294,
0.03731006011366844,
-0.012698291800916195,
0.013928478583693504,
-0.03094956837594509,
-0.031753890216350555,
-0.018948959186673164,
-0.02276037260890007,
0.004049021750688553,
0.0096351383253932,
-0.004966837354004383,
0.01973891071975231,
-0.04392150789499283,
-0.08526460081338882,
-0.021774843335151672,
-0.03372565284371376,
-0.03916362300515175,
0.06460247188806534,
-0.02398626320064068,
-0.02073265053331852,
-0.030505208298563957,
-0.000533824902959168,
0.04942870885133743,
-0.045218534767627716,
0.015055599622428417,
0.03548822179436684,
0.027526643127202988,
-0.0016908644465729594,
-0.014713870361447334,
0.05612950772047043,
0.0026719162706285715,
0.043989039957523346,
-0.0537562370300293,
-0.019476430490612984,
-0.01885678805410862,
-0.029212865978479385,
-0.006508884485810995,
-0.0023582554422318935,
-0.032354239374399185,
0.048500314354896545,
0.03025365248322487,
0.03409816697239876,
0.029098104685544968,
-0.013033650815486908,
0.010902250185608864,
-0.041950471699237823,
-0.02748481184244156,
-0.007204397115856409,
0.009046724997460842,
0.01075794082134962,
-0.043042249977588654,
0.03210535645484924,
0.03352474793791771,
0.0025362996384501457,
0.012050275690853596,
0.011672619730234146,
0.05374716594815254,
0.02809826470911503,
-0.01518174260854721,
-0.057353127747774124,
0.0039912257343530655,
-0.023191088810563087,
0.03803616017103195,
-0.04376944154500961,
0.027478070929646492,
0.008919795043766499,
0.0435200110077858,
0.06969557702541351,
0.009789194911718369,
-0.05435183271765709,
0.0710344985127449,
0.1050615906715393,
-0.008872631937265396,
-0.009219243191182613,
0.02769535966217518,
0.011501649394631386,
-0.04506712779402733,
-0.0416940413415432,
0.01930862106382847,
0.023346295580267906,
-0.009927036240696907,
-0.008953705430030823,
-0.013607633300125599,
-0.0005810839938931167,
0.012758168391883373,
0.007840641774237156,
0.015367073938250542,
0.026203246787190437,
-0.04192286729812622,
-0.004663500934839249,
-0.01226805429905653,
0.02439958043396473,
0.003926713485270739,
0.029811086133122444,
0.07208374887704849,
0.04010818526148796,
-0.09911183267831802,
-0.009581608697772026,
-0.010957099497318268,
0.006652995478361845,
-0.019378777593374252,
0.08763082325458527,
0.03592666611075401,
0.06433398276567459,
0.0015289352741092443,
-0.02305823564529419,
0.07284990698099136,
0.06973588466644287,
0.002868511015549302,
-0.056880299001932144,
0.017103619873523712,
0.0030374396592378616,
-0.048714779317379,
-0.03891526162624359,
0.029669158160686493,
-0.06105431541800499,
-0.008915782906115055,
-0.013992222025990486,
-0.04680389165878296,
-0.08035852015018463,
-0.05543414130806923,
0.0244245957583189,
0.025449147447943687,
-0.016315795481204987,
-0.0033739814534783363,
0.02215350605547428,
0.011718039400875568,
0.03158072009682655,
-0.0038237362168729305,
0.03330162540078163,
-0.01996089518070221,
-0.04238109290599823,
-0.01678900234401226,
0.034067291766405106,
0.01138976588845253,
-0.029649905860424042,
-0.14888472855091095,
-0.05263548344373703,
-0.01050843670964241,
-0.016944125294685364,
-0.014565616846084595,
0.0091341407969594,
-0.031302474439144135,
0.038793519139289856,
0.011167509481310844,
-0.019321035593748093,
-0.09394492954015732,
-0.023047221824526787,
-0.0021496163681149483,
-0.004596373997628689,
-0.017587555572390556,
-0.016827519983053207,
-0.009385291486978531,
-0.03766871988773346,
0.018037045374512672,
0.004139685537666082,
-0.05804867297410965,
0.027395358309149742,
-0.01695312187075615,
-0.03159984573721886,
-0.05369725078344345,
0.0006861682632006705,
0.04974646493792534,
0.014795009978115559,
0.039722394198179245,
-0.00555469049140811,
-0.021959291771054268,
-0.06464829295873642,
0.0009960526367649436,
0.024454141035676003,
-0.015109214931726456,
0.014093426056206226,
0.06348302215337753,
-0.02833043970167637,
0.022345909848809242,
-0.008902469649910927,
0.06070001795887947,
-0.01280262228101492,
-0.0060109286569058895,
-0.01550214271992445,
-0.03074871562421322,
-0.039156146347522736,
0.01644895039498806,
0.01094343513250351,
0.005711550358682871,
0.0583803653717041,
-0.005790314637124538,
0.057099588215351105,
0.030571434646844864,
0.0022501153871417046,
0.014996513724327087,
-0.0285351425409317,
0.009289447218179703,
-0.05646267533302307,
-0.03336741775274277,
-0.035814158618450165,
0.008486959151923656
] |
<p>I was looking through some conformal Ward identity related things when I noticed that this paper (<a href="http://arxiv.org/abs/1212.3788" rel="nofollow">arXiv:1212.3788</a>) writes in their equation (33), a 3-point function between a conserved current and two scalars, complex conjugate of each other and having the same conformal dimensions. The equation reads
\begin{equation}
\partial_\mu\langle j^\mu\mathcal{O}(y_1)\bar{\mathcal{O}}(y_2)\rangle=-iq\langle \mathcal{O}(y_1)\bar{\mathcal{O}}(y_2)\rangle(\delta(x-y_1)-\delta(x-y_2))
\end{equation}
They also comment on the next page that this equation shows, Ward identity guarantees a vanishing three point function for scalar operators of unequal conformal dimensions. How to see that? Also, is this a general outcome of Ward identity that the operators inside (in such cases; may be instead of current, some other conserved tensor) the operators have to have equal conformal dimensions to have a non-vanishing correlator? A reference will be excellent. Thanks in advance!</p> | g7858 | [
0.032435592263936996,
-0.04867396876215935,
0.009525846689939499,
-0.005448180716484785,
0.06784816831350327,
0.041659168899059296,
0.049118611961603165,
-0.01018914207816124,
-0.01011673640459776,
0.03522595763206482,
-0.03185269236564636,
0.013528367504477501,
0.01653582602739334,
0.020668920129537582,
-0.010902095586061478,
-0.02764640375971794,
0.030882300809025764,
-0.020798515528440475,
0.04268850013613701,
0.003059059614315629,
0.02404627948999405,
0.062498971819877625,
0.012683358043432236,
-0.01018926128745079,
0.028231745585799217,
-0.008608180098235607,
0.030394405126571655,
-0.013805822469294071,
0.013165266253054142,
-0.05337945744395256,
0.11717872321605682,
0.0873890146613121,
0.0700363740324974,
-0.0004997054347768426,
-0.023933792486786842,
0.018374577164649963,
0.06072230637073517,
0.0537424236536026,
0.009652513079345226,
0.024919556453824043,
-0.019954221323132515,
0.016667615622282028,
0.02580765075981617,
-0.009369868785142899,
-0.0035180121194571257,
0.025023071095347404,
-0.01553336065262556,
-0.0008092838106676936,
0.01589423045516014,
-0.037588972598314285,
-0.01117551326751709,
0.08854018896818161,
0.005126515403389931,
-0.04400179535150528,
-0.046817146241664886,
0.035993319004774094,
-0.0036670381668955088,
-0.04655005410313606,
0.030094219371676445,
0.0531696192920208,
-0.017530040815472603,
-0.02565200999379158,
0.03401169553399086,
0.054791830480098724,
0.07900873571634293,
-0.03980214148759842,
-0.06909111887216568,
-0.023637667298316956,
0.02344813197851181,
-0.017173411324620247,
-0.023677892982959747,
-0.0003102240152657032,
0.026258815079927444,
-0.0042409044690430164,
0.03967740759253502,
0.04450109601020813,
0.07788936048746109,
-0.0407722070813179,
-0.03127352520823479,
-0.010591216385364532,
-0.09445322304964066,
-0.015795359387993813,
0.025520004332065582,
0.08394644409418106,
0.09772519022226334,
0.024355903267860413,
0.02260136790573597,
-0.026753295212984085,
-0.0154138607904315,
0.026896100491285324,
0.003768137888982892,
0.015757611021399498,
0.02094278298318386,
0.022937040776014328,
0.03521997854113579,
-0.01093786209821701,
0.034726038575172424,
-0.018445676192641258,
0.02938293293118477,
0.026923779398202896,
-0.04396674782037735,
0.007061480078846216,
0.013931318186223507,
0.0060118152759969234,
0.027989154681563377,
0.02317020855844021,
0.018499145284295082,
-0.022997528314590454,
-0.021106118336319923,
-0.007802130654454231,
-0.019458523020148277,
-0.0006910699303261936,
-0.06905551999807358,
-0.013991004787385464,
0.001543720019981265,
0.021934611722826958,
0.0038344881031662226,
-0.060767315328121185,
-0.000038692833186360076,
0.031531449407339096,
0.020704369992017746,
-0.018345553427934647,
0.05774873495101929,
0.06028291583061218,
0.0433543398976326,
0.036746297031641006,
0.007601544726639986,
0.029780138283967972,
0.030382083728909492,
0.005972240585833788,
-0.0007682484574615955,
-0.011033025570213795,
0.045725904405117035,
0.014255627989768982,
0.005007671657949686,
-0.03951673582196236,
-0.024380089715123177,
0.004959532059729099,
0.016553711146116257,
0.0090715317055583,
-0.07286076992750168,
-0.04687339812517166,
-0.028110353276133537,
0.011642152443528175,
-0.001455417019315064,
-0.037937525659799576,
0.018722837790846825,
-0.07088041305541992,
0.048903677612543106,
-0.03001859411597252,
0.04870867356657982,
0.06152407452464104,
0.022634383291006088,
-0.0066646384075284,
-0.017265604808926582,
-0.011883885599672794,
-0.027110856026411057,
-0.07566497474908829,
-0.03490084037184715,
-0.03994986042380333,
0.01904701255261898,
0.006370672024786472,
0.04677874594926834,
0.06372269988059998,
-0.009785372763872147,
-0.11118578165769577,
0.07466425001621246,
-0.05482489615678787,
-0.04506149888038635,
0.01550353318452835,
-0.03384273499250412,
0.027561601251363754,
0.0742984488606453,
0.024844536557793617,
0.009240471757948399,
0.004257104359567165,
-0.07911534607410431,
-0.057374559342861176,
0.025790490210056305,
-0.04036535322666168,
-0.05237779766321182,
-0.00008530743070878088,
0.006156515330076218,
-0.0496256984770298,
0.008532453328371048,
0.02272825688123703,
-0.009289954788982868,
0.02228100225329399,
0.018971791490912437,
-0.024172911420464516,
-0.027411531656980515,
-0.028053533285856247,
-0.0017635051626712084,
0.03968067094683647,
-0.01556489896029234,
0.03574464097619057,
0.045565493404865265,
-0.042212486267089844,
-0.010991212911903858,
-0.0006850499776192009,
-0.033990707248449326,
-0.020625106990337372,
0.05511714145541191,
0.03929134085774422,
-0.03616572916507721,
0.005722250323742628,
-0.02136291190981865,
-0.0033852921333163977,
0.04693843424320221,
-0.017323514446616173,
-0.03470015898346901,
-0.060956574976444244,
-0.05108727142214775,
-0.007768822368234396,
0.0319669134914875,
-0.02194562368094921,
-0.004818009212613106,
-0.0004001701017841697,
-0.07383229583501816,
-0.0062033566646277905,
-0.04445714130997658,
-0.04227433726191521,
0.08525189757347107,
0.006422289181500673,
-0.029873421415686607,
0.012728328816592693,
-0.05694640055298805,
-0.038061730563640594,
0.01184751559048891,
-0.025864798575639725,
-0.01274897437542677,
0.04494224861264229,
0.008282257243990898,
-0.0013780792942270637,
-0.026666976511478424,
0.03617062792181969,
-0.04253115877509117,
0.02832437865436077,
0.009859886951744556,
0.04128120839595795,
0.005748489871621132,
0.059332866221666336,
-0.014888190664350986,
0.02523394301533699,
0.07503023743629456,
0.025753965601325035,
-0.002665358129888773,
0.03814786300063133,
0.04107094556093216,
0.049054451286792755,
0.015609732829034328,
-0.006981656886637211,
-0.010131264105439186,
0.03084936924278736,
-0.014937322586774826,
0.003490581177175045,
0.04942978918552399,
-0.005296590272337198,
-0.018487978726625443,
-0.0056502376683056355,
-0.0034721435513347387,
-0.06600445508956909,
0.00729873264208436,
0.06045598164200783,
-0.00593151431530714,
-0.043915875256061554,
0.04097341373562813,
0.029067380353808403,
0.001871130894869566,
0.02077646739780903,
-0.038109853863716125,
0.03189306706190109,
-0.02183135785162449,
0.01834247261285782,
-0.03407856076955795,
-0.009725533425807953,
-0.05675503611564636,
-0.04060622304677963,
0.011432564817368984,
0.008087915368378162,
0.01706918329000473,
0.07162430882453918,
-0.041958265006542206,
0.040168341249227524,
0.02706596814095974,
0.01480701845139265,
-0.012187929823994637,
0.04307061433792114,
-0.01001976802945137,
0.041545767337083817,
-0.007161097135394812,
0.012359485030174255,
-0.026919273659586906,
0.022514238953590393,
0.006391600705683231,
-0.010755147784948349,
-0.03641899302601814,
-0.04817609861493111,
-0.008357047103345394,
0.008766927756369114,
0.034159451723098755,
0.029013998806476593,
0.029820255935192108,
0.002631955314427614,
0.029497453942894936,
-0.02501305751502514,
-0.042809464037418365,
-0.023911260068416595,
-0.024419978260993958,
-0.005568970926105976,
-0.050903819501399994,
-0.039459507912397385,
-0.0024989007506519556,
-0.045329540967941284,
-0.01773254945874214,
0.014025313779711723,
0.005807047244161367,
0.008259383030235767,
-0.06732477247714996,
-0.02710539847612381,
-0.0026001876685768366,
0.04035152494907379,
0.01176280528306961,
0.026405127719044685,
0.0149727463722229,
0.0018855588277801871,
-0.03899234160780907,
0.04974132031202316,
-0.043292056769132614,
0.0019867620430886745,
-0.02293216995894909,
-0.027427390217781067,
0.01772039383649826,
0.008847703225910664,
-0.050602275878190994,
-0.0779879093170166,
-0.05150824412703514,
0.025977496057748795,
0.06287019699811935,
-0.04060254991054535,
0.02090218849480152,
-0.01744517683982849,
-0.03820944204926491,
-0.03590171039104462,
0.00939817912876606,
-0.02580450102686882,
-0.05515829846262932,
0.03553372621536255,
0.04527731239795685,
-0.017075929790735245,
-0.010259857401251793,
0.0012290800223127007,
0.018864404410123825,
-0.05585643649101257,
-0.008968246169388294,
-0.019265007227659225,
0.025270657613873482,
0.07068979740142822,
-0.046037014573812485,
0.02406613901257515,
-0.004276291932910681,
-0.031208982691168785,
0.05581394582986832,
0.0016497110482305288,
0.013137386180460453,
-0.015006017871201038,
0.016174793243408203,
-0.03252081200480461,
0.01706390641629696,
-0.00032227690098807216,
0.044530969113111496,
-0.03187083452939987,
-0.03259369730949402,
0.0001471642463002354,
-0.019925471395254135,
-0.09958251565694809,
-0.047053247690200806,
0.050131671130657196,
-0.05790981277823448,
0.017033668234944344,
-0.010382996872067451,
-0.01613914594054222,
-0.00744020938873291,
-0.048374954611063004,
-0.010659551247954369,
-0.0011205815244466066,
-0.048066940158605576,
-0.00019997553317807615,
-0.013417738489806652,
-0.04126545041799545,
-0.007267387583851814,
0.06603166460990906,
-0.046535395085811615,
-0.01050671935081482,
0.0672360435128212,
-0.004806546028703451,
-0.020665032789111137,
0.008724847808480263,
-0.058123838156461716,
0.007128722965717316,
-0.02706718258559704,
0.0003745504072867334,
0.006953428033739328,
0.00754943210631609,
-0.043721988797187805,
-0.02955949306488037,
0.02283223159611225,
0.023279638960957527,
0.07546018809080124,
-0.02033202350139618,
-0.07158641517162323,
-0.007452245336025953,
0.04022384434938431,
-0.02546524628996849,
0.05795576795935631,
-0.025298932567238808,
-0.012477708049118519,
-0.016624443233013153,
0.01595197059214115,
0.012549878098070621,
0.06213255599141121,
0.006862242706120014,
-0.029001519083976746,
0.005413143429905176,
0.055627256631851196,
0.03434412553906441,
0.05662180855870247,
-0.008146865293383598,
-0.08301053941249847,
0.0031934422440826893,
0.0029451458249241114,
0.04481331259012222,
-0.0014016529312357306,
0.03105057403445244,
-0.07122374325990677,
0.03110118955373764,
-0.07813450694084167,
0.0521625317633152,
-0.03253539651632309,
0.07955969870090485,
0.00628787511959672,
0.004271385725587606,
-0.012800303287804127,
-0.04634741693735123,
0.02021634206175804,
-0.03576282411813736,
-0.03560803085565567,
-0.03242203965783119,
0.05422776937484741,
0.02182263880968094,
0.010017369873821735,
0.0039835707284510136,
0.02108766883611679,
-0.029331255704164505,
0.021731408312916756,
-0.019908316433429718,
-0.00527609046548605,
-0.018004244193434715,
-0.0026633755769580603,
0.013051246292889118,
0.0016423669876530766,
-0.03120792657136917,
-0.00024253001902252436,
0.009054932743310928,
0.05041844770312309,
-0.028111431747674942,
-0.0049822102300822735,
0.020880866795778275,
-0.012816532514989376,
-0.0063985008746385574,
0.024923592805862427,
0.032123565673828125,
0.0002533314982429147,
-0.02444739267230034,
-0.019585948437452316,
-0.025742579251527786,
0.014868072234094143,
-0.026378128677606583,
-0.08308742195367813,
-0.005822140723466873,
-0.03034333512187004,
0.028092727065086365,
-0.009688664227724075,
0.04076708108186722,
0.028267692774534225,
0.046451032161712646,
0.020553292706608772,
0.019677646458148956,
-0.02645893581211567,
0.027873799204826355,
0.053890492767095566,
0.003544194856658578,
-0.0030157631263136864,
0.041954394429922104,
-0.039735157042741776,
-0.004482161719352007,
0.018338831141591072,
-0.016036713495850563,
-0.05670500546693802,
0.032073479145765305,
-0.016298944130539894,
-0.008906380273401737,
-0.055350832641124725,
-0.018336232751607895,
-0.02506551332771778,
0.05746841803193092,
0.0544695146381855,
0.012494063936173916,
0.057790935039520264,
-0.00897749699652195,
-0.018664438277482986,
-0.056249216198921204,
0.02239355631172657,
0.0006097191944718361,
0.017008010298013687,
0.009587808512151241,
-0.0685688853263855,
-0.011612468399107456,
-0.004882128909230232,
0.012721260078251362,
0.01626521721482277,
0.04647088050842285,
0.009871994145214558,
0.003043732140213251,
-0.0062515996396541595,
0.026966897770762444,
0.00788562186062336,
-0.026400048285722733,
0.012187200598418713,
0.02065354213118553,
0.020354438573122025,
0.034957338124513626,
-0.02231205441057682,
0.030872702598571777,
0.011065313592553139,
-0.03531436622142792,
-0.022077446803450584,
0.05024607479572296,
0.03695739060640335,
0.030158519744873047,
-0.030050795525312424,
-0.0036087180487811565,
-0.05012063309550285,
0.04432639852166176,
-0.008269617334008217,
0.006461746525019407,
-0.019045043736696243,
-0.05147268623113632,
0.01358263473957777,
-0.02007065713405609,
-0.004137602634727955,
-0.016244323924183846,
-0.04554058611392975,
0.02223590388894081,
0.000039923132135299966,
-0.014370505698025227,
0.04462183266878128,
0.008531447499990463,
-0.04595595970749855,
0.011558952741324902,
-0.057677265256643295,
-0.008061661384999752,
0.0030889511108398438,
-0.04267103597521782,
-0.03163759410381317,
-0.06302931159734726,
-0.06883799284696579,
0.015292350202798843,
0.015290513634681702,
0.011193914338946342,
-0.030634084716439247,
0.008010154590010643,
0.009322481229901314,
0.045491717755794525,
0.028987517580389977,
0.03148350864648819,
-0.05051471292972565,
-0.03528759628534317,
-0.016459986567497253,
0.01191363763064146,
0.017711680382490158,
-0.004433618858456612,
0.02084905095398426,
-0.13926319777965546,
-0.02396479994058609,
-0.002544977469369769,
-0.010477682575583458,
-0.09303586930036545,
-0.001637089648284018,
0.055419813841581345,
-0.02415914088487625,
0.0031193101312965155,
0.04723145067691803,
-0.007570382207632065,
0.0585043802857399,
-0.029092619195580482,
-0.03875302895903587,
0.03953166678547859,
-0.020232317969202995,
0.005925736390054226,
0.024228345602750778,
0.036004438996315,
0.030178962275385857,
0.009956513531506062,
-0.009562330320477486,
0.04716653749346733,
-0.07168149948120117,
-0.035536352545022964,
0.020854651927947998,
0.02348150685429573,
0.01067159790545702,
0.036592256277799606,
0.0234189685434103,
0.01888873800635338,
0.00973525084555149,
-0.05715113505721092,
0.034381166100502014,
0.053310975432395935,
-0.03261030092835426,
0.02552221156656742,
0.04614592343568802,
-0.015862734988331795,
0.019946660846471786,
0.04826413094997406,
0.010233159177005291,
0.006882541812956333,
0.02374926395714283,
-0.05215271934866905,
-0.04686465486884117,
0.06313584744930267,
-0.03949403762817383,
-0.016243575140833855,
-0.004748835228383541,
-0.012857158668339252,
0.03806280344724655,
0.006742756813764572,
-0.007909959182143211,
-0.030363110825419426,
0.018875323235988617,
-0.014735043048858643,
-0.021142566576600075,
0.010626300238072872,
0.06054786220192909,
-0.007851838134229183,
-0.10670193284749985,
-0.003289031097665429,
0.03404152765870094,
-0.0185718834400177,
-0.13357695937156677,
0.04360169917345047,
0.06844675540924072,
0.00830893125385046,
-0.03143550083041191,
-0.010805844329297543,
-0.016093425452709198,
-0.013099207542836666,
0.047774914652109146,
0.004255861509591341,
-0.05380912870168686,
0.03928004577755928,
0.023532159626483917,
-0.02605951577425003,
0.014544853940606117,
0.019074266776442528,
-0.012446259148418903,
0.05288277193903923,
-0.005268627777695656,
-0.13136085867881775,
0.009192902594804764,
0.02166000008583069,
-0.010490898974239826,
-0.011291480623185635,
-0.017741143703460693,
-0.002948477165773511,
0.05574924871325493,
-0.03282633051276207,
0.000663017388433218,
-0.007661421783268452,
0.013448710553348064,
0.024451779201626778,
-0.019404737278819084,
0.04099555313587189,
-0.005278110038489103,
-0.03783884271979332,
-0.0678735300898552,
0.03416260704398155,
0.025952864438295364,
-0.05705934390425682,
-0.027227630838751793,
0.015079963020980358,
0.0034024445340037346,
0.01879669725894928,
0.04474335163831711,
-0.03625362366437912,
0.02822663076221943,
-0.011895287781953812,
-0.0035047053825110197,
0.027183208614587784,
0.00006364280125126243,
0.08381208032369614,
0.0426204688847065,
-0.010008555836975574,
-0.004523521289229393,
0.007033251225948334,
0.00502764480188489,
-0.015871742740273476,
0.00273833516985178,
-0.09069342166185379,
0.03236650675535202,
-0.008655915036797523,
0.06678085029125214,
0.002477069618180394,
-0.021628979593515396,
-0.03130055218935013,
0.04566686600446701,
0.016306057572364807,
-0.019366873428225517,
-0.06305000931024551,
0.05735582113265991,
-0.005949797574430704,
0.00203268276527524,
-0.0004588073934428394,
-0.04938589408993721,
-0.04596822336316109,
-0.03652024641633034,
-0.01560627669095993,
-0.03642438352108002,
0.03897314891219139,
-0.03214382380247116,
0.03746043145656586,
-0.08111634105443954,
-0.0033529321663081646,
-0.04329070821404457,
0.005342773627489805,
-0.03372775763273239,
0.025963418185710907,
-0.045607421547174454,
-0.02164321392774582,
-0.023678408935666084,
-0.040158748626708984,
-0.010564880445599556,
0.0042066751047968864,
-0.0010222317650914192,
-0.05496948957443237,
-0.023545170202851295,
-0.0023745582439005375,
0.039686791598796844,
0.05207321047782898,
0.03660516440868378,
-0.035199131816625595,
0.044021036475896835,
0.05536581575870514,
-0.028178852051496506,
0.06415144354104996,
0.04960813373327255,
-0.003879350842908025,
0.033850014209747314,
-0.027800332754850388,
-0.02032228745520115,
0.0055444082245230675,
-0.052756138145923615,
-0.029983945190906525,
0.04364480823278427,
0.03417029604315758,
0.007574192248284817,
-0.037173230201005936,
-0.02761002443730831,
0.0008855988271534443
] |
<p>I'm currently taking a high school physics class and we're doing friction problems now. I've been doing the ones that use MKS perfectly well, but when the problems start to use the FPS system, I'm always getting a relative error of around 12%. This mostly stems from my not knowing how to deal with FPS using the $ F = ma $ formula. I've tried converting FPS to MKS for it, but it still ends up with a large relative error.</p>
<p>How do I apply the FPS system to a formula like $ F = ma $ that is defined using MKS units and why? For the why, I'm just wondering if I'm to consider pounds when used in a physics problem at my level as a force unit and my mistakes are just the results of not using proper significant figures, or am I supposed to convert to MKS force units? If I'm to convert to MKS units, is using the rate of 4.44822162 (NIST) lbf to one Newton appropriate?</p>
<p>Thank you for reading my question, I hope I'm not skirting on the edge of the rules too much. I tried consulting Google and searching this site for related questions, but I guess the answer is obvious and I can't see it :(</p>
<p><strong>EDIT:</strong> <br /> Here are two problems that display my attempt to convert, then plug in the values, and my attempt to just use the values as-is then plug in.</p>
<p><strong>Problem 1</strong> <br /> "A horizontal force of 6 lbs is applied to a 10 lb block which moves along a horizontal surface. If the coefficient of kinetic friction is 0.4, determine the acceleration of the block. <strong>($a = 6.4 ft/s^2$)</strong>" <br /><br />
<strong>$F_N$</strong> = Normal Force, <strong>$F_k$</strong> = Kinetic Friction Force, <strong>$F_h$</strong> = Forward Force, <strong>$F_w$</strong> = Weight Force <br /><br /><br />
$F_h = 6 lb$ <br />
$F_h = 6 lb * 4.44822162$ (conversion factor to Newtons) <br />
$F_h = 26.69 N$ <br /> <br />
$F_w = 10 lb$ <br />
$F_w = 10 lb * 4.44822162$ (conversion factor to Newtons) <br />
$F_w = 44.48 N$<br /> <br />
$F_w = mg$ <br />
$44.48 N = m * 9.8 m/s^2$ <br />
$m = 4.54 kg$ <br /> <br />
$μ_k = \frac{F_k}{F_N}$ <br /><br />
$0.4 = \frac{F_k}{44.48 N}$ <br /> <br />
$F_k = 17.79N$<br /><br /><br />
$-F_k + F_h = ma$ <br />
$-17.79 N + 26.69 N = 4.54 kg * a$<br />
$a = 4.54 m/s^2$<br /><br />
Need to convert now...<br /><br />
<strong>Final:</strong> $a = 14.89 ft/s^2$
<br /><br /><br /></p>
<p>There's another problem where I just directly put in the FPS values without converting, but if this method is right, there's no point in posting it. If this method is wrong, I'll write it out here.</p> | g7859 | [
0.0372992567718029,
0.019901109859347343,
0.017227083444595337,
-0.017933864146471024,
0.033592864871025085,
-0.011115293949842453,
0.038548171520233154,
0.026818489655852318,
-0.04164912551641464,
-0.01859002560377121,
0.01753942482173443,
-0.023122964426875114,
0.022800633683800697,
0.0303021427243948,
-0.0029403818771243095,
0.03864971548318863,
0.04685346409678459,
-0.017442557960748672,
0.024657873436808586,
0.0364350900053978,
-0.05799093097448349,
0.021961351856589317,
-0.07559914141893387,
-0.05455004423856735,
0.03678051382303238,
-0.011607066728174686,
-0.02530256286263466,
-0.008821739815175533,
-0.02741018868982792,
0.027440739795565605,
-0.0010411599650979042,
-0.001029033213853836,
0.04437396675348282,
-0.053794603794813156,
-0.059239163994789124,
-0.009070738218724728,
0.04356544464826584,
0.0031438330188393593,
0.016771459951996803,
-0.08344465494155884,
0.043355610221624374,
-0.07591564208269119,
0.014841889031231403,
0.01573215052485466,
-0.031137533485889435,
-0.0167107991874218,
-0.03420909494161606,
-0.03952055424451828,
-0.03766649588942528,
0.047007005661726,
-0.015016373246908188,
0.048485420644283295,
0.033836834132671356,
0.0360979288816452,
-0.02993731200695038,
0.05665673315525055,
0.012582282535731792,
-0.028249774128198624,
0.0357198603451252,
0.023594459518790245,
0.0013130075531080365,
0.003132560756057501,
0.026043929159641266,
-0.05498810112476349,
0.038495127111673355,
0.01475606020539999,
-0.03094896301627159,
0.04780919477343559,
-0.007868332788348198,
0.011241239495575428,
-0.02984234318137169,
0.029343346133828163,
0.019000662490725517,
0.01121061947196722,
-0.006530871614813805,
-0.018045533448457718,
0.0007512712618336082,
0.009306407533586025,
0.0398915633559227,
0.03949567303061485,
-0.007819926366209984,
0.04341486841440201,
0.042654287070035934,
-0.021737996488809586,
0.02181573025882244,
-0.025603288784623146,
0.0022335341200232506,
0.050493985414505005,
-0.0054017724469304085,
0.0033105455804616213,
-0.010124249383807182,
0.03850158676505089,
0.0835992693901062,
0.02770092338323593,
-0.010135025717318058,
0.005076117813587189,
-0.0036645582877099514,
0.04158538952469826,
0.037180088460445404,
0.017492854967713356,
-0.022346332669258118,
0.027473511174321175,
-0.023486075922846794,
-0.03437862917780876,
-0.00905738677829504,
-0.048229869455099106,
0.06273473799228668,
0.10512097924947739,
-0.02876575104892254,
-0.02414500154554844,
-0.007310505956411362,
0.002997897332534194,
-0.0021648250985890627,
-0.012139666825532913,
-0.031152816489338875,
-0.013611454516649246,
0.007366613019257784,
-0.007606779225170612,
-0.03332838416099548,
0.028752829879522324,
0.010175872594118118,
-0.025702599436044693,
0.041728097945451736,
0.017518140375614166,
-0.024170735850930214,
-0.056125201284885406,
0.02065497636795044,
-0.02186213806271553,
0.08716113865375519,
-0.022345654666423798,
0.004421750083565712,
-0.018660644069314003,
-0.014528722502291203,
-0.054488878697156906,
-0.028268495574593544,
0.09043128788471222,
-0.008592607453465462,
0.02186432294547558,
0.0083551537245512,
-0.002605411456897855,
-0.022655829787254333,
-0.04499341920018196,
0.0019191490719094872,
-0.031965043395757675,
-0.0512138232588768,
0.05012600123882294,
-0.0692409873008728,
-0.03689653053879738,
0.0909126028418541,
-0.0019920533522963524,
0.02730058692395687,
0.04397035390138626,
-0.0377148762345314,
-0.009061653167009354,
0.04345540329813957,
-0.013876952230930328,
0.055581048130989075,
0.03527761995792389,
0.01648261770606041,
-0.007432613521814346,
0.06180683150887489,
-0.011889937333762646,
0.03624691814184189,
-0.0024300895165652037,
-0.04076503589749336,
0.024757124483585358,
-0.04111483320593834,
-0.03160373494029045,
0.04252185672521591,
-0.011352808214724064,
-0.07143710553646088,
-0.03944031149148941,
0.0392470508813858,
-0.002960901940241456,
-0.02548096887767315,
-0.010069728828966618,
0.06306297332048416,
0.01062893308699131,
0.04902322590351105,
0.001912695006467402,
0.021931229159235954,
-0.004685496911406517,
0.054110635071992874,
0.021331828087568283,
-0.04072161763906479,
0.04967226833105087,
0.016044851392507553,
0.06281010806560516,
-0.0535324327647686,
0.010546471923589706,
-0.04586508497595787,
-0.018933091312646866,
0.016783244907855988,
0.031499918550252914,
-0.006136318668723106,
0.05286284163594246,
-0.06523913890123367,
-0.059424083679914474,
-0.04780493304133415,
0.00597729254513979,
-0.011503896676003933,
0.054325565695762634,
0.02924673818051815,
0.031246012076735497,
0.05337097868323326,
0.026937922462821007,
-0.009206577204167843,
0.0017820275388658047,
0.015398943796753883,
0.016159210354089737,
0.008138415403664112,
0.033818308264017105,
-0.01828443817794323,
0.0635923221707344,
-0.023081280291080475,
-0.034195736050605774,
-0.033811382949352264,
-0.006718199700117111,
-0.047436900436878204,
0.05580642819404602,
-0.035358890891075134,
-0.004420046228915453,
0.029238566756248474,
0.027218785136938095,
-0.044175222516059875,
-0.034370504319667816,
-0.03785109519958496,
0.007455057464540005,
-0.004806686658412218,
0.021053627133369446,
-0.043218255043029785,
0.04325878620147705,
0.0031479760073125362,
0.04554861783981323,
0.03198924660682678,
0.06451302766799927,
-0.0043989489786326885,
0.022717811167240143,
0.01030630711466074,
0.05060195177793503,
0.025030039250850677,
-0.050799380987882614,
-0.01100904680788517,
-0.029528053477406502,
-0.013271085917949677,
-0.018166031688451767,
0.029832562431693077,
0.01730957441031933,
-0.016633694991469383,
0.001265111262910068,
-0.056105539202690125,
-0.0090598464012146,
-0.027702737599611282,
-0.0001252184301847592,
0.012215771712362766,
0.037760648876428604,
-0.07013574242591858,
0.0034265557769685984,
-0.0008708331151865423,
0.006380071863532066,
0.015608237124979496,
0.020320504903793335,
-0.03239556401968002,
0.057815201580524445,
-0.044791825115680695,
0.019244972616434097,
-0.08126082271337509,
-0.0008384433458559215,
0.053981050848960876,
0.02389434352517128,
0.030663371086120605,
0.005882057826966047,
0.05880553647875786,
0.04779532924294472,
0.03827739879488945,
-0.02128228172659874,
0.039779018610715866,
-0.01615111343562603,
0.0034899613820016384,
0.01842537894845009,
-0.030656753107905388,
-0.026798173785209656,
0.06217818707227707,
-0.012671612203121185,
0.010924197733402252,
-0.0610833466053009,
0.03852017596364021,
0.052988264709711075,
0.015149063430726528,
0.019794100895524025,
-0.020324552431702614,
0.0279864352196455,
0.029583275318145752,
0.0032411273568868637,
-0.00024799341917969286,
0.053990136831998825,
0.051777854561805725,
-0.05670697242021561,
-0.03176786005496979,
0.015123764052987099,
0.07031182944774628,
-0.028253912925720215,
0.014276063069701195,
0.025870995596051216,
0.006931803189218044,
0.03760349377989769,
0.013137218542397022,
-0.01017368957400322,
0.00659051351249218,
0.015196718275547028,
-0.013899791054427624,
0.037448618561029434,
0.04005195572972298,
-0.0016361643793061376,
-0.07426264882087708,
-0.058351971209049225,
0.023259680718183517,
0.007871060632169247,
-0.018231837078928947,
0.00592401809990406,
-0.02042960748076439,
-0.09085868299007416,
0.05321848765015602,
0.0005853797774761915,
-0.0013773604296147823,
0.044952765107154846,
-0.05399109423160553,
-0.049757394939661026,
0.040038082748651505,
-0.004947375971823931,
0.004025210626423359,
-0.004014570731669664,
0.005424715578556061,
-0.023306159302592278,
-0.09515853226184845,
-0.020722197368741035,
-0.024217482656240463,
-0.018200121819972992,
-0.028146469965577126,
-0.03485196828842163,
-0.029641658067703247,
-0.006473663728684187,
-0.02518591843545437,
0.007643272168934345,
-0.021671203896403313,
0.004117853473871946,
0.03055291250348091,
-0.009394817054271698,
-0.022690465673804283,
-0.049946729093790054,
0.008561348542571068,
0.03580636903643608,
0.014053371734917164,
0.011559228412806988,
-0.0012326419819146395,
0.010065747424960136,
0.03362911567091942,
0.03521352261304855,
-0.03815412521362305,
0.008722877129912376,
0.0035141247790306807,
0.006199612747877836,
-0.04456664249300957,
0.05187947303056717,
-0.026651158928871155,
0.051471248269081116,
0.00038056776975281537,
0.04533873498439789,
-0.043600790202617645,
-0.06831100583076477,
0.002095994306728244,
-0.025924477726221085,
0.07098902016878128,
-0.06270623952150345,
-0.005541153252124786,
-0.05614161863923073,
0.009733757004141808,
-0.0341939702630043,
0.0006518024601973593,
-0.006261425092816353,
-0.0017078326782211661,
0.039509087800979614,
-0.07153645157814026,
0.025406740605831146,
0.031280335038900375,
0.004361139610409737,
-0.04657658562064171,
-0.016122346743941307,
0.05733463168144226,
0.02796885371208191,
-0.00622576242312789,
-0.035968780517578125,
-0.046847596764564514,
0.02881670743227005,
0.001800279482267797,
-0.05304858833551407,
0.03162984177470207,
0.016911732032895088,
0.006745229009538889,
0.004020520485937595,
-0.00047330278903245926,
0.0233309306204319,
0.004458701238036156,
0.032026078552007675,
-0.026249181479215622,
-0.021686976775527,
-0.008056184276938438,
0.0064021991565823555,
0.03158950433135033,
0.056815844029188156,
-0.0009646984399296343,
-0.06783843785524368,
0.014387897215783596,
-0.04494502767920494,
-0.031786199659109116,
0.0049511282704770565,
-0.027083994820713997,
0.022610407322645187,
0.021672898903489113,
-0.053466685116291046,
0.0049847825430333614,
0.09394717216491699,
-0.011479283683001995,
-0.013254856690764427,
0.02402765490114689,
0.002742029959335923,
0.05620069429278374,
0.040754999965429306,
0.0681607574224472,
-0.02592439204454422,
-0.009899823926389217,
0.07470132410526276,
0.027753733098506927,
0.006884157657623291,
-0.00915142148733139,
0.05871136859059334,
-0.02913372591137886,
-0.06588953733444214,
0.037920959293842316,
0.03212389349937439,
-0.03094629943370819,
0.018271522596478462,
-0.02510269172489643,
-0.02232394367456436,
-0.04577634111046791,
-0.001562320627272129,
0.004384628497064114,
-0.03144843876361847,
-0.02189866080880165,
-0.04959217458963394,
-0.024757688865065575,
-0.0336679108440876,
-0.037227798253297806,
-0.02180255576968193,
-0.01047012209892273,
0.008332885801792145,
0.007183170411735773,
0.005898551549762487,
-0.006868478376418352,
0.013596163131296635,
0.020098578184843063,
0.04147917032241821,
-0.02681294083595276,
-0.018613336607813835,
-0.06149758771061897,
-0.01301982905715704,
-0.017160210758447647,
0.02024177275598049,
-0.04909290745854378,
-0.015350503847002983,
0.030014486983418465,
-0.08773494511842728,
0.027508515864610672,
-0.003780106781050563,
0.0627702996134758,
0.048195429146289825,
0.015040621161460876,
-0.0185512937605381,
0.05211348831653595,
-0.038304537534713745,
-0.0046989694237709045,
-0.007602544501423836,
0.018595468252897263,
0.0020635684486478567,
-0.030113711953163147,
0.038525380194187164,
0.003432283876463771,
0.0003791032650042325,
0.027536774054169655,
-0.02523736096918583,
0.06112314760684967,
0.024228723719716072,
-0.012962608598172665,
-0.03471743315458298,
0.02313130348920822,
0.04499059543013573,
0.01694655790925026,
0.01198603492230177,
0.015317792072892189,
0.005928438622504473,
-0.042352210730314255,
-0.0014248953666538,
-0.02183937095105648,
0.013365712948143482,
0.040090762078762054,
-0.01878313161432743,
0.05614318326115608,
-0.002397810574620962,
0.0268877986818552,
0.02958165854215622,
0.05171504244208336,
0.05805644020438194,
0.07811379432678223,
-0.04383307695388794,
-0.051714543253183365,
-0.029543429613113403,
0.03841093182563782,
0.03485622629523277,
-0.05615511164069176,
-0.048849400132894516,
0.07337475568056107,
-0.010553736239671707,
-0.009511863812804222,
0.02288190647959709,
0.0021804836578667164,
0.0027431303169578314,
0.028897736221551895,
-0.05273447930812836,
-0.05426802858710289,
-0.011349874548614025,
-0.057548146694898605,
-0.052643999457359314,
0.02049282193183899,
0.022595679387450218,
0.014493328519165516,
-0.03720374405384064,
0.03784194961190224,
-0.06377533823251724,
0.003734266385436058,
-0.08468221127986908,
-0.027989855036139488,
0.010539868846535683,
-0.011240323074162006,
-0.008287462405860424,
-0.08076918125152588,
0.018318668007850647,
0.020003434270620346,
-0.046533286571502686,
-0.006398594006896019,
-0.049953360110521317,
-0.06704328209161758,
0.06838046759366989,
-0.01790221966803074,
-0.09620905667543411,
-0.00055972661357373,
0.027241993695497513,
-0.0797424167394638,
-0.04268382862210274,
0.004479008261114359,
-0.008793395012617111,
0.05776498094201088,
-0.018107758834958076,
0.03199921175837517,
0.047363366931676865,
0.046417105942964554,
-0.0629536360502243,
0.013377801515161991,
0.023366905748844147,
0.0068699633702635765,
0.011860906146466732,
-0.07182831317186356,
0.0022157218772917986,
-0.04917178303003311,
0.03587322309613228,
0.030027730390429497,
0.013156672939658165,
-0.02678907848894596,
-0.0386287122964859,
0.029072230681777,
0.041603319346904755,
-0.0021997622679919004,
0.0014839053619652987,
-0.024221433326601982,
-0.04130931571125984,
-0.053614769130945206,
0.02157784067094326,
-0.03605244681239128,
0.0027492402587085962,
-0.03053201176226139,
-0.033447667956352234,
-0.03357645124197006,
0.01839294843375683,
-0.029959475621581078,
0.023603476583957672,
0.022260380908846855,
-0.011533890850841999,
-0.014148526825010777,
-0.017977377399802208,
0.014819596894085407,
-0.014646409079432487,
0.03440409526228905,
0.038942791521549225,
0.022261694073677063,
-0.06525134295225143,
-0.030510304495692253,
-0.02563762106001377,
-0.013688724488019943,
0.02896297350525856,
-0.02841397374868393,
0.04779801890254021,
0.016356611624360085,
0.032323479652404785,
-0.021124711260199547,
0.03470684960484505,
0.03710583224892616,
-0.0157635398209095,
0.060867566615343094,
-0.0307293850928545,
-0.035970546305179596,
-0.025795133784413338,
-0.013090036809444427,
-0.015296160243451595,
0.028326481580734253,
-0.04178129509091377,
0.007834112271666527,
-0.005816682707518339,
-0.023077018558979034,
0.07394501566886902,
0.04210268706083298,
0.010197438299655914,
0.055364321917295456,
-0.013054863549768925,
-0.02180640958249569,
-0.021345697343349457,
-0.042551685124635696,
0.09135258942842484,
-0.0077917370945215225,
0.02719525806605816,
0.03791853040456772,
0.040658608078956604,
-0.05928860232234001,
-0.017584210261702538,
0.00431408453732729,
0.0031713140197098255,
-0.036109283566474915,
-0.027990806847810745,
0.031085681170225143,
0.02840414084494114,
-0.08740909397602081,
0.0417323112487793,
-0.036159683018922806,
-0.032503630965948105,
0.004839766770601273,
0.007024602498859167,
0.0038588063325732946,
0.05198043957352638,
-0.010187077336013317,
0.049270473420619965,
0.07414503395557404,
-0.0127664590254426,
0.0011359869968146086,
-0.06097360700368881,
0.018748044967651367,
-0.0002452745393384248,
-0.01670226640999317,
0.04845616966485977,
-0.02778170071542263,
0.021268123760819435,
0.023021772503852844,
-0.021094363182783127,
0.027109479531645775,
-0.0408247709274292,
-0.0024383137933909893,
0.04136108607053757,
0.034785278141498566,
0.030039474368095398,
0.00045007880544289947,
0.0026584514416754246,
0.007300680503249168,
0.0281248576939106,
-0.03366153687238693,
0.038917358964681625,
-0.040372591465711594,
0.019853144884109497,
0.00028672159533016384,
-0.04284613952040672,
-0.05238908901810646,
0.0021259256172925234,
0.040908679366111755,
-0.024725256487727165,
-0.004028692841529846,
0.09225690364837646,
0.02213672734797001,
0.01776880957186222,
0.0023664713371545076,
-0.01515271794050932,
0.051022399216890335,
0.04828818514943123,
0.0754585862159729,
-0.007581420708447695,
0.011164434254169464,
-0.006218037102371454,
-0.04106590896844864,
0.008062753826379776,
0.03172122687101364,
0.038088031113147736,
-0.0469687357544899,
-0.027796506881713867,
-0.05812479928135872,
0.01024589128792286,
-0.015682168304920197,
0.014046155847609043,
-0.0014798903139308095,
0.023653240874409676,
0.033427201211452484,
0.03161189332604408,
-0.008431275375187397,
0.004416567739099264,
-0.01850840263068676,
-0.04176071286201477,
0.0017999844858422875,
-0.03768504410982132,
-0.02709531970322132,
-0.04114506393671036,
-0.030335722491145134,
-0.07805593311786652,
0.014419877901673317,
-0.048707082867622375,
-0.0792095735669136,
-0.041624560952186584,
-0.021139618009328842,
-0.07512117922306061,
-0.000441196869360283,
0.05172758176922798,
-0.05417345464229584,
-0.041011516004800797,
-0.02897133305668831,
-0.020669028162956238,
-0.04327782243490219,
0.1015564426779747,
-0.033781591802835464,
-0.035909175872802734,
-0.027755318209528923,
0.01657286286354065,
0.016741979867219925,
-0.03730100393295288,
-0.05425631254911423,
0.08759313821792603,
-0.017030980437994003,
-0.022334707900881767,
0.01882639154791832,
0.031117243692278862,
-0.03139910101890564,
-0.03826531395316124,
-0.03348476067185402,
-0.03975745290517807,
-0.0079201003536582,
0.018617896363139153,
0.0009277507779188454,
-0.02576473355293274,
0.0077218771912157536,
0.008200163953006268,
-0.03711314871907234,
0.008375504054129124,
0.05202474817633629,
-0.08649523556232452,
-0.04941560700535774,
0.031840529292821884
] |
<p>I found a really cool sounding order-of-magnitude modeling question but am a bit at a loss on how to approach this:</p>
<blockquote>
<p>The Milky Way contains 100 billion stars and has a radius of 250,000 light years. Suppose that humans set a long term goal to colonize every inhabitable star system in the Milky Way and that 10% of star systems are suitable. This colonization might be accomplished by sending out a ship of settlers to a nearby solar system, establishing a colony, and then waiting long enough - 500 years? - for the colony to develop enough that it can send its own settler ships. Do an order of magnitude estimate of how long it would take to colonize the galaxy, explaining any assumptions you make.</p>
</blockquote>
<p>My first assumption is to put our solar system into the center of the galaxy with the argument that this makes calculations more symmetric, assuming that it will change the results by a factor of order 1. (I'm shorter away from the "ends" of the solar system but I benefit more from the hopefully exponential growth). </p>
<p>Now the question is how to model things further. A crude estimate of the average distance between inhabitable star systems tells me that they are about 5 light years apart from each other. I guess since 5 is much smaller than 250,000 I could move to some sort of continuum description of colonization progress, but then I'm not sure on how to proceed from there. </p>
<p>Another important question would be the speed of my colony ships. I guess it should be at least on the order of the escape velocity of the earth-sun-system, so again using crude estimates I'll get something like $5\cdot 10^4\, \mathrm{m}/\mathrm{s}$ which means that a ship needs about 5000 years for a journey.</p>
<p>If the time per journey was significantly larger than the time to prepare the next ship (500 years), I guess I could ignore the 500 year delay and assume instant readiness, but that doesn't seem to be appropriate here. And if I don't do that, then the process seems a bit tricky: During the 5000 year journey of the first ship, I can produce 10 additional ships and send them to a journey, i.e., growth of colonized space is not just proportional to the number of fringe systems but depends in a non-obvious complicated way on the number of colonized planets AND when they were colonized. (Similar to "broadcasting in networks" scenarious?)</p>
<p>Maybe someone immediately recognizes a commonly used underlying model that is appropriate here? </p>
<p>PS: I'm open for suggestions re tags.</p> | g7860 | [
-0.026653742417693138,
0.0785008892416954,
0.023726878687739372,
-0.07762821763753891,
-0.026973459869623184,
-0.04603688418865204,
0.01521726232022047,
-0.007662198506295681,
-0.01609473116695881,
-0.023024460300803185,
0.02241307497024536,
0.053049374371767044,
0.07607563585042953,
0.011944099329411983,
0.03992456570267677,
-0.01168115995824337,
0.026602808386087418,
-0.023330507799983025,
-0.0027816349174827337,
0.054827358573675156,
0.041933223605155945,
-0.015540776774287224,
0.02649848908185959,
-0.011838733218610287,
-0.08642551302909851,
-0.013378472067415714,
0.06694254279136658,
-0.009301546029746532,
-0.010248038917779922,
-0.060044098645448685,
-0.008039894513785839,
-0.012433820404112339,
0.024934981018304825,
-0.04458412900567055,
-0.09263890981674194,
-0.0025429553352296352,
-0.022077905014157295,
-0.006865642033517361,
0.011781693436205387,
-0.028805024921894073,
0.048298489302396774,
-0.05072483420372009,
0.03736869990825653,
0.005338815040886402,
0.06984704732894897,
-0.002388820517808199,
0.01180275622755289,
-0.06340085715055466,
0.05144382268190384,
0.0021962649188935757,
-0.015207912772893906,
0.04556930437684059,
-0.011394322849810123,
0.0428130105137825,
-0.06568741053342819,
0.07185214012861252,
-0.01381093543022871,
