question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
|---|---|---|
<p>Suppose i have an optical lattice with particles loaded onto it, the potential due to the optical lattice is $V_{0}Cos\left(x\right)$. Assume that the particles interact with eachother through contact interaction $C*\left|\Psi\right|^{2}$ where $\Psi$ is the mean field wavefunction. what will be the effective potential.
(From sources i know the answer is $frac({V_{0}Cos\left(c\right)})({1+4C})$ but how?</p> | g4728 | [
-0.0009254302713088691,
-0.004129852633923292,
-0.003955530934035778,
-0.029298247769474983,
0.04800886660814285,
0.014353376813232899,
-0.0064784386195242405,
0.00451918737962842,
-0.020815666764974594,
0.06713104993104935,
-0.0018044546013697982,
0.0837988406419754,
-0.030651526525616646,
-0.005349457263946533,
0.007611195556819439,
0.07982781529426575,
0.07802344113588333,
0.026116102933883667,
0.012802069075405598,
0.01717694103717804,
-0.08775614947080612,
0.0025848967488855124,
-0.038358174264431,
-0.03751182183623314,
-0.004991479218006134,
0.008409211412072182,
0.03223281353712082,
0.008377996273338795,
-0.022508997470140457,
-0.00674720061942935,
0.03556926175951958,
0.014708868227899075,
0.02399829961359501,
-0.01757345348596573,
-0.044882841408252716,
0.014095443300902843,
0.036788295954465866,
-0.00032743762130849063,
-0.010964300483465195,
-0.07250630110502243,
0.009289443492889404,
-0.016857482492923737,
0.029667599126696587,
-0.015255139209330082,
0.01839773915708065,
0.015065415762364864,
-0.03798626363277435,
0.009590936824679375,
-0.002345295390114188,
-0.0169064998626709,
0.01631152257323265,
0.020023366436362267,
-0.016013987362384796,
0.03842175751924515,
0.016819145530462265,
0.06634531915187836,
0.032222945243120193,
-0.04039251431822777,
0.05477739870548248,
0.023953069001436234,
0.029480256140232086,
0.022631462663412094,
-0.00034075474832206964,
0.02054545097053051,
0.02662433683872223,
0.018269209191203117,
0.0008090237970463932,
0.04435105249285698,
0.031366150826215744,
-0.04715283215045929,
0.00008193619578378275,
0.0016010153340175748,
-0.030574403703212738,
-0.0015746988356113434,
-0.08376467972993851,
0.012004096060991287,
0.04220908507704735,
-0.0196310356259346,
-0.007710480131208897,
-0.03462624549865723,
-0.006674379575997591,
-0.10390835255384445,
-0.005931592080742121,
-0.0550171434879303,
0.02719062753021717,
-0.01674126833677292,
-0.0136808380484581,
-0.033571552485227585,
-0.08303157985210419,
-0.020783817395567894,
0.05637610703706741,
-0.034102387726306915,
0.0394744835793972,
-0.014948802068829536,
-0.003212765557691455,
0.028969181701540947,
0.018917836248874664,
0.016728390008211136,
-0.054028935730457306,
-0.054817523807287216,
-0.014448191970586777,
-0.011068427935242653,
0.0019302685977891088,
0.024598529562354088,
-0.045756906270980835,
0.002839162014424801,
0.010150120593607426,
0.011812197975814342,
0.021281644701957703,
0.009921825490891933,
-0.03679431974887848,
0.009886630810797215,
-0.004405682440847158,
-0.04122687131166458,
-0.05065985023975372,
-0.07118916511535645,
0.06815734505653381,
-0.00581290852278471,
-0.018420850858092308,
0.03261430934071541,
-0.028065938502550125,
0.0385323092341423,
0.028667548671364784,
0.0039056469686329365,
-0.02871813252568245,
0.0201726071536541,
-0.005040781572461128,
-0.008899134583771229,
0.0046668448485434055,
-0.005417698994278908,
0.01737815886735916,
0.009723732247948647,
0.014059508219361305,
-0.009148167446255684,
-0.0235114935785532,
0.003844637656584382,
-0.017521504312753677,
0.02573557198047638,
0.0060342708602547646,
-0.010912483558058739,
0.009584973566234112,
-0.06817615032196045,
0.02004939131438732,
0.026509732007980347,
-0.02216591127216816,
0.007302561774849892,
0.014055508188903332,
-0.0573837049305439,
-0.004812407307326794,
-0.026940731331706047,
0.04538079351186752,
0.07548712193965912,
0.011664365418255329,
-0.049785953015089035,
0.001606917823664844,
-0.04152723401784897,
0.007049628999084234,
-0.04464200511574745,
-0.018459411337971687,
0.022490553557872772,
0.04988298565149307,
-0.008599979802966118,
0.023229112848639488,
0.007495276629924774,
-0.04130692034959793,
-0.008972874842584133,
0.04489682614803314,
-0.06003262847661972,
0.000973051879554987,
-0.02959362417459488,
-0.013551458716392517,
-0.0022019767202436924,
0.01899736374616623,
0.03770643100142479,
-0.02154918946325779,
0.03964196890592575,
-0.0978536307811737,
-0.016204172745347023,
0.06824100017547607,
0.08602386713027954,
0.012594986706972122,
-0.11905072629451752,
0.06111501529812813,
-0.037807807326316833,
-0.012681128457188606,
-0.018658306449651718,
0.013147921301424503,
0.006362938322126865,
-0.03278053179383278,
-0.0012911712983623147,
-0.050379373133182526,
0.01778545044362545,
0.037549324333667755,
-0.003903041360899806,
-0.017838723957538605,
0.042698901146650314,
0.04622366279363632,
-0.061572905629873276,
-0.004475025925785303,
-0.044449497014284134,
-0.064296193420887,
0.044466547667980194,
0.050978951156139374,
0.008311460725963116,
0.003862834768369794,
0.032162513583898544,
-0.013141060248017311,
0.019427550956606865,
-0.002415744587779045,
0.0172929335385561,
-0.04127836599946022,
-0.05750131607055664,
-0.0031102581415325403,
0.02730008214712143,
-0.03768685460090637,
-0.038044340908527374,
-0.03149351850152016,
0.023560646921396255,
-0.041402265429496765,
0.028469741344451904,
-0.04672978073358536,
0.009201554581522942,
0.04811834171414375,
-0.0019405231578275561,
-0.04017581418156624,
0.02741648070514202,
0.005338598042726517,
0.05805302411317825,
0.036570899188518524,
0.03893040493130684,
-0.0630921944975853,
0.05130033195018768,
0.030269218608736992,
-0.05877456068992615,
0.004646035376936197,
0.02119230292737484,
-0.032123830169439316,
-0.010381567291915417,
0.013685493730008602,
0.015759756788611412,
0.03074527345597744,
-0.09164154529571533,
-0.043617699295282364,
-0.047914110124111176,
0.02881830371916294,
0.034111566841602325,
0.01981494016945362,
0.05062592774629593,
-0.0002958871773444116,
-0.0005962585564702749,
0.03485707938671112,
0.03805765509605408,
-0.021789705380797386,
-0.004457216709852219,
-0.003464924404397607,
0.010847394354641438,
-0.06095895171165466,
0.03690696880221367,
-0.044953640550374985,
0.005918453447520733,
-0.03943294659256935,
-0.032649289816617966,
-0.018045224249362946,
-0.005352152045816183,
0.0014802201185375452,
0.04802466556429863,
-0.0061857388354837894,
-0.008505895733833313,
-0.029375841841101646,
0.023154407739639282,
0.0631454810500145,
0.024682974442839622,
0.029234346002340317,
0.015490557998418808,
0.027473557740449905,
-0.01685943827033043,
0.018098127096891403,
-0.020145952701568604,
0.041537102311849594,
-0.03060397505760193,
-0.008083921857178211,
0.024626603350043297,
-0.022839531302452087,
0.007804287597537041,
0.015316159464418888,
-0.08737964928150177,
0.02935902029275894,
0.018542973324656487,
0.03704362362623215,
-0.046529415994882584,
0.03516458347439766,
0.04318768158555031,
0.01788238063454628,
0.035225313156843185,
0.020809253677725792,
-0.03243717923760414,
0.06711035966873169,
-0.02040589042007923,
-0.02849266678094864,
0.05988773703575134,
-0.005776878446340561,
0.001111880992539227,
-0.054999034851789474,
-0.03850175067782402,
-0.0037288793828338385,
-0.014993589371442795,
-0.00624859519302845,
-0.0382954441010952,
-0.024216944351792336,
0.00904536247253418,
0.020608318969607353,
0.08257047832012177,
0.047309983521699905,
-0.01764840818941593,
-0.05692748725414276,
0.00479301530867815,
0.02689988724887371,
-0.030297143384814262,
-0.047872576862573624,
-0.02373788133263588,
0.043314334005117416,
0.026711318641901016,
0.05015956610441208,
-0.047397296875715256,
0.0011450746096670628,
0.02239537611603737,
-0.021101975813508034,
-0.008504127152264118,
-0.03489385545253754,
-0.004382445476949215,
0.004497496876865625,
0.044784508645534515,
0.03820314258337021,
-0.05067512020468712,
-0.010703817941248417,
-0.03660564497113228,
-0.020230069756507874,
0.0471731498837471,
0.04285923391580582,
0.03852153569459915,
-0.06480139493942261,
-0.009556249715387821,
-0.07540388405323029,
-0.027007604017853737,
-0.03633340075612068,
-0.01059064082801342,
-0.01295414101332426,
0.07677946239709854,
0.013878715224564075,
-0.06788341701030731,
-0.04205836355686188,
-0.0369323305785656,
-0.017953164875507355,
-0.002754679648205638,
0.04562344402074814,
-0.022526055574417114,
0.04206205531954765,
0.060920558869838715,
0.02830738201737404,
0.007227486930787563,
-0.010730136185884476,
-0.04114421084523201,
0.026129448786377907,
0.017824098467826843,
-0.016411613672971725,
-0.01790637895464897,
-0.060918018221855164,
0.03944516181945801,
0.022378157824277878,
0.0077503216452896595,
-0.03722009062767029,
-0.04899512231349945,
0.01083997543901205,
-0.01978776790201664,
-0.024829285219311714,
0.0043693967163562775,
-0.04632208123803139,
-0.07848089188337326,
-0.0016783064929768443,
-0.014072897844016552,
-0.04761601239442825,
0.027393344789743423,
0.035179831087589264,
-0.00973581150174141,
0.03174266591668129,
0.03936353325843811,
-0.03534319996833801,
-0.01835973933339119,
-0.012056817300617695,
0.026204975321888924,
0.0088057741522789,
-0.04523785784840584,
-0.04531501233577728,
0.042899373918771744,
0.013323585502803326,
0.004740158095955849,
0.019595682621002197,
-0.01529322937130928,
0.01272563636302948,
-0.0069696116261184216,
0.04136598855257034,
-0.05831523612141609,
-0.003285891143605113,
-0.029730435460805893,
-0.042603421956300735,
0.03667202219367027,
0.05255201831459999,
-0.06602010875940323,
-0.0245458222925663,
0.010724660009145737,
-0.0016975875478237867,
-0.009726444259285927,
0.038348663598299026,
-0.05148348957300186,
0.0332166887819767,
0.01652052067220211,
0.0462900809943676,
0.005856309551745653,
0.04531676694750786,
0.022737160325050354,
0.0036854238715022802,
-0.05006255581974983,
0.05994905158877373,
-0.01764557510614395,
-0.028802521526813507,
0.08620751649141312,
0.004307877738028765,
-0.020899362862110138,
-0.020249314606189728,
0.0013412570115178823,
0.026867197826504707,
0.07589808106422424,
-0.022194556891918182,
0.03356737270951271,
-0.04442401975393295,
0.0369877852499485,
-0.020042328163981438,
-0.061847295612096786,
0.04837045073509216,
0.11137958616018295,
0.014369416981935501,
0.011094056069850922,
-0.017855428159236908,
-0.06748659163713455,
0.04455718770623207,
0.06762222200632095,
-0.056594450026750565,
-0.07885599881410599,
-0.04323204606771469,
-0.050881776958703995,
0.04273775592446327,
-0.046232920140028,
-0.04811955243349075,
-0.04159640520811081,
0.04252839460968971,
0.02054976299405098,
-0.026266230270266533,
0.04356459528207779,
-0.013629231601953506,
-0.04079950228333473,
0.02194509282708168,
-0.006869280245155096,
-0.0023623579181730747,
-0.04108951985836029,
0.049998342990875244,
-0.005547957960516214,
-0.0072143785655498505,
-0.006035574246197939,
-0.04424259066581726,
0.0053986795246601105,
-0.011984629556536674,
-0.032780133187770844,
0.042934343218803406,
-0.00035915779881179333,
-0.024753320962190628,
-0.01978703774511814,
-0.012157388031482697,
0.013669786043465137,
0.04974748194217682,
0.0047448319382965565,
0.0019400165183469653,
0.011842476204037666,
0.037232160568237305,
0.022210661321878433,
-0.02734401263296604,
-0.012397604994475842,
-0.005269358400255442,
0.06958014518022537,
-0.048654209822416306,
-0.018276209011673927,
0.0034238891676068306,
0.0045796833001077175,
-0.02909989096224308,
-0.02109113335609436,
0.012600141577422619,
0.04614948853850365,
0.007213223725557327,
-0.0072275507263839245,
0.035198986530303955,
0.04212038964033127,
0.004194022621959448,
-0.038196343928575516,
-0.06200527027249336,
0.03913222253322601,
-0.10194797813892365,
0.042752210050821304,
0.024873461574316025,
-0.048487525433301926,
-0.0002866963332053274,
-0.02255645953118801,
-0.026643991470336914,
-0.00709053548052907,
0.061478812247514725,
0.03434888646006584,
-0.013089518062770367,
-0.004367234650999308,
-0.02462603710591793,
-0.04490314796566963,
-0.022999560460448265,
-0.037761639803647995,
0.018109695985913277,
0.034218061715364456,
-0.05778534710407257,
-0.00659868773072958,
0.01917797140777111,
-0.05712683126330376,
-0.01650528982281685,
-0.037697892636060715,
0.017341388389468193,
0.024275129660964012,
-0.009706340730190277,
0.02783316560089588,
-0.014695603400468826,
0.026709841564297676,
0.052098777145147324,
-0.04610494524240494,
-0.008028082549571991,
0.016127238050103188,
0.014066256582736969,
-0.019614042714238167,
0.010417978279292583,
-0.04941347613930702,
0.016698436811566353,
0.027193544432520866,
0.011542098596692085,
0.04760352522134781,
0.01360810361802578,
0.033773235976696014,
0.05401207506656647,
-0.014232155866920948,
-0.031455084681510925,
0.01640717312693596,
-0.01863519847393036,
-0.016390159726142883,
0.047060541808605194,
0.026551280170679092,
-0.02487524412572384,
-0.01215559896081686,
0.03052324242889881,
-0.05190198868513107,
0.07990573346614838,
-0.02450738474726677,
-0.03028888814151287,
-0.052028246223926544,
-0.020253032445907593,
-0.006700707133859396,
-0.0699692815542221,
-0.0024235325399786234,
0.015224229544401169,
-0.0246149692684412,
-0.016641536727547646,
0.028513234108686447,
-0.005193446297198534,
-0.019208839163184166,
0.027077801525592804,
0.061710283160209656,
0.003406437812373042,
-0.017275895923376083,
-0.0036018092650920153,
0.024785634130239487,
-0.0432809554040432,
0.0316278412938118,
0.04866120219230652,
-0.02080990932881832,
-0.008831992745399475,
0.018170718103647232,
-0.010901035740971565,
-0.055646996945142746,
0.043861981481313705,
-0.06062799692153931,
-0.029220914468169212,
-0.04357244446873665,
0.01727881096303463,
0.01699374057352543,
0.022143961861729622,
-0.07200159877538681,
-0.037329256534576416,
0.000592424301430583,
0.0038623244035989046,
0.10486308485269547,
0.022411461919546127,
-0.014096708036959171,
0.024468103423714638,
0.01724330149590969,
0.05845601111650467,
-0.025853745639324188,
-0.08919789642095566,
-0.05378453806042671,
-0.032539624720811844,
0.004103843122720718,
-0.03903947398066521,
0.00736746471375227,
0.02210751548409462,
0.03513726219534874,
0.06729370355606079,
-0.019774610176682472,
-0.009266777895390987,
0.047555163502693176,
-0.022863930091261864,
0.002070682356134057,
0.016741525381803513,
-0.013788171112537384,
0.0019446250516921282,
-0.08974098414182663,
0.03434927761554718,
-0.01867220550775528,
-0.03359851986169815,
-0.06926066428422928,
0.03913521394133568,
-0.017740830779075623,
0.022502664476633072,
0.0006064799381420016,
0.019839154556393623,
0.021745270118117332,
-0.03559890389442444,
0.061930060386657715,
-0.02182176150381565,
0.02505478449165821,
0.01930098421871662,
0.002113430993631482,
0.005979826208204031,
0.051245611160993576,
0.07244561612606049,
0.009749053977429867,
0.030203163623809814,
-0.00016256172966677696,
0.03736329451203346,
0.022811535745859146,
-0.023097964003682137,
0.037969231605529785,
0.00021888513583689928,
-0.04012810066342354,
0.05157284811139107,
0.018309246748685837,
-0.03189796581864357,
-0.03434354439377785,
0.006428807508200407,
0.06407953053712845,
-0.03310956433415413,
-0.02813638001680374,
-0.04949086531996727,
-0.04789804294705391,
-0.043598901480436325,
-0.0017376350006088614,
0.0023441084194928408,
0.03623214364051819,
0.03889019414782524,
-0.02704475447535515,
-0.05873856320977211,
-0.07057259231805801,
-0.07558908313512802,
-0.0483456626534462,
-0.0746745839715004,
0.010032729245722294,
0.01709449104964733,
-0.04246871545910835,
0.003568547312170267,
0.08062896132469177,
-0.022869467735290527,
-0.01880001649260521,
0.008156993426382542,
-0.016066623851656914,
0.028169605880975723,
0.003980010747909546,
0.018036192283034325,
0.026795556768774986,
0.029721762984991074,
-0.013150906190276146,
-0.027467500418424606,
0.004478436429053545,
0.01808316633105278,
0.021145811304450035,
-0.017067916691303253,
0.001051330822519958,
-0.030850820243358612,
0.012765292078256607,
0.04152406379580498,
0.05758624151349068,
0.06140752509236336,
0.0620168000459671,
-0.007254111580550671,
0.0034813806414604187,
0.02915036492049694,
0.017133276909589767,
0.022713515907526016,
-0.055389780551195145,
-0.02971295453608036,
0.0375208742916584,
0.0051666488870978355,
-0.01488177478313446,
0.058018218725919724,
0.01820346713066101,
0.027831459417939186,
0.03725431486964226,
0.012289940379559994,
-0.0025393213145434856,
0.00577832106500864,
0.0836748257279396,
0.01823299378156662,
0.03518814966082573,
-0.011603113263845444,
0.024480989202857018,
-0.037624794989824295,
-0.035074226558208466,
-0.025297928601503372,
0.002489448292180896,
-0.05041512846946716,
-0.01847919635474682,
0.02098218724131584,
-0.02693493478000164,
0.011415674351155758,
0.03488001599907875,
-0.055267881602048874,
0.006859207060188055,
-0.011072002351284027,
0.025664323940873146,
-0.006826614961028099,
0.015110361389815807,
-0.01421270426362753,
0.03887748345732689,
-0.022358592599630356,
-0.08026774227619171,
0.026337234303355217,
-0.04784691333770752,
-0.01557429414242506,
0.028442634269595146,
-0.04174213856458664,
0.02614699676632881,
0.05026986449956894,
0.004152500070631504,
-0.032379332929849625,
0.04724109172821045,
0.0032808948308229446,
0.02732011117041111,
0.02382744662463665,
-0.07485468685626984,
-0.06823846697807312,
0.05506078898906708,
0.030041983351111412,
0.04413730651140213,
0.036608949303627014,
0.03931039944291115,
0.006952914409339428,
0.04953346773982048,
0.02730206772685051,
0.012236182577908039,
0.03560687229037285,
0.03433924540877342
] |
<p>I'm doing a basic realtime simulation of two bodies, but the orbits are unstable for some reason.</p>
<p>This code is run at every timestep:</p>
<pre><code>rsq = (a.x - b.x)*(a.x - b.x) + (a.y - b.y)*(a.y - b.y)
a.vx = a.vx - (a.x - b.x) * g * b.m * (1/rsq) * dt
a.vy = a.vy - (a.y - b.y) * g * b.m * (1/rsq) * dt
b.vx = b.vx - (b.x - a.x) * g * a.m * (1/rsq) * dt
b.vy = b.vy - (b.y - a.y) * g * a.m * (1/rsq) * dt
a.x = a.x + a.vx * dt
a.y = a.y + a.vy * dt
b.x = b.x + b.vx * dt
b.y = b.y + b.vy * dt
</code></pre>
<p>Where m is mass, x&y are position, vx&vy are velocity, g is the gravitational constant, and dt is the elapsed time.</p>
<p>My bodies orbit eachother but the orbit is unstable and acts as though R is to an exponent other than 2.</p>
<p>Have I missed something in my understanding of this problem or somewhere in my code?</p> | g4729 | [
-0.00916493684053421,
0.03788251057267189,
-0.012282906100153923,
-0.011507892049849033,
0.0716380923986435,
0.03861798346042633,
-0.012065540999174118,
-0.011807951144874096,
-0.03577587381005287,
0.014407003298401833,
-0.006038758438080549,
0.06592340022325516,
0.04100828990340233,
0.02050042524933815,
-0.027787070721387863,
0.0133185014128685,
0.05122743546962738,
0.00412643002346158,
0.031317468732595444,
0.032254621386528015,
0.01028602197766304,
0.011860538274049759,
0.005429752636700869,
0.00551357539370656,
0.04526324197649956,
0.01774974726140499,
0.062425240874290466,
-0.0016902554780244827,
-0.06281756609678268,
0.01666998490691185,
0.020754413679242134,
0.0255200807005167,
0.04054785892367363,
-0.05896792188286781,
-0.017983540892601013,
0.002305768895894289,
0.05710437148809433,
-0.029217299073934555,
-0.036994293332099915,
-0.004404615610837936,
0.029784202575683594,
-0.06542225182056427,
-0.004683322738856077,
0.04548128694295883,
0.03934045881032944,
-0.048841025680303574,
0.008537414483726025,
-0.032588861882686615,
-0.0327778086066246,
-0.015714243054389954,
0.01936899498105049,
0.08360302448272705,
0.013033607043325901,
-0.09459905326366425,
-0.006976159289479256,
0.0450131930410862,
-0.03649357333779335,
-0.004893424455076456,
-0.03907319903373718,
0.03909453749656677,
0.012314965017139912,
-0.015177933499217033,
0.034052424132823944,
-0.016258513554930687,
0.043182261288166046,
-0.023958668112754822,
-0.04095131531357765,
0.0043170638382434845,
0.0013738750712946057,
0.034685488790273666,
-0.02017487958073616,
-0.006974338088184595,
-0.0113483602181077,
-0.04619365558028221,
-0.050689928233623505,
-0.015343195758759975,
0.06135359779000282,
-0.008548128418624401,
-0.024603962898254395,
-0.00475511746481061,
-0.01056615449488163,
0.059308603405952454,
0.04463231936097145,
0.01561765093356371,
-0.06365106254816055,
-0.0029566867742687464,
0.01786232367157936,
0.020201580598950386,
-0.05194732919335365,
0.005736404564231634,
0.0013136707711964846,
-0.04524490237236023,
-0.014302280731499195,
0.05657876282930374,
0.013580212369561195,
-0.02964557521045208,
-0.06692694872617722,
0.10569074749946594,
-0.0016074009472504258,
-0.003257397562265396,
0.036484550684690475,
0.03436599299311638,
0.014165390282869339,
0.029144885018467903,
-0.03799246624112129,
-0.03364712744951248,
0.03536665439605713,
0.008377375081181526,
-0.010584380477666855,
-0.05030296742916107,
-0.04857645183801651,
-0.0030356082133948803,
-0.04470205679535866,
-0.04225260764360428,
-0.004512160085141659,
0.004897479899227619,
0.02410280704498291,
-0.05491606891155243,
0.005301528610289097,
-0.01654175855219364,
-0.0010951466392725706,
0.0018358799861744046,
-0.04353461414575577,
0.03383650630712509,
-0.01609712466597557,
-0.005655697081238031,
0.009100483730435371,
0.051932383328676224,
0.07777950912714005,
0.02388804219663143,
-0.023692764341831207,
0.024423768743872643,
-0.01929890364408493,
0.0021379466634243727,
-0.04172591120004654,
0.021559707820415497,
0.02542685903608799,
0.0058194734156131744,
-0.061232998967170715,
-0.0031778858974575996,
-0.00020650635997299105,
-0.055393122136592865,
0.01392837893217802,
-0.07626277208328247,
-0.06198316439986229,
0.04239852726459503,
-0.012635191902518272,
0.009758676402270794,
0.0013391561806201935,
0.028657399117946625,
-0.00202012131921947,
0.108475461602211,
-0.012374768033623695,
-0.03461233153939247,
0.008106089197099209,
0.02925954945385456,
0.03181646019220352,
0.0034392669331282377,
-0.03825997933745384,
0.009027461521327496,
0.026900846511125565,
0.01252856757491827,
-0.006207604426890612,
0.014413317665457726,
-0.07515468448400497,
0.09876970946788788,
-0.03891174867749214,
-0.02046254649758339,
-0.01681760884821415,
0.008686628192663193,
0.003975586965680122,
-0.10182403028011322,
0.005043999291956425,
0.08586633950471878,
-0.012411057017743587,
0.024379806593060493,
0.025663593783974648,
0.004711149726063013,
0.0416874885559082,
0.0054450067691504955,
0.051160722970962524,
0.03663042187690735,
-0.026850467547774315,
-0.03437291830778122,
0.009516997262835503,
0.011900444515049458,
-0.009400593116879463,
0.054190631955862045,
-0.1123432070016861,
-0.0370490700006485,
-0.01031907182186842,
0.0011089277686551213,
0.0018165811197832227,
0.00027573914849199355,
0.06212040036916733,
-0.02387923002243042,
0.009842977859079838,
-0.041031286120414734,
0.023361941799521446,
0.03681434690952301,
0.02542787231504917,
-0.020792001858353615,
0.003584258956834674,
0.02356654405593872,
-0.019365612417459488,
-0.026499859988689423,
-0.05879683792591095,
0.01884700357913971,
-0.0464673712849617,
-0.020872974768280983,
0.04719119891524315,
0.0004946374101564288,
0.023447221145033836,
0.010540512390434742,
0.003917050547897816,
-0.04278683289885521,
0.021189354360103607,
-0.0015990197425708175,
-0.014285619370639324,
0.02321702428162098,
-0.0070724934339523315,
-0.029252909123897552,
0.012467315420508385,
0.03867142274975777,
-0.02816127985715866,
-0.06736201047897339,
-0.029619883745908737,
0.02794872410595417,
0.020944509655237198,
-0.007533824536949396,
-0.03653055801987648,
0.017606530338525772,
0.01136623602360487,
0.050476640462875366,
0.019313935190439224,
-0.03624821826815605,
-0.0031378709245473146,
0.010523693636059761,
0.03520163893699646,
0.025543484836816788,
0.018007230013608932,
-0.008601710200309753,
-0.0653609111905098,
0.013143781572580338,
0.07210957258939743,
-0.0766775906085968,
0.07985780388116837,
0.014828934334218502,
-0.03581097349524498,
-0.005631048232316971,
-0.02611704356968403,
-0.015206522308290005,
-0.086031474173069,
-0.0014427328715100884,
-0.05044986680150032,
-0.01849592663347721,
-0.04128429666161537,
-0.016539303585886955,
-0.06623345613479614,
0.00595242902636528,
0.013056429103016853,
0.017540521919727325,
0.017679838463664055,
0.009038037620484829,
-0.04453423246741295,
0.001993493875488639,
0.024874676018953323,
-0.04675361141562462,
-0.012721117585897446,
-0.031836140900850296,
0.014363197609782219,
0.01444395910948515,
0.018096258863806725,
0.04696454852819443,
-0.06182969734072685,
0.048297908157110214,
0.0011226908536627889,
-0.06518498063087463,
0.00536967720836401,
0.022513551637530327,
0.009542603977024555,
-0.054656218737363815,
-0.033344268798828125,
-0.027312884107232094,
0.036963123828172684,
0.005522942636162043,
-0.0011310765985399485,
0.08541788160800934,
0.011031098663806915,
-0.03587164729833603,
-0.01004207506775856,
0.029697783291339874,
-0.0025665860157459974,
0.05275922641158104,