-0.08150062710046768,
0.02206679806113243,
-0.021734442561864853,
0.01766558550298214,
-0.015069830231368542,
0.027120904996991158,
-0.026093613356351852,
0.021167971193790436,
0.061873212456703186,
0.003213713876903057,
0.04137303680181503,
0.0362304262816906,
-0.06179054081439972,
0.010792193002998829,
-0.07092183083295822,
-0.006576580461114645,
-0.07001611590385437,
-0.0720357745885849,
0.0461396686732769,
-0.03284153714776039,
-0.015313021838665009,
-0.0020423023961484432,
0.06896562874317169,
0.01136824395507574,
0.01794806867837906,
0.032316844910383224,
0.03546329587697983,
0.00815504975616932,
0.00043709849705919623,
-0.036501966416835785,
-0.08247324824333191,
0.007389903999865055,
0.0022400973830372095,
-0.007380293216556311,
0.03980627655982971,
0.0076232245191931725,
-0.01554618775844574,
-0.01415256131440401,
0.029099764302372932,
-0.05630752444267273,
0.0001975302875507623,
0.013160666450858116,
0.009572269394993782,
-0.028306787833571434,
0.028725100681185722,
-0.0006888057105243206,
-0.04878082126379013,
-0.03927961736917496,
-0.013506618328392506,
0.04917670041322708,
0.05075240507721901,
0.05682406574487686,
-0.029022669419646263,
-0.011036907322704792,
-0.056530267000198364,
-0.0132962791249156,
-0.006331791169941425,
-0.030525237321853638,
-0.0076522380113601685,
0.02564948983490467,
0.044181372970342636,
-0.0019014875870198011,
0.053001027554273605,
0.045780256390571594,
-0.01259096059948206,
-0.033877529203891754,
-0.00899522751569748,
-0.0520736500620842,
-0.05302993208169937,
-0.025918224826455116,
0.03323300555348396,
0.00391318229958415,
0.03830743953585625,
0.01499873399734497,
0.031163902953267097,
0.009238325990736485,
0.02831573784351349,
-0.01885756477713585,
0.006017531733959913,
-0.0027172251138836145,
0.020842213183641434,
-0.022272661328315735,
0.025437310338020325,
0.0030305448453873396,
-0.03783461079001427,
0.04687107354402542,
-0.007513964548707008,
-0.07085815072059631,
0.052458878606557846,
0.02658236399292946,
-0.03723980486392975,
0.039648957550525665,
-0.03747533634305,
0.002452237531542778,
0.07547788321971893,
-0.04838620126247406,
0.006162860430777073,
-0.01621256209909916,
0.04638424143195152,
0.024126088246703148,
-0.045498304069042206,
-0.031682875007390976,
-0.01461167261004448,
-0.0018315977649763227,
-0.02107386663556099,
0.003283025464043021,
-0.01868298277258873,
-0.043429695069789886,
0.009151975624263287,
0.047551512718200684,
-0.11736011505126953,
-0.012806336395442486,
-0.011129201389849186,
-0.017582617700099945,
-0.023216716945171356,
0.061190199106931686,
0.048238325864076614,
-0.018748318776488304,
-0.007039150223135948,
0.11296238005161285,
-0.05301651731133461,
-0.04025319963693619,
0.00560398306697607,
0.036485571414232254,
-0.07256412506103516,
0.026620637625455856,
0.009691630490124226,
-0.009827460162341595,
-0.051405929028987885,
0.030178964138031006,
0.0210706889629364,
0.007761106360703707,
0.033136092126369476,
0.0038076890632510185,
0.0036096295807510614,
0.001273329951800406,
0.04410754516720772,
-0.04030470550060272,
-0.0046120393089950085,
0.03851870819926262,
-0.03715505078434944,
-0.03793174400925636,
-0.010278301313519478,
0.0023014347534626722,
0.056750692427158356,
-0.04530199617147446,
-0.0027195820584893227,
-0.017837798222899437,
0.007476198021322489,
-0.011842215433716774,
0.017556380480527878,
0.008151333779096603,
0.024793121963739395,
0.01320330984890461,
-0.08018322288990021,
-0.08021195977926254,
0.05175919830799103,
-0.025998083874583244,
-0.053286414593458176,
-0.03370407968759537,
0.04313543066382408,
0.040713466703891754,
-0.00856976117938757,
0.024051086977124214,
-0.03330564498901367,
0.06633447855710983,
0.014616342261433601,
0.020124180242419243,
-0.01636161096394062,
-0.005804309621453285,
-0.025934657081961632,
0.033298395574092865,
0.07212894409894943,
-0.01021512970328331,
0.02950405888259411,
0.006009232252836227,
-0.013694818131625652,
0.04923142492771149,
0.04494113102555275,
-0.006147244945168495,
-0.029797762632369995,
0.002352632349357009,
0.007866733707487583,
0.05270270258188248,
0.02371029742062092,
-0.008417283184826374,
0.0189844761043787,
-0.009264538995921612,
-0.10913542658090591,
0.03060929849743843,
-0.029033329337835312,
-0.03566184267401695,
0.037163667380809784,
0.017017444595694542,
0.013805083930492401,
0.032314930111169815,
-0.03895151615142822,
-0.0075937178917229176,
-0.05424903333187103,
0.03456966578960419,
0.08435739576816559,
-0.04823778197169304,
-0.004615864250808954,
-0.04308523237705231,
-0.04764414206147194,
0.0033649089746177197,
-0.012637191452085972,
0.03634841740131378,
-0.011874550022184849,
-0.014169341884553432,
-0.025554481893777847,
0.010225234553217888,
-0.027611078694462776,
-0.0023309176322072744,
-0.035600241273641586,
0.01990123651921749,
0.0389615036547184,
0.014087902382016182,
-0.008319768123328686,
0.011457321234047413,
-0.018772706389427185,
0.015355144627392292,
0.055423635989427567,
-0.009251133538782597,
-0.06331600248813629,
-0.04463904723525047,
0.03088366985321045,
0.026757756248116493,
-0.033639948815107346,
0.03403697907924652,
0.030819986015558243,
0.06911014765501022,
-0.0031457392033189535,
-0.004583626054227352,
0.006337634287774563,
0.008662090636789799,
0.03235824778676033,
0.004307706840336323,
0.06559888273477554,
-0.058495473116636276,
0.014738223515450954,
0.011181503534317017,
-0.025583453476428986,
0.03028317354619503,
-0.03291817754507065,
0.04693495109677315,
0.03203461319208145,
-0.019770296290516853,
0.009996353648602962,
-0.042702674865722656,
0.0054032327607274055,
-0.011492861434817314,
-0.068951815366745,
0.058433983474969864,
0.0392414927482605,
-0.05661246180534363,
-0.027935439720749855,
0.01880865916609764,
-0.0335005559027195,
0.023291219025850296,
0.024627940729260445,
0.010759808123111725,
-0.008892735466361046,
0.02346888743340969,
-0.046941205859184265,
-0.029323279857635498,
-0.004541768692433834,
0.004216431640088558,
0.05163571611046791,
-0.054289329797029495,
-0.0020911095198243856,
-0.04361230880022049,
0.019704533740878105,
0.03114699013531208,
0.0003219973004888743,
-0.04377027973532677,
0.013024447485804558,
0.016617655754089355,
-0.07713533937931061,
-0.0047829970717430115,
0.0018212308641523123,
0.03361598774790764,
0.049825266003608704,
-0.06319623440504074,
0.014183362014591694,
0.005544855259358883,
0.042753566056489944,
-0.004191860556602478,
-0.03122359700500965,
0.02672339417040348,
-0.0473935604095459,
-0.027849165722727776,
-0.03948631137609482,
0.02498180791735649,
-0.08472452312707901,
-0.008203865960240364,
-0.02653510496020317,
0.01996094547212124,
0.06870666891336441,
0.026263905689120293,
0.0401962511241436,
0.08318696171045303,
-0.021054046228528023,
0.025170529261231422,
0.013171978294849396,
0.023773379623889923,
0.06001156568527222,
0.015862202271819115,
-0.002840008120983839,
0.0652889758348465,
0.016613919287919998,
0.04712066054344177,
-0.05990578606724739,
-0.01667126454412937,
-0.03765915706753731,
-0.012288559228181839,
-0.04019017145037651,
0.03975248709321022,
-0.014959829859435558,
0.019042806699872017,
0.0026332337874919176,
-0.02307540737092495,
0.05764003470540047,
0.033284034579992294,
0.06593487411737442,
0.009645535610616207,
-0.03907904401421547,
0.022025011479854584,
0.011047246865928173,
0.01954759657382965,
-0.050422895699739456,
-0.015805726870894432,
-0.015178680419921875,
0.028689425438642502,
-0.08459646999835968,
-0.021259786561131477,
-0.02415190264582634,
0.0032023375388234854,
-0.012461692094802856,
0.010425110347568989,
0.029842576012015343,
0.023811200633645058,
-0.0067804413847625256,
0.00356369954533875,
-0.027528870850801468,
-0.016572361811995506,
0.017790459096431732,
-0.004486917518079281,
-0.013635019771754742,
-0.014377967454493046,
-0.012378414161503315,
-0.027383659034967422,
0.02613053098320961,
0.003708252217620611,
0.015418641269207,
0.016907811164855957,
-0.06132436543703079,
0.020479850471019745,
0.0018349619349464774,
0.05778469145298004,
-0.07461065798997879,
-0.005410971585661173,
0.0459502674639225,
-0.03359999880194664,
0.031534407287836075,
-0.02266533114016056,
-0.06898637861013412,
0.04532506316900253,
0.08881185203790665,
-0.053004857152700424,
0.0043264105916023254,
-0.0034586794208735228,
-0.016716308891773224,
0.024063358083367348,
0.06731845438480377,
0.012747843749821186,
0.03923821076750755,
-0.030634794384241104,
0.02976123057305813,
-0.0005652065156027675,
0.04807654395699501,
0.024603895843029022,
-0.047678012400865555,
-0.028380341827869415,
0.00748097151517868,
0.017597483471035957,
0.01129983738064766,
0.025095229968428612,
0.033884502947330475,
-0.017424730584025383,
-0.0331428200006485,
-0.0021597291342914104,
-0.02719903737306595,
0.07152292877435684,
0.015964286401867867,
-0.027345508337020874,
0.03363597020506859,
-0.003741249907761812,
-0.026497233659029007,
-0.025406351312994957,
-0.01121987123042345,
0.05896845832467079,
0.013244487345218658,
-0.0038965228013694286,
0.013941132463514805,
-0.029886415228247643,
-0.007076623383909464,
0.02449178136885166,
0.026139352470636368,
0.005264000501483679,
-0.009702123701572418,
-0.028043458238244057,
0.0761428251862526,
-0.04606292024254799,
0.0015243596863001585,
0.0397111251950264,
0.016305284574627876,
-0.08089550584554672,
0.07546673715114594,
-0.06749854236841202,
-0.005937076173722744,
0.030238496139645576,
0.007193731144070625,
-0.010885985568165779,
-0.06918635964393616,
-0.020360561087727547,
0.015552320517599583,
0.01941106468439102,
-0.009027079679071903,
-0.001389268203638494,
-0.0576014406979084,
0.010497501119971275,
0.011299758218228817,
-0.04889368265867233,
0.002928447909653187,
0.009782712906599045,
0.042375512421131134,
-0.026489268988370895,
-0.0012631386052817106,
-0.020354386419057846,
-0.052077844738960266,
0.022805603221058846,
-0.026305528357625008,
-0.01191377267241478,
0.11406650394201279,
0.03541896492242813,
-0.03565368801355362,
-0.0369073711335659,
0.022702939808368683,
0.0018491712398827076,
0.004534263629466295,
-0.004695464391261339,
0.02414078265428543,
0.0034462071489542723,
0.09229879826307297,
0.051726095378398895,
0.015190528705716133,
-0.006863864604383707,
-0.11016739904880524,
-0.027492349967360497,
0.02263352833688259,
0.0015482039889320731,
-0.03998424857854843,
-0.006300002336502075,
-0.06022760644555092,
0.023297714069485664,
0.017078738659620285,
0.03242546692490578,
0.0047612967900931835,
-0.016248956322669983,
-0.04488798975944519,
0.026024911552667618,
-0.012692476622760296,
0.03651824966073036,
0.007505325600504875,
-0.04388461261987686,
-0.05313718691468239,
0.007015271112322807,
0.04261099174618721,
-0.0028487113304436207,
0.019451476633548737,
0.024397263303399086,
-0.06007121130824089,
-0.0689711645245552,
0.005591715686023235,
0.0330832302570343,
-0.003466659225523472,
0.04180329665541649,
-0.02938513644039631,
0.02368096448481083,
0.007764880079776049,
0.027672292664647102,
-0.016676655039191246,
-0.0375521183013916,
-0.026687778532505035,
0.02725912444293499,
0.03585553541779518,
-0.023350676521658897,
0.0246563833206892,
-0.0321883000433445,
0.0005403664545156062,
0.01829620450735092,
-0.014108561910688877,
0.028294285759329796,
-0.006326681934297085,
0.0406528003513813,
0.02151380106806755,
-0.01336453016847372,
-0.058016687631607056,
-0.006937697064131498,
-0.006465918384492397,
0.06311364471912384,
0.03039657138288021,
0.07848778367042542,
-0.04299405589699745,
0.017628155648708344,
0.03695649281144142,
0.0063086398877203465,
-0.031939249485731125,
0.018032072111964226,
-0.01983795315027237,
0.0013007490197196603,
-0.00042291689896956086,
-0.045853640884160995,
-0.0012115946738049388,
-0.01433371752500534,
-0.014234219677746296,
0.0021136223804205656,
0.014247155748307705,
0.01261990051716566,
-0.019169732928276062,
0.03628795966506004,
0.017079699784517288,
0.011339657939970493,
-0.017741655930876732,
0.023631568998098373,
-0.03229888528585434,
0.019695350900292397,
-0.010552770458161831,
0.024528997018933296,
-0.021140530705451965,
-0.0057122851721942425,
0.014839117415249348,
-0.03124098666012287,
0.015136340633034706,
0.07918336242437363,
-0.04988284409046173,
0.038676150143146515,
-0.040683943778276443,
-0.04739990085363388,
0.018924163654446602,
0.10077982395887375,
-0.0182015560567379,
0.04428453370928764,
0.05799439176917076,
0.020209703594446182,
0.005861764773726463,
0.04303381219506264,
0.019135605543851852,
0.006463920697569847,
0.0539180263876915,
-0.0033381658140569925,
0.07949919253587723,
0.01213794108480215,
0.042321816086769104,
-0.06786321848630905,
-0.05358525738120079,
0.010201453231275082,
0.014235557988286018,
0.04213044419884682,
-0.019471099600195885,
0.008561190217733383,
0.045317359268665314,
-0.0153323570266366,
-0.044848907738924026,
-0.03724614903330803,
0.0014287485973909497,
0.0368240587413311,
-0.028309443965554237,
-0.07421611249446869,
0.009845797903835773,
-0.002491955878213048,
0.003935293294489384,
-0.010150622576475143,
-0.08167467266321182,
-0.021984301507472992,
-0.006104155909270048,
0.0013294130330905318,
-0.0023694231640547514,
-0.0019704147707670927,
-0.011690591461956501,
-0.012877332977950573,
0.04089050740003586,
-0.02279721386730671,
-0.022100336849689484,
-0.025838563218712807,
-0.03334006294608116,
-0.015964332967996597,
0.037596847862005234,
-0.007435689680278301,
0.004173378925770521,
-0.036832209676504135,
0.05580596625804901,
-0.025660322979092598,
-0.06669443100690842,
-0.04646225646138191,
-0.0024166430812329054,
-0.0034049199894070625,
0.044110629707574844,
0.002736093243584037,
-0.006260371766984463,
0.0006146470550447702,
-0.013436286710202694,
0.03230971470475197,
-0.0038522924296557903,
-0.08654747158288956,
0.0084517328068614,
-0.03547661378979683,
-0.013702397234737873,
0.018112124875187874,
-0.04516557231545448,
0.0555635429918766,
-0.005579674616456032,
0.04501781612634659,
0.013425633311271667,
-0.00873972661793232,
0.045319780707359314,
0.055800680071115494,
0.029158709570765495,
0.0008373422897420824,
0.03554023057222366,
0.012173461727797985,
-0.045253098011016846,
-0.032357633113861084,
0.02512141317129135,
-0.04904934763908386,
0.033321332186460495,
0.029678206890821457,
0.025371819734573364,
-0.008049050346016884,
0.02521228976547718,
0.03132554143667221,
0.06820098310709,
-0.016414150595664978,
-0.01673145778477192,
-0.02024812437593937,
-0.07670413702726364,
0.006490766070783138,
-0.023708704859018326,
-0.054888878017663956,
0.0002177723654313013,
-0.008331597782671452,
-0.05225644260644913,
-0.0023010026197880507,
0.0013415992725640535,
-0.003059757873415947,
-0.00009501297608949244,
-0.03955414146184921,
-0.02363591454923153,
-0.07433643937110901,
0.056071557104587555,
0.026126792654395103,
-0.0186352226883173,
-0.06719430536031723,
0.022519240155816078,
0.028152331709861755,
-0.03405694290995598,
0.034229133278131485,
0.0033101774752140045,
-0.012794972397387028,
-0.009102622978389263,
-0.06494268774986267,
-0.03341696038842201,
0.013637406751513481,
-0.045745864510536194,
-0.049771055579185486,
0.01365253422409296,
0.027498582378029823,
0.03514375165104866,
-0.008669566363096237,
-0.04171974956989288,
-0.04286612570285797,
-0.013176428154110909,
-0.05151043087244034,
-0.016245495527982712,
0.02974850870668888,
0.014411301352083683,
0.04758860170841217,
0.039233189076185226,
0.01922856830060482,
0.029797663912177086,
0.04480631276965141,
-0.017535915598273277,
0.01578475534915924,
0.027657270431518555,
0.033315498381853104,
-0.007367459125816822,
-0.00787800457328558,
-0.0017639693105593324,
-0.02458435297012329,
-0.03534010425209999,
-0.03341593220829964,
-0.060968246310949326,
-0.031139811500906944,
-0.008225321769714355,
0.004834196530282497,
0.008577228523790836,
0.009572720155119896,
-0.019469061866402626,
-0.04043872281908989,
0.00903062243014574
] |
<p>I have been reading the paper <a href="http://arxiv.org/abs/0810.1545" rel="nofollow">The Incompressible Non-Relativistic Navier-Stokes Equation from Gravity</a>. In it they state, </p>
<blockquote>
<p>"An instability, if it occurs, must necessarily break a symmetry ...
that the background solution preserves."</p>
</blockquote>
<p>There is also discussion about the non-linear terms contributing to instabilities. Although I have some thoughts about how this should be interpreted. I wanted to see if there is some standard discussion relating to non linear instabilities in this context.</p>
<p>Addendum:</p>
<p>In order to provide more specificity, in standard discussion for understanding string theory, weak field approximations for gravity involve linearized fluctuations around a Minkowski metric: $$g_{\mu\nu}(x) = \eta_{\mu\nu}+h_{\mu\nu}(x)$$</p>
<p>In stronger fields, the fluctuations become highly non-linear. The non-linearity is thus understood as being associated with strong gravitational fields.</p>
<p>The Navier-Stokes equations can be understood as a composition of two types of equations, the <a href="http://en.wikipedia.org/wiki/Heat_equation" rel="nofollow">Heat equations</a> and the <a href="http://en.wikipedia.org/wiki/Euler_equations_%28fluid_dynamics%29" rel="nofollow">Euler equations</a>. In a crude sense, the unforced heat equations generally govern the diffusion of energy throughout an object, and the Euler equations govern the conservation of mass. </p>
<p>The incompressible Navier-Stokes equations in cartesian coordinates are:</p>
<p>$\partial_tu+u\partial_xu+v\partial_yu+w\partial_zu = -\partial_xp + \nu(\partial_{xx}u+\partial_{yy}u+\partial_{zz}u)$</p>
<p>$\partial_tv+u\partial_xv+v\partial_yv+w\partial_zv = -\partial_yp + \nu(\partial_{xx}v+\partial_{yy}v+\partial_{zz}v)$</p>
<p>$\partial_tw+u\partial_xw+v\partial_yw+w\partial_zw = -\partial_zp + \nu(\partial_{xx}w+\partial_{yy}w+\partial_{zz}w)$</p>
<p>$\partial_xu+\partial_yv+\partial_zw=0$ </p>
<p>Where one can identify the "heat equation terms" as (noting that in complex form these are the Schrodinger equations):</p>
<p>$\partial_tu = \nu(\partial_{xx}u+\partial_{yy}u+\partial_{zz}u)$</p>
<p>$\partial_tv = \nu(\partial_{xx}v+\partial_{yy}v+\partial_{zz}v)$</p>
<p>$\partial_tw = \nu(\partial_{xx}w+\partial_{yy}w+\partial_{zz}w)$</p>
<p>And one can identify the "Eulerian terms" as:</p>
<p>$u\partial_xu+v\partial_yu+w\partial_zu = -\partial_xp$</p>
<p>$u\partial_xv+v\partial_yv+w\partial_zv = -\partial_yp$</p>
<p>$u\partial_xw+v\partial_yw+w\partial_zw = -\partial_zp$</p>
<p>In the solution <a href="http://physics.stackexchange.com/q/52523/2451">I provided in a previous question</a>, the interesting characteristics is that solution satisfies both sets of equations (sans the pressure term for the heat equation). The pressure identified is also negative, and the solution is unbounded. This doesn't seem to be the type of space identified with the AdS in the above referenced paper or the <a href="http://arxiv.org/abs/0712.2456" rel="nofollow">related paper</a> discussing the gravity-fluid dynamics relationship. There is one other thing that is of interest, and that is the vanishing of the non-linear and pressure terms with the given solution (related to the apparent separability of terms).</p>
<p>If I relate the Eulerian terms with gravity, then the solution in my mind suggest that there are possibly some set of solutions that can be shared in common with both the Heat equation terms and the Eulerian terms (and the number of these are unknown). </p>
<p>It seems that those solutions would have some sort of privileged status, or perhaps they are completely trivial and not interesting, but I am thinking that answer is context dependent. However, I am somewhat encouraged that those solutions are not trivial, since <a href="http://en.wikipedia.org/wiki/Euler_equations_%28fluid_dynamics%29#Shock_waves" rel="nofollow">bifurcation is not generally considered a good thing in equations describing physical phenomenon</a>.</p>
<p>So getting back to the original question, in the above referenced paper it is implied that instability at high Reynolds numbers ($\frac{1}{\nu} >> 1$) is associated with symmetry breaking, which is a necessary physical phenomenon that is not well understood. So I am trying to tie these thoughts together and was wondering what misconceptions I might have on this or how these are tied together in academic settings.</p> | g7861 | [
0.012602661736309528,
-0.012354659847915173,
0.006893881130963564,
-0.007543225772678852,
0.05432067811489105,
-0.001894623041152954,
0.06690255552530289,
-0.04837195202708244,
-0.07771976292133331,
-0.03987838327884674,
0.006156834773719311,
-0.0004319000872783363,
0.0016402374021708965,
0.022843163460493088,
-0.04148441180586815,
-0.006284069735556841,
0.04775013029575348,
0.001038427697494626,
0.029284007847309113,
0.014956452883780003,
-0.0232388898730278,
0.049815624952316284,
0.07719408720731735,
-0.019856875762343407,
-0.02097131684422493,
-0.015990540385246277,
0.042139265686273575,
-0.05420999974012375,
-0.05422680079936981,
0.0009127696393989027,
0.10396527498960495,
-0.002010370371863246,
0.000572830205783248,
-0.06715448200702667,
-0.04415953531861305,
-0.037362679839134216,
0.0401897095143795,
0.02309407666325569,
0.03597613796591759,
0.03159118816256523,
0.05244245380163193,
-0.007682368159294128,
0.030210701748728752,
-0.007693977560847998,
-0.03580518066883087,
-0.016915753483772278,
-0.05092602223157883,
0.002804535673931241,
0.01781827211380005,
-0.017898686230182648,
0.04711360111832619,
0.04074525833129883,
0.08399240672588348,
-0.030151689425110817,
0.016986533999443054,
0.022538013756275177,
0.022516462951898575,
0.010254266671836376,
0.026396173983812332,
-0.015753915533423424,
-0.009542246349155903,
-0.0320272371172905,
-0.01693148724734783,
-0.0171413104981184,
0.00606569554656744,
-0.04383415728807449,
-0.04611704871058464,
-0.007769788149744272,
0.00647739227861166,
-0.0636453703045845,
-0.030374739319086075,
0.012384088709950447,
0.0067353276535868645,
-0.019829608500003815,
-0.013824645429849625,
0.02218211442232132,
-0.02365179732441902,
0.04207878187298775,
-0.0017002486856654286,
-0.03786959871649742,
-0.020522886887192726,
0.028370194137096405,
-0.010638671927154064,
0.04122433066368103,
0.0653936117887497,
-0.06363742798566818,
0.05667244642972946,
0.0027410858310759068,
-0.004599613603204489,
0.028211133554577827,
-0.006940872874110937,
0.0232480950653553,
0.023798376321792603,
0.009656586684286594,
0.022003011777997017,
0.03416593000292778,
0.006574236322194338,
0.03450314700603485,
-0.02801930345594883,
-0.026654843240976334,
-0.010252418927848339,
-0.02883876860141754,
-0.028981570154428482,
0.008292748592793941,
0.007286566775292158,
-0.02839985303580761,
0.08517680317163467,
0.1291312873363495,
-0.017317065969109535,
-0.019041141495108604,
-0.02455814741551876,
0.02729763276875019,
-0.034841764718294144,
-0.03555658087134361,
-0.05009183660149574,
-0.01706968992948532,
0.0034631078597158194,
-0.011687369085848331,
0.05922606959939003,
0.042440157383680344,
-0.0059747411869466305,
0.036078572273254395,
0.04431551694869995,
0.049858659505844116,
-0.03434282913804054,
-0.011045549064874649,
0.02326260879635811,
0.006550459656864405,
0.1178799644112587,
-0.02718193829059601,
0.010543186217546463,
0.030070006847381592,
0.003842569887638092,
0.05939459055662155,
-0.023967226967215538,
-0.025055943056941032,
-0.008586430922150612,
0.029193030670285225,
-0.045458320528268814,
0.0024731133598834276,
-0.0365903414785862,
-0.02930525504052639,
0.002688745968043804,
-0.0424082949757576,
-0.04278219863772392,
0.00011237127182539552,
0.012989453971385956,
-0.01075812615454197,
0.023737294599413872,
0.003885869635269046,
-0.03760039061307907,
0.037870656698942184,
-0.031528931111097336,
-0.03971673175692558,
-0.03721609711647034,
0.030695408582687378,
0.0029753530398011208,
-0.0015095968265086412,
-0.02100454829633236,
-0.03237459436058998,
0.05535838007926941,
-0.025360772386193275,
0.022751830518245697,
0.026706183329224586,
-0.06995873153209686,
0.026093745604157448,
-0.05049961432814598,
-0.07145165652036667,
0.05739812180399895,
-0.039742108434438705,
-0.03553472459316254,
0.027300318703055382,
0.022088611498475075,
0.038929298520088196,
0.05719469487667084,
0.029202841222286224,
0.058462608605623245,
0.0006323732668533921,
-0.04883681982755661,
-0.01934020407497883,
-0.05568600818514824,
-0.06078217923641205,
0.029970010742545128,
0.005699604749679565,
0.02854156866669655,
0.03978060185909271,
-0.0023606845643371344,
-0.005274367984384298,
-0.06047298014163971,
-0.012785346247255802,
-0.0449242889881134,
-0.0056730713695287704,
0.02507789246737957,
0.07528223842382431,
0.05148787796497345,
0.035661645233631134,
0.04238969832658768,
-0.030698653310537338,
-0.10064748674631119,
0.056651800870895386,
0.010632451623678207,
0.07005100697278976,
-0.013301217928528786,
-0.01098028663545847,
-0.009397502057254314,
0.01596931926906109,
-0.02527409791946411,
-0.014307540841400623,
-0.0018727222923189402,
-0.002428467618301511,
0.008794249966740608,
-0.08789221942424774,
-0.00401875376701355,
-0.057454995810985565,
0.004223906435072422,
-0.02022567018866539,
0.06256898492574692,
0.02260345220565796,
-0.04258086904883385,
0.03881651908159256,
-0.014768041670322418,
0.0017913886113092303,
-0.008257090114057064,
0.027752071619033813,
-0.036042939871549606,
0.0020204526372253895,
-0.03043052740395069,
-0.027500396594405174,
0.061515651643276215,
-0.014026480726897717,
-0.00030638676253147423,
0.02484312653541565,
-0.006169652566313744,
0.007754883263260126,
0.02580101415514946,
-0.010636309161782265,
0.04203912988305092,
0.007211812771856785,
-0.0071637979708611965,
0.07186020910739899,
-0.009828535839915276,
0.03282986208796501,
-0.06251228600740433,
0.04191145673394203,
0.018320497125387192,
-0.021133778616786003,
0.01267064269632101,
-0.034794144332408905,
-0.028561167418956757,
-0.0069461604580283165,
0.015568021684885025,
-0.05207080394029617,
-0.01795175112783909,
-0.01454446092247963,
0.02478712424635887,
-0.03243529796600342,
0.037621185183525085,
0.046202875673770905,
-0.06360331177711487,
-0.03144802898168564,
0.022159231826663017,
0.03371390327811241,
-0.073167584836483,
-0.021719027310609818,
-0.0593835711479187,
-0.0017038693185895681,
-0.025035586208105087,
0.003412000834941864,
-0.019926007837057114,
0.03720327466726303,
0.026555687189102173,
0.02500161901116371,
0.00936874095350504,
0.04589397460222244,
0.019157685339450836,
0.04392388090491295,
-0.06723854690790176,
0.02325225993990898,
-0.03076254390180111,
-0.027818938717246056,
0.04763365909457207,
0.048056114464998245,
-0.006314076017588377,
-0.04216891899704933,
0.009683732874691486,
-0.024748051539063454,
-0.0019268550677224994,
0.02060476876795292,
0.006528711877763271,
0.05780261009931564,
0.03262554109096527,
0.030138937756419182,
-0.0062396530993282795,
-0.009555630385875702,
-0.02860061451792717,
0.004145123064517975,
-0.014000236056745052,
-0.06595759093761444,
-0.027635259553790092,
-0.05656749755144119,
0.0680527463555336,
-0.036315951496362686,
-0.032572872936725616,
0.015051310881972313,
0.0007671809289604425,
-0.04055704548954964,
-0.11846686154603958,
-0.04327945411205292,
0.013701630756258965,
-0.005092612002044916,
0.011786547489464283,
-0.04913801699876785,
-0.0002849313896149397,
0.0200605858117342,
-0.020979201421141624,
0.09914302825927734,
-0.04140989109873772,
-0.019970452412962914,
0.048474811017513275,
-0.04400357976555824,
-0.0687890574336052,
-0.008532961830496788,
-0.02330283634364605,
-0.008409165777266026,
0.036380305886268616,
0.037231408059597015,
0.03587695583701134,
-0.006131317000836134,
-0.025532405823469162,
0.01176875177770853,
-0.0004116600612178445,
-0.06055701896548271,
0.04380135238170624,
-0.02052335813641548,
-0.04786892235279083,
-0.03733879700303078,
0.009530959650874138,
-0.01448262482881546,
0.028871873393654823,
0.04860341176390648,
0.06442217528820038,
0.00906702782958746,
-0.0004673837684094906,
-0.03962324932217598,
-0.022200483828783035,
0.01081524696201086,
0.025316298007965088,
0.02699625864624977,
-0.015551014803349972,
0.03732963651418686,
0.060388293117284775,
-0.01983419992029667,
0.02462116815149784,
-0.027354059740900993,
-0.04805954918265343,
0.01988069899380207,
-0.0043724006973207,
-0.01826108619570732,
0.031103970482945442,
0.014327077195048332,
-0.018403325229883194,
-0.038715660572052,
0.0025633862242102623,
0.027708157896995544,
0.01632879115641117,
0.0356307253241539,
0.03798379749059677,
-0.007847579196095467,
-0.11607613414525986,
-0.09781741350889206,
0.0009319433593191206,
-0.013265740126371384,
-0.04185723140835762,
-0.00408640131354332,
0.026666579768061638,
-0.04741894453763962,
0.06476692855358124,
-0.027209827676415443,
-0.034860413521528244,
0.002366012427955866,
0.0677075907588005,
-0.06039268150925636,
0.022027410566806793,
0.0297833438962698,
0.056589655578136444,
-0.03130485862493515,
-0.018225643783807755,
-0.006127915345132351,
0.023853963240981102,
-0.03043268248438835,
-0.003708166303113103,
-0.007459690328687429,
0.024892903864383698,
0.008417811244726181,
0.049854375422000885,
0.024656089022755623,
-0.0061199851334095,
0.03655620664358139,
0.002476427238434553,
0.0004897263133898377,
0.003983977250754833,
0.005738327279686928,
-0.005525957327336073,
-0.010086043737828732,
-0.027483465149998665,
-0.028872782364487648,
-0.004180551040917635,
-0.03534882143139839,
-0.05833097919821739,
-0.030385619029402733,
0.09174636751413345,
-0.02274252288043499,
-0.03628059849143028,
-0.07384102791547775,
0.07045183330774307,
-0.02659936621785164,
0.027615899220108986,
-0.014081900008022785,
0.029622996225953102,
-0.0008268779492937028,
0.07289063185453415,
0.033726196736097336,
-0.03572000190615654,
0.01147762406617403,
0.006764591205865145,
0.04036495089530945,
0.057110995054244995,
0.01010699663311243,
-0.005183667875826359,
-0.008416436612606049,
-0.008713369257748127,
0.00786315742880106,
0.021775783970952034,
0.022795721888542175,
-0.012457286939024925,
-0.010562737472355366,
-0.0195708516985178,
0.012522254139184952,
-0.021911542862653732,
0.0024106528144329786,
-0.005227576941251755,
0.012339411303400993,
0.04277452826499939,
-0.055379945784807205,
0.011557920835912228,
0.05434310808777809,
0.016940519213676453,
-0.0183594711124897,
0.00457355659455061,
0.025742415338754654,
-0.05420007184147835,
0.03719014674425125,
0.07956139743328094,
0.013959487900137901,
-0.0013375835260376334,
0.012696479447185993,
-0.012643661350011826,
0.02819734811782837,
-0.018901672214269638,
-0.04091139882802963,
0.019456304609775543,
-0.03981771320104599,
0.02250286564230919,
0.0574529655277729,
0.0159104373306036,
-0.033769410103559494,
-0.032950833439826965,
-0.06308431923389435,
-0.00017069035675376654,
-0.06446322798728943,
0.05577655881643295,
0.006226248573511839,
0.024859406054019928,
-0.015659740194678307,
0.0001655703817959875,
0.05419923737645149,
0.01739952713251114,
-0.023666834458708763,
-0.06783458590507507,
-0.07347448915243149,
-0.0010978420032188296,
0.009532850235700607,
0.057813435792922974,
0.041597139090299606,
0.02520473301410675,
-0.031020641326904297,
-0.04690992087125778,
0.0022586623672395945,
0.01322968304157257,
0.010521194897592068,
0.0074245319701731205,
0.01653805933892727,
-0.03271402418613434,
-0.0014657151186838746,
-0.05492288991808891,
-0.02680068649351597,
-0.0007057175389491022,
-0.011182784102857113,
-0.029993798583745956,
0.020469732582569122,
-0.039446644484996796,
0.03254382684826851,
0.031330451369285583,
-0.009777122177183628,
0.05098722130060196,
0.031886227428913116,
0.03948528319597244,
0.04934219270944595,
0.03545374423265457,
0.034142185002565384,
0.04018979147076607,
-0.0031238917727023363,
-0.027625011280179024,
0.023481762036681175,
-0.014691386371850967,
-0.04075130447745323,
0.02105356566607952,
-0.03346843272447586,
0.008367461152374744,
-0.02111184224486351,
0.03322489559650421,
-0.008322867564857006,
0.009740551933646202,
0.058092016726732254,
0.06053946539759636,
0.05918397009372711,
-0.053200460970401764,
-0.047871265560388565,
0.018823526799678802,
0.015501106157898903,
0.00827390793710947,
0.019114572554826736,
0.023837128654122353,
0.021381782367825508,
0.008755085989832878,
-0.042464178055524826,
-0.005452674813568592,
0.0216521006077528,
0.016519831493496895,
-0.026429735124111176,
-0.02706156112253666,
0.03362742438912392,
0.004320498090237379,
0.08471760898828506,
-0.03740904480218887,
-0.0026637702248990536,
-0.05029728263616562,
0.02490178868174553,
-0.0016216648509725928,
-0.04846803471446037,
0.00938020832836628,
-0.009993252344429493,
0.006533604580909014,
0.007271660957485437,
0.02846461907029152,
-0.02733752131462097,
0.044458143413066864,
-0.026652302592992783,
-0.0352943018078804,
-0.034344665706157684,
-0.017312509939074516,
0.021194038912653923,
-0.0032910665031522512,
0.042822353541851044,
0.02878844365477562,
0.04846722632646561,
0.0021948134526610374,
-0.09630919992923737,
0.0009688702411949635,
0.01251568179577589,
-0.021159015595912933,
0.05639510974287987,
-0.02459668554365635,
-0.04436418041586876,
0.008269106037914753,
-0.024542586877942085,
-0.07207965105772018,
-0.027814500033855438,
-0.07186076045036316,
-0.028899574652314186,
-0.07037609070539474,
-0.0018323156982660294,
0.017188485711812973,
-0.02657794952392578,
-0.06435994803905487,
-0.05193426460027695,
-0.050700344145298004,
0.027373841032385826,
0.01985037885606289,
0.03720393404364586,
-0.008747627027332783,
0.018017340451478958,
-0.01558766234666109,
0.014716562815010548,
-0.011624841019511223,
0.05992916226387024,
-0.0026576966047286987,
-0.02919428050518036,
-0.03967820480465889,
0.018287282437086105,
-0.010641444474458694,
0.04287952557206154,
0.012283630669116974,
0.030830159783363342,
0.015311378054320812,
0.03363463282585144,
0.004778050351887941,
0.04053962603211403,
-0.05679132789373398,
0.04710644483566284,
-0.018811576068401337,
0.03424590080976486,
0.03299802169203758,
-0.027202555909752846,
-0.017783867195248604,
-0.013453603722155094,
-0.020472954958677292,
-0.02588387206196785,
-0.010564745403826237,
-0.024631615728139877,
-0.05769786611199379,
-0.06188960000872612,
0.024814005941152573,
0.05891893059015274,
0.0070283422246575356,
0.05239378660917282,
-0.05359327048063278,
-0.007394206244498491,
-0.0004137396172154695,
0.017260747030377388,
0.03131260722875595,
-0.02225501462817192,
-0.02607075870037079,
0.016308745369315147,
-0.013090463355183601,
-0.041384126991033554,
-0.09317407757043839,
0.03554355725646019,
0.0262850783765316,
0.0015541046159341931,
-0.031043536961078644,
0.027972791343927383,
0.014399823732674122,
-0.024963945150375366,
-0.04478799179196358,
0.029210945591330528,
0.00811487715691328,
0.042832355946302414,
-0.04093741625547409,
-0.02956012822687626,
0.00641215406358242,
-0.03845567628741264,
-0.009356535971164703,
-0.0219473447650671,
-0.0031344068702310324,
0.021250026300549507,
-0.016672283411026,
0.0062243398278951645,
-0.007465016096830368,
-0.009591374546289444,
-0.0338609553873539,
0.057256340980529785,
0.03321683406829834,
0.037443675100803375,
-0.03328658267855644,
0.02464110590517521,
0.03536520525813103,
-0.003814171766862273,
-0.014694261364638805,
0.057919662445783615,
0.04758346080780029,
-0.029585083946585655,
-0.022702984511852264,
-0.014087606221437454,
-0.02713160775601864,
-0.021517101675271988,
0.03256998211145401,
0.0017098080134019256,
0.01841636747121811,
0.009098825044929981,
0.05766860023140907,
0.00036590974195860326,
0.022314343601465225,
0.036382123827934265,
-0.008619189262390137,
-0.025206271559000015,
-0.010266789235174656,
0.0022905466612428427,
0.042232267558574677,
0.04580143466591835,
-0.058138709515333176,
0.09802932292222977,
0.012296884320676327,
-0.028807995840907097,
-0.02117825113236904,
0.019278863444924355,
-0.030673619359731674,
0.02932577021420002,
-0.00006763372948626056,
-0.007458730600774288,
0.016864614561200142,
-0.0012010554783046246,
0.0027417985256761312,
0.0007200067630037665,
-0.024621695280075073,
-0.02712475135922432,
0.05812540650367737,
-0.0764569640159607,
-0.023433737456798553,
0.010514400899410248,
-0.020101066678762436,
0.030811766162514687,
0.016938775777816772,
-0.005315398331731558,
0.06068762019276619,
-0.008812657557427883,
-0.023317009210586548,
-0.03786792606115341,
-0.03979311138391495,
0.04750956594944,
-0.02729637548327446,
-0.039988644421100616,
0.0005422605318017304,
-0.024080375209450722,
-0.011099744588136673,
-0.03305433318018913,
0.014766580425202847,
-0.001291247084736824,
-0.010327693074941635,
-0.008636770769953728,
-0.12456795573234558,
-0.020067619159817696,
-0.040588557720184326,
-0.01084502786397934,
-0.005708411801606417,
0.05011354014277458,
0.03924504294991493,
0.0049371118657290936,
0.06423375755548477,
-0.027146829292178154,
0.07278377562761307,
-0.058691129088401794,
0.041955556720495224,
-0.05941309407353401,
-0.02465047687292099,
0.013017707504332066,
0.01589902862906456,
0.00208276673220098,
0.014623494818806648,
-0.023885663598775864,
0.076612189412117,
0.018428221344947815,
-0.007658854126930237,
0.06389867514371872,
0.027626173570752144,
-0.024747980758547783,
-0.05441116914153099,
0.005960931070148945,
0.021884538233280182,
-0.005685477517545223,
0.045147329568862915,
-0.02881935052573681,
0.008979279547929764,
-0.056218404322862625,
-0.05151423066854477,
-0.009640220552682877,
-0.01903555914759636,
0.007126417942345142
] |
<p>Iron is the most stable single element (I don't know about combinations of elements, but oh well, not applicable to question). Stars go through cycles where they change the materials of their cores, culminating in iron for the longest lasting and largest stars. The cores of stars naturally have tremedous forces. My question: Has humanity managed to combine to iron nuclei together? and if yes why can we do it but not stars? Alternatively, where would the progression past iron nuclei go, since no element is more stable?</p> | g7862 | [
-0.02940288931131363,
0.060358382761478424,
0.019744649529457092,
-0.02738887444138527,
0.07732193917036057,
0.02193513698875904,
-0.043028414249420166,
0.011466741561889648,
-0.035564981400966644,
-0.013425118289887905,
-0.009546991437673569,
0.03256233409047127,
0.031627051532268524,
0.0025946262758225203,
-0.021837085485458374,
0.04869488999247551,
0.06370393186807632,
0.040391333401203156,
0.014643386006355286,
0.016936354339122772,
0.039057329297065735,
-0.007022662553936243,
0.021504200994968414,
0.02683163434267044,
-0.01635885052382946,
-0.017122782766819,
0.056813061237335205,
-0.0069830939173698425,
-0.0010788259096443653,
-0.013312896713614464,
0.058529358357191086,
-0.04627750813961029,
0.06411231309175491,
-0.008358294144272804,
0.02833031862974167,
-0.12010272592306137,
-0.0664839819073677,
-0.02896561659872532,
0.055665552616119385,
-0.040659695863723755,
-0.043169405311346054,
-0.0457267127931118,
0.03396163508296013,
-0.06203031912446022,
-0.009614547714591026,
0.004300626926124096,
0.03994958475232124,
-0.05793927237391472,
0.023089546710252762,
-0.00332733360119164,
-0.00034512748243287206,
0.036733269691467285,
0.004716209601610899,
0.012172950431704521,
0.017680050805211067,
-0.009460880421102047,
0.0002351308212382719,
-0.035829827189445496,
0.04328196123242378,
0.0035522617399692535,
-0.03184686228632927,
0.04048975557088852,
0.01341228000819683,
0.03276145085692406,
0.040901344269514084,
-0.03614126145839691,
-0.03599674627184868,
0.03715616464614868,
0.04011216387152672,
0.036328043788671494,
0.01275873277336359,
-0.07817898690700531,
0.017810722813010216,
0.03539462387561798,
-0.02685856632888317,
0.009640559554100037,
0.028686843812465668,
-0.025741200894117355,
0.013706076890230179,
0.04459375515580177,
0.029186049476265907,
-0.04863695055246353,
0.049941010773181915,
0.025775359943509102,
-0.00931983906775713,
0.022650374099612236,
0.006231165025383234,
-0.01857459917664528,
-0.028210695832967758,
0.03510085865855217,
0.03075447306036949,
0.03413555771112442,
-0.013439158909022808,
-0.021703163161873817,
-0.022830931469798088,
0.008450801484286785,
-0.00823722779750824,
0.05044737830758095,
-0.06177453324198723,
0.0006313063204288483,
-0.027051163837313652,
-0.01233604084700346,
0.0462135449051857,
-0.023731902241706848,
0.001987349707633257,
0.013272850774228573,
0.021466007456183434,
0.024192268028855324,
0.018601980060338974,
0.014140581712126732,
-0.0028915859293192625,
-0.01218863669782877,
-0.011814129538834095,
0.005791559815406799,
0.017129503190517426,
0.020483341068029404,
0.03437911719083786,
0.020693423226475716,
0.020099397748708725,
0.03790970891714096,
0.0032326376531273127,
-0.016903158277273178,
0.008949238806962967,
0.05740271136164665,
-0.08287490159273148,
-0.02076907828450203,
0.02353077195584774,
0.022052451968193054,
0.030088409781455994,
-0.034842684864997864,
-0.05236755311489105,
0.01270381547510624,
-0.023658595979213715,
-0.03083442896604538,
-0.03132941201329231,
0.01617307774722576,
-0.05383163318037987,
0.02997395768761635,
-0.05280613899230957,
0.017650000751018524,
0.009817199781537056,
0.009994343854486942,
0.03702473267912865,
-0.011640643700957298,
-0.019199421629309654,
0.031709250062704086,
-0.003980792593210936,
0.006967153400182724,
-0.04693019762635231,
0.04660029336810112,
0.04679450765252113,
0.00013944711827207357,
0.032145023345947266,
-0.09733432531356812,
-0.019273478537797928,
-0.009223880246281624,
0.05782986432313919,
-0.016770504415035248,
-0.03584262728691101,
-0.01773703657090664,
0.04515078663825989,
0.004491088911890984,
-0.05460960045456886,
-0.034689247608184814,
0.000046675435442011803,
0.016443317756056786,
-0.05138782039284706,
-0.024478677660226822,
0.06449916958808899,
0.008377636782824993,
0.04437043145298958,
-0.018089212477207184,
-0.012110027484595776,
0.07548712193965912,
-0.009535273537039757,
-0.019488690420985222,
0.07085415720939636,
-0.06396692246198654,
-0.06884173303842545,
0.010975983925163746,
-0.023760229349136353,
0.0027081016451120377,
0.004896966274827719,
0.019114572554826736,
0.048192501068115234,
0.0016573525499552488,
0.021641528233885765,
0.05055398494005203,
-0.021909059956669807,
0.03689884766936302,
-0.04161718115210533,
-0.011871254071593285,
0.03937560319900513,
0.029546787962317467,
0.027473652735352516,
-0.04761727526783943,
0.008986097760498524,
-0.03280079364776611,
-0.006899397354573011,
0.03439093008637428,
-0.031337540596723557,
0.019865356385707855,
-0.065078504383564,
0.01974019594490528,
0.009388051927089691,
-0.007550565991550684,
-0.002774248830974102,
0.038018640130758286,
0.04291599243879318,
-0.003700803266838193,
0.011381413787603378,
0.06970097124576569,
-0.05623787268996239,
-0.03999372944235802,
-0.04592946171760559,
-0.08278512209653854,
-0.0027865550946444273,
-0.033046189695596695,
-0.022461120039224625,
0.019759848713874817,
-0.022455547004938126,
-0.04363597184419632,
-0.011257636360824108,
0.04089660570025444,
0.01676345244050026,
0.013922319747507572,
0.02672230452299118,
-0.007959640584886074,
0.01938091404736042,
-0.004586998838931322,
-0.05614066869020462,
0.02388676069676876,
-0.0004217778623569757,
-0.02125006914138794,
-0.009286637417972088,
0.04435885697603226,
0.00797764677554369,
-0.008864066563546658,
-0.07075569033622742,
0.05567420646548271,
-0.0019185731653124094,
-0.04681231454014778,
-0.01950126886367798,
-0.056515343487262726,
0.06530832499265671,
-0.00576164573431015,
0.001554146409034729,
0.006060582119971514,
-0.012449909932911396,
0.024487322196364403,
0.02395617961883545,
-0.048335377126932144,
-0.08103637397289276,
0.0035534603521227837,
-0.045959390699863434,
-0.044444818049669266,
-0.02827470377087593,
0.08218199759721756,
-0.06135305017232895,
-0.010414236225187778,
0.017268624156713486,
-0.024070026353001595,
0.001199888065457344,
0.006110678426921368,
-0.07135473191738129,
-0.013680126518011093,
-0.03763333708047867,
-0.06914529949426651,
0.0407632514834404,
-0.0013601478422060609,
-0.06664840877056122,
-0.03728839382529259,
0.008436154574155807,
0.008709871210157871,
-0.08437193185091019,
-0.035698797553777695,
-0.025756889954209328,
-0.003223574021831155,
0.019045481458306313,
0.013302484527230263,
0.011228553019464016,
0.04009299352765083,
0.0008137994445860386,
-0.03998243808746338,
-0.027140360325574875,
0.03518638014793396,
-0.0020729701500386,
0.010899217799305916,
0.08691848069429398,
0.05094878748059273,
0.027425609529018402,
-0.053021349012851715,
0.09015274792909622,
-0.03848307579755783,
0.029568392783403397,
0.012294486165046692,
0.06171771138906479,
-0.032097041606903076,
-0.05434638261795044,
0.0640801414847374,
0.06173224747180939,
-0.011002170853316784,
-0.007267975714057684,
0.019360696896910667,
0.038783445954322815,
0.017068346962332726,
-0.039212554693222046,
0.013044136576354504,
-0.0016597099602222443,
-0.09572568535804749,
0.04369097948074341,
0.10232890397310257,
-0.01767413504421711,
0.04047417268157005,
-0.05792135000228882,
-0.0005129532073624432,
-0.012530237436294556,
-0.007918168790638447,
0.05433144420385361,
-0.03904344141483307,
0.0005311091663315892,
-0.01582973450422287,
0.0012521616881713271,
-0.09229358285665512,
0.018585899844765663,
-0.014689658768475056,
-0.016435656696558,
-0.009927133098244667,
-0.055879704654216766,
-0.0070650614798069,
-0.030875971540808678,
0.01153079979121685,
-0.03335212543606758,
0.04950427636504173,
-0.1021866500377655,
0.012545516714453697,
-0.029740875586867332,
0.013200946152210236,
0.05594080686569214,
0.007702341303229332,
-0.03407453000545502,
0.004693199414759874,
-0.009320314042270184,
-0.01860998198390007,
0.003622679738327861,
0.08082565665245056,
0.007000229321420193,
0.0085752559825778,
0.002296141581609845,
-0.00855463370680809,
-0.0024177171289920807,
0.007802288513630629,
0.02506452240049839,
-0.027825122699141502,
0.01607844978570938,
0.014477947726845741,
0.013585234060883522,
0.019908245652914047,
-0.024707159027457237,
-0.028037529438734055,
-0.03029346652328968,
0.03976387903094292,
0.0021334404591470957,
-0.0004494586319196969,