-0.032719869166612625,
0.001576005481183529,
-0.0354570597410202,
-0.06435779482126236,
0.001744038425385952,
0.00534052075818181,
0.014634167775511742,
0.03412185609340668,
0.06370634585618973,
0.020047785714268684,
0.01390495989471674,
-0.010146409273147583,
-0.01827731356024742,
-0.014089539647102356,
0.00842061173170805,
-0.026123737916350365,
0.04650590568780899,
-0.0019577492494136095,
-0.07854664325714111,
0.029639292508363724,
0.0014865100383758545,
0.07246945053339005,
-0.04876556247472763,
-0.01471456978470087,
0.03037249855697155,
-0.06138494238257408,
-0.035451821982860565,
-0.014640556648373604,
-0.01927810348570347,
0.01126275584101677,
0.03633337467908859,
0.023517267778515816,
-0.0032434100285172462,
-0.03933127224445343,
-0.04518522322177887,
0.002744153141975403,
-0.012769334949553013,
-0.004409435670822859,
0.05113048478960991,
-0.01607769913971424,
-0.00434315437451005,
-0.017866861075162888,
0.044336967170238495,
-0.007146112155169249,
0.01038377359509468,
0.010897701606154442,
-0.006755712907761335,
-0.028656506910920143,
0.008155357092618942,
-0.006071342155337334,
0.01179724745452404,
0.013034923002123833,
0.04749646037817001,
-0.011487309820950031,
-0.004495634231716394,
-0.0636252760887146,
0.04098426178097725,
-0.007173990365117788,
0.06438760459423065,
-0.04574768617749214,
-0.04219459369778633,
0.01966802403330803,
-0.005428658798336983,
-0.03562484681606293,
-0.025320401415228844,
0.009995374828577042,
-0.025716222822666168,
0.008185448125004768,
-0.091739222407341,
0.08305732160806656,
0.04504035413265228,
-0.003967245575040579,
-0.04250479117035866,
0.05683159455657005,
0.033511869609355927,
-0.038194622844457626,
-0.004360455088317394,
0.0023222360759973526,
0.004357681144028902,
-0.03869828209280968,
0.06777014583349228,
-0.041285447776317596,
0.024512017145752907,
0.016886016353964806,
0.03991542011499405,
0.07085049152374268,
0.06724772602319717,
-0.03495384752750397,
-0.016999278217554092,
-0.0008310182602144778,
0.03170602396130562,
0.07268715649843216,
-0.02026735246181488,
-0.035111021250486374,
0.04697275906801224,
-0.025040600448846817,
0.03264123573899269,
-0.05600550025701523,
0.03923340141773224,
0.012184372171759605,
0.05684876814484596,
-0.009181036613881588,
-0.0055207060649991035,
0.04434730112552643,
0.03648211434483528,
0.0007882147911004722,
-0.03448479250073433,
0.0052078962326049805,
-0.0395490787923336,
-0.04315759986639023,
-0.07954507321119308,
0.014492151327431202,
-0.022986343130469322,
-0.01587001606822014,
-0.03195309266448021,
0.04517926275730133,
0.031466588377952576,
0.0065592131577432156,
0.01808583177626133,
-0.04205719009041786,
0.01912670210003853,
0.051251672208309174,
0.020494775846600533,
0.03660331666469574,
0.01817268133163452,
0.03792379051446915,
-0.041594088077545166,
0.10514182597398758,
0.04696602374315262,
-0.06198960542678833,
0.016268327832221985,
0.041389934718608856,
0.039643242955207825,
-0.008545566350221634,
0.05085039883852005,
0.024595100432634354,
0.0028323624283075333,
0.04423026740550995,
0.012565850280225277,
0.003938603214919567,
-0.048661038279533386,
0.07410510629415512,
-0.018148595467209816,
-0.006680648308247328,
0.01494916807860136,
0.04239726439118385,
0.04311036691069603,
-0.020756617188453674,
0.0012754806084558368,
-0.018611134961247444,
0.005626191385090351,
0.053935665637254715,
-0.03541175648570061,
-0.04573138803243637,
0.021958479657769203,
-0.03634476289153099,
-0.039063770323991776,
0.013852770440280437,
0.07904327660799026,
0.009471099823713303,
-0.010157870128750801,
0.007285523694008589,
0.015206009149551392,
0.015803257003426552,
-0.006913687568157911,
0.016802122816443443,
0.02356291562318802,
-0.021010417491197586,
-0.021516796201467514,
0.006628310773521662,
-0.013562756590545177,
-0.025912422686815262,
-0.034838590770959854,
-0.005199565552175045,
0.035644132643938065,
-0.03747391328215599,
0.0352875255048275,
0.003316968446597457,
-0.026797112077474594,
0.014462629333138466,
0.032225385308265686,
0.02936670556664467,
-0.003246136475354433,
0.0036850208416581154,
0.06268437206745148,
-0.009452628903090954,
-0.05999496951699257,
0.025283746421337128,
0.010535907000303268,
0.04066813364624977,
-0.025391770526766777,
-0.008861234411597252,
0.004478896036744118,
-0.016617409884929657,
0.09144914895296097,
0.03504514694213867,
0.027537502348423004,
-0.04516451805830002,
0.049827948212623596,
-0.026901932433247566,
-0.0015788086457177997,
0.004629052244126797,
0.0029955559875816107,
-0.01890864223241806,
0.012201691046357155,
-0.012963888235390186,
-0.05222634971141815,
-0.03990554437041283,
0.001760551007464528,
-0.023202983662486076,
0.03164044767618179,
0.07319329679012299,
0.03135707229375839,
-0.037714049220085144,
-0.03215089440345764,
-0.0316058024764061,
-0.00036574876867234707,
0.036847442388534546,
0.05588306859135628,
0.044179726392030716,
-0.03829944133758545,
-0.07610557973384857,
0.05011243745684624,
-0.045925021171569824,
-0.05281950533390045,
-0.057282235473394394,
0.07540075480937958,
-0.0022348102647811174,
-0.020737936720252037,
0.0018883488373830914,
0.008146821521222591,
0.05479573458433151,
-0.0029356060549616814,
-0.046154703944921494,
-0.009028440341353416,
0.03100547567009926,
-0.018913963809609413,
-0.041494354605674744,
-0.029905598610639572,
-0.04655344411730766,
-0.03843431547284126,
-0.04980824142694473,
0.012426547706127167,
-0.02095385082066059,
0.016927659511566162,
-0.06730986386537552,
-0.003088098717853427,
0.017031321302056313,
-0.04221265763044357,
0.031951673328876495,
-0.07537443190813065,
-0.03319220617413521,
-0.07038194686174393,
-0.0017713119741529226,
0.041070036590099335,
-0.06371142715215683,
0.042287636548280716,
0.04103405028581619,
-0.011631693691015244,
0.014422310516238213,
-0.017047174274921417,
0.06659126281738281,
-0.047534290701150894,
-0.015967994928359985,
-0.04643755406141281,
-0.002067958004772663,
0.017138812690973282,
-0.029616402462124825,
0.01834099367260933,
0.03231057524681091,
0.03781941905617714,
-0.03215615823864937,
-0.02658895030617714,
0.011793957091867924,
0.00446708220988512,
0.02570829540491104,
-0.018143022432923317,
-0.00009543326450511813,
-0.04841786250472069,
0.004210130777209997,
0.010407178662717342,
0.0508091077208519,
-0.051321934908628464,
-0.03282001242041588,
0.028369197621941566,
-0.04487117752432823,
-0.00012883033195976168,
0.022098984569311142,
-0.01954169012606144,
0.012025712989270687,
-0.03561360388994217,
0.04311060905456543,
-0.03528850898146629,
-0.03842419758439064,
0.016249127686023712,
-0.009038906544446945,
-0.06258533149957657,
0.02047388069331646,
-0.03644715994596481,
-0.0348297581076622,
-0.0321173220872879,
0.039569832384586334,
-0.05501381307840347,
0.02266649156808853,
-0.03224680945277214,
0.006554152350872755,
-0.00923791155219078,
0.003670122940093279,
0.05507047846913338,
0.01742972806096077,
-0.031120166182518005,
-0.025122420862317085,
-0.06772328168153763,
0.04348967596888542,
0.012541383504867554,
0.06303351372480392,
0.024911966174840927,
-0.019963335245847702,
-0.006991564761847258,
0.03306622430682182,
-0.008266553282737732,
-0.024469144642353058,
0.02565774880349636,
0.04198157787322998,
-0.03644470125436783,
-0.008704396896064281,
0.04548872262239456,
-0.016049453988671303,
-0.005575084593147039,
0.009408448822796345,
0.023539654910564423,
-0.0154212461784482,
-0.04615240544080734,
-0.023514799773693085,
0.036775197833776474,
-0.04608737677335739,
0.008301733061671257,
-0.018741589039564133,
-0.06212252378463745,
0.05614420399069786,
0.0264767874032259,
0.022254083305597305,
-0.06982705742120743,
0.08327079564332962,
-0.010882251895964146,
0.044449444860219955,
0.04700762405991554,
0.01546233519911766,
-0.00130549690220505,
0.005255802534520626,
-0.03662283346056938,
-0.0215288233011961,
0.07434029877185822,
0.04244888946413994,
0.0064471266232430935,
0.05267352610826492,
0.02933591417968273,
0.007647193502634764,
-0.04254273697733879,
-0.010762096382677555,
0.0124557139351964,
0.008353149518370628,
-0.007809057366102934,
0.016019219532608986,
-0.01735098846256733,
-0.06454344838857651,
-0.030514834448695183,
0.02242736704647541,
-0.006130165886133909,
0.04205173999071121,
0.05674067884683609,
-0.0003648634592536837,
0.00834527239203453,
0.01068586390465498,
0.021188002079725266,
-0.006269341334700584,
0.01179040689021349,
-0.002930224873125553,
-0.022261863574385643,
0.023745309561491013,
0.013037987053394318,
0.015313267707824707,
0.01947309449315071,
-0.008202613331377506,
-0.02393004111945629,
0.008503968827426434,
0.019368736073374748,
0.002450221450999379,
-0.000963828235398978,
0.05117880925536156,
-0.004143093712627888,
0.0811353400349617,
-0.01792074739933014,
-0.00871069822460413,
-0.02930651418864727,
0.03186316043138504,
-0.007892340421676636,
0.1302792727947235,
0.005295653827488422,
0.020054461434483528,
-0.038382500410079956,
-0.033227864652872086,
-0.05649144574999809,
0.023769037798047066,
0.059366047382354736,
-0.006287874188274145,
0.01687438040971756,
-0.05746438354253769,
0.07500297576189041,
0.04626316577196121,
-0.016758596524596214,
0.0010374143021181226,
-0.017485573887825012,
-0.008074220269918442,
-0.00045817039790563285,
0.003217363962903619,
0.001435353304259479,
0.0053664338774979115,
-0.011795456521213055,
-0.08346486836671829,
-0.039438776671886444,
-0.016535818576812744,
-0.010886911302804947,
0.016927437856793404,
-0.02440248243510723,
-0.0035468395799398422,
-0.04946190118789673,
-0.05356307327747345,
-0.024031613022089005,
-0.06779352575540543,
0.013683217577636242,
-0.0649806335568428,
0.010628506541252136,
-0.05590059608221054,
-0.013854538090527058,
-0.04124071076512337,
-0.049569837749004364,
-0.009701492264866829,
-0.05840371176600456,
0.018660956993699074,
0.02225734293460846,
0.016467804089188576,
-0.034929271787405014,
-0.06016938388347626,
-0.02471690997481346,
0.005880396813154221,
0.009497265331447124,
-0.08455364406108856,
-0.007464824244379997,
0.03352377191185951,
0.00978805124759674,
0.009957574307918549,
0.008232173509895802,
0.033887919038534164,
0.045513030141592026,
-0.06220530346035957,
0.016255253925919533,
0.04757741838693619,
-0.07748346030712128,
0.011443554423749447,
-0.0024433243088424206,
0.005222578998655081,
-0.007846202701330185,
-0.007887515239417553,
-0.01056638639420271,
0.0202214065939188,
-0.01969844102859497,
-0.017363201826810837,
-0.022652262821793556,
-0.011173725128173828,
-0.014415094628930092,
0.013873700983822346,
-0.00803313497453928,
0.0018751024035736918
] |
<p>I found the following question on an standardized test, and was debating with some friends what the answer would be:</p>
<p>A car of mass <strong>M</strong> is travelling with a constant velocity through a plane in which friction is non-existent. An object of mass <strong>m</strong> (<code>m = M/3)</code> that is falling perpendicularly to the car lands inside of it. How will the velocity of the car be affected?</p>
<p>This illustration can help explain the problem.</p>
<p><img src="http://i.stack.imgur.com/ZYLtp.jpg" alt="Problem Illustration"></p>
<p>My initial thought was that the velocity would be the same, given that friction is non-existent and that the momentum of the falling object is perpendicular to that of the car. However, some friends suggested that, since the mass of the car increases, the velocity should decrease.</p> | g4730 | [
0.06232874095439911,
0.014169028028845787,
0.02026863768696785,
-0.0008649836527183652,
0.05941518396139145,
0.05619129538536072,
0.02222484163939953,
0.04398561641573906,
-0.07249264419078827,
-0.05051502212882042,
-0.00376938097178936,
-0.0649695172905922,
0.0010014217114076018,
0.019800307229161263,
0.003023825353011489,
0.03313905745744705,
0.039239175617694855,
-0.026492372155189514,
0.019360702484846115,
0.007061027456074953,
-0.036222830414772034,
0.03845979645848274,
-0.008238266222178936,
0.02966909296810627,
0.018628042191267014,
-0.057058680802583694,
-0.01087434682995081,
-0.038123343139886856,
0.012839434668421745,
-0.01185681577771902,
0.06003129109740257,
-0.024216845631599426,
0.0026275443378835917,
-0.06070500239729881,
-0.023251648992300034,
-0.016861235722899437,
0.05213416367769241,
0.0587257482111454,
0.03258976340293884,
0.011578375473618507,
0.04043087735772133,
-0.06048716604709625,
0.011765996925532818,
-0.007475897669792175,
0.012534841895103455,
-0.0220731720328331,
-0.0014639232540503144,
-0.031654175370931625,
-0.014025493524968624,
0.04878932610154152,
-0.05593818798661232,
0.023242687806487083,
0.07870917022228241,
0.005018205847591162,
-0.02057785540819168,
0.0011456952197477221,
0.026189148426055908,
-0.024692049250006676,
-0.04445367678999901,
0.0412888266146183,
-0.022269248962402344,
-0.006191666703671217,
-0.013432182371616364,
-0.06785760074853897,
0.041848354041576385,
-0.039988674223423004,
-0.09156163036823273,
0.030116109177470207,
0.00651128264144063,
-0.021486489102244377,
0.021993720903992653,
0.036963362246751785,
-0.0329231359064579,
-0.08281870931386948,
-0.05073947831988335,
-0.04390282556414604,
0.021628670394420624,
-0.04132937267422676,
0.03963151201605797,
0.001237444463185966,
-0.026381462812423706,
0.05945373699069023,
0.01763063482940197,
0.04182620346546173,
0.0676828995347023,
-0.028279349207878113,
0.047583431005477905,
0.017077947035431862,
-0.024929620325565338,
-0.035450633615255356,
0.016921430826187134,
-0.05608770251274109,
0.052774567157030106,
0.0372297577559948,
-0.01931011863052845,
-0.08226735144853592,
-0.018829157575964928,
0.06475044041872025,
-0.005193936172872782,
0.00718741724267602,
0.015805648639798164,
-0.03648998588323593,
-0.004839892033487558,
-0.029992680996656418,
0.042189281433820724,
-0.015947014093399048,
0.04772273823618889,
0.06217675656080246,
-0.03520205244421959,
-0.043678801506757736,
0.003103028517216444,
-0.019665667787194252,
-0.049944110214710236,
-0.06185630336403847,
-0.045566048473119736,
-0.062135834246873856,
0.04512794315814972,
0.04338153824210167,
0.02336779423058033,
0.05099242925643921,
-0.018122104927897453,
0.05181179195642471,
0.007071845233440399,
0.11070819944143295,
0.03937767446041107,
0.018141543492674828,
-0.012131493538618088,
0.02285396307706833,
0.006587545853108168,
-0.032795846462249756,
-0.039935264736413956,
0.017818309366703033,
0.041341956704854965,
-0.00724058598279953,
-0.028668034821748734,
0.05155355855822563,
-0.04375937953591347,
0.027583179995417595,
-0.0035525206476449966,
0.015103449113667011,
0.026423750445246696,
0.028950022533535957,
0.00010877756722038612,
0.03551050275564194,
-0.056083641946315765,
-0.013301284052431583,
0.015208757482469082,
0.04710819944739342,
0.02806095965206623,
-0.030937695875763893,
0.005982471164315939,
0.02401326783001423,
-0.00005151454752194695,
-0.028803326189517975,
0.005282022524625063,
0.01930263265967369,
0.04258036985993385,
-0.030305080115795135,
0.025564340874552727,
0.03478972613811493,
0.036537401378154755,
-0.0385134257376194,
0.038101207464933395,
-0.03365687280893326,
-0.11719373613595963,
0.014425569213926792,
-0.04495362192392349,
0.01574130728840828,
0.012829049490392208,
0.00832374393939972,
-0.024842264130711555,
-0.032303765416145325,
0.012737587094306946,
0.09445732086896896,
-0.048582617193460464,
-0.028453296050429344,
0.05728473886847496,
-0.03205522522330284,
0.046097733080387115,
-0.0380917526781559,
0.000049082154873758554,
-0.008256567642092705,
0.038868095725774765,
-0.008679541759192944,
0.017561165615916252,
0.013030953705310822,
0.03650389239192009,
0.05254991725087166,
-0.06106506660580635,
0.003098185872659087,
-0.03314048796892166,
-0.03596286103129387,
0.023493986576795578,
-0.02525138482451439,
-0.029997872188687325,
-0.026685556396842003,
-0.005026062484830618,
0.00136153947096318,
-0.029915232211351395,
-0.01595623977482319,
-0.04007507115602493,
0.02782229520380497,
0.06943468004465103,
0.012276976369321346,
-0.00005645967030432075,
-0.0362040251493454,
-0.02902211621403694,
0.00752346683293581,
0.024101393297314644,
0.018190301954746246,
0.06612103432416916,
0.05507197231054306,
0.020689312368631363,
0.00722935376688838,
0.023589378222823143,
-0.003194465534761548,
-0.0005088419420644641,
0.0454033799469471,
0.002005396643653512,
-0.017484396696090698,
0.00136104307603091,
-0.05730665102601051,
-0.018005069345235825,
-0.01338889915496111,
-0.030226493254303932,
-0.005193816497921944,
-0.055849675089120865,
-0.054941337555646896,
-0.0015720754163339734,
0.001707565737888217,
0.01344500295817852,
-0.0012261336669325829,
0.011637983843684196,
-0.018161775544285774,
0.023283477872610092,
0.020800810307264328,
0.001809231354855001,
-0.00139188626781106,
0.0025028090458363295,
0.024972615763545036,
0.001718841609545052,
-0.037665992975234985,
-0.016174007207155228,
-0.07267715781927109,
0.016978107392787933,
-0.06195526570081711,
-0.031132377684116364,
-0.0029337708838284016,
0.03317135199904442,
0.06594819575548172,
0.0006337703089229763,
0.02576642856001854,
-0.050215527415275574,
-0.009737828746438026,
0.009726726450026035,
0.015232146717607975,
-0.05290861427783966,
-0.0003980263427365571,
-0.024554062634706497,
0.011634036898612976,
-0.007553863804787397,
-0.014331852085888386,
0.04672510176897049,
0.007807815447449684,
-0.07011625170707703,
0.027356445789337158,
-0.03978108987212181,
-0.008427435532212257,
0.04929331690073013,
-0.0020934247877448797,
-0.036833301186561584,
0.019337637349963188,
-0.00031932033016346395,
0.07842244952917099,
0.03094872646033764,
-0.013789329677820206,
0.009346401318907738,
-0.014733259566128254,
-0.02660810574889183,
-0.005523256026208401,
-0.0014220335287973285,
0.03837059438228607,
-0.008361272513866425,
0.0032616162206977606,
-0.010137971490621567,
-0.04269719868898392,
0.03690323606133461,
0.022521648555994034,
-0.06466671079397202,
0.05634824186563492,
-0.04485693946480751,
0.044922567903995514,
0.04711548984050751,
0.02366509847342968,
0.06420674175024033,
0.058557458221912384,
0.03122158907353878,
-0.027666274458169937,
-0.03728673607110977,
-0.05002991855144501,
-0.016576623544096947,
-0.012579066678881645,
0.015286210924386978,
0.03633357957005501,
0.0382503904402256,
0.052736908197402954,
-0.032365832477808,
-0.014629417099058628,
-0.019329367205500603,
0.018646538257598877,
0.0004704058519564569,
0.03593405336141586,
-0.0013943143421784043,
-0.0001081648952094838,
-0.09696884453296661,
0.01571694016456604,
0.002573107834905386,
0.029574034735560417,
-0.0036771195009350777,
0.09501218795776367,
-0.01623350754380226,
-0.04197005182504654,
0.041795287281274796,
-0.005470206495374441,
0.028521379455924034,
0.028005754575133324,
0.022329850122332573,
0.0010619242675602436,
-0.02184416353702545,
-0.03930360823869705,
-0.011739818379282951,
0.08040229231119156,
-0.00024830506299622357,
-0.04816783219575882,
0.00286573707126081,
0.044105906039476395,
0.05406063050031662,
-0.032356563955545425,
0.004972019232809544,
0.05569477006793022,
0.04979149252176285,
-0.07557493448257446,
-0.016972752287983894,
-0.03382328525185585,
0.011860543861985207,
0.01733512431383133,
0.03391899913549423,
-0.0026569198817014694,
0.007224312052130699,
0.002463891403749585,
0.11178062856197357,
-0.042857762426137924,
0.005644530989229679,
-0.024284783750772476,
-0.02852151170372963,
-0.017745299264788628,
-0.058879829943180084,
0.03542671352624893,
-0.07326922565698624,
0.00540067907422781,
0.008329587057232857,
-0.030320486053824425,
-0.011513047851622105,
0.04651614651083946,
0.05415496230125427,
0.009390175342559814,
-0.023525448516011238,
-0.006179505959153175,
0.032634999603033066,
-0.0005819813814014196,
0.004235181957483292,
-0.036108214408159256,
-0.02870994061231613,
-0.0056715053506195545,
0.02138805016875267,
-0.02171584591269493,
0.08333998173475266,
-0.005303230136632919,
-0.043258532881736755,
0.037693560123443604,
0.03686387836933136,
0.021413138136267662,
-0.043698158115148544,
0.03874259442090988,
-0.007201893720775843,
0.0542423240840435,
-0.06492963433265686,
-0.009080611169338226,
0.029752081260085106,
0.014886284247040749,
0.015758799389004707,
-0.01672087237238884,
0.02918427065014839,
0.03483634814620018,
0.005869919899851084,
-0.06572293490171432,
-0.016481993719935417,
-0.05268386751413345,
-0.03189346194267273,
0.027762629091739655,
0.028134610503911972,
0.03899006545543671,
-0.026405591517686844,
0.015560045838356018,
-0.012714349664747715,
0.006516465917229652,
0.009679682552814484,
-0.01670433208346367,
-0.04865153878927231,
0.00440188916400075,
0.028415000066161156,
-0.05219370871782303,
-0.06597983837127686,
-0.04267071932554245,
0.006463613826781511,
0.01601204089820385,
-0.002790040336549282,
0.05953366309404373,
-0.041348665952682495,
0.029163185507059097,
-0.006828319281339645,
0.08844292908906937,
-0.048692766577005386,
-0.008223493583500385,
0.005173949059098959,
-0.010148693807423115,
0.006964794360101223,
0.043090127408504486,
0.0026595776434987783,
0.03567952662706375,
-0.0011926922015845776,
0.039899252355098724,
-0.01629895530641079,
0.03906150534749031,
-0.03150922805070877,
0.09822447597980499,
-0.03501574695110321,
0.013849526643753052,
0.010882874019443989,
-0.010908816009759903,
-0.02724383771419525,
0.03931959345936775,
-0.004694654140621424,
-0.009742599911987782,
-0.05254898965358734,
0.06786278635263443,
-0.009251276962459087,
-0.0168202705681324,
0.02224072627723217,
-0.05535667762160301,
-0.0833551436662674,
0.01663544401526451,
0.004971880000084639,
0.009591183625161648,
-0.04050774499773979,
0.007629939820617437,
-0.04392942041158676,
-0.016579337418079376,
-0.04622189328074455,
0.009496324695646763,
-0.022273732349276543,
0.023620856925845146,
-0.01202755980193615,
0.006300594191998243,
-0.021328672766685486,
-0.044998522847890854,
0.027278687804937363,
0.011672820895910263,
-0.0029173120856285095,
-0.002116331597790122,
-0.038744550198316574,
-0.010888632386922836,
0.019122054800391197,
0.044203393161296844,
0.012703516520559788,
0.009096045978367329,
0.014078248292207718,
-0.026228928938508034,
0.006861880421638489,
-0.0550219789147377,
-0.022182373329997063,
-0.03596849739551544,
0.04491151124238968,
-0.06274787336587906,
0.00727097550407052,
0.00008171398076228797,
-0.04820655286312103,
-0.014053089544177055,
0.03955482691526413,
-0.045862603932619095,
0.02624233067035675,
0.007101649418473244,
-0.12016914784908295,
0.005317401606589556,
-0.03411237150430679,
-0.04545426741242409,
0.020045524463057518,
-0.00464480509981513,
-0.02456284500658512,
-0.038780249655246735,
-0.06282983720302582,
-0.006989100947976112,
0.0626140609383583,
-0.0014490961330011487,
0.022877361625432968,
-0.006240664515644312,
0.06531402468681335,
-0.022403288632631302,
0.02086338773369789,
0.0721653550863266,
0.02192365750670433,
0.028893515467643738,
0.08585816621780396,
-0.03210853412747383,
-0.07891453057527542,
0.0020087379962205887,
0.03756166622042656,
0.002395163755863905,
0.019217194989323616,
0.03695724904537201,
0.04247433319687843,
0.006253690458834171,
-0.03696295991539955,
-0.006027421448379755,
-0.012391041032969952,
-0.004737803712487221,
-0.04886602237820625,
-0.041764698922634125,
-0.031903404742479324,
0.01837599091231823,
0.011462456546723843,
-0.011269099079072475,
0.04963044449687004,
-0.02308659255504608,
-0.020461782813072205,
-0.0414142906665802,
0.03321773186326027,
-0.02483745664358139,
0.01222067791968584,
-0.015600956976413727,
-0.0831429734826088,
-0.027252018451690674,
0.011295320466160774,
0.10175057500600815,
-0.013987136073410511,
0.00779031403362751,
-0.019119564443826675,
-0.03741942346096039,
0.03274060785770416,
-0.10063084959983826,
-0.05734729394316673,
0.033998191356658936,
-0.0818558856844902,
-0.002188077662140131,
0.0007629115134477615,
0.012812305241823196,
0.019648956134915352,
-0.001655129250138998,
-0.014467712491750717,
-0.023667164146900177,
0.0337119959294796,
-0.09037280082702637,
0.0633721724152565,
0.02387881465256214,
0.041605934500694275,
-0.045971669256687164,
-0.009765868075191975,
-0.046651192009449005,
0.06041961908340454,
0.0051574320532381535,
-0.039200544357299805,
0.004778238944709301,
-0.013288569636642933,
-0.00969009380787611,
0.08549980074167252,
0.0246512982994318,
-0.03426148742437363,
-0.026472805067896843,
-0.037849366664886475,
0.02661154791712761,
0.05404375120997429,
-0.00423826090991497,
0.013570503331720829,
0.008307547308504581,
0.007980667985975742,
-0.004823112860321999,
-0.07952509820461273,
-0.018620973452925682,
0.03238632157444954,
-0.05236385762691498,
-0.048576563596725464,
0.04691310226917267,
0.006589693482965231,
-0.03134950250387192,
-0.008877960033714771,
0.0042520626448094845,
-0.01936989650130272,
0.002935656812041998,
-0.009246650151908398,
0.038190945982933044,
0.02151152864098549,
0.01652044802904129,
0.022183945402503014,
-0.0026218679267913103,
-0.027232997119426727,
-0.0034935155417770147,
0.05327014997601509,
-0.0032858604099601507,
0.027029508724808693,