-0.030942171812057495,
0.00950971432030201,
0.023441283032298088,
0.04201740771532059,
0.02051825076341629,
-0.008976510725915432,
-0.003184734610840678,
-0.022636855021119118,
-0.05893627181649208,
-0.021011238917708397,
0.0037685290444642305,
-0.004169963765889406,
0.01800875924527645,
0.02660316415131092,
-0.017873235046863556,
0.030359800904989243,
-0.01599486544728279,
0.016715997830033302,
0.008502145297825336,
0.05121087655425072,
-0.008416874334216118,
0.004308808594942093,
0.026523243635892868,
-0.053312961012125015,
-0.037218742072582245,
0.02853415720164776,
-0.0004680918646045029,
-0.07411280274391174,
0.032623063772916794,
-0.03689458221197128,
0.013819620944559574,
-0.0494314469397068,
-0.06699097156524658,
0.034061308950185776,
-0.000011666723366943188,
-0.004228015895932913,
-0.015523607842624187,
-0.03207022324204445,
-0.009411552920937538,
-0.01747947558760643,
0.01885700598359108,
0.00440369825810194,
-0.06159798055887222,
-0.060482487082481384,
-0.032098375260829926,
-0.02520923502743244,
0.04929334297776222,
0.06209776550531387,
0.010549040511250496,
0.013360689394176006,
0.06816694140434265,
-0.028952844440937042,
-0.02827928587794304,
-0.0031906608492136,
-0.01412838976830244,
-0.08378917723894119,
0.01753438077867031,
0.015807023271918297,
-0.012637224979698658,
0.03465775027871132,
0.05699305981397629,
0.024043351411819458,
-0.03904103487730026,
-0.05446765199303627,
0.00670517748221755,
0.06620956212282181,
0.004068418871611357,
0.011916118673980236,
0.06501951813697815,
0.0006415381794795394,
-0.020097028464078903,
-0.006098643876612186,
0.005625829566270113,
0.0093170665204525,
0.00001601310577825643,
0.036230526864528656,
0.04502766951918602,
0.04037019610404968,
0.020266743376851082,
0.056322794407606125,
-0.004171870183199644,
0.037359584122896194,
-0.019948165863752365,
-0.0027843567077070475,
-0.0308400709182024,
-0.008078877814114094,
0.06978201866149902,
0.0008583630551584065,
-0.01872039958834648,
0.03592570126056671,
-0.013127517886459827,
-0.013573198579251766,
-0.020438607782125473,
0.006254763808101416,
0.015089530497789383,
0.016821369528770447,
-0.0007962377858348191,
-0.020417368039488792,
-0.0003743533743545413,
0.07782433182001114,
0.06855396181344986,
0.01578344963490963,
0.007863073609769344,
-0.036091748625040054,
-0.036285240203142166,
0.023626599460840225,
-0.005999945569783449,
0.01609840616583824,
0.02636055089533329,
0.0018208300461992621,
0.04063819348812103,
-0.035627756267786026,
-0.01173892430961132,
-0.07476340234279633,
0.026457153260707855,
-0.023612018674612045,
-0.00813750084489584,
0.028117792680859566,
-0.012334001250565052,
0.060402993112802505,
-0.04059303551912308,
0.012344866059720516,
-0.03583309426903725,
-0.010740222409367561,
-0.014243519864976406,
-0.0046994942240417,
-0.09288770705461502,
0.01347268931567669,
0.1095217615365982,
-0.050313979387283325,
0.015442841686308384,
-0.053589627146720886,
-0.005618900526314974,
-0.07905042916536331,
0.013489999808371067,
-0.02273436449468136,
-0.032617680728435516,
-0.00028103037038818,
-0.0013050498673692346,
0.029743878170847893,
0.012686192989349365,
0.01300241518765688,
0.06985858827829361,
-0.050724614411592484,
0.043844275176525116,
0.027007518336176872,
0.01459967065602541,
0.030734430998563766,
-0.015042507089674473,
0.06264263391494751,
-0.026736805215477943,
-0.02192908711731434,
0.0029835838358849287,
0.00453326478600502,
0.019747039303183556,
-0.11505686491727829,
-0.045747194439172745,
-0.04066324979066849,
0.02160130813717842,
0.008604378439486027,
0.019524257630109787,
0.054219502955675125,
0.025886693969368935,
0.013551151379942894,
-0.022471116855740547,
0.017713362351059914,
0.005398190580308437,
-0.035034891217947006,
0.022924814373254776,
-0.00635661231353879,
-0.03535570949316025,
-0.0152030223980546,
-0.02423851378262043,
-0.005809031426906586,
0.028521860018372536,
0.06121303141117096,
0.002113952999934554,
-0.004836114123463631,
0.023634538054466248,
0.0726415291428566,
0.008945497684180737,
-0.00827835127711296,
0.009473337791860104,
0.06194475293159485,
-0.0356857106089592,
0.014201905578374863,
-0.020014416426420212,
0.057200707495212555,
-0.04365983232855797,
0.020843468606472015,
-0.017750533297657967,
0.044233907014131546,
0.04234486445784569,
-0.03468635305762291,
0.030044756829738617,
-0.011793464422225952,
0.027748899534344673,
-0.02340809814631939,
-0.03154449537396431,
0.009005136787891388,
0.050867389887571335,
-0.02406970225274563,
0.0056000747717916965,
-0.06890137493610382,
0.00768532557412982,
0.04044235125184059,
0.022557072341442108,
-0.0028853309340775013,
0.020560268312692642,
0.03791432082653046,
0.03507417067885399,
-0.055393803864717484,
-0.023366069421172142,
0.01829400472342968,
0.005959062837064266,
-0.06308519840240479,
0.02786351926624775,
-0.027045628055930138,
-0.023608902469277382,
-0.02862171269953251,
0.026742160320281982,
-0.024269863963127136,
-0.020547546446323395,
-0.0018389637116342783,
-0.019115440547466278,
-0.05600595846772194,
0.01713183894753456,
0.021487127989530563,
0.02773919515311718,
0.02566642314195633,
-0.029313376173377037,
-0.03181331604719162,
-0.006256913300603628,
0.02210027165710926,
-0.0313279815018177,
0.012627944350242615,
-0.002880362095311284,
0.032487351447343826,
0.051987405866384506,
0.036990515887737274,
0.04493631422519684,
0.03173014521598816,
-0.003905524266883731,
0.003749546129256487,
0.0675680860877037,
0.008331306278705597,
0.018311887979507446,
0.0022789672948420048,
-0.02205534279346466,
0.02663821540772915,
-0.03332238271832466,
-0.06620106101036072,
0.06665582954883575,
-0.020506536588072777,
-0.07387944310903549,
0.09583883732557297,
-0.05368435010313988,
-0.05738508701324463,
-0.02457547001540661,
-0.09634359925985336,
0.009249540977180004,
-0.010671194642782211,
0.021380091086030006,
0.004832439124584198,
0.008254289627075195,
0.0032114428468048573,
-0.03184468299150467,
0.024174312129616737,
0.04949512332677841,
-0.0033621203619986773,
0.029889311641454697,
-0.011424712836742401,
-0.04470568522810936,
-0.014022012241184711,
0.027828654274344444,
0.021429099142551422,
-0.01483188383281231,
-0.01705068349838257,
-0.011323243379592896,
0.07461954653263092,
-0.029731960967183113,
0.061091579496860504,
0.03563714399933815,
-0.02128230594098568,
-0.03392348065972328,
0.011598462238907814,
0.014639968052506447,
-0.007491391152143478,
-0.03128724917769432,
-0.029370561242103577,
-0.06049470230937004,
0.006026226095855236,
0.00022486463421955705,
-0.02948159910738468,
-0.04861975833773613,
-0.014483725652098656,
-0.023634832352399826,
0.06953383982181549,
-0.03179577738046646,
-0.0008142302394844592,
0.03447622060775757,
0.015338377095758915,
0.06088942661881447,
-0.03328431770205498,
-0.040598951280117035,
-0.009805606678128242,
-0.003962487448006868,
0.0013430521357804537,
-0.024778267368674278,
-0.033806778490543365,
0.01263634767383337,
0.030659249052405357,
-0.009988361038267612,
-0.048501089215278625,
0.08132189512252808,
-0.020249808207154274,
-0.017741896212100983,
0.04338231682777405,
0.022257834672927856,
-0.0032317950390279293,
-0.0004263708833605051,
0.01358012855052948,
-0.015967411920428276,
0.04780888184905052,
0.01005307212471962,
0.014902829192578793,
0.0062705413438379765,
0.042035821825265884,
0.018545761704444885,
0.054003939032554626,
-0.03591310977935791,
-0.03409625589847565,
0.008391378447413445,
-0.005607624538242817,
0.03574706241488457,
0.03071564994752407,
-0.024477602913975716,
-0.018772322684526443,
0.0562044158577919,
-0.013488942757248878,
0.015284419059753418,
-0.00047420032205991447,
-0.0611298531293869,
0.02597859874367714,
-0.010230028070509434,
0.013974550180137157,
0.03207772597670555,
0.08933569490909576,
-0.02487834356725216,
-0.04797970876097679,
0.039878033101558685,
-0.018455523997545242,
0.034865960478782654,
0.0035091936588287354,
0.00023447703279089183,
0.0665842741727829,
-0.03210915997624397,
-0.05188807472586632,
-0.042182885110378265,
-0.027890771627426147,
-0.020406672731041908,
0.044927164912223816,
0.039740387350320816,
-0.05331536382436752,
0.01690567657351494,
-0.008103955537080765,
-0.007288963999599218,
-0.041740790009498596,
-0.044215794652700424,
-0.020352678373456,
-0.0004955168697051704,
-0.03628671169281006,
-0.008900097571313381,
-0.03426957130432129,
-0.09083884209394455,
0.014996198937296867,
-0.06276295334100723,
-0.02976498194038868,
-0.008395700715482235,
-0.065823495388031,
0.0037401653826236725,
-0.015575122088193893,
-0.04991154745221138,
0.03509308770298958,
0.039741598069667816,
-0.00493089621886611,
0.029512787237763405,
0.056739915162324905,
-0.016872981563210487,
0.023799655959010124,
0.03134879097342491,
0.0026502313558012247,
-0.00245222938247025,
0.08612538874149323,
-0.04823008552193642,
-0.013812713325023651,
0.006155257113277912,
-0.00008306724339490756,
-0.047181643545627594,
-0.022592971101403236,
0.020666800439357758,
-0.003924911841750145,
-0.027303751558065414,
-0.004951206501573324
] |
<p>I'm having trouble with the following problem.</p>
<p><img src="http://i.stack.imgur.com/ed8nE.png" alt="Problem"></p>
<p><em>What I've done so far:</em></p>
<p>x-y is the usual coordinate system.</p>
<p>$a=\frac{F}{m}=\frac{800}{60}$ and the y component of this is $a_y=a\sin{60^\circ}$.</p>
<p>To figure out the force acting on the rod and contributing to the momentum, I take the sum of all forces in the y direction. Note that from now on, I am thinking about the rod as being separated from the rest of the body. The weld is represented by forces ($O_y, O_x$), and the rod is moving upwards with the acceleration calculated above.</p>
<p>$\Sigma F_y= O_y-20g = 20a_y\implies O_y=20a_y+20g$</p>
<p>Now, the momentum equation about the center of mass of the rod should be</p>
<p>$\Sigma M_G=0.7O_y+\bar{I}\omega_G=\bar{I}\alpha=0$</p>
<p>Because the rod is not rotating. Is this equation right? (Why not?)</p>
<p>If it is right, it implies that $\bar{I}\omega_G=-0.7O_y$. Where do I go from here? The things I've tried from here on don't yield the right answer, and I do not have much confidence in those strategies.</p>
<p>The correct answer, if anyone cares, is 196 Nm.</p> | g7863 | [
0.025751614943146706,
0.018265726044774055,
-0.009344852529466152,
-0.08357405662536621,
0.03353707492351532,
-0.02571455016732216,
0.07257106900215149,
0.035240475088357925,
-0.011324967257678509,
-0.0024356681387871504,
0.03137646242976189,
0.017829645425081253,
-0.031453996896743774,
-0.013836842030286789,
0.06304433941841125,
-0.02540704607963562,
0.05779610201716423,
-0.00006026348637533374,
0.017924968153238297,
0.031583938747644424,
0.0064419289119541645,
0.015964850783348083,
0.010388568975031376,
-0.015209661796689034,
0.04231409355998039,
0.01593843474984169,
-0.02115829847753048,
-0.0016054167645052075,
-0.05019903555512428,
0.03856896609067917,
-0.003182939486578107,
0.03736935555934906,
0.03453284502029419,
-0.0640982985496521,
-0.009630594402551651,
-0.001695992425084114,
0.017524458467960358,
0.023308448493480682,
0.02252635732293129,
-0.04531233012676239,
-0.0714484229683876,
-0.03078676387667656,
0.004529648460447788,
0.04456488788127899,
0.011232288554310799,
-0.02655024640262127,
-0.027484366670250893,
-0.06109905615448952,
-0.043085623532533646,
0.013383131474256516,
-0.010867360979318619,
0.004728039260953665,
0.035962849855422974,
-0.012660251930356026,
0.0020689708180725574,
0.04722430184483528,
0.024391084909439087,
-0.024517521262168884,
0.02701382152736187,
0.0549243725836277,
-0.0027925821486860514,
-0.026243271306157112,
0.005468353163450956,
-0.09605260193347931,
0.006488282233476639,
-0.012541255913674831,
-0.0027299278881400824,
0.001745192101225257,
0.004119266755878925,
-0.01237682905048132,
0.04037663713097572,
-0.02820582687854767,
0.014123276807367802,
-0.051252733916044235,
-0.10247471928596497,
0.022580858319997787,
0.0025854716077446938,
0.013336964882910252,
-0.031992971897125244,
-0.037510666996240616,
-0.0398930199444294,
0.0037486532237380743,
0.08113928884267807,
-0.0076122283935546875,
0.0008566471515223384,
-0.009608875960111618,
-0.00416534673422575,
0.08275912702083588,
-0.053087856620550156,
-0.011323113925755024,
0.028826234862208366,
0.01715891808271408,
0.017090894281864166,
0.03107428550720215,
0.02055838331580162,
-0.056876637041568756,
-0.030164191499352455,
0.08058273792266846,
0.021609576418995857,
0.008554792031645775,
-0.01075162086635828,
-0.017312753945589066,
-0.04546897113323212,
0.00822317972779274,
0.025294290855526924,
-0.03038296103477478,
0.026670632883906364,
0.028155572712421417,
-0.032292451709508896,
-0.0032586962915956974,
-0.04282555729150772,
-0.03393230959773064,
-0.038994863629341125,
-0.08829847723245621,
-0.07100856304168701,
-0.06510154157876968,
0.09076664596796036,
-0.017549913376569748,
-0.013779806904494762,
0.011293776333332062,
-0.007168578915297985,
-0.008741967380046844,
0.011425483971834183,
0.09331201016902924,
-0.013470951467752457,
-0.023780787363648415,
-0.02769796922802925,
-0.0027522780001163483,
0.02054019831120968,
0.004056878853589296,
-0.008287998847663403,
-0.026832716539502144,
0.05977362021803856,
0.00047651006025262177,
0.004831087309867144,
-0.004604175221174955,
-0.024260157719254494,
0.010425473563373089,
0.026771511882543564,
0.06342019885778427,
0.01103258691728115,
-0.04932442307472229,
0.024923985823988914,
-0.04264644905924797,
-0.035100944340229034,
0.018772341310977936,
-0.04083230718970299,
0.0030123889446258545,
0.056159768253564835,
0.0006986789521761239,
0.015703365206718445,
0.08346773684024811,
-0.01650223881006241,
-0.00751644279807806,
0.008353475481271744,
-0.055886924266815186,
0.012994040735065937,
-0.0035838026087731123,
0.027611548081040382,
-0.004726573824882507,
0.04119972139596939,
-0.024586843326687813,
0.03266036882996559,
-0.04224616289138794,
-0.06560128182172775,
0.03026130236685276,
-0.019828656688332558,
-0.03850891813635826,
-0.03928818553686142,
0.0034351034555584192,
-0.031198598444461823,
-0.061652351170778275,
-0.015425380319356918,
0.0049972739070653915,
0.01418901327997446,
0.07769975066184998,
0.03568124398589134,
-0.04387536644935608,
-0.0070828706957399845,
0.08772335946559906,
0.03233705833554268,
-0.014908378012478352,
0.07510378956794739,
0.016135210171341896,
-0.007324105128645897,
-0.010063146241009235,
0.02984016202390194,
0.09441422671079636,
-0.044717300683259964,
-0.0009666866390034556,
-0.008293394930660725,
0.005979602690786123,
-0.024809997528791428,
0.07200579345226288,
-0.06628990173339844,
-0.006420048885047436,
0.003111938014626503,
-0.08020271360874176,
0.0069242906756699085,
0.025849422439932823,
-0.004706792999058962,
0.030609114095568657,
0.013235976919531822,
0.0389932319521904,
0.04423058032989502,
-0.011151542887091637,
-0.0032800398766994476,
0.010128071531653404,
-0.00913034938275814,
0.001782238599844277,
-0.021701017394661903,
-0.025177864357829094,
-0.03600079566240311,
0.052137915045022964,
-0.03714689984917641,
-0.09206826984882355,
0.03496210649609566,
0.030518481507897377,
-0.04084501788020134,
0.020039470866322517,
-0.00924074836075306,
0.010242022573947906,
0.008394964970648289,
0.010686629451811314,
-0.05272893235087395,
-0.034881994128227234,
0.01385290827602148,
0.004532237071543932,
0.013305800035595894,
0.0009318634984083474,
-0.054435648024082184,
0.015535516664385796,
0.015048425644636154,
0.012826384976506233,
0.06212673708796501,
0.0020183457527309656,
-0.008942077867686749,
0.01707642339169979,
-0.04156532138586044,
0.00849171169102192,
0.03658292070031166,
0.008884629234671593,
0.01176015380769968,
-0.09900404512882233,
0.07480797916650772,
0.004730596672743559,
0.07020339369773865,
0.022704703733325005,
0.0037312807980924845,
-0.012873606756329536,
0.05035371333360672,
0.0017747003585100174,
-0.06778339296579361,
-0.002519760513678193,
-0.0034344105515629053,
-0.021836040541529655,
-0.05680388957262039,
0.018239282071590424,
-0.0601920485496521,
-0.03815814480185509,
-0.05075512453913689,
-0.031177308410406113,
0.023067167028784752,
0.045324910432100296,
-0.08809010684490204,
0.04666725546121597,
-0.07044952362775803,
-0.040820635855197906,
0.02661009319126606,
-0.0223220344632864,
-0.08535097539424896,
-0.02770189382135868,
0.0017560076666995883,
0.014141368679702282,
0.005465385969728231,
-0.05587342008948326,
0.027803469449281693,
-0.015195207670331001,
-0.03191778063774109,
0.05553104728460312,
-0.019950514659285545,
0.030875040218234062,
0.01461821049451828,
0.04857819154858589,
0.016764910891652107,
0.011542378924787045,
-0.0037871331442147493,
0.025008168071508408,
0.028416922315955162,
0.030466267839074135,
-0.045992933213710785,
0.011902501806616783,
0.058773305267095566,
-0.018886618316173553,
-0.009775425307452679,
0.07645288109779358,
0.020447473973035812,
-0.04834789037704468,
-0.00782322883605957,
0.006701645441353321,
-0.0019436648581176996,
-0.0007200894760899246,
-0.03224357217550278,
0.00844020489603281,
0.0471029095351696,
0.017173221334815025,
-0.025203336030244827,
-0.017243651673197746,
0.01583697646856308,
-0.021649392321705818,
-0.04311002790927887,
0.027095681056380272,
0.01117540244013071,
-0.03186873719096184,
-0.025623740628361702,
-0.03282209113240242,
-0.01868119277060032,
-0.01874691992998123,
0.013774298131465912,
0.001532797934487462,
-0.042959313839673996,
-0.054639432579278946,
0.009532671421766281,
0.004747857805341482,
0.02271655946969986,
0.04730818048119545,
0.0032572925556451082,
0.04105905070900917,
-0.03708779066801071,
0.02208670601248741,
0.020111490041017532,
0.016682924702763557,
0.01954391971230507,
0.0007728505879640579,
-0.06013716384768486,
-0.0319100059568882,
-0.006343035958707333,
0.04503296688199043,
0.004188441205769777,
0.0365351177752018,
-0.04279589280486107,
-0.005819791462272406,
0.03065405786037445,
-0.021121662110090256,
0.018737921491265297,
0.02313443273305893,
-0.008094998076558113,
0.075894296169281,
0.04784747585654259,
-0.017014697194099426,
-0.014130892232060432,
-0.006182542536407709,
-0.02345678210258484,
0.024215368553996086,
-0.008919366635382175,
0.05026708543300629,
0.05726935714483261,
-0.010085382498800755,
-0.06136313080787659,
-0.0059346770867705345,
0.0068262009881436825,
-0.013044684194028378,
0.006399194709956646,
0.012370776385068893,
0.009366761893033981,
-0.01183407660573721,
0.0019491697894409299,
0.032108426094055176,
-0.027698591351509094,
-0.031004194170236588,
-0.01029367558658123,
-0.06631085276603699,
-0.034417420625686646,
-0.034021683037281036,
-0.023625114932656288,
-0.04953892529010773,
0.03563814237713814,
-0.01898491382598877,
0.018297191709280014,
0.058525487780570984,
0.04554438591003418,
0.021704338490962982,
-0.0609680712223053,
0.015487189404666424,
0.011091156862676144,
0.025869173929095268,
0.004021793603897095,
0.03928504139184952,
0.04226994141936302,
-0.027429873123764992,
0.05615398660302162,
-0.04932298883795738,
-0.032895851880311966,
0.035515476018190384,
0.034792035818099976,
-0.062173519283533096,
0.04547119140625,
-0.0007962872041389346,
-0.06116309389472008,
-0.04078580066561699,
0.01528023649007082,
0.026218488812446594,
0.030255332589149475,
0.015548809431493282,
-0.02481752447783947,
0.13054439425468445,
0.03102351911365986,
-0.010744020342826843,
-0.0006954430718906224,
-0.0032283859327435493,
0.02845582738518715,
-0.009686759673058987,
0.028793679550290108,
-0.03129870444536209,
0.04966193810105324,
-0.01381517294794321,
-0.004794036038219929,
0.02691732719540596,
-0.01699158363044262,
-0.002430025488138199,
0.03191022574901581,
0.06880609691143036,
0.05341116338968277,
-0.02290581911802292,
-0.00043072979315184057,
0.025053631514310837,
0.030379774048924446,
-0.0015142438933253288,
0.07298313826322556,
-0.018176091834902763,
-0.019853269681334496,
0.013376540504395962,
-0.03658550605177879,
-0.04545272886753082,
-0.03990611806511879,
0.06064239889383316,
-0.02391974814236164,
-0.03643941134214401,
0.02464178390800953,
0.09029150009155273,
0.05026018247008324,
0.04308801144361496,
0.032377101480960846,
-0.0030978876166045666,
-0.02014687843620777,
0.047068096697330475,
-0.015586388297379017,
-0.020388547331094742,
-0.02614140324294567,
0.023453377187252045,
-0.034193966537714005,
-0.029805785045027733,
0.0030830318573862314,
-0.04689302667975426,
0.05604778975248337,
0.04775741323828697,
-0.028977248817682266,
-0.008942441083490849,
0.014010943472385406,
-0.008141102269291878,
-0.007215105462819338,
-0.04975953698158264,
-0.02982291579246521,
-0.02587210200726986,
0.048270490020513535,
0.021044667810201645,
0.01514438446611166,
-0.0044241915456950665,
-0.01155448704957962,
-0.033555928617715836,
0.05581081286072731,
-0.011616130359470844,
0.01987997069954872,
-0.025283565744757652,
-0.045710716396570206,
0.035091109573841095,
0.0017775833839550614,
0.011646812781691551,
0.06289101392030716,
-0.017539016902446747,
-0.06164082512259483,
0.034450821578502655,
0.004371595568954945,
-0.04022098332643509,
0.02583497203886509,
-0.061527252197265625,
-0.018670253455638885,
-0.008225847966969013,
0.03397277370095253,
0.02039761282503605,
-0.00174615322612226,
0.07658226788043976,
-0.04509255290031433,
-0.039603594690561295,
-0.004262914881110191,
0.028112957254052162,
-0.01843271218240261,
-0.04955018684267998,
0.00058766920119524,
0.008462788537144661,
-0.054302241653203964,
0.004181799478828907,
-0.05262676998972893,
0.014573854394257069,
0.007561082020401955,
0.07365919649600983,
0.04620137810707092,
0.026433268561959267,
-0.015436890535056591,
0.09343340247869492,
0.009109675884246826,
0.01687023788690567,
0.04726376757025719,
-0.04556931182742119,
-0.027341332286596298,
-0.0525701530277729,
0.023637430742383003,
0.015077430754899979,
-0.002227321034297347,
0.004591094329953194,
0.061188820749521255,
0.01635037548840046,
0.02519364096224308,
-0.08881694823503494,
-0.03514069318771362,
0.025220276787877083,
-0.0040023308247327805,
-0.009212751872837543,
-0.04494401067495346,
-0.0003449613868724555,
0.011484362185001373,
-0.06317611783742905,
0.0033925685565918684,
0.004411725793033838,
-0.0014318630564957857,
0.00040833771345205605,
0.05511537194252014,
-0.02698625437915325,
0.020656388252973557,
-0.07513360679149628,
0.02265756018459797,
-0.020061569288372993,
0.04989651218056679,
0.030424777418375015,
-0.08952273428440094,
0.003606815356761217,
-0.04294099286198616,
-0.03415752202272415,
0.031823351979255676,
0.005232421215623617,
-0.008416549302637577,
0.062580406665802,
-0.03156080096960068,
0.011213988065719604,
0.036553800106048584,
-0.0007729080971330404,
0.003449472365900874,
-0.016115684062242508,
-0.018429849296808243,
-0.009101778268814087,
0.03577110171318054,
-0.05399049445986748,
0.03414154052734375,
0.03730844706296921,
0.04767671599984169,
0.013944685459136963,
-0.0035456412006169558,
-0.05401286855340004,
0.038417570292949677,
0.0476205088198185,
0.024218617007136345,
-0.0035298296716064215,
-0.006871889811009169,
0.03909154608845711,
0.041499268263578415,
0.039444152265787125,
-0.07465827465057373,
0.02366524562239647,
-0.01589745469391346,
0.034659456461668015,
0.002467753365635872,
0.04776071384549141,
0.006556581240147352,
-0.03181225806474686,
-0.021048689261078835,
0.001740962383337319,
-0.03141281008720398,
-0.04055361449718475,
-0.0090626897290349,
0.0033343916293233633,
-0.045941825956106186,
0.027110889554023743,
-0.011098379269242287,
0.02487736940383911,
-0.037369757890701294,
-0.0052328105084598064,
0.037826985120773315,
-0.020507996901869774,
-0.000859549269080162,
0.05034665763378143,
-0.0053228335455060005,
0.010810649022459984,
0.03966006636619568,
0.011979861184954643,
0.04283623397350311,
-0.006079336628317833,
-0.010230214335024357,
0.005334945861250162,
-0.027207553386688232,
-0.0359746553003788,
0.04668097198009491,
0.031204713508486748,
-0.024312753230333328,
0.015162005089223385,
0.024429839104413986,
0.001791271846741438,
0.009729059413075447,
0.05340826138854027,
-0.007004050072282553,
0.031833715736866,
0.022970814257860184,
-0.011410152539610863,
-0.01468248013406992,
-0.007639109157025814,
0.013870594091713428,
0.005235668271780014,
-0.09125136584043503,
-0.03778224065899849,
0.034294143319129944,
-0.002372058806940913,
0.04126716032624245,
-0.03293749690055847,
-0.014487847685813904,
-0.0022276020608842373,
-0.0005269151879474521,
0.06047616899013519,
0.026083149015903473,
0.05844439938664436,
0.03219380974769592,
0.0611330009996891,
-0.0022761046420782804,
0.01602163352072239,
-0.006622993387281895,
0.03396710008382797,
-0.053000081330537796,
-0.025902386754751205,
-0.01537251751869917,
0.007890232838690281,
-0.10436033457517624,
0.049145426601171494,
0.002403141697868705,
-0.06347144395112991,
0.007321013603359461,
0.058733128011226654,
-0.02461175061762333,
0.014133024960756302,
-0.00701391976326704,
0.029325854033231735,
0.044077545404434204,
0.018104014918208122,
-0.025861969217658043,
-0.02863987721502781,
0.024596020579338074,
0.006617940496653318,
-0.08062426000833511,
0.050716228783130646,
-0.007609232794493437,
-0.007098057772964239,
-0.004362812731415033,
-0.017875131219625473,
-0.025450287386775017,
-0.01737169362604618,
-0.024582933634519577,
-0.027011532336473465,
0.014381066896021366,
0.021016648039221764,
0.011479443870484829,
-0.04632080718874931,
-0.05368974432349205,
0.006313766818493605,
-0.025579284876585007,
0.0514066144824028,
-0.04863351956009865,
-0.00949939340353012,
0.023320337757468224,
-0.017179902642965317,
0.02652936987578869,
-0.005019049625843763,
0.02966815046966076,
0.004041837062686682,
-0.03298724442720413,
0.1022394523024559,
0.0055845752358436584,
-0.004554857034236193,
0.006366519257426262,
0.01346833910793066,
-0.051031194627285004,
0.03838634118437767,
0.011701822280883789,
0.000022666928998660296,
0.023727279156446457,
-0.04582943394780159,
-0.02212134376168251,
0.010248581878840923,
-0.03174378722906113,
0.0006519862217828631,
-0.033651791512966156,
-0.02481783740222454,
-0.005502872634679079,
-0.04453786462545395,
0.005028157960623503,
-0.003934560809284449,
-0.009232115931808949,
-0.05241801589727402,
0.007403640076518059,
0.07314783334732056,
-0.040482740849256516,
0.06627872586250305,
0.014948328956961632,
-0.003713733982294798,
-0.029704052954912186,
0.022403234615921974,
-0.011180490255355835,
-0.06648924201726913,
-0.03418984264135361,
-0.05002461373806,
-0.026043031364679337,
0.0011733631836250424,
0.016780326142907143,
-0.026841266080737114,
-0.018724408000707626,
-0.02377178892493248,
-0.049811143428087234,
-0.02391793578863144,
-0.015713242813944817,
-0.06245315819978714,
-0.0034265273716300726,
-0.05133972316980362,
0.02422170713543892,
0.0061481064185500145,
-0.0038324003107845783,
-0.07046999782323837,
-0.04210704192519188,
-0.0311807282269001,
0.011573941446840763,
0.0199950709939003,
-0.05682873725891113,
0.07406356930732727,
-0.003277434268966317,
0.04652882367372513,
0.017887821421027184,
0.028723130002617836,
-0.04538589343428612,
-0.048154182732105255,
0.02069520764052868,
-0.021752847358584404,
-0.028366267681121826,
0.0768754854798317,
-0.004298369400203228,
0.005126774776726961,
-0.026560576632618904,
0.035912930965423584,
-0.06373201310634613,
-0.0295120682567358,
0.031190233305096626,
-0.03980464115738869,
-0.062445685267448425,
-0.0186923798173666
] |
<p>Let's consider a spring. I am a strong man(well, lets assume) and I am pulling the spring. the work I do is being stored in the spring in the form of its elastic potential energy. Then suddenly, elastic limit is crossed and the spring reaches to the yielding region. then, at that very moment, i become exhausted and release the spring. then I realise that the spring doesn't budge. the energy i stored is lost. its gone. Nowhere to be found. Mind helping me find it?</p> | g7864 | [
0.04827595874667168,
0.015724167227745056,
0.019661258906126022,
-0.013621017336845398,
-0.0059245917946100235,
0.012500395067036152,
-0.005945396609604359,
0.029300685971975327,
-0.046288177371025085,
-0.03409427031874657,
-0.05320651829242706,
-0.039355698972940445,
-0.026399556547403336,
-0.03241991624236107,
0.006537186447530985,
0.011586794629693031,
0.09931571781635284,
-0.009742110967636108,
0.018691083416342735,
-0.013931356370449066,
0.013009123504161835,
-0.00675966264680028,
0.05144640430808067,
0.024384843185544014,
-0.008934678509831429,
0.029129838570952415,
-0.0010687803151085973,
0.021879184991121292,
-0.07352306693792343,
-0.026024023070931435,
-0.0025699299294501543,
-0.008711966685950756,
0.032672565430402756,
-0.050308939069509506,
-0.07208959013223648,
0.006847493816167116,
0.07209432125091553,
0.023550448939204216,
0.009224687702953815,
0.038467809557914734,
0.015320542268455029,
-0.05023067444562912,
-0.0059027583338320255,
0.00626587588340044,
0.010689719580113888,
0.0035137906670570374,
0.023092450574040413,
0.024520771577954292,
0.016687117516994476,
-0.0462694875895977,
-0.0029520527459681034,
0.021475547924637794,
0.01566869392991066,
-0.04415339231491089,
0.034659795463085175,
-0.03579245135188103,
0.011294478550553322,
-0.015324363484978676,
0.08409862220287323,
-0.038484133780002594,
0.06636268645524979,
-0.006660046987235546,
0.0012950570089742541,
-0.02437182329595089,
0.02828238718211651,
0.008207004517316818,
-0.0380001999437809,
-0.01334390603005886,
0.0423474945127964,
-0.04633577540516853,
0.020188072696328163,
-0.01266401819884777,
-0.00042044988367706537,
-0.05158673971891403,
-0.055980585515499115,
0.04405631124973297,
-0.0063596973195672035,
0.04328475147485733,
-0.011756791733205318,
-0.03780052810907364,
-0.007397213019430637,
0.03641222044825554,
-0.018761564046144485,
-0.009191934019327164,
0.04162554442882538,
0.02016066014766693,
0.02633238583803177,
0.03703176602721214,
0.0026036729104816914,
0.035248104482889175,
0.01949303224682808,
0.0037104019429534674,
0.054562877863645554,
-0.00354640930891037,
-0.024843791499733925,
-0.02861090749502182,
0.01296919770538807,
0.043289318680763245,
-0.05455825477838516,
0.0008686560904607177,
-0.01705736294388771,
-0.10905316472053528,
-0.05752481892704964,
-0.03204274922609329,
0.008560292422771454,
-0.02288244292140007,
-0.004251542035490274,
-0.012931196950376034,
-0.0239715576171875,
0.020404331386089325,
0.057955920696258545,
-0.018733320757746696,
-0.008866647258400917,
-0.06969812512397766,
-0.008693267591297626,
-0.05676651373505592,
0.028601936995983124,
0.003675507614389062,
0.001311361906118691,
0.01241990178823471,
0.0014364221133291721,
0.05391142889857292,
0.06454329192638397,
0.030285362154245377,
0.005026421044021845,
-0.0027075193356722593,
-0.012823635712265968,
0.008818584494292736,
-0.02666577324271202,
0.00831226073205471,
-0.019096387550234795,
-0.0167922992259264,
0.03794410824775696,
0.011689873412251472,
0.00322362850420177,
0.029887011274695396,
0.0029272991232573986,
0.013812483288347721,
0.004805525299161673,
0.031066900119185448,
0.01990271918475628,
-0.0297672338783741,
-0.007418985944241285,
-0.007320794276893139,
-0.014273514971137047,
0.05439786985516548,
0.021372070536017418,
-0.024082977324724197,
0.010191908106207848,
-0.03860193490982056,
0.014745969325304031,
0.06924498826265335,
-0.07308607548475266,
-0.058019571006298065,
0.06170893833041191,
-0.04636785015463829,
-0.00005549878187594004,
-0.012964243069291115,
-0.018904786556959152,
0.015461106784641743,
0.03687536343932152,
-0.036829352378845215,
-0.04334012046456337,
0.022769691422581673,
-0.04612006992101669,
-0.004589932505041361,
-0.014280198141932487,
0.0031818323768675327,
0.050173137336969376,
-0.026364615187048912,
-0.05190960317850113,
-0.04443709924817085,
0.04334577918052673,
0.044333744794130325,
-0.0181567519903183,
0.05944423750042915,
0.08617822825908661,
-0.04719075933098793,
0.04900876805186272,
-0.00844036415219307,
0.011320914141833782,
-0.024454178288578987,
0.05049295350909233,
-0.03076009266078472,
-0.009432188235223293,
-0.011401827447116375,
0.013668485917150974,
0.06715753674507141,
-0.0038546391297131777,
-0.05634975805878639,
-0.010096505284309387,
-0.012712209485471249,
0.043685078620910645,
0.038311924785375595,
0.018678788095712662,
-0.009281476028263569,
0.02923077717423439,
-0.06564287841320038,
0.011879034340381622,
0.03289368376135826,
0.021011393517255783,
-0.03179553896188736,
0.054402563720941544,
0.008880531415343285,
0.009089135564863682,
-0.06126873195171356,
-0.01505979709327221,
0.02337445691227913,
-0.00790372770279646,
-0.022521214559674263,
0.039426982402801514,
-0.036183468997478485,
-0.019505375996232033,
0.0281620342284441,
-0.008597404696047306,
-0.012505763210356236,
-0.005803926382213831,
0.00671347975730896,
0.00708865188062191,
-0.003118478460237384,
-0.010386522859334946,
-0.016423070803284645,
0.02997342124581337,
0.008243100717663765,
-0.04205603152513504,
0.006506031844764948,
-0.026633089408278465,
-0.02578742243349552,
-0.026614801958203316,
-0.028473958373069763,
-0.021357078105211258,
0.05488450825214386,
0.023908961564302444,
0.007486778777092695,
0.001568019506521523,
0.0412355400621891,
-0.02626926451921463,
0.01954810321331024,
-0.02498791180551052,
-0.04530366137623787,
-0.016949908807873726,
-0.010781505145132542,
-0.029374195262789726,
-0.008151494897902012,
-0.006627628579735756,
0.03868527337908745,
0.013960778713226318,
-0.011940475553274155,
0.05180145800113678,
0.04191367328166962,
0.05880318582057953,
0.022276904433965683,
-0.005675201769918203,
0.03441156446933746,
0.002231291960924864,
0.02421148493885994,
-0.02280515991151333,
0.014438656158745289,
-0.03654041141271591,
-0.09281887114048004,
-0.027379415929317474,
0.02428201213479042,
0.03155950829386711,
0.008101150393486023,
-0.025502754375338554,
-0.024748381227254868,
-0.013685925863683224,
-0.07765031605958939,
-0.03273814544081688,
-0.007971114479005337,
-0.04407096654176712,
0.07211209088563919,
0.036276474595069885,
0.05930650606751442,
0.04381117597222328,
-0.005689741112291813,
-0.0056963590905070305,
0.024299729615449905,
0.009305051527917385,
-0.030728181824088097,
0.007415613159537315,
0.029497308656573296,
0.0055800750851631165,
0.009846587665379047,
-0.03836461901664734,
-0.06838109344244003,
-0.0023958913516253233,
0.036384087055921555,
0.0015692897140979767,
-0.0022788923233747482,
-0.031678929924964905,
0.03768232837319374,
0.0517469085752964,
0.014914436265826225,
-0.04913061857223511,
0.049253109842538834,
0.017422756180167198,
-0.01386234536767006,
-0.056007515639066696,
0.02750951424241066,
-0.01924940198659897,
-0.04101910442113876,
0.002965519204735756,
-0.03637108579277992,
0.03381148725748062,
0.0030500562861561775,
0.03363032639026642,
-0.021280324086546898,
0.033645354211330414,
0.012730194255709648,
0.0010913104051724076,
0.025461656972765923,
0.10153025388717651,
-0.011137896217405796,
-0.08832201361656189,
0.05751887336373329,
0.0066756391897797585,
-0.0808921679854393,
0.025474796071648598,
-0.03894040361046791,
0.032697707414627075,
-0.03308862820267677,
0.043442584574222565,
0.022875435650348663,
-0.025629013776779175,
0.024361230432987213,
-0.10101474076509476,
0.026768658310174942,
-0.07798970490694046,
-0.017645252868533134,
-0.05739486590027809,
-0.015638107433915138,
-0.0006660885410383344,
-0.040324874222278595,
-0.05864677578210831,
-0.025334838777780533,
0.0016949500422924757,
0.0021344709675759077,
0.06920482963323593,
0.006185377482324839,
0.00201909220777452,
0.029134733602404594,
-0.006919958628714085,
-0.009136597625911236,
0.029299484565854073,
0.027578318491578102,
-0.014206375926733017,
0.0020109647884964943,
0.022867048159241676,
-0.0264421533793211,
0.013693689368665218,
-0.014464176259934902,
-0.022077100351452827,
-0.05514616146683693,
0.013754119165241718,
0.010007797740399837,
0.022668281570076942,
-0.0029591547790914774,
-0.07871010899543762,
0.0050436025485396385,
-0.01989133469760418,
-0.056608088314533234,
0.07709924131631851,
-0.01832403615117073,
-0.036447346210479736,
0.016812287271022797,
-0.013660470955073833,
0.03600950539112091,
-0.02606649324297905,
-0.0204783882945776,
0.07970702648162842,
-0.02206682413816452,
-0.004034803714603186,
0.05806151032447815,
-0.03667350858449936,
-0.07944772392511368,
-0.011857166886329651,
0.0122948307543993,
-0.030153194442391396,
-0.0006086038774810731,
0.043772220611572266,
0.00183851458132267,
-0.0406893789768219,
0.0010338103165850043,
0.006785805802792311,
-0.014132737182080746,
0.01855655014514923,
-0.0014878183137625456,
0.017638957127928734,
-0.0033515067771077156,
0.011385860852897167,
-0.015538041479885578,
-0.039547961205244064,
0.05494006350636482,
-0.029652424156665802,
-0.027372285723686218,
-0.004074485972523689,
-0.00956515409052372,
-0.03303537145256996,
0.007676825858652592,
-0.02871915139257908,
0.05360272899270058,
-0.047390300780534744,
0.0068997712805867195,
0.012598300352692604,
0.031220633536577225,
0.051985275000333786,
-0.042631201446056366,
0.014038212597370148,
-0.04018348082900047,
0.04254620149731636,
-0.05135396122932434,
-0.014032313600182533,
-0.033802278339862823,
-0.020067496225237846,
-0.06017083302140236,
0.0631522536277771,
-0.019287822768092155,
0.01939805969595909,
0.011760464869439602,
0.019246991723775864,
0.0024212589487433434,
-0.004256781656295061,
0.010778656229376793,
-0.011280003935098648,
0.029198581352829933,
-0.026292765513062477,
-0.029948225244879723,
0.025225648656487465,
-0.05486056208610535,
-0.05127875506877899,
0.01058879867196083,
0.01854747347533703,
-0.01881820522248745,
-0.019673774018883705,
0.08352560549974442,
0.016682220622897148,
0.01355730090290308,
-0.057844117283821106,
0.0740324854850769,
0.00099125225096941,
-0.0009962506592273712,
0.048892803490161896,
0.061682943254709244,
-0.051097024232149124,
0.014534094370901585,
0.010190827772021294,
-0.015049885027110577,
-0.011890614405274391,
-0.06205517053604126,
-0.022043678909540176,
-0.05499298870563507,
-0.007367092650383711,
-0.02344553731381893,
0.014163857325911522,
0.005553300492465496,
-0.052377570420503616,
-0.016896381974220276,
0.022763682529330254,
0.043835803866386414,
-0.004281239118427038,
-0.07615341991186142,
0.009409367106854916,
0.04989149793982506,
0.008939755149185658,
-0.05952727422118187,
0.021319245919585228,
-0.03617313504219055,
0.015616677701473236,
-0.005705597344785929,
0.02472076751291752,
0.01568615436553955,
0.03525680676102638,
0.06295963376760483,
0.037649016827344894,
0.015610216185450554,
0.04899635165929794,
-0.007322859019041061,
0.06708370894193649,
-0.010468225926160812,
-0.044423915445804596,
0.005263425409793854,
-0.05460365116596222,
0.0007183723500929773,
-0.025336265563964844,
0.017957797273993492,
-0.026809820905327797,
0.022549254819750786,
0.013599837198853493,
0.01681603491306305,
0.05728753283619881,
0.05269327387213707,
0.0032142987474799156,
-0.021791143342852592,
0.05406125634908676,
0.04161270707845688,
-0.011506099253892899,
0.031781699508428574,
-0.05282201990485191,
0.02181096002459526,
-0.0620078444480896,
0.041504837572574615,
-0.027584291994571686,
0.04870573431253433,
-0.019200723618268967,
-0.009399290196597576,
-0.02367584966123104,
0.024133218452334404,
-0.00035362879862077534,
-0.023396572098135948,
-0.022439418360590935,
-0.0024217264726758003,
-0.03698332607746124,
0.023721318691968918,
0.047758251428604126,
0.02646552212536335,
0.0078175263479352,
0.01349545270204544,
-0.06588112562894821,
-0.022140659391880035,
0.031280357390642166,
0.035111840814352036,
0.04588892683386803,
-0.03642768785357475,
0.02421499602496624,
-0.031900554895401,
-0.05709807574748993,
0.023888275027275085,
-0.010400636121630669,
0.029014674946665764,
0.07244712114334106,
-0.03556566685438156,
-0.035191480070352554,
0.0032881007064133883,
0.011526697315275669,
0.02042829617857933,
-0.022404745221138,
-0.0016154367476701736,
-0.043718576431274414,
-0.001466250279918313,
-0.012910556979477406,
-0.016557492315769196,
0.012880250811576843,
-0.007043669931590557,
-0.03644688427448273,
-0.017982179298996925,
-0.1213231161236763,
-0.03136239945888519,
0.07949446141719818,
0.017233802005648613,
0.04310009256005287,
0.06308240443468094,
-0.026694737374782562,
0.04355694353580475,
0.010143491439521313,
-0.019297702237963676,
0.011277666315436363,
-0.054563526064157486,
-0.03705388680100441,
0.027979036793112755,
-0.029123075306415558,
0.04671404883265495,
0.014831503853201866,
0.04013834148645401,
0.038219232112169266,
-0.04677120968699455,
-0.014167220331728458,
-0.06893982738256454,
0.0401102639734745,
0.05641937628388405,
0.03797941654920578,
0.08132678270339966,
0.09212309867143631,
0.018792161718010902,
-0.026083538308739662,
0.024669785052537918,
-0.06324461102485657,
-0.008416806347668171,
-0.009926250204443932,
-0.013137910515069962,
-0.016723325476050377,
0.011964352801442146,
0.09870181977748871,
0.004054455552250147,
-0.05121299996972084,
0.02589992806315422,
-0.022114792838692665,
-0.02258467487990856,
0.042363956570625305,
-0.011389297433197498,
0.00541733531281352,
0.01979357749223709,
0.03966374322772026,
0.007793040480464697,
-0.020375465974211693,
0.01781602017581463,
-0.027319757267832756,
-0.06128360703587532,
-0.02575775794684887,
0.0614737905561924,
0.0031965174712240696,
0.02064054273068905,
0.054564230144023895,
-0.028490755707025528,
0.03964316472411156,
-0.0033740040380507708,
-0.009404445067048073,
-0.008396505378186703,
-0.07134940475225449,
-0.016762565821409225,
-0.02387790009379387,
0.0217906441539526,
-0.01902545988559723,
0.02281547151505947,
-0.034864045679569244,
0.015018421225249767,
0.03625090792775154,
0.021894827485084534,
0.025558454915881157,
-0.061345260590314865,
0.05414368212223053,
-0.01570255681872368,
0.1013902798295021,
-0.07777436822652817,
-0.03636415675282478,
-0.05951891094446182,
-0.09899110347032547,
-0.011668495833873749,
-0.02972065657377243,
-0.004792862106114626,
0.003763404209166765,
0.01713235303759575,
-0.015074518509209156,
0.03659839183092117,
-0.027983076870441437,
0.03986958786845207,
-0.04149559885263443,
0.04213595762848854,
0.04846483841538429,
0.025462599471211433,
-0.01219475269317627,
0.019983625039458275,
-0.010240954346954823,
0.002820702036842704,
-0.04981623962521553,
0.013150003738701344,
0.033183783292770386,
-0.03130805119872093,
-0.014209860004484653,
-0.027828399091959,
-0.011701530776917934,
0.02198064886033535,
-0.009865744039416313,
-0.0023067016154527664,
-0.016629954800009727,
0.048006948083639145,
-0.05179540067911148,
-0.04383179545402527,
0.01665113866329193,
-0.05128084868192673,
-0.03868022561073303,
0.021553562954068184,
-0.0023701556492596865,
0.0036470401100814342,
-0.02963309735059738,
0.08206772804260254,
0.00510426377877593,
-0.04539899528026581,
-0.009297801181674004,
-0.024234158918261528,
0.039088308811187744,
-0.0320526659488678,
-0.053549766540527344,
-0.004620198626071215,
0.015420232899487019,
0.009187450632452965,
0.018284767866134644,
0.03268985450267792,
0.01420980878174305,
-0.021691633388400078,
-0.07078942656517029,
-0.014715093187987804,
-0.06807250529527664,
0.01784774474799633,
0.00921202078461647,
0.0510491319000721,
-0.04632409289479256,
0.05168020725250244,
-0.02213825285434723,
0.06871196627616882,
-0.03236932307481766,
0.05589527636766434,
0.025611937046051025,
-0.03408613055944443,
0.0015320489183068275,
-0.04829419404268265,
-0.014958730898797512,
0.005532639566808939,
0.06785330921411514,
-0.03853699564933777,
0.03244740515947342,
0.027664098888635635,
0.018031949177384377,
0.07424281537532806,
-0.029571056365966797,
0.00650416174903512,
-0.03927042335271835,
-0.041480179876089096,
-0.03438891842961311,
0.05186115950345993,
0.04389147087931633,
0.03948434069752693,
0.058163952082395554,
0.009488627314567566,
0.029492158442735672,
0.060832519084215164,
-0.019516266882419586,
0.0684596374630928,
0.04125054180622101,
-0.00843648612499237,
-0.0007016683230176568,
0.028262784704566002,
-0.01537499763071537,
-0.03498082980513573,
-0.061461202800273895,
0.05148874223232269,
-0.01639951393008232,
0.01905060186982155,
-0.008180201053619385,
-0.001997419400140643,
-0.0040295016951859,
-0.039946287870407104,
0.023318098857998848,
-0.0187666155397892,
-0.05298333242535591,
-0.016887720674276352,
0.0030216833110898733,
0.011884315870702267,
-0.02800762467086315,
-0.019315345212817192,
-0.040601540356874466,
-0.08018451184034348,
-0.01725398376584053,
-0.022069895640015602,
0.04991476610302925,
-0.04030553624033928,
-0.028308885172009468,
0.06671161204576492,
0.07950413972139359,
-0.050790321081876755,
0.017395811155438423,
-0.052947159856557846,
0.03873484209179878,
0.04676194489002228,
-0.009337060153484344,
-0.03124299645423889,
-0.028871098533272743,
-0.005492680240422487,
0.004405154846608639,
0.01794157363474369,
-0.06783798336982727,
-0.0035582794807851315,
-0.0026849310379475355,
-0.03391529247164726,
0.020735466852784157,
0.010844385251402855,
0.02644686959683895,
0.01918649487197399
] |
<p>In Mudelung's book, Introduction to Solid-State Theory, I am confused by the following statement.</p>
<blockquote>
<p>For many applications a further simplification is helpful. The concept of the hole presents us with the confusing situationthat a hole in the state $\mathbf{k},\sigma$ has a momentum $-ħ\mathbf{k}$, while an electron has a momentum $ħ\mathbf{k}$. This asymmetry can be avoided by defining new <em>quasi-particles</em> which have momentum $ħ\mathbf{k}$ inside and outside the Fermi sphere. When we note that the creation of a particle with $+ħ\mathbf{k}$ is achieved by the operator $c_{\mathbf{k}\sigma}^+$ when outside the Fermi sphere and by $c_{-\mathbf{k},-\sigma}$ when inside the Fermi sphere, it is only a small step to define the following operators:
$$
\begin{align}
\alpha_{\mathbf{k}\sigma}^+=u_\mathbf{k}c_{\mathbf{k}\sigma}^++v_{-\mathbf{k}}c_{-\mathbf{k},-\sigma}
\\
\alpha_{\mathbf{k}\sigma}=u_\mathbf{k}c_{\mathbf{k}\sigma}+v_{-\mathbf{k}}c_{-\mathbf{k},-\sigma}^+
\end{align}
$$
with
$$
\begin{align}
u_\mathbf{k}=1,\; v_\mathbf{k}=0\quad\text{ for }\quad k>k_\text{F},
\\
u_\mathbf{k}=0,\; v_\mathbf{k}=1\quad\text{ for }\quad k<k_\text{F}.