-0.024345066398382187,
0.03828544169664383,
0.027973275631666183,
0.0011050956090912223,
0.012762891128659248,
-0.0009526911308057606,
0.016899865120649338,
-0.012616943567991257,
-0.06540090590715408,
0.0013801680179312825,
-0.07110624760389328,
-0.050196658819913864,
0.005195436999201775,
0.04703572019934654,
-0.047483254224061966,
0.023625334724783897,
-0.020273566246032715,
-0.057507216930389404,
-0.030962171033024788,
0.04063666611909866,
0.024078059941530228,
0.0013363672187551856,
-0.006388192996382713,
-0.007333407178521156,
-0.05241958051919937,
-0.027475859969854355,
0.05260502174496651,
-0.035226572304964066,
0.024078385904431343,
0.07738054543733597,
-0.005244087427854538,
0.03230790048837662,
0.03536522388458252,
-0.004793382715433836,
-0.02127484232187271,
-0.05000297352671623,
-0.0237872451543808,
0.02828107587993145,
0.03907255828380585,
-0.0036873752251267433,
-0.055319685488939285,
-0.03380263224244118,
-0.028458265587687492,
-0.030332664027810097,
0.04008696228265762,
0.026749510318040848,
0.0025518720503896475,
0.03783557564020157,
0.044605452567338943,
0.03450000658631325,
-0.002495646709576249,
-0.028462998569011688,
-0.021424662321805954,
0.04477883130311966,
0.015713168308138847,
0.03923209756612778,
0.04850727319717407,
-0.035671573132276535,
-0.04407220333814621,
0.017955157905817032,
0.05857255682349205,
0.00916155893355608,
-0.03039068728685379,
-0.012119500897824764,
-0.0018535931594669819,
0.022061854600906372,
0.031087400391697884,
-0.03054230287671089,
-0.000980595126748085,
0.003656717948615551,
0.005504608154296875,
0.019882263615727425,
0.008291522972285748,
-0.010304314084351063,
-0.0003462603490334004,
0.0128677012398839,
-0.03495318815112114,
-0.027458881959319115,
0.02488134428858757,
0.010019470006227493,
-0.06152625009417534,
0.01836167462170124,
-0.004323075525462627,
-0.006045666057616472,
-0.0033141477033495903,
-0.011663149110972881,
-0.02244778722524643,
0.02961271069943905,
0.05789230763912201,
0.018771007657051086,
0.026041598990559578,
0.007224313914775848,
-0.0033071935176849365,
0.019582880660891533,
0.06329058110713959,
-0.0418182834982872,
0.02792206034064293,
-0.03711748495697975,
-0.026836678385734558,
-0.05768624693155289,
-0.010509119369089603,
0.02422892302274704,
0.06667183339595795,
0.032602205872535706,
-0.04494074732065201,
-0.008605035953223705,
-0.02214204892516136,
0.05680152028799057,
-0.013423886150121689,
-0.03348071128129959,
0.013938707299530506,
-0.0035771706607192755,
-0.005206624511629343,
0.0485009104013443,
-0.06224773824214935,
-0.021587084978818893,
-0.05529588460922241,
-0.010053779929876328,
-0.0077904039062559605,
-0.018769847229123116,
0.008601821027696133,
0.02377740480005741,
0.06280308961868286,
-0.019486209377646446,
0.022559210658073425,
-0.04267004504799843,
-0.04960848018527031,
0.015240919776260853,
-0.014919494278728962,
-0.023699341341853142,
-0.008600885048508644,
-0.02922414429485798,
-0.06218248978257179,
0.019125621765851974,
0.011637218296527863,
0.029644539579749107,
0.009187155403196812,
0.02445431798696518,
0.06854552030563354,
0.04320672154426575,
-0.02275712788105011,
0.0344119556248188,
0.01652255654335022,
-0.02269410528242588,
0.014758562669157982,
0.015514377504587173,
-0.019530126824975014,
-0.023758908733725548,
-0.02678341418504715,
-0.007931475527584553,
-0.02094648964703083,
0.0007322666933760047,
0.0075308168306946754,
0.0001015852831187658,
-0.07301946729421616,
-0.0017194958636537194,
-0.03081556223332882,
-0.011564023792743683,
0.010412609204649925
] |
<p>There are numerous pictures, obviously, of the blackness of space from the shuttle, the space station, and even the moon. But they all suffer from being from the perspective of a camera, which is not sensitive enough to pick up the stars in the background when compared to the bright foreground objects (the limb of the Earth, the station, moon, etc). I've seen some photos that show a few of the brightest stars, but nothing special.</p>
<p>Are there any photos or eye witness accounts from astronauts of what it looks like to a human with night-adjusted vision? If I were in an orbit similar to the space station and looked away from the Earth, would I be able to see more stars than I ever could on Earth, or would it only be marginally better than the best terrestrial night viewing?</p> | g4731 | [
-0.05649252608418465,
0.07283055037260056,
0.02046993002295494,
0.02416580356657505,
-0.06531969457864761,
0.025016313418745995,
-0.06996852159500122,
-0.02498227171599865,
0.04065437987446785,
-0.01504790224134922,
0.09828924387693405,
0.013108068145811558,
0.05614085495471954,
0.007628211285918951,
0.031216992065310478,
-0.0167370717972517,
0.012106020003557205,
-0.03654370829463005,
-0.0017536227824166417,
-0.04563969746232033,
0.08621173352003098,
0.02104845456779003,
-0.02585732191801071,
0.02997150644659996,
-0.056450508534908295,
0.01308633852750063,
0.014376319944858551,
-0.02176559343934059,
0.02702943980693817,
0.044309429824352264,
0.027731476351618767,
-0.02167961187660694,
0.014834092929959297,
-0.06466428190469742,
0.012489519082009792,
0.021085085347294807,
-0.018991775810718536,
0.02545045129954815,
-0.051348283886909485,
-0.009456031024456024,
-0.03340248763561249,
-0.039742931723594666,
-0.0274030864238739,
-0.010434606112539768,
0.006109082605689764,
0.0015694734174758196,
-0.017515311017632484,
-0.006328711286187172,
0.03528604283928871,
0.016969021409749985,
-0.003835229203104973,
0.03731462359428406,
-0.0062294756062328815,
0.04271601140499115,
0.05276883766055107,
-0.018587419763207436,
0.00018983054906129837,
0.003488877322524786,
0.06922343373298645,
0.032388266175985336,
-0.00022447090304922312,
0.010226398706436157,
0.0039535947144031525,
-0.032194674015045166,
-0.022474320605397224,
0.04577387124300003,
-0.028334325179457664,
0.00686547951772809,
0.056151192635297775,
0.01131629478186369,
0.021895259618759155,
0.023341655731201172,
-0.10968528687953949,
0.022511759772896767,
-0.055248912423849106,
0.014241309836506844,
-0.01238114945590496,
0.006431132089346647,
-0.006498466245830059,
0.0859755352139473,
-0.00907972827553749,
0.0008347373805008829,
-0.07830918580293655,
0.017989875748753548,
0.07167455554008484,
0.0017675994895398617,
0.027708454057574272,
-0.04851125553250313,
0.04280254244804382,
0.02368870936334133,
0.04481081664562225,
0.033063288778066635,
0.008123247884213924,
-0.010807585902512074,
-0.0005506465095095336,
0.05676450952887535,
0.04546770825982094,
0.029593467712402344,
-0.026843175292015076,
0.02630794793367386,
-0.0058347792364656925,
0.016356181353330612,
0.05278322473168373,
0.03797970712184906,
-0.021594783291220665,
-0.009543173015117645,
0.017709147185087204,
0.0029516099020838737,
0.00737313786521554,
0.004997604060918093,
-0.042941540479660034,
-0.018114717677235603,
0.05527676269412041,
0.0038605877198278904,
-0.030307777225971222,
-0.03927510976791382,
0.02984166517853737,
-0.010348446667194366,
-0.010283175855875015,
-0.006386362481862307,
0.004528862424194813,
0.04792427644133568,
-0.01226068940013647,
0.007279476150870323,
-0.008412876166403294,
-0.025565341114997864,
-0.005094761494547129,
-0.04428559169173241,
0.00846155732870102,
-0.006446811370551586,
-0.018626384437084198,
0.012954364530742168,
-0.0011273163836449385,
0.011815045028924942,
0.0029607058968394995,
0.005034971050918102,
0.009589770808815956,
-0.03679553419351578,
-0.029406622052192688,
0.040859468281269073,
0.0393829420208931,
0.025696421042084694,
-0.035062242299318314,
0.04353503882884979,
-0.03727080300450325,
0.037203915417194366,
-0.042301636189222336,
0.020073646679520607,
-0.01165798120200634,
0.051240064203739166,
-0.05453280732035637,
0.006938884034752846,
0.09857795387506485,
-0.018419742584228516,
-0.024046026170253754,
-0.03184143081307411,
-0.0036429516039788723,
-0.014926660805940628,
0.008468403480947018,
0.021086309105157852,
0.029954053461551666,
0.024589266628026962,
-0.008439320139586926,
0.0002590105577837676,
-0.01320180855691433,
-0.05249353498220444,
-0.04749321937561035,
-0.04006208851933479,
0.04770147427916527,
-0.022966476157307625,
0.011545462533831596,
-0.07201830297708511,
0.04034137353301048,
0.03228938952088356,
0.015562755055725574,
-0.03215253725647926,
0.0299232080578804,
-0.009408989921212196,
-0.010076243430376053,
0.010134221985936165,
-0.007709856610745192,
-0.0029739970341324806,
-0.03608165681362152,
0.010503013618290424,
-0.0001320911105722189,
-0.06283421069383621,
-0.006290064193308353,
-0.019662145525217056,
-0.0011575177777558565,
0.032088592648506165,
0.0446145124733448,
-0.023879241198301315,
-0.0012573075946420431,
0.04929933324456215,
0.01626335084438324,
-0.08709628134965897,
-0.0241073165088892,
0.04443362355232239,
-0.010608700104057789,
0.028747426345944405,
0.004223268013447523,
0.05471646413207054,
0.018913686275482178,
-0.02036699652671814,
-0.007603931240737438,
-0.0061379773542284966,
-0.025235088542103767,
-0.01732604391872883,
-0.027223622426390648,
-0.0794295072555542,
0.002738830167800188,
-0.01049384567886591,
0.06834238767623901,
-0.012130459770560265,
-0.030076831579208374,
0.06988371908664703,
-0.04674990475177765,
0.0048298402689397335,
0.06295580416917801,
-0.05593325197696686,
-0.003326136851683259,
-0.05196229740977287,
0.009523454122245312,
-0.004513194784522057,
0.02880641631782055,
-0.014764674939215183,
-0.05027473345398903,
0.009980212897062302,
0.10222935676574707,
0.03589251637458801,
-0.05483072251081467,
-0.0027580601163208485,
0.022342966869473457,
0.042884711176157,
-0.04114043340086937,
-0.02267525903880596,
-0.005844700615853071,
0.015149117447435856,
0.06728840619325638,
0.021908754482865334,
-0.026770977303385735,
-0.043743107467889786,
-0.06335669755935669,
-0.04320572316646576,
0.0433703288435936,
-0.007616380229592323,
0.012289540842175484,
0.009941504336893559,
-0.03060849756002426,
-0.009007883258163929,
0.02069593407213688,
0.06047111749649048,
-0.03987668827176094,
-0.037574656307697296,
0.013617527671158314,
0.039836857467889786,
-0.042764533311128616,
0.042247701436281204,
-0.08138522505760193,
0.0070786611177027225,
-0.03663773089647293,
-0.05894193425774574,
-0.031827863305807114,
0.03610511124134064,
0.08311688154935837,
0.04203546419739723,
0.04301375523209572,
0.004435614682734013,
0.06706943362951279,
0.020624255761504173,
0.022450676187872887,
0.04240523651242256,
-0.03148558363318443,
0.04284711182117462,
-0.03069467470049858,
0.01287787314504385,
-0.04579973593354225,
0.017135269939899445,
-0.015727132558822632,
-0.05602653697133064,
0.06930626183748245,
0.01007915660738945,
-0.05057995021343231,
0.036605674773454666,
-0.008829502388834953,
0.02336914651095867,
0.035047661513090134,
-0.005864079110324383,
0.04694609344005585,
0.0037671800237149,
-0.06963936984539032,
-0.006765326485037804,
0.02421238087117672,
0.018127037212252617,
-0.052440956234931946,
-0.028356436640024185,
0.05349386855959892,
0.0214606374502182,
-0.03188279643654823,
0.005379373673349619,
0.024312786757946014,
-0.014442373998463154,
0.05999777466058731,
0.09771449863910675,
-0.021904319524765015,
0.0148021774366498,
-0.025912415236234665,
-0.0259640421718359,
-0.009288365021348,
-0.07244789600372314,
-0.01624770648777485,
-0.017822684720158577,
-0.030577626079320908,
0.04469521716237068,
0.011684117838740349,
0.0017779761692509055,
0.010154315270483494,
0.03980621322989464,
-0.03420087322592735,
0.008992675691843033,
0.0691412016749382,
0.012280534952878952,
-0.04099446162581444,
-0.021488450467586517,
0.021878859028220177,
-0.0207475908100605,
0.008218446746468544,
-0.048419345170259476,
-0.017818830907344818,
0.03420903906226158,
0.044986795634031296,
0.024891790002584457,
-0.0028186552226543427,
0.0016080155037343502,
-0.01678803376853466,
0.08428092300891876,
-0.040919430553913116,
-0.017114130780100822,
0.021164575591683388,
0.01035066694021225,
0.0225507989525795,
0.053045984357595444,
-0.061135776340961456,
-0.026608766987919807,
0.017092101275920868,
-0.023578263819217682,
0.002512336941435933,
-0.0616418682038784,
0.029064007103443146,
-0.020761918276548386,
0.02813347987830639,
-0.04904072731733322,
0.013259370811283588,
-0.031958047300577164,
-0.01774914190173149,
0.03209243714809418,
-0.017121540382504463,
0.006037696730345488,
0.010797703638672829,
-0.07564937323331833,
-0.007805137429386377,
-0.003225460182875395,
0.009150754660367966,
-0.04125763475894928,
0.001800577505491674,
-0.06594761461019516,
0.04794033616781235,
-0.008911315351724625,
-0.002179221948608756,
-0.017173249274492264,
-0.04428167641162872,
0.0017462351825088263,
0.005641145631670952,
-0.02508428506553173,
0.025043293833732605,
0.006658649537712336,
0.02079511620104313,
0.015612993389368057,
0.0193624347448349,
0.016679227352142334,
-0.0029120713006705046,
0.028107158839702606,
-0.0193242896348238,
-0.0014850266743451357,
0.0714840516448021,
0.019839970394968987,
0.025482388213276863,
-0.037573084235191345,
-0.013514215126633644,
0.030395088717341423,
-0.05157771334052086,
-0.06928200274705887,
-0.035009320825338364,
-0.04421672597527504,
0.023043442517518997,
-0.011640728451311588,
0.03444268926978111,
0.023894401267170906,
0.016543693840503693,
-0.01924843154847622,
0.04606824368238449,
0.03826497122645378,
0.06149034574627876,
0.03342602401971817,
-0.03459470346570015,
-0.03698579594492912,
-0.0668659657239914,
0.05150771141052246,
-0.06521178781986237,
0.03489719331264496,
0.042982038110494614,
0.01452587265521288,
-0.022221827879548073,
-0.06770338863134384,
0.017599664628505707,
0.05686128884553909,
0.0028355466201901436,
-0.012857813388109207,
0.06599968671798706,
0.005876670125871897,
0.00876549631357193,
0.025639759376645088,
-0.06888076663017273,
-0.0538044236600399,
0.03877958655357361,
0.052710384130477905,
0.01568182371556759,
-0.01092769019305706,
0.012078475207090378,
0.046844106167554855,
0.055291760712862015,
-0.03597142547369003,
-0.027892038226127625,
0.06515739858150482,
0.007207384333014488,
0.013050439767539501,
0.024252409115433693,
0.00987196620553732,
-0.01157617848366499,
-0.022549016401171684,
0.014354821294546127,
0.015011796727776527,
0.019834376871585846,
-0.005108338315039873,
-0.010755082592368126,
0.05578354746103287,
0.05440369248390198,
0.0150397764518857,
-0.029644230380654335,
0.011989706195890903,
0.014872372150421143,
-0.020442435517907143,
0.0011677370639517903,
0.008985155262053013,
-0.03295808285474777,
0.010997263714671135,
-0.030944040045142174,
-0.030594589188694954,
0.00729738874360919,
0.04088985174894333,
0.0033500236459076405,
-0.021946070715785027,
-0.013345751911401749,
-0.005845656618475914,
-0.00620527658611536,
0.04924522340297699,
-0.1086626723408699,
-0.017127543687820435,
0.009124229662120342,
0.016586067155003548,
-0.017219604924321175,
0.02603268437087536,
0.07559920847415924,
-0.016926482319831848,
-0.05747095122933388,
-0.029841100797057152,
-0.02922525629401207,
-0.011873521842062473,
0.0024988579098135233,
0.0093794334679842,
0.006699089892208576,
0.004476756788790226,
0.034323208034038544,
-0.018177000805735588,
-0.036579277366399765,
0.041033849120140076,
0.018036598339676857,
0.024846317246556282,
-0.023197509348392487,
0.00848680641502142,
-0.060920894145965576,
-0.02503511868417263,
-0.028975605964660645,
0.014826834201812744,
-0.06317689269781113,
0.004220137372612953,
-0.025981901213526726,
-0.01126925554126501,
0.04394081234931946,
0.08508030325174332,
-0.011438954621553421,
0.0034622889943420887,
0.01654067076742649,
-0.025986695662140846,
-0.0057907127775251865,
0.04576756805181503,
-0.06871163100004196,
-0.07217835634946823,
-0.029314836487174034,
0.08439122885465622,
-0.05839698389172554,
-0.03126315772533417,
-0.05074379965662956,
0.04055199399590492,
-0.0019901746418327093,
-0.05197267606854439,
-0.06273853778839111,
0.028240088373422623,
0.020989997312426567,
-0.037080295383930206,
-0.008008085191249847,
-0.024117324501276016,
0.021139176562428474,
0.049492985010147095,
-0.028628891333937645,
0.0059303478337824345,
0.004901285748928785,
0.0804385095834732,
0.002275013830512762,
-0.008008125238120556,
-0.02701941691339016,
0.015230911783874035,
0.02105933241546154,
-0.029698973521590233,
0.00624809879809618,
0.016184205189347267,
0.03062390722334385,
0.06741909682750702,
0.01572446897625923,
-0.009896834380924702,
-0.05582525208592415,
0.017628751695156097,
0.010503820143640041,
0.029005536809563637,
0.010459277778863907,
-0.020406600087881088,
-0.038077112287282944,
0.021909955888986588,
-0.01600756123661995,
0.0366031639277935,
-0.053679052740335464,
-0.02665533311665058,
-0.027819490060210228,
0.03937463089823723,
-0.07965520024299622,
0.010989172384142876,
-0.055677592754364014,
0.020878534764051437,
0.011206548660993576,
-0.036642324179410934,
0.05747997760772705,
-0.05710305646061897,
-0.011796205304563046,
-0.008322220295667648,
0.02657078392803669,
-0.03086441196501255,
-0.0016122286906465888,
-0.008621355518698692,
0.041823484003543854,
-0.029961366206407547,
-0.013963277451694012,
-0.04225865751504898,
-0.014301908202469349,
-0.023002581670880318,
-0.004730442073196173,
-0.02710885927081108,
0.047190289944410324,
0.030514663085341454,
-0.06226291134953499,
-0.011398665606975555,
0.0008292791899293661,
-0.026390722021460533,
-0.014837860129773617,
-0.027724048122763634,
-0.03597636893391609,
0.007118941284716129,
0.03471093997359276,
0.05784979462623596,
-0.015032919123768806,
-0.06588932126760483,
0.009517746046185493,
-0.004294722806662321,
0.0013239587424322963,
0.020376060158014297,
-0.0020850857254117727,
-0.008220118470489979,
-0.05509515106678009,
0.01664647087454796,
-0.05652552843093872,
0.0181410051882267,
0.019340503960847855,
0.008340291678905487,
0.00007610661850776523,
0.05033363401889801,
0.04543287307024002,
-0.014277797192335129,
-0.02534395456314087,
-0.023867415264248848,
0.09956248849630356,
-0.001644167467020452,
0.06071252375841141,
0.04914804920554161,
-0.051988136023283005,
0.020981376990675926,
-0.027980804443359375,
-0.015295135788619518,
0.01306289341300726,
-0.011202977038919926,
0.00031388038769364357,
-0.004134294111281633,
-0.030284244567155838,
0.009071207605302334,
-0.042909394949674606,
0.061025552451610565,
-0.03324979543685913,
0.021927786991000175,
-0.005560294725000858,
0.03791351988911629,
0.013737385161221027,
0.017866842448711395,
-0.001971630146726966,
-0.024020275101065636,
0.007720103021711111,
-0.0027238342445343733,
0.04691319540143013,
-0.02543134056031704,
-0.01814251020550728,
-0.01545761339366436,
-0.04813089594244957,
0.0001186367153422907,
0.003237776691094041,
-0.052973970770835876,
-0.03396943211555481,
-0.029681086540222168,
-0.004881963599473238,
0.03397183120250702,
0.0178266242146492,
-0.0379219651222229,
0.025570878759026527,
-0.08266326785087585,
0.01066727563738823,
-0.0485810860991478,
0.010282191447913647,
-0.0419454462826252,
-0.015526743605732918,
0.05767826363444328,
0.005971729755401611,
0.026156829670071602,
-0.020810285583138466,
-0.06267471611499786,
0.011326038278639317,
0.03193015232682228,
-0.07980018854141235,
-0.002834614599123597,
-0.0018129468662664294,
0.004009879659861326,
0.07680045813322067,
-0.013823587447404861,
-0.034231673926115036,
0.051564767956733704,
0.047901298850774765,
-0.019959058612585068,
-0.009425447322428226,
0.029881730675697327,
-0.042463067919015884,
0.007140676490962505,
-0.042121898382902145,
0.02215367928147316,
-0.029165249317884445,
0.003245415398851037,
-0.012950994074344635,
0.00527547299861908,
0.03726201504468918,
0.057023786008358,
-0.0005924804136157036,
-0.03484104946255684,
-0.019794771447777748,
-0.0727212131023407,
0.017261745408177376,
-0.06650896370410919,
-0.03973289206624031,
-0.031898245215415955,
-0.04031732305884361,
-0.08406242728233337,
0.005337877199053764,
-0.06518492847681046,
0.011104765348136425,
0.03633859381079674,
0.02608500048518181,
-0.08250385522842407,
0.03606681898236275,
0.021141422912478447,
-0.003955674823373556,
-0.05598771572113037,
0.030404794961214066,
-0.05388390272855759,
0.029491281136870384,
0.0038524135015904903,
-0.02908475697040558,
0.021468976512551308,
0.0782892033457756,
0.07968653738498688,
-0.004351084586232901,
-0.02648773230612278,
0.029170842841267586,
-0.003558587282896042,
-0.05021597072482109,
0.00733952596783638,
-0.03248102217912674,
0.04104120284318924,
-0.031050249934196472,
0.021579883992671967,
0.009829442016780376,
0.028669456019997597,
0.051129404455423355,
0.04596501216292381,
0.0006319901440292597,
-0.00759594701230526,
0.058528587222099304,
-0.0501377172768116,
0.03823735564947128,
0.022142305970191956,
-0.02235240302979946,
-0.06736082583665848,
-0.030487634241580963,
0.021638361737132072,
-0.0428396500647068,
-0.036563508212566376,
-0.005985638592392206,
-0.010931139811873436,
-0.07190845906734467,
0.01481018215417862,
0.00903596356511116,
-0.02240643836557865,
0.0026733423583209515,
0.029419073835015297,
0.021720213815569878,
-0.016868647187948227,
0.020522957667708397,
0.03127548471093178,
0.01911422610282898,
0.09332384914159775,
0.004322780296206474,
-0.006904008332639933,
0.02809027023613453,
0.04129744693636894,
-0.019203584641218185,
-0.09725511074066162,
-0.04136595129966736,
0.01299949362874031,
0.031128987669944763,
0.019671861082315445,
-0.00822201557457447,
-0.014643284492194653,
-0.02427871897816658,
0.0018062667222693563,
0.02146328054368496,
-0.03730778023600578
] |
<p>I am interested in astronomy/astrophysics, but I am not science major (I am a computer science graduate). Facts and results of the field are presented to the public without showing how these facts/results got known or inferred. And I have that curiosity to know how we know what we know about the universe (either observationally or mathematically).</p>
<p>So my question is, what book(s) do you recommend for someone who has knowledge of</p>
<ul>
<li>algebra, trigonometry and geometry</li>
<li>college-level calculus</li>
<li>classical mechanics</li>
</ul>
<p>and does not get intimidated by mathematical language?</p>
<p>I expect the book(s) to answer questions like (not necessarily all of the questions, but questions of the same level and kind as these):</p>
<ul>
<li>How do we know how distant from the earth a celestial body (for example, a star) is?</li>
<li>How do we know the volume/mass of celestial bodies?</li>
<li>How do we know the materials that a planet is made of?</li>
<li>How do we know that our solar system orbits around the center of the galaxy?</li>
<li>How do we calculate the total mass of the galaxy?</li>
</ul> | g4732 | [
0.06255711615085602,
0.029210323467850685,
0.02293456345796585,
-0.056758586317300797,
0.009691212326288223,
0.02837536856532097,
-0.012560278177261353,
-0.022101184353232384,
0.04813869297504425,
0.010922310873866081,
0.035412535071372986,
0.007594825234264135,
0.0870838537812233,
-0.033894799649715424,
0.0039323465898633,
-0.03146503120660782,
0.023037396371364594,
-0.013106976635754108,
0.05474242568016052,
-0.004310197662562132,
0.01838388666510582,
0.09147555381059647,
0.018857916817069054,
-0.03907562792301178,
-0.06298565119504929,
-0.0016738203121349216,
-0.0015657299663871527,
-0.03744061291217804,
0.03831098601222038,
-0.02067727781832218,
-0.02452242560684681,
-0.101354219019413,
0.037907205522060394,
-0.055952299386262894,
0.00378872430883348,
0.022657230496406555,
0.030813952907919884,
-0.004790587816387415,
0.014712397009134293,
-0.014803857542574406,
0.01926182024180889,
-0.00020621232397388667,
0.005846555344760418,
0.010597244836390018,
0.022867167368531227,
-0.015401428565382957,
-0.006521816365420818,
-0.016236091032624245,
0.021200546994805336,
0.016421359032392502,
-0.015113050118088722,
-0.014359423890709877,
0.06692253053188324,
0.020353568717837334,
-0.0660589411854744,
0.05215981602668762,
0.033188607543706894,
-0.03107011690735817,
-0.016257479786872864,
-0.06562510132789612,
0.044536884874105453,
-0.007971836254000664,
-0.03411512449383736,
-0.06842492520809174,
-0.022419312968850136,
0.004675531294196844,
0.03313133493065834,
0.02375096082687378,
0.034398507326841354,
-0.0020557763054966927,
-0.0056952801533043385,
0.011027521453797817,
0.012339428067207336,
0.0013587904395535588,
-0.05841616913676262,
0.016388049349188805,
0.040641169995069504,
0.024119101464748383,
0.03370697423815727,
0.047232795506715775,
-0.031483739614486694,
0.018443919718265533,
0.036836009472608566,
0.030099820345640182,
0.033682893961668015,
-0.03283838927745819,
-0.03740628808736801,
-0.03761087357997894,
-0.024859335273504257,
0.034345321357250214,
-0.01962876506149769,
0.010338924825191498,
0.056286122649908066,
-0.04178531467914581,
-0.00004246969547239132,
0.04423291236162186,
-0.020174803212285042,
-0.012626278214156628,
0.0039046290330588818,
0.027020858600735664,
-0.03224826604127884,
0.02332616038620472,
0.030356567353010178,
-0.005519566126167774,
0.022506194189190865,
0.05710199475288391,
0.024277839809656143,
-0.012263615615665913,
-0.01776791177690029,
0.02719678170979023,
-0.03997901454567909,
-0.023746810853481293,
-0.00030425371369346976,
-0.0075129615142941475,
-0.03960529714822769,
0.0454874150454998,
0.05875314399600029,
-0.009557913988828659,
0.08445421606302261,
0.06337194889783859,
-0.029087569564580917,
0.04049264267086983,
0.03886624798178673,
-0.007117678876966238,
-0.02881675958633423,
-0.051713116466999054,
0.011898616328835487,
0.0030734797473996878,
0.02898702770471573,
-0.027839915826916695,
0.01042578648775816,
0.050978340208530426,
-0.0646073967218399,
0.011587779968976974,
-0.0451011024415493,
0.07181114703416824,
0.010273666121065617,
0.020071417093276978,
0.01262001320719719,
-0.02263779565691948,
0.015694251284003258,
0.022942695766687393,
0.016872422769665718,
-0.030549615621566772,
-0.022917209193110466,
0.04043238237500191,
-0.07221438735723495,
0.014060652814805508,
0.0190407894551754,
-0.014003430493175983,
-0.012088192626833916,
0.03379066288471222,
0.020393850281834602,
-0.009775797836482525,
-0.009550458751618862,
0.009068370796740055,
0.013633881695568562,
-0.018367458134889603,
0.013605665415525436,
-0.0764554962515831,
0.03678411617875099,
-0.008633654564619064,
-0.01723054051399231,
0.06752318143844604,
-0.025775039568543434,
0.05480474233627319,
-0.03380230441689491,
-0.09266382455825806,
0.05291119962930679,
0.02550189569592476,
-0.024476945400238037,
-0.008077326230704784,
0.0371108278632164,
0.042894769459962845,
-0.05543062463402748,
-0.011144761927425861,
0.05167720466852188,
-0.011409656144678593,
-0.03564576059579849,
0.02353445440530777,
0.006776050198823214,
-0.0805283635854721,
0.026453105732798576,
0.005532138980925083,
-0.07682289928197861,
-0.0027133601251989603,
0.003956200554966927,
0.05211515352129936,
-0.05390481650829315,
0.01784024015069008,
-0.050690773874521255,
-0.01068155188113451,
0.04175688698887825,
-0.004734961315989494,
-0.025913003832101822,
-0.01031945738941431,
0.023412048816680908,
0.014244509860873222,
-0.05230192467570305,
0.045936841517686844,
-0.0030982610769569874,
0.024220241233706474,
0.019974084571003914,
0.006214621942490339,
-0.008546446450054646,
0.001635763212107122,
0.013935297727584839,
0.009097907692193985,
0.04141358286142349,
-0.007313840091228485,
0.014054476283490658,
-0.048691149801015854,
0.04061150550842285,
-0.008405863307416439,
-0.008701940067112446,
-0.03271763399243355,
-0.06058333069086075,
0.024998994544148445,
-0.0023833143059164286,
-0.018015634268522263,
0.013476526364684105,
-0.07143154740333557,
0.023984448984265327,
0.004595414735376835,
0.04668436571955681,
0.029818950220942497,
-0.02186424285173416,
0.018014956265687943,
0.039315689355134964,
-0.012095297686755657,
-0.0831463485956192,
-0.03743179142475128,
0.10911912471055984,
0.02612876519560814,
0.053868819028139114,
0.028253743425011635,
0.02318280190229416,
0.00365954777225852,
0.06488332152366638,
0.06505183130502701,
0.015610560774803162,
0.020689211785793304,
-0.018602687865495682,
-0.0040046451613307,
0.02128617651760578,
-0.04211268201470375,
0.049093157052993774,
-0.011823402717709541,
-0.013965419493615627,
0.006934287492185831,
0.01089400053024292,
0.00637367507442832,
-0.04662644490599632,
-0.03850945457816124,
-0.05773933604359627,
0.026789965108036995,
-0.030195720493793488,
0.03925914689898491,
-0.004327497910708189,
0.0006525141652673483,
0.021027475595474243,
-0.03843284025788307,
0.03664686530828476,
0.022912198677659035,
-0.028970902785658836,
-0.020413151010870934,
-0.050760816782712936,
-0.009453787468373775,
-0.01823432929813862,
-0.027887674048542976,
0.05972501263022423,
0.03340362757444382,
0.04068343713879585,
0.022303611040115356,
0.003267972031608224,
-0.004132427740842104,
-0.00578202772885561,
-0.026280108839273453,
-0.02172476053237915,
-0.03699792921543121,
0.030699405819177628,
-0.04213622957468033,
-0.035311970859766006,
0.06737318634986877,
0.03949243575334549,
0.024523822590708733,
-0.06784766167402267,
0.02909332513809204,
0.05791270360350609,
-0.021775618195533752,
-0.00014941343397367746,
0.03156374767422676,
0.036566104739904404,
0.005514735821634531,
-0.010102195665240288,
-0.006580921821296215,
-0.0023307434748858213,
0.043895650655031204,
-0.07844623178243637,
-0.05238515883684158,
-0.056062545627355576,
-0.04310086369514465,
0.032116129994392395,
-0.015634866431355476,
-0.03890110179781914,
0.015012631192803383,
0.012956980615854263,
-0.009687324985861778,
0.06226734444499016,
-0.006697274744510651,
-0.0249191764742136,
-0.04815950244665146,
0.03204196318984032,
0.007656548172235489,
-0.0016546794213354588,
0.003838619915768504,
-0.03887262940406799,
0.03442520648241043,
-0.05340011790394783,
-0.02121952548623085,
-0.004789468366652727,
-0.015563976019620895,
0.01153907086700201,
-0.03397054597735405,
0.007262414786964655,
0.011406456120312214,
-0.00030752710881642997,
-0.0451141782104969,
-0.04777729511260986,
-0.04608067125082016,
-0.0007516467594541609,
-0.009191031567752361,
0.0009759239619597793,
-0.0017997670220211148,
-0.027038337662816048,
-0.013289137743413448,
0.013015824370086193,
-0.0299510657787323,
0.030588001012802124,
-0.055147960782051086,
-0.014327333308756351,
0.0036437788512557745,
0.018134213984012604,
-0.02816467359662056,
-0.04324806481599808,
0.01997506245970726,
-0.0444960743188858,
-0.05430787801742554,
-0.030293051153421402,
-0.0615742951631546,
0.016408054158091545,
0.010315564461052418,
0.010131915099918842,
-0.017172979190945625,
-0.009517702274024487,
0.051752761006355286,
-0.0006193030858412385,
0.05173749849200249,
0.04337378963828087,
-0.01919662207365036,
-0.03380385786294937,
0.02469691075384617,
-0.004446492530405521,
0.0016246618470177054,
0.011941615492105484,
0.007117182947695255,
0.015574483200907707,
-0.006395244970917702,
-0.026822341606020927,
0.017325958237051964,
-0.03571503981947899,
0.008087960071861744,
0.023756956681609154,
-0.027651332318782806,
-0.0000985413498710841,
-0.011469359509646893,
0.05680745095014572,
-0.009364001452922821,
-0.07161282747983932,
-0.005812101066112518,
-0.004519009962677956,
0.001001802273094654,
0.060763776302337646,
-0.00719080213457346,
0.06395458430051804,
0.03998057171702385,
0.010083221830427647,
-0.02514996938407421,
0.07419722527265549,
0.011119517497718334,
0.07951626926660538,
-0.08902109414339066,
-0.06056760251522064,
0.0018995306454598904,
0.037821877747774124,
-0.10632388293743134,
0.052376363426446915,
0.00419981125742197,
-0.03305339068174362,
-0.01809440366923809,
0.030726725235581398,
-0.012976383790373802,
0.008278829045593739,
0.02842136286199093,
0.010544467717409134,
0.02951992303133011,
0.04137740656733513,
-0.01548155676573515,
-0.0009290875750593841,
-0.04641729220747948,
0.044359683990478516,
-0.05934351682662964,
0.01431644894182682,
-0.029003795236349106,
0.013823507353663445,
0.02518714964389801,
0.0004193283384665847,
-0.04646194726228714,
0.025362562388181686,
0.0230757724493742,
-0.05958146974444389,
0.0856882855296135,
-0.014252610504627228,
-0.06016125902533531,
-0.012596084736287594,
0.0366336815059185,
0.04704376682639122,
-0.011702937074005604,
-0.028438938781619072,
0.059580493718385696,
0.03422229737043381,
-0.04548989608883858,
0.01973801665008068,
0.0422898605465889,
-0.02917894348502159,
-0.03829137235879898,
0.018946008756756783,
0.09946274012327194,
-0.027605991810560226,
-0.022332269698381424,
-0.02736671268939972,
0.029802309349179268,
-0.00007692684448556975,
0.005934510845690966,
-0.05317892134189606,
0.05253719910979271,
-0.03480206057429314,
0.02172701433300972,
0.003946156706660986,
-0.030083686113357544,
-0.019986217841506004,
0.029971228912472725,
-0.021504200994968414,
0.01850423775613308,
-0.04657989740371704,
-0.00938752293586731,
-0.005579093936830759,
0.024451306089758873,
0.029372604563832283,
0.030356237664818764,
0.0129781449213624,
-0.014940101653337479,
0.009855148382484913,
0.0677899718284607,
0.044056862592697144,
-0.027978995814919472,
-0.0340406559407711,
0.014963596127927303,
-0.013708371669054031,
-0.024478457868099213,
-0.020057780668139458,
0.02464887499809265,
0.043657854199409485,
-0.03172904625535011,
-0.04005841165781021,
-0.0212206169962883,
-0.022817889228463173,
-0.028960227966308594,
-0.03096470795571804,
0.003680076450109482,
-0.015130988322198391,
0.033894311636686325,
0.011302879080176353,
0.08238251507282257,
-0.01277611218392849,
0.03243444859981537,
-0.008937763050198555,
-0.029071606695652008,
0.0005140898865647614,
-0.035503827035427094,
-0.026533527299761772,
-0.04960894212126732,
0.08123449236154556,
-0.03221533074975014,
-0.08780110627412796,
-0.014471783302724361,
0.02426561899483204,
-0.021511653438210487,
0.02127879671752453,
0.03725590929389,
-0.045613549649715424,
0.06532300263643265,
-0.04142402485013008,
-0.02095450460910797,
0.02480977587401867,
-0.008846895769238472,
-0.02087319828569889,
-0.015271012671291828,
-0.025956984609365463,
0.012493266724050045,
0.013520359992980957,
-0.017895905300974846,
-0.01265065185725689,
0.03095252439379692,
-0.01848362758755684,
-0.015776652842760086,
0.018426258116960526,
0.07194048911333084,
0.018351400271058083,
0.004580309614539146,
-0.04736202210187912,
-0.0012781053083017468,
0.034774355590343475,
0.03349405154585838,
0.01637037843465805,
-0.062137335538864136,
-0.0395442433655262,
0.010144451633095741,
-0.00993196852505207,
0.05759922415018082,
0.027096815407276154,
0.030230354517698288,
-0.03144436329603195,
-0.04068443551659584,
-0.014979812316596508,
0.04779941961169243,
0.003012200817465782,
0.0029489072039723396,
-0.013891763053834438,
0.0018697621999308467,
0.009372690692543983,
0.03613697364926338,
0.06096813455224037,
0.026570213958621025,
0.04089383780956268,
0.023664576932787895,
-0.019009895622730255,
0.06902763992547989,
0.11719514429569244,
-0.023002583533525467,
-0.06920456886291504,
0.024533407762646675,
0.04411982372403145,
-0.036581311374902725,
-0.028422897681593895,
0.023341046646237373,
-0.016667870804667473,
-0.002181808929890394,
0.01622256450355053,
0.001301433308981359,
-0.026789098978042603,
-0.004146104212850332,
0.011472536250948906,
-0.0055602253414690495,
0.04057838395237923,
-0.029948081821203232,
0.01665898784995079,
-0.056516606360673904,
0.09676089137792587,
-0.002105414867401123,
0.00864220317453146,
-0.0203164741396904,
-0.009491766802966595,
-0.025749726220965385,
0.08415926992893219,
0.04686363786458969,
-0.04851869121193886,
-0.08319087326526642,
0.020406944677233696,
-0.04044476896524429,
0.054001450538635254,
-0.028716739267110825,
0.00621340237557888,
-0.058817166835069656,
0.03864936903119087,
0.017526432871818542,
0.015710728242993355,
0.02150597982108593,
-0.0017765003722161055,
-0.07986512035131454,
-0.0040955496951937675,
0.02102264203131199,
0.032535284757614136,
-0.003171344054862857,
0.020967474207282066,
-0.032274551689624786,
0.0203428752720356,
0.03763968497514725,
0.04853913560509682,
-0.00044543022522702813,
-0.0624074712395668,
-0.03915681317448616,
0.0579645074903965,
-0.04469456523656845,
0.05230758339166641,
0.030060773715376854,
-0.024823220446705818,
-0.01119945663958788,
0.07968976348638535,
-0.031632475554943085,
0.014133165590465069,
-0.013336529955267906,
0.002066367771476507,
0.04279476776719093,
-0.04491788148880005,
-0.05538034439086914,
-0.036970820277929306,
-0.010183717124164104,
0.010808979161083698,
-0.04109380021691322,
0.01968500204384327,
0.03329898416996002,
0.003170253708958626,
-0.022856255993247032,
-0.04729009047150612,
-0.01806655339896679,
-0.032029684633016586,
0.023744070902466774,
0.06121597811579704,
0.02914794720709324,
-0.014783916063606739,
0.003937503322958946,
0.0666157454252243,
0.01780042052268982,
0.005514721851795912,
0.008244430646300316,
-0.03710528835654259,
0.01320729497820139,
0.05366225913167,
-0.0223282091319561,
-0.03333541378378868,
-0.0084994500502944,
0.043554507195949554,
0.0019077952019870281,
-0.018116123974323273,
-0.10610435158014297,
-0.03983519598841667,
-0.05399861931800842,
-0.062495261430740356,
0.0030719523783773184,
0.018934695050120354,
0.008411827497184277,
-0.013388179242610931,
0.0009327530860900879,
-0.021568162366747856,
0.020439451560378075,
0.05828844755887985,
0.014775254763662815,
-0.006746287923306227,
-0.08588916063308716,
-0.005946673918515444,
0.015295218676328659,
0.02254449762403965,
-0.0027748020365834236,
-0.01028837263584137,
0.0046497671864926815,
-0.017132051289081573,
-0.05418688431382179,
-0.0372740738093853,
-0.02114066295325756,
0.009339440613985062,
-0.007764839101582766,
-0.0683523565530777,
0.044388942420482635,
-0.018071526661515236,
0.027763865888118744,
-0.04183453321456909,
-0.030607134103775024,
0.01834740675985813,
-0.06213880330324173,
-0.008147262036800385,
0.06620124727487564,
-0.011671663261950016,
-0.007873634807765484,
-0.06129062548279762,
0.001765312161296606,
-0.026340166106820107,
-0.030442116782069206,
0.005106172524392605,
-0.025862988084554672,
-0.02171291410923004,
-0.008353061974048615,
-0.022615090012550354,
-0.041319090873003006,
0.024046096950769424,
-0.026899347081780434,
0.022053280845284462,
0.049007296562194824,
0.04357907176017761,
-0.056223876774311066,
-0.030032554641366005,
0.057288430631160736,
0.012904605828225613,
-0.01579837128520012,
0.028309620916843414,
-0.03506956249475479,
-0.04343085363507271,
0.030633779242634773,
-0.004341069143265486,
0.02685021050274372,
0.032944146543741226,
0.005287757609039545,
-0.012000230140984058,
-0.021371381357312202,
0.040498193353414536,
0.00029075215570628643,
0.04343273490667343,
0.06728842854499817,
-0.051160380244255066,
0.004728288855403662,
-0.02834051288664341,
-0.06304369866847992,
0.050210896879434586,
-0.07288230210542679,
0.009896759875118732,
-0.029706602916121483,
-0.03097236156463623,
0.032683178782463074,
-0.039271511137485504,
0.016880817711353302,
0.026406342163681984,
0.05570819973945618,
-0.014482236467301846,
0.003287870204076171,
-0.03154892474412918,
-0.004953357391059399,
-0.011986637488007545,
-0.04205816239118576,
0.013335148803889751,
0.0012288481229916215,
0.0025595694314688444,
-0.024360619485378265,
0.022180676460266113,
0.01100572943687439,
-0.014995281584560871,
-0.0961175486445427,
-0.04483325034379959,
0.009467054158449173,
0.02938893251121044,
-0.03173302486538887,
-0.08695925772190094,
0.06406934559345245,
-0.011951849795877934,
0.00019811204401776195,
-0.03811300918459892,
-0.028973886743187904,
0.015290573239326477,
-0.04157087579369545,
0.011406676843762398,
-0.045740727335214615,
0.006547261495143175,
-0.0028187958523631096,
0.08067864179611206,
-0.005170825403183699,
-0.024058246985077858,
-0.0085413483902812,
-0.010778089053928852,
0.046580810099840164
] |
<p>Right now, I am considering moving from 1.25" eyepieces to 2". While I'm convinced of the quality of the premium eyepieces, it would take me years to afford a complete set and, if I go that route, I will necessarily pick them up piecemeal. Would I be wise to follow that route, knowing that in a few years time I'll have not wasted any money? </p>
<p>Or would I be wiser to buy a complete set of design <em>X</em>, which have great price/performance ratios and slowly replacing them with premium eyepieces?</p>
<p>Or would I be wiser to buy a few of type <em>Y</em> for higher-power viewing, which are still pretty expensive, but not as expensive as the 100 degrees field-of-view eyepieces, but maybe just buy 1 of those for wide-angle viewing? </p>
<p>Or another strategy? I like to look at everything, so <em>ultimately</em> I do want a pretty wide range of eyepieces. But I kind of hate that with my current mish-mash, I have a "lumpy distribution" in quality.</p> | g4733 | [
-0.021448660641908646,
0.04778166115283966,
-0.022529399022459984,
0.03961179405450821,
-0.059467822313308716,
-0.05722527951002121,
0.054703399538993835,
-0.06827244162559509,
0.03387123718857765,
0.010198412463068962,
-0.000934620329644531,
0.001724155037663877,
0.03337935730814934,
-0.004879102110862732,
-0.020737843587994576,
0.006794796325266361,
-0.0017483907286077738,
-0.024436477571725845,
0.029441988095641136,
0.03391305357217789,
-0.0031448553781956434,
0.00646907277405262,
0.007931601256132126,
-0.05003290995955467,
-0.043408989906311035,
0.0207911878824234,
0.05857257544994354,
0.03940771147608757,
-0.03441055119037628,
0.01298239454627037,
0.008041192777454853,
-0.01430855318903923,
0.03961285948753357,
-0.028866523876786232,
-0.005148342810571194,
0.032054949551820755,
0.021539803594350815,
0.059370413422584534,
-0.01914418488740921,
0.011644551530480385,
0.02345401421189308,
-0.04037687927484512,
0.028372786939144135,
-0.027851363644003868,
0.02445228211581707,
-0.014485209248960018,
-0.018654271960258484,
-0.003563182894140482,
0.08933978527784348,
-0.044511035084724426,
0.050781235098838806,
0.03385253995656967,
0.035326212644577026,
0.06874562799930573,
0.00967230275273323,
0.010765450075268745,
0.008108071982860565,
0.005641030613332987,
0.020347462967038155,
-0.013921949081122875,
-0.04729469120502472,
0.015694210305809975,
-0.004942114930599928,
-0.07988861948251724,
-0.0036182119511067867,
0.020515667274594307,
-0.04092197120189667,
-0.015543513931334019,
-0.009678380563855171,
-0.02272212505340576,
-0.06153940409421921,
-0.05511984974145889,
-0.009650557301938534,
-0.030585480853915215,
0.011538146995007992,
-0.01464645192027092,
-0.05948004499077797,
-0.007120287977159023,
0.02632998302578926,
0.025358455255627632,
-0.03591898828744888,
-0.02847624570131302,
-0.007079527713358402,
-0.015308528207242489,
0.09197210520505905,
0.0030259559862315655,
0.06228729709982872,
0.00039742980152368546,
0.031188657507300377,
0.052633725106716156,
0.01839328743517399,
-0.04827595874667168,
-0.008868438191711903,
-0.02135610580444336,
-0.03965219855308533,
0.027868151664733887,
0.038010623306035995,
0.0016921752830967307,
0.07957195490598679,
0.04541679099202156,
0.027958950027823448,
-0.04829108715057373,
-0.04215655475854874,
0.03533933311700821,
-0.008689086884260178,
0.007156917359679937,
-0.00873485580086708,
0.03767717257142067,
-0.0016839856980368495,
0.06349789351224899,
-0.06323734670877457,
0.02410200610756874,
-0.03804374486207962,
0.003936538472771645,
-0.09444649517536163,
-0.009659937582910061,
0.058764711022377014,
0.05755176395177841,
-0.036808423697948456,
0.019438717514276505,
0.02120765671133995,
-0.022581366822123528,
0.048438262194395065,
0.037263207137584686,
-0.013135246001183987,
0.016568800434470177,
-0.007701800670474768,
0.0013031810522079468,
0.036833107471466064,
0.058088477700948715,
-0.04208192974328995,
0.01265164464712143,
-0.03181593865156174,
-0.046919334679841995,
-0.010882587172091007,
-0.017575355246663094,
0.04263681918382645,
-0.01582660712301731,
-0.024867568165063858,
0.0011261494364589453,
-0.00972328893840313,
-0.04650915786623955,
-0.0027060816064476967,
-0.0415651835501194,
-0.04769304767251015,
-0.007028373423963785,
-0.033079322427511215,
-0.007482296321541071,
0.030682560056447983,
0.004742574878036976,
-0.00885085854679346,
0.046279385685920715,
0.043035831302404404,
-0.005679822992533445,
-0.018075712025165558,
-0.07915382832288742,
-0.029066704213619232,
-0.0018697631312534213,
0.016337359324097633,
-0.030291859060525894,
0.012076810002326965,
0.06717696040868759,
0.011446069926023483,
-0.0130827771499753,
0.04501475766301155,
0.020056607201695442,
-0.05465017631649971,
-0.04222774878144264,
-0.01716345176100731,
-0.06327608972787857,
0.023040512576699257,
0.019360605627298355,
0.020108142867684364,
-0.02245127223432064,
0.058811575174331665,
-0.07979677617549896,
0.05287811532616615,
0.004369658883661032,
-0.04643630236387253,
-0.04164876788854599,
-0.022002670913934708,
0.04884178936481476,
-0.028908584266901016,
-0.021135037764906883,
0.036054324358701706,
-0.0328575037419796,
0.022227590903639793,
-0.10371541976928711,
0.018746890127658844,
0.03695499524474144,
0.03787952661514282,
-0.043401941657066345,
-0.03130195662379265,
0.06418497115373611,
0.00004962380262441002,
0.010902827605605125,
-0.006178407929837704,
0.03207394480705261,
-0.08287335187196732,
-0.011667324230074883,
0.013040253892540932,
-0.03570319712162018,
-0.03801799565553665,
0.04285867139697075,
-0.05615928769111633,
0.014992833137512207,
0.0414171926677227,
0.02057679183781147,
-0.061239492148160934,
-0.03956933319568634,
-0.05661487206816673,
0.0011807726696133614,
-0.015101772733032703,
-0.02019483409821987,
0.03366845101118088,
0.02660379558801651,
-0.03640545532107353,
0.02341315522789955,
-0.0031102660577744246,
0.0050623430870473385,
-0.0414731502532959,
0.08189770579338074,
0.06300218403339386,
0.010323937982320786,
0.02819216065108776,
-0.04223577305674553,
0.06526536494493484,
0.008617389015853405,
0.06870279461145401,
0.006180086638778448,
-0.028895584866404533,
0.008763052523136139,
0.0114023108035326,
-0.01059798989444971,
0.03394175320863724,
0.05695577338337898,
0.008861969225108624,
-0.0302394051104784,
0.013011973351240158,
-0.007683210540562868,
0.10460487753152847,
0.00515378313139081,
-0.019235067069530487,
-0.05468077212572098,
0.05175105482339859,
-0.058556318283081055,
0.022628463804721832,
0.08892776817083359,
-0.030113516375422478,
-0.01476450078189373,
0.026800056919455528,
-0.054194219410419464,
0.0033657958265393972,
-0.037733279168605804,
-0.06783484667539597,
-0.015152819454669952,
0.04869644343852997,
0.04557817801833153,
0.005103868432343006,
0.06182755157351494,
-0.07479070127010345,
-0.028021780773997307,
0.011104990728199482,
-0.04298046976327896,
-0.01216867845505476,
0.06255011260509491,
-0.04678883031010628,
0.0033167931251227856,
-0.012059688568115234,
0.040425997227430344,
-0.0009079970768652856,
0.009721299633383751,
-0.011524553410708904,
0.03323422744870186,
0.02148883417248726,
-0.03706226870417595,
-0.07462901622056961,
-0.03716263547539711,
0.0070016090758144855,
0.036919206380844116,
0.06327168643474579,
-0.0058837765827775,
-0.02121761068701744,
0.05442633479833603,
0.08797883242368698,
0.06929107010364532,
0.05663854256272316,
0.027125881984829903,
0.01918930560350418,
-0.001596365706063807,
-0.018202388659119606,
0.05022107809782028,
0.01062082964926958,
-0.017368918284773827,
0.014719191938638687,
-0.033833667635917664,
-0.0009395551169291139,
0.029669765383005142,
-0.0215352401137352,
-0.009381773881614208,
0.013260380364954472,
0.027058012783527374,
0.01299525797367096,
0.02296200394630432,
0.041074227541685104,
0.021871313452720642,
-0.10289303213357925,
-0.019476432353258133,
0.03445049002766609,
-0.01684463396668434,
0.03156745806336403,
0.036358486860990524,
0.0015083394246175885,
0.010116912424564362,
0.011513604782521725,
-0.05478262901306152,
0.025072798132896423,
0.043706264346838,
-0.04456033185124397,
0.025677789002656937,
0.04487999901175499,
0.036620788276195526,
0.0043409643694758415,
-0.032354917377233505,
-0.009505029767751694,
0.03539581224322319,
0.029532814398407936,
-0.037180352956056595,
-0.01673247665166855,
0.060028962790966034,
0.02084655687212944,
-0.00865644495934248,
-0.022336889058351517,
0.056221384555101395,
0.01763167418539524,
0.026118557900190353,
0.04053766280412674,
-0.020485740154981613,
0.0471031628549099,
0.018971795216202736,
-0.0055955820716917515,
0.061170317232608795,
0.022173017263412476,
0.013299346901476383,
0.03550104424357414,
-0.0801469162106514,
-0.01880393549799919,
-0.017748242244124413,
-0.010320347733795643,
-0.0660080537199974,
-0.015712864696979523,
-0.05332425609230995,
0.035571422427892685,
0.058840539306402206,
-0.013826989568769932,
-0.0008386380504816771,
0.0005277420277707279,
-0.04852151870727539,
0.028275419026613235,
-0.0008369184215553105,
0.03886202722787857,
-0.040633268654346466,
0.019589697942137718,
-0.03512873128056526,
-0.047647662460803986,
-0.028151581063866615,
-0.03624434769153595,
0.0064535425044596195,
0.007528663147240877,
-0.020667800679802895,
0.01605634205043316,
-0.0057520936243236065,
-0.011607373133301735,
-0.008159118704497814,
-0.0783853679895401,
-0.007673258427530527,
0.04983943700790405,
-0.06960158795118332,
0.04395783320069313,
-0.03418789058923721,
-0.005861916113644838,
0.0721941590309143,
-0.047104984521865845,
0.015754396095871925,
0.016460951417684555,
-0.028507832437753677,
-0.018350424244999886,
-0.06803324818611145,
0.00017053584451787174,
-0.030989032238721848,
0.05446791276335716,
-0.008131110109388828,
0.003202521475031972,
-0.0051855891942977905,
0.0343964546918869,
-0.06600352376699448,
-0.012287560850381851,
-0.029295410960912704,
-0.009370577521622181,
0.04691064730286598,
0.01514266338199377,
0.018759485334157944,
0.007454914040863514,
0.006012477912008762,
0.008094800636172295,
-0.03357476741075516,
-0.03909540921449661,
0.0066953315399587154,
-0.04297565668821335,
-0.06103017181158066,
-0.00972217321395874,
-0.008584655821323395,
0.05261767655611038,
0.011960132047533989,
0.00962283555418253,
0.013492497615516186,
-0.07996722310781479,
-0.02766484208405018,