\end{align}
$$</p>
</blockquote>
<p>He showed the motivation of introducing Bogoliubov tansformation. But I don't understand his statement. "Creation of a particle with $+\mathbf k$ is acvieved by the operator $c^{+}_{\mathbf k,\sigma}$ when outside the Fermi shere and by $c_{-\mathbf k,-\sigma}$ when inside the Fermi sphere".</p>
<p>$c^{+}_{\mathbf k,\sigma}$ means create a particle with $\mathbf k$. So, why must we distinguish ouside and inside the Fermi sphere? And why does annihilation operator $c_{-\mathbf k,-\sigma}$ inside the Fermi sphere have the same effect as creation operator outside the Fermi sphere?</p> | g7865 | [
0.017518555745482445,
0.01413676980882883,
-0.016996679827570915,
-0.024279752746224403,
0.06548897922039032,
0.00023928043083287776,
0.05730927363038063,
0.01561290305107832,
0.0019447606755420566,
0.03150913864374161,
-0.05036935582756996,
0.04309821128845215,
0.05064811930060387,
0.054028283804655075,
-0.02439798414707184,
-0.020054494962096214,
0.017039788886904716,
-0.004468765575438738,
0.03182408958673477,
-0.014973974786698818,
-0.042301926761865616,
0.039382077753543854,
0.03728676587343216,
-0.05009061470627785,
0.019471535459160805,
-0.007588924374431372,
0.018906550481915474,
-0.07797147333621979,
0.016127685084939003,
0.04619201645255089,
0.07796558737754822,
-0.006551081780344248,
0.008502678945660591,
-0.0011366175021976233,
-0.0006336543010547757,
-0.046123817563056946,
0.13110662996768951,
0.0074638319201767445,
0.033375173807144165,
-0.03913245350122452,
0.010879512876272202,
-0.06546471267938614,
-0.012875046581029892,
0.004779447801411152,
-0.035162750631570816,
0.0398828461766243,
-0.03952251374721527,
0.03079790435731411,
0.043102070689201355,
-0.024004947394132614,
-0.05447574332356453,
0.03118795156478882,
0.05724021792411804,
-0.02490820363163948,
0.012736205942928791,
0.0018838242394849658,
0.028753412887454033,
-0.005169462878257036,
0.021066544577479362,
0.037465229630470276,
0.008407649584114552,
-0.04053668677806854,
-0.01523306593298912,
-0.01539057120680809,
0.050432998687028885,
0.00225902465172112,
-0.00926170963793993,
0.027320867404341698,
-0.03216688334941864,
0.013105486519634724,
-0.008001458831131458,
-0.046827226877212524,
-0.025793885812163353,
-0.005469216499477625,
0.02872922457754612,
0.022275051102042198,
0.016005685552954674,
-0.0070947506465017796,
0.08122100681066513,
0.005160381551831961,
-0.01254682894796133,
-0.019989460706710815,
0.0928342267870903,
-0.006496737711131573,
0.0798184871673584,
-0.00676716910675168,
-0.05148150771856308,
0.00010832404223037884,
-0.044996798038482666,
0.010029261000454426,
-0.017970018088817596,
-0.03923887759447098,
-0.01443033292889595,
0.02989131398499012,
-0.058231182396411896,
-0.007011244539171457,
-0.015812773257493973,
0.05559108406305313,
-0.045687831938266754,
-0.0038238412234932184,
-0.006766838021576405,
0.004616504535079002,
0.006342853885143995,
-0.00035488983849063516,
-0.037359051406383514,
0.02492210827767849,
0.012163195759057999,
-0.00010851211845874786,
-0.00863372441381216,
0.04713326692581177,
-0.041846636682748795,
0.0006995302392169833,
-0.022164635360240936,
-0.041723527014255524,
-0.026672372594475746,
0.04620892554521561,
0.05664319545030594,
-0.01408188883215189,
0.01814182661473751,
0.10521902143955231,
-0.009381626732647419,
0.0247560553252697,
0.003427363932132721,
0.030870582908391953,
-0.011343616992235184,
-0.020750241354107857,
-0.004875974729657173,
0.01718686707317829,
0.07695158571004868,
0.004918115679174662,
-0.0007737318519502878,
-0.030478572472929955,
-0.0002837143256329,
0.02367720566689968,
0.0007715210085734725,
-0.003866972168907523,
-0.025746243074536324,
0.040488675236701965,
0.04303523898124695,
-0.0026073281187564135,
-0.0054488894529640675,
0.025366779416799545,
-0.01769232004880905,
-0.021460553631186485,
-0.014066727831959724,
-0.04708404093980789,
-0.028191624209284782,
-0.04352793097496033,
-0.006434426177293062,
0.06545063853263855,
0.029831532388925552,
0.020203985273838043,
-0.013327457010746002,
-0.0026269862428307533,
-0.01586417853832245,
0.007061305921524763,
0.004913895856589079,
0.009701640345156193,
0.006919883191585541,
0.025036780163645744,
0.034701157361269,
-0.03238753601908684,
0.010511556640267372,
0.01700691506266594,
-0.06172006577253342,
-0.027417870238423347,
0.013455215841531754,
-0.088180311024189,
-0.038531944155693054,
-0.0762426033616066,
-0.03706491366028786,
0.0549500547349453,
-0.00638543302193284,
0.05592229589819908,
0.019844982773065567,
0.006395168602466583,
-0.029327213764190674,
-0.021319933235645294,
0.03684432432055473,
0.03583350032567978,
-0.031265098601579666,
-0.018976742401719093,
0.03570249304175377,
0.03327123075723648,
0.003331378335133195,
0.022022342309355736,
-0.00805234257131815,
0.02262168750166893,
-0.06507503986358643,
0.007149906828999519,
0.05223650112748146,
-0.03946046903729439,
0.018846755847334862,
0.11176430433988571,
-0.0020515010692179203,
0.027343327179551125,
0.04545627906918526,
-0.03744864463806152,
-0.03432675451040268,
0.029648510739207268,
-0.008843808434903622,
0.04627968370914459,
0.03382246196269989,
-0.01659528538584709,
0.0586598739027977,
0.02317669987678528,
-0.005621214862912893,
0.011189589276909828,
0.02946767769753933,
0.013731393963098526,
0.03628203645348549,
0.011497259140014648,
-0.024812376126646996,
0.040894608944654465,
0.0022720308043062687,
-0.05922328680753708,
-0.007360471412539482,
0.053133584558963776,
-0.015390082262456417,
-0.043905194848775864,
-0.0333603173494339,
-0.04669369012117386,
0.0003539014724083245,
-0.07742071151733398,
-0.02436003088951111,
0.06159646436572075,
-0.0037633113097399473,
0.007874148897826672,
0.006486990954726934,
0.010103490203619003,
-0.11429136991500854,
-0.01274388562887907,
-0.0026695856358855963,
-0.03245675191283226,
0.00563183706253767,
0.050531335175037384,
-0.013369944877922535,
0.05320730060338974,
-0.020068610087037086,
-0.001850030617788434,
-0.00291256420314312,
0.008145182393491268,
-0.03970053791999817,
0.009707476012408733,
0.01489442028105259,
0.010718886740505695,
0.08604162186384201,
-0.025786085054278374,
-0.01412662398070097,
0.03314798325300217,
0.03943079337477684,
-0.016182245686650276,
-0.028248092159628868,
-0.00614928686991334,
0.020671147853136063,
-0.030109748244285583,
-0.004829540383070707,
0.03777092322707176,
-0.03844348341226578,
0.04619690403342247,
-0.007861398160457611,
-0.01822168380022049,
0.009037706069648266,
-0.015858611091971397,
-0.013482221402227879,
-0.004840608220547438,
-0.04508878290653229,
0.045280493795871735,
0.0192579235881567,
-0.0308150015771389,
-0.056314241141080856,
0.06876571476459503,
0.03656294196844101,
0.026413043960928917,
-0.019465792924165726,
-0.06142466515302658,
-0.042117055505514145,
0.032548654824495316,
0.043601471930742264,
-0.03413385525345802,
-0.03917825594544411,
0.08030811697244644,
-0.09498473256826401,
0.035477593541145325,
-0.02445630542933941,
-0.02186577394604683,
0.030627746134996414,
0.004330876283347607,
-0.018679862841963768,
-0.028026020154356956,
-0.02142600528895855,
-0.008876051753759384,
0.03755342960357666,
0.060199446976184845,
0.03436708450317383,
0.06506915390491486,
-0.006553350016474724,
-0.058644503355026245,
-0.006784099619835615,
0.030220938846468925,
0.037150632590055466,
0.013890298083424568,
-0.03845740482211113,
0.022650403901934624,
0.07484351098537445,
0.04451122507452965,
-0.05734027549624443,
-0.008257979527115822,
-0.06271646171808243,
-0.004542041569948196,
-0.015850601717829704,
0.09314475208520889,
-0.030146967619657516,
-0.03098038211464882,
-0.025991171598434448,
0.010677705518901348,
-0.05934599041938782,
0.01017009373754263,
-0.002512120408937335,
-0.0357421413064003,
-0.04871160164475441,
0.02924967184662819,
0.020543480291962624,
-0.040128108114004135,
-0.003921832889318466,
0.03587160259485245,
-0.04956571385264397,
-0.049133241176605225,
-0.011433891952037811,
-0.056042831391096115,
-0.011544641107320786,
0.008444640785455704,
-0.0034780162386596203,
-0.02464781515300274,
-0.08217047899961472,
-0.06636743992567062,
-0.045692071318626404,
0.050294868648052216,
0.026752380654215813,
-0.005147639662027359,
0.03987199813127518,
-0.0030512677039951086,
0.02314402349293232,
-0.022777119651436806,
0.003883615368977189,
0.03143375739455223,
-0.01282440684735775,
-0.015324559062719345,
0.012710150331258774,
0.006655149161815643,
0.012238985858857632,
0.057755064219236374,
0.014180826023221016,
0.017499679699540138,
-0.04789310321211815,
0.05433563515543938,
0.034331295639276505,
0.0166421327739954,
0.004573567770421505,
-0.011875542812049389,
0.0350959487259388,
-0.030838618054986,
0.0018873738590627909,
-0.0021300369407981634,
0.0008904991555027664,
0.003960519563406706,
0.00426724087446928,
-0.000054343694500857964,
-0.025569302961230278,
-0.0040422542952001095,
-0.04759061336517334,
-0.052262961864471436,
-0.04210643097758293,
0.012711326591670513,
0.03084113635122776,
-0.0749012753367424,
0.03390884771943092,
0.07211607694625854,
-0.04812569171190262,
-0.039174143224954605,
0.026272140443325043,
0.012800834141671658,
-0.03281860426068306,
0.052937209606170654,
0.03731174021959305,
0.058482371270656586,
-0.006097753066569567,
0.036417461931705475,
0.04142596945166588,
-0.05330304801464081,
0.04149957746267319,
-0.0454975850880146,
-0.05786515772342682,
0.042366981506347656,
0.034481845796108246,
0.06276118010282516,
0.02955303154885769,
-0.1032886877655983,
0.01997496373951435,
0.04276767745614052,
0.012011353857815266,
0.002216481603682041,
-0.034816283732652664,
-0.039840374141931534,
0.07514902949333191,
-0.006680523511022329,
0.06355392187833786,
-0.01362841110676527,
-0.024840107187628746,
-0.0730433315038681,
0.015522691421210766,
0.06124993413686752,
0.0060578458942472935,
-0.032829053699970245,
0.03407306596636772,
-0.0493515208363533,
-0.031186699867248535,
0.027104146778583527,
0.01025855727493763,
-0.04183617979288101,
0.050274889916181564,
0.03824784606695175,
0.01045737974345684,
-0.005878681316971779,
0.08123660087585449,
0.006399960722774267,
-0.03667775169014931,
-0.005264094565063715,
-0.0028774209786206484,
-0.021262330934405327,
0.004769815597683191,
0.01740085519850254,
-0.024434657767415047,
-0.001161302556283772,
-0.0731218084692955,
-0.011003023944795132,
-0.09334209561347961,
-0.0027851127088069916,
-0.012439291924238205,
0.030941683799028397,
0.06205401569604874,
0.01590413600206375,
0.008283010683953762,
-0.05067641660571098,
0.06445679813623428,
0.006688487250357866,
-0.037714883685112,
0.013530848547816277,
-0.008770588785409927,
-0.009411507286131382,
-0.02769932895898819,
0.02599368616938591,
0.03747503086924553,
-0.05751712620258331,
-0.015533250756561756,
-0.023033488541841507,
0.033244308084249496,
0.0044242870062589645,
-0.027331484481692314,
0.01849823258817196,
-0.041969601064920425,
-0.004652589093893766,
-0.020826246589422226,
-0.023820333182811737,
0.011684480123221874,
-0.010132006369531155,
-0.012565096840262413,
0.021177705377340317,
-0.03204384073615074,
0.026426224038004875,
0.03683850169181824,
0.0034313099458813667,
0.0007197445956990123,
-0.01755334809422493,
0.06460931897163391,
0.053818490356206894,
-0.013730859383940697,
-0.05223166570067406,
0.015227756462991238,
-0.01702810823917389,
-0.0007707856129854918,
-0.04354096204042435,
0.02810589037835598,
-0.0016974840546026826,
0.004724896978586912,
0.07150814682245255,
-0.00425837654620409,
-0.019163627177476883,
-0.041030168533325195,
0.0049842288717627525,
0.03599102795124054,
-0.003241738071665168,
-0.001224751234985888,
-0.029315389692783356,
0.007562540005892515,
0.03801824524998665,
0.04974108189344406,
-0.012215833179652691,
-0.022642329335212708,
0.04274066165089607,
-0.04304271563887596,
-0.018359338864684105,
-0.010534379631280899,
0.033410247415304184,
0.024468399584293365,
0.05313095450401306,
0.08364257216453552,
0.00885461363941431,
0.08072443306446075,
-0.06111003831028938,
0.03207901492714882,
0.030506020411849022,
0.0668715313076973,
-0.0633571594953537,
0.03451656550168991,
-0.014058277010917664,
0.03060023859143257,
-0.01112807635217905,
-0.02963988296687603,
-0.029489194974303246,
-0.03690342605113983,
-0.0160602368414402,
0.010681351646780968,
0.009007809683680534,
0.03605680540204048,
0.028107140213251114,
-0.06281746178865433,
-0.0695047453045845,
0.03376789018511772,
0.06984331458806992,
-0.0015385588631033897,
0.002024819143116474,
0.016753848642110825,
-0.028314730152487755,
-0.008981007151305676,
-0.09432105720043182,
-0.026827525347471237,
0.032176610082387924,
0.03683862462639809,
-0.024753427132964134,
-0.007325334474444389,
-0.03043343871831894,
-0.026072844862937927,
0.0341448113322258,
-0.04226749762892723,
-0.00456070713698864,
-0.03527999669313431,
0.03153803572058678,
0.008985249325633049,
-0.010751737281680107,
-0.047622665762901306,
0.02982999198138714,
-0.021961621940135956,
-0.013981538824737072,
0.06220155954360962,
0.014232225716114044,
-0.003580145537853241,
0.014525544829666615,
-0.04101886227726936,
-0.08827152103185654,
-0.036144550889730453,
0.022683920338749886,
-0.01058416161686182,
-0.030972179025411606,
0.0543622151017189,
-0.04807334020733833,
-0.0476340726017952,
-0.01354537345468998,
0.030279722064733505,
0.02596079371869564,
-0.01176281739026308,
-0.0004976180498488247,
-0.05207117274403572,
0.004933388903737068,
-0.022966817021369934,
0.04406805336475372,
-0.0036651890259236097,
0.028047693893313408,
0.004658044315874577,
0.06291516870260239,
0.07079419493675232,
0.003911155741661787,
-0.007032222114503384,
-0.016272902488708496,
0.02683928608894348,
0.017783844843506813,
-0.056651871651411057,
-0.03830784931778908,
0.028987901285290718,
-0.01082749105989933,
-0.05789383128285408,
0.05285253748297691,
-0.011757958680391312,
0.012646602466702461,
0.022744009271264076,
0.011410577222704887,
-0.03086669184267521,
-0.03574936091899872,
-0.030084747821092606,
0.002839456545189023,
-0.014734181575477123,
0.032929424196481705,
-0.006713171489536762,
0.003078741254284978,
-0.001859108335338533,
0.07036831974983215,
-0.013870198279619217,
-0.012071521021425724,
-0.021984409540891647,
0.026029551401734352,
-0.004302836488932371,
0.06993112713098526,
-0.023396383970975876,
0.01303465198725462,
0.019676022231578827,
-0.03352644294500351,
-0.03206811472773552,
0.019900912418961525,
-0.01995464786887169,
-0.03134101256728172,
0.03568654507398605,
0.06104782223701477,
0.013764348812401295,
-0.038429781794548035,
0.009356283582746983,
0.07686670869588852,
-0.0349307507276535,
0.016667934134602547,
0.05205988511443138,
0.025949273258447647,
-0.02778341807425022,
-0.04475047066807747,
-0.03323397785425186,
0.024354442954063416,
-0.03257298097014427,
0.06068256124854088,
0.03293952718377113,
0.04196227714419365,
-0.014396757818758488,
-0.0019436260918155313,
0.00035804836079478264,
-0.02326328121125698,
0.059142496436834335,
-0.008378187194466591,
-0.05553740635514259,
-0.01685512624680996,
0.019957490265369415,
-0.03842075914144516,
-0.10163495689630508,
-0.02858668379485607,
-0.02762114256620407,
0.0010088348062708974,
-0.010539224371314049,
-0.05191262438893318,
0.02838187664747238,
-0.0014686573995277286,
0.028882648795843124,
0.007469887845218182,
-0.015198249369859695,
-0.026844939216971397,
-0.017528001219034195,
-0.017548944801092148,
-0.001207489287480712,
-0.003125016111880541,
0.009211156517267227,
0.016488051041960716,
-0.00820764061063528,
-0.0021022013388574123,
0.024339696392416954,
-0.021517504006624222,
-0.037983257323503494,
0.017625179141759872,
-0.0570695586502552,
-0.012719744816422462,
-0.03595844656229019,
-0.0012354535283520818,
0.01921313814818859,
0.0716819167137146,
-0.05515381693840027,
-0.03862043097615242,
0.018869351595640182,
0.08776941150426865,
-0.05152569338679314,
-0.03931805118918419,
-0.043424226343631744,
-0.08199698477983475,
-0.03424512594938278,
0.012167109176516533,
-0.0032911673188209534,
-0.017247259616851807,
0.030282802879810333,
0.025082064792513847,
0.01519552432000637,
-0.02315017394721508,
-0.00587637210264802,
0.010340009815990925,
0.03800494223833084,
0.06826969236135483,
0.00798537116497755,
0.05494670569896698,
0.014660373330116272,
-0.00926952064037323,
-0.040528230369091034,
-0.026581542566418648,
0.04071076214313507,
0.0027456863317638636,
0.0058330451138317585,
0.029189400374889374,
-0.03424152359366417,
-0.007965770550072193,
-0.014586023986339569,
-0.0194767527282238,
0.032989900559186935,
-0.04179273173213005,
-0.02550974301993847,
-0.0193781815469265,
-0.05208147317171097,
0.04835547134280205,
-0.007514302618801594,
-0.019801542162895203,
0.03515451401472092,
-0.008493166416883469,
-0.01769527979195118,
0.01521088182926178,
-0.013956441543996334,
-0.05455605313181877,
0.01701129414141178,
0.06825636327266693,
-0.009559365920722485,
-0.019373605027794838,
-0.02189142443239689,
0.00542883574962616,
-0.02397005446255207,
-0.019042037427425385,
-0.0223256666213274,
-0.055214256048202515,
0.0035506021231412888,
-0.03719703480601311,
0.042164113372564316,
-0.018820494413375854,
0.010028441436588764,
-0.03176715224981308,
0.04774382710456848,
-0.012919656932353973,
-0.04299841448664665,
-0.03395133838057518,
-0.06247574836015701,
0.044340506196022034,
-0.009523800574243069,
-0.019997181370854378,
0.043187133967876434,
-0.02452966384589672,
-0.004517895169556141,
0.021272169426083565,
0.02236432582139969,
-0.02340536192059517,
0.010964172892272472,
-0.0011998633854091167,
0.020358212292194366,
-0.032272305339574814,
-0.0368836410343647,
0.013013201765716076,
0.03965933620929718,
-0.03289517015218735,
0.007440752815455198,
-0.06395994126796722,
0.0011627043131738901,
-0.005337622482329607
] |
<p>The <a href="http://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect" rel="nofollow">Aharonov–Bohm effect</a> shows the vector potential $\mathbf{A}$ is more fundamental than magnetic flux density $\mathbf{B}$. However, vector potential is introduced by
$$ \nabla \times \mathbf{A} = \mathbf{B} $$ or $$ \mathrm{d} \mathbf{A} = \mathbf{B} $$
which requires the Poincaré's lemma to ensure the existence of $\mathbf{A}$. If the manifold is not contractible, there is no guarantee that $\mathbf{A}$ exists. On a non-contractible manifold, what would happen for the Aharonov–Bohm effect?</p> | g7866 | [
0.014440729282796383,
0.06090085580945015,
-0.000280297506833449,
0.013497861102223396,
0.04412714019417763,
0.006902738474309444,
0.02275669202208519,
0.026175817474722862,
-0.030417732894420624,
0.01689280942082405,
0.0018076917622238398,
0.02107592299580574,
-0.01585031859576702,
0.023946058005094528,
-0.02620520070195198,
0.05994764715433121,
-0.05363234132528305,
0.015792490914463997,
0.06031491607427597,
-0.013531484641134739,
-0.04061078280210495,
0.03404875099658966,
0.0063263471238315105,
0.00519778486341238,
0.013815137557685375,
-0.020270371809601784,
0.04469965770840645,
-0.04493845999240875,
-0.01958751119673252,
-0.0689709410071373,
0.024959132075309753,
-0.018804533407092094,
0.09598523378372192,
-0.00702693173661828,
0.022773198783397675,
-0.011870482936501503,
0.0025024274364113808,
0.020021993666887283,
-0.004126321990042925,
-0.04240367189049721,
0.0034097929019480944,
-0.017335038632154465,
0.0020900240633636713,
0.016644561663269997,
-0.051268935203552246,
0.014590829610824585,
-0.045530062168836594,
0.050184790045022964,
0.03056788630783558,
-0.00528216827660799,
0.05718391016125679,
-0.034461550414562225,
0.04577576741576195,
0.012997300364077091,
-0.010730458423495293,
0.003701943438500166,
0.052561886608600616,
0.030273351818323135,
0.018258310854434967,
0.014399420469999313,
-0.029347440227866173,
0.044990502297878265,
0.01707659848034382,
0.03996771574020386,
-0.039909884333610535,
-0.0463314950466156,
-0.034533917903900146,
-0.003059725509956479,
-0.04352238401770592,
0.021156536415219307,
0.01023158710449934,
-0.03015219047665596,
-0.019594741985201836,
-0.027994753792881966,
-0.010175111703574657,
0.021164709702134132,
0.02984306402504444,
-0.026286045089364052,
0.030942823737859726,
-0.06005772948265076,
-0.04337484762072563,
0.0030594654381275177,
0.021626019850373268,
0.030604766681790352,
0.08079931139945984,
-0.034494366496801376,
-0.044401515275239944,
0.027575785294175148,
0.04377582669258118,
-0.04102690517902374,
-0.006156998686492443,
-0.025706006214022636,
-0.013401716016232967,
0.02400118298828602,
0.030115729197859764,
-0.020050009712576866,
0.03662663698196411,
0.04849075525999069,
-0.06497452408075333,
-0.02058730088174343,
0.004015415906906128,
0.021113544702529907,
-0.04241526126861572,
0.0013904543593525887,
-0.0010626075090840459,
-0.04171669855713844,
0.024310795590281487,
-0.01947878673672676,
0.007365489844232798,
0.004167244303971529,
0.0013523752568289638,
-0.05091016739606857,
-0.0119272880256176,
0.02430739998817444,
-0.017875008285045624,
0.007969457656145096,
0.0403500571846962,
-0.020231865346431732,
-0.001525998581200838,
0.007472767494618893,
-0.011995619162917137,
0.0303837601095438,
0.012106185778975487,
0.08478152751922607,
0.00967275071889162,
0.03314495086669922,
-0.019128970801830292,
0.030020035803318024,
0.014949008822441101,
-0.030576981604099274,
0.008002609014511108,
0.009101101197302341,
0.0016141972737386823,
0.0228742565959692,
0.006796360015869141,
-0.0015950683737173676,
0.010500156320631504,
0.027295570820569992,
0.03894143924117088,
0.07078824192285538,
0.007114244159311056,
-0.05209251865744591,
0.04537366330623627,
-0.04869167134165764,
-0.039085086435079575,
0.05442732200026512,
0.009381936863064766,
-0.03938467428088188,
0.04967047646641731,
0.03063894994556904,
0.019682489335536957,
0.06176960468292236,
-0.021115615963935852,
-0.010082384571433067,
0.03590339422225952,
0.03930290415883064,
0.04505547508597374,
0.0029833924490958452,
-0.03082582913339138,
0.01327644195407629,
0.01004323922097683,
-0.031751640141010284,
0.03867073729634285,
0.005967774894088507,
-0.03081340342760086,
0.014156877063214779,
0.02791760489344597,
-0.0015515696723014116,
-0.0021960404701530933,
-0.03226984292268753,
-0.060875676572322845,
-0.0005777844344265759,
0.005975537467747927,
0.02667756751179695,
0.019330253824591637,
0.011213147081434727,
-0.0817401334643364,
0.03218759596347809,
0.07032868266105652,
-0.03392091765999794,
-0.030760714784264565,
0.010956818237900734,
0.013685560785233974,
-0.01170256081968546,
0.0400514118373394,
0.06907155364751816,
0.0004605606955010444,
0.017993154004216194,
-0.05314630642533302,
-0.0005424072151072323,
-0.030484840273857117,
0.058805033564567566,
-0.009372064843773842,
0.00687312800437212,
0.029973937198519707,
-0.004332211799919605,
0.03888385370373726,
-0.05706864967942238,
0.036201830953359604,
0.009519128128886223,
-0.024152232334017754,
0.06675368547439575,
0.02641848288476467,
-0.014902815222740173,
0.020250096917152405,
0.020024513825774193,
0.031368188560009,
-0.029298659414052963,
0.03485327214002609,
-0.05193858966231346,
0.07330265641212463,
-0.021351708099246025,
0.0014824155950918794,
0.03453157842159271,
-0.024659553542733192,
-0.03998219594359398,
-0.05580468475818634,
-0.005138814449310303,
-0.05109650641679764,
-0.0008046387229114771,
0.023181285709142685,
-0.010777886025607586,
0.048018816858530045,
0.01001480221748352,
-0.009401097893714905,
0.009065724909305573,
-0.025729084387421608,
-0.0743260532617569,
-0.021618664264678955,
-0.0020780027844011784,
-0.0026213927194476128,
-0.016783609986305237,
0.03991119563579559,
-0.0024945929180830717,
-0.0282910019159317,
0.02003474533557892,
-0.024555636569857597,
-0.015206187032163143,
0.03219694644212723,
0.05158260464668274,
-0.01970727927982807,
-0.03372448310256004,
-0.00824684277176857,
0.024342581629753113,
0.0625385120511055,
-0.0005117007531225681,
0.00807648990303278,
-0.04697659984230995,
0.07824360579252243,
0.05214487016201019,
-0.007007998414337635,
-0.05824390798807144,
0.05515386164188385,
-0.0527142658829689,
0.023480147123336792,
0.07226821780204773,
-0.017344780266284943,
0.07192237675189972,
-0.044848065823316574,
-0.054040707647800446,
-0.05646420270204544,
0.02112816832959652,
0.020462093874812126,
-0.03788627311587334,
-0.06241977587342262,
0.06370052695274353,
-0.0674196109175682,
0.023342376574873924,
0.025344768539071083,
0.01526733860373497,
-0.021091928705573082,
0.027073930948972702,
-0.01992032304406166,
-0.0336189828813076,
-0.031030096113681793,
0.07884403318166733,
-0.010889503173530102,
-0.06607436388731003,
0.025645850226283073,
-0.061409953981637955,
-0.06272103637456894,
-0.019603125751018524,
0.017175164073705673,
-0.04850257188081741,
0.014887225814163685,
-0.022926224395632744,
-0.01603241078555584,
-0.02935543842613697,
-0.02704928256571293,
-0.02044602856040001,
-0.07591616362333298,
-0.015771226957440376,
0.018805284053087234,
0.017304835841059685,
-0.024344203993678093,
0.022006072103977203,
-0.029279300943017006,
0.008437690325081348,
-0.045012976974248886,
-0.007387820165604353,
0.014462612569332123,
0.010623873211443424,
-0.005171577446162701,
-0.027814500033855438,
0.0688590481877327,
0.011154412291944027,
-0.06385631114244461,
-0.0845363587141037,
0.029109913855791092,
0.0007493978482671082,
-0.018139122053980827,
0.009400536306202412,
-0.02627643570303917,
0.0041273972019553185,
-0.0150316646322608,
0.010574884712696075,
0.002367182169109583,
0.011431747116148472,
0.04103692248463631,
-0.04804167151451111,
0.006157540250569582,
-0.009426281787455082,
0.015150063671171665,
-0.09035085886716843,
0.07773296535015106,
-0.040543314069509506,
-0.02604362554848194,
-0.015539386309683323,
-0.04325929284095764,
-0.01825598068535328,
0.03664127737283707,
0.0039642807096242905,
0.019547002390027046,
-0.035396479070186615,
-0.02918347716331482,
-0.08224456012248993,
-0.004927405621856451,
-0.019510114565491676,
-0.006538336630910635,
0.0322464294731617,
-0.06942221522331238,
-0.04989376664161682,
-0.027958190068602562,
-0.01989685371518135,
0.0023107249289751053,
0.05149177461862564,
0.007539323065429926,
0.018730074167251587,
0.03432721272110939,
0.033363740891218185,
0.03189869970083237,
-0.07626774162054062,
0.09866636246442795,
0.0025516103487461805,
0.04864718019962311,
-0.03085876628756523,
0.06582221388816833,
-0.02787095494568348,
0.01395568810403347,
0.005580378230661154,
-0.011674907058477402,
-0.048533692955970764,
-0.007852254435420036,
-0.006729584652930498,
0.023383906111121178,
0.01676287315785885,
0.00366677506826818,
0.08246472477912903,
0.040796298533678055,
0.0010313126258552074,
-0.010510494001209736,
-0.045172929763793945,
0.0255297739058733,
0.04304228723049164,
0.06371880322694778,
-0.003968443255871534,
-0.0100941751152277,
-0.006426637526601553,
0.005398023407906294,
0.020811228081583977,
0.013550679199397564,
0.09157539904117584,
0.030447419732809067,
-0.0018837902462109923,
0.012140847742557526,
0.00003749991083168425,
-0.00287587009370327,
-0.0010323800379410386,
-0.004171194043010473,
-0.03993109613656998,
-0.006989943794906139,
-0.0038750669918954372,
0.01724996231496334,
0.04662024602293968,
0.011595062911510468,
-0.043945569545030594,
-0.0033163519110530615,
-0.04371374472975731,
-0.008887765929102898,
-0.027166683226823807,
0.01770652085542679,
0.010767742991447449,
-0.05278630927205086,
0.003129328601062298,
0.027573827654123306,
-0.018405936658382416,
0.06710757315158844,
0.035778459161520004,
0.04776449128985405,
-0.01052883267402649,
0.005491935648024082,
-0.06136447936296463,
-0.04106678068637848,
-0.04780777171254158,
0.007612532936036587,
0.006360103841871023,
0.019587621092796326,
-0.04035264998674393,
-0.04872947931289673,
0.00009922866593115032,
-0.005596738774329424,
0.02787567302584648,
0.01393501553684473,
-0.004335661418735981,
-0.0023914561606943607,
0.07626998424530029,
-0.015913240611553192,
-0.03171282634139061,
0.021719273179769516,
-0.00009573173883836716,
-0.04688616096973419,
0.08099310845136642,
-0.048018887639045715,
0.03725928068161011,
-0.03727208822965622,
0.07790758460760117,
-0.11410712450742722,
0.0236516073346138,
0.07137349992990494,
-0.0009489518706686795,
0.003636747132986784,
-0.02111675776541233,
0.04143982380628586,
-0.028824519366025925,
0.027888605371117592,
0.06604965776205063,
-0.09161432832479477,
-0.06815626472234726,
-0.010730395093560219,
-0.05128810182213783,
-0.052248284220695496,
-0.02436664141714573,
-0.03102477639913559,
-0.02194538153707981,
0.0008641591994091868,
0.0023626124020665884,
0.0404764749109745,
0.008664780296385288,
0.05173841863870621,
0.013609593734145164,
-0.01930196024477482,
0.013067556545138359,
-0.02518276497721672,
-0.002654709853231907,
0.06676989048719406,
-0.03739772364497185,
-0.020671097561717033,
0.04737650975584984,
-0.04847078025341034,
-0.011894299648702145,
0.01644132100045681,
0.004602120257914066,
0.016459442675113678,
0.009564906358718872,
0.025924010202288628,
-0.006880029104650021,
0.046345800161361694,
0.021841634064912796,
-0.021967794746160507,
0.012868691235780716,
-0.012397922575473785,
0.013882567174732685,
-0.004979234654456377,
0.004385767038911581,
-0.0015022850129753351,
0.012421499006450176,
-0.05782870203256607,
-0.015360239893198013,
-0.03699938952922821,
0.011344440281391144,
0.04148607328534126,
0.0002707139356061816,
-0.013513621874153614,
0.006938413716852665,
0.010060813277959824,
-0.07207179814577103,
-0.023638281971216202,
-0.03182736784219742,
-0.05005604028701782,
-0.005476720165461302,
-0.04648183658719063,
-0.041407082229852676,
0.009708811528980732,
-0.025278983637690544,
-0.018444806337356567,
0.015087854117155075,
0.06305553764104843,
0.0020432693418115377,
-0.0011210659286007285,
0.04753990098834038,
-0.044103626161813736,
-0.026823239400982857,
0.0068158432841300964,
0.020021596923470497,
0.06264876574277878,
0.06560258567333221,
-0.03948591649532318,
-0.014575664885342121,
-0.02474891021847725,
-0.06137879192829132,
0.04274462163448334,
0.02174309454858303,
0.04098854213953018,
-0.0038277392741292715,
0.04103720933198929,
-0.013807426206767559,
-0.06049454212188721,
-0.054842572659254074,
-0.015082396566867828,
0.11632983386516571,
-0.0712096318602562,
0.022910602390766144,
0.032895777374506,
-0.02432318590581417,
0.030708905309438705,
-0.017294991761446,
0.009097280912101269,
-0.007126508746296167,
0.015208659693598747,
0.03428037464618683,
-0.03204696998000145,
-0.048289597034454346,
0.04612138494849205,
0.045662421733140945,
-0.04307567700743675,
0.01878916285932064,
-0.049907032400369644,
0.02737698331475258,
0.04122205823659897,
0.0014145103050395846,
-0.0756450816988945,
-0.026559948921203613,
-0.02706972137093544,
-0.01973310299217701,
-0.005735707934945822,
-0.011910810135304928,
-0.03411713242530823,
0.045201271772384644,
-0.01823447272181511,
0.012365718372166157,
0.080611452460289,
-0.0392921045422554,
0.014783044345676899,
-0.035823892802000046,
-0.0347871370613575,
-0.02129981480538845,
-0.03103451430797577,
0.016590841114521027,
0.1055794432759285,
0.015086838975548744,
0.010572792962193489,
0.05210956558585167,
0.003342428943142295,
-0.04284235090017319,
0.04498389735817909,
0.027388665825128555,
-0.0035762619227170944,
-0.04037090390920639,
-0.07923802733421326,
0.00012958445586264133,
-0.022817255929112434,
0.024396957829594612,
0.10713546723127365,
-0.055048126727342606,
0.038323819637298584,
0.0022479358594864607,
-0.04874207451939583,
-0.047678835690021515,
0.06406235694885254,
0.01949693076312542,
0.024181140586733818,
0.003126047784462571,
-0.004491632338613272,
0.05683324486017227,
-0.07630864530801773,
0.02893958054482937,
-0.010582642629742622,
0.03436441347002983,
-0.029823584482073784,
-0.009247059002518654,
0.03590041399002075,
0.013595026917755604,
0.019965529441833496,
0.051949676126241684,
0.014355135150253773,
0.02806764841079712,
0.0005039231036789715,
-0.005650258157402277,
-0.021728264167904854,
0.009366926737129688,
-0.05356304347515106,
0.012636884115636349,
-0.02256731502711773,
-0.01365106925368309,
0.038991641253232956,
0.0017202818999066949,
0.0027212072163820267,
0.005443981848657131,
-0.00877046026289463,
0.03315969184041023,
-0.05318063125014305,
-0.030501918867230415,
0.01638474501669407,
-0.010172559879720211,
-0.030252039432525635,
0.03226027265191078,
-0.03472311422228813,
-0.00037731422344222665,
0.03168565034866333,
0.0010926955146715045,
-0.009005257859826088,
-0.014348147436976433,
-0.06271304935216904,
0.030180232599377632,
0.00857145618647337,
0.019279394298791885,
-0.042212583124637604,
-0.014549823477864265,
0.0441722609102726,
-0.04314378276467323,
-0.049102164804935455,
0.019612479954957962,
0.09168601036071777,
-0.012070753611624241,
0.017595630139112473,
-0.06453602761030197,
-0.07772404700517654,
-0.007498621474951506,
-0.03304947540163994,
0.035827867686748505,
0.04180794581770897,
0.04504498466849327,
-0.023455562070012093,
-0.040012065321207047,
-0.010872673243284225,
-0.009750566445291042,
-0.01867743395268917,
0.02799985185265541,
0.02128622494637966,
-0.014451650902628899,
-0.008785625919699669,
-0.02256472036242485,
0.026672083884477615,
0.0053831953555345535,
0.018640339374542236,
0.016651038080453873,
0.008665882050991058,
-0.027078768238425255,
0.027661152184009552,
0.0027087328489869833,
0.008424068801105022,
0.019478043541312218,
-0.04503322020173073,
0.022431576624512672,
-0.0323236919939518,
-0.03804134950041771,
0.050469376146793365,
0.021289370954036713,
0.006497665774077177,
0.013287358917295933,
0.01994846947491169,
0.019808385521173477,
0.0742938369512558,
0.013128363527357578,
-0.05399245023727417,
0.01903577893972397,
-0.01944379322230816,
0.03872893750667572,
0.03342070430517197,
0.029098639264702797,
0.013936576433479786,
-0.008935094811022282,
0.04309270530939102,
-0.02937501296401024,
-0.022521276026964188,
-0.007924970239400864,
0.049100250005722046,
0.006089933216571808,
-0.024861231446266174,
0.02376120164990425,
0.02778428979218006,
-0.05562783032655716,
-0.03660920634865761,
-0.04013357684016228,
0.03446519002318382,
0.014631913043558598,
-0.04375311732292175,
-0.007994533516466618,
-0.08649932593107224,
-0.021034270524978638,
0.023660993203520775,
0.06033258140087128,
-0.027091316878795624,
-0.019667072221636772,
-0.01115397084504366,
-0.003589148633182049,
-0.004642574582248926,
0.019137732684612274,
-0.008349405601620674,
0.008441789075732231,
-0.04983433336019516,
-0.07266031950712204,
-0.0009320324752479792,
-0.07742178440093994,
-0.02166818082332611,
-0.023468106985092163,
-0.043318964540958405,
-0.012954399921000004,
0.01423559244722128,
-0.010895987041294575,
0.0009966226061806083,
-0.058694008737802505,
-0.00816418044269085,
-0.038688383996486664,
-0.06613756716251373,
-0.04814556986093521,
0.03769880160689354,
0.06961505860090256,
0.022349752485752106,
-0.039493292570114136,
-0.02519817277789116,
-0.04835321754217148,
0.018122415989637375,
-0.03097914718091488,
0.012097453698515892,
0.025173496454954147,
-0.04654352366924286,
0.048317231237888336,
0.021839085966348648,
0.01889040693640709,
0.0005159968859516084,
-0.024154076352715492,
0.03635718673467636,
0.03814012557268143,
0.08450889587402344,
-0.03535965830087662,
-0.023822298273444176,
0.010073504410684109,
0.04218073934316635,
-0.0033666144590824842,
-0.005745952948927879,
-0.0067433021031320095,
-0.011903379112482071,
0.02077762968838215,
-0.05297403410077095,
-0.04055969789624214,
0.00047203723806887865,
-0.026147067546844482
] |
<p>How I determine the center of mass of a semicircle using the definition of center of mass? I only know solve this using the Pappus theorem. Consider that the semicircle is centered on the origin and a homogeneous mass distribution.</p> | g7867 | [
0.05532361939549446,
0.018296033143997192,
-0.003777633188292384,
-0.06216077506542206,
0.03541024401783943,
-0.04301794618368149,
0.01667683571577072,
0.04227505624294281,
0.03976580500602722,
0.0003428806667216122,
-0.05956987664103508,
-0.030185164883732796,
0.012700304388999939,
-0.013889268040657043,
0.022937968373298645,
-0.01614074781537056,
0.010776551440358162,
0.004903738386929035,
0.017148494720458984,
0.04050108790397644,
-0.009649178944528103,
-0.013903191313147545,
-0.009690768085420132,
0.01557020004838705,
-0.024653319269418716,
0.00747106596827507,
-0.0005573800881393254,
0.048948533833026886,
-0.03499796614050865,
0.028411122038960457,
-0.03759981319308281,
0.034376490861177444,
0.08546420186758041,
-0.026031676679849625,
0.03736526891589165,
0.01839059218764305,
0.01203382108360529,
-0.01126883365213871,
-0.04046650230884552,
0.06777241826057434,
0.00630089221522212,
-0.03903130441904068,
-0.019902320578694344,
-0.000027112946554552764,
-0.008454746566712856,
0.06026332080364227,
-0.06545349955558777,
-0.030795076861977577,
-0.01118276733905077,
-0.026823116466403008,
-0.0275002159178257,
0.010440044105052948,
0.05606904253363609,
-0.03150900825858116,
-0.06391286849975586,
-0.022360317409038544,
0.03935111314058304,
-0.008569074794650078,
0.06154296174645424,
-0.014638498425483704,
0.027490666136145592,
-0.013842911459505558,
-0.031042879447340965,
-0.024071527644991875,
0.013938081450760365,
-0.014491208828985691,
0.022501733154058456,
0.027601713314652443,
-0.03568582236766815,
0.024386374279856682,
-0.00451683858409524,
-0.05546889826655388,
0.002945546992123127,
-0.022790435701608658,
-0.0529610738158226,
-0.008020590990781784,
-0.02358153834939003,
-0.005586904473602772,
0.04340304434299469,
-0.007683365140110254,
0.025945888832211494,
0.015457195229828358,
0.026900120079517365,
-0.001933790510520339,
-0.017604054883122444,
-0.029614530503749847,
-0.027623075991868973,
0.014216093346476555,
-0.02527964673936367,
-0.015645679086446762,
-0.010472610592842102,
0.014965830370783806,
0.014338305220007896,
0.01421707309782505,
0.03515726327896118,
-0.03298936039209366,
0.01511827390640974,
0.07020629197359085,
-0.07264360040426254,
0.03097408637404442,
-0.005323558114469051,
0.022006748244166374,
-0.034820567816495895,
-0.018191633746027946,
0.015939144417643547,
-0.011497188359498978,
0.011691257357597351,
0.035954102873802185,
-0.00570353539660573,
-0.004284904804080725,
0.011058279313147068,
-0.03832602500915527,
-0.04245121777057648,
-0.041865669190883636,
-0.049911193549633026,
0.024523194879293442,
0.1475023627281189,
0.030917992815375328,
-0.0207111444324255,
0.013191591948270798,
0.013159622438251972,
-0.03569302707910538,
-0.0054019661620259285,
0.04206682741641998,
-0.06386817991733551,
-0.02895696833729744,
0.02491447702050209,
-0.013449851423501968,
0.017333723604679108,
0.004981751088052988,
0.016511768102645874,
0.0244231466203928,
-0.001102991751395166,
-0.011519748717546463,
-0.021077677607536316,
0.02543453685939312,
-0.07413297891616821,
0.006330744829028845,
-0.008459960110485554,
0.03485380858182907,
0.018516991287469864,
0.0342412032186985,
0.05477292835712433,
-0.004484008066356182,
-0.07056112587451935,
-0.01494417805224657,
0.047766946256160736,
-0.020655300468206406,
0.03444522246718407,
0.08018315583467484,
-0.06862792372703552,
0.03153792768716812,
-0.07431983202695847,
-0.02468530647456646,
0.025160005316138268,
-0.01439274288713932,
-0.05303870141506195,
0.0009170599514618516,
0.0026126678567379713,
-0.005706448573619127,
0.008295087143778801,
0.01421772874891758,
-0.007582629099488258,
-0.04581323638558388,
0.01650068536400795,
0.004152219742536545,
-0.028693031519651413,
-0.027199963107705116,
0.0011927075684070587,
-0.08763041347265244,
-0.016127226874232292,
0.0009319190867245197,
-0.06083999574184418,
0.05108942463994026,
-0.05116235092282295,
-0.03333636000752449,
-0.004444876220077276,
-0.003327392041683197,
0.09285394847393036,
0.01914554089307785,
0.01707267574965954,
-0.008701369166374207,
0.011127179488539696,
-0.031869493424892426,
0.011423579417169094,
0.042330820113420486,
0.0410018265247345,
0.01701464131474495,
-0.03672543168067932,
0.004960719030350447,
-0.02399464324116707,
0.009022703394293785,
-0.033936213701963425,
0.047758955508470535,
-0.01041324995458126,
-0.023445645347237587,
0.04560393840074539,
-0.029943406581878662,
-0.0011338723124936223,
-0.008398011326789856,
-0.014168963767588139,
-0.04474444314837456,
0.0026794641744345427,
0.07344848662614822,
0.006960571743547916,
0.04145834967494011,
-0.009515556506812572,
0.012463354505598545,
-0.02157234586775303,
0.03905539587140083,
-0.015418300405144691,
0.0027230610139667988,
0.03596597909927368,
0.021619556471705437,
-0.06552403420209885,
0.03838455304503441,
0.026842400431632996,
-0.009108681231737137,
0.04159976914525032,
-0.006280439905822277,
-0.017960553988814354,
-0.0066421120427548885,
-0.02584930695593357,
-0.0055032754316926,
0.03347752243280411,
0.014258475974202156,
0.012028192169964314,
-0.0021442824508994818,
0.006464156787842512,
-0.0005855114432051778,
-0.04027668014168739,
0.03340482711791992,
0.006052256561815739,
-0.014896522276103497,
0.05923277884721756,
-0.03839917480945587,
-0.010139784775674343,
-0.04167194664478302,
0.015264960937201977,
-0.005283968988806009,
-0.015004212036728859,
-0.03384033218026161,
0.035798266530036926,
-0.02223888598382473,
-0.0072306194342672825,
-0.06832631677389145,
0.06626483798027039,
-0.01528257504105568,
-0.016242042183876038,
0.017873350530862808,
-0.027692575007677078,
0.02548324316740036,
0.013535668142139912,
-0.014976833947002888,
0.014751859940588474,
-0.01873079501092434,
-0.044630296528339386,
-0.017537016421556473,
-0.053427550941705704,
-0.03780962899327278,
-0.06424644589424133,
-0.09897162020206451,
0.04984881728887558,
0.039226461201906204,
-0.012587849982082844,
0.028299784287810326,
-0.034106992185115814,
-0.036536503583192825,
0.006468367762863636,
-0.015770258381962776,
-0.03642503544688225,
0.09440447390079498,
-0.012204522266983986,
0.07716729491949081,
-0.0278797447681427,
-0.01129908487200737,
0.014417774975299835,
-0.01514370832592249,
-0.03788965567946434,
0.016543565317988396,
0.03831204026937485,
0.04587618261575699,
0.02890259586274624,
0.06742745637893677,
0.02662273682653904,
-0.013386735692620277,
-0.03639524430036545,
0.05222662165760994,
0.015338634140789509,
-0.022450009360909462,
0.09380403161048889,
-0.007343083620071411,
-0.008818620815873146,
-0.029080476611852646,
0.05922362953424454,
0.11341117322444916,
0.005800887010991573,
0.00925488118082285,
0.026748700067400932,
0.006626041606068611,
-0.00925011932849884,
0.00609190808609128,
0.03922826796770096,
0.0003534654970280826,
0.036391060799360275,
0.03728025034070015,
0.05846291780471802,
-0.004613102879375219,
0.05542544648051262,
0.0047174980863928795,
-0.009415674954652786,
0.014222357422113419,
0.044656410813331604,
-0.03817126899957657,
-0.025728564709424973,
0.028726983815431595,
0.03321247920393944,
-0.0433310903608799,
-0.025302449241280556,
0.005082492716610432,
-0.06021455302834511,
-0.02180880308151245,
0.06181265413761139,
-0.0024446132592856884,
0.03808976709842682,
0.05779885873198509,
-0.002025655470788479,
-0.007389777339994907,
-0.068429134786129,
-0.05535443127155304,
-0.03825508430600166,
-0.008930422365665436,
-0.042727891355752945,
0.03387930244207382,
0.015022899024188519,
-0.07953570038080215,
0.038503728806972504,
-0.023816175758838654,
0.0005720171611756086,
0.02124159224331379,
0.013266230002045631,
0.010280836373567581,
-0.024741554632782936,
-0.026972752064466476,
-0.008798908442258835,
0.007720270659774542,
0.006284323055297136,
0.0365302637219429,
0.02786545269191265,
-0.006105453707277775,
-0.018854264169931412,
0.02383570745587349,
0.0006032554665580392,
0.03710118681192398,
-0.07229959219694138,
0.044439103454351425,
-0.04063695669174194,
-0.015959789976477623,
-0.042277440428733826,
0.02192002721130848,
0.009678131900727749,
-0.015252064913511276,
-0.026131296530365944,
0.019244663417339325,
0.06927108764648438,
-0.04333830624818802,
0.0471809096634388,
0.02993096597492695,
0.03336110711097717,
-0.0012284928234294057,
-0.009040866047143936,
-0.05260574445128441,
0.04070945456624031,
-0.023138847202062607,
-0.011317134834825993,
-0.0266211349517107,
-0.01762881688773632,
0.0004382117185741663,
-0.039423879235982895,
0.03892366960644722,
-0.0054270317777991295,
-0.040208835154771805,
-0.017121322453022003,
-0.017957700416445732,
-0.008192707784473896,
0.023747513070702553,
-0.06196713447570801,
-0.0111156664788723,
0.0633317157626152,
-0.032042596489191055,
0.0034872661344707012,
-0.009245002642273903,
-0.02049797959625721,
-0.0967644676566124,
0.0008182344026863575,
0.016173802316188812,
0.013118317350745201,
-0.06970438361167908,
-0.061872731894254684,
0.03847299888730049,
0.07954972237348557,
0.0230120699852705,
0.024880873039364815,
-0.03913644701242447,
0.02296127751469612,
0.045789673924446106,
-0.021014146506786346,
-0.029969211667776108,
0.04523542895913124,
0.03302081301808357,
0.033792801201343536,
0.01559753343462944,
0.012105435132980347,
-0.040139876306056976,
0.06147680804133415,
0.011990422382950783,
-0.008605575188994408,
-0.031793706119060516,
-0.04430418089032173,
0.016852859407663345,
-0.057260267436504364,
-0.05966274440288544,
-0.08240552246570587,
-0.05249401554465294,
0.005201517604291439,
0.01262038666754961,
0.026738904416561127,
-0.028964843600988388,
0.01773405261337757,
0.018379706889390945,
-0.0037046787329018116,
0.03063473291695118,
0.03099903091788292,
0.02892577461898327,
-0.029177987948060036,
-0.01488740649074316,
-0.01724882237613201,
-0.028957074508070946,
0.039586570113897324,
-0.05566556751728058,
-0.01250253152102232,
0.0737638995051384,
-0.06356990337371826,
-0.01815495826303959,
-0.05551746115088463,
0.010437841527163982,
0.009139920584857464,
-0.026108236983418465,
0.001327191828750074,
-0.03780307620763779,
-0.03158612921833992,
0.017095424234867096,
-0.028750669211149216,
-0.03221897780895233,
-0.01383496355265379,
-0.009686017408967018,
-0.020000679418444633,
0.018833864480257034,
-0.020187729969620705,
0.028824742883443832,
0.007671560626477003,
-0.020612657070159912,
0.016859134659171104,
0.009951661340892315,
0.03807130083441734,
-0.04113175347447395,
-0.05350688472390175,
0.05274122208356857,
0.034223273396492004,
0.022687925025820732,
-0.002999292453750968,
0.045291781425476074,
0.053620826452970505,
0.0010289009660482407,
0.008183592930436134,
0.06041167676448822,
-0.041544411331415176,
0.024467481300234795,
0.02250705473124981,
0.003625220851972699,
-0.04313886910676956,
-0.03410029411315918,
-0.04761539772152901,
-0.008321649394929409,
0.0242287740111351,
0.06162813678383827,
0.008106508292257786,
0.006145508959889412,
0.036073874682188034,
-0.04209388047456741,
-0.03193438798189163,
0.02246081456542015,
-0.021249081939458847,
-0.0330442376434803,
0.04147809371352196,
-0.10016372799873352,
0.013198883272707462,
-0.028755072504281998,
0.03333904966711998,
0.003451503347605467,
-0.015247207134962082,
0.052960339933633804,
0.024023566395044327,
0.04090790078043938,
-0.03513203561306,
-0.006903399713337421,
0.014938591048121452,
0.05100375786423683,
0.009302221238613129,
0.05930909514427185,
0.05247417464852333,
-0.0031396164558827877,
0.04746992513537407,
-0.0014324273215606809,
-0.02170460857450962,
-0.03351116552948952,
-0.021823151037096977,
0.01257506012916565,
0.03673651069402695,
0.03114190325140953,
0.04816349595785141,
0.005380577873438597,
0.012978222221136093,
-0.026831045746803284,
0.02880421094596386,
-0.03829222545027733,
-0.00016417868027929217,
-0.012233317829668522,
-0.07520373165607452,
0.015696628019213676,
-0.03301457688212395,
-0.026743793860077858,
0.05781072378158569,
-0.02240726351737976,
0.008355244994163513,
-0.06349775940179825,
0.023764584213495255,
-0.008704477921128273,
0.053363487124443054,
-0.048726242035627365,
-0.021990029141306877,
-0.06605193018913269,
0.0032274555414915085,
0.030659781768918037,
0.02126432955265045,
0.016121920198202133,
0.03838744014501572,
-0.011785190552473068,
0.0320858396589756,
-0.04306340217590332,
-0.005800801329314709,
0.04523777216672897,
0.024852357804775238,
0.016710583120584488,
-0.06126614287495613,
-0.005758228711783886,
0.006630684714764357,
-0.026029739528894424,
0.04056906700134277,
-0.04874987527728081,
-0.000911888899281621,
-0.04540823772549629,
0.020473072305321693,
-0.0019391538808122277,
0.0029706754721701145,
-0.05074991658329964,
-0.042931657284498215,
-0.028699439018964767,
0.055838316679000854,
-0.013952494598925114,
0.045341603457927704,
-0.0022909825202077627,
-0.06257341057062149,
0.027966173365712166,
0.05006719380617142,
0.03292309492826462,
-0.06423041969537735,
-0.02445308119058609,
-0.015767905861139297,
0.02356390468776226,
0.028495585545897484,
-0.014217866584658623,
0.03952483460307121,
-0.04554276168346405,
0.005614245310425758,
0.013962721452116966,
-0.036468178033828735,
0.03220584616065025,
0.00502089923247695,
0.031818438321352005,
0.03517214208841324,
0.00715534808114171,
-0.03335338830947876,
-0.02001894637942314,
-0.02293628640472889,
0.007846583612263203,
-0.00545368529856205,
0.018552403897047043,
0.0162079818546772,
0.013906742446124554,
0.0009557849261909723,
-0.03136478736996651,
-0.025340324267745018,
0.028201032429933548,
0.027924953028559685,
-0.02838241495192051,
0.0486450232565403,
-0.0004328747163526714,
-0.05331101268529892,
-0.05667971447110176,
0.03419323265552521,
0.034045662730932236,
-0.045158807188272476,
-0.05806918442249298,
0.03317847475409508,
-0.007509139366447926,
-0.03799187019467354,
0.035944730043411255,
-0.021510321646928787,
-0.03354089334607124,
0.011438249610364437,
0.03734440356492996,
-0.025310589000582695,
-0.02567293494939804,
0.03651881217956543,
0.005032304208725691,
0.02433903142809868,
-0.012055140919983387,
0.05841990187764168,
-0.03384263068437576,
0.007967652752995491,
0.00744582386687398,
0.006225971505045891,
-0.028761690482497215,
-0.010309293866157532,
0.03134552389383316,
-0.0003410234930925071,
0.03599550202488899,
0.04275098443031311,
0.07271970808506012,
-0.01109952200204134,
0.009725001640617847,
-0.001695673679932952,
0.017258400097489357,
-0.09329506009817123,
0.02267240174114704,
0.05354928597807884,
0.05965219438076019,
-0.03465447947382927,
-0.03950275853276253,
0.012812068685889244,
0.08161710202693939,
0.0095066512003541,
-0.011703561060130596,
-0.031608257442712784,
0.03066791035234928,
0.06777222454547882,
0.009300504811108112,
0.01669066958129406,
-0.03778408095240593,
-0.07742393761873245,
0.016255410388112068,
0.025474796071648598,
0.01695646345615387,
-0.012887327931821346,
0.030135227367281914,
0.056750014424324036,
0.012648544274270535,
-0.027662446722388268,
-0.055322352796792984,
-0.06676110625267029,
-0.01778491400182247,
-0.043721213936805725,
-0.020632535219192505,
0.03090442344546318,
0.07938044518232346,
0.008817700669169426,
-0.042171869426965714,
-0.008228844031691551,
0.0229097381234169,
-0.025637732818722725,
-0.03428160771727562,
-0.016156740486621857,
-0.06302312761545181,
0.0055970740504562855,
0.029391132295131683,
-0.03166256099939346,
-0.061565101146698,
0.08261547237634659,
0.019363565370440483,
0.017342176288366318,
0.04920794069766998,
0.008909949101507664,
-0.029978612437844276,
-0.07112333178520203,
0.024793576449155807,
0.0003798615070991218,
0.06480742245912552,
0.06995213031768799,
-0.019085954874753952,
0.01555813942104578,
-0.1059037521481514,
0.00921513419598341,
0.004710159730166197,
0.013230089098215103,
-0.027389442548155785,
-0.05077676102519035,
0.036490749567747116,
-0.04609774798154831,
0.07073551416397095,
0.0320550762116909,
-0.004779831040650606,
-0.014945738948881626,
-0.010192773304879665,
-0.08208516240119934,
0.03649459034204483,
-0.08929175138473511,
0.0826207771897316,
0.015356769785284996,
0.002840355969965458,
0.008353739976882935,
0.041556209325790405,
-0.043959859758615494,
-0.04412680119276047,
-0.019392600283026695,
-0.01988126151263714,
0.05867395177483559,
-0.07026280462741852,
0.019104277715086937,
-0.024241497740149498,
0.03314771130681038,
0.020748350769281387,
0.020552201196551323,
0.032927751541137695,
0.009229356423020363,
0.022125277668237686,
-0.023310739547014236,
-0.04138926789164543,
-0.0015873090596869588,
-0.05025115981698036,
-0.019202323630452156,
-0.07776255905628204,
0.0003234868054278195,
0.0005255325231701136,
0.00922064483165741,
0.04371997341513634,
-0.047398317605257034,
0.01856379397213459,
0.05206964164972305,
0.019581912085413933,
0.0009606245439499617,
-0.023250749334692955,
0.01925010047852993,
0.03626125305891037,
0.005977163091301918,
-0.07303033769130707,
0.047517646104097366,
-0.009329868480563164,
-0.0018139552557840943,
-0.01834270730614662,
-0.03163068741559982,
-0.049936119467020035,
0.024697480723261833,
0.013274861499667168,
0.01079916674643755,
-0.0025036982260644436,
0.03124411031603813,
-0.024724915623664856
] |
<p>I'm supposed to calculate the inversion pressure $p_i$ of a <a href="https://en.wikipedia.org/wiki/Van_der_Waals_gas" rel="nofollow">Van der Waals gas</a>. The state equation of the Van der Waals gas is: $$(p + \frac{a}{V^2})(V-b) = RT.$$ To get a hold of the inversion temperature, I differentiate this equation with respect to $T$, while keeping $p$ constant. This gives me:
$$\frac{(\frac{\partial V}{\partial T})_p \cdot (2ab - aV + pV^3)}{V^3} = R,$$ which with the condition for the inversion curve $T(\frac{\partial V}{\partial T})_p = V$ I get:
$$\frac{1}{T_i}(\frac{2ab}{V^2} - \frac{a}{V} + pV) = R,$$ which gives me an easy to solve equation for $T_i$. But to get $p_i$, I'd have to solve the equation for $V$ and put it back into the state equation. But solving this equation for $V$ gets really messy. That's why I'm thinking I went wrong somewhere.</p>
<p>Can you guys help me out here?</p> | g7868 | [
0.013321920298039913,
-0.002980397315695882,
-0.01309623010456562,
-0.03313756734132767,
0.013270547613501549,
-0.029265834018588066,
0.010475855320692062,
0.02725544199347496,
-0.03060734085738659,
0.028991399332880974,
-0.011117372661828995,
0.049729522317647934,
-0.041860755532979965,
-0.05566610395908356,
0.03265363350510597,
-0.02313360944390297,
0.04836752265691757,
-0.02210797555744648,
0.026028549298644066,
-0.014769278466701508,
0.007086380384862423,
-0.05909621715545654,
0.03550302982330322,
-0.08883875608444214,
-0.010080605745315552,
-0.04329182952642441,
-0.04002907872200012,
0.037437181919813156,
-0.07915027439594269,
0.028223413974046707,
-0.025003952905535698,
0.015745094045996666,
0.022836899384856224,
0.009001600556075573,
0.017180409282445908,
-0.015916580334305763,
0.044039200991392136,
0.014412369579076767,
0.024578677490353584,
-0.008611023426055908,
-0.03411034494638443,
-0.029766781255602837,
0.041526686400175095,
0.10166727006435394,
0.008417240343987942,
0.014729557558894157,
-0.031007280573248863,
-0.003968292847275734,
-0.05143982544541359,
-0.022270597517490387,
0.0531688891351223,
0.038870591670274734,
-0.009645665995776653,
-0.053609706461429596,
-0.05246502906084061,
-0.010407811962068081,
0.005302612669765949,
-0.03747318312525749,
0.0642402172088623,
0.009968931786715984,
-0.030470749363303185,
-0.0854000598192215,
0.003662346163764596,
0.017321867868304253,
-0.00361767434515059,
-0.051041875034570694,
-0.03294651210308075,
0.00009813982615014538,
0.004436084069311619,
-0.05528357997536659,
0.025500820949673653,
-0.021395398303866386,
0.004567170049995184,
-0.043911274522542953,
-0.011062253266572952,
0.0015280211810022593,
0.04667066037654877,
-0.08200442045927048,
0.01028334442526102,
-0.002527922624722123,
0.0164595115929842,
0.03290945664048195,
0.04039650782942772,
-0.010533611290156841,
-0.04012322053313255,
-0.05527389049530029,
0.031817156821489334,
-0.015521552413702011,
-0.059759024530649185,
-0.010086641646921635,
-0.02436429262161255,
-0.00574535084888339,
0.05832232907414436,
0.051386959850788116,
-0.02019052766263485,
0.0019422286422923207,
0.007960201241075993,
0.07468429952859879,
-0.012876723892986774,
0.006390868686139584,
-0.019783375784754753,
-0.05961666628718376,
-0.01390046440064907,
-0.01839405857026577,
-0.00123549101408571,
-0.018698904663324356,
0.015323336236178875,
0.04084067791700363,
0.0015900960424914956,
-0.06658801436424255,
-0.0367874912917614,
0.017998646944761276,
-0.01234058290719986,
-0.05084177851676941,
-0.040594249963760376,
0.024138787761330605,
-0.05138038098812103,
-0.04779994860291481,
0.006004443857818842,
0.049150872975587845,
0.027380123734474182,
0.023882536217570305,
0.017471661791205406,
0.06560324132442474,
0.04112245887517929,
-0.03231572359800339,
-0.01907167211174965,
-0.0031134227756410837,
0.05842195078730583,
-0.04358259215950966,
-0.05144244059920311,
0.005445763934403658,
0.0035534664057195187,
-0.012669084593653679,
-0.006312632467597723,
-0.028593063354492188,
-0.0618729442358017,
0.05206200107932091,
-0.05038825422525406,
0.08355288952589035,
-0.004835988394916058,
0.006260884925723076,
-0.04008673131465912,
0.040366385132074356,
-0.044641684740781784,
0.006703747436404228,
-0.04788225516676903,
0.010394702665507793,
-0.00438346341252327,
-0.04657629877328873,
0.019065937027335167,
0.020076649263501167,
0.05429208278656006,
-0.012476094998419285,
-0.02590285800397396,
-0.020347489044070244,
0.08418464660644531,
-0.01006210595369339,
0.05094785615801811,
0.01721826195716858,
0.061583224684000015,
-0.005724264308810234,
0.04057629406452179,
0.0003278350632172078,
0.00544332480058074,
0.04929553344845772,
-0.002569235861301422,
0.024303050711750984,
-0.04501892998814583,
-0.030271116644144058,
-0.019141310825943947,
-0.002125033875927329,
0.044640328735113144,
0.032411519438028336,
0.044963203370571136,
-0.009424878284335136,
0.0280511025339365,
0.04383844509720802,
-0.020215388387441635,
0.03260146081447601,
0.02018902823328972,
0.009658810682594776,
0.029289288446307182,
-0.01691291108727455,
-0.043981123715639114,
-0.03184927999973297,
-0.03753064200282097,
0.021989556029438972,
-0.041856445372104645,
-0.022714177146553993,
0.05867328122258186,
0.04883028566837311,
-0.012210958637297153,
0.006567187607288361,
-0.0050472961738705635,
-0.0032704765908420086,
0.04243416711688042,
-0.06509881466627121,
-0.04423739016056061,
0.009110482409596443,
-0.04973730072379112,
0.04533231630921364,
0.057408738881349564,
0.01705019362270832,
0.011414374224841595,
0.0054242173209786415,
-0.03594036400318146,
-0.021316207945346832,
-0.026434017345309258,
0.04261316731572151,
-0.03998646140098572,
-0.027504971250891685,
0.005864003207534552,
-0.0002608512295410037,
-0.013769959099590778,
-0.010986089706420898,
0.05294397473335266,
-0.03035772033035755,
-0.05010334402322769,
-0.00023830471036490053,
-0.041243430227041245,
0.018518319353461266,
0.017264673486351967,
-0.015893084928393364,
-0.00737638957798481,
-0.027842238545417786,
0.03536934033036232,
0.04228302836418152,
-0.015566523186862469,
-0.009701737202703953,
0.000520469038747251,
0.0025413017719984055,
-0.031032197177410126,
-0.015396465547382832,
0.05039341747760773,
0.0006295897183008492,
-0.05182156339287758,
-0.0019854882266372442,
0.01680389605462551,
0.04557237774133682,
-0.03771212697029114,
-0.01030021347105503,
0.01078860368579626,
0.08963900059461594,
0.028518415987491608,
0.02416832558810711,
-0.006627216003835201,
0.006684863939881325,
-0.004074678756296635,
-0.0477634072303772,
-0.037963803857564926,
0.0028320185374468565,
-0.009013045579195023,
-0.03863651305437088,
-0.025950752198696136,
-0.06276324391365051,
-0.012355794198811054,
0.0315389521420002,
0.023160720244050026,
-0.016321903094649315,
-0.02328968606889248,
-0.012147204019129276,
0.03853835538029671,
0.02547372132539749,
-0.08481486141681671,
-0.008759856224060059,
0.02308625355362892,
-0.0004544148105196655,
0.033750612288713455,
-0.0030808919109404087,
0.015069834887981415,
0.022314928472042084,
-0.027295134961605072,
0.018345100805163383,
0.004386257380247116,
-0.04621006175875664,
0.03470491245388985,
-0.02520774118602276,
0.02736623026430607,
0.0006759395473636687,
-0.017659518867731094,
-0.004945117514580488,
0.0029361897613853216,
0.016201049089431763,
0.028735630214214325,
-0.04950575530529022,
0.03374667093157768,
0.04426874220371246,
0.01525105070322752,
-0.04204903915524483,
-0.02485315129160881,
0.014863749034702778,
-0.014323567971587181,
0.05206839740276337,
0.010042864829301834,
-0.020385222509503365,
-0.005953700747340918,
-0.039983030408620834,
0.011247929185628891,
0.0011257113656029105,
0.04013843834400177,
-0.013880363665521145,
-0.021975722163915634,
-0.01839972659945488,
-0.016490651294589043,
-0.08826319873332977,
0.02309236116707325,
-0.02138451114296913,
0.005014945287257433,
0.056077294051647186,
-0.07075946033000946,
-0.014802481047809124,
0.07187872380018234,
-0.03191915899515152,
0.0299092885106802,
-0.007278681732714176,
-0.057524316012859344,
-0.03287092223763466,
-0.0002369367575738579,
0.04572922736406326,
-0.07356106489896774,
-0.028811033815145493,
0.015077744610607624,
0.013259039260447025,
0.03285911679267883,
0.03377443924546242,
-0.05674823746085167,
-0.04063903167843819,
-0.008292963728308678,
-0.03752700611948967,
0.04262937605381012,
0.03888097405433655,
0.0415920652449131,
-0.025653040036559105,
-0.0028427380602806807,
-0.009504219517111778,
-0.01082127820700407,
0.02047043666243553,
0.015454635955393314,
-0.030771726742386818,
-0.03416424244642258,
-0.045880306512117386,
0.009394989348948002,
-0.004126181825995445,
-0.03578142821788788,
-0.006458205170929432,
-0.04441365972161293,
0.05652165040373802,
0.005444181617349386,
-0.0033857848029583693,
0.022794676944613457,
0.028015201911330223,
0.06351154297590256,
-0.01791689544916153,
-0.03557097911834717,
-0.03106020949780941,
0.0727127268910408,
0.03930598497390747,
-0.028161650523543358,
0.010876285843551159,
-0.009615983814001083,
-0.018749156966805458,
-0.02916933409869671,
0.039102572947740555,
0.01508012879639864,
-0.020477190613746643,
-0.013662854209542274,
0.0639965757727623,
-0.012877828441560268,
-0.059455420821905136,
-0.016696784645318985,
-0.001265892991796136,
0.04082378372550011,
0.043444424867630005,
0.03505060076713562,
-0.05539647117257118,
-0.008087540976703167,
0.03292084112763405,
-0.0451720654964447,
0.049916476011276245,
0.07432029396295547,
-0.019869104027748108,
0.03002244606614113,
0.0016524988459423184,
0.055282119661569595,
-0.005615582223981619,
-0.025400569662451744,
0.05297163128852844,
0.09068110585212708,
-0.06713888049125671,
0.05922162905335426,
-0.0007809067610651255,
-0.05000023543834686,
0.031171679496765137,
-0.00887646060436964,
0.01878204196691513,
-0.00574355386197567,
0.058203961700201035,
-0.07644544541835785,
0.0070845442824065685,
-0.024838004261255264,
0.005333516746759415,
0.05562630668282509,
0.013676231727004051,
-0.05296631157398224,
0.01335547212511301,
0.032022442668676376,
-0.06603492051362991,
0.004370369017124176,
0.046434275805950165,
-0.026178525760769844,
-0.007469506934285164,
-0.02371801994740963,
-0.04699185863137245,
-0.009589304216206074,
0.00814683735370636,
0.010559615679085255,
0.011558645404875278,
-0.005657118279486895,
0.026772836223244667,
-0.038886409252882004,
0.01209090556949377,
0.0360817052423954,
-0.019149454310536385,
0.033206015825271606,
0.06403815746307373,
0.029762281104922295,
-0.0023137207608669996,
0.008175376802682877,
0.008592484518885612,
0.012647046707570553,
-0.011519845575094223,
-0.027775628492236137,
-0.01990518905222416,
0.02158576436340809,
0.07284924387931824,
-0.026206124573946,
-0.008684063330292702,
-0.03717518225312233,
0.004714132286608219,
0.0061821783892810345,
-0.037968628108501434,
-0.018748361617326736,
0.022952988743782043,
-0.018286990001797676,
0.04730777069926262,
0.009349747560918331,
0.003303390694782138,
0.02255803905427456,
-0.023271972313523293,
-0.03560652583837509,
-0.0012071244418621063,
-0.0003375558590050787,
-0.054301586002111435,
-0.008565961383283138,
-0.00158915133215487,
-0.03443417325615883,
0.02703198231756687,
0.0011535901576280594,
0.022373277693986893,
-0.06699420511722565,
0.029371757060289383,
0.015353198163211346,
0.004817886743694544,
0.0668192207813263,
-0.038931041955947876,
-0.07905066758394241,
0.03027249500155449,
0.06716897338628769,
-0.0481317974627018,
-0.007992163300514221,
-0.007122247014194727,
0.014759231358766556,
0.032314419746398926,
0.017284531146287918,
0.06634936481714249,
0.00966720748692751,
-0.03451843932271004,
0.005776123143732548,
-0.0280731450766325,
-0.02449781261384487,
0.08299539983272552,
0.03647538647055626,
0.06434118002653122,
-0.01880786567926407,
0.018095381557941437,
-0.013989394530653954,
0.004572263453155756,
0.013038204982876778,
0.02901913784444332,
-0.02552194893360138,
0.03569118678569794,
0.040633272379636765,
0.02542373165488243,
0.016161225736141205,
0.008692124858498573,
0.01809507980942726,
-0.023144612088799477,
0.013951572589576244,
0.05306289345026016,
-0.10557253658771515,
-0.0042542447336018085,
0.005823676474392414,
0.02910825051367283,
0.00886751338839531,
0.06995205581188202,
0.023989776149392128,
0.059236135333776474,
-0.010089589282870293,
0.027327757328748703,
0.030721182003617287,
-0.057444799691438675,
0.029078735038638115,
-0.017260640859603882,
-0.025114595890045166,
-0.011819153092801571,
-0.001009155879728496,
-0.0169079452753067,
-0.04319851100444794,
-0.07731159776449203,
0.01630955934524536,
0.03216475993394852,
0.03806794807314873,
-0.005699956323951483,
-0.012479223310947418,
0.008576137945055962,
-0.040958013385534286,
-0.053301941603422165,
-0.010728081688284874,
-0.03961766138672829,
-0.058923617005348206,
-0.05276346579194069,
0.021887779235839844,
0.0031164325773715973,
0.025832893326878548,
-0.008381159976124763,
-0.013538677245378494,
0.01571136899292469,
0.07985872775316238,
0.00223194295540452,
-0.027307042852044106,
0.019275978207588196,
-0.033334411680698395,
0.05620356276631355,
-0.0018266636179760098,
0.006924229208379984,
-0.0016403356567025185,
0.025190144777297974,
0.05470478907227516,
0.04210938513278961,
0.022302454337477684,
-0.025328634306788445,
-0.021991007030010223,
-0.04127723351120949,
-0.0010456832824274898,
-0.006516472902148962,
0.03268376737833023,
0.0016928325640037656,
0.000025257984816562384,
-0.0034314484801143408,
-0.013995991088449955,
-0.0334220714867115,
-0.03571324795484543,
0.058821383863687515,
0.014219527132809162,
-0.03683413192629814,
0.028630027547478676,
0.045700252056121826,
0.010009583085775375,
-0.0117948604747653,
0.025483813136816025,
-0.021559422835707664,
-0.024084892123937607,
-0.026692774146795273,
-0.0036163239274173975,
-0.021130215376615524,
-0.05150953680276871,
-0.06558006256818771,
0.029830504208803177,
0.018231021240353584,
-0.04983940348029137,
0.012472918257117271,
0.05705463886260986,
-0.013737771660089493,
-0.02512202598154545,
0.015659235417842865,
-0.026063011959195137,
-0.06305863708257675,
-0.02862483263015747,
-0.013584166765213013,
0.02736235037446022,
0.02585289627313614,
-0.0345245897769928,
0.020865444093942642,
0.009994449093937874,
-0.040957849472761154,
0.029539864510297775,
-0.034708116203546524,
0.006557832472026348,
0.012856465764343739,
0.06315720826387405,
0.04033898934721947,
-0.023767242208123207,
0.025005141273140907,
0.023622779175639153,
-0.04268483817577362,
0.00299177598208189,
0.0913611650466919,
-0.017368806526064873,
-0.04076622799038887,
0.013217136263847351,
0.030244868248701096,
0.006347083020955324,
0.012508224695920944,
0.07139891386032104,
-0.02426270768046379,
0.034569934010505676,
0.08641909062862396,
0.03802751749753952,
-0.011764355935156345,
-0.017250528559088707,
0.003992242738604546,
0.05229254812002182,
0.011937719769775867,
0.05601609870791435,
-0.020028002560138702,
-0.06189298629760742,
0.0020220947917550802,
0.04243572801351547,
-0.022197475656867027,
0.0655251070857048,
-0.07904230058193207,
-0.037642352283000946,
0.007802385371178389,
0.06908997148275375,
0.020405491814017296,
-0.029324589297175407,
0.01786130852997303,
-0.0015826731687411666,
0.11187426000833511,
-0.02424483746290207,
0.019671674817800522,
-0.012005877681076527,
0.025227218866348267,
-0.06174832209944725,
-0.0036994139663875103,
-0.0493401437997818,
-0.04898902773857117,
-0.03380940109491348,
0.0665883719921112,
0.07029570639133453,
0.02222255803644657,
-0.05784274637699127,
-0.0003784058499149978,
0.02243630960583687,
0.02287772297859192,
0.002281901193782687,
0.07236713916063309,
0.03474561870098114,
0.008620237000286579,
-0.003994151949882507,
-0.0065664127469062805,
-0.07787541300058365,
-0.02493141032755375,
0.029732000082731247,
0.0360979326069355,
0.019521737471222878,
-0.05999773368239403,
0.07396524399518967,
-0.050661731511354446,
-0.014184065163135529,
-0.0020296096336096525,
-0.009611036628484726,
-0.026500385254621506,
0.0521281436085701,
0.015710068866610527,
0.02444433979690075,
0.054655954241752625,
0.004677949007600546,
-0.006214356515556574,
-0.07995451241731644,
0.021221734583377838,
-0.009913360700011253,
-0.06352095305919647,
-0.030353035777807236,
-0.025835352018475533,
-0.013311471790075302,
-0.036678995937108994,
-0.029929209500551224,
0.06519793719053268,
-0.009742746129631996,
0.03819906711578369,
0.027958746999502182,
0.02188601903617382,
-0.034628551453351974,
-0.01228040549904108,
0.014871641993522644,
-0.025977078825235367,
0.06780222058296204,
-0.048714641481637955,
0.05587516725063324,
-0.01666274294257164,
0.009751464240252972,
-0.022487539798021317,
-0.06641136854887009,
0.03837486356496811,
-0.010421163402497768,
0.00005166289338376373,
-0.020945385098457336,
0.009899741038680077,
0.00958567950874567,
-0.04562479630112648,
0.020794909447431564,
0.005411637015640736,
0.049938831478357315,
-0.011681262403726578,
-0.059223633259534836,
0.0033566588535904884,
-0.02605796605348587,
-0.048665162175893784,
-0.04560410976409912,
-0.03542562946677208,
0.008681440725922585,
-0.010728544555604458,
-0.0014047925360500813,
0.004068378824740648,
-0.02032151073217392,
0.0017126990715041757,
0.020781470462679863,
-0.037191905081272125,
-0.020866598933935165,
0.09195884317159653,
-0.027427678927779198,
0.0441395603120327,
0.021035268902778625,
0.01707090437412262,
0.05592853203415871,
-0.06430517882108688,
0.052473034709692,
0.014346427284181118,
-0.02437695674598217,
-0.03963777795433998,
-0.010762861929833889,
-0.018491704016923904,
0.07241430878639221,
-0.048062242567539215,
-0.03085273690521717,
0.02168755605816841,
0.08422525227069855,
-0.05565619096159935,
0.053103797137737274,
-0.024130092933773994,
-0.04697834700345993,
-0.022936079651117325,
0.03910309076309204,
-0.0353424996137619,
0.0019868887029588223,
0.019966600462794304,
0.01877775974571705,
-0.009530652314424515,
-0.07670515775680542,
-0.015404168516397476,
-0.04858052730560303,
0.015170647762715816,
0.043162889778614044,
-0.04631544649600983,
-0.0213620625436306,
-0.025014882907271385
] |
<p>This is sort of a silly question because I'm a total beginner, and I debated whether it was better to ask here or on Math.SE. I decided on here because it's about how physicists use terminology, even though the terminology is intrinsically mathematical and there's not actually any physical content in the question.</p>
<p>It's a well-known fact in theoretical physics that the conformal group of Minkowski space is $\operatorname{SO}(4,2)$ (or sometimes its double cover $\operatorname{SU}(2,2)$ is chosen instead). This is infinitesimally generated by the standard Poincare generators $M_{\mu \nu}$ and $P_\mu$ together with scale transformation $D$ and special conformal generators $K_\mu$. I've also seen conformal groups discussed for other manifolds (the case which lead me to this question is Witten's 2003 paper <a href="http://arxiv.org/abs/hep-th/0312171">Perturbative Gauge Theory As A String Theory In Twistor Space</a>, which includes the conformal group of $\mathbb{R}^4$ with all possible signatures.)</p>
<p>However, the above doesn't seem to agree with the definition of the term "conformal group" which I know from the minimal amount of conformal geometry I know. Specifically, the conformal group of a pseudo-Riemannian manifold $M$ is the group of conformal self-maps on $M$, that is, self-diffeomorphisms for which the pullback metric is conformally equivalent to the original metric. (Two metrics $g$, $h$ are conformally equivalent if there is a positive real-valued function $u$ such that at each point $x \in M$ we have $g_{x, \mu \nu}=u(x)h_{x, \mu \nu}$.)</p>
<p>The trouble is that the conformal group of Minkowski space isn't $\operatorname{SO}(4,2)$ with the above definition. The special conformal transformations, given by the expression (for some vector $b_\mu$) $$ x' ^\mu = \frac{x^\mu - x^2 b^\mu}{1-2b \cdot x +b^2 x^2}$$ aren't self-maps of Minkowski space at all. The denominator can become 0 (while the numerator remains finite), and at that particular $x^\mu$ the transformation given by $b^\mu$ is undefined. For an example, take $x=(1,0,0,0)$ and $b=(0,1,0,0)$. So in fact the special conformal transformations are only maps from a subset of Minkowski space back to the full Minkowski space, and shouldn't be included as part of the conformal group if we take the above definition. It's difficult to tell from this formula, but from the fact that $$ \frac{x'^\mu}{x'^2} = \frac{x^\mu}{x^2} - b^\mu$$
we can tell that the inverse transformation is just given by $-b^\mu$, another special conformal transformation, which means these maps aren't surjective either.</p>
<p>These problems stem from the fact that the conformal group is typically derived in physics by considering the algebra of vector fields (which we think of as infinitesimal coordinate transformations) which satisfy the conformal Killing equation. There's in general no reason to expect that the corresponding finite transformation to be well-behaved away from the origin.</p>
<p><strong>How, exactly, are conformal groups defined in physics for arbitrary (in particular noncompact) pseudo-Riemannnian manifolds so that we get the expected result for Minkowski space?</strong></p>
<p>To be perfectly clear, I don't want answers of the form "find the Lie algebra, then exponentiate everything". I know that this works, but I want a definition for the conformal group as a group, without referencing algebras. In my opinion, there ought to be a way to define it this way, and it seems a bit important to me since <em>a priori</em> I don't see any reason why the group of conformal self-maps of a manifold needs to be a (possibly infinite-dimensional) Lie group at all. There are probably some high-power theorems (perhaps in PDE) which would imply this trivially, but naturally we need to know an actual group structure to be able to apply them. In the case of the conformal group as I defined it above (so excluding special conformal transformations) I believe I know a way to prove this for the "mathematician" definition, but when we start throwing in maps that are not everywhere defined the approach I came up with fails. Hence, even if this is how most physicists would define it, I'm looking for an alternate global definition to get some better geometric intuition which produces the correct answers.</p>
<hr>
<p>Some thoughts on this (feel free to ignore, especially if I'm on the wrong track):</p>
<p>It seems to me possible to remedy this in a fairly trivial way. We can consider all injective conformal maps from dense open sets of Minkowski space to (possibly distinct) dense open sets of Minkowski space. We also need to define compositions to be restricted to the subset of Minkowski space on which they are defined. Furthermore, we impose an equivalence relation that two maps which restrict to the same map on the intersection of their domains are equal. Using these definitions, we can at least get a group which contains all of the conformal transformations it should. It also contains some other less desirable sorts of transformations (for instance, take two rotations and patch them together on the interior and exterior respectively of $\mathbb{R} \times S^2$; incidentally, this is essentially why the proof I have could potentially fail for the "physicist's" conformal groups), but by imposing some conditions on the behavior of the maps in a neighborhood of the boundary of the region on which they are defined it should be possible to get back the get back the ordinary conformal group. (I have not checked this, nor do I know exactly what conditions should be applied, though I could figure it out in the case of Minkowski space based on an alternate model below for the conformal group.)</p>
<p>That approach, while easy to justify based on our above assumptions, is not very intuitive. It requires a lot of technical work to get everything to work out properly. We're implicitly using the fact that finite intersections of dense open sets are dense and open. The conditions required as the functions approach the boundary of their domains to get everything to work are also not obvious. More importantly, the whole thing seems to be suggesting an alternate approach which is much more geometrical; that we should view Minkowski space as contained within some slightly larger space on which the conformal group acts more nicely, where we view the complement of Minkowski space as points at $\infty$.</p>
<p>Specifically (and at this point I'm just making conjectures because they seem helpful) for any psuedo-Riemannian manifold $M$, there ought to be some unique space $\bar M$ which has the properties that $M \subset \bar M$ is dense (this is based on the above observations, and might not be necessary or desirable in the general case; however, it seems reasonable), the restriction of the metric on $\bar M$ to $M$ produces a conformally equivalent metric to the standard metric on $M$, and such that all the conformal self-maps of $M$ which "should exist" can be legitimately interpreted as conformal self-maps of $\bar M$. I don't know that this actually implies $\bar M$ is compact, but certainly if $M$ is compact then the sorts of problems we run into for Minkowski space can't happen. We can then just define the conformal group of an arbitrary manifold $M$ to be the conformal group, in the "mathematics definition", of $\bar M$. A construction of $\bar M$ would thus be a perfectly reasonable answer to this question, though at this point I'm still not sure that any space $\bar M$ need exist in general. I briefly tried to do this myself, but I was not able to come up with anything general enough to be satisfactory, nor was I able to prove that the few cases I know of this construction are unique.</p>
<p>I do know that this approach works for Minkowski space in some sense. Specifically, we can complete Minkowski space in this sense by including it into the projective light cone (i.e. the space of all null lines through the origin) in 6-dimensional Euclidean space with $(4,2)$ signature. The particular embedding is well-known and not so important for my purposes. However, this doesn't generalize particularly well when presented in this way. The reason why it works, at least intuitively for me, is that $\operatorname{SO}(4,2)$ naturally acts on this space, which to me seems like a big coincidence that can't be expected to continue to work if we consider arbitrary spaces. I considered using Penrose diagrams to try to do the equivalent construction for all of the cases I care about, but these only work for asymptotically flat spaces as far as I know and that misses some cases of interest for me (e.g. AdS), plus a general construction would be far more satisfying.</p>
<p>I also considered the possibility that physicists may be using the term inconsistently outside the context of Minkowski space. That is, there may be a number of constructions of "conformal groups", all of which give the same $\operatorname{SO}(4,2)$ on Minkowski space. That would actually be more interesting for my purposes if it's true.</p> | g7869 | [
-0.0016799932345747948,
-0.01648469641804695,
0.010863843373954296,
-0.016403596848249435,
-0.040974393486976624,
0.005703202448785305,
0.03329126164317131,
0.03357596695423126,
0.0026099849492311478,
-0.01521985698491335,
-0.005993344355374575,
-0.0043176766484975815,
0.01817389577627182,
-0.005025597754865885,
-0.026646694168448448,
-0.0217589084059,
0.084773488342762,
0.015687596052885056,
0.09235427528619766,
-0.03373398259282112,
-0.00416259141638875,
-0.022348519414663315,
0.04503496736288071,
-0.05447638779878616,
-0.04582090303301811,
-0.035908158868551254,
0.097681924700737,
-0.05511251464486122,
0.001947052194736898,
-0.05218975618481636,
0.06932761520147324,
0.07051416486501694,
0.011112775653600693,
-0.062322765588760376,
-0.04368629679083824,
-0.04119831323623657,
0.03478499874472618,
0.014051278121769428,
0.07952375710010529,
0.05527625232934952,
-0.006614541634917259,
-0.02767893299460411,
0.031866416335105896,
-0.05659598857164383,
-0.018171153962612152,
-0.0043891058303415775,
-0.05220461264252663,
0.046085067093372345,
0.032661378383636475,
-0.02207188680768013,
0.052289269864559174,
0.001015098299831152,
0.005068951286375523,
0.0033167602960020304,
0.017306717112660408,
0.05853605270385742,
0.028038620948791504,
0.021494753658771515,
0.09729034453630447,
-0.006996471434831619,
-0.028126128017902374,
-0.0010607970179989934,
-0.03061346337199211,
0.04614752158522606,
0.07960038632154465,
-0.0325624980032444,
-0.021167399361729622,
0.017472123727202415,
-0.017406295984983444,
0.02399040013551712,
0.0005271122208796442,
-0.03963753208518028,
0.06473775953054428,
-0.016536550596356392,
0.00905123632401228,
0.03196517005562782,
-0.019070610404014587,
-0.03966623917222023,
-0.008945359848439693,
-0.045020874589681625,
-0.039293479174375534,
-0.020388225093483925,
0.03239542245864868,
0.03677275404334068,
0.039801932871341705,
0.009553009644150734,
-0.039561677724123,
0.02107979543507099,
-0.053525160998106,
-0.02112235128879547,
-0.019150197505950928,
0.02113151364028454,
0.020912718027830124,
-0.033091288059949875,
0.00930799264460802,
0.017420513555407524,
0.04954950511455536,
-0.019262142479419708,
-0.01411473285406828,
-0.001866402686573565,
-0.01926758885383606,
-0.01363968662917614,
-0.030297597870230675,
0.05179484561085701,
-0.019318806007504463,
-0.0039833299815654755,
0.056596849113702774,
0.04660157486796379,
0.022480620071291924,
0.004845087416470051,
-0.03485649451613426,
0.03105931356549263,
0.02525925636291504,
-0.013826331123709679,
-0.022998470813035965,
-0.018688509240746498,
-0.014289661310613155,
-0.008597156032919884,
-0.005909816827625036,
0.12466555833816528,
0.01898632012307644,
-0.029744725674390793,
0.07082384079694748,
0.040448982268571854,
-0.03864267095923424,
-0.009955444373190403,
-0.01469817291945219,
0.03293750062584877,
0.010097243823111057,
-0.07828710228204727,
0.0006800814298912883,
-0.015323054976761341,
0.020471833646297455,
0.005413788836449385,
-0.012027768418192863,
-0.008991196751594543,
0.020045502111315727,
-0.04496253281831741,
0.08825396001338959,
-0.020023759454488754,
-0.025188669562339783,
-0.010948911309242249,
-0.010119523853063583,
0.022214876487851143,
-0.017277037724852562,
-0.015256298705935478,
0.0311956275254488,
-0.04300451651215553,
-0.0006895755068399012,
0.048972371965646744,
0.00832024123519659,
0.04264040291309357,
0.0555034875869751,
-0.028981266543269157,
0.015039688907563686,
0.0319245345890522,
0.03980059176683426,
-0.013228042051196098,
-0.024801993742585182,
0.013391938991844654,
0.07912154495716095,
0.022081520408391953,
-0.014865228906273842,
0.03733157366514206,
-0.07962583005428314,
0.03915680572390556,
0.02121288701891899,
-0.010199688374996185,
-0.010570538230240345,
-0.04927501082420349,
-0.06928062438964844,
0.010552608408033848,
0.03998690843582153,
0.02198311872780323,
0.033413488417863846,
-0.0015792733756825328,
-0.02416909672319889,
0.0008144635357894003,
0.03682643175125122,
-0.009993097744882107,
-0.01383870281279087,
-0.03694862127304077,
0.04580586031079292,
-0.02616484835743904,
0.0004322343156673014,
0.046082183718681335,
-0.01998935639858246,
0.014070682227611542,
0.018486108630895615,
0.010357271879911423,
0.027418896555900574,
0.03458566218614578,
0.0565546415746212,
-0.03121199831366539,
0.04668441414833069,
0.05201209709048271,
-0.008046803064644337,
-0.021215686574578285,
0.00664095114916563,
-0.05592188239097595,
0.01692809723317623,
0.005681019742041826,
0.03734608367085457,
-0.016960443928837776,
-0.014488658867776394,
0.028872031718492508,
-0.021775560453534126,
-0.07799898833036423,
0.008037502877414227,
0.014785834588110447,
0.01669018529355526,
-0.025582147762179375,
0.00993156898766756,
-0.003206058871001005,
0.012163331732153893,
-0.009327172301709652,
-0.0962713360786438,
0.0002661914622876793,
-0.04586555063724518,
0.04056285694241524,
-0.003827449167147279,
0.010380061343312263,
0.05044739693403244,
0.009296519681811333,
-0.03600047528743744,
0.011593295261263847,
-0.04657463729381561,
-0.04030042514204979,
0.030958767980337143,
0.015111275017261505,
-0.04286476969718933,
-0.014320858754217625,
-0.019062427803874016,
-0.007523032370954752,
-0.0502132810652256,
-0.00787715706974268,
-0.022074662148952484,
0.08016234636306763,
0.05640915781259537,
0.04037913680076599,
0.025212615728378296,
-0.017244987189769745,
-0.03410564363002777,
-0.01426461897790432,
0.00024330269661732018,
-0.04308459535241127,
0.0006051958189345896,
-0.022116627544164658,
-0.029466217383742332,
0.03710838779807091,
0.01691180095076561,
-0.03141816332936287,
-0.052608005702495575,
-0.026012012735009193,
0.025695761665701866,
0.014732266776263714,
0.03941052407026291,
0.02350517176091671,
-0.03963487595319748,
-0.027624089270830154,
-0.009288134053349495,
-0.03384910896420479,
0.004193682689219713,
0.04992515966296196,
-0.06858416646718979,
0.043568238615989685,
-0.014829088933765888,
0.043442100286483765,
0.0019339834107086062,
0.04771725833415985,
0.013441096991300583,
0.03552482649683952,
-0.0004923193482682109,
0.05523476004600525,
-0.036965277045965195,
0.03293657675385475,
-0.003280885750427842,
-0.01797349378466606,
0.011998318135738373,
-0.030112620443105698,
-0.03237418830394745,
0.021420860663056374,
-0.019597971811890602,
-0.0424438901245594,
0.005912343040108681,
-0.07671378552913666,
0.002525710966438055,
-0.05325089395046234,
-0.02611481212079525,
0.1045769527554512,
0.0064621977508068085,
-0.03900168836116791,
0.015340236015617847,
0.04264024272561073,
-0.024259058758616447,
0.04206462576985359,
-0.056433334946632385,
0.023424968123435974,
0.024695832282304764,
0.027466343715786934,
0.0247914120554924,
-0.026478394865989685,
0.035935577005147934,
0.06028701737523079,
0.037786293774843216,
-0.040083449333906174,
-0.08262098580598831,
-0.03491930291056633,
-0.015268981456756592,
0.011181164532899857,
-0.06307949125766754,
-0.0019247622694820166,
0.049180496484041214,
0.015575842000544071,
-0.01025271788239479,
-0.009814922697842121,
-0.018783601000905037,
0.017500601708889008,
-0.049253083765506744,
-0.09176327288150787,
0.018621575087308884,
0.005877778399735689,
0.0285150445997715,
-0.022163240239024162,
0.04274791479110718,
0.03255552053451538,
-0.009804327972233295,
-0.03370711952447891,
-0.02206135168671608,
-0.008817116729915142,
0.034345224499702454,
-0.026509085670113564,
-0.01762988045811653,
-0.02898716926574707,
-0.07733136415481567,
-0.04079224914312363,
-0.05132155492901802,
0.03874148055911064,
0.03123878687620163,
-0.036074843257665634,
0.00964701734483242,
-0.06099126487970352,
-0.02615269646048546,
-0.013142496347427368,
-0.0021790103055536747,
-0.0076611097902059555,
-0.000052129587857052684,
0.021194878965616226,
-0.004152483772486448,
-0.0018074687104672194,
0.019963370636105537,
-0.013617483898997307,
0.046237122267484665,
-0.005975645501166582,
0.026813756674528122,
-0.0024296303745359182,
0.0442754290997982,
0.05831504985690117,
-0.013395490124821663,
-0.043154846876859665,
0.021108994260430336,
-0.04280857741832733,
0.02537757158279419,
0.026156708598136902,
-0.007436690852046013,
0.022140376269817352,
0.0075074550695717335,
-0.029083693400025368,
-0.016256235539913177,
0.009984449483454227,
0.05421299859881401,
-0.027321266010403633,
-0.030411984771490097,
0.04732676222920418,
-0.018655026331543922,
-0.035390861332416534,
-0.022902535274624825,
0.008109689690172672,
-0.05234447866678238,
-0.03462343290448189,
-0.012992684729397297,
0.00891503319144249,
0.060655951499938965,
0.049575503915548325,
0.017511680722236633,
0.048388414084911346,
-0.014326645992696285,
-0.05096842348575592,
0.00110008311457932,
0.01751127280294895,
-0.031389810144901276,
0.01938639208674431,
-0.021810805425047874,
-0.02713964134454727,
-0.017986968159675598,
-0.017082909122109413,
0.05541083589196205,
-0.03090231493115425,
-0.015970872715115547,
-0.00881203729659319,
-0.014017356559634209,
0.009867754764854908,
0.013592786155641079,
-0.02221379615366459,
-0.001901397597976029,