0.052573032677173615,
-0.0035032702144235373,
-0.050315678119659424,
0.04717718064785004,
0.02444830723106861,
-0.0051765539683401585,
0.05435079708695412,
-0.023146528750658035,
0.021068310365080833,
-0.06339354813098907,
-0.02156144194304943,
0.002028352115303278,
0.01099548302590847,
-0.013968356885015965,
0.029544051736593246,
-0.03342898562550545,
0.034754324704408646,
0.01509212888777256,
0.06046614050865173,
-0.008988650515675545,
-0.05419200658798218,
0.032731737941503525,
0.02905484288930893,
0.06684552878141403,
-0.041546061635017395,
-0.04046143963932991,
-0.0007493027951568365,
-0.04358983784914017,
-0.05889855697751045,
0.02296389266848564,
-0.01644757390022278,
-0.037889447063207626,
-0.019795628264546394,
0.005510234273970127,
0.02157246321439743,
-0.06374500691890717,
0.012713390402495861,
-0.0334455743432045,
-0.01905805617570877,
0.035381216555833817,
0.04904697835445404,
-0.018146930262446404,
0.03268728777766228,
-0.0289287306368351,
-0.026889530941843987,
0.030776476487517357,
0.05354057997465134,
0.030182231217622757,
-0.06267840415239334,
-0.03748910874128342,
-0.04179910197854042,
-0.025212757289409637,
-0.06538596004247665,
-0.01466442458331585,
0.011577993631362915,
-0.011097480542957783,
-0.046819064766168594,
0.021520672366023064,
-0.0017689827363938093,
-0.05492272973060608,
0.004185746889561415,
0.024676619097590446,
-0.031846385449171066,
-0.06396490335464478,
0.0330265611410141,
-0.030376024544239044,
0.03656497597694397,
-0.06315750628709793,
0.006831227336078882,
-0.018353743478655815,
0.04100016877055168,
0.04381689801812172,
-0.011901562102138996,
0.0006499348673969507,
-0.01175413466989994,
-0.010068321600556374,
-0.10591340065002441,
0.03147508576512337,
0.08321435749530792,
-0.0010966466506943107,
0.04619312658905983,
-0.033595215529203415,
-0.0068373847752809525,
0.03506787121295929,
0.011884565465152264,
-0.028745273128151894,
-0.007407584227621555,
-0.01490151509642601,
0.030236901715397835,
0.015603708103299141,
-0.001775204436853528,
0.010642643086612225,
0.005840899422764778,
-0.024093328043818474,
-0.028216134756803513,
-0.020072823390364647,
0.025650344789028168,
-0.046132832765579224,
-0.029093045741319656,
0.07473162561655045,
-0.00981327798217535,
-0.009919573552906513,
0.032635144889354706,
-0.025970950722694397,
0.019067734479904175,
0.036861319094896317,
0.020861182361841202,
0.05635062977671623,
-0.015793101862072945,
0.030474258586764336,
-0.02095818892121315,
-0.016849350184202194,
0.0300726480782032,
-0.005681545473635197,
-0.010998129844665527,
-0.007188372779637575,
-0.05077963322401047,
0.06162586808204651,
-0.029468171298503876,
0.06692968308925629,
-0.022100506350398064,
-0.03719435632228851,
-0.0600372776389122,
0.021653195843100548,
0.036302272230386734,
0.020606841892004013,
-0.019862528890371323,
-0.013267659582197666,
0.007508410606533289,
0.017312290146946907,
0.03879363834857941,
-0.020530302077531815,
-0.023765914142131805,
-0.0016409100499004126,
0.005388920661062002,
-0.02541940286755562,
0.05905217304825783,
0.022488363087177277,
0.04401570186018944,
0.03269844874739647,
0.05362551286816597,
-0.03172796592116356,
-0.011255431920289993,
-0.01693429797887802,
-0.0064445557072758675,
-0.02693210542201996,
0.02072644978761673,
-0.0004810988320969045,
0.014389204792678356,
-0.01277109794318676,
-0.035466477274894714,
0.09950801730155945,
-0.017161626368761063,
-0.03880903124809265,
-0.030019911006093025,
0.024486109614372253,
0.01604815013706684,
0.004677302204072475,
-0.013309188187122345,
-0.03347007930278778,
0.033027924597263336,
0.03265483304858208,
-0.008524101227521896,
-0.024478232488036156,
-0.009043280966579914,
0.02761090360581875,
-0.030604802072048187,
0.028327591717243195,
0.05252461135387421,
-0.03230427950620651,
0.0004660642589442432,
-0.01363434363156557,
-0.0387171246111393,
0.006931029260158539,
0.02963835373520851,
0.0074947671964764595,
-0.00809434149414301,
0.020341865718364716,
0.02684379555284977,
0.03330075740814209,
-0.03888761252164841,
0.02874123491346836,
0.016679449006915092,
-0.000284418259980157,
0.04364553838968277,
-0.04644780233502388,
0.026419077068567276,
-0.03464120626449585,
-0.027046723291277885,
-0.026157444342970848,
0.011778137646615505,
-0.012716992758214474,
-0.050363168120384216,
-0.01772279106080532,
0.007494717836380005,
0.017050543799996376,
0.03413941338658333,
0.050000421702861786,
-0.0071064261719584465,
-0.010524631477892399,
-0.0300142839550972,
0.01772371493279934,
0.01067348476499319,
0.008107693865895271,
-0.041537441313266754,
0.03211072459816933,
-0.028807757422327995,
0.0423675961792469,
0.05604081228375435,
-0.04044622182846069,
0.09508342295885086,
-0.0069606248289346695,
0.07480116933584213,
-0.03220357373356819,
-0.011015634983778,
0.032185912132263184,
-0.03709273785352707,
-0.03579883277416229,
-0.03810914605855942,
-0.002003322122618556,
-0.032579660415649414,
-0.008347533643245697,
0.026141205802559853,
0.003469947027042508,
-0.0006225547404028475,
0.018496574833989143,
0.06088627874851227,
0.003480561776086688,
-0.010931557044386864,
0.027884196490049362,
-0.008123449981212616,
-0.01876724883913994,
0.02307095378637314,
0.00946040078997612,
-0.046818848699331284,
-0.009071214124560356,
-0.01391564030200243,
0.082523413002491,
0.04562652111053467,
0.004247494041919708,
0.06407178193330765,
-0.02334461733698845,
0.028011787682771683,
-0.03607278689742088,
-0.008485650643706322,
-0.007798456121236086,
-0.029348164796829224,
-0.047344714403152466,
-0.02658350020647049,
-0.021214773878455162,
0.003284874837845564,
-0.005620424170047045,
0.0582890510559082,
0.02328607812523842,
-0.05213095247745514,
-0.04023133963346481,
0.023801451548933983,
-0.02407900243997574,
-0.08879414200782776,
-0.05789151415228844,
-0.03455023467540741,
0.024595098569989204,
-0.007966510020196438,
-0.010216985829174519,
0.05235777795314789,
-0.01710168458521366,
-0.07599403709173203,
0.08183635771274567,
-0.0455741286277771,
-0.050173766911029816,
0.04203272983431816,
-0.013952563516795635,
0.02093689702451229,
-0.04300889000296593,
0.019671887159347534,
0.06662130355834961,
-0.018933771178126335,
-0.0014321160269901156,
0.029857372865080833,
-0.008291199803352356,
-0.035789184272289276,
-0.018212469294667244,
-0.020753666758537292,
0.03188786655664444,
-0.01645187847316265,
-0.03889797627925873,
-0.05048840492963791,
0.02102925255894661,
0.011164965108036995,
-0.023672383278608322,
0.03695300221443176,
0.04251686856150627,
-0.009554565884172916,
0.03769757226109505,
0.022183241322636604,
0.023282986134290695,
-0.03832518681883812,
-0.02676955983042717,
0.02182014100253582,
-0.045095134526491165,
-0.017082205042243004,
0.03506280109286308,
-0.028252048417925835,
-0.006851819343864918,
0.03192643076181412,
-0.003963723313063383,
0.026597583666443825,
0.03729373216629028,
0.012867114506661892,
-0.05202923342585564,
-0.03689204156398773,
-0.05060388147830963,
-0.0035391550045460463,
-0.008461729623377323,
-0.05946950986981392,
0.011346598155796528,
0.033804308623075485,
0.027504362165927887,
0.007674825843423605,
0.012578591704368591,
-0.04876898229122162,
0.0024531299713999033,
0.0058576189912855625,
0.011524169705808163,
-0.016649113968014717,
-0.012672103010118008,
-0.042923703789711,
0.04346741735935211,
-0.014668541960418224,
-0.007778529077768326,
-0.046638522297143936,
0.016982456669211388,
-0.044191036373376846,
0.0308359544724226,
-0.02384592592716217,
-0.02272759936749935,
0.007059830706566572,
0.03102440945804119,
0.07657216489315033,
-0.04090046510100365,
-0.02519499696791172,
0.06933073699474335,
-0.00003632991501945071,
0.01111588254570961,
0.0000011949592817472876,
0.0034274524077773094,
-0.06025480851531029,
-0.021526658907532692,
0.0010867646196857095,
-0.03269471973180771
] |
<p>When talking about the spinor-helicity formalism in his new textbook on quantum field theory, Matthew D. Schwartz claims as a highly nontrivial example, it is quite easy to use the Parke-Taylor formula to calculate the $gg\to ggg$ scattering cross section at tree level by hand, which is also one of the problems in the book. (Problem is found on page 560, problem 27.6)</p>
<p>Can anyone tell me how to do this exactly? It looks like we cannot avoid summing $24^2$ terms, and in the paper, <a href="http://www.sciencedirect.com/science/article/pii/0550321386902300" rel="nofollow">http://www.sciencedirect.com/science/article/pii/0550321386902300</a>, the cross section of $gg\rightarrow gggg$ spans several pages! This makes me expect the cross section for $gg\rightarrow ggg$ is also complicated. Is there any smart way to do it?</p> | g4734 | [
-0.028108900412917137,
0.06661267578601837,
-0.026453804224729538,
-0.01257249154150486,
0.003917820286005735,
-0.019588831812143326,
0.021400898694992065,
0.029938476160168648,
-0.04866214096546173,
0.06500200182199478,
0.012393324635922909,
0.005514998454600573,
0.03347906470298767,
-0.020768044516444206,
0.06101695075631142,
0.006494726520031691,
0.06534011662006378,
0.046941064298152924,
0.014280016534030437,
-0.0033595962449908257,
-0.008255761116743088,
0.002196164336055517,
-0.0168819148093462,
-0.04229073226451874,
0.013714938424527645,
-0.07033875584602356,
-0.022794021293520927,
-0.0037558842450380325,
-0.030819762498140335,
-0.02180601842701435,
-0.004165756516158581,
0.03897678479552269,
-0.0106344697996974,
-0.04076971113681793,
-0.01903632842004299,
0.0036778287030756474,
0.033858366310596466,
0.00031037876033224165,
-0.020174264907836914,
0.01471208967268467,
0.009343349374830723,
0.04045134410262108,
0.027383001521229744,
-0.009531023912131786,
-0.05107688531279564,
-0.016489606350660324,
0.05110250413417816,
0.018418995663523674,
-0.03206426650285721,
-0.02882593870162964,
-0.09830330312252045,
0.00803639367222786,
0.04622792825102806,
-0.02707497403025627,
-0.01912892982363701,
0.039764583110809326,
-0.016143066808581352,
0.00461937952786684,
0.01585601270198822,
0.00928928330540657,
0.0474294014275074,
-0.016085321083664894,
0.044621791690588,
0.0026252632960677147,
0.00881102029234171,
-0.03840315714478493,
-0.003537948476150632,
0.032002467662096024,
-0.050478123128414154,
0.011119838804006577,
0.035077329725027084,
-0.027958454564213753,
0.0783495232462883,
0.02663499116897583,
-0.015814317390322685,
-0.04316950589418411,
-0.006356753874570131,
0.05363424867391586,
0.03511010482907295,
0.0264685470610857,
-0.040125522762537,
-0.02853957936167717,
-0.041224170476198196,
-0.036613579839468,
-0.05619677156209946,
-0.04526067152619362,
0.025488151237368584,
0.05720552057027817,
-0.05783851817250252,
0.04635394737124443,
0.03822823986411095,
-0.01914951018989086,
0.010359038598835468,
-0.004269260913133621,
-0.017818931490182877,
-0.019241884350776672,
-0.03596355766057968,
0.045350581407547,
-0.010649805888533592,
-0.01383418869227171,
-0.024277515709400177,
0.07486609369516373,
0.02559875138103962,
0.009120478294789791,
0.0011532556964084506,
0.021829865872859955,
-0.006793066393584013,
-0.015359870158135891,
-0.020777836441993713,
0.014100734144449234,
-0.055310022085905075,
-0.018247539177536964,
-0.025508658960461617,
0.053044967353343964,
-0.029504962265491486,
-0.024073367938399315,
0.09236299991607666,
0.007322085555642843,
0.029843460768461227,
0.011257493868470192,
-0.010351236909627914,
0.012344184331595898,
0.004248655401170254,
0.06357923895120621,
-0.0020422465167939663,
-0.012901989743113518,
-0.007718679495155811,
0.006560939829796553,
0.05580897256731987,
-0.0399499386548996,
0.014593640342354774,
-0.005201971158385277,
0.03917921334505081,
0.08865653723478317,
0.02320210076868534,
0.0014199899742379785,
0.019235020503401756,
0.052083659917116165,
-0.007227346766740084,
-0.03556356951594353,
-0.042981866747140884,
-0.01853860355913639,
-0.032780829817056656,
0.003235637443140149,
0.06255342066287994,
0.013027522712945938,
0.016900915652513504,
-0.07127007842063904,
-0.009339661337435246,
-0.0603383332490921,
0.0405721515417099,
-0.01097381953150034,
0.07327073067426682,
-0.061967410147190094,
0.0367296002805233,
-0.02244698815047741,
0.023291677236557007,
-0.027043141424655914,
0.03461749479174614,
-0.01391954068094492,
-0.0020075151696801186,
-0.039752472192049026,
-0.025969740003347397,
0.0007699662237428129,
-0.0059949541464447975,
0.05599912628531456,
-0.011083715595304966,
-0.049391765147447586,
-0.06909967213869095,
-0.03581256419420242,
0.010930871590971947,
-0.00995196308940649,
0.03661299869418144,
-0.026745421811938286,
-0.012537567876279354,
0.04816218838095665,
0.021840550005435944,
-0.023616086691617966,
0.019785620272159576,
0.004788538906723261,
0.013533573597669601,
-0.02763311006128788,
-0.03426789119839668,
0.04280874505639076,
0.007779233623296022,
0.01853463612496853,
0.021588241681456566,
0.0010356251150369644,
0.03632967919111252,
0.029124416410923004,
-0.06345222890377045,
0.02764384262263775,
-0.03312181308865547,
0.024825653061270714,
-0.021273884922266006,
0.05956519395112991,
0.05738511681556702,
-0.012307524681091309,
-0.039763931185007095,
0.02269178256392479,
-0.030593764036893845,
0.029990127310156822,
-0.022411121055483818,
0.0033334391191601753,
0.0501127690076828,
-0.002847763244062662,
-0.0008949316688813269,
0.014538794755935669,
-0.022742751985788345,
-0.04823438823223114,
0.027170032262802124,
-0.01748441904783249,
0.006723525933921337,
0.05211591348052025,
-0.03309347480535507,
-0.010402620770037174,
-0.01842769980430603,
0.004141129553318024,
-0.014784436672925949,
0.06429890543222427,
-0.05020535737276077,
0.03266739845275879,
0.005074335727840662,
0.044740814715623856,
-0.013389389961957932,
0.06259706616401672,
0.03713894635438919,
0.005181256216019392,
-0.01688750460743904,
-0.09242045134305954,
-0.05519029498100281,
0.0016884824726730585,
-0.09873253852128983,
-0.0550241693854332,
-0.011438563466072083,
-0.01731562614440918,
-0.021389279514551163,
0.0034317593090236187,
0.04510365426540375,
-0.0004670123744290322,
0.027781009674072266,
-0.032290372997522354,
-0.006332459859549999,
0.02729751728475094,
0.02599981427192688,
-0.017108237370848656,
-0.01453405525535345,
0.004793202970176935,
-0.02698826789855957,
0.015988577157258987,
0.04256175458431244,
-0.01066303439438343,
-0.00902516208589077,
-0.021627170965075493,
-0.025862917304039,
-0.008486136794090271,
0.010957828722894192,
0.003259118879213929,
0.011450685560703278,
0.011445245705544949,
0.030967993661761284,
-0.030475065112113953,
0.0638909637928009,
0.021308941766619682,
-0.10111939162015915,
-0.014514891430735588,
0.00914972648024559,
-0.013658804818987846,
-0.021396467462182045,
-0.051861170679330826,
-0.066716268658638,
0.037048615515232086,
-0.0006036824779585004,
-0.02373679168522358,
-0.03822731599211693,
-0.041418056935071945,
-0.012607676908373833,
0.021569792181253433,
0.019324876368045807,
0.020681777969002724,
-0.007961796596646309,
-0.05728461593389511,
0.007240870967507362,
0.011663304641842842,
0.0637955591082573,
-0.007482513319700956,
0.017360812053084373,
0.044808048754930496,
0.06355414539575577,
0.03550759330391884,
-0.009021161124110222,
-0.0034119703341275454,
-0.010446654632687569,
-0.0017318534664809704,
-0.06745242327451706,
0.03605810925364494,
0.03654683008790016,
-0.01631796918809414,
0.04380624741315842,
0.03917066380381584,
-0.009375710971653461,
0.017770269885659218,
0.010683032684028149,
0.07691484689712524,
0.007773214485496283,
0.0009908732026815414,
-0.005293107125908136,
-0.015395079739391804,
0.027261126786470413,
-0.013100067153573036,
0.006514038424938917,
0.00889081321656704,
0.05731130763888359,
0.00804821029305458,
0.024200554937124252,
-0.028022289276123047,
0.008162940852344036,
0.004602457862347364,
0.02677604742348194,
-0.0018499490106478333,
-0.010105338878929615,
-0.022746818140149117,
0.030515996739268303,
0.01786067523062229,
-0.048348259180784225,
0.04000980406999588,
-0.08950472623109818,
0.042353078722953796,
-0.0059701986610889435,
-0.021634403616189957,
0.017920490354299545,
-0.016956815496087074,
0.023757750168442726,
-0.01370931975543499,
-0.009023747406899929,
-0.057216912508010864,
-0.01597713492810726,
0.014078047126531601,
0.008100016973912716,
0.012831289321184158,
-0.047647424042224884,
-0.09092938154935837,
-0.050933606922626495,
-0.04431668296456337,
-0.03993383049964905,
0.014455098658800125,
-0.01991894841194153,
0.033828601241111755,
0.007990316487848759,
0.0001738312712404877,
-0.025210531428456306,
0.02652476169168949,
-0.019673354923725128,
0.04241868853569031,
0.00003020006261067465,
0.04960576444864273,
-0.021902238950133324,
-0.007760625798255205,
-0.00014453631592914462,
-0.005863857455551624,
0.02875569276511669,
-0.0002739409974310547,
0.009823249652981758,
0.03304620459675789,
0.031670551747083664,
0.033906567841768265,
-0.02155505120754242,
0.01995629072189331,
0.011551916599273682,
0.04135186970233917,
0.006824362091720104,
-0.014024208299815655,
0.08150183409452438,
0.006959880236536264,
0.019259976223111153,
-0.034259308129549026,
0.04388825595378876,
-0.06397925317287445,
-0.04565740376710892,
-0.011660589836537838,
-0.017367688938975334,
0.032511405646800995,
0.004008991178125143,
0.022077279165387154,
0.05934557691216469,
0.00010490947170183063,
-0.06225649267435074,
-0.00979560986161232,
0.0038705056067556143,
0.08545249700546265,
0.03033476695418358,
-0.004611160606145859,
-0.009138436056673527,
0.006288400385528803,
0.02715180441737175,
-0.009031806141138077,
-0.04946137219667435,
0.014145821332931519,
-0.10760655254125595,
0.05415552109479904,
0.017802098765969276,
-0.009166243486106396,
0.05981476604938507,
-0.0376921147108078,
-0.02282235585153103,
-0.0340726412832737,
0.0224202498793602,
0.01827501319348812,
0.010543000884354115,
0.0402446910738945,
0.0055487132631242275,
-0.02723095379769802,
0.010148802772164345,
-0.021466217935085297,
0.0771254301071167,
-0.019183119758963585,
0.04237746447324753,
-0.05675435811281204,
-0.012243378907442093,
-0.028797529637813568,
0.04960119351744652,
-0.007181862834841013,
0.06704584509134293,
-0.03483273833990097,
-0.02725926786661148,
0.02662394568324089,
-0.048021070659160614,
0.019916336983442307,
-0.0075089591555297375,
-0.009892413392663002,
0.0699542835354805,
0.015172746963799,
-0.03742806613445282,
0.020023023709654808,
-0.07191190868616104,
0.04883478209376335,
-0.07888460904359818,
0.03463435545563698,
0.026298951357603073,
-0.004921963904052973,
0.02288070321083069,
0.0002622836909722537,
0.023431116715073586,
0.036876529455184937,
0.02007860504090786,
0.014954302459955215,
-0.049375854432582855,
-0.06075217202305794,
-0.00193597876932472,
-0.03131807968020439,
-0.0638556107878685,
-0.03613512963056564,
0.04727160558104515,
0.00884932279586792,
-0.020863043144345284,
-0.003623256692662835,
-0.0815977081656456,
0.03730257973074913,
-0.0003421771398279816,
0.03434296324849129,
-0.0019642950501292944,
0.014509189873933792,
-0.05874337628483772,
0.031718477606773376,
-0.015162074007093906,
0.03470117971301079,
-0.07476431876420975,
0.04280755668878555,
0.04477667808532715,
-0.0006547293742187321,
-0.002530050463974476,
0.02295319363474846,
0.0023411542642861605,
-0.06525819003582001,
-0.09954055398702621,
0.03467665612697601,
-0.04364124685525894,
0.014369980432093143,
-0.061129529029130936,
0.012001232244074345,
-0.04925989732146263,
-0.055641692131757736,
-0.001021063420921564,
-0.01964448019862175,
0.005565737374126911,
0.022186897695064545,
0.06224226951599121,
0.008333530277013779,
-0.035586025565862656,
0.001633521867915988,
-0.000950413930695504,
-0.04057212546467781,
0.008284679614007473,
-0.029796134680509567,
-0.019431615248322487,
-0.037206683307886124,
0.13331866264343262,
-0.013433395884931087,
-0.009626300074160099,
-0.011680260300636292,
-0.0005688434466719627,
0.004304082132875919,
-0.004941668827086687,
0.03802962228655815,
-0.0174788236618042,
0.08356936275959015,
0.09269046038389206,
0.010129457339644432,
0.001086078817024827,
0.030053887516260147,
0.04855290800333023,
-0.03883511200547218,
0.04508226737380028,
0.02518482133746147,
-0.007911148481070995,
-0.0357678160071373,
-0.009637386538088322,
0.019970403984189034,
-0.037285659462213516,
0.03457287698984146,
0.04536646977066994,
0.006209921091794968,
-0.05157976225018501,
-0.04709722474217415,
0.020949847996234894,
0.03675917163491249,
-0.02404932491481304,
-0.017603924497961998,
-0.014057189226150513,
0.040185198187828064,
0.006445511244237423,
-0.0775630921125412,
-0.015199851244688034,
0.014058067463338375,
-0.0029259349685162306,
-0.046031177043914795,
-0.0034110327251255512,
-0.033689189702272415,
0.057693082839250565,
0.013261353597044945,
-0.04017651453614235,
-0.010553560219705105,
0.03367355465888977,
0.023101460188627243,
-0.010371779091656208,
-0.027251143008470535,
-0.020267179235816002,
-0.004286469891667366,
-0.0004484491073526442,
-0.05703836679458618,
-0.040019016712903976,
-0.015897702425718307,
0.03501752391457558,
0.026558781042695045,
0.012758057564496994,
0.004372748546302319,
-0.01804923638701439,
-0.06692015379667282,
0.014122865162789822,
0.04172910004854202,
0.026414617896080017,
-0.05204411596059799,
0.013634136877954006,
-0.048328567296266556,
0.02748684398829937,
-0.0032208433840423822,
-0.022282321006059647,
-0.07106322795152664,
0.05587155744433403,
0.018256723880767822,
-0.02719481848180294,
-0.03276802971959114,
0.005943713244050741,
0.050188980996608734,
-0.003505146596580744,
-0.009902753867208958,
0.014193796552717686,
-0.045293472707271576,
-0.0024744230322539806,
0.05021682381629944,
-0.002650774782523513,
0.031142937019467354,
-0.009190508164465427,
-0.013259727507829666,
-0.015658657997846603,
0.0267525315284729,
-0.011397273279726505,
-0.054970599710941315,
-0.01687757670879364,
0.0059498874470591545,
-0.0701792985200882,
0.02725972607731819,
-0.00545987393707037,
0.013793249614536762,
-0.008075828664004803,
-0.07269331812858582,
0.04743117094039917,
0.062059156596660614,
0.011037411168217659,
-0.023383254185318947,
0.010616633109748363,
-0.03965874761343002,
0.060048189014196396,
-0.018461337313055992,
0.0051769171841442585,
0.06919638067483902,
-0.059107668697834015,
0.002795287873595953,
0.01719639264047146,
-0.03555389866232872,
0.05462052673101425,
0.005842482205480337,
0.03532443568110466,
-0.0023202255833894014,
-0.008061544969677925,
0.0014494966017082334,
-0.05154000222682953,
-0.005571268033236265,
0.020394595339894295,
0.030883150175213814,
0.0465230867266655,
0.0023277769796550274,
0.004618532955646515,
-0.07288696616888046,
0.02397104725241661,
0.07828943431377411,
-0.015423963777720928,
0.02888420596718788,
0.020699594169855118,
-0.04972927272319794,
0.059166423976421356,
0.034233804792165756,
-0.017444249242544174,
0.02661331370472908,
0.0004157617222517729,
0.01299339160323143,
-0.07100245356559753,
0.015910863876342773,
-0.019330499693751335,
0.10226383805274963,
-0.039043694734573364,
-0.02084382064640522,
0.03497873991727829,
-0.017597662284970284,
-0.015285888686776161,
-0.01296372152864933,
-0.03608737885951996,
-0.05438847839832306,
-0.061783939599990845,
0.033593203872442245,
0.06639385968446732,
-0.023750202730298042,
0.02872287668287754,
0.01788236014544964,
0.002810639562085271,
-0.01697482168674469,
0.06475772708654404,
0.0065637254156172276,
0.027235329151153564,
0.024012744426727295,
-0.07693704962730408,
0.0017650587251409888,
0.017930414527654648,
-0.0008905446156859398,
-0.01283565815538168,
0.04625624045729637,
0.046422310173511505,
-0.016305234283208847,
0.030235737562179565,
0.013394936919212341,
-0.03569749742746353,
-0.08003687858581543,
-0.08360261470079422,
-0.0014474274357780814,
-0.0026004903484135866,
-0.027914131060242653,
-0.030469782650470734,
-0.0003844595921691507,
-0.0414084754884243,
-0.029610591009259224,
-0.022065361961722374,
-0.00253154244273901,
-0.06023314967751503,
0.015088824555277824,
-0.00043215471669100225,
0.0002300029300386086,
-0.03034008853137493,
0.05180590599775314,
0.028804823756217957,
-0.007877261377871037,
-0.024573594331741333,
0.021676406264305115,
0.011329296976327896,
0.01925206370651722,
0.003979342989623547,
0.050466619431972504,
-0.037782348692417145,
-0.01552128791809082,
0.0004962058737874031,
0.029340090230107307,
0.04510245472192764,
0.005762091837823391,
0.00011319740588078275,
-0.040565285831689835,
0.009138285182416439,
-0.03824097663164139,
0.0002994630194734782,
-0.006194666028022766,
-0.01634911261498928,
-0.03980512544512749,
0.009873650036752224,
0.06847939640283585,
-0.0936577096581459,
0.033083099871873856,
0.03909076750278473,
-0.004952709656208754,
-0.002501297742128372,
0.04005854204297066,
-0.006026109214872122,
0.01765863038599491,
0.007681312505155802,
-0.04499568045139313,
-0.00465770810842514,
0.0016829242231324315,
0.035861141979694366,
0.00008738240285310894,
0.007013258524239063,
-0.024287404492497444,
0.05685735121369362,
0.06815697997808456,
-0.01539544202387333,
-0.030658986419439316,