-0.050337765365839005,
0.012868375517427921,
-0.012967457994818687,
0.05216706171631813,
-0.025593919679522514,
0.02198086678981781,
-0.05112325772643089,
0.0025911463890224695,
-0.023559320718050003,
0.003243350423872471,
0.008803737349808216,
0.033375635743141174,
-0.042729701846838,
-0.014619085937738419,
-0.02732931822538376,
-0.012545689940452576,
0.005936992820352316,
0.008849618025124073,
-0.013742395676672459,
0.03485395386815071,
0.11099740862846375,
0.04151534289121628,
-0.019145280122756958,
-0.04998372122645378,
-0.03180146962404251,
0.031443845480680466,
0.015604807995259762,
0.019358938559889793,
0.05798822641372681,
-0.06215452402830124,
0.029400832951068878,
-0.03490807116031647,
0.01373288594186306,
-0.014951479621231556,
0.03484255447983742,
0.02453973889350891,
-0.024214427918195724,
-0.026841135695576668,
-0.06371504813432693,
-0.059653375297784805,
0.022964172065258026,
-0.03908785805106163,
-0.013321501202881336,
-0.039918817579746246,
0.022462129592895508,
-0.06395785510540009,
-0.004852797836065292,
0.06989184767007828,
0.023766610771417618,
-0.009054756723344326,
0.01221003383398056,
0.0027253953740000725,
0.02735770493745804,
0.011461516842246056,
-0.02397649735212326,
-0.07002008706331253,
-0.08147894591093063,
-0.0039591118693351746,
0.03808589652180672,
0.006931094452738762,
0.02085881493985653,
-0.029657140374183655,
0.022367656230926514,
-0.05371411144733429,
-0.009601970203220844,
0.04788249731063843,
0.03535939380526543,
-0.04129946231842041,
-0.08310974389314651,
0.013536200858652592,
0.0758771151304245,
0.022005198523402214,
0.0130867138504982,
-0.02295210398733616,
-0.04402442276477814,
0.02793928049504757,
0.040157392621040344,
-0.034434013068675995,
0.013659561052918434,
0.03332890197634697,
0.05240999162197113,
-0.023824499920010567,
0.02970281057059765,
0.0013885245425626636,
-0.04762817174196243,
0.0014543971046805382,
-0.008938050828874111,
0.021840987727046013,
-0.02854129485785961,
-0.005441085901111364,
0.03831949830055237,
-0.004398659337311983,
-0.043374188244342804,
-0.06020159646868706,
-0.01566821150481701,
-0.010815580375492573,
0.05314447358250618,
0.01075135450810194,
-0.014710498042404652,
-0.013503631576895714,
0.026476770639419556,
0.08014222979545593,
0.039410583674907684,
0.01411798968911171,
0.027083998546004295,
-0.008262982591986656,
-0.00642597209662199,
0.05101906880736351,
-0.015536956489086151,
0.059303272515535355,
0.01156939473003149,
-0.020311152562499046,
-0.03664195165038109,
0.01323008257895708,
-0.022512685507535934,
-0.005065586883574724,
-0.007711086422204971,
0.0314030759036541,
0.06647459417581558,
0.10459918528795242,
0.07270463556051254,
-0.03610943630337715,
-0.05456516146659851,
-0.004015374928712845,
0.021793974563479424,
0.0336858294904232,
-0.04956158623099327,
0.029202554374933243,
-0.02643170766532421,
-0.020086856558918953,
0.01761799305677414,
-0.0390847772359848,
0.05665076896548271,
0.07991767674684525,
-0.014878240413963795,
-0.010935320518910885,
-0.04462926462292671,
-0.010888113640248775,
0.02427608147263527,
0.03799689933657646,
-0.0023498530499637127,
0.027210401371121407,
0.004704337567090988,
0.022931504994630814,
-0.06559673696756363,
-0.031119126826524734,
0.06823695451021194,
0.03232555836439133,
-0.036058686673641205,
0.053470488637685776,
0.02147917076945305,
-0.01652396097779274,
-0.009429407306015491,
-0.012881025671958923,
0.007527957204729319,
-0.012470044195652008,
-0.037065573036670685,
-0.05858580768108368,
-0.01969214528799057,
-0.010096029378473759,
-0.01126654352992773,
-0.024813294410705566,
-0.04247067868709564,
0.060722723603248596,
0.023482782766222954,
-0.03573288023471832,
0.06586195528507233,
0.05097334459424019,
0.0158604197204113,
-0.03514055907726288,
-0.007781616877764463,
0.02924632467329502,
0.028503432869911194,
0.007144847884774208,
-0.00285564037039876,
-0.007613522000610828,
-0.028325797989964485,
0.0003164114896208048,
-0.052470140159130096,
-0.10293877124786377,
0.010062575340270996,
-0.020140986889600754,
-0.006274040322750807,
0.017354324460029602,
-0.045414168387651443,
-0.059354715049266815,
0.016231192275881767,
0.03468124940991402,
0.05718446150422096,
-0.04050496593117714,
0.0049542938359081745,
-0.000782616960350424,
0.017446065321564674,
-0.01095629297196865,
0.015891138464212418,
-0.038342662155628204,
0.02825447916984558,
-0.008929909206926823,
0.07595960795879364,
0.05947249010205269,
0.023952143266797066,
-0.06871987879276276,
-0.0020113952923566103,
-0.013849100098013878,
-0.007307440508157015,
-0.030904503539204597,
0.045955412089824677,
-0.05022909492254257,
0.04508017376065254,
-0.021742410957813263,
-0.00692462082952261,
-0.03466842696070671,
-0.00032479024957865477,
-0.008871329016983509,
-0.02104225941002369,
0.08756931126117706,
0.000028299247787799686,
0.02926100604236126,
-0.0005679901223629713,
-0.0334642268717289,
0.004848027136176825,
0.03228288143873215,
-0.003623001044616103,
0.05523499846458435,
-0.0053449831902980804,
-0.019213398918509483,
-0.01762797124683857,
-0.03431503474712372,
0.04331699758768082,
0.018590226769447327,
0.004984416998922825,
-0.041267700493335724,
-0.0282155591994524,
0.018651997670531273,
-0.005332519765943289,
-0.012197786942124367,
-0.048733364790678024,
0.043167151510715485,
-0.016974959522485733,
-0.028050152584910393,
-0.036764487624168396,
-0.03217625245451927,
-0.0010861312039196491,
-0.03936205059289932,
0.0705534890294075,
0.012147740460932255,
-0.009847582317888737,
-0.028575913980603218,
-0.013575558550655842,
-0.03834245353937149,
-0.011649581603705883,
0.01939239725470543,
0.02044045925140381,
0.020906565710902214,
-0.11281148344278336,
0.016445450484752655,
-0.019242482259869576,
0.026819216087460518,
0.0017992286011576653,
-0.03977574035525322,
-0.001695940736681223,
-0.05640796571969986,
0.008223116397857666,
-0.00257686385884881,
-0.012482542544603348,
0.013205588795244694,
0.035703349858522415,
-0.001422374276444316,
0.040999557822942734,
0.034677837044000626,
-0.057154346257448196,
0.037225354462862015,
0.05993938446044922,
0.006235158536583185,
0.0013279044069349766,
0.02143699862062931,
0.026565220206975937,
0.008131947368383408,
0.023336375132203102,
-0.05043495073914528,
0.05458220839500427,
0.013948912732303143,
-0.012347823940217495,
-0.03236826881766319,
-0.005955690052360296,
0.05693778395652771,
0.0033407434821128845,
0.0083191292360425,
-0.013623804785311222,
-0.022295815870165825,
-0.03457385301589966,
0.011838591657578945,
0.01848595403134823,
-0.07819246500730515,
-0.025960059836506844,
-0.0028759913984686136,
-0.02322223037481308,
-0.048148393630981445,
-0.018319521099328995,
-0.025117287412285805,
0.013591433875262737,
-0.005098920315504074,
-0.03321653977036476,
-0.03068823739886284,
-0.0026768341194838285,
-0.014278308488428593,
0.07124693691730499,
0.025452198460698128,
0.03846849873661995,
-0.0025965305976569653,
-0.003702762071043253,
-0.06693728268146515,
-0.047069352120161057,
0.035037800669670105,
-0.04079780727624893,
-0.03729485720396042,
0.015428590588271618,
-0.05155414715409279,
-0.018087411299347878,
-0.006179226562380791,
0.03866807743906975,
-0.05202506482601166,
-0.03503270819783211,
0.009698520414531231,
-0.049178604036569595,
-0.016877446323633194,
-0.03616148978471756,
-0.01668701507151127,
0.028494272381067276,
0.03660569339990616,
-0.02625388652086258,
-0.008629673160612583,
-0.04100487381219864,
0.04016115143895149,
0.0272987000644207,
-0.03455417975783348,
-0.05424439534544945,
0.012746530584990978,
-0.011911490000784397,
-0.05618595704436302,
-0.04175041243433952,
-0.019113857299089432,
0.07319119572639465,
-0.08264119178056717,
0.004260846879333258,
0.007436663843691349,
0.07099273800849915,
0.0046247923746705055,
0.0818890854716301,
0.046982891857624054,
-0.02739368937909603,
0.014539847150444984,
0.01943284645676613,
0.050450243055820465,
0.04809477552771568,
-0.0010385466739535332,
0.01987895555794239,
0.03204129636287689,
0.06185372918844223,
-0.07496566325426102,
-0.02173757553100586,
0.013271375559270382,
0.015604430809617043
] |
<p>The <a href="http://en.wikipedia.org/wiki/Cross_section_%28physics%29" rel="nofollow">cross section</a> is a tiny area, measured in barns ($10^{-28} \mathrm{m^2}$), which relates to the probability of a reaction.</p>
<p>But I have trouble interpreting that number.</p>
<p>For example how can I calculate, when two deuterons collide what's the chance that they fuse? I read in forums that they much more likely scatter.</p> | g7870 | [
-0.00765913724899292,
0.021197309717535973,
0.003235542681068182,
-0.038196347653865814,
0.05728219076991081,
0.018749291077256203,
0.008659259416162968,
0.07544402033090591,
-0.02382880635559559,
-0.08796520531177521,
0.008121781051158905,
0.0016347089549526572,
0.050254154950380325,
-0.015616190619766712,
0.014729464426636696,
-0.005072771105915308,
0.050954338163137436,
0.007416603155434132,
0.022361524403095245,
0.06767436861991882,
-0.02573295868933201,
0.039247699081897736,
-0.05210137367248535,
-0.05133814364671707,
0.03313314542174339,
0.0025067096576094627,
-0.010611720383167267,
0.010934682562947273,
-0.06437752395868301,
-0.038649290800094604,
-0.03429223224520683,
0.05203110724687576,
0.05510120838880539,
-0.05605166032910347,
-0.08889393508434296,
-0.03963863477110863,
-0.03451062738895416,
-0.07580655813217163,
0.013032034039497375,
-0.01660325936973095,
0.01790553331375122,
-0.015030906535685062,
0.017715873196721077,
-0.02999209612607956,
-0.037431832402944565,
0.030343499034643173,
-0.02116202563047409,
-0.030012667179107666,
0.038064584136009216,
-0.003867132356390357,
-0.037623919546604156,
0.0534713976085186,
0.06076596677303314,
-0.0010508516570553184,
0.039272330701351166,
0.009191143326461315,
0.01913948729634285,
-0.04378929361701012,
0.09363140165805817,
0.04067007452249527,
0.020723391324281693,
0.05780941620469093,
0.02515498548746109,
-0.04574911296367645,
0.08827294409275055,
0.031036967411637306,
-0.0400904156267643,
0.02204270288348198,
0.04890476539731026,
-0.014033635146915913,
0.020642153918743134,
-0.04316028952598572,
0.027719730511307716,
0.004377149511128664,
-0.031298816204071045,
-0.01146269403398037,
0.019578296691179276,
0.02308213897049427,
0.002506377873942256,
0.025479145348072052,
-0.029179368168115616,
0.015330664813518524,
-0.005723298527300358,
-0.001962037291377783,
0.04780805855989456,
0.021497154608368874,
-0.03210707753896713,
-0.009234052151441574,
-0.050731781870126724,
-0.025284241884946823,
0.06299707293510437,
0.0221688412129879,
0.020490236580371857,
-0.03165179118514061,
0.019640106707811356,
-0.022168630734086037,
-0.054385408759117126,
0.05041983723640442,
0.006357899401336908,
0.03328100964426994,
-0.0557449571788311,
0.01578463427722454,
-0.0000690844317432493,
0.010397734120488167,
-0.00291041168384254,
-0.033298250287771225,
-0.0264096949249506,
-0.003493823343887925,
-0.0009672476444393396,
-0.02873423509299755,
-0.06606309860944748,
-0.04657430201768875,
-0.04988103359937668,
-0.046325597912073135,
0.05247841775417328,
0.03529512509703636,
0.04750087112188339,
-0.023253194987773895,
0.029501184821128845,
0.044374264776706696,
0.07630936801433563,
0.017363836988806725,
-0.02083411067724228,
0.03307466208934784,
-0.0600067600607872,
-0.04084803909063339,
-0.060112591832876205,
0.024814123287796974,
0.06365381181240082,
0.018809132277965546,
-0.030885979533195496,
-0.05364224314689636,
0.029036810621619225,
0.02976144663989544,
0.05537125840783119,
0.04316030815243721,
0.05175745114684105,
0.01040121540427208,
-0.032195910811424255,
-0.0109252342954278,
0.059306416660547256,
0.03243434429168701,
0.010129986330866814,
-0.043256938457489014,
-0.07567336410284042,
-0.02051188424229622,
0.0012392231728881598,
-0.020758839324116707,
0.0045884051360189915,
-0.05548465624451637,
-0.0021273258607834578,
0.00285202800296247,
0.04027579724788666,
-0.06328136473894119,
-0.011539378203451633,
0.007157104089856148,
0.020306004211306572,
-0.015695730224251747,
-0.03415341302752495,
-0.004781411960721016,
0.00011781397188315168,
0.005596760660409927,
0.0046838452108204365,
-0.030997881665825844,
-0.06876623630523682,
0.02368107996881008,
0.04474160075187683,
-0.08007878065109253,
0.032512955367565155,
-0.047304704785346985,
0.005868253763765097,
-0.04335150122642517,
0.05131112039089203,
0.00961383432149887,
-0.04851573705673218,
0.030516522005200386,
-0.01601182296872139,
-0.004824923817068338,
-0.011251039803028107,
0.018047187477350235,
0.008423369377851486,
0.008917886763811111,
0.07860416918992996,
0.02346949279308319,
0.01616845466196537,
-0.09034944325685501,
0.00411062128841877,
0.06965889781713486,
-0.020854627713561058,
0.010070402175188065,
-0.06129710376262665,
-0.03627583757042885,
0.011464892886579037,
-0.027583777904510498,
0.032002247869968414,
-0.0016214249189943075,
-0.013273384422063828,
-0.028946684673428535,
-0.0221671462059021,
0.01453543920069933,
-0.022278986871242523,
0.05033772811293602,
0.016340790316462517,
0.05938524752855301,
0.043033212423324585,
0.03323142230510712,
-0.03237006813287735,
0.02507530339062214,
0.013211626559495926,
-0.04026664048433304,
-0.023019468411803246,
0.008426483720541,
-0.022009504958987236,
-0.017388662323355675,
-0.018388278782367706,
0.0015908722998574376,
0.019477706402540207,
-0.007955876179039478,
-0.02760365605354309,
0.005311647895723581,
0.008372765965759754,
0.015353466384112835,
0.08833862841129303,
-0.0617261566221714,
0.034163832664489746,
0.08746299147605896,
-0.023084785789251328,
-0.005111420061439276,
0.009458966553211212,
-0.002130156150087714,
-0.025376424193382263,
0.054981689900159836,
-0.10156112909317017,
-0.04029778018593788,
0.0017757723107933998,
0.03132103011012077,
0.04523273929953575,
-0.019823715090751648,
-0.0005696080042980611,
0.0396382175385952,
0.022853126749396324,
-0.014690970070660114,
-0.04755241796374321,
0.015944918617606163,
0.0283537358045578,
-0.03271459415555,
0.010975943878293037,
-0.0005611794767901301,
-0.027281953021883965,
0.019619382917881012,
0.012577928602695465,
-0.03988933190703392,
-0.024151580408215523,
0.007253284100443125,
-0.04082688316702843,
-0.022269366309046745,
-0.06252948939800262,
0.002240621717646718,
-0.04135730862617493,
-0.022014617919921875,
0.002799142384901643,
-0.0006614867015741765,
0.031106287613511086,
0.025693541392683983,
-0.0572812519967556,
-0.058138035237789154,
-0.04445559158921242,
-0.02199161797761917,
0.018694914877414703,
-0.013266835361719131,
-0.023498503491282463,
0.048209019005298615,
-0.02383561246097088,
0.04160196706652641,
-0.00037193327443674207,
-0.016220876947045326,
0.07159765809774399,
-0.030033094808459282,
-0.017409417778253555,
-0.0574386790394783,
-0.01883537508547306,
0.035833295434713364,
0.03374101594090462,
0.0069673252291977406,
0.06993862986564636,
-0.03867026045918465,
0.01333686988800764,
0.05698569118976593,
0.041860152035951614,
0.0853872075676918,
0.032875511795282364,
-0.04186823591589928,
0.007597381714731455,
-0.002078239805996418,
0.014322251081466675,
0.05076991766691208,
0.08897298574447632,
0.0058444105088710785,
0.02884981781244278,
-0.041581545025110245,
-0.029353691264986992,
-0.004064211621880531,
-0.026438279077410698,
-0.011440330184996128,
0.001156964572146535,
0.005200521554797888,
-0.019918270409107208,
-0.019002428278326988,
0.02121291123330593,
-0.0473099909722805,
-0.0036676686722785234,
0.04834485054016113,
0.02875705063343048,
-0.014608262106776237,
-0.027366677299141884,
-0.011390904895961285,
0.06046799570322037,
0.04757450148463249,
0.046785276383161545,
0.005411236081272364,
-0.014442289248108864,
-0.061957232654094696,
0.02180776186287403,
-0.026920411735773087,
0.01051636878401041,
-0.0014238880248740315,
-0.04851352050900459,
0.04259327054023743,
0.008296103216707706,
0.003508331486955285,
0.0015349827008321881,
0.0030992126557976007,
-0.07758142054080963,
-0.006815196480602026,
-0.055996086448431015,
-0.07480215281248093,
0.013436096720397472,
0.040613457560539246,
0.035553913563489914,
0.06191117689013481,
0.0007180475513450801,
-0.008342058397829533,
-0.00472571374848485,
-0.01525228563696146,
0.013392947614192963,
0.024682514369487762,
0.016386615112423897,
0.03925112634897232,
0.021312836557626724,
-0.0618709959089756,
0.025145962834358215,
-0.020274758338928223,
0.018263859674334526,
0.020128002390265465,
0.034749843180179596,
0.03751680999994278,
-0.019977353513240814,
-0.016727648675441742,
-0.04319623112678528,
0.07264754921197891,
-0.03296488896012306,
-0.04254921153187752,
-0.009272788651287556,
0.008487342856824398,
-0.037370968610048294,
-0.038731370121240616,
-0.039530497044324875,
0.06539469957351685,
0.03397129476070404,
-0.009867844171822071,
-0.03598833456635475,
0.012832196429371834,
0.005575515329837799,
0.04405069351196289,
0.029192131012678146,
-0.02371075749397278,
0.002980685094371438,
0.021164581179618835,
0.022855285555124283,
0.014662310481071472,
0.027659323066473007,
0.0660318061709404,
0.006793709471821785,
-0.00932761374861002,
0.01915731281042099,
-0.054792217910289764,
-0.011904032900929451,
-0.018936771899461746,
0.014620273374021053,
-0.05127958208322525,
0.03467996045947075,
-0.019724130630493164,
-0.04809993878006935,
0.019297318533062935,
0.014058222062885761,
-0.043833814561367035,
0.021709464490413666,
0.0208299458026886,
-0.006010072771459818,
0.015987185761332512,
-0.012635921128094196,
-0.017945490777492523,
0.00015047646593302488,
-0.04712098091840744,
-0.0012041983427479863,
0.015248165465891361,
0.041448481380939484,
-0.001740446430630982,
0.04801206663250923,
0.017380613833665848,
0.043593090027570724,
0.0271297637373209,
0.01960860937833786,
-0.04280880466103554,
0.006610932759940624,
0.019519012421369553,
0.047945961356163025,
-0.01885918155312538,
0.011007151566445827,
0.03888979181647301,
0.0028190233279019594,
-0.019874893128871918,
0.029652969911694527,
0.0026794513687491417,
-0.08197679370641708,
0.0050630029290914536,
0.030748728662729263,
-0.017484458163380623,
0.0010388197842985392,
0.01620684377849102,
0.1108904629945755,
0.024568218737840652,
-0.05691372603178024,
0.00843720231205225,
-0.08900562673807144,
0.07366987317800522,
-0.018223101273179054,
0.05133049562573433,
0.009871793910861015,
0.08418336510658264,
0.031599387526512146,
0.02060997299849987,
-0.06119006872177124,
0.021435203030705452,
0.01130696851760149,
0.05632543936371803,
-0.0044416082091629505,
-0.0985630676150322,
-0.012461545877158642,
-0.09299683570861816,
-0.08506152778863907,
-0.015027041547000408,
-0.033208657056093216,
-0.05652832239866257,
0.020028023049235344,
-0.022117892280220985,
-0.01882077567279339,
0.00807752925902605,
0.027741502970457077,
0.06471902132034302,
-0.05041784048080444,
0.000081734309787862,
0.02299456112086773,
-0.010252684354782104,
0.023886600509285927,
0.04051923006772995,
-0.013724246993660927,
-0.02468174323439598,
-0.057451747357845306,
-0.009549427777528763,
-0.0528259314596653,
0.007464522961527109,
-0.021370645612478256,
-0.04970318451523781,
0.008088872767984867,
0.04594505578279495,
0.009526877664029598,
0.01612977683544159,
0.02279057539999485,
-0.006148497108370066,
-0.016061339527368546,
-0.022875165566802025,
-0.024332767352461815,
0.011786114424467087,
-0.018435345962643623,
0.04497358202934265,
-0.03820554167032242,
0.040181707590818405,
0.029701722785830498,
-0.024823639541864395,
-0.01177997887134552,
-0.013802783563733101,
-0.0032300283201038837,
-0.0031642834655940533,
0.020915841683745384,
-0.012716262601315975,
0.012148666195571423,
-0.051524724811315536,
0.0016820826567709446,
0.015446093864738941,
-0.02092219702899456,
0.014370372518897057,
-0.04564366117119789,
0.00838103611022234,
-0.04985088109970093,
0.06482180207967758,
0.04196314141154289,
-0.020755121484398842,
0.0029249866493046284,
0.013365495949983597,
0.0009427953045815229,
-0.00524690467864275,
0.038246963173151016,
0.033347003161907196,
-0.05158251151442528,
0.002874571830034256,
-0.05679628998041153,
0.04246797412633896,
-0.013811388052999973,
0.024148589000105858,
0.04413646087050438,
-0.004185549449175596,
0.003153577446937561,
-0.02393033169209957,
0.0007934790337458253,
-0.08363806456327438,
-0.047807469964027405,
-0.04759370535612106,
0.012170812115073204,
0.021919284015893936,
0.001345233991742134,
-0.020777102559804916,
-0.040241580456495285,
0.03215900436043739,
-0.03250885009765625,
-0.01695059798657894,
-0.0026104922872036695,
-0.0037865214981138706,
0.06094617024064064,
0.008851355873048306,
0.0028439878951758146,
0.06767063587903976,
-0.015967370942234993,
0.052872732281684875,
-0.008418438956141472,
-0.0010667912429198623,
-0.0007302040467038751,
0.019915759563446045,
0.0038257078267633915,
0.03793852776288986,
0.027692601084709167,
0.02036217413842678,
0.04195777699351311,
-0.03605905920267105,
0.053288958966732025,
0.014210939407348633,
-0.018258798867464066,
-0.009462296031415462,
0.019661426544189453,
0.0008990990463644266,
0.042056288570165634,
-0.018044184893369675,
-0.01742418482899666,
0.059744663536548615,
-0.005202878266572952,
-0.0679645836353302,
-0.04213057830929756,
-0.0035400791093707085,
0.010736856609582901,
0.020431362092494965,
-0.0009119993192143738,
-0.040248241275548935,
0.023012608289718628,
-0.03631442412734032,
0.041213374584913254,
0.027235722169280052,
0.004699127282947302,
-0.0433221310377121,
-0.028205767273902893,
-0.01084054820239544,
0.0035969610325992107,
0.003954002633690834,
0.05230584740638733,
-0.0574648417532444,
-0.043734777718782425,
0.04974471777677536,
0.023064756765961647,
-0.009436003863811493,
-0.01045590452849865,
-0.0005058901733718812,
-0.00253868056461215,
-0.011750577948987484,
0.0007691786740906537,
0.024821851402521133,
-0.01436949148774147,
-0.06992680579423904,
-0.026524748653173447,
0.020289167761802673,
-0.021270787343382835,
0.03880426287651062,
-0.027489854022860527,
0.024578716605901718,
0.04940610006451607,
0.04032778739929199,
0.0028287589084357023,
0.030650189146399498,
-0.038851212710142136,
0.015969952568411827,
-0.02597128413617611,
-0.007061253301799297,
0.02054569497704506,
0.014294727705419064,
-0.00575343519449234,
0.041332583874464035,
0.009551928378641605,
-0.03230471536517143,
-0.05059695243835449,
-0.038813501596450806,
0.018919868394732475,
0.029177075251936913,
0.03183712065219879,
-0.06371811032295227,
-0.0234091654419899,
-0.02308524399995804,
-0.016613777726888657,
0.025018712505698204,
-0.011500065214931965,
-0.0168993528932333,
0.04252476617693901,
-0.03735174238681793,
-0.000636761833447963,
0.0064981854520738125,
0.016738884150981903,
0.038825154304504395,
-0.01742834411561489,
0.05703521892428398,
-0.026846973225474358,
-0.02706035040318966,
0.00940447486937046,
0.06895565986633301,
-0.029765693470835686,
-0.03549452871084213,
0.047126442193984985,
0.050223808735609055,
-0.012040703557431698,
-0.02104593999683857,
-0.014874703250825405,
-0.022716354578733444,
-0.023498868569731712,
0.011814061552286148,
-0.057525213807821274,
-0.008868711069226265,
0.04800416901707649,
-0.0016595636261627078,
-0.06742662936449051,
0.0634438619017601,
0.04273467883467674,
0.019701313227415085,
0.02687790058553219,
-0.01695096679031849,
-0.02514161728322506,
-0.059705957770347595,
-0.06141508370637894,
-0.03825073316693306,
0.0018375060753896832,
-0.013467361219227314,
0.039973724633455276,
0.019304372370243073,
0.005152248311787844,
-0.05397234857082367,
-0.004747453611344099,
-0.04794624447822571,
-0.08155138790607452,
-0.023184606805443764,
0.013077406212687492,
0.01488461159169674,
0.027830859646201134,
-0.0019852924160659313,
0.06779224425554276,
0.04938845336437225,
0.029985874891281128,
-0.020365001633763313,
-0.0014824160607531667,
-0.023079730570316315,
0.012563775293529034,
-0.022871874272823334,
-0.021495070308446884,
0.007941415533423424,
0.052665118128061295,
0.04367808997631073,
0.016065232455730438,
0.0035960248205810785,
0.04934018477797508,
-0.049808237701654434,
-0.018985096365213394,
0.009029700420796871,
0.01798979379236698,
-0.027823759242892265,
0.012664792127907276,
-0.030770640820264816,
0.04061044007539749,
0.0020033938344568014,
0.023656873032450676,
-0.06783780455589294,
-0.025322768837213516,
0.033777009695768356,
0.02931417152285576,
-0.024418771266937256,
-0.010488306172192097,
-0.052222996950149536,
0.0682024285197258,
0.09210091084241867,
-0.016012966632843018,
-0.027528129518032074,
-0.030761253088712692,
0.029292123392224312,
-0.022307448089122772,
-0.012761550955474377,
0.020707303658127785,
0.07138646394014359,
0.0061105540953576565,
-0.07146235555410385,
0.00850395206362009,
-0.01632184162735939,
-0.006191154941916466,
-0.05972905457019806,
0.004334684461355209,
0.05898550897836685,
0.010371522977948189,
0.026884503662586212,
0.009149881079792976,
-0.02460099384188652,
-0.01701083406805992,
-0.027927646413445473,
-0.004225851036608219,
-0.024562299251556396,
0.04013419151306152,
-0.024946078658103943,
-0.07099585980176926,
0.037236399948596954,
0.020349331200122833,
-0.020031079649925232,
-0.02397141605615616,
-0.007604105398058891,
-0.0654449388384819,
-0.008042755536735058,
-0.0326400101184845,
0.06372679024934769,
0.0301065631210804,
-0.014212437905371189,
0.010373465716838837,
-0.015816213563084602,
0.036019306629896164,
0.006156567018479109,
0.08053634315729141,
-0.05385034903883934,
-0.031883541494607925,
0.04561006650328636,
-0.045885685831308365,
-0.027991468086838722,
0.03143310546875,
0.006311694160103798,
-0.03228140249848366,
0.01175693143159151,
-0.04720761626958847,
-0.05137351527810097,
-0.05119059607386589,
-0.04384668916463852
] |
<p>Imagine some sort of textile (as in very light, not metallic) that is tightly rolled up, can be easily unrolled by applying some force (i.e pulling it) but when released will eventually return to it's rolled up state, over and over again.</p>
<p>Does something like this exist?</p> | g7871 | [
-0.017198676243424416,
0.021738888695836067,
0.011625906452536583,
-0.049888644367456436,
-0.043309830129146576,
-0.025394119322299957,
-0.007709290832281113,
-0.030354738235473633,
0.008295038715004921,
-0.03954940661787987,
0.018202314153313637,
-0.04881315678358078,
0.051240552216768265,
-0.01980125717818737,
0.012407159432768822,
0.022596316412091255,
0.027395185083150864,
-0.013470744714140892,
0.046878863126039505,
-0.011117611080408096,
0.013670317828655243,
0.039720311760902405,
0.05418849736452103,
-0.022908853366971016,
-0.06525250524282455,
0.022052204236388206,
0.025314491242170334,
-0.04422133415937424,
-0.017353974282741547,
0.0011799988569691777,
-0.03203175961971283,
-0.10371165722608566,
0.018490856513381004,
-0.07155156135559082,
-0.002273084130138159,
-0.052268512547016144,
-0.021195728331804276,
-0.06997479498386383,
0.011723882518708706,
0.05456629395484924,
0.031357795000076294,
0.05586445704102516,
0.033060938119888306,
-0.00241833389736712,
0.04203135892748833,
0.0676526129245758,
0.027923140674829483,
0.0561596043407917,
0.017511660233139992,
-0.042728353291749954,
-0.023107796907424927,
-0.0076705822721123695,
-0.017392905429005623,
-0.05031915009021759,
0.05369102209806442,
-0.05000333860516548,
-0.009823749773204327,
0.012260646559298038,
0.033578354865312576,
0.009910994209349155,
-0.03990259766578674,
0.022349681705236435,
0.014920296147465706,
0.014439927414059639,
0.0006021317094564438,
-0.004641116131097078,
-0.031039318069815636,
-0.013124448247253895,
0.06266417354345322,
-0.002006018999963999,
0.011070632375776768,
0.008526169694960117,
0.0018565381178632379,
-0.05606440082192421,
0.017860593274235725,
0.04748937115073204,
-0.05184512585401535,
-0.0223831944167614,
-0.05982525274157524,
-0.003908172715455294,
-0.06635076552629471,
-0.006542091723531485,
-0.024149935692548752,
0.03371911868453026,
0.02208048477768898,
-0.013482710346579552,
0.031837355345487595,
-0.010824723169207573,
-0.004275364335626364,
0.04058506339788437,
0.07383669167757034,
0.02758689783513546,
-0.013897259719669819,
-0.03766593337059021,
-0.03337724134325981,
-0.008512075990438461,
0.022235218435525894,
-0.056305091828107834,
-0.0646878033876419,
-0.025443198159337044,
-0.0006267786957323551,
-0.06673087924718857,
0.03388815373182297,
-0.028835374861955643,
-0.039812929928302765,
-0.026777347549796104,
-0.009050286374986172,
-0.022434115409851074,
-0.0024938732385635376,
-0.029266636818647385,
0.012331092730164528,
0.0455237440764904,
-0.010527795180678368,
0.021949835121631622,
0.0673975944519043,
-0.002825320465490222,
-0.013905972242355347,
0.0660269483923912,
0.017517806962132454,
0.038113437592983246,
-0.005625525489449501,
-0.05568472668528557,
0.032891273498535156,
0.04868798702955246,
-0.013678554445505142,
-0.01014530286192894,
0.007947658188641071,
0.031836703419685364,
-0.030152643099427223,
-0.004811146762222052,
0.0325470007956028,
-0.023141304031014442,
0.07263395935297012,
-0.028728751465678215,
-0.031266290694475174,
0.012967990711331367,
-0.02807779610157013,
-0.04133865237236023,
0.02967599220573902,
0.004648155998438597,
0.009570524096488953,
-0.09530534595251083,
-0.05979044362902641,
0.058332089334726334,
0.01938576065003872,
0.0049629188142716885,
0.04900309070944786,
0.03459464758634567,
-0.018504450097680092,
0.023656371980905533,
0.010215876623988152,
-0.016289664432406425,
0.0003723163390532136,
-0.04494506120681763,
0.012759468518197536,
0.01608571782708168,
0.10717769712209702,
0.03547921031713486,
0.03547019883990288,
0.00803268700838089,
0.05775156617164612,
0.02115398831665516,
-0.045709654688835144,
-0.012307769618928432,
0.0008868336444720626,
0.013831475749611855,
-0.053626466542482376,
0.03397107124328613,
-0.03286248445510864,
-0.016722368076443672,
-0.05402521789073944,
-0.053139787167310715,
-0.006676350254565477,
0.05145096778869629,
0.04152066260576248,
-0.011132566258311272,
0.058306753635406494,
-0.00805517379194498,
0.0355476513504982,
-0.0435757078230381,
-0.011669697239995003,
-0.004532953724265099,
0.020547831431031227,
-0.012881160713732243,
0.01973290927708149,
0.0020154935773462057,
0.025290681049227715,
0.012886406853795052,
-0.03624385967850685,
-0.03715234622359276,
0.0032802203204482794,
0.02886801026761532,
-0.012361743487417698,
0.01110026054084301,
-0.049428541213274,
-0.05299792438745499,
0.05138298124074936,
-0.05280985310673714,
0.008996589109301567,
0.01273208949714899,
0.03603561595082283,
-0.015382256358861923,
0.05600402131676674,
-0.0072553884238004684,
-0.05279696360230446,
-0.03983689099550247,
0.022910919040441513,
0.0244730357080698,
0.03141733631491661,
-0.0006494536646641791,
0.0687992051243782,
-0.003981327172368765,
-0.009479493834078312,
0.04675648733973503,
-0.008448539301753044,
-0.005003529135137796,
0.017744986340403557,
0.019085828214883804,
0.005506923887878656,
0.029542958363890648,
0.03825617954134941,
0.01781013235449791,
0.01474062167108059,
0.027052026242017746,
0.017173614352941513,
-0.05168676748871803,
-0.016814876347780228,
-0.043080586940050125,
0.01718192547559738,
0.0180555060505867,
-0.030562931671738625,
-0.011016495525836945,
0.02737262286245823,
0.01567021757364273,
0.03319312632083893,
0.016067510470747948,
-0.00535134831443429,
0.03799153119325638,
-0.05200729891657829,
-0.07843731343746185,
0.0007722126902081072,
-0.007151005789637566,
0.0026672943495213985,
-0.09842829406261444,
-0.02381553128361702,
0.001281813601963222,
-0.018195530399680138,
-0.003299359930679202,
0.13611358404159546,
0.04429783672094345,
0.03373098000884056,
-0.04623817279934883,
-0.006207780446857214,
0.03330065682530403,
0.0026789954863488674,
-0.020309733226895332,
0.008034877479076385,
0.008570045232772827,
-0.04137932509183884,
0.010175111703574657,
0.014162935316562653,
0.01956178992986679,
0.02190508134663105,
-0.011687482707202435,
0.021299464628100395,
0.02327888458967209,
-0.02265431173145771,
-0.04146081954240799,
-0.04634533077478409,
0.09151989221572876,
-0.030906297266483307,
-0.039388712495565414,
0.06864231824874878,
0.006136549636721611,
0.01827063225209713,
-0.016883723437786102,
-0.012867103330790997,
-0.013554411008954048,
-0.01960557885468006,
0.04038040339946747,
0.042124565690755844,
-0.024729706346988678,
-0.004532698076218367,
0.0015649085398763418,
-0.060672275722026825,
-0.03175989165902138,
-0.03145588934421539,
0.027271462604403496,
-0.012907681055366993,
0.0671285018324852,
-0.03769562393426895,
0.017243502661585808,
0.009772717952728271,
-0.020456530153751373,
-0.03835151717066765,
0.013996502384543419,
-0.012574608437716961,
0.0372491292655468,
-0.05294721573591232,
0.06658222526311874,
-0.018246542662382126,
0.01203151699155569,
0.06122235953807831,
-0.011645069345831871,
0.0016898507019504905,
0.043446753174066544,
0.03886360675096512,
-0.016434451565146446,
0.05179598182439804,
-0.024772316217422485,
0.012395030818879604,
0.021538404747843742,
0.054624054580926895,
0.06290257722139359,
-0.059924930334091187,
-0.017594855278730392,
0.049483321607112885,
-0.024715760722756386,
0.0568314827978611,
-0.023195317015051842,
0.05048983916640282,
0.016226332634687424,
0.02010115422308445,
0.008865918964147568,
-0.05494733899831772,
-0.02255096286535263,
-0.06513673067092896,
0.010257460176944733,
-0.00520732719451189,
-0.04189758747816086,
0.050083767622709274,
0.02919241599738598,
0.01524332258850336,
-0.0774361863732338,
-0.030393078923225403,
0.0050211078487336636,
-0.035311780869960785,
-0.012281958013772964,
0.08093474805355072,
-0.008863565512001514,
-0.011986713856458664,
0.004367572255432606,
-0.011018848046660423,
0.03119717538356781,
0.012223741970956326,
0.07061713188886642,
0.03845221549272537,
-0.0342361181974411,
-0.01307212095707655,
0.014445573091506958,
-0.001961050322279334,
-0.01485039945691824,
0.03638593479990959,
-0.08516514301300049,
0.08830781280994415,
0.015561018139123917,
0.018964366987347603,
0.00356171652674675,
0.06478763371706009,
-0.034863848239183426,
-0.06093001365661621,
-0.04621920362114906,
-0.04661393165588379,
-0.06316228210926056,
0.016541987657546997,
0.029379550367593765,
0.0593327060341835,
0.041234757751226425,
-0.042614780366420746,
0.016366340219974518,
-0.007979798130691051,
-0.03867020457983017,
-0.013099903240799904,
0.016759268939495087,
-0.049282681196928024,
0.03939950838685036,
-0.011809219606220722,
0.000020082221453776583,
0.002285061636939645,
-0.022481191903352737,
0.04392208531498909,
0.04718657582998276,
0.01405069325119257,
0.04325395077466965,
-0.05214203521609306,
0.035347193479537964,
-0.015753742307424545,
-0.018511876463890076,
0.03170749172568321,
0.00296211801469326,
0.024882880970835686,
0.01607583649456501,
0.002474051434546709,
-0.028347298502922058,
0.012689962983131409,
0.02151809073984623,
0.03893096372485161,
-0.038306061178445816,
-0.03037330135703087,
-0.06008851155638695,
0.056419555097818375,
-0.03182993456721306,
-0.06231061741709709,
0.032624825835227966,
-0.040126100182533264,
-0.04986045882105827,
0.032226137816905975,
0.010229475796222687,
-0.024390563368797302,
-0.02623678743839264,
-0.023732509464025497,
-0.027397336438298225,
0.01505774725228548,
0.02674000896513462,
0.017471151426434517,
-0.020232584327459335,
0.029128242284059525,
0.001267087645828724,
-0.019472312182188034,
0.034407082945108414,
-0.016108186915516853,
0.04283018037676811,
-0.02690105140209198,
0.01711595430970192,
-0.052217427641153336,
0.06336318701505661,
0.009590201079845428,
0.015039580874145031,
0.011931895278394222,
-0.04387011006474495,
0.05143235623836517,
0.028563668951392174,
-0.029996290802955627,
0.01622864603996277,
0.0427643358707428,
-0.02281733974814415,
-0.03088928386569023,
-0.03417159616947174,
0.022459520027041435,
0.04091805964708328,
0.006800580304116011,
-0.030090661719441414,
0.028698597103357315,
0.02316387929022312,
-0.030420169234275818,
0.08292324095964432,
-0.03426045551896095,
0.05021273344755173,
-0.04975713789463043,
-0.03363124281167984,
-0.040466852486133575,
-0.039661698043346405,
-0.020055444911122322,
0.013342224061489105,
-0.03329923748970032,
-0.038419898599386215,
-0.03408152982592583,
-0.02350030280649662,
0.023535937070846558,
-0.008385367691516876,
0.03650457039475441,
-0.02428773045539856,
-0.0007433253340423107,
0.016054382547736168,
-0.04213397204875946,
0.024883290752768517,
-0.043176259845495224,
0.054079797118902206,
-0.011989431455731392,
0.0173636581748724,
-0.03065020591020584,
0.0966748371720314,
0.005543690174818039,
0.06656085699796677,
-0.0330568328499794,
-0.030541788786649704,
-0.013020355254411697,
0.016618723049759865,
-0.015244988724589348,
0.00630104960873723,
-0.03445078432559967,
-0.049530722200870514,
-0.05065708979964256,
-0.042463142424821854,
0.028957752510905266,
0.003164533292874694,
-0.013065204955637455,
0.01831115409731865,
-0.002676322590559721,
-0.04173875227570534,
0.008404136635363102,
-0.062010664492845535,
-0.00534513033926487,
0.031515609472990036,
0.04586232826113701,
-0.014506714418530464,
0.0036593580152839422,
0.016147326678037643,
-0.04114552214741707,
0.019125448539853096,
-0.06459347158670425,
0.01232132874429226,
0.01815805584192276,
0.044104475528001785,
0.015184937976300716,
0.02010112814605236,
-0.05021393671631813,
-0.01828063651919365,
0.006724077742546797,
0.03902816027402878,
-0.035692647099494934,
0.0014658481813967228,
-0.04735250398516655,
-0.0025697429664433002,
0.010119829326868057,
0.040179941803216934,
0.012366099283099174,
0.022572824731469154,
0.06078551709651947,
0.011038151569664478,
-0.04811016470193863,
0.017122020944952965,
0.01753101870417595,
0.04604504257440567,
-0.00801479909569025,
0.009914586320519447,
-0.03796078637242317,
0.0660085380077362,
-0.015685243532061577,
0.009221906773746014,
0.0847255289554596,
-0.017954042181372643,
0.058148790150880814,
-0.023840025067329407,
-0.02266741171479225,
0.014724116772413254,
0.073044553399086,
0.08700928092002869,
0.014039027504622936,
0.01929757557809353,
-0.009111221879720688,
-0.01893538422882557,
0.0005619869916699827,
0.02065083011984825,
0.015454891137778759,
-0.02348155900835991,
-0.026351215317845345,
-0.0004903000663034618,
0.002279475098475814,
-0.017561400309205055,
-0.004398993216454983,
0.015665534883737564,
0.01540994830429554,
0.02894558385014534,
-0.03582705929875374,
-0.03187384083867073,
-0.01683882251381874,
-0.03995241969823837,
0.009797452948987484,
0.06943390518426895,
0.014623844064772129,
0.006431663408875465,
-0.017188405618071556,
-0.005125582683831453,
-0.05509446933865547,
-0.00830415915697813,
0.0034667877480387688,
-0.004530855920165777,
0.024010075256228447,
0.058496806770563126,
0.03139485791325569,
0.038477178663015366,
0.0629749745130539,
0.025939207524061203,
-0.0363495834171772,
-0.05254827439785004,
-0.005693506449460983,
-0.06574027985334396,
0.033645760267972946,
0.00396349560469389,
0.002538057044148445,
0.009637650102376938,
-0.002702851314097643,
-0.002545838477090001,
-0.009263196028769016,
-0.0019824595656245947,
-0.03348669782280922,
-0.0058434284292161465,
0.018727917224168777,
-0.025762369856238365,
-0.022520355880260468,
0.040380410850048065,
-0.05743458867073059,
0.019391369074583054,
-0.016710994765162468,
0.048361245542764664,
-0.021732952445745468,
0.0077616130001842976,
0.01605326309800148,
-0.0034801207948476076,
-0.010743063874542713,
-0.002022098284214735,
0.03854906186461449,
-0.0003228209388907999,
-0.010731478221714497,
0.0494789220392704,
0.007763441186398268,
0.023585522547364235,
0.08296866714954376,
0.005231976509094238,
-0.061302825808525085,
-0.051695335656404495,
-0.024397678673267365,
0.011674282141029835,
-0.027873344719409943,
-0.0367751270532608,
0.038163185119628906,
0.015515018254518509,
0.05173328518867493,
-0.02303212694823742,
-0.04801221936941147,
-0.035798877477645874,
0.012806490063667297,
-0.04791250079870224,
-0.06265362352132797,
-0.04452374950051308,
-0.036101896315813065,
0.04231179133057594,
-0.00014718399324920028,
0.032331276684999466,
0.00935576856136322,
-0.04186691343784332,
0.0019044122891500592,
0.02329978533089161,
-0.006700955331325531,
0.027461256831884384,
-0.07340813428163528,
0.029065828770399094,
0.07053498178720474,
-0.006050457712262869,
-0.040261272341012955,
0.04949317127466202,
0.03730294853448868,
0.03259703889489174,
0.003053277963772416,
0.01800433173775673,
-0.04402472451329231,
-0.034655746072530746,
0.0265079103410244,
-0.005915835965424776,
-0.015854625031352043,
-0.03558613359928131,
-0.03825262561440468,
-0.017604144290089607,
-0.03338344395160675,
0.007871161215007305,
0.005350543651729822,
-0.032118625938892365,
-0.022943999618291855,
-0.0028086937963962555,
-0.0057312664575874805,
-0.04219841957092285,
-0.005360522773116827,
-0.02403595857322216,
-0.07373248785734177,
0.02291681617498398,
0.05683431029319763,
0.003277071751654148,
-0.06452623754739761,
0.015205243602395058,
0.06042877957224846,
-0.0004647816822398454,
-0.0017369567649438977,
-0.04668325558304787,
0.02520413137972355,
-0.06865132600069046,
-0.024072809144854546,
0.010151514783501625,
0.06936586648225784,
0.0013183890841901302,
-0.04113928601145744,
-0.010278847999870777,
0.06884503364562988,
0.01563301868736744,
-0.013226895593106747,
0.044203925877809525,
0.014522075653076172,
0.05445552617311478,
0.037598393857479095,
0.0259665846824646,
0.013484062626957893,
0.10916195809841156,
0.007214825600385666,
0.011832018382847309,
0.03628028929233551,
-0.03284129872918129,
0.014484856277704239,
-0.0275261327624321,
-0.018091965466737747,
-0.03639713302254677,
-0.02875031903386116,
-0.017576664686203003,
-0.02472628839313984,
-0.0493743009865284,
-0.017708808183670044,
0.025141185149550438,
-0.1217396929860115,
-0.005367225036025047,
-0.03773333504796028,
-0.018563246354460716,
-0.02222769893705845,
0.0047530378215014935,
-0.009571278467774391,
-0.0012024588650092483,
-0.00025643364642746747,
-0.02490420453250408,
-0.07680608332157135,
0.03066181018948555,
-0.016331681981682777,
0.03725862503051758,
-0.0155195202678442,
0.004724921192973852,
-0.02239024080336094,
-0.00983447302132845,
0.01919960230588913,
0.033711664378643036,
-0.038320157676935196,
-0.01540896762162447,
0.04235874116420746,
0.03276558965444565,
0.0378851480782032,
-0.09428159892559052,
0.05465899780392647,
-0.04318742826581001,
0.025175832211971283,
0.004051628988236189,
-0.009914854541420937,
0.006911403965204954,
-0.02712421864271164,
-0.01568416878581047,
-0.00904641579836607,
-0.06030254065990448,
-0.015243547968566418,
-0.02098950371146202,
0.08303141593933105,
0.08004213124513626,
-0.014302349649369717,
0.006256709340959787,
0.00409227330237627,
-0.029687197878956795,
0.002726386534050107,
-0.03622395545244217,
-0.00009041039447765797,
-0.001661490648984909,
0.06959054619073868,
0.02972928062081337,
-0.04371379315853119,
0.026710378006100655,
-0.005198764614760876,
-0.01948384940624237,
-0.0772731676697731,
-0.02372991293668747,
-0.053970303386449814,
0.006185248959809542,
-0.021800512447953224,
-0.07671719044446945,
0.005805567838251591,
0.0026591166388243437
] |
<p>I thought this would be a simple question, but I'm having trouble figuring it out. Not a homework assignment btw. I am a physics student and am just genuinely interested in physics problems involving math, which would be all of them.</p>
<p>So lets say we drop an object from a height, $R+r$, it falls toward earth. This height, $R+r$, is far enough away that the $g$ it experiences is a fraction of $g$ at sea-level. Let's just say that air resistance is negligible, and it wouldn't be that complicated to just integrate from $0$ velocity to the terminal velocity piece wise and deal with the rest of it later.</p>
<p>So the key here is that acceleration is changing with time. I thought I could simplify this by saying it changes with distance, and it has nothing to do with time, but this didn't really help, my guess is that maybe time is important (doh).</p>
<p>I tried integrating acceleration with time, and ended up nowhere. I tried integrating $a=GM/R^2$ with respect to $R$ from $R+r$ to $R$ and ended up with a negative function.</p>
<p>I saw somewhere someone tried to expand with taylor series, they even have something similar on hyperphysics, but I can't figure out how to obtain the polynomials that precede the variables.</p>
<p><a href="http://hyperphysics.phy-astr.gsu.edu/hbase/images/avari.gif" rel="nofollow">http://hyperphysics.phy-astr.gsu.edu/hbase/images/avari.gif</a></p>
<p>This is the hyperphysics site where they use polynomials to find the distance.
<a href="http://hyperphysics.phy-astr.gsu.edu/hbase/avari.html#c1" rel="nofollow">http://hyperphysics.phy-astr.gsu.edu/hbase/avari.html#c1</a></p>
<p>Maybe I can't solve this because I haven't taken a course in differential equations yet.
What I want to know is how to calculate the distance at any time.</p> | g999 | [
0.09016318619251251,
0.06665769219398499,
-0.009590226225554943,
-0.019923033192753792,
-0.010378753766417503,
0.06679569184780121,
0.02244936302304268,
-0.02268032170832157,
-0.08296044915914536,
-0.014569035731256008,
-0.014772743918001652,
0.04109121114015579,
0.0363612063229084,
0.019369304180145264,
0.0036728691775351763,
-0.0005197783466428518,
0.05321373790502548,
-0.057070884853601456,
0.0012846034951508045,
-0.017994025722146034,
0.006323020905256271,
-0.03522776439785957,
-0.015188813209533691,
-0.052282825112342834,
0.0108038280159235,
-0.043912529945373535,
0.023347746580839157,
-0.006627577822655439,
-0.08766759932041168,
0.04043572023510933,
-0.059256475418806076,
-0.02625127136707306,
-0.008986485190689564,
-0.025610674172639847,
0.003922309260815382,
-0.03158432990312576,
0.0038573206402361393,
0.009539860300719738,
0.029782189056277275,
-0.006879941560328007,
-0.008242975920438766,
-0.05531565472483635,
0.0014349453849717975,
0.008500305004417896,
0.03218238428235054,
-0.0013525477843359113,
-0.016832277178764343,
-0.023855911567807198,
-0.0029220033902674913,
-0.010640890337526798,
-0.015054614283144474,
0.0512242466211319,
-0.05115356668829918,
-0.003499184036627412,
-0.03373125195503235,
0.055074892938137054,
0.03716215118765831,
-0.018987512215971947,
0.031137891113758087,
0.0624600425362587,
-0.007481060456484556,
-0.05085178092122078,
0.009878679178655148,
-0.02513035386800766,
0.08929795026779175,
0.0018092967802658677,
-0.026670431718230247,
-0.01403448823839426,
-0.03838835284113884,
0.009566220454871655,
0.028114767745137215,
-0.05197127163410187,
-0.043408092111349106,
-0.011369239538908005,
-0.04824639856815338,
-0.017507273703813553,
0.008641589432954788,
0.017372775822877884,
0.072016641497612,
0.04829921945929527,
-0.048626016825437546,
0.05397116020321846,
0.023861201480031013,
-0.010941718704998493,
0.00663768220692873,
-0.02625151164829731,
0.030772017315030098,
0.06963889300823212,
-0.02466004341840744,
-0.018585000187158585,
0.011974520981311798,
0.0003916629357263446,
0.06480857729911804,
0.005165486596524715,
0.021725110709667206,
-0.008822833187878132,
-0.02765665389597416,
0.06856433302164078,
0.02633044868707657,
-0.0687459260225296,
0.0040986500680446625,
0.011040383018553257,
0.07835331559181213,
-0.04891691729426384,
-0.009583062492311,
-0.001389659708365798,
0.04933134466409683,
0.02520199492573738,
0.01950390823185444,
-0.04705676808953285,
-0.007963431067764759,
-0.022179875522851944,
-0.04054690897464752,
-0.07566629350185394,
-0.01470209937542677,
-0.04999767243862152,
-0.00016438716556876898,
0.022871950641274452,
-0.02895193360745907,
0.012543078511953354,
-0.029278075322508812,
0.08251645416021347,
-0.01917177438735962,
0.04317519813776016,
-0.03559783846139908,
-0.025578152388334274,
-0.03097943589091301,
-0.026624193415045738,
-0.007585106883198023,
0.0019504312658682466,
0.004559834487736225,
-0.009835922159254551,
0.03180059418082237,
0.04985849931836128,
-0.040772635489702225,
-0.0014765922678634524,
-0.013292261399328709,
0.02931349165737629,
-0.04063925892114639,
0.08838904649019241,
-0.011339462362229824,
-0.06803347915410995,
0.003693192731589079,
-0.014982427470386028,
-0.05071910098195076,
0.053211938589811325,
-0.004705427214503288,
-0.03882954269647598,
0.005274655297398567,
-0.0058102733455598354,
0.004446269944310188,
0.0656043291091919,
-0.000895813456736505,
0.035065438598394394,
0.05562351271510124,
-0.0025226569268852472,
0.0032172196079045534,
-0.0028791476506739855,
0.03250117599964142,
-0.02256830409169197,
0.03670111298561096,
0.0072474246844649315,
0.007233398966491222,
0.009816317819058895,
-0.06327005475759506,
0.0629991814494133,
0.004054115153849125,
0.0003043991164304316,
-0.014854919165372849,
-0.034665949642658234,
-0.057055383920669556,
-0.01752428710460663,
0.042099833488464355,
-0.006842238362878561,
-0.049774885177612305,
0.031194129958748817,
0.02564740739762783,
-0.017027219757437706,
-0.06855828315019608,
-0.005912058055400848,
0.00781814381480217,
-0.044781394302845,
0.05194353312253952,
-0.048870671540498734,
-0.005846286658197641,
0.02277771197259426,
0.030608879402279854,
0.03629979491233826,
-0.0879412442445755,
-0.015292069874703884,
-0.005208349321037531,
-0.007752211298793554,
0.014434967190027237,
0.026836644858121872,
-0.09078352153301239,
0.008659839630126953,
0.052400264889001846,
-0.018164873123168945,
-0.04303295910358429,
0.07680127024650574,
0.019172480329871178,
0.07049886137247086,
0.07106669992208481,
0.06069503724575043,
0.044786613434553146,
-0.014592867344617844,
0.03082490898668766,
-0.020540256053209305,
-0.035444896668195724,
-0.027036910876631737,
0.011143617331981659,
-0.011121709831058979,
0.026538195088505745,
0.0404348149895668,
0.04337456449866295,
-0.023746030405163765,
-0.022258494049310684,
0.006425999104976654,
0.018786532804369926,
0.004048032220453024,
-0.004597753752022982,
-0.012282924726605415,
-0.004654526710510254,
-0.035721324384212494,
-0.023655179888010025,
0.015590519644320011,
0.00620862003415823,
-0.040312040597200394,
-0.013235115446150303,
-0.027153367176651955,
-0.055746205151081085,
0.0741628110408783,
-0.0220844354480505,
-0.013605037704110146,
0.06693266332149506,
0.03773265704512596,
-0.02641991525888443,
-0.004282030742615461,
-0.0023296335712075233,
0.04933036491274834,
0.01058879867196083,
-0.048489026725292206,
-0.027249624952673912,
0.01754062809050083,
0.04200100526213646,
-0.04382148012518883,
0.04110100120306015,
0.026715027168393135,
-0.03561107814311981,
-0.03516344726085663,
-0.011595715768635273,
-0.008550229482352734,
-0.04823765158653259,
0.028026597574353218,
-0.026447638869285583,
0.019268861040472984,
-0.06441599875688553,
0.0013023661449551582,
-0.009121148847043514,
-0.05996832996606827,
-0.02599988877773285,
-0.011425605043768883,
0.03811541199684143,
0.016689395532011986,
-0.07508628815412521,
0.022625422105193138,
-0.04451611638069153,
-0.017651379108428955,
0.017038879916071892,
0.00022441140026785433,
-0.0150628462433815,
0.0428936630487442,
0.04202279448509216,
0.037610333412885666,
-0.02725982666015625,
-0.02270539291203022,
0.020897846668958664,
-0.010738336481153965,
0.03939639404416084,
0.036032162606716156,
-0.016789203509688377,
-0.07750529050827026,
-0.03968594968318939,
0.04166913777589798,
0.005178708117455244,
-0.02954225242137909,
0.09113985300064087,
0.1320430189371109,
-0.0021555908024311066,
-0.03164466843008995,
0.018169520422816277,
-0.010613120160996914,
0.040697526186704636,
0.008229686878621578,
0.008833004161715508,
0.06177313253283501,
0.022655082866549492,
-0.020546872168779373,
0.02614961937069893,
0.005443238653242588,
-0.0027756858617067337,
-0.0652862936258316,
0.057757750153541565,
-0.00639703031629324,
-0.04279231280088425,
0.007925783284008503,
-0.012862383387982845,
-0.06191423535346985,
-0.046494387090206146,
-0.008903685957193375,
-0.036622967571020126,
-0.0027498239651322365,
-0.015505587682127953,
0.00984059739857912,
-0.01918664760887623,
-0.017382651567459106,
0.02832220122218132,
0.0061964066699147224,
0.056380242109298706,
0.04550866037607193,
-0.017792919650673866,
-0.11641626060009003,
-0.02836679108440876,
0.012934981845319271,
0.00403187982738018,
0.014004313386976719,
0.0014865741832181811,
0.04043755307793617,
-0.05567016825079918,
-0.0017702054465189576,
0.009856115095317364,
-0.01836901716887951,
0.019159257411956787,
-0.05002953112125397,
-0.03148564696311951,
-0.007510656490921974,
0.04543859139084816,
0.010098796337842941,
0.022471696138381958,
0.03933810442686081,
-0.055635686963796616,
-0.03586433827877045,
-0.030881226062774658,
0.021221457049250603,
-0.013851137831807137,
-0.029980730265378952,
0.0030446655582636595,
0.06551823019981384,
-0.005758375860750675,
-0.03207450360059738,
0.02672269195318222,
0.006994373165071011,
0.0232806708663702,
-0.03864821791648865,
-0.029722919687628746,
0.037885136902332306,
-0.0016192870680242777,
-0.0015441968571394682,
-0.045720167458057404,
0.022483984008431435,
-0.010423919185996056,
-0.022149167954921722,
-0.03417135402560234,
0.04129882901906967,
0.029098326340317726,
-0.05101877450942993,
-0.03397358953952789,
0.07202155143022537,
-0.018610773608088493,
-0.014866124838590622,
0.0730152279138565,
0.0025652041658759117,
0.007962554693222046,
0.006690944544970989,
0.029335351660847664,
-0.054373931139707565,
0.032597173005342484,
-0.013568462803959846,
-0.006748702377080917,
0.0190734900534153,
0.022603165358304977,
0.0023690105881541967,
-0.006379018537700176,
-0.010675344616174698,
0.006989844609051943,
-0.01973172463476658,
-0.028053460642695427,
-0.019792864099144936,
-0.0033296544570475817,
-0.012436825782060623,
-0.019566675648093224,
-0.0631948933005333,
-0.01301669143140316,
0.030928000807762146,
0.016606710851192474,
-0.0225636288523674,
-0.024982184171676636,
0.011002523824572563,
-0.04555419459939003,
0.059671904891729355,
-0.013119075447320938,
0.020028134807944298,
0.037668365985155106,
0.018647946417331696,
-0.025395715609192848,
-0.020238226279616356,
0.0640692189335823,
-0.020593522116541862,
-0.026241017505526543,
0.029975922778248787,
0.015384340658783913,
-0.05301789566874504,
-0.020132169127464294,
-0.07558493316173553,
0.031479932367801666,
-0.005418418440967798,
0.06322245299816132,
-0.016756970435380936,
-0.028030335903167725,
0.010583242401480675,
0.017624376341700554,
0.055668141692876816,
0.01829667203128338,
-0.055757928639650345,
-0.02700483426451683,
0.019763831049203873,
0.01559395994991064,
-0.00819707103073597,
0.002986064413562417,
0.021801691502332687,
-0.006149879191070795,
0.0027277872432023287,
0.038515251129865646,
0.014345217496156693,
-0.007170886732637882,
0.04455205798149109,
0.05129147693514824,
0.03809857368469238,
0.03435323014855385,
0.04480127990245819,
0.03772921860218048,
0.012547587044537067,
-0.0016338492278009653,
-0.006622807588428259,
0.005411596968770027,
0.07334346324205399,
-0.07549247145652771,
-0.0874117761850357,
0.0743921548128128,
0.019245678558945656,
-0.05930918827652931,
0.052335225045681,
0.01045471616089344,
0.0034275625366717577,
-0.043709009885787964,
0.02728515863418579,
-0.07312484830617905,
0.008057493716478348,
0.0333687923848629,
0.0014038641238585114,
-0.06612721085548401,
0.04288359358906746,
-0.06530183553695679,
-0.028484461829066277,
-0.009918104857206345,
-0.024741724133491516,
-0.03856712952256203,
0.008862781338393688,
-0.019919568672776222,
0.021522099152207375,
-0.0165049210190773,
-0.0328657291829586,
0.010226154699921608,
-0.013202425092458725,
0.013900642283260822,
0.030247503891587257,
-0.0043261670507490635,
0.0021110032685101032,
0.08214811235666275,
-0.025444399565458298,
-0.01026878785341978,
-0.00025973847368732095,
-0.04720586910843849,
0.019485507160425186,
-0.01654537208378315,
0.036295466125011444,
-0.016918230801820755,
-0.009439302608370781,
0.06472741067409515,
0.00285107153467834,
-0.008635957725346088,
-0.01639060489833355,
-0.022416910156607628,
0.01276499405503273,
-0.04408274590969086,
-0.012127556838095188,
0.014996353536844254,
-0.0012991726398468018,
-0.02078365907073021,
-0.03254486620426178,
-0.08531901240348816,
-0.0037862735334783792,
0.0003421904402785003,
0.004979284945875406,
-0.007616130635142326,
0.025451872497797012,
0.07488145679235458,
0.04279696196317673,
-0.033795446157455444,
0.09232020378112793,
0.016901543363928795,
0.03505927324295044,
0.017807941883802414,
0.03914075717329979,
-0.02125389687716961,
-0.026165569201111794,
-0.03424897417426109,
0.049825944006443024,
-0.034048862755298615,
-0.024339161813259125,
0.07458589226007462,
-0.0379895381629467,
0.04148758575320244,
0.0057722595520317554,
0.04240342602133751,
0.04367229342460632,
-0.050913553684949875,
-0.05517318844795227,
-0.02112904004752636,
0.0021863810252398252,
-0.010232481174170971,
-0.03591657802462578,
-0.010136674158275127,
-0.0367698036134243,
-0.03705707564949989,
-0.0023696026764810085,
-0.0272033903747797,
-0.007042514625936747,
0.05180950462818146,
-0.06170104071497917,
-0.09784546494483948,
-0.0013799769803881645,
-0.009357089176774025,
0.06918777525424957,
-0.046110108494758606,
0.0169853363186121,
-0.03810408338904381,
0.03345252573490143,
0.07691642642021179,
-0.0385480560362339,
-0.03413049131631851,
-0.011543155647814274,
0.011515785939991474,
0.01240584161132574,
-0.029481958597898483,
0.030628787353634834,
0.025992102921009064,
-0.03323708102107048,
-0.02452368661761284,
-0.0018642782233655453,
0.047865405678749084,
-0.018239222466945648,
-0.027335138991475105,
0.01139974407851696,
0.020824233070015907,
-0.028077125549316406,
0.038718800991773605,
0.02416699379682541,
0.05652725324034691,
0.002029357710853219,
-0.027471626177430153,
-0.058949388563632965,
-0.030454838648438454,
0.005816412158310413,
0.03847957029938698,
0.019709467887878418,
-0.0008421256789006293,
-0.04334790259599686,
-0.008968533016741276,
-0.017025938257575035,
-0.05224671959877014,
-0.007928858511149883,
0.014427588321268559,
-0.041288018226623535,
-0.021166402846574783,
-0.0028630525339394808,
-0.020719148218631744,
-0.029562367126345634,
0.04561946168541908,
0.016390226781368256,
-0.043509043753147125,
0.011529341340065002,
0.006562427617609501,
-0.042759306728839874,
-0.04624704644083977,
-0.028701482340693474,
0.021555937826633453,
-0.009484722279012203,
-0.005065346602350473,
0.026933716610074043,
0.02049512416124344,
-0.007618467789143324,
0.12382257729768753,
-0.03172517195343971,
-0.0008824685355648398,
0.0029625226743519306,
0.0022322367876768112,
-0.03518320247530937,
0.024149514734745026,
-0.07335703819990158,
0.026261547580361366,
0.056728068739175797,
0.028089672327041626,
0.0550561398267746,
-0.002558319829404354,
-0.03713465481996536,
0.07033262401819229,
-0.020721035078167915,
-0.0027770567685365677,
-0.017975082620978355,
0.0074135004542768,
0.0001468337286496535,
-0.0013406560756266117,
0.002013055607676506,
0.018257157877087593,
-0.006929817143827677,
-0.02727552503347397,
0.013680432923138142,
0.026668604463338852,
-0.024702252820134163,
0.08636026084423065,
0.0018046183977276087,
-0.017254892736673355,
0.04950109124183655,
0.015378297306597233,
0.07456398010253906,
0.03192831575870514,
0.032732121646404266,
0.0099558774381876,
0.06967173516750336,
0.04345085471868515,
0.012759944424033165,
-0.03481674939393997,
0.008734297938644886,
-0.041730381548404694,
-0.03943134844303131,
0.03574085235595703,
-0.03962016850709915,
-0.06525920331478119,
0.004952414892613888,
0.06184357404708862,
-0.03684840723872185,
-0.056580375880002975,
0.0764995664358139,
0.012949774973094463,
-0.019303513690829277,
0.03280089423060417,
0.02278096415102482,
-0.0030305625405162573,
-0.010227777995169163,
-0.028979236260056496,
-0.04735834151506424,
-0.006775598041713238,
0.005188481416553259,
-0.029831279069185257,
0.0853588730096817,
-0.003257511416450143,
-0.07089598476886749,
0.006355356890708208,
-0.000633237708825618,
0.01941690780222416,
-0.0027054229285568,
-0.028221115469932556,
0.0010296442778781056,
-0.0034099433105438948,
0.027999188750982285,
-0.036375101655721664,
-0.033549051731824875,
-0.049974456429481506,
0.031054973602294922,
0.00046879041474312544,
0.04411288723349571,
-0.007149661425501108,
-0.021076397970318794,
0.01871931180357933,
0.027248883619904518,
-0.009074660018086433,
0.035586386919021606,
0.03890987113118172,
-0.008543086238205433,
-0.03611679747700691,
0.037445973604917526,
0.00688900938257575,
0.0069000911898911,
0.01443849503993988,
-0.001602778909727931,
0.04639102518558502,
-0.011789600364863873,
-0.009279227815568447,
-0.026762545108795166,
0.004873504862189293,
-0.02108251303434372,
0.05880873277783394,
-0.010567652992904186,
-0.03722326457500458,
0.01610533334314823,
-0.010379333980381489,
0.011200928129255772,
-0.02876625396311283,
0.04743688926100731,
-0.007853043265640736,
0.04469738155603409,
-0.007786125410348177,
-0.01687856949865818,
0.0014254872221499681,
0.032099947333335876,
0.036990612745285034,
-0.024710601195693016,
-0.05564599484205246,
-0.03520195931196213,
0.008637064136564732,
-0.04337975010275841,
0.007242507766932249,
-0.08622303605079651,
0.027224667370319366,
-0.00960008054971695,
-0.04501665011048317,
-0.04858089238405228,
0.015273140743374825,
-0.015055038966238499,
-0.010638867504894733,
-0.02133520506322384,
-0.022435281425714493,
0.0481916107237339,
0.021565353497862816,
-0.011554986238479614,
-0.01429490651935339,
-0.022417951375246048,
0.02459576725959778,
0.028996039181947708,
-0.025964699685573578,
-0.056848544627428055,
-0.014985954388976097,
0.06963767111301422,
-0.015487536787986755,
-0.055772412568330765,
0.024121113121509552,
0.08697972446680069,
0.060734495520591736,
-0.02780778706073761,
0.013123522512614727,
0.03875689208507538,
-0.02566298469901085,
0.03497070074081421,
0.03246242552995682,
-0.029278380796313286,
-0.014756439253687859,
-0.005601746030151844,
0.0077207558788359165,
-0.055649448186159134,
-0.004363343119621277,
0.000016014093489502557,
0.027595365419983864,
0.019637038931250572,
0.02794850803911686,
-0.022290538996458054,
-0.015938036143779755,
0.00447975704446435
] |
<p>In paramagnetic-to-ferromagnetic phase transitions, the symmetry spontaneously breaks down from SO(3) to the subgroup SO(2) below $T_\text{crit}$. This implies that there should be two Goldstone modes and not one because SO(3) has three generators and SO(2) has one. How do we distinguish between these two excitations physically?</p> | g7872 | [
-0.005361249204725027,
0.07697548717260361,
-0.011613328941166401,
-0.019603628665208817,
0.05746160447597504,
0.0631672590970993,
0.04215414822101593,
0.03652477636933327,
-0.012234236113727093,
0.02599705383181572,
-0.08930552750825882,
-0.04270417243242264,
0.025283897295594215,
-0.022565828636288643,
-0.005455504637211561,
0.0017801163485273719,
0.06564847379922867,
0.05491596460342407,
0.04527010768651962,
-0.00959934201091528,
-0.05193214863538742,
0.006910759024322033,
-0.013608189299702644,
-0.028507281094789505,
0.03693113476037979,
0.07641886174678802,
-0.026556096971035004,
-0.002273721154779196,
0.0030816029757261276,
-0.043893687427043915,
0.07851129025220871,
0.09307153522968292,
0.006695850286632776,
-0.04469688981771469,
0.020589172840118408,
-0.03817166015505791,
0.060284338891506195,
0.01919807307422161,
-0.01773071475327015,
0.015387438237667084,
0.02393869124352932,
-0.016315294429659843,
0.031201601028442383,
-0.0492730587720871,
0.011889244429767132,
-0.03860766440629959,
-0.019307104870676994,
0.0319305844604969,
-0.07483712583780289,
0.00431816978380084,
0.058311592787504196,
0.08713077753782272,
0.1134272962808609,
0.024909790605306625,
0.008328579366207123,
0.021711084991693497,
-0.003798277582973242,
-0.006852139253169298,
0.04404698312282562,
0.0048149703070521355,
-0.014258117415010929,
0.01971329003572464,
0.013042574748396873,
-0.03112669475376606,
0.038815341889858246,
-0.026495449244976044,
-0.038731783628463745,
-0.012966634705662727,
-0.02277805469930172,
-0.025560086593031883,
-0.019147291779518127,
-0.045609280467033386,
-0.0013682962162420154,
0.014996550045907497,
-0.031135274097323418,
0.013817943632602692,
0.007946692407131195,
-0.014868680387735367,
-0.0026946065481752157,
-0.001604077173396945,
-0.019561070948839188,
-0.030838483944535255,
-0.02181238867342472,
0.0016805606428533792,
-0.0107918381690979,
0.012830073945224285,
-0.042149387300014496,
0.06722231209278107,
-0.014635097235441208,
-0.0009866721229627728,
-0.020007388666272163,
0.02549455128610134,
0.004078914411365986,
-0.024384306743741035,
0.014005604200065136,
0.06597722321748734,
0.016497774049639702,
0.06838826090097427,
-0.04619941860437393,
0.007329972926527262,
-0.01501027587801218,
-0.00527165224775672,
-0.001285481615923345,
-0.005912842229008675,
-0.002976102288812399,
-0.03313128277659416,
0.02424672432243824,
-0.0034780874848365784,
0.004542193375527859,
0.039175864309072495,
-0.026515686884522438,
0.016669081524014473,
-0.040067754685878754,
0.0058393459767103195,
-0.07144931703805923,
-0.023576699197292328,
0.06286033987998962,
-0.06706805527210236,
0.0025015645660459995,
-0.002321276580914855,
0.04412390664219856,
-0.04542712867259979,
-0.021824441850185394,
0.0702771320939064,
-0.02292449213564396,
0.041740939021110535,
-0.008350525982677937,
0.02696780487895012,
0.02205541729927063,
-0.0019103053491562605,
-0.0696290135383606,
-0.02646620385348797,
0.04224298521876335,
0.06533966958522797,
0.05545609071850777,
0.03798172250390053,
0.03339049220085144,
0.03956719487905502,
-0.06406687945127487,
-0.006379035767167807,
0.0001839892938733101,
-0.0007816642755642533,
-0.03838734328746796,
-0.018948081880807877,
-0.00894197914749384,
-0.05520221218466759,
0.036961447447538376,
-0.0343545526266098,
0.020600201562047005,
0.05487006530165672,
0.0541616827249527,
0.018340587615966797,
0.04191199690103531,
-0.012182360514998436,
-0.0018656854517757893,
-0.06597431749105453,
0.038361188024282455,
-0.04094195365905762,
0.006163731217384338,
0.029035210609436035,
0.015083803795278072,
-0.10527855157852173,
0.018688855692744255,
0.04472346231341362,
-0.0248067919164896,
-0.021054189652204514,
0.0609399676322937,
-0.012581674382090569,
-0.011686689220368862,
-0.012779072858393192,
-0.01331434864550829,
0.024844517931342125,
0.00490616075694561,
0.04904914274811745,
-0.00892811268568039,
0.08659189194440842,
-0.05033035948872566,
-0.03229125589132309,
0.014920594170689583,
0.07427466660737991,
-0.013686268590390682,
0.02643313817679882,
-0.015315348282456398,
0.01588222198188305,
0.05237887054681778,
-0.0033093278761953115,
0.025259029120206833,
0.02971094474196434,
-0.02035609632730484,
0.014413275755941868,
-0.014944309368729591,
0.01618906296789646,
-0.024166971445083618,
0.006982681341469288,
0.020664526149630547,
0.007208880968391895,
-0.04298311471939087,
0.020622476935386658,
-0.05392580106854439,
-0.039330337196588516,
0.023899244144558907,
-0.013567322865128517,
0.011594739742577076,
0.017802786082029343,
-0.012720181606709957,
0.000502096489071846,
0.026556504890322685,
0.006542636081576347,
0.03171181306242943,
-0.02231553941965103,
0.04179278388619423,
0.06011543422937393,
-0.035978514701128006,
-0.014477144926786423,
-0.04892212152481079,
0.029659543186426163,
0.018911831080913544,
-0.010558908805251122,
-0.02512131817638874,
0.04857420548796654,
-0.048022251576185226,
0.02705686166882515,
0.0326937772333622,
-0.0025373848620802164,
-0.015067062340676785,
0.02102849818766117,
-0.07307010889053345,
-0.012714455835521221,
0.0014632557285949588,
-0.021790286526083946,
-0.026718763634562492,
-0.002482746494933963,
-0.021367883309721947,
-0.0592985562980175,
0.011404585093259811,
-0.004729013424366713,
-0.02886693738400936,
-0.01738409511744976,
-0.00015200607595033944,
-0.0430704765021801,
-0.023198574781417847,
0.016295552253723145,
0.015859128907322884,
-0.002037183614447713,
-0.0044195763766765594,
-0.048898279666900635,
0.023646723479032516,
0.0033238183241337538,
-0.03603396564722061,
-0.023065827786922455,
0.013422952964901924,
-0.0029241994488984346,
-0.054461799561977386,
-0.057301513850688934,
-0.04693201929330826,
0.0255871769040823,
0.04698223993182182,
0.0663759633898735,
-0.05815943703055382,
-0.012159571051597595,
-0.02130216918885708,
-0.028901133686304092,
0.03159326687455177,
0.006448336876928806,
0.0010686793830245733,
-0.0519137904047966,
-0.030905291438102722,
0.012275795452296734,
-0.02010273188352585,
-0.033696915954351425,
-0.0600728839635849,
0.044011350721120834,
0.07735524326562881,
0.008110759779810905,
-0.028324345126748085,
-0.01735653541982174,
0.03840557858347893,
-0.012499487027525902,
0.025487471371889114,
-0.05048316344618797,
-0.06416409462690353,
0.013671156950294971,
-0.009106794372200966,
-0.045162785798311234,
-0.003002722980454564,
-0.055252477526664734,
-0.02050221897661686,
0.015502873808145523,
-0.03536274656653404,
0.01888362690806389,
0.0016236951341852546,
0.026087220758199692,
0.07536166906356812,
0.0369853712618351,
-0.008129263296723366,
0.018194032832980156,
-0.02297983504831791,
-0.05932072922587395,
0.008478963747620583,
0.021832576021552086,
0.029136452823877335,
0.022628052160143852,
-0.009324916638433933,
-0.01299577858299017,
0.007525418885052204,
-0.006255011074244976,
-0.016033008694648743,
0.04590021073818207,
-0.0040024821646511555,
-0.010594743303954601,
-0.060939520597457886,
0.04281163960695267,
0.017945554107427597,
0.02228569984436035,
0.005541112739592791,
0.015324694104492664,
-0.02362120896577835,
0.029593579471111298,
0.007116337306797504,
-0.02305505983531475,
-0.12729132175445557,
0.018568161875009537,
0.021692976355552673,
-0.014637712389230728,
0.006261396687477827,
-0.017252525314688683,
-0.029349245131015778,
0.0036272029392421246,
-0.035689160227775574,
-0.05157075077295303,
-0.03738419711589813,
-0.013967511244118214,
-0.008360477164387703,
-0.003678954439237714,
-0.07723279297351837,
-0.002801349852234125,
0.0033031899947673082,
0.06439404934644699,
-0.019449833780527115,
0.02012563683092594,
0.03415485471487045,
-0.0002774630265776068,
-0.014632130973041058,
0.029455507174134254,
0.009272273629903793,
0.047037798911333084,
-0.020248545333743095,
0.0010440339101478457,
-0.0036585822235792875,
-0.006818863563239574,
-0.03816724568605423,
0.05819486454129219,
0.03151078522205353,
-0.00007727283809799701,
-0.04725340008735657,
0.028455102816224098,
0.014770139940083027,
0.0011840721126645803,
0.0000872695236466825,
0.02274472452700138,
0.009597561322152615,
-0.0341961532831192,
0.01871751807630062,
-0.057658396661281586,
-0.03060685656964779,
0.04756437614560127,
-0.05105879530310631,
0.014864553697407246,
0.08207321166992188,
-0.018976466730237007,
0.08522122353315353,
-0.056644633412361145,
-0.002593543380498886,
-0.02748124673962593,
0.021542085334658623,
-0.006952801253646612,
-0.013979610987007618,
-0.04146980121731758,
-0.024974556639790535,
0.04227617010474205,
-0.004336951766163111,
-0.0030206001829355955,
0.08245578408241272,
-0.04112745076417923,
0.058102138340473175,
0.015586440451443195,
-0.01085004210472107,
-0.010568938218057156,
-0.04627786576747894,
-0.04686050862073898,
0.030984705314040184,
0.02886301279067993,
0.014681226573884487,
-0.03151819109916687,
-0.01211406197398901,
-0.0174232330173254,
0.01185048371553421,
-0.0017247307114303112,
0.021936174482107162,
0.06494646519422531,
-0.00801172200590372,
-0.0033323566894978285,
-0.04183806851506233,
-0.04588215425610542,
-0.00444831745699048,
0.02578131854534149,
0.0353141725063324,
-0.05384887754917145,
0.00651985127478838,
0.015168391168117523,
0.018191156908869743,
0.011922165751457214,
0.04806632921099663,
-0.013210194185376167,
0.0689898133277893,
-0.015835292637348175,
0.0036082190927118063,
-0.011950119398534298,
-0.003484942950308323,
-0.04446147754788399,
0.013326097279787064,
-0.015446815639734268,
-0.03948374092578888,
0.020289693027734756,
-0.022379379719495773,
0.04702186584472656,
0.0014886182034388185,
-0.04017418995499611,
-0.037456806749105453,
0.002654103795066476,
0.04024730622768402,
-0.021964192390441895,
0.003810718422755599,
-0.004677861463278532,
-0.054566752165555954,
-0.044818904250860214,
-0.0749918520450592,
0.0705883726477623,
-0.09872902184724808,
0.07036437839269638,
0.07275550067424774,
-0.032374635338783264,
0.014218466356396675,
-0.0040888478979468346,
0.04921642690896988,
-0.05244894698262215,
0.05508435517549515,
-0.039583198726177216,
0.019381016492843628,
-0.009584016166627407,
-0.045468688011169434,
0.016585348173975945,
-0.038337886333465576,
-0.02464229054749012,
0.006577706895768642,
-0.014874269254505634,
-0.033685557544231415,
0.08585347980260849,
0.0034646932035684586,
-0.021308664232492447,
0.00762300007045269,
-0.08493622392416,
-0.02782510034739971,
-0.04354877397418022,
0.00040706503205001354,
0.0653630942106247,
-0.07042520493268967,
0.0022624589037150145,
-0.002018325962126255,
-0.055132362991571426,
0.00912673119455576,
-0.006338244304060936,
-0.03662741184234619,
-0.02037300541996956,
0.04473105072975159,
0.015458949841558933,
0.05120442435145378,
-0.029120920225977898,
0.002028847811743617,
-0.018440451472997665,
0.021867578849196434,
-0.007711826357990503,
0.046027518808841705,
-0.023103639483451843,
-0.025296339765191078,
0.03203601390123367,
0.01858614757657051,
-0.029917648062109947,
-0.04895396530628204,
-0.009638151153922081,
0.07098628580570221,
0.022028425708413124,
0.0005469184834510088,
-0.016180625185370445,
-0.02145446464419365,
0.013623660430312157,
0.05520499870181084,
-0.037389107048511505,
0.011236920021474361,
-0.016351835802197456,
-0.06512066721916199,
0.008071698248386383,
0.061964251101017,
0.015223082154989243,
-0.027999239042401314,
0.030170395970344543,
0.07556262612342834,
0.012489027343690395,
0.03376958519220352,
0.030969353392720222,
0.01218902412801981,
-0.06313230842351913,
0.013764535076916218,
-0.012697044759988785,
0.06423468142747879,
0.01437376532703638,
0.0723809227347374,
0.017308229580521584,
-0.04037462919950485,
-0.02915864996612072,
-0.07922305911779404,
-0.0007115273620001972,
0.018399707973003387,
-0.10105602443218231,
0.002126588486135006,
0.02369256690144539,
-0.04482387378811836,
-0.013386569917201996,
0.06354963034391403,
0.0013899027835577726,
0.028330719098448753,
-0.03705582767724991,
0.03056635521352291,
-0.05949891731142998,
0.09608301520347595,
-0.05619889497756958,
-0.001345312688499689,
-0.020507309585809708,
-0.05719713494181633,
0.024404652416706085,
-0.0484791100025177,
-0.050897590816020966,
0.013716653920710087,
-0.010341640561819077,
-0.02168148010969162,
-0.001965660834684968,
-0.002418156713247299,
0.009937239810824394,
-0.010972756892442703,
-0.009639169089496136,
0.018472962081432343,
-0.01973186433315277,
0.02331005409359932,
-0.048973262310028076,
0.031894292682409286,
0.01630251482129097,
-0.036730777472257614,
0.013251134194433689,
-0.014133994467556477,
-0.04653241112828255,
0.05576533079147339,
-0.013430404476821423,
0.04278383031487465,
-0.04492536559700966,
0.0592852346599102,
-0.03582838177680969,
-0.06340581923723221,
-0.03504742681980133,
0.011824117973446846,
0.010678503662347794,
0.04300016909837723,
0.047881487756967545,
-0.0007632022025063634,
0.022587554529309273,
-0.027615051716566086,
-0.019903061911463737,
0.0038988743908703327,
-0.008577222935855389,
0.06689044833183289,
0.02308797650039196,
-0.0007294189417734742,
0.021548157557845116,
0.013162104412913322,
0.026964176446199417,
-0.01940407231450081,
0.06119479984045029,
-0.06720238924026489,
-0.05675887688994408,
0.019203459843993187,
-0.0020645379554480314,
-0.02215474471449852,
-0.010536767542362213,
-0.05194329097867012,
0.040790855884552,
0.08066291362047195,
0.034963130950927734,
-0.03313778340816498,
-0.017744094133377075,
0.031025368720293045,
0.030808305367827415,
0.0504833422601223,
0.024397019296884537,
0.048350051045417786,
-0.01930749975144863,
0.005274339113384485,
0.06829428672790527,
-0.02012321911752224,
0.07200146466493607,
0.01873418129980564,
0.007701816502958536,
-0.02972833439707756,
0.022813500836491585,
-0.02370227314531803,
0.0023224675096571445,
0.04305807873606682,
0.002798989647999406,
0.000024672441213624552,
-0.007563031744211912,
0.004075764212757349,
0.02529115602374077,
0.0025496601592749357,
-0.05153698846697807,
-0.0070335036143660545,
-0.05064995214343071,
-0.0063627976924180984,
0.03037700615823269,
0.022157127037644386,
0.001735652331262827,
-0.0142141068354249,
0.016528651118278503,
0.016049707308411598,
-0.001674842438660562,
-0.009901929646730423,
-0.0224008671939373,
0.01756034418940544,
-0.012872101739048958,
-0.013785097748041153,
-0.058833688497543335,
-0.002928555943071842,
0.04344221204519272,
-0.009718205779790878,
0.05254943296313286,
-0.005877996329218149,
-0.039065830409526825,
0.004834557417780161,
0.03828774020075798,
0.018425704911351204,
-0.034418486058712006,
-0.038133714348077774,
0.02858995646238327,
0.014616269618272781,
-0.017564479261636734,
-0.01897803135216236,
0.017797350883483887,
-0.028525957837700844,
0.007441473193466663,
0.023438863456249237,
-0.0022808306384831667,
0.028890222311019897,
-0.04245270788669586,
-0.017151586711406708,
0.017209121957421303,
0.023968100547790527,
-0.043881502002477646,
0.012549136765301228,
0.044255372136831284,
0.005268537439405918,
-0.01467808336019516,
-0.011288847774267197,
-0.052392248064279556,
-0.04188069701194763,
0.0412183478474617,
-0.017312539741396904,
0.015441679395735264,
-0.008798499591648579,
-0.04337573051452637,
-0.017165228724479675,
0.020253406837582588,
0.012507385574281216,
-0.037499282509088516,
-0.03723049536347389,
-0.034934576600790024,
-0.025168025866150856,
-0.012226441875100136,
0.019454853609204292,
0.039716582745313644,
-0.023903863504529,
0.02224079519510269,
0.007679843809455633,
0.058580707758665085,
-0.011850482784211636,
0.01692992076277733,
0.027217386290431023,
0.02671835385262966,
-0.017310135066509247,
0.017007745802402496,
-0.018544942140579224,
0.030089085921645164,
0.0002936661767307669,
-0.01140075083822012,
0.013323457911610603,
-0.011623633094131947,
0.01896229013800621,
0.049552369862794876,
0.010100826621055603,
-0.07109588384628296,
0.031015649437904358,
-0.07143213599920273,
-0.010834547691047192,
-0.02835732512176037,
-0.07878933101892471,
0.09717683494091034,
0.034957025200128555,
0.023311646655201912,
0.03132487088441849,
-0.008188765496015549,
-0.058603111654520035,
-0.012655980885028839,
0.03401663526892662,
0.034780461341142654,
-0.06018967926502228,
-0.024560166522860527,
-0.03316330537199974,
-0.02696947567164898,
-0.03948870301246643,
-0.03661811351776123,
0.06075020506978035,
0.012602991424500942,
0.10373454540967941,
0.026350608095526695,
-0.07384541630744934,
0.01745465397834778,
0.02452552132308483,
0.05150577425956726,
0.008959733881056309,
0.006390779744833708,
0.03764847666025162,
-0.014973134733736515,
0.014717379584908485,
0.01250513270497322,
-0.0020266110077500343,
0.025569161400198936,
0.023786509409546852,
0.008247999474406242,
-0.03201421722769737,
0.008944926783442497,
-0.04351213201880455,
0.027710923925042152,
-0.005230123642832041,
-0.04105553403496742,
-0.05700380727648735,
-0.041473809629678726,
0.029361294582486153,
0.01585226319730282,
0.010816569440066814,
0.0007275548996403813,
-0.018184924498200417,
0.0011571665527299047,
0.06964250653982162,
-0.05732909217476845,
-0.0020042138639837503,
0.031130004674196243,
-0.07601265609264374,
-0.002839908469468355,
-0.04583344981074333,
-0.0508112832903862,
-0.014244887046515942,
0.04467878118157387
] |
<p>When a photon is emitted from a far away source and then measured by an observer, there is a loss of energy or redshift which takes place. Why does this happen?</p>
<p>I have read <a href="http://physics.stackexchange.com/questions/4821/redshifted-photon-energy">this</a> similar post, however the confusion I'm having is due to the invariance of photons, which travel at the speed of light, to non-inertial reference frames. If they are invariant then why would there be a perceived energy loss as it switches from one reference frame to the other?</p> | g7873 | [
0.03719322010874748,
-0.020268751308321953,
0.0010252074571326375,
-0.0009845010936260223,
0.032705433666706085,
0.014688760042190552,
0.04325583577156067,
0.09070917963981628,
-0.04042770713567734,
-0.033243242651224136,
0.011545085348188877,
0.022764313966035843,
0.012970706447958946,
0.025464963167905807,
-0.011840681545436382,
0.006121173035353422,
0.092274971306324,
0.023071028292179108,
0.04755657911300659,
0.027670500800013542,
-0.040513645857572556,
0.011232933960855007,
-0.06216898933053017,
-0.023533934727311134,
-0.03235134482383728,
-0.012640468776226044,
0.06053958460688591,
-0.07417096197605133,
0.004176937974989414,
-0.04092041030526161,
0.014722797088325024,
-0.046274784952402115,
0.04066586121916771,
0.000413634319556877,
0.037122126668691635,
-0.02927737683057785,
0.03916839510202408,
0.000339078571414575,
0.030553976073861122,
0.03919065371155739,
0.04585401713848114,
0.02761024981737137,
-0.015982041135430336,
0.0033804981503635645,
0.0509810596704483,
0.052645500749349594,
0.045509204268455505,
0.01676229201257229,
0.01429761666804552,
-0.03193548694252968,
-0.018248504027724266,
-0.00031705855508334935,
0.017362454906105995,
0.06225036829710007,
0.03262276574969292,
-0.006756563670933247,
-0.006128951907157898,
0.009235508739948273,
0.05801010504364967,
0.014094810001552105,
0.01366177573800087,
-0.04449717700481415,
0.005607109982520342,
-0.006119543686509132,
0.022752560675144196,
0.012907948344945908,
-0.04354351386427879,
-0.00959718320518732,
-0.00024865957675501704,
-0.002911348594352603,
0.026745520532131195,
0.015612254850566387,
-0.04298112168908119,
0.029660671949386597,
0.008769088424742222,
-0.03874043747782707,
0.0018628539983183146,
-0.014952002093195915,
-0.06228271871805191,
0.030632372945547104,
-0.019960202276706696,
0.014354884624481201,
0.0264007356017828,
0.04907682538032532,
0.09807883203029633,
0.06317776441574097,
0.0028430193196982145,
0.05085962265729904,
0.011082124896347523,
-0.012113726697862148,
0.026460867375135422,
-0.01906568929553032,
0.09541980177164078,
-0.023490918800234795,
-0.019716335460543633,
0.015421106480062008,
-0.07657240331172943,
0.07220678776502609,
0.02327652834355831,
-0.01171897817403078,
-0.03215063735842705,
-0.014980677515268326,
-0.01071516890078783,
0.008360960520803928,
0.07178188860416412,
-0.03465795889496803,
-0.0011695469729602337,
0.004631303250789642,
-0.006313113495707512,
-0.06460696458816528,
0.023041220381855965,
-0.04884997382760048,
-0.015452911145985126,
-0.07581557333469391,
-0.05126340687274933,
-0.03371482342481613,
0.07591735571622849,
-0.035201795399188995,
0.03840753808617592,
0.041085101664066315,
0.005928123369812965,
0.019659284502267838,
-0.028793660923838615,
0.064933642745018,
0.004842838272452354,
0.06975704431533813,
0.015948079526424408,
-0.03290103003382683,
-0.010310694575309753,
0.0030948040075600147,
-0.01015982124954462,
-0.0035999936517328024,
-0.009871017187833786,
0.019346874207258224,
-0.00438897218555212,
-0.02736404910683632,
0.04522174596786499,
-0.017576325684785843,
0.025468342006206512,
0.062289219349622726,
0.03303692862391472,
-0.002952002687379718,
0.018701821565628052,
-0.03615816310048103,
-0.048731036484241486,
0.031234581023454666,
-0.03748577833175659,
-0.040488019585609436,
0.08142857253551483,
-0.01147743035107851,
0.07105499505996704,
0.033664777874946594,
-0.0352359414100647,
-0.06693772971630096,
0.07820238918066025,
-0.050921257585287094,
-0.005970843601971865,
0.002886132337152958,
-0.054448921233415604,
0.00561754684895277,
0.06338518857955933,
0.036117419600486755,
-0.0040011596865952015,
0.019775299355387688,
-0.013710579834878445,
0.003469430608674884,
0.01054405141621828,
-0.07926537096500397,
-0.007359888404607773,
-0.07200558483600616,
-0.014542696997523308,
0.006532398983836174,
0.04624417796730995,
0.0136614590883255,
-0.03293582797050476,
0.05374603345990181,
0.026144441217184067,
-0.01727302186191082,
-0.01521422527730465,
0.008400081656873226,
-0.03394303098320961,
0.014467377215623856,
0.01319483295083046,
-0.08966442197561264,
0.024258026853203773,
0.037611812353134155,
-0.020283618941903114,
-0.01924893818795681,
-0.046147845685482025,
-0.01377645693719387,
0.02121223323047161,
-0.03581086918711662,
0.003163679037243128,
0.017773382365703583,
-0.033542387187480927,
-0.0015668964479118586,
-0.020342424511909485,
-0.03358621522784233,
-0.03315439075231552,
0.016197381541132927,
-0.035149432718753815,
-0.004519410897046328,
-0.03722280636429787,
-0.03292175754904747,
-0.03359488397836685,
0.017269499599933624,
0.01700373739004135,
-0.0008252713596448302,
-0.01184051763266325,
-0.0459456592798233,
-0.012238829396665096,
0.00046574443695135415,
-0.008595414459705353,
-0.02287178300321102,
0.04072700813412666,
0.04948413744568825,
0.016913631930947304,
-0.02165558934211731,
-0.018929017707705498,
0.056324221193790436,
0.006046885624527931,
-0.02503374218940735,
0.09051597118377686,
-0.05691288784146309,
-0.021328981965780258,
-0.02555173449218273,
-0.09826140850782394,
-0.03686806932091713,
0.0061143552884459496,
0.019840430468320847,
-0.027008865028619766,
0.04315822198987007,
-0.029721295461058617,
0.027553409337997437,
0.051432233303785324,
0.0014185403706505895,
-0.005403262563049793,
0.019376561045646667,
0.03371915593743324,
-0.06024324521422386,
0.010700575076043606,
-0.03171271085739136,
-0.05433953180909157,
0.001569439540617168,
-0.036484263837337494,
-0.06371516734361649,
0.05215758457779884,
-0.035125214606523514,
-0.03319014981389046,
-0.03957156091928482,
-0.001993800513446331,
0.012370411306619644,
0.016464222222566605,
-0.010658634826540947,
-0.017756743356585503,
-0.012548147700726986,
0.02773209661245346,
0.03254585340619087,
-0.07311693578958511,
0.011041664518415928,
-0.03744874149560928,
-0.06537555158138275,
-0.003552692709490657,
-0.03186941519379616,
0.030808331444859505,
-0.0060323746874928474,
0.06915365904569626,
0.03477564454078674,
-0.032089173793792725,
-0.0554799921810627,
0.02769317850470543,
0.07207334786653519,
0.04186774790287018,
0.0393889881670475,
0.030010929331183434,
0.05154690146446228,
-0.014704563654959202,
-0.009125170297920704,
0.030681820586323738,
-0.04922798275947571,
-0.031165936961770058,
-0.003990386612713337,
-0.06727546453475952,
-0.006658542901277542,
0.03668656945228577,
-0.08467934280633926,
-0.0288787130266428,
-0.012852937914431095,
-0.005137863103300333,
-0.037305500358343124,
-0.021556740626692772,
0.020244279876351357,
-0.003937630448490381,
0.035954512655735016,
-0.0030510439537465572,
0.01508530043065548,
0.03277679532766342,
0.010265391319990158,
-0.04731626436114311,
0.04392077401280403,
0.03975469619035721,
0.026195285841822624,
0.008303078822791576,
-0.030550949275493622,
0.025549346581101418,
0.02259671688079834,
-0.07040916383266449,
-0.054594893008470535,
-0.05575362220406532,
0.050922028720378876,
-0.03027982823550701,
-0.022386889904737473,
0.0030969104263931513,
0.03337082266807556,
-0.021182021126151085,
-0.007950853556394577,
-0.02265065908432007,
-0.016545558348298073,
-0.029020169749855995,
0.0052914004772901535,
-0.002034596400335431,
0.04322236776351929,
-0.02386241964995861,
0.01952938176691532,
0.01568804308772087,
0.018974019214510918,
-0.01809285767376423,
-0.054885994642972946,
-0.039438389241695404,
-0.025033922865986824,
-0.011758167296648026,
-0.03339670971035957,
-0.029856134206056595,
-0.005715806037187576,
-0.044257115572690964,
0.012437061406672001,
-0.041138920933008194,
0.03524596989154816,
0.03309330344200134,
-0.018410105258226395,
0.03699922561645508,
-0.006512612570077181,
-0.05519285798072815,
0.0242536049336195,
0.04247291013598442,
0.035158269107341766,
-0.0059836083091795444,
-0.005534997675567865,
-0.0015006011817604303,
-0.06255458295345306,
0.06238904967904091,
-0.021899132058024406,
0.006907668896019459,
-0.053170863538980484,
-0.07736703753471375,
-0.007635196670889854,
-0.05648369714617729,
-0.01860159821808338,
-0.02245243452489376,
0.011069596745073795,
0.008043541572988033,
0.046185847371816635,
0.0162512119859457,
-0.01365011278539896,
-0.04298381507396698,
0.022479338571429253,
-0.00009127814701059833,
0.012742211110889912,
0.018458861857652664,
-0.029569273814558983,
0.00960503239184618,
-0.00788467563688755,
-0.10435578972101212,
0.04773373156785965,
-0.04898221790790558,
-0.058946408331394196,
0.02848215214908123,
-0.005857122130692005,
-0.03125913813710213,
0.008419050835072994,
0.022446656599640846,
0.00483050849288702,
-0.0016248049214482307,
0.0013668922474607825,
0.09411536902189255,
0.03277137875556946,
0.030516106635332108,
0.01027488149702549,
-0.004319668281823397,
-0.00870501808822155,
0.004275924991816282,
-0.07422289252281189,
-0.022922268137335777,
0.026654312387108803,
0.04264936223626137,
0.010956531390547752,
-0.0034383039455860853,
-0.024014441296458244,
0.06866060942411423,
0.06119104474782944,
-0.020190786570310593,
0.04629921913146973,
-0.037904947996139526,
-0.02334839478135109,
0.007187653798609972,
0.0030644722282886505,
0.034994810819625854,
-0.03370118886232376,
-0.06333882361650467,
0.03585866838693619,
-0.03405510261654854,
0.01608489640057087,
-0.0169675312936306,
-0.09296226501464844,
-0.008911891840398312,
0.009229635819792747,
0.037247754633426666,
0.0010265621822327375,
0.06423482298851013,
-0.015059585683047771,
-0.007127983495593071,
0.03534252196550369,
0.019150078296661377,
-0.014868376776576042,
-0.012286764569580555,
0.09793299436569214,
0.02786959894001484,
-0.011185884475708008,
0.022730156779289246,
-0.012569263577461243,
0.05503109470009804,
0.02823559194803238,
0.07140850275754929,
0.03455982357263565,
-0.03771960362792015,
0.07398927211761475,
-0.017494982108473778,
0.01598449982702732,
-0.01530107669532299,
0.030052833259105682,
0.08813605457544327,
0.019978398457169533,
0.02996116690337658,
-0.04455644637346268,
0.003093622624874115,
0.027989909052848816,
-0.029258226975798607,
-0.010342339985072613,
-0.00024399264657404274,
-0.0687650516629219,
-0.02919860929250717,
0.02187216468155384,
-0.02818911150097847,
-0.0003222981176804751,
0.009751461446285248,
-0.041905611753463745,
-0.057474929839372635,
-0.04440848156809807,
0.03066577948629856,
0.04206432029604912,
-0.03746812790632248,
-0.007832684554159641,
0.020993780344724655,
-0.0175829716026783,
-0.011906030587852001,
0.012772900052368641,
-0.0416797399520874,
-0.03531578183174133,
-0.05098418518900871,
0.010926433838903904,
0.01631963811814785,
-0.03300943598151207,
-0.051604460924863815,
0.05172000080347061,
0.054295800626277924,
0.044067323207855225,
-0.03085976466536522,
-0.04190327599644661,
0.030442900955677032,
-0.06266231834888458,
-0.028108898550271988,
0.005788710433989763,
0.05195390060544014,
0.0044944691471755505,
-0.04206595569849014,
0.02435026504099369,
-0.03191152215003967,
0.007781236432492733,
0.03449908643960953,
-0.046423349529504776,
0.023522526025772095,
0.00048483911086805165,
-0.025129081681370735,
-0.025406837463378906,
0.051742661744356155,
0.07440634071826935,
-0.005486768204718828,
0.01773099973797798,
-0.02276693284511566,
-0.015917954966425896,
-0.03088873066008091,
0.03286769613623619,
-0.009212290868163109,
-0.012043527327477932,
-0.006451417226344347,
0.012194043025374413,
0.06300020217895508,
0.023566601797938347,
0.020802509039640427,
0.03219100460410118,
-0.056267254054546356,
0.011420843191444874,
-0.016262955963611603,
0.014162006787955761,
0.06336730718612671,
-0.04788283631205559,
0.021386360749602318,
-0.017333218827843666,
-0.010661933571100235,
-0.038513023406267166,
-0.022734137251973152,
0.0436953529715538,
-0.018465017899870872,
-0.03107827715575695,
0.0017823668895289302,
0.017387164756655693,
-0.007609885651618242,
0.047764312475919724,
-0.04869646206498146,
-0.01941028982400894,
0.013077722862362862,
0.031224559992551804,
-0.0049739102832973,
0.029464885592460632,
0.0192917101085186,
0.024426454678177834,
0.017915252596139908,
-0.04080215469002724,
-0.012421146035194397,
-0.016293466091156006,
-0.04564131796360016,
0.006699306890368462,
0.0008950122864916921,
0.05488603562116623,
-0.018879642710089684,
-0.007534788455814123,
-0.013087619096040726,
-0.0067818183451890945,
0.015750454738736153,
-0.02348434552550316,
0.023433228954672813,
0.011027909815311432,
0.013712105341255665,
-0.00275677302852273,
0.017804333940148354,
-0.006854361854493618,
0.03545404598116875,
-0.01968998648226261,
-0.03517363965511322,
-0.017350047826766968,
0.008073650300502777,
0.034514009952545166,
0.031960826367139816,
0.020178331062197685,
0.04296942800283432,
0.004974263720214367,
0.02142268978059292,
-0.07010328024625778,
-0.012193508446216583,
0.00029211005312390625,
0.02171018347144127,
-0.002427144208922982,
0.026809923350811005,
-0.041214440017938614,
-0.05516481399536133,
0.05220663174986839,
-0.06869357824325562,
-0.07886750996112823,
-0.056071244180202484,
-0.0599278062582016,
0.03263923525810242,
-0.015582745894789696,
0.043969105929136276,
-0.03063221462070942,
0.004078176338225603,
0.019817356020212173,
0.015557651408016682,
0.01211943943053484,
0.09111812710762024,
0.03752012550830841,
-0.0024667480029165745,
-0.041869595646858215,
0.007550944108515978,
-0.045008279383182526,
-0.09484215825796127,
0.0025445688515901566,
-0.05356914550065994,
-0.02119387313723564,
-0.05726296827197075,
-0.0012560328468680382,
-0.024001671001315117,
-0.0460747592151165,
0.06008003652095795,
-0.0345342792570591,
0.014820114709436893,
0.03404678404331207,
-0.04906291887164116,
-0.005225202534347773,
0.035552285611629486,
0.047065719962120056,
0.004117206670343876,
-0.013536079786717892,
0.021379679441452026,
0.0231833104044199,
-0.010634863749146461,
-0.027203785255551338,
-0.022109130397439003,
-0.001424069283530116,
-0.02144663967192173,
0.002054296201094985,
-0.013093936257064342,
-0.06531759351491928,
0.049155354499816895,
0.03506319597363472,
0.028836434707045555,
0.11578463017940521,
-0.02836102619767189,
0.012959486804902554,
0.0016963769448921084,
-0.0077220075763762,
-0.09449276328086853,
0.046898093074560165,
-0.021174810826778412,
0.040224481374025345,
-0.0010056206956505775,
-0.0006211486179381609,
-0.04724712297320366,
0.002427594969049096,
0.023166047409176826,
-0.028171932324767113,
0.040185075253248215,
0.020245445892214775,
0.04604756832122803,
-0.03056929260492325,
-0.06756039708852768,
0.05682870373129845,
0.001741791027598083,
-0.0334971658885479,
-0.044509101659059525,
0.011264889501035213,
-0.05229499563574791,
0.02882077544927597,
-0.03658498823642731,
0.010328640230000019,
0.011935658752918243,
0.03967961296439171,
-0.013749845325946808,
0.029252389445900917,
0.029208175837993622,
-0.06487169116735458,
-0.027075620368123055,
-0.056529175490140915,
-0.039680302143096924,
0.04290347173810005,
0.009834733791649342,
0.043006397783756256,
-0.006070268806070089,
-0.10797342658042908,
-0.02803231216967106,
0.05844331532716751,
-0.008943857625126839,
-0.04009724408388138,
-0.015719978138804436,
0.011000232771039009,
0.000818164786323905,
-0.0022330929059535265,
-0.016874592751264572,
0.05555814132094383,
0.0033755984622985125,
-0.02776474878191948,
-0.036166127771139145,
0.05156606063246727,
0.03602519631385803,
0.04334728792309761,
-0.06189978867769241,
0.04430326819419861,
0.024841058999300003,
0.025336341932415962,
0.00009245781984645873,
-0.0062653301283717155,
-0.04372351989150047,
0.0368872731924057,
0.05439579486846924,
-0.013720812276005745,
-0.013484872877597809,
0.0026222234591841698,
0.07054027169942856,
-0.019355030730366707,
0.0082527631893754,
-0.006768908351659775,
0.018385719507932663,
-0.04807237535715103,
0.024976059794425964,
0.05248025804758072,
0.0028007153887301683,
0.0032105324789881706,
0.004484863020479679,
-0.02304064668715,
0.020313454791903496,
0.007839707657694817,
0.03234729915857315,
-0.026652509346604347,
0.05377950891852379,
0.019258182495832443,
-0.0011846686247736216,
0.0026700571179389954,
-0.026017557829618454,
0.046748384833335876,
0.024700215086340904,
-0.016716064885258675,
-0.009484570473432541,
-0.016049204394221306,
0.02110888436436653,
-0.010042110458016396,
0.0300922654569149,
-0.022513434290885925,
0.051260389387607574,
-0.0308467335999012,
0.011025979183614254,
-0.01692330278456211,
-0.024925582110881805,
0.026199262589216232,
-0.01939055137336254,
-0.010842496529221535,
-0.025553692132234573,
0.011551973409950733,
0.033321090042591095,
-0.007447960786521435,
-0.03000713884830475,
0.0013236686354503036,
0.051044825464487076,
-0.05177146941423416,
0.004410951863974333,
0.022246820852160454,
0.015809129923582077,
-0.046270862221717834,
0.028373872861266136,
0.007979518733918667,
-0.0008459605160169303,
-0.0430605448782444,
0.028050320222973824,
0.03308878466486931,
-0.007770516909658909,
0.05969204008579254,
0.058595407754182816,
-0.042375389486551285,
-0.014040887355804443,
-0.04507584869861603,
-0.022549409419298172,
-0.008546849712729454,
-0.005932121071964502,
-0.010684598237276077,
-0.01592930592596531,
-0.01945173740386963,
-0.009338811971247196,
-0.04850350320339203,
-0.0013994628097862005,
0.05773351714015007
] |
<p>(Please bear with me.)