-0.05414169654250145,
-0.008095509372651577,
-0.0004556939238682389,
0.004113002214580774,
-0.06778713315725327,
-0.1328885853290558,
0.033515676856040955,
0.012982034124433994,
0.020502382889389992,
-0.03198878467082977,
0.01240171492099762,
-0.033227138221263885,
-0.07054680585861206,
0.04184945672750473,
-0.058168210089206696,
0.010953748598694801,
0.018161095678806305,
-0.0032570529729127884,
-0.0011863576946780086,
0.0365045890212059,
-0.0033895347733050585,
0.07427792251110077,
0.05356302112340927,
-0.054032545536756516,
0.0080888532102108,
0.02561490796506405,
-0.013815359212458134,
0.05393582582473755,
-0.035137154161930084,
-0.003986228257417679,
-0.01999988965690136,
0.02855444885790348,
0.007853050716221333,
-0.043354135006666183,
-0.012162686325609684,
0.02094384655356407
] |
<p>I was reading Wikipedia article about <a href="http://en.wikipedia.org/wiki/Universe">universe</a> and stumbled upon pie chart which represents what universe contains. <a href="http://upload.wikimedia.org/wikipedia/commons/7/76/Cosmological_Composition_%E2%80%93_Pie_Chart.svg">It says</a> that stars make up 0.5% of whole universe. </p>
<p>I tried to find average distance between stars in the universe, but came to some different numbers, but either way distance is more than 1 light year. At the same time even largest stars in the universe which have 1400 sun radius are 0.00020584 light years in diameter (by my calculations), so it makes absolutely no sense that 0.5% of universe consists of stars, number should be many times smaller. What I am missing here?</p> | g4735 | [
-0.027661515399813652,
0.02324873022735119,
-0.005981073714792728,
-0.06370122730731964,
-0.04235023260116577,
-0.004546519368886948,
0.019234593957662582,
-0.028457364067435265,
0.010879280045628548,
-0.03165507689118385,
0.02866975963115692,
-0.048143673688173294,
0.01359513308852911,
-0.010763250291347504,
0.013719236478209496,
0.026431430131196976,
-0.0008217043941840529,
-0.06253217905759811,
0.026484040543437004,
0.02335236966609955,
-0.009057513438165188,
-0.022698454558849335,
0.03405548632144928,
-0.07698322832584381,
-0.00963146798312664,
0.004421930760145187,
0.016559161245822906,
0.004611765965819359,
-0.04602660611271858,
0.008817258290946484,
0.005302671808749437,
0.013931901194155216,
0.06461944431066513,
-0.011153990402817726,
-0.011144617572426796,
-0.008286354131996632,
-0.03987428918480873,
-0.017097387462854385,
0.0746026337146759,
0.006938274949789047,
-0.015361519530415535,
0.03218091279268265,
0.03656098246574402,
-0.026981987059116364,
0.010891414247453213,
-0.027611829340457916,
-0.07235835492610931,
0.04070383310317993,
0.05531322583556175,
-0.02135700173676014,
0.0010628040181472898,
-0.01653079129755497,
0.05485008284449577,
0.02653210237622261,
0.04965125396847725,
0.03223264962434769,
0.008276672102510929,
-0.07945133745670319,
0.04577744007110596,
0.021464696153998375,
-0.007417665328830481,
-0.043547749519348145,
0.012376784346997738,
0.03556133434176445,
0.029097484424710274,
0.016049249097704887,
-0.02391069009900093,
-0.018592393025755882,
0.05322699621319771,
-0.030061431229114532,
-0.019132915884256363,
-0.04873562604188919,
0.02852656878530979,
-0.03859076276421547,
-0.06768305599689484,
0.02174212597310543,
-0.026906972751021385,
0.02376604825258255,
-0.016500717028975487,
0.06219936162233353,
0.03160056471824646,
-0.05088008940219879,
-0.011982081457972527,
0.037910498678684235,
-0.004609560593962669,
-0.04928294196724892,
-0.03503875434398651,
-0.007740208879113197,
-0.005951171275228262,
0.09292107820510864,
-0.02376781776547432,
-0.010371372103691101,
0.08038382977247238,
-0.03054094687104225,
0.01540039200335741,
0.009812092408537865,
-0.0147025678306818,
0.013724852353334427,
-0.04879222437739372,
0.03291130065917969,
-0.028984028846025467,
-0.0005432642647065222,
0.069098100066185,
0.0013759492430835962,
0.019431423395872116,
0.03869976848363876,
0.016652408987283707,
-0.04690949618816376,
-0.016205117106437683,
0.03496532514691353,
-0.023170147091150284,
-0.0034757365938276052,
-0.018713127821683884,
-0.01195626799017191,
0.014632968232035637,
-0.0640202984213829,
0.05582297220826149,
-0.015706511214375496,
0.03368725627660751,
0.032328881323337555,
0.018450332805514336,
0.04053551331162453,
-0.007739992346614599,
0.004739245865494013,
-0.10383392870426178,
-0.05090092867612839,
0.01685994863510132,
-0.017275307327508926,
0.03653154894709587,
-0.05009846016764641,
-0.046343304216861725,
-0.02484017051756382,
-0.03156311810016632,
-0.011806022375822067,
-0.00461854413151741,
0.02631187066435814,
0.055050965398550034,
-0.03544941172003746,
-0.06046072766184807,
0.018029095605015755,
0.01473618671298027,
-0.00029418544727377594,
0.03204819932579994,
-0.06334371864795685,
-0.02908473275601864,
0.009224255569279194,
-0.016474543139338493,
-0.02021564543247223,
-0.051780931651592255,
-0.035472337156534195,
0.06616208702325821,
0.03317011520266533,
-0.0008821306400932372,
-0.015670832246541977,
-0.037256963551044464,
-0.0651366114616394,
-0.034431762993335724,
0.034101419150829315,
-0.013108981773257256,
-0.01889493316411972,
0.008946364745497704,
0.014798581600189209,
0.05063250660896301,
-0.02543172612786293,
0.004234290681779385,
0.07371737062931061,
-0.0018305648118257523,
-0.062729112803936,
-0.025701912119984627,
-0.03920302540063858,
-0.05565191060304642,
-0.03182563558220863,
0.04044824466109276,
0.026460057124495506,
-0.004892576485872269,
0.01946742832660675,
0.09089211374521255,
0.011940632946789265,
-0.060463741421699524,
0.07722679525613785,
-0.009014325216412544,
-0.043807804584503174,
0.029385454952716827,
0.021227238699793816,
-0.03092111088335514,
-0.04379262402653694,
0.009935997426509857,
-0.03139087185263634,
0.04143357276916504,
0.03772991895675659,
0.040115851908922195,
-0.036361876875162125,
0.004201375879347324,
-0.03554467856884003,
0.004161357879638672,
-0.023528916761279106,
0.02474772185087204,
-0.02577861398458481,
-0.056911785155534744,
-0.022723671048879623,
-0.010872835293412209,
0.03344099968671799,
-0.0030791531316936016,
-0.01946224458515644,
-0.013308024033904076,
0.002126990118995309,
-0.04374547675251961,
0.03985820710659027,
-0.04509291425347328,
0.02117479033768177,
-0.011049186810851097,
-0.046615973114967346,
-0.0002774893946480006,
0.019198600202798843,
-0.03318824991583824,
-0.043104808777570724,
-0.048790425062179565,
0.01731669157743454,
-0.02806241251528263,
0.021438032388687134,
0.0596175342798233,
0.031507473438978195,
0.06374488025903702,
-0.06157049164175987,
0.014861397445201874,
0.04689354449510574,
-0.01612342707812786,
0.014286012388765812,
0.04458407312631607,
0.03116466850042343,
-0.0390721932053566,
-0.010091145522892475,
0.012439679354429245,
0.019464999437332153,
0.012993913143873215,
-0.02789665199816227,
0.031896043568849564,
0.0063614314422011375,
-0.02605525217950344,
0.034317996352910995,
0.04732494056224823,
-0.02338552474975586,
0.010416324250400066,
0.06716553121805191,
0.06322222948074341,
-0.05375418812036514,
-0.010338571853935719,
-0.08563155680894852,
-0.06033213064074516,
0.05357242003083229,
0.022115828469395638,
0.03665986657142639,
0.02028241567313671,
0.0068056476302444935,
0.0017957889940589666,
-0.010339452885091305,
0.004525597207248211,
0.037648409605026245,
0.0027428418397903442,
-0.03757935017347336,
0.026295190677046776,
-0.05063250660896301,
0.044487956911325455,
-0.020536066964268684,
0.001829645480029285,
0.013686707243323326,
-0.0583125576376915,
-0.042157892137765884,
-0.020116036757826805,
-0.034223347902297974,
-0.07239481806755066,
0.011192678473889828,
0.002334309509024024,
-0.004521760158240795,
0.002306559821590781,
-0.007549413479864597,
0.0229641180485487,
-0.00850831251591444,
0.003078291891142726,
0.02334260381758213,
0.06281211972236633,
-0.0035368935205042362,
-0.09582445025444031,
-0.023736851289868355,
-0.012069999240338802,
-0.03491963446140289,
0.02099582552909851,
0.010655215941369534,
-0.0007184103596955538,
-0.016114022582769394,
0.04896530136466026,
-0.04757937043905258,
-0.012921621091663837,
0.011076032184064388,
0.07578874379396439,
0.01019129529595375,
0.04691478610038757,
0.026348773390054703,
-0.03500670567154884,
-0.023776257410645485,
0.004236845299601555,
-0.05941155180335045,
0.019239842891693115,
-0.0028289328329265118,
-0.02782352827489376,
0.024484090507030487,
0.008458452299237251,
-0.057170189917087555,
-0.07959691435098648,
-0.053403522819280624,
0.03386526182293892,
0.027359487488865852,
0.042298272252082825,
0.03716077655553818,
0.019197678193449974,
0.005326627753674984,
-0.009925439022481441,
0.03633373603224754,
0.013544995337724686,
0.07610247284173965,
0.05696490406990051,
-0.05222191661596298,
0.017765948548913002,
0.07085876911878586,
0.03555632010102272,
0.006379272323101759,
-0.017333095893263817,
0.03199348971247673,
-0.009089784696698189,
-0.011749585159122944,
-0.03302757441997528,
-0.009546546265482903,
-0.04023260995745659,
-0.005537413526326418,
-0.06511124968528748,
-0.013234389014542103,
0.00804675742983818,
-0.032180093228816986,
0.05335390195250511,
0.0013400166062638164,
-0.057869236916303635,
0.016185998916625977,
-0.006550397723913193,
-0.0024043056182563305,
0.054905425757169724,
0.038590800017118454,
-0.010473784990608692,
-0.0010074219899252057,
0.054679956287145615,
-0.03368164971470833,
0.011904431506991386,
-0.042904529720544815,
-0.001362823648378253,
-0.07027368992567062,
0.025997627526521683,
0.03582027927041054,
-0.040745772421360016,
0.030886132270097733,
0.04321840777993202,
-0.04920373484492302,
0.09029524028301239,
-0.04256103187799454,
0.03216753527522087,
-0.0027786835562437773,
-0.031548380851745605,
-0.04765961691737175,
0.002452179091051221,
-0.03426499664783478,
-0.023812493309378624,
0.026347607374191284,
-0.06279323250055313,
-0.01738266460597515,
0.012089638970792294,
-0.05801203474402428,
0.07075429707765579,
-0.026114454492926598,
0.04237215220928192,
0.011198938824236393,
0.00564341526478529,
0.04529646411538124,
0.05449313297867775,
0.0703577771782875,
-0.0008837446803227067,
-0.01692238263785839,
-0.009661124087870121,
0.01058523915708065,
-0.006836745887994766,
-0.027253074571490288,
-0.0021459374111145735,
-0.04682126268744469,
0.012938713654875755,
-0.11654961109161377,
0.017783287912607193,
-0.0022899871692061424,
0.04176666587591171,
-0.04592079296708107,
-0.002380847232416272,
0.07101156562566757,
0.03691935911774635,
0.01796245202422142,
0.011022851802408695,
-0.013362633995711803,
0.04279906675219536,
0.05988704785704613,
0.04376320540904999,
0.01289702020585537,
-0.00646254001185298,
0.0015406677266582847,
-0.003193734446540475,
-0.0023152537178248167,
0.007430645637214184,
0.04640185832977295,
-0.029686275869607925,
-0.06431963294744492,
0.09936220943927765,
0.00008061633707256988,
-0.06369197368621826,
-0.0885370746254921,
0.003905534977093339,
0.03422539681196213,
-0.010699811391532421,
0.002577488776296377,
0.029435746371746063,
0.018071401864290237,
0.05325604975223541,
0.04594352841377258,
-0.005914092529565096,
-0.03202405571937561,
-0.0035043559037148952,
0.006659716367721558,
0.029201984405517578,
0.04070254787802696,
0.015710320323705673,
0.05785753205418587,
-0.020711220800876617,
0.04391409829258919,
0.0776175782084465,
0.05082276463508606,
0.00549717852845788,
-0.06705759465694427,
-0.011433381587266922,
-0.03065742552280426,
-0.008472459390759468,
0.020778685808181763,
-0.011268203146755695,
0.026424262672662735,
-0.01812155358493328,
0.0016152265015989542,
-0.08940266072750092,
-0.022144867107272148,
0.046368472278118134,
0.00718456506729126,
-0.0681062564253807,
0.013880073092877865,
-0.03415146470069885,
-0.026023019105196,
0.032925162464380264,
-0.0030995788984000683,
0.033837612718343735,
0.04704403504729271,
-0.04052247852087021,
-0.008320555090904236,
0.027222447097301483,
0.06145108491182327,
0.03690588101744652,
0.009826259687542915,
-0.01254937332123518,
-0.0016333666862919927,
-0.014805041253566742,
0.05339124798774719,
-0.021096980199217796,
0.03094097413122654,
-0.02142535150051117,
-0.028844837099313736,
-0.02448754757642746,
0.04315757751464844,
-0.056081004440784454,
0.006147362291812897,
-0.0019183550029993057,
0.013276662677526474,
-0.04263632372021675,
-0.020949779078364372,
0.009123981930315495,
0.032357070595026016,
0.022634156048297882,
0.08389804512262344,
-0.014353776350617409,
0.002455425914376974,
0.022761298343539238,
-0.006236545741558075,
-0.047949619591236115,
-0.0008391772280447185,
0.04312848299741745,
0.011088271625339985,
-0.043403591960668564,
-0.05309785529971123,
0.03363174572587013,
-0.059693001210689545,
-0.03252653032541275,
-0.009173051454126835,
0.06428766995668411,
0.03173363581299782,
0.020760267972946167,
-0.03746393695473671,
-0.012838661670684814,
0.02313769981265068,
0.03831036761403084,
-0.02237451635301113,
0.013541397638618946,
0.03840331360697746,
0.05957129970192909,
-0.00025618888321332633,
0.00597571674734354,
0.015163606032729149,
0.005919808521866798,
-0.06860396265983582,
-0.019044991582632065,
0.040434323251247406,
0.03302164748311043,
-0.01421724446117878,
-0.005403560120612383,
-0.0006172349094413221,
-0.01399435754865408,
-0.012236995622515678,
0.05085962265729904,
-0.001229555462487042,
0.003003891557455063,
-0.043478142470121384,
0.0064965225756168365,
-0.010595790110528469,
0.03344004973769188,
0.03842484578490257,
-0.0002757491311058402,
-0.044529758393764496,
-0.031059039756655693,
0.026355866342782974,
-0.03638377785682678,
-0.004260864108800888,
0.06373202800750732,
-0.007873565889894962,
-0.023022089153528214,
-0.013943266123533249,
-0.05791119858622551,
-0.0026820132043212652,
0.04810550808906555,
-0.004403284285217524,
0.013272696174681187,
0.021677667275071144,
0.05301155522465706,
0.006316719111055136,
0.020258594304323196,
0.052446309477090836,
0.02444230392575264,
0.003180663101375103,
-0.03727484866976738,
-0.014656877145171165,
0.023792684078216553,
0.008041326887905598,
-0.020844759419560432,
-0.017009053379297256,
-0.007710027974098921,
0.02174110896885395,
-0.01321131456643343,
0.017067451030015945,
-0.006536309141665697,
-0.06337742507457733,
0.04506811127066612,
-0.039913151413202286,
0.07529790699481964,
0.01611492782831192,
0.03978457674384117,
0.009423850104212761,
0.039979130029678345,
0.013616308569908142,
-0.0005560815916396677,
0.0085801025852561,
-0.00653855362907052,
-0.005718243774026632,
-0.04111830145120621,
-0.03439393639564514,
0.0522531196475029,
-0.04463418573141098,
0.0036448361352086067,
-0.021288076415657997,
0.02575930766761303,
0.010344556532800198,
0.040485650300979614,
-0.023597797378897667,
0.008108760230243206,
-0.06275283545255661,
0.014988262206315994,
0.02999054826796055,
0.01197922881692648,
-0.038574036210775375,
0.005356114823371172,
-0.048569776117801666,
0.019814450293779373,
-0.02774033136665821,
-0.05630217120051384,
-0.012327083386480808,
0.0017780916532501578,
0.015938811004161835,
0.09509715437889099,
0.02366551198065281,
0.028276657685637474,
-0.02195018157362938,
-0.07060299068689346,
-0.000001755831362970639,
0.023540012538433075,
-0.0005864265258423984,
0.03179723024368286,
0.022038014605641365,
-0.025594715029001236,
0.05004987493157387,
-0.028463969007134438,
-0.027881262823939323,
0.00935707613825798,
-0.018661051988601685,
-0.03839429095387459,
0.008754447102546692,
-0.026214342564344406,
-0.003393991617485881,
-0.026193613186478615,
0.019791973754763603,
0.04761814326047897,
0.0883253887295723,
-0.014921103604137897,
0.056074000895023346,
0.020881079137325287,
-0.023538993671536446,
0.012489698827266693,
-0.0225501861423254,
-0.00041153922211378813,
0.050253696739673615,
0.03536761924624443,
0.02569594979286194,
-0.028109751641750336,
0.014590333215892315,
0.02483775094151497,
-0.005165730137377977,
0.0003036193083971739,
-0.04960433393716812,
0.05672534182667732,
0.05407920107245445,
-0.0013371143722906709,
-0.017180107533931732,
-0.01866750419139862,
-0.018497105687856674,
-0.01920354552567005,
0.015584953129291534,
-0.01007792167365551,
0.027127349749207497,
-0.01218066830188036,
-0.021487418562173843,
-0.04703384265303612,
-0.011396710760891438,
0.00020025721460115165,
0.004041982349008322,
-0.06328397989273071,
-0.0898297131061554,
-0.004317129962146282,
-0.028398890048265457,
-0.05940072238445282,
0.017319897189736366,
0.05740431696176529,
0.06580399721860886,
0.015981940552592278,
-0.01989334635436535,
0.0002979690325446427,
-0.062139663845300674,
-0.052125826478004456,
0.012734352611005306,
-0.061417654156684875,
-0.033481307327747345,
0.006719875615090132,
0.005090735852718353,
0.012249412015080452,
-0.06541386246681213,
0.058146484196186066,
-0.006286023184657097,
0.023962046951055527,
0.03783392533659935,
-0.031243763864040375,
0.034340642392635345,
-0.0005203483160585165,
0.042102355509996414,
-0.002668928587809205,
-0.053481802344322205,
0.04647861421108246,
-0.00235068635083735,
-0.021799154579639435,
-0.019253037869930267,
-0.07590284198522568,
-0.042694807052612305,
0.022701246663928032,
-0.008871875703334808,
0.01556665264070034,
0.03419169783592224,
0.03451615571975708,
-0.06946202367544174,
0.04842465743422508,
-0.016771070659160614,
-0.0028139944188296795,
-0.028648510575294495,
0.044174689799547195,
0.054497264325618744,
0.016112614423036575,
0.03365965932607651,
-0.0670434907078743,
-0.05043351277709007,
0.053621355444192886,
0.03314216062426567,
0.03227575495839119,
-0.042977482080459595,
0.03605122119188309,
0.03533384948968887,
-0.0031611700542271137,
-0.029415743425488472,
-0.03747498244047165,
-0.03245919197797775,
-0.026218919083476067,
-0.051610540598630905,
0.0736563503742218,
-0.025465866550803185,
-0.01765521429479122,
0.020848624408245087,
0.025093937292695045,
-0.003427228657528758,
-0.004326874390244484,
-0.02447212114930153,
0.04067450761795044,
0.016425834968686104,
-0.04047480598092079,
-0.013428331352770329,
-0.04288211092352867,
-0.017892898991703987,
-0.008256602101027966,
-0.007727287709712982,
-0.029135428369045258,
0.03998802229762077,
-0.03354323282837868,
-0.06307036429643631,
0.020635094493627548,
0.007590342313051224,
-0.014837287366390228,
-0.052143726497888565,
-0.04920732602477074,
0.03880475461483002,
0.04541788995265961,
-0.028871072456240654,
-0.007697043940424919,
0.00780086126178503,
-0.01418334525078535,
0.004357072524726391,
0.029292432591319084,
0.019204717129468918,
0.0017780449707061052,
-0.056895554065704346,
-0.07561292499303818,
-0.028187325224280357,
-0.02187003754079342,
0.010147088207304478,
-0.00696118688210845,
0.05919579789042473,
0.03365858644247055,
-0.009282042272388935,
-0.015314118936657906,
0.003245317144319415
] |
<p>Suppose a point charge $q$ is located at $(x=0,y=0,z=d)$, and that along the $x$-$y$ plane is a infinite plate of potential $V = 0$. Then the method of images solves Laplace's equation for the potential for $z>0$, $$V(x,y,z) = \frac{1}{4\pi\epsilon_0}\left(\frac{q}{\sqrt{x^2+y^2+\left(z-d\right)^2}} - \frac{q}{\sqrt{x^2 + y^2 + \left(z + d\right)^2}}\right).$$ This satisfies the boundary conditions $V(x,y,0) = 0$ and $V(r\rightarrow\infty) = 0$.</p>
<p>Suppose instead the plate has potential $V(x,y,0) = V_0 \ne0$. Although very simple, it seems to me that the method of images cannot be used in this case. Is this correct?</p> | g4736 | [
0.04963599517941475,
0.015958119183778763,
0.0029681106097996235,
-0.029540227726101875,
0.06643993407487869,
-0.004698405973613262,
0.025272376835346222,
-0.01390138827264309,
-0.04042607173323631,
0.02570447139441967,
0.007865590043365955,
0.05162305757403374,
0.015798890963196754,
0.03251019865274429,
0.00780129199847579,
-0.007561099715530872,
0.06139165535569191,
-0.04340704530477524,
-0.004107234068214893,
-0.00496804341673851,
-0.03393233194947243,
0.033783670514822006,
0.016406334936618805,
0.020283345133066177,
-0.038559090346097946,
0.00044768970110453665,
-0.010305555537343025,
0.02036900259554386,
-0.03911098092794418,
-0.006734712515026331,
-0.008128180168569088,
-0.019818095490336418,
0.032204121351242065,
0.0009002575534395874,
-0.023808669298887253,
-0.01964499056339264,
0.06729362159967422,
0.04608200863003731,
0.05654082074761391,
-0.053412146866321564,
0.009312532842159271,
-0.01989748515188694,
0.0569457933306694,
0.027489908039569855,
-0.003484194166958332,
-0.02800546959042549,
-0.041138697415590286,
0.007623979821801186,
-0.005010227207094431,
0.03817934915423393,
-0.002005611313506961,
0.03799137845635414,
0.013470854610204697,
-0.05160323902964592,
-0.010897110216319561,
0.037074975669384,
-0.0028331272769719362,
-0.034120697528123856,
-0.005174434278160334,
0.04135455563664436,
-0.023814981803297997,
0.024786876514554024,
0.000592304568272084,
0.028861381113529205,
0.045060668140649796,
-0.02326270192861557,
-0.10626915842294693,
-0.05374477058649063,
0.03040997125208378,
-0.007804740685969591,
-0.007411820348352194,
-0.05992095172405243,
-0.026056015864014626,
-0.02739325724542141,
-0.06516555696725845,
0.010360069572925568,
0.026977431029081345,
-0.017786532640457153,
0.013506054878234863,
-0.021366426721215248,
-0.015831420198082924,
-0.030869709327816963,
0.021307695657014847,
0.015090773813426495,
0.009515288285911083,
0.032131556421518326,
0.07687720656394958,
0.02635425329208374,
-0.03784744814038277,
-0.018794145435094833,
-0.06672468781471252,
-0.01580760069191456,
0.016062019392848015,
-0.00013082737859804183,
-0.003299082163721323,
0.0037596505135297775,
0.036956723779439926,
0.030462080612778664,
-0.011902817524969578,
-0.004946962930262089,
-0.05464997887611389,
0.03453148156404495,
0.013652541674673557,
0.030682794749736786,
-0.024566324427723885,
-0.017212051898241043,
0.04415200278162956,
-0.001475178636610508,
0.032860107719898224,
-0.0438416413962841,
-0.016004253178834915,
-0.04339873045682907,
-0.029396584257483482,
-0.009990309365093708,
-0.05823076143860817,
0.03336910158395767,
0.042843595147132874,
-0.02116554044187069,
-0.0187800582498312,
0.040263932198286057,
0.006930789444595575,
0.04379752278327942,
0.020621178671717644,
0.03321690112352371,
0.04168016463518143,
0.020305775105953217,
-0.028909724205732346,
0.029320478439331055,
0.06716708093881607,
0.023379681631922722,
-0.019121766090393066,
0.013093926943838596,
0.03244062140583992,
-0.022753389552235603,
0.006848081015050411,
-0.014541330747306347,
-0.025528505444526672,
-0.0244496650993824,
0.048008859157562256,
0.02448539063334465,
0.00567390164360404,
-0.05966798961162567,
-0.029160909354686737,
0.0033389918971806765,
-0.020145084708929062,
0.011273637413978577,
0.023123297840356827,
-0.05228620767593384,
0.01968264766037464,
-0.02112571708858013,
-0.035636309534311295,
0.058186981827020645,
0.024607397615909576,
0.06673247367143631,
-0.008623545058071613,
-0.018719863146543503,
0.06338786333799362,
0.025380749255418777,
0.05371351167559624,
0.008742475882172585,
-0.010432572104036808,
0.010942219756543636,
0.04116041213274002,
-0.03360516205430031,
-0.06075835973024368,
-0.007017652038484812,
0.0042785778641700745,
-0.06524448096752167,
0.01129860244691372,
-0.04290992021560669,
0.050019122660160065,
0.01227305456995964,
0.038540273904800415,
-0.0011714226566255093,
0.05893595889210701,
-0.006423108279705048,
-0.06519705802202225,
-0.009977860376238823,
0.05545132979750633,
0.007868298329412937,
-0.04313178360462189,
0.01016470417380333,
0.025556184351444244,
-0.038124002516269684,
0.024895602837204933,
-0.00928476545959711,
0.018769582733511925,
0.02913815900683403,
0.019658410921692848,
-0.044327616691589355,
-0.03696054592728615,
0.0022155584301799536,
0.014288011938333511,
0.02667979709804058,
-0.021772144362330437,
0.05685395002365112,
0.0667368695139885,
-0.06813426315784454,
-0.03713720291852951,
-0.033562518656253815,
-0.01958603225648403,
0.10716503858566284,
0.05728454887866974,
0.029423296451568604,
-0.015193140134215355,
-0.04174245521426201,
-0.030804751440882683,
-0.015443270094692707,
0.015410189516842365,
0.005524325184524059,
-0.05345223471522331,
-0.02811041660606861,
-0.0029895270708948374,
0.04836174100637436,
-0.03328544646501541,
-0.0580785907804966,
-0.03340834006667137,
0.021580584347248077,
-0.012974686920642853,
0.014597038738429546,
-0.05684896558523178,
0.02522466704249382,
0.021961279213428497,
-0.0090097077190876,
-0.012523079290986061,
0.04006711393594742,
0.033378008753061295,
-0.043409477919340134,
-0.0300615131855011,
0.03916588053107262,
-0.07722584158182144,
-0.07972162961959839,
0.01625550165772438,
-0.024090487509965897,
0.0373082272708416,
0.019575927406549454,
-0.06544926017522812,
0.022114627063274384,
-0.04386536777019501,
-0.017930960282683372,
-0.00033860112307593226,
-0.05542641505599022,
-0.021073458716273308,
0.03601759672164917,
0.017033368349075317,
0.03530517593026161,
0.003840469289571047,
-0.031939394772052765,
0.04219377785921097,
0.044034119695425034,
0.0386003814637661,
0.014873981475830078,
0.044997721910476685,
0.022248554974794388,