If the universe included multi-universes, and black holes transferred matter between them, AND yet there was a large, but FINITE amount of matter and space, How would that max-limit change our understanding/perception or theories of the universe? Would it make any difference or change current concepts? </p> | g7874 | [
-0.022303679957985878,
0.04820743948221207,
0.004306381102651358,
-0.013610768131911755,
-0.022489232942461967,
0.0028585914988070726,
-0.043721575289964676,
0.05962454527616501,
0.042825594544410706,
-0.03848059102892876,
0.013887732289731503,
-0.058378830552101135,
0.057081401348114014,
0.05534983426332474,
0.011353442445397377,
0.005992657504975796,
-0.011125413700938225,
-0.03148350864648819,
-0.0006645956309512258,
-0.01908748969435692,
-0.0052384063601493835,
-0.01173283439129591,
0.002540390472859144,
-0.037679318338632584,
-0.07379794120788574,
0.0032266234047710896,
0.04347849264740944,
0.007994887419044971,
-0.04157590493559837,
0.03845847770571709,
0.039273254573345184,
-0.0752854198217392,
-0.030810751020908356,
-0.003487449139356613,
-0.001901867799460888,
-0.0018075965344905853,
0.019089922308921814,
-0.0014321388443931937,
0.013474587351083755,
0.0007502395892515779,
0.03326040878891945,
-0.03860461711883545,
-0.00203525647521019,
-0.027437036857008934,
-0.034154437482357025,
-0.030964335426688194,
-0.007455748505890369,
0.017426997423171997,
0.08437825739383698,
-0.050379544496536255,
-0.0008527690079063177,
-0.011038225144147873,
0.018464505672454834,
0.09337099641561508,
0.04478900507092476,
0.011107985861599445,
0.030196500942111015,
0.009655210189521313,
0.028028860688209534,
0.002161160111427307,
-0.04274469614028931,
-0.013032756745815277,
-0.0019264117581769824,
0.02985154464840889,
-0.019894616678357124,
0.04612233489751816,
-0.06411950290203094,
0.007700358983129263,
0.005030801985412836,
0.03886864334344864,
0.06421776115894318,
0.02349628135561943,
-0.009259957820177078,
-0.030101967975497246,
-0.0025678249076008797,
0.07578493654727936,
0.0040785470046103,
0.038843728601932526,
0.007493370678275824,
-0.0268847793340683,
-0.005622193217277527,
-0.039993997663259506,
0.047241657972335815,
-0.026193220168352127,
0.04020225256681442,
-0.027043497189879417,
0.0007187500013969839,
-0.01334218867123127,
-0.010118531063199043,
0.043803583830595016,
0.004543493036180735,
-0.01630876399576664,
0.018474271520972252,
0.02221653051674366,
0.009720110334455967,
0.015778932720422745,
0.022810084745287895,
0.037447165697813034,
-0.0003778721147682518,
0.02588570863008499,
-0.06947652250528336,
0.033213574439287186,
0.05760708451271057,
-0.0439930185675621,
0.01600577123463154,
0.0438731387257576,
-0.0005258872406557202,
0.029950469732284546,
0.04106844216585159,
0.028139004483819008,
-0.05543474480509758,
-0.06707439571619034,
-0.05324561521410942,
0.00022747268667444587,
-0.04840661585330963,
-0.016367608681321144,
0.03148937597870827,
0.05128541961312294,
0.005124383606016636,
0.030042288824915886,
0.007787576410919428,
0.0069613088853657246,
0.04647577553987503,
0.027539700269699097,
-0.03570801392197609,
-0.0901653990149498,
-0.05244498699903488,
0.022846262902021408,
0.013244700618088245,
-0.042422108352184296,
0.023362385109066963,
-0.0355595201253891,
-0.005313412752002478,
0.0750960260629654,
-0.07228171080350876,
-0.017774702981114388,
-0.01781988888978958,
-0.01548172440379858,
-0.05502089485526085,
0.02269347757101059,
0.011142682284116745,
-0.03896751627326012,
-0.02855672314763069,
0.04148077219724655,
-0.002426911611109972,
0.016613049432635307,
-0.02456173673272133,
-0.018976053223013878,
-0.0539405383169651,
-0.04225396364927292,
0.0572720505297184,
0.05196579918265343,
0.017700528725981712,
0.022885503247380257,
-0.03433360159397125,
0.0077057634480297565,
0.011216766200959682,
0.00038332867552526295,
-0.016400650143623352,
-0.03377922624349594,
-0.007783796638250351,
0.014795410446822643,
-0.013053745962679386,
0.003863553050905466,
-0.04357658326625824,
0.043592918664216995,
-0.028299277648329735,
-0.04206521436572075,
0.011611388064920902,
0.01384594663977623,
-0.0340699665248394,
0.006388315465301275,
-0.00697494950145483,
0.0032029496505856514,
0.041422318667173386,
0.04914041981101036,
0.02340978942811489,
-0.008763995952904224,
-0.04145028069615364,
0.06585175544023514,
-0.06058724969625473,
-0.04144682362675667,
-0.014718708582222462,
0.01658352091908455,
0.02322153002023697,
0.004988084081560373,
0.00307396799325943,
-0.0001746743801049888,
0.03991054743528366,
0.016302408650517464,
-0.03803321346640587,
-0.022403549402952194,
0.04557235911488533,
0.0642227828502655,
-0.0013535525649785995,
0.008836492896080017,
0.02910827286541462,
0.014783832244575024,
-0.0002591839001979679,
-0.02269815094769001,
-0.010467042215168476,
0.03163587301969528,
0.054763179272413254,
-0.04003336280584335,
0.043855976313352585,
-0.07405632734298706,
-0.054138731211423874,
0.0277881883084774,
0.0004839691100642085,
-0.053041961044073105,
0.04313167184591293,
-0.056243520230054855,
0.0013470837147906423,
0.04141655191779137,
-0.022917257621884346,
0.03506230190396309,
-0.07067753374576569,
0.02119898796081543,
0.03673834726214409,
0.03075547330081463,
-0.007522220723330975,
-0.013593672774732113,
0.017006490379571915,
-0.009408509358763695,
0.04025810584425926,
-0.033467862755060196,
-0.005696754902601242,
-0.09208276867866516,
0.04372065141797066,
0.04058975726366043,
-0.0512315072119236,
0.03767266124486923,
0.06197519972920418,
0.0006932221003808081,
-0.025348568335175514,
0.01592261902987957,
-0.002648062538355589,
-0.014277634210884571,
-0.04296594113111496,
-0.0016490669222548604,
0.008421702310442924,
0.033229582011699677,
-0.03799106553196907,
-0.005323528777807951,
-0.01986115053296089,
-0.05292993038892746,
0.00039527518674731255,
-0.0512789823114872,
-0.017724771052598953,
0.005211715120822191,
-0.004832070786505938,
0.010603300295770168,
0.01770825870335102,
-0.007605765480548143,
-0.0018967086216434836,
-0.003553749294951558,
0.022545360028743744,
0.07190471142530441,
-0.07479573041200638,
-0.03448326885700226,
0.08391312509775162,
-0.01169222965836525,
0.0101326210424304,
0.014937011525034904,
-0.012417688965797424,
-0.01909247599542141,
-0.06795050948858261,
0.05867106467485428,
-0.018882032483816147,
0.05736102536320686,
0.06982969492673874,
-0.00200379709713161,
0.014780612662434578,
0.010859217494726181,
0.026377562433481216,
0.026406383141875267,
-0.032026030123233795,
-0.04575209692120552,
0.07173971831798553,
-0.029772289097309113,
-0.06214907392859459,
0.016491489484906197,
-0.06237833574414253,
0.0008693213458172977,
-0.01816944219172001,
-0.03380502760410309,
-0.0313522145152092,
-0.0023211997468024492,
-0.00042802668758668005,
0.038120511919260025,
-0.01372804120182991,
0.055763568729162216,
0.008329571224749088,
0.02082671783864498,
0.024691816419363022,
0.0016682783607393503,
-0.01681184209883213,
-0.021910283714532852,
-0.06613854318857193,
-0.03170955553650856,
-0.04383879527449608,
0.004887268412858248,
0.03608174994587898,
0.013929832726716995,
-0.0516791045665741,
0.01650870218873024,
-0.013444000855088234,
0.008451792411506176,
0.028370866551995277,
-0.029314041137695312,
-0.019323697313666344,
-0.019309330731630325,
0.040496375411748886,
0.02792753465473652,
-0.026844562962651253,
0.007605859078466892,
0.06119513884186745,
0.05936521291732788,
-0.016982993111014366,
-0.014359128661453724,
0.025596633553504944,
0.002826378680765629,
0.017560619860887527,
0.008514892309904099,
0.013227684423327446,
0.07175283133983612,
-0.02007090486586094,
-0.04080583155155182,
-0.09606274217367172,
0.06754348427057266,
-0.020649338141083717,
-0.02789480797946453,
-0.003602810436859727,
0.04463895410299301,
-0.04385543614625931,
0.03837137296795845,
-0.015947770327329636,
-0.06865836679935455,
0.08568186312913895,
-0.051886409521102905,
-0.0036518487613648176,
-0.02563159354031086,
0.0045355623587965965,
-0.024732723832130432,
0.06048350781202316,
0.07031160593032837,
0.017930638045072556,
-0.01552037987858057,
0.012943197973072529,
0.013136999681591988,
0.05016903951764107,
0.016951784491539,
0.012281032279133797,
0.008715018630027771,
0.043405257165431976,
-0.0068616061471402645,
0.015873150900006294,
0.06582002341747284,
0.009494077414274216,
-0.05154115706682205,
-0.03730851411819458,
-0.028503332287073135,
-0.030573222786188126,
0.010722382925450802,
0.021426398307085037,
0.0122520187869668,
0.02665933594107628,
-0.055391889065504074,
0.0012580737238749862,
0.008655179291963577,
0.007594432216137648,
0.017420614138245583,
-0.04939919337630272,
0.0013591633178293705,
0.055460911244153976,
-0.034037891775369644,
0.048572566360235214,
-0.004397344775497913,
0.0046700965613126755,
0.057051561772823334,
0.05188174918293953,
-0.0029545777942985296,
-0.013146030716598034,
-0.02866288088262081,
-0.055145956575870514,
0.0026251908857375383,
-0.008025453425943851,
-0.052391402423381805,
-0.04305877536535263,
-0.000957279116846621,
-0.016909364610910416,
-0.02190898358821869,
0.027415860444307327,
-0.06785067170858383,
-0.00010133337491424754,
-0.04191694036126137,
-0.05223497375845909,
-0.02339390479028225,
0.025555942207574844,
0.02241428755223751,
0.028639942407608032,
0.027481161057949066,
0.0015816162340342999,
-0.007199942134320736,
0.034287214279174805,
-0.06607283651828766,
0.04451128840446472,
0.016113340854644775,
-0.013372133485972881,
-0.035840436816215515,
0.04612154886126518,
-0.0422007292509079,
-0.025598658248782158,
-0.010735373012721539,
0.00518404645845294,
-0.005042828619480133,
-0.016417574137449265,
-0.07361951470375061,
-0.016314372420310974,
0.027401601895689964,
0.03981495276093483,
-0.04368921369314194,
-0.0388907752931118,
0.03746619448065758,
0.04299513250589371,
-0.07555478066205978,
-0.004385218024253845,
-0.006376920733600855,
0.004288944415748119,
0.029246510937809944,
-0.03661724925041199,
0.029149530455470085,
-0.03148850053548813,
0.044785093516111374,
-0.013748886995017529,
0.014607054181396961,
-0.01520412415266037,
0.034405793994665146,
-0.031207283958792686,
-0.016751782968640327,
0.06596188992261887,
-0.004417434800416231,
-0.03968697786331177,
0.002690855646505952,
0.024172939360141754,
0.023004943504929543,
-0.012075723148882389,
-0.05222618579864502,
-0.003782019717618823,
-0.035244282335042953,
-0.05743491277098656,
-0.03318817913532257,
-0.017497632652521133,
-0.026791175827383995,
-0.0193138737231493,
-0.012142005376517773,
-0.017667317762970924,
0.04304293915629387,
0.02588093839585781,
0.02221931889653206,
-0.10506930947303772,
0.016863422468304634,
-0.04102393612265587,
0.0658363625407219,
0.003926628269255161,
-0.04609033837914467,
-0.006874099839478731,
-0.02235773205757141,
-0.03674282878637314,
0.03638368844985962,
-0.07410085946321487,
0.011664454825222492,
0.028242643922567368,
0.06355761736631393,
-0.011110778898000717,
0.031008576974272728,
-0.047558482736349106,
-0.023816978558897972,
-0.02440158650279045,
-0.03729422390460968,
-0.0028633682522922754,
-0.032710228115320206,
0.09634086489677429,
-0.01193070225417614,
-0.027301423251628876,
0.04666396230459213,
-0.066134512424469,
0.015317236073315144,
-0.023422110825777054,
0.040637578815221786,
0.024439502507448196,
-0.003840707940980792,
0.01665998063981533,
0.046254344284534454,
-0.05917565897107124,
0.011195397935807705,
-0.004925676621496677,
-0.02474069595336914,
0.006941624917089939,
0.028849156573414803,
0.023193394765257835,
0.05189771205186844,
0.06839100271463394,
-0.02690582349896431,
-0.0343390628695488,
0.01572021096944809,
0.009975441731512547,
-0.022337622940540314,
0.017723174765706062,
0.05619495362043381,
-0.004149933345615864,
0.04326208308339119,
-0.02781510539352894,
0.011769718490540981,
0.07839260250329971,
-0.022640621289610863,
-0.038299623876810074,
-0.02077898196876049,
0.012511086650192738,
-0.03763237223029137,
-0.017361992970108986,
-0.034092068672180176,
0.0692475438117981,
0.049040019512176514,
0.02443164959549904,
0.02886318601667881,
0.027598274871706963,
-0.02048325538635254,
0.011361942626535892,
-0.006503819487988949,
0.06007992476224899,
0.04478878155350685,
0.018005196005105972,
-0.006860542576760054,
0.016182459890842438,
0.03344585373997688,
-0.03596008941531181,
0.01369685959070921,
0.06343186646699905,
-0.03808067366480827,
0.010498729534447193,
-0.0011968391481786966,
0.0018031431827694178,
0.012834451161324978,
0.04807096719741821,
-0.006813802290707827,
-0.07153940200805664,
0.018567152321338654,
0.035223234444856644,
-0.026904284954071045,
-0.049267061054706573,
-0.0306170042604208,
0.02476290985941887,
0.022857988253235817,
0.03477673977613449,
0.05396173894405365,
0.04073414206504822,
-0.01984662003815174,
-0.044829756021499634,
-0.027674056589603424,
-0.0009980351896956563,
0.01848761737346649,
-0.02756994403898716,
-0.027202753350138664,
-0.009492241777479649,
-0.05414614453911781,
-0.0040034581907093525,
-0.060026198625564575,
0.03602232038974762,
-0.008787949569523335,
-0.019095560535788536,
0.00386656797491014,
0.07219976931810379,
-0.05692214146256447,
0.012077650055289268,
0.009951530955731869,
0.031077643856406212,
0.016167951747775078,
-0.022406524047255516,
-0.06626134365797043,
-0.0048929303884506226,
-0.0327354297041893,
0.01680518314242363,
-0.03159598633646965,
0.02101925201714039,
0.050030291080474854,
-0.0032924911938607693,
0.017211632803082466,
0.05158345028758049,
-0.048068977892398834,
-0.017568832263350487,
0.007586716208606958,
0.06794193387031555,
-0.05816402658820152,
0.0002614265540614724,
0.019363485276699066,
0.01084643043577671,
-0.05398811772465706,
-0.0362064503133297,
-0.013410587795078754,
-0.0022493323776870966,
0.038624975830316544,
0.011263690888881683,
0.013427513651549816,
0.03321003541350365,
-0.009291024878621101,
-0.056421078741550446,
-0.06851667910814285,
0.04930286854505539,
0.01705797389149666,
0.05514729022979736,
-0.02571726217865944,
-0.0053408886305987835,
0.026782291010022163,
-0.01226968877017498,
0.0034052582923322916,
0.01186701562255621,
-0.11066918820142746,
-0.009135881438851357,
-0.014076021499931812,
-0.01445067673921585,
0.027501165866851807,
-0.017484411597251892,
-0.0017004294786602259,
-0.044123630970716476,
0.06332413107156754,
-0.028860559687018394,
0.0009004361927509308,
0.035432543605566025,
0.0025621592067182064,
0.03437941521406174,
0.0014837895287200809,
0.025053270161151886,
0.018832102417945862,
0.015026012435555458,
0.05159591883420944,
-0.015570756047964096,
-0.0031501108314841986,
-0.02921539545059204,
-0.00892992876470089,
0.0002519244735594839,
-0.028253652155399323,
-0.019504470750689507,
0.0051168231293559074,
0.04892672598361969,
-0.005921682342886925,
0.025894353166222572,
0.028936969116330147,
-0.05343038961291313,
-0.03247598186135292,
-0.06699692457914352,
-0.06264293938875198,
-0.07583562284708023,
0.035593271255493164,
-0.04406903684139252,
-0.023739807307720184,
0.0009048996143974364,
0.013900170102715492,
0.0058980113826692104,
-0.062879778444767,
-0.014517346397042274,
0.04889262467622757,
-0.03085254691541195,
-0.030811723321676254,
-0.003265533596277237,
0.058041803538799286,
0.07188064604997635,
-0.02586239203810692,
-0.00586805772036314,
-0.029152872040867805,
-0.007157158572226763,
0.04497953876852989,
-0.03484225273132324,
0.027803935110569,
0.00024230105918832123,
-0.0701790526509285,
-0.022331634536385536,
0.007263317704200745,
-0.021099023520946503,
0.10985761135816574,
0.00479468610137701,
-0.006896310020238161,
0.05299007520079613,
0.05143480375409126,
-0.06630433350801468,
-0.021651480346918106,
0.006709432695060968,
0.06651367992162704,
-0.026039475575089455,
-0.009247319772839546,
-0.001978781074285507,
-0.05401885136961937,
-0.016158347949385643,
-0.009458315558731556,
0.00242034113034606,
0.051917653530836105,
0.01643187738955021,
0.011070308275520802,
0.10005027800798416,
-0.04182707145810127,
-0.04592243954539299,
-0.020429594442248344,
-0.05482340231537819,
-0.03155931830406189,
0.08790044486522675,
0.011663922108709812,
0.005743150133639574,
-0.008337092585861683,
0.021622564643621445,
-0.017165150493383408,
-0.01679566130042076,
0.06631040573120117,
-0.045093435794115067,
0.04980852082371712,
-0.022356383502483368,
-0.004520825110375881,
0.0038381428457796574,
-0.01062072068452835,
-0.006972344126552343,
-0.007698084693402052,
0.003771638497710228,
0.017518499866127968,
-0.02862432599067688,
-0.019019488245248795,
-0.01566786877810955,
0.05159234255552292,
-0.02448076196014881,
-0.07362230867147446,
-0.07422842085361481,
-0.037672627717256546,
-0.04104948416352272,
-0.01609944924712181,
-0.033160239458084106,
-0.006115158088505268,
-0.06652984768152237,
0.028186621144413948,
0.00404146546497941,
0.08088015764951706,
-0.005885956343263388,
-0.013798017054796219,
-0.028479373082518578,
-0.023275967687368393,
0.004305168986320496,
0.053759656846523285,
-0.0023282424081116915,
0.00014213990652933717,
-0.002953368704766035,
0.02799210697412491,
0.06942875683307648,
-0.03239035978913307,
-0.018938720226287842,
0.01988453045487404,
0.04771547392010689,
0.009832145646214485,
0.026596592739224434,
0.0049397582188248634,
-0.005467641167342663,
-0.006747434381395578,
-0.04135479778051376,
0.02627401612699032,
-0.019210191443562508,
0.04111525043845177,
0.03306950256228447,
-0.026332911103963852,
-0.008816024288535118,
-0.014758538454771042,
0.04421771317720413,
0.04125972464680672
] |
<p>An electron in a cathode-ray tube is traveling horizontally at 2.10×10^9 cm/s when deflection plates give it an upward acceleration of 5.30×10^17 cm/s^2 .</p>
<p>B.) What is its vertical displacement during this time?</p>
<p>My work <a href="http://i.imgur.com/AqKlTuX.jpg" rel="nofollow">http://i.imgur.com/AqKlTuX.jpg</a></p>
<p>I am asking this because the answer my teacher gave is 2.3cm</p>
<p>Thanks in advance</p> | g7875 | [
0.08438935875892639,
0.049069423228502274,
-0.012072503566741943,
0.01589863747358322,
0.05996226146817207,
0.048183515667915344,
0.035071130841970444,
-0.018857317045331,
-0.05779656022787094,
0.01737843081355095,
-0.022538311779499054,
0.08331544697284698,
-0.0244270171970129,
-0.014525000005960464,
0.02127601020038128,
-0.03110925853252411,
0.04402681812644005,
-0.02165082097053528,
-0.009309164248406887,
0.04336456581950188,
-0.0005793102318421006,
0.0024030040949583054,
-0.07558968663215637,
-0.04087386280298233,
0.051026418805122375,
0.050410013645887375,
0.015921784564852715,
-0.009845136664807796,
-0.04416853189468384,
-0.01647048257291317,
-0.029532037675380707,
0.012311275117099285,
0.006574575789272785,
-0.023397428914904594,
-0.005704574286937714,
-0.02882247231900692,
0.05829315260052681,
-0.03442484512925148,
0.04804109036922455,
-0.019219715148210526,
0.008784285746514797,
-0.013542675413191319,
0.010641894303262234,
0.028210846707224846,
0.04279707372188568,
-0.011159759014844894,
-0.022039685398340225,
-0.041364822536706924,
-0.03349820524454117,
-0.027591977268457413,
-0.05232784524559975,
0.03550586476922035,
-0.022355593740940094,
-0.03333180025219917,
0.020752040669322014,
-0.019162403419613838,
0.018412085250020027,
0.0091555155813694,
0.057098329067230225,
0.022978568449616432,
-0.03137596324086189,
-0.022575613111257553,
-0.001385413808748126,
-0.005446681287139654,
0.05788617581129074,
-0.0033493908122181892,
-0.05060397461056709,
0.006028047762811184,
0.024181870743632317,
-0.03545365482568741,
0.05814317241311073,
-0.08758116513490677,
-0.05328242480754852,
-0.0420011542737484,
-0.04262591153383255,
-0.03992057591676712,
-0.031755369156599045,
-0.019314199686050415,
0.02938893996179104,
-0.0029988866299390793,
-0.05880659446120262,
0.01991068385541439,
0.01102879922837019,
-0.05089234933257103,
0.05732203647494316,
0.0034799822606146336,
0.019395336508750916,
0.054328594356775284,
-0.07024801522493362,
-0.01895216852426529,
0.013123678974807262,
-0.04969930276274681,
0.034304630011320114,
0.045355502516031265,
-0.028095701709389687,
-0.03961293771862984,
-0.043012041598558426,
0.09771791100502014,
0.0325639583170414,
-0.03250027820467949,
-0.018425697460770607,
-0.07218857854604721,
-0.003578493371605873,
-0.009413442574441433,
0.04622865468263626,
-0.03422805294394493,
0.013912825845181942,
-0.033714890480041504,
0.023796334862709045,
-0.014079120010137558,
-0.01454377081245184,
-0.07775076478719711,
-0.035321783274412155,
-0.05473335087299347,
-0.019953664392232895,
-0.05261729657649994,
0.03988061845302582,
-0.014932957477867603,
-0.005747295916080475,
0.035487011075019836,
0.04610098525881767,
0.026129990816116333,
-0.006414140108972788,
0.021065816283226013,
-0.03273630514740944,
-0.03781874477863312,
-0.04944271594285965,
-0.05275261774659157,
-0.008173909038305283,
0.02851482294499874,
0.0013038323959335685,
0.02462887577712536,
-0.03347110375761986,
0.027713298797607422,
0.014551879838109016,
0.0449499748647213,
0.03378933668136597,
0.018634214997291565,
0.0019133557798340917,
0.04851272702217102,
0.0323534831404686,
-0.04330933839082718,
-0.0007287180633284152,
0.01020150538533926,
0.013719991780817509,
-0.040705785155296326,
-0.016662349924445152,
0.024708427488803864,
0.06252925097942352,
0.032820142805576324,
-0.00003912907777703367,
0.044610507786273956,
-0.011745664291083813,
-0.048366695642471313,
0.04249380901455879,
-0.026507768779993057,
0.06337025761604309,
0.030615441501140594,
0.03310108184814453,
0.04341979697346687,
0.0352875292301178,
-0.011448908597230911,
-0.046907782554626465,
-0.013324582949280739,
-0.08444687724113464,
-0.021843604743480682,
0.0006260822410695255,
-0.015627209097146988,
0.04718213900923729,
0.006109565030783415,
-0.012088843621313572,
-0.021639276295900345,
0.05764935910701752,
0.016766536980867386,
-0.035497937351465225,
0.04605383798480034,
0.023525694385170937,
-0.012313364073634148,
0.0010424862848594785,
-0.002961877267807722,
-0.033686935901641846,
-0.04649213328957558,
0.02104620821774006,
-0.037593234330415726,
0.03220704197883606,
-0.05475284531712532,
-0.0008103494765236974,
0.017387764528393745,
-0.03610176965594292,
-0.014618788845837116,
0.07295665889978409,
-0.04950795695185661,
0.012111536227166653,
-0.0341070331633091,
-0.06809092313051224,
-0.07708484679460526,
0.02644743025302887,
-0.034196071326732635,
-0.020808108150959015,
-0.013484993018209934,
0.03819609060883522,
0.013479214161634445,
0.1058693677186966,
-0.003706319024786353,
0.09060758352279663,
-0.0018372130580246449,
-0.05489692464470863,
-0.026580870151519775,
-0.024277355521917343,
-0.01018503773957491,
0.028551535680890083,
0.0412994809448719,
-0.018747195601463318,
0.030021503567695618,
0.009478221647441387,
-0.022094180807471275,
-0.014311163686215878,
0.06735514104366302,
-0.015478529967367649,
0.038636885583400726,
-0.020896920934319496,
-0.020697327330708504,
0.027284914627671242,
-0.010050457902252674,
-0.0112998578697443,
-0.021552475169301033,
0.025885358452796936,
-0.04777822643518448,
0.003838995937258005,
0.002382112666964531,
-0.05059993267059326,
0.06906995177268982,
-0.034854404628276825,
-0.058099325746297836,
0.07888337224721909,
0.05462434142827988,
-0.026944518089294434,
0.000691529712639749,
-0.019323034211993217,
-0.0318063423037529,
0.067221499979496,
0.006961087230592966,
-0.012812348082661629,
-0.041984520852565765,
-0.012700852006673813,
-0.0011175861582159996,
0.09166697412729263,
0.04039764776825905,
-0.019875263795256615,
-0.0446866899728775,
0.030696695670485497,
-0.04090616852045059,
0.001950160483829677,
0.055315468460321426,
-0.0013160525122657418,
0.0514812171459198,
-0.08361392468214035,
0.027464112266898155,
-0.03602885454893112,
-0.0695999339222908,
0.01579642854630947,
-0.0420052595436573,
-0.005535570438951254,
-0.05853795260190964,
-0.02319597266614437,
-0.05175456777215004,
0.002659120364114642,
-0.029017938300967216,
0.022976750507950783,
-0.022092964500188828,
0.05244161933660507,
0.054843440651893616,
-0.0031252517364919186,
0.01621220074594021,
-0.00621602451428771,
-0.06083362549543381,
0.04237080737948418,
0.016544189304113388,
-0.0015150256222113967,
-0.03284621611237526,
-0.02558673545718193,
-0.012041487731039524,
-0.02657257206737995,
0.03697444498538971,
-0.0021233202423900366,
0.06250840425491333,
-0.021277107298374176,
-0.01362194400280714,
-0.047840289771556854,
0.02470291033387184,
-0.07567482441663742,
-0.024999914690852165,
0.04344179853796959,
0.04513493925333023,
0.027102980762720108,
0.07746928185224533,
0.06682456284761429,
-0.014537326991558075,
-0.03144098073244095,
-0.003517288016155362,
0.008226207457482815,
-0.021685170009732246,
-0.03277023136615753,
0.028291909024119377,
-0.02072209306061268,
-0.006092188414186239,
0.0048526679165661335,
-0.049394767731428146,
-0.07159653306007385,
0.01843559741973877,
-0.025277841836214066,
0.025465385988354683,
0.006887341383844614,
0.019203973934054375,
-0.061442676931619644,
-0.06204518303275108,
-0.008399571292102337,
-0.025556951761245728,
0.007890574634075165,
0.0459042452275753,
-0.04553338140249252,
-0.0701608806848526,
-0.04134036600589752,
0.050145287066698074,
-0.002172960666939616,
0.002503106603398919,
0.018260888755321503,
0.014666457660496235,
-0.008007696829736233,
-0.025453463196754456,
-0.014841967262327671,
-0.00105290487408638,
-0.050454866141080856,
0.0011405384866520762,
0.03153298422694206,
0.019755549728870392,
0.02523459866642952,
0.05791554972529411,
0.02908794954419136,
-0.03209136053919792,
-0.02218150906264782,
0.015116593800485134,
-0.05452539026737213,
-0.020071500912308693,
0.06381374597549438,
-0.05300603434443474,
-0.03358255699276924,
0.02439078502357006,
-0.022223057225346565,
0.03862127661705017,
0.020646724849939346,
0.010356813669204712,
-0.009839463979005814,
-0.001677673077210784,
-0.009474273771047592,
0.02358531765639782,
0.025928234681487083,
0.02489597350358963,
-0.04193085432052612,
-0.043798886239528656,
-0.0052296011708676815,
-0.019848423078656197,
0.00114462710916996,
0.050457652658224106,
-0.021091435104608536,
-0.018931616097688675,
-0.05927510932087898,
0.09225232154130936,
0.019640332087874413,
0.003362982999533415,
-0.0374860055744648,
-0.040344856679439545,
0.003267178777605295,
0.04810481518507004,
0.0036556252744048834,
-0.04365703836083412,
0.005125211551785469,
0.028477104380726814,
-0.023403044790029526,
0.041454751044511795,
0.039843082427978516,
0.03237152099609375,
0.038418758660554886,
0.020891379565000534,
-0.01953488402068615,
0.026774689555168152,
-0.04474761337041855,
0.0437963604927063,
-0.006402058992534876,
-0.03999212011694908,
0.048142604529857635,
0.005412390921264887,
-0.006232286337763071,
-0.018882671371102333,
0.01462235301733017,
-0.01084204576909542,
0.08147579431533813,
0.012061894871294498,
0.014618792571127415,
-0.007896693423390388,
0.031805187463760376,
0.0122281014919281,
0.02273290976881981,
0.004685630556195974,
-0.06107575073838234,
0.057839471846818924,
0.042154885828495026,
-0.04368225857615471,
0.0032274581026285887,
-0.02872447855770588,
-0.0029537775553762913,
0.008059972897171974,
-0.07627497613430023,
-0.03438911214470863,
0.007454713340848684,
0.019448814913630486,
-0.0276723001152277,
0.04720477759838104,
0.011902916245162487,
0.038742195814847946,
0.09041465818881989,
0.0831797868013382,
0.021676745265722275,
-0.015790769830346107,
0.008388192392885685,
0.0849352777004242,
-0.01677650958299637,
0.007074104622006416,
0.001763006905093789,
-0.00014944947906769812,
0.019128315150737762,
-0.008857396431267262,
0.008867161348462105,
0.0020189937204122543,
-0.012342585250735283,
0.05577808618545532,
0.05695962533354759,
0.03145512193441391,
-0.0009060411248356104,
0.009268472902476788,
0.07995607703924179,
-0.08834559470415115,
0.016058089211583138,
0.0274676326662302,
-0.017071371898055077,
0.050584398210048676,
-0.018987124785780907,
-0.021598076447844505,
0.03350768983364105,
0.011914564296603203,
-0.01487605832517147,
-0.0005454342463053763,
-0.03051861748099327,
-0.004978340119123459,
0.014606548473238945,
-0.021124497056007385,
-0.018182069063186646,
-0.0784461721777916,
-0.03188599273562431,
0.02024880424141884,
-0.06189872324466705,
0.054598525166511536,
0.031726278364658356,
-0.02155446447432041,
0.01694640889763832,
-0.05849720537662506,
-0.027973521500825882,
-0.015629872679710388,
-0.07066105306148529,
-0.005133103579282761,
-0.017562001943588257,
-0.044753119349479675,
0.024781905114650726,
0.028158029541373253,
0.056188490241765976,
0.05624916031956673,
-0.060331832617521286,
-0.02876363880932331,
-0.03289123624563217,
-0.03853254392743111,
-0.028839627280831337,
0.003991808742284775,
0.040826261043548584,
-0.007300977129489183,
-0.0032955873757600784,
0.003627962665632367,
0.023219378665089607,
0.05020148679614067,
0.06772710382938385,
-0.02795952558517456,
0.007305288687348366,
0.06727063655853271,
-0.02424433082342148,
-0.03759752959012985,
-0.017395777627825737,
-0.04728534445166588,
0.020593242719769478,
-0.019118215888738632,
0.024399861693382263,
0.0780767872929573,
-0.02657349407672882,
-0.047466155141592026,
0.010860702022910118,
0.0067390333861112595,
0.0005135929095558822,
0.04747955873608589,
0.005026734434068203,
-0.00573932658880949,
-0.005011571105569601,
-0.020904412493109703,
0.0057683950290083885,
0.015961837023496628,
0.05525542423129082,
-0.03759248927235603,
0.0007408751407638192,
-0.0539226308465004,
0.0036839598324149847,
0.027336133643984795,
-0.02548522874712944,
0.014892584644258022,
0.05216922610998154,
0.020008133724331856,
0.06382003426551819,
-0.020562512800097466,
0.013133278116583824,
-0.0012798606185242534,
-0.04311182722449303,
-0.005589050706475973,
0.037488434463739395,
0.03398852422833443,
0.03094298392534256,
-0.06132311373949051,
0.03935959190130234,
-0.029794394969940186,
-0.028699234127998352,
-0.00187298480886966,
0.0671483650803566,
-0.022367408499121666,
0.019592486321926117,
-0.014628607779741287,
-0.06518074870109558,
0.00278970948420465,
0.008478611707687378,
0.08822936564683914,
0.003964823205024004,
0.0015670765424147248,
-0.04966435208916664,
-0.010072159580886364,
0.029497681185603142,
-0.0031787038315087557,
-0.011440458707511425,
0.03635147958993912,
0.020626626908779144,
0.0032949720043689013,
-0.0157341156154871,
0.056956108659505844,
0.028120256960392,
-0.02915177121758461,
-0.0011641228338703513,
-0.08492640405893326,
0.053070273250341415,
0.009908388368785381,
0.028441743925213814,
-0.0036403900012373924,
0.02869994007050991,
-0.04058791697025299,
0.005344510078430176,
0.01853100396692753,
0.1026114895939827,
-0.011424727737903595,
0.014443593099713326,
-0.010747612453997135,
-0.017354000359773636,
0.01624022051692009,
0.01960131898522377,
0.039756909012794495,
-0.041093528270721436,
0.03664263337850571,
-0.09933944046497345,
0.03083777241408825,
-0.008591393008828163,
0.03902561590075493,
-0.041278403252363205,
0.01316432561725378,
-0.04504333436489105,
0.023688150569796562,
-0.013739155605435371,
0.010281761176884174,
0.04136323183774948,
-0.036941129714250565,
-0.044190824031829834,
0.0009296517237089574,
-0.013217655010521412,
-0.015706494450569153,
-0.029500199481844902,
-0.0287522803992033,
-0.020401649177074432,
-0.0027306764386594296,
-0.020266583189368248,
0.06984416395425797,
0.023498117923736572,
0.07466091215610504,
-0.020188426598906517,
-0.005575690884143114,
0.0689748004078865,
-0.03178279846906662,
0.012806795537471771,
0.09295406192541122,
0.004923384170979261,
0.004192807245999575,
-0.02739032730460167,
0.032818492501974106,
0.004563664551824331,
-0.02254924364387989,
-0.015270140022039413,
-0.004460602533072233,
0.04755251854658127,
-0.01793082058429718,
-0.022536898031830788,
0.04102866351604462,
-0.023712968453764915,
0.005720419809222221,
-0.031837765127420425,
0.0008787905098870397,
-0.026018235832452774,
-0.025623345747590065,
-0.02920207753777504,
-0.026750806719064713,
0.05608690530061722,
-0.04041428491473198,
0.0018612032290548086,
0.021751154214143753,
0.009130963124334812,
0.007189205847680569,
0.03928852826356888,
0.05515380948781967,
-0.008867223747074604,
0.04213590547442436,
-0.0010232847416773438,
0.034465573728084564,
-0.001902115298435092,
0.010847209021449089,
0.002733484609052539,
-0.019469574093818665,
-0.007385111413896084,
0.029708588495850563,
0.006358361337333918,
0.03215751796960831,
0.0124606192111969,
-0.046144165098667145,
0.025648022070527077,
-0.009618407115340233,
-0.05299174040555954,
0.06452053785324097,
-0.017262987792491913,
-0.01728694885969162,
-0.032620180398225784,
0.01519517507404089,
0.026770565658807755,
-0.030793197453022003,
-0.03434493765234947,
-0.07944159209728241,
0.018021082505583763,
0.0041654640808701515,
0.02298859693109989,
-0.0031446805223822594,
-0.10395050793886185,
-0.014349465258419514,
-0.04065508395433426,
-0.032411277294158936,
0.0008432980976067483,
0.027849672362208366,
0.0019501728238537908,
0.001294692512601614,
-0.010137947276234627,
-0.043515753000974655,
-0.05615675449371338,
-0.031070249155163765,
-0.04544162005186081,
-0.03177102655172348,
-0.01347524393349886,
0.009268836118280888,
0.02035565674304962,
-0.02232380583882332,
-0.020655030384659767,
-0.051620762795209885,
-0.006055332720279694,
-0.011237327009439468,
0.034116942435503006,
-0.008027389645576477,
0.004702644422650337,
-0.03741287440061569,
0.01568864844739437,
-0.02203715406358242,
0.0385885126888752,
0.021370526403188705,
-0.013127913698554039,
-0.007332504726946354,
0.0166171882301569,
-0.018122682347893715,
-0.00612506503239274,
0.032464586198329926,
-0.004969352390617132,
0.04583165794610977,
0.034764230251312256,
-0.038586702197790146,
0.01437710877507925,
-0.016724469140172005,
-0.0018836349481716752,
-0.034987255930900574,
0.016263114288449287,
-0.0015670964494347572,
0.056693896651268005,
-0.017452754080295563,
0.04805774986743927,
0.0021552443504333496,
-0.030842101201415062,
0.022012166678905487,
-0.018445758149027824,
-0.011706303805112839,
0.011705144308507442,
0.023046893998980522,
0.03389358893036842,
-0.031238514930009842,
0.03377500921487808,
-0.028987469151616096,
0.018197281286120415,
0.007692061364650726,
0.003782789222896099,
-0.0203623678535223,
0.008464036509394646,
0.041530948132276535,
-0.028091656044125557,
0.014532544650137424,
-0.0681375116109848,
0.02462645247578621,
0.006044227629899979,
0.0042979298159480095,
0.027262825518846512,
0.00554993562400341,
0.03854048624634743,
0.037224747240543365,
-0.08218090981245041,
0.011976883746683598,
-0.0550360344350338,
0.0016487848479300737,
0.04020209237933159,
0.015035227872431278,
0.05619696527719498,
-0.03845629096031189,
0.05399899184703827,
-0.008008450269699097,
0.025548601523041725,
-0.010914204642176628,
0.014590883627533913,
-0.03838161379098892,
-0.020271331071853638,
-0.03933960944414139,
-0.003779908875003457,
0.0029828331898897886,
-0.006506004370748997,
0.006566852796822786,
0.023473022505640984,
-0.047566451132297516,
0.026243003085255623,
-0.017775963991880417,
-0.06406577676534653,
-0.04191304370760918
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.