0.002499053720384836,
0.002312383381649852,
-0.01727890595793724,
0.018955662846565247,
0.019314417615532875,
-0.0382523275911808,
-0.07099984586238861,
0.04217328876256943,
-0.08206131309270859,
-0.04563870653510094,
-0.03756440803408623,
0.004998793359845877,
-0.04689386114478111,
0.018445970490574837,
0.049868129193782806,
0.035163167864084244,
0.0020196542609483004,
0.015055639669299126,
0.052086230367422104,
0.018929334357380867,
-0.013296667486429214,
-0.04739442467689514,
0.009926565922796726,
-0.01883094757795334,
0.005004941485822201,
-0.050822027027606964,
0.03183094412088394,
-0.07594332844018936,
-0.012991080060601234,
0.08087141066789627,
0.014448815025389194,
-0.0353810153901577,
0.025799553841352463,
0.029145030304789543,
0.04137416556477547,
-0.041944798082113266,
-0.047007765620946884,
-0.0037599510978907347,
0.04539606347680092,
-0.04586980864405632,
-0.009626136161386967,
-0.006752439308911562,
0.0672442689538002,
-0.055469710379838943,
-0.008343935012817383,
-0.004496813286095858,
-0.0029522685799747705,
0.010562081821262836,
-0.0019749465864151716,
0.0009396448149345815,
0.10857363045215607,
-0.007722063921391964,
-0.020388547331094742,
-0.05741291120648384,
0.020056480541825294,
0.012451470829546452,
0.02428235113620758,
0.017632247880101204,
-0.040340520441532135,
0.0240560881793499,
0.027238130569458008,
0.015100457705557346,
-0.019273603335022926,
-0.07651941478252411,
-0.02420572005212307,
0.009117490611970425,
-0.012798299081623554,
0.012101599015295506,
0.010282698087394238,
0.034095946699380875,
-0.0011366362450644374,
0.07760731875896454,
-0.07514706999063492,
0.013852335512638092,
-0.03241145983338356,
0.04827367141842842,
0.018218787387013435,
0.09331130981445312,
0.023526713252067566,
-0.018161658197641373,
0.06144540384411812,
-0.04359694570302963,
-0.029471445828676224,
0.04211591184139252,
0.09813142567873001,
0.0032469804864376783,
-0.014178182929754257,
-0.005262932274490595,
-0.030645938590168953,
-0.040047772228717804,
0.03491596132516861,
-0.04002239182591438,
0.013504112139344215,
0.07285190373659134,
-0.03992714732885361,
-0.028700578957796097,
0.006543143652379513,
0.006234246771782637,
0.03179192170500755,
0.030189169570803642,
0.0006704035913571715,
0.0004625708388630301,
0.0062144179828464985,
0.03645964339375496,
-0.0434708334505558,
0.015171447768807411,
0.06937196850776672,
-0.008928968571126461,
-0.012787321582436562,
-0.003326716832816601,
0.043774548918008804,
-0.05822425335645676,
-0.007991332560777664,
0.00043660050141625106,
-0.031005026772618294,
-0.07433304190635681,
0.01973513700067997,
-0.07660353928804398,
0.03339257463812828,
0.020568745210766792,
0.010815982706844807,
0.009091957472264767,
-0.03598514199256897,
-0.07541810721158981,
-0.024634694680571556,
0.02552570402622223,
-0.011641735211014748,
-0.01630929484963417,
0.008672126568853855,
0.03709379583597183,
0.04636117443442345,
0.02355130761861801,
0.0026228264905512333,
-0.012402048334479332,
0.04125889390707016,
-0.008512009866535664,
0.06588807702064514,
-0.05758235976099968,
-0.045996543020009995,
0.020321819931268692,
-0.024862179532647133,
-0.011400578543543816,
0.0009010343928821385,
-0.06111183390021324,
-0.018811846151947975,
-0.024020306766033173,
0.012830715626478195,
-0.011655720882117748,
0.016728240996599197,
0.009250614792108536,
-0.014295403845608234,
-0.02695254422724247,
0.027527330443263054,
-0.04073087126016617,
0.058507055044174194,
0.008263198658823967,
-0.04258766397833824,
-0.05857011303305626,
0.010600653477013111,
-0.026155361905694008,
0.005016849841922522,
-0.03249916061758995,
0.033275555819272995,
0.013920517638325691,
-0.039088908582925797,
0.026634681969881058,
-0.013336874544620514,
-0.02666339837014675,
-0.06420352309942245,
-0.061660077422857285,
0.01826789416372776,
0.017565257847309113,
0.017402254045009613,
-0.010489816777408123,
0.02157777175307274,
-0.02121439203619957,
-0.017802568152546883,
0.08099174499511719,
-0.05240240693092346,
0.053581368178129196,
-0.05676311254501343,
0.023003151640295982,
-0.038996513932943344,
-0.0010587073629722,
-0.017177199944853783,
0.0202863160520792,
0.043623555451631546,
0.004482039716094732,
0.058558389544487,
0.045953232795000076,
-0.018119946122169495,
0.06962639838457108,
-0.021637091413140297,
-0.0521833561360836,
0.06981273740530014,
-0.02922159619629383,
-0.05487477779388428,
0.004494793247431517,
0.012151077389717102,
0.00828394666314125,
0.06127904728055,
-0.03553794324398041,
-0.07351823896169662,
0.013741462491452694,
-0.04562552645802498,
0.035510241985321045,
0.03142383694648743,
0.02437359094619751,
-0.024796169251203537,
0.03324965760111809,
0.06473161280155182,
-0.00246390956453979,
-0.06421569734811783,
-0.027038944885134697,
-0.036590784788131714,
-0.03167800232768059,
-0.0021228736732155085,
0.034418974071741104,
0.1043168380856514,
-0.018681801855564117,
-0.024570845067501068,
-0.0490930937230587,
-0.018774626776576042,
0.027903785929083824,
-0.004490282852202654,
0.002105254214257002,
-0.03141145035624504,
0.005867507308721542,
-0.04613561928272247,
-0.0005596911651082337,
0.0017948535969480872,
0.007114892825484276,
-0.058228034526109695,
0.04132414236664772,
-0.014821917749941349,
0.03363629803061485,
0.018160570412874222,
0.012337589636445045,
-0.019758006557822227,
0.016081172972917557,
0.06379415839910507,
-0.013562324456870556,
0.0407913401722908,
0.0014134942321106791,
-0.027246931567788124,
0.05522618815302849,
-0.030341550707817078,
-0.01656964235007763,
-0.03066411428153515,
-0.034136928617954254,
0.018508775159716606,
0.03491103649139404,
0.06967192143201828,
-0.022690897807478905,
-0.0005089954356662929,
0.02627629227936268,
-0.00937662087380886,
-0.037526655942201614,
0.07363265007734299,
0.039415981620550156,
0.06637108325958252,
-0.04972979426383972,
-0.06540362536907196,
-0.0038279304280877113,
-0.055518120527267456,
-0.023524003103375435,
0.08758288621902466,
-0.028173720464110374,
-0.018783733248710632,
-0.0007822393090464175,
0.07686048746109009,
-0.0068556866608560085,
-0.015040605328977108,
-0.039303917437791824,
-0.023304592818021774,
-0.03090977482497692,
-0.015452978201210499,
-0.018750758841633797,
-0.07457059621810913,
0.009488580748438835,
0.0042939139530062675,
-0.025731248781085014,
-0.029625503346323967,
-0.03419501706957817,
0.023744210600852966,
-0.01064584031701088,
0.05752444267272949,
-0.026181135326623917,
-0.0008634943515062332,
0.06185009330511093,
-0.0507524237036705,
-0.010194423608481884,
-0.02079162560403347,
0.001688011921942234,
-0.027313824743032455,
-0.038902025669813156,
0.012887746095657349,
-0.00011772144353017211,
-0.01214521937072277,
0.007615948561578989,
-0.014782321639358997,
-0.026622004806995392,
0.0036999464500695467,
-0.0050473702140152454,
-0.046933580189943314,
-0.02641354873776436,
0.07949740439653397,
-0.02656286396086216,
0.0010269001359120011,
0.03539949283003807,
0.0013042116770520806,
-0.005775561090558767,
0.02468404360115528,
-0.00898846797645092,
0.051845524460077286,
0.000649968278594315,
0.006400267127901316,
-0.001678641652688384,
0.04791649430990219,
-0.004420122597366571,
0.044193267822265625,
0.00950143113732338,
0.03772876039147377,
0.04129013791680336,
-0.034311693161726,
0.005207109730690718,
-0.06383561342954636,
0.07549300044775009,
-0.006018699146807194,
-0.021607588976621628,
0.04326590895652771,
0.07950432598590851,
-0.00469265878200531,
-0.1147877499461174,
-0.0017849886789917946,
-0.05884065106511116,
-0.002061025472357869,
-0.027501162141561508,
-0.009475871920585632,
-0.008448658511042595,
0.05853649973869324,
0.005483058746904135,
0.03866950049996376,
0.02757614105939865,
-0.0018761077662929893,
0.07821298390626907,
0.049264080822467804,
0.01264056097716093,
-0.029006775468587875,
0.011733777821063995,
-0.04207274317741394,
-0.05548795312643051,
0.010926265269517899,
-0.014028741978108883,
-0.017199194058775902,
-0.05186820402741432,
-0.0010561570525169373,
0.05771297216415405,
-0.012600908055901527,
-0.014630159363150597,
0.027477039024233818,
-0.006728758104145527,
-0.01658931002020836,
-0.017065204679965973,
-0.01690991409122944,
0.01614132523536682,
0.035692643374204636,
-0.010929142124950886,
-0.01959400810301304,
-0.016160745173692703,
0.008679727092385292,
-0.018751084804534912,
-0.020229412242770195,
0.03711420297622681,
0.05332893133163452,
0.03889267519116402,
0.04689565300941467,
-0.023887265473604202,
-0.05480506643652916,
0.002925800858065486,
-0.04456499218940735,
-0.0011441545793786645,
0.008690943010151386,
0.017791613936424255,
0.045653898268938065,
0.05390378087759018,
-0.03121297061443329,
0.04508660361170769,
0.04481353238224983,
-0.019231999292969704,
-0.01637496054172516,
-0.023091807961463928,
-0.03881435841321945,
-0.006017806939780712,
-0.06485586613416672,
-0.010539752431213856,
0.07095618546009064,
0.04211283475160599,
-0.00490108085796237,
0.03611518070101738,
-0.021241921931505203,
-0.0022383714094758034,
-0.014211641624569893,
-0.0042808945290744305,
-0.03676845505833626,
-0.02428053505718708,
-0.007545675616711378,
0.013476090505719185,
-0.04939322546124458,
-0.00772792287170887,
-0.04098699241876602,
0.019436130300164223,
-0.040056630969047546,
-0.022174514830112457,
-0.02992556057870388,
-0.03245488926768303,
0.012317383661866188,
-0.007144987117499113,
-0.02376747690141201,
0.04186270013451576,
0.015327218919992447,
0.057283852249383926,
0.0668899267911911,
0.03744366019964218,
-0.012791250832378864,
0.019163375720381737,
0.03713582828640938,
0.06418731063604355,
-0.03612113744020462,
-0.007694059517234564,
-0.050122976303100586,
-0.048248760402202606,
0.008205347694456577,
-0.051397014409303665,
-0.018635377287864685,
0.019304072484374046,
0.0015750566963106394,
-0.028752755373716354,
0.01901182346045971,
0.014847286976873875,
0.016687817871570587,
-0.01759200543165207,
-0.023446112871170044,
0.016560815274715424,
0.0211658738553524,
0.009248727932572365,
0.01381621416658163,
-0.0553312785923481,
0.011384648270905018,
0.008146608248353004,
-0.049109019339084625,
-0.07753605395555496,
-0.00013946638500783592,
-0.011974123306572437,
0.025239210575819016,
-0.019287792965769768,
0.00397612014785409,
0.029360098764300346,
-0.036927759647369385,
-0.005791429430246353,
0.02137472666800022,
0.008260692469775677,
-0.004438535310328007,
0.06534481048583984,
0.0012769156601279974,
0.010045037604868412,
-0.009208721108734608,
0.0026893592439591885,
0.001642807386815548,
-0.06668750196695328,
0.022027064114809036,
0.026832668110728264,
-0.00628676638007164,
-0.03935293108224869,
0.020163187757134438,
-0.03749174252152443,
0.021362317726016045,
-0.0005208496586419642,
-0.035713545978069305,
-0.014924800954759121,
-0.005889412946999073,
-0.029375450685620308,
-0.008485808968544006,
-0.0025987219996750355,
0.0617884062230587,
0.0002541342983022332,
0.008365174755454063,
-0.03200223669409752,
-0.012854240834712982,
-0.07886283099651337,
-0.007134343031793833,
0.037770938128232956,
-0.030913179740309715,
-0.023012284189462662,
0.08015618473291397,
0.06679544597864151,
-0.00600266782566905,
0.020279349759221077,
0.019583186134696007,
-0.008290142752230167,
0.021265462040901184,
0.030150776728987694,
-0.03587953746318817,
0.004197254311293364,
0.053230054676532745,
0.02146879956126213,
-0.02827104926109314,
-0.05611100792884827,
-0.030881501734256744,
0.0048531424254179,
0.0016123062232509255,
-0.12028085440397263,
-0.0001689776690909639,
0.027489250525832176
] |
<p>The magnetic moment of a closed current loop is $$\mathbf{m} = \frac{I}{2}\int\mathbf{r}\times d\mathbf{r}.$$ Note that $\mathbf{m}$ is independent of any coordinate frame. How, then, does one determine the <em>location</em> of a magnetic moment?</p>
<p>Certainly the vector potential due to a magnetic dipole $$\mathbf{A}(\mathbf{r}) = \frac{\mu_0}{4\pi}\frac{\mathbf{m}\times\mathbf{r}}{r^3}$$ <em>does</em> depend on the location of the coordinate frame, since $r$ is by definition the distance between the magnetic dipole and the target point, therefore it is important to know the location of the dipole (or the current loop we are approximating as a dipole).</p>
<p>How does one determine where to set the origin of the coordinate system so as to use the expression for $\mathbf{A}(\mathbf{r})$ above, given an arbitrarily-shaped current loop?</p> | g4737 | [
-0.013248184695839882,
-0.03783053532242775,
-0.008062222972512245,
-0.05026371777057648,
0.02049696259200573,
0.017256973311305046,
0.05827558785676956,
0.020909132435917854,
-0.08078641444444656,
-0.00469269510358572,
-0.02572527714073658,
0.021856727078557014,
-0.0036106212064623833,
-0.007020934019237757,
0.029831459745764732,
0.011019696481525898,
0.031621284782886505,
0.014613552019000053,
0.052843671292066574,
-0.03098808415234089,
0.06377054005861282,
-0.048965297639369965,
0.03455842286348343,
-0.031912773847579956,
-0.0026726126670837402,
-0.005337935872375965,
0.016740186139941216,
0.011928652413189411,
-0.0353081114590168,
-0.01943054050207138,
-0.034522004425525665,
0.0035947721917182207,
0.09224318712949753,
-0.05682438984513283,
0.002514309948310256,
-0.015678340569138527,
0.008606468327343464,
0.07532627880573273,
0.05596713721752167,
0.01929338462650776,
-0.060484886169433594,
-0.052460815757513046,
-0.0031575497705489397,
0.04821275919675827,
-0.019400523975491524,
0.010321123525500298,
-0.06865928322076797,
-0.006896661128848791,
0.0011625211918726563,
0.020105930045247078,
-0.05453041195869446,
0.084688700735569,
0.05394749343395233,
-0.012845340184867382,
0.032578080892562866,
0.011172077618539333,
-0.019322186708450317,
-0.025429068133234978,
-0.014112698845565319,
0.005638616159558296,
0.003997994586825371,
0.03474656865000725,
0.031048966571688652,
0.0020145848393440247,
-0.04612547904253006,
-0.010995082557201385,
-0.06799377501010895,
-0.02402964048087597,
-0.03894451633095741,
0.025712763890624046,
0.014730120077729225,
-0.08880816400051117,
-0.047217193990945816,
-0.07393112778663635,
-0.08589291572570801,
0.046688880771398544,
-0.011991755105555058,
-0.02299349568784237,
0.013121004216372967,
0.011784805916249752,
-0.019884267821907997,
-0.0065029580146074295,
0.06357061862945557,
-0.004358525853604078,
0.044350408017635345,
0.035197705030441284,
-0.021114395931363106,
0.0471961684525013,
0.03915292024612427,
-0.025976309552788734,
0.0035375887528061867,
-0.0353643037378788,
0.02426997572183609,
-0.029176363721489906,
0.007084172684699297,
-0.02686018869280815,
0.03524598851799965,
0.0221936646848917,
0.0015194232109934092,
0.040586814284324646,
-0.006106563378125429,
-0.009929523803293705,
-0.04804965853691101,
0.03218377009034157,
0.002456825226545334,
0.002561144530773163,
0.03650781139731407,
-0.0254246573895216,
-0.013333925977349281,
-0.03736387938261032,
0.005137481726706028,
-0.06266436725854874,
-0.0765763446688652,
0.018748242408037186,
-0.08806619048118591,
-0.024585042148828506,
0.028628159314393997,
-0.059591345489025116,
0.01219834666699171,
0.09466837346553802,
0.012278828769922256,
0.0334591343998909,
-0.012111534364521503,
0.07541864365339279,
-0.005793794523924589,
0.004747097380459309,
-0.03547805920243263,
0.01087740994989872,
0.056229520589113235,
0.007921005599200726,
-0.0030222474597394466,
-0.06522493064403534,
0.028451459482312202,
-0.012299432419240475,
-0.038394760340452194,
-0.01273417565971613,
0.025840608403086662,
-0.0036141565069556236,
0.020025646314024925,
0.05155080929398537,
0.014808289706707,
0.009321220219135284,
0.03956414386630058,
-0.0798633024096489,
-0.02134528011083603,
0.016274068504571915,
-0.01890926994383335,
-0.04680399224162102,
0.095055490732193,
-0.03587271273136139,
-0.0270491074770689,
0.0333450511097908,
-0.0874539166688919,
0.010553904809057713,
0.0504273883998394,
0.02104387991130352,
-0.0023379274643957615,
0.0067748017609119415,
0.03729908913373947,
0.039921440184116364,
0.031246161088347435,
-0.017383549362421036,
0.020313948392868042,
-0.011838790029287338,
-0.022753847762942314,
-0.06839828193187714,
0.035188399255275726,
-0.0337940938770771,
-0.008790502324700356,
-0.10724294185638428,
-0.009254519827663898,
-0.0034582708030939102,
0.024647993966937065,
-0.027987642213702202,
-0.046503275632858276,
0.047147855162620544,
-0.03008865937590599,
-0.029648682102560997,
0.0499250553548336,
0.02753249742090702,
0.019668975844979286,
0.02517622336745262,
0.03408466652035713,
0.0402195081114769,
-0.025651995092630386,
0.012525823898613453,
-0.027993010357022285,
0.04300567880272865,
0.028342101722955704,
-0.0453624352812767,
-0.019476283341646194,
-0.004685548599809408,
0.0007466352544724941,
0.06162094697356224,
-0.025393154472112656,
0.013479293324053288,
0.006789621897041798,
-0.022358665242791176,
0.015514632686972618,
0.0760815367102623,
-0.05956000089645386,
0.029898911714553833,
0.03969377651810646,
0.04091279208660126,
-0.02557712234556675,
0.04436355456709862,
0.05365510284900665,
0.031248334795236588,
0.02693023905158043,
0.036099303513765335,
-0.0028485076036304235,
-0.01105596125125885,
-0.04396801441907883,
0.025100771337747574,
-0.028413033112883568,
-0.009537863545119762,
0.022158153355121613,
0.04747912287712097,
-0.050981100648641586,
0.015420782379806042,
-0.01636219583451748,
0.004856616258621216,
0.06167349964380264,
0.007377311121672392,
-0.033789556473493576,
0.016213560476899147,
-0.029725801199674606,
-0.004461959004402161,
0.025078708305954933,
-0.020918574184179306,
-0.03753397986292839,
0.008410164155066013,
-0.012275648303329945,
0.025166047737002373,
0.03658321872353554,
-0.0003176162426825613,
-0.06961414963006973,
-0.027659954503178596,
-0.017213953658938408,
-0.002000294392928481,
-0.04377085343003273,
0.03936139494180679,
0.05466847121715546,
0.011863804422318935,
-0.000707325991243124,
0.015886371955275536,
0.12627717852592468,
0.009978744201362133,
0.0072286613285541534,
0.03598245605826378,
0.02758176624774933,
0.01299457810819149,
0.046967197209596634,
-0.0029218322597444057,
-0.023079073056578636,
0.016306497156620026,
-0.002539687557145953,
0.027501359581947327,
-0.0899454802274704,
-0.06994348764419556,
-0.037331949919462204,
-0.021756695583462715,
0.04077579826116562,
0.03803583234548569,
-0.01915370486676693,
0.04393034800887108,
-0.07427173107862473,
-0.04656797647476196,
-0.011736360378563404,
0.0038125573191791773,
-0.04866443946957588,
0.04715185984969139,
0.06655697524547577,
0.009004754945635796,
-0.0018250024877488613,
-0.06526876240968704,
0.042108938097953796,
0.018340030685067177,
0.00929240696132183,
0.030949169769883156,
-0.01968265511095524,
0.044387295842170715,
0.010312987491488457,
0.011650163680315018,
0.01978425681591034,
-0.04751580208539963,
-0.009121854789555073,
0.005186097230762243,
-0.016155708581209183,
-0.09088829159736633,
-0.03228745236992836,
0.04706375673413277,
0.06011958047747612,
-0.04361012205481529,
-0.012034573592245579,
0.053021661937236786,
0.023761073127388954,
-0.037065472453832626,
-0.016231520101428032,
0.06327909976243973,
0.043286316096782684,
-0.009963305667042732,
-0.01863185688853264,
-0.032794300466775894,
0.05305899679660797,
0.06722288578748703,
0.023460140451788902,
-0.04408445954322815,
-0.0004722933517768979,
0.02826378308236599,
-0.007917467504739761,
0.0233625341206789,
0.015893850475549698,
0.009790260344743729,
-0.044742051512002945,
0.0336112417280674,
-0.0248478464782238,
-0.06985139101743698,
-0.01117908675223589,
0.005928038153797388,
-0.013022205792367458,
-0.022117458283901215,
-0.005649745464324951,
-0.008520610630512238,
0.03737252205610275,
0.037503864616155624,
-0.02623109519481659,
0.03245624154806137,
-0.013814030215144157,
-0.014899082481861115,
-0.057878054678440094,
0.012972033582627773,
0.011113390326499939,
0.00983155146241188,
-0.05410895124077797,
-0.08340974152088165,
-0.015165177173912525,
0.014158297330141068,
0.009700815193355083,
-0.005339691415429115,
-0.015289980918169022,
-0.009277749806642532,
-0.03476047143340111,
0.012144165113568306,
0.055105213075876236,
0.05361504480242729,
0.024445373564958572,
0.039156120270490646,
0.06620636582374573,
-0.02645869366824627,
-0.029979607090353966,
0.013084059581160545,
0.02066565677523613,
0.024983393028378487,
-0.0034394320100545883,
0.004398863762617111,
-0.05088570713996887,
0.0363650768995285,
-0.016046499833464622,
0.05285890772938728,
0.038736481219530106,
-0.034724000841379166,
-0.021843599155545235,
-0.03551626577973366,
0.046000078320503235,
-0.012028864584863186,
-0.015786632895469666,
-0.000027692072762874886,
0.012674378231167793,
-0.04513632878661156,
0.03862223029136658,
0.017561448737978935,
0.003052768297493458,
0.015926850959658623,
0.04248451441526413,
-0.018340427428483963,
-0.01665506698191166,
0.045208532363176346,
-0.06384854018688202,
0.030320487916469574,
-0.038603708148002625,
0.04139581322669983,
-0.023023629561066628,
0.019188420847058296,
-0.0016546939732506871,
-0.020390832796692848,
-0.04098625108599663,
0.061921071261167526,
-0.016674011945724487,
-0.02502075582742691,
0.04694772884249687,
-0.014976982958614826,
-0.011715341359376907,
0.016388600692152977,
0.02854742854833603,
0.0069572459906339645,
0.008410644717514515,
-0.0018618828617036343,
-0.023733453825116158,
0.021074576303362846,
0.045790158212184906,
0.006483599543571472,
-0.009764500893652439,
-0.006940079387277365,
0.03102656826376915,
-0.0033462538849562407,
-0.002919064834713936,
-0.013289041817188263,
0.04474702104926109,
0.03667924180626869,
-0.01408903393894434,
0.0334470272064209,
0.04331423342227936,
-0.031038418412208557,
0.058540746569633484,
-0.02474534697830677,
0.02433587796986103,
-0.001671693637035787,
-0.005787300877273083,
-0.0029123714193701744,
-0.02214856445789337,
-0.007545861881226301,
0.042674630880355835,
-0.02085145004093647,
-0.02655748277902603,
0.03676031157374382,
0.0010786696802824736,
-0.01799342781305313,
0.055547989904880524,
-0.009756810963153839,
-0.047691360116004944,
0.04199470207095146,
-0.03643085062503815,
0.022610483691096306,
-0.04312805086374283,
0.006943327374756336,
-0.061624281108379364,
-0.06084232032299042,
0.04219511151313782,
0.060426924377679825,
0.007491490337997675,
0.02672720141708851,
0.01862628012895584,
-0.012448401190340519,
-0.06673932075500488,
0.02518816478550434,
-0.06449893116950989,
0.01239832490682602,
-0.01780823804438114,
-0.04201648384332657,
0.006953224074095488,
-0.03479956090450287,
-0.04502631351351738,
-0.01755397394299507,
0.01417775172740221,
0.004802168346941471,
-0.001118666841648519,
-0.03590890020132065,
0.023748455569148064,
0.008059157989919186,
-0.0034748518373817205,
-0.004986841231584549,
-0.09000051021575928,
0.030221309512853622,
0.008344798348844051,
0.021005451679229736,
-0.012357420288026333,
-0.032027874141931534,
-0.0020619211718440056,
0.0028566892724484205,
0.012582961469888687,
0.043475888669490814,
-0.00788248423486948,
-0.001478653633967042,
0.012914860621094704,
0.045650407671928406,
-0.018292555585503578,
-0.014275060966610909,
-0.018806781619787216,
0.019794952124357224,
-0.01608830876648426,
-0.03579286113381386,
-0.028429636731743813,
0.009535283781588078,
0.0270609762519598,
-0.030214080587029457,
0.019867951050400734,
-0.050548795610666275,
-0.012708917260169983,
-0.020903507247567177,
0.02254801243543625,
0.05187419056892395,
0.014343932271003723,
-0.056742578744888306,
0.007445009425282478,
-0.01694503054022789,
-0.0232088565826416,
-0.015247767791152,
0.0066307964734733105,
-0.04205337166786194,
-0.04387165233492851,
-0.016930803656578064,
-0.013544673100113869,
0.05381837859749794,
-0.04926266148686409,
0.11720624566078186,
0.041129130870103836,
-0.04150604084134102,
0.00433050561696291,
0.051015570759773254,
-0.008773638866841793,
0.03828371316194534,
-0.027462007477879524,
0.00910965446382761,
-0.0033906393218785524,
-0.041064873337745667,
-0.013637824915349483,
0.04986463859677315,
0.017008448019623756,
-0.02810332179069519,
0.030716868117451668,
0.04846229776740074,
-0.013806382194161415,
-0.03480149060487747,
-0.0044151186011731625,
-0.011108922772109509,
-0.0342123843729496,
-0.020365620031952858,
-0.031313277781009674,
-0.0074106790125370026,
-0.0072689298540353775,
0.0255808737128973,
-0.003605413716286421,
-0.039689335972070694,
-0.015439694747328758,
-0.055618222802877426,
0.06971634924411774,
-0.04303958639502525,
-0.003732098266482353,
0.005430696532130241,
-0.021339280530810356,
-0.05866473913192749,
-0.002551423152908683,
0.019368506968021393,
-0.0750388503074646,
-0.002534035127609968,
0.01838015392422676,
-0.005915789399296045,
0.03320799395442009,
-0.08213687688112259,
-0.08142610639333725,
-0.0033890672493726015,
0.004421662539243698,
0.030341729521751404,
-0.028158249333500862,
0.012618612498044968,
0.017521057277917862,
0.053384196013212204,
-0.03405887633562088,
-0.008419601246714592,
0.01576816849410534,
-0.07960665225982666,
-0.023749899119138718,
0.036221958696842194,
0.00030890380730852485,
0.015257359482347965,
-0.03949878364801407,
-0.017410993576049805,
0.082371287047863,
0.027663035318255424,
-0.013690204359591007,
-0.04728382080793381,
-0.09366308152675629,
-0.009469699114561081,
0.08503604680299759,
-0.0008603712194599211,
-0.021539248526096344,
0.028257617726922035,
0.0028695454820990562,
0.006855341140180826,
-0.015163629315793514,
0.001103911199606955,
0.08044686168432236,
-0.039536528289318085,
0.021919364109635353,
0.06962203234434128,
-0.04421055689454079,
-0.03791331872344017,
0.030611248686909676,
0.017876721918582916,
0.04040161147713661,
0.008105461485683918,
0.013575581833720207,
-0.012910251505672932,
-0.00020793585281353444,
-0.04969228431582451,
-0.0007064364617690444,
-0.006837880704551935,
-0.011116832494735718,
0.035089489072561264,
0.047844789922237396,
0.0011479792883619666,
-0.0038563688285648823,
-0.005484485998749733,
0.010046915151178837,
0.0130051514133811,
0.005055698566138744,
-0.005979272071272135,
-0.02039957605302334,
-0.06587275117635727,
0.059085048735141754,
0.013674959540367126,
-0.030394770205020905,
0.03653792664408684,
0.06471691280603409,
-0.002203039824962616,
-0.031169502064585686,
-0.018638134002685547,
-0.05899430811405182,
0.022337300702929497,
-0.008471235632896423,
-0.015157264657318592,
-0.08047010004520416,
-0.05676756426692009,
0.009009488858282566,
0.016888290643692017,
0.012128719128668308,
-0.024293281137943268,
0.006864393595606089,
-0.005394675303250551,
0.02433779649436474,
0.017968662083148956,
-0.07896561920642853,
0.028219670057296753,
-0.01009775698184967,
0.03490768000483513,
0.027814825996756554,
0.017910560593008995,
0.013750137761235237,
0.023927364498376846,
-0.0043398854322731495,
-0.015489908866584301,
-0.014131786301732063,
0.020446481183171272,
-0.015272656455636024,
-0.05790621042251587,
0.019576698541641235,
0.033845022320747375,
-0.04230997711420059,
0.025044789537787437,
0.04555198550224304,
-0.030551891773939133,
-0.0342559888958931,
0.018742356449365616,
-0.0054031359031796455,
-0.0035956427454948425,
-0.003717203624546528,
0.04527250677347183,
0.02605425752699375,
-0.06186801940202713,
-0.024356165900826454,
-0.01621312089264393,
-0.027787528932094574,
0.003807258792221546,
-0.007024894468486309,
-0.018738791346549988,
0.023577282205224037,
-0.06305587291717529,
0.009379568509757519,
-0.027793757617473602,
-0.0064202649518847466,
-0.03393184766173363,
-0.023351261392235756,
0.02289310097694397,
-0.03798291087150574,
0.04443872720003128,
-0.02524707466363907,
-0.061437174677848816,
-0.021350635215640068,
-0.011466264724731445,
-0.012357069179415703,
0.022049320861697197,
0.0051049343310296535,
-0.06022071838378906,
-0.05462924763560295,
0.04744359478354454,
-0.04410810023546219,
0.016133585944771767,
0.0068939924240112305,
-0.03925652801990509,
0.010303815826773643,
0.09165222197771072,
0.05513359606266022,
-0.049069058150053024,
-0.007091876585036516,
0.031251147389411926,
0.053169962018728256,
-0.0038392585702240467,
0.03537244349718094,
-0.006742812227457762,
0.062062714248895645,
-0.07382292300462723,
0.056590478867292404,
-0.0018849867628887296,
0.04090831056237221,
-0.01262130681425333,
-0.05264272913336754,
0.018318556249141693,
-0.05311566963791847,
0.016705486923456192,
0.03168686106801033,
-0.005992684047669172,
-0.0033274965826421976,
-0.06273655593395233,
-0.062087513506412506,
0.037653785198926926,
-0.005414010491222143,
0.07797620445489883,
0.033865995705127716,
0.008054393343627453,
0.03003215789794922,
-0.027224352583289146,
-0.055025625973939896,
-0.01717326231300831,
0.0027821247931569815,
0.014002785086631775,
0.05405813083052635,
-0.01845247484743595,
-0.005520767066627741,
-0.015665026381611824,
0.017755964770913124,
-0.02859085611999035,
-0.016019746661186218,
0.0042787762358784676,
0.023979810997843742,
-0.0005201874882914126,
-0.01403848733752966,
-0.10756169259548187,
-0.002690589055418968,
-0.015923356637358665,
-0.02653757482767105,
-0.06637755781412125,
-0.009847226552665234,
0.012771588750183582,
0.020384138450026512,
0.012388625182211399,
-0.0025498108007013798,
0.05817754194140434,
0.01778402365744114,
0.014701771549880505,
0.004802505485713482,
0.016589244827628136,
-0.0379047766327858,
-0.026048513129353523,
0.0639895498752594,
0.050256479531526566,
-0.02336513251066208,
0.021562378853559494,
0.03175677731633186,
0.03408365696668625,
0.01689412258565426,
0.051712796092033386,
0.00205390271730721,
0.07796219736337662,
0.0009026774205267429,
-0.008452066220343113,
0.001607377314940095,
-0.0009153063874691725
] |
<p>I'm looking to plot the band gap $\Delta(T)$ as a function of temperature between $T = 0$ and $T = T_c$ by numerical evaluation of the band gap equation</p>
<p>$$\frac{1}{\mathcal{N}(0)V} = \int_0^{\hbar\omega_D}{d\xi\frac{\tanh{\frac{\sqrt{\Delta^2+\xi^2}}{2k_BT}}}{\sqrt{\Delta^2+\xi^2}}}$$</p>
<p>where $\omega_D$ is the Debye frequency, $\mathcal{N}(0)$ is the density of states at the Fermi level and $V$ is the interaction strength in the BCS model. Now, in order to do this, I need values for both $\omega_D$ and $\mathcal{N}(0)V$.</p>
<p>I think I have a pretty good idea about the order of magnitude for $\omega_D$ if I assume longitudinal optical phonons (I find $\hbar\omega_{LO} \propto 10\,\mathrm{meV}$, but please do correct me if that doesn't seem right).</p>
<p>However, I still need a value for $\mathcal{N}(0)V$. <a href="http://en.wikipedia.org/wiki/Cooper_pairs" rel="nofollow">Wikipedia</a> mentions </p>
<blockquote>
<p>The energy of the pairing interaction is quite weak, of the order of $10^{−3}\,\mathrm{eV}$, and thermal energy can easily break the pairs.</p>
</blockquote>
<p>but it's not clear what quantity exactly is meant by 'the energy of the pairing interaction' (I could imagine it being one of two things). I'm guessing $\mathcal{N}(0) \propto 10^{28}$ for a metal (again, correct me if I'm wrong), so my question is really quite straightforward: what is the value of the interaction strength $V$ in the BCS model? (provide a reference please)</p> | g4738 | [
-0.0346403531730175,
-0.006411537993699312,
0.0021795567590743303,
-0.05759193375706673,
0.013993185944855213,
-0.04089224338531494,
0.018971025943756104,
0.024264344945549965,
-0.002323136432096362,
-0.005451025441288948,
-0.0026546225417405367,
0.042870957404375076,
-0.049050334841012955,
-0.004972709808498621,
0.06849350035190582,
0.053395163267850876,
-0.00902218371629715,
-0.0052439323626458645,
0.03131072223186493,
0.009160413406789303,
-0.027799418196082115,
-0.004363579209893942,
-0.03802970424294472,
-0.0513736829161644,
0.009698606096208096,
-0.01573304831981659,
0.014009250327944756,
-0.0066445390693843365,
-0.03446481004357338,
0.01570655032992363,
0.0051867119036614895,
0.07451608031988144,
0.10421935468912125,
-0.027003901079297066,
-0.0827164426445961,
0.013183976523578167,
0.02994583174586296,
0.007337524555623531,
0.018934378400444984,
-0.024729853495955467,
-0.018916437402367592,
-0.014423657208681107,
0.013035250827670097,
-0.012462741695344448,
-0.009827799163758755,
-0.03868892788887024,
-0.042277995496988297,
-0.0014394778991118073,
-0.0813981145620346,
0.01029097568243742,
0.055290888994932175,
0.05334211885929108,
0.10838118940591812,
-0.022281356155872345,
-0.012793853878974915,
0.013749264180660248,
-0.0420205183327198,
-0.026686478406190872,
0.01772208884358406,
0.028519660234451294,
0.0384407602250576,
0.04065132886171341,
-0.008861491456627846,
0.008030340075492859,
0.07541698217391968,
0.018278051167726517,
0.005708596669137478,
0.021517306566238403,
-0.03143355995416641,
-0.06489036232233047,
-0.06126197800040245,
-0.008794521912932396,
-0.03998968377709389,
0.015328231267631054,
-0.033166661858558655,
-0.02216287888586521,
-0.03498128056526184,
-0.041380587965250015,
-0.019179273396730423,
0.004203457850962877,
-0.006000066176056862,
0.010429106652736664,
0.034501250833272934,
-0.007601444143801928,
0.005138468462973833,
-0.06354150921106339,
-0.006100522819906473,
0.01914258301258087,
-0.04857425391674042,
0.060267411172389984,
-0.012919552624225616,
-0.03627323359251022,
0.02796075865626335,
-0.006517128087580204,
0.02618011273443699,
0.00629396690055728,
0.02203490398824215,
0.02687179297208786,
-0.01661836728453636,
-0.007785456720739603,
-0.017115527763962746,
-0.0032876774203032255,
0.04604233801364899,
-0.01904331147670746,
-0.0674685537815094,
-0.004488393198698759,
0.009774601086974144,
-0.014702788554131985,
-0.016049453988671303,
0.021555263549089432,
-0.025826429948210716,
-0.00019398279255256057,
-0.014111611060798168,
-0.021477000787854195,
0.030072975903749466,
-0.00778944231569767,
0.0004694302915595472,
-0.017224056646227837,
-0.042359814047813416,
0.04192807152867317,
0.009579853154718876,
0.022848043590784073,
0.015314307063817978,
0.0508866161108017,
-0.02775828167796135,
-0.049947116523981094,
-0.03695036098361015,
0.008926743641495705,
0.02940213680267334,
-0.020230939611792564,
-0.03285804018378258,
-0.006007971242070198,
0.02979212999343872,
0.02598641626536846,
0.006853311788290739,
-0.005754589568823576,
0.04202829301357269,
-0.02701830491423607,
0.002238811459392309,
-0.0255380030721426,
-0.043395936489105225,
-0.03409036621451378,
-0.033195093274116516,
-0.05821457877755165,
-0.04424764961004257,
0.03811824321746826,
-0.039253074675798416,
-0.027714351192116737,
-0.007413949817419052,
0.02786382846534252,
0.04304306581616402,
0.01982223428785801,
0.005026200786232948,
-0.04178138077259064,
-0.06656818836927414,
-0.0012082542525604367,
0.09236348420381546,
-0.002867641858756542,
-0.03842272236943245,
0.006136935204267502,
0.0037377832923084497,
0.0101345619186759,
0.02115529775619507,
-0.0666947215795517,
-0.02269299514591694,
-0.0324593186378479,
0.031460490077733994,
-0.06566908210515976,
0.007809558417648077,
-0.0005324864177964628,
-0.04017965495586395,
-0.00925816036760807,
0.004783601965755224,
0.025267064571380615,
0.0024370376486331224,
0.08114772289991379,
-0.02253543771803379,
0.01854681968688965,
0.03342968225479126,
0.00810228567570448,
0.07272882014513016,
-0.04759310930967331,
0.0796947255730629,
0.019011512398719788,
-0.0591961145401001,
0.00649891747161746,
0.030424853786826134,
0.032880496233701706,
-0.032276686280965805,
0.006488095037639141,
-0.018278872594237328,
-0.014856327325105667,
-0.010981692932546139,
-0.01859734207391739,
-0.00859934650361538,
0.007852327078580856,
0.0358213372528553,
-0.032921940088272095,
-0.007206580601632595,
-0.051965031772851944,
-0.06370982527732849,
0.06322044879198074,
0.04092448204755783,
0.008204115554690361,
-0.0012889779172837734,
0.006568837445229292,
-0.0028292459901422262,
0.00786079466342926,
-0.05200408771634102,
0.0069795832969248295,
-0.0396418496966362,
-0.04786418378353119,
-0.03165864571928978,
0.04658622667193413,
-0.0002531229401938617,
-0.06536412239074707,
0.019413437694311142,
0.04039544612169266,
-0.022585740312933922,
0.04936959594488144,
-0.027901379391551018,
-0.008918799459934235,
-0.009815627709031105,
0.028753088787198067,
-0.037615712732076645,
-0.057501163333654404,
-0.00004670754060498439,
0.01256801187992096,
0.013794712722301483,
0.04957971349358559,
-0.041776079684495926,
0.061821818351745605,
0.00005139324639458209,
-0.005757820792496204,
-0.014306786470115185,
0.06241634115576744,
0.037098027765750885,
-0.04953121766448021,
-0.006562020163983107,
0.04607110098004341,
-0.001202089013531804,
-0.015832170844078064,
-0.0710609033703804,
0.026546403765678406,
0.021256186068058014,
0.023953834548592567,
0.009272926487028599,
-0.008218305185437202,
-0.0017204624600708485,
-0.0016875183209776878,
0.03256438672542572,
0.0056434147991240025,
0.01804077811539173,
0.01764211244881153,
-0.014493568800389767,
-0.020918503403663635,
-0.056149598211050034,
0.004021546803414822,
-0.026388250291347504,
-0.018106475472450256,
-0.04217102751135826,
0.01921716332435608,
0.01183175016194582,
-0.01934886910021305,
-0.022271214053034782,
-0.04833124577999115,
-0.04899249225854874,
-0.08314724266529083,
-0.0014739567413926125,
-0.022521236911416054,
0.027594193816184998,
0.03923049569129944,
0.02346964366734028,
-0.012542112730443478,
0.0044384850189089775,
-0.08021492511034012,
0.008806471712887287,
-0.014390891417860985,
0.004546713549643755,
-0.0534895658493042,
0.007375860586762428,
-0.042121876031160355,
0.02123074047267437,
0.034877993166446686,
0.05116889998316765,
-0.07891198992729187,
-0.0009529207600280643,
0.030655693262815475,
0.057329773902893066,
-0.01848367601633072,
-0.02081373706459999,
-0.009367601945996284,
-0.005826076027005911,
0.0486583337187767,
-0.013546900823712349,
-0.013708561658859253,
0.07059227675199509,
-0.019951608031988144,
-0.004759922157973051,
0.05895412340760231,
0.05264990031719208,
-0.011837956495583057,
-0.015807487070560455,
-0.02205229364335537,
0.02657432109117508,
-0.02380257286131382,
-0.016710029914975166,
-0.039411552250385284,
-0.007418752647936344,
-0.00827245693653822,
0.00609975541010499,
0.011458372697234154,
0.041730958968400955,
-0.05304576829075813,
-0.01900237239897251,
0.03473527356982231,
0.03640950843691826,
-0.013972588814795017,
-0.0037513934075832367,
-0.03647186607122421,
0.044273775070905685,
-0.030659200623631477,
0.017481448128819466,
-0.07414507120847702,
-0.018458183854818344,
0.005550136789679527,
0.0018902543233707547,
-0.07357440143823624,
-0.07700422406196594,
0.009422346018254757,
-0.01138707622885704,
-0.044557444751262665,
0.07250449806451797,
-0.0046788607724010944,
0.009209305047988892,
-0.029235871508717537,
-0.020916396751999855,
0.009232843294739723,
0.10493209213018417,
0.08609123528003693,
-0.028934519737958908,
0.013515164144337177,
0.007670747581869364,
0.02037329226732254,
0.0535522997379303,
-0.042539164423942566,
-0.013105819933116436,
0.059972867369651794,
-0.0161330197006464,
-0.06700369715690613,
-0.011797526851296425,
-0.045432332903146744,
-0.028092633932828903,
-0.0343204140663147,
-0.012174825184047222,
0.01268345769494772,
0.025863710790872574,
0.008083011023700237,
0.044495757669210434,
-0.00012444885214790702,
0.06720177084207535,
-0.012212807312607765,
-0.0016308593330904841,
-0.019092056900262833,
-0.06790561228990555,
-0.03545713797211647,
-0.04014227166771889,
0.054237041622400284,
0.03736892715096474,
-0.026143213734030724,
-0.05085127055644989,
-0.013224354013800621,
0.009377589449286461,
0.008408166468143463,
0.07334794849157333,
-0.020571528002619743,
0.0014010416343808174,
-0.021344386041164398,
0.01116270199418068,
0.0390818826854229,
-0.030593110248446465,
0.03982993960380554,
0.03965276479721069,
0.062113530933856964,
0.053359255194664,
-0.06252814084291458,
0.02958667278289795,
-0.00024017227406147867,
-0.010873840190470219,
-0.035229530185461044,
0.018995244055986404,
-0.029371734708547592,
-0.06556157022714615,
0.054125890135765076,
-0.007065868005156517,
-0.028385575860738754,
0.04325812682509422,
0.019159367308020592,
-0.006625548470765352,
-0.010052145458757877,
-0.0599500797688961,
-0.03832779452204704,
-0.01056879572570324,
-0.03848380967974663,
0.0023146821185946465,
0.0023804567754268646,
0.019078707322478294,
-0.006163463927805424,
-0.032328151166439056,
-0.0062019662000238895,
-0.009006558917462826,
-0.02809799835085869,
0.013882791623473167,
-0.024071577936410904,
-0.004420803394168615,
0.004427036270499229,
0.008313620463013649,
-0.026757195591926575,
0.04641203582286835,
0.009483842179179192,
-0.002290781121701002,
0.01229594461619854,
-0.030976347625255585,
-0.03823794424533844,
-0.027490440756082535,
0.07261937856674194,
0.026193883270025253,
0.005823603831231594,
0.05256064981222153,
0.009894930757582188,
0.009238975122570992,
0.02247886173427105,
-0.02506040409207344,
0.03370031341910362,
-0.06407386809587479,
0.09069517254829407,
-0.04332945495843887,
-0.000724709068890661,
-0.0030800988897681236,
0.061542071402072906,
0.011618335731327534,
0.02169903740286827,
0.003677631728351116,
0.007120915222913027,
0.07022853195667267,
0.03647525981068611,
-0.02978086844086647,
-0.04877176880836487,
-0.012582463212311268,
-0.03728165104985237,
0.01731412298977375,
0.002673596143722534,
-0.054287753999233246,
-0.008177711628377438,
0.014444920234382153,
0.004782363306730986,
0.02836470492184162,
0.0037044354248791933,
0.053997088223695755,
-0.003169179428368807,
-0.00997159257531166,
0.012784069404006004,
-0.013538854196667671,
-0.0227245781570673,
0.023396283388137817,
-0.04515625536441803,
-0.0035053046885877848,
0.016610518097877502,
-0.04182437062263489,
0.01608762890100479,
0.0066213347017765045,
-0.016706056892871857,
0.08558458834886551,
-0.026354070752859116,
-0.030430156737565994,
-0.020122015848755836,
-0.058442410081624985,
-0.031231114640831947,
0.0399157851934433,
-0.003373049898073077,
-0.020242923870682716,
0.05262027308344841,
0.00664172088727355,
0.09687283635139465,
-0.016929959878325462,
-0.016128763556480408,
-0.06826987862586975,
0.0012710968730971217,
0.03402353823184967,
-0.01253551710397005,
0.005960822571069002,
-0.014345875009894371,
0.009766348637640476,
0.025954334065318108,
0.0022726794704794884,
-0.03845524415373802,
0.009420192800462246,
-0.01248642522841692,
0.041449517011642456,
0.010143967345356941,
-0.039135921746492386,
0.050786424428224564,
-0.020249413326382637,
0.008741765283048153,
0.021330533549189568,
0.09905701130628586,
0.047372959554195404,
0.00656190374866128,
0.03283381834626198,
0.05308517813682556,
-0.005671327002346516,
0.0437588170170784,
0.05590616166591644,
0.05182751268148422,
-0.034464478492736816,
-0.006634840741753578,
0.020541293546557426,
-0.013008049689233303,
-0.029050149023532867,
-0.04206644743680954,
0.08030176907777786,
0.019248655065894127,
0.004465256351977587,
-0.024549346417188644,
0.04536285251379013,
-0.029732583090662956,
-0.02149655856192112,
-0.020586837083101273,
0.031164085492491722,
-0.01628289185464382,
0.0012841304996982217,
0.005108265671879053,
-0.008762718178331852,
-0.01075202040374279,
0.02931429073214531,
-0.0029884742107242346,
-0.0038551243487745523,
0.012525011785328388,
-0.04393821582198143,
0.024979162961244583,
0.0014188244240358472,
0.024279816076159477,
0.012531626969575882,
0.03891994059085846,
0.01857658661901951,
-0.006095345597714186,
-0.010513418354094028,
0.013019019737839699,
0.014092407189309597,
0.08369386941194534,
-0.03480636700987816,
-0.004104682244360447,
-0.03784380108118057,
0.010121290571987629,
0.06647613644599915,
0.025484532117843628,
0.017629748210310936,
0.007187030278146267,
-0.033933158963918686,
0.019820604473352432,
0.023313554003834724,
-0.003916745539754629,
0.036140862852334976,
0.11761730164289474,
0.0014285329962149262,
-0.01439517829567194,
-0.08493855595588684,
0.008363871835172176,
-0.0021303140092641115,
-0.036990679800510406,
0.009310964494943619,
-0.022578973323106766,
-0.05837051942944527,
-0.0022686519660055637,
0.03618255630135536,
0.044446397572755814,
-0.008016747422516346,
-0.04364093020558357,
-0.03045513667166233,
0.0014006684068590403,
-0.07019899785518646,
0.07131695747375488,
0.007044606376439333,
0.04196860268712044,
0.011240593157708645,
0.0547160841524601,
-0.004732238128781319,
-0.015059804543852806,
0.022573266178369522,
-0.04466453939676285,
0.004245710093528032,
-0.04158481955528259,
-0.008893049322068691,
0.000758341106120497,
0.018771464005112648,
-0.029255272820591927,
0.06266424059867859,
-0.015399695374071598,
-0.024842161685228348,
0.061386629939079285,
0.07565709948539734,
-0.009282853454351425,
0.02410886436700821,
0.02895117923617363,
0.01848791167140007,
-0.021974602714180946,
0.019966566935181618,
-0.02041550539433956,
-0.045633602887392044,
0.03313982114195824,
-0.04419099912047386,
0.034892573952674866,
0.024693023413419724,
0.021028373390436172,
0.04194851592183113,
-0.007637734990566969,
0.05626202002167702,
0.03281406685709953,
-0.07125300168991089,
0.08476213365793228,
-0.03177538514137268,
-0.044328443706035614,
-0.025765344500541687,
-0.04298738017678261,
0.04218154028058052,
0.0272555872797966,
-0.031435247510671616,
0.02105056680738926,
0.029728248715400696,
-0.030500352382659912,
0.003130463883280754,
0.0014276584843173623,
-0.014150448143482208,
0.028484728187322617,
-0.011896624229848385,
0.04787715896964073,
-0.03196299448609352,
0.019719626754522324,
-0.004076091106981039,
0.045125219970941544,
-0.02371789701282978,
-0.056915830820798874,
0.07954846322536469,
0.020397398620843887,
-0.03059876523911953,
0.023203933611512184,
0.02486451156437397,
0.005578325130045414,
-0.03464656323194504,
-0.0020792074501514435,
0.05718265473842621,
-0.013037518598139286,
-0.01394715066999197,
0.024984583258628845,
-0.048553917557001114,
-0.01099262572824955,
-0.03190105780959129,
0.044536396861076355,
0.06625550985336304,
0.0316787026822567,
0.017082078382372856,
-0.10914822667837143,
-0.021825794130563736,
0.003954838030040264,
0.02327815070748329,
0.05602726340293884,
0.02652217634022236,
-0.022581640630960464,
0.031352654099464417,
-0.06822334229946136,
-0.012445628643035889,
-0.12277300655841827,
-0.04442878067493439,
-0.000693698413670063,
-0.015332258306443691,
0.02078947424888611,
-0.013381474651396275,
0.008014067076146603,
-0.018543049693107605,
-0.03504413366317749,
0.007800303399562836,
-0.05392414703965187,
0.010123299434781075,
-0.06568805128335953,
0.008746793493628502,
0.03188079595565796,
0.001564095146022737,
-0.015934815630316734,
0.0600009486079216,
0.09035084396600723,
-0.04556591808795929,
0.015927264466881752,
-0.015405106358230114,
-0.04885803163051605,
0.000982298282906413,
-0.012037273496389389,
-0.02449180744588375,
0.024390514940023422,
0.061461515724658966,
0.06247888505458832,
0.07691247761249542,
-0.024330459535121918,
-0.009287756867706776,
-0.03233719617128372,
0.009391517378389835,
0.05134353041648865,
0.016406811773777008,
-0.04270826652646065,
-0.047415900975465775,
-0.04303497448563576,
0.05173606052994728,
0.02978985384106636,
0.036096446216106415,
0.029431195929646492,
0.04887459799647331,
-0.070279560983181,
-0.04366610571742058,
0.04245974123477936,
0.017011208459734917,
-0.005985137075185776,
0.003839209210127592,
-0.019349751994013786,
0.03785346820950508,
-0.010603042319417,
-0.0028987876139581203,
-0.06301755458116531,
-0.03518139198422432,
0.06216798722743988,
0.02156272903084755,
0.03882039710879326,
-0.01611367240548134,
-0.0338008850812912,
-0.028991922736167908,
0.016941452398896217,
-0.014118889346718788,
0.04258251562714577,
-0.0003804348816629499,
0.01605333760380745,
-0.0030272577423602343,
0.022188005968928337,
0.016725411638617516,
-0.0677347332239151,
0.010795346461236477,
-0.04029376059770584,
-0.012355908751487732,
-0.03404055908322334,
-0.03548344969749451,
0.014244060032069683,
0.10202174633741379,
-0.029534628614783287,
-0.0332157202064991,
-0.005164281465113163,
-0.008495239540934563,
0.04145123437047005,
0.03483698144555092,
-0.06002441421151161,
-0.03420725092291832,
-0.03286112844944,
0.030211225152015686,
-0.010136148892343044,
-0.0034794704988598824,
-0.03587666526436806,
-0.036852236837148666,
0.03363177925348282,
0.01730305701494217,
-0.02081548422574997,
-0.029440706595778465,
-0.014057156629860401
] |
<p>In a phi fourth theory, the Hamiltonian density is:</p>
<p>$$\mathcal{H}=\frac{1}{2}\pi^2+\frac{1}{2}(\nabla \phi)^2+\frac{1}{2}m^2\phi^2+\frac{\lambda}{4!}\phi^4$$</p>
<p>Now I impose the usual equal time canonical commutation relations for fields ($\hbar=1$)</p>
<p>$$[\phi(\vec{x}),\pi(\vec{y})]=i \delta^3(\vec{x}-\vec{y})$$</p>
<p>where </p>
<p>$$\pi=\frac{\partial \mathcal{L}}{\partial (\dot{\phi})} \equiv \dot{\phi}$$</p>
<p>Heisenberg equation of motion for the field is just the definition of the conjugate momentum</p>
<p>$$\frac{d}{dt}\phi(\vec{x},t)=\pi(\vec{x},t) $$</p>
<p>and for $\pi(\vec{x})$ I have to calculate the commutator (not writing time dependence)</p>
<p>$$[H,\pi(\vec{x},t)]=\int d^3x'\left[\frac{1}{2}\pi^2(\vec{x}')+\frac{1}{2}(\nabla \phi)^2(\vec{x}')+\frac{1}{2}m^2\phi^2(\vec{x}')+\frac{\lambda}{4!}\phi^4(\vec{x}'),\pi(\vec{x}) \right] $$</p>
<p>First term gives zero, third and fourth terms give $i\left(m^2\phi(\vec{x})+\frac{\lambda}{3!}\phi^3(\vec{x})\right)$</p>
<p>My question is, how can I calculate</p>
<p>$$\frac{1}{2}\int d^3x' [(\nabla \phi)^2(\vec{x}'),\pi(\vec{x})] $$</p>
<p>As an analogy with the integral of the commutator is the commutator of the integral, may I write $\nabla \phi^2=\nabla \phi \cdot \nabla \phi$ and integrate by parts? How can I show that that is true?</p> | g4739 | [
0.02675619162619114,
-0.0015604794025421143,
-0.03512454777956009,
-0.03178339824080467,
0.031306371092796326,
-0.01069390494376421,
0.05755585804581642,
0.016232382506132126,
-0.012912544421851635,
0.06163879856467247,
-0.06852073222398758,
-0.017957357689738274,
-0.08949723094701767,
0.030602525919675827,
0.0388982929289341,
0.03595028445124626,
0.06372786313295364,
0.03881509229540825,
0.010957591235637665,
-0.020712709054350853,
-0.06784362345933914,
-0.007928773760795593,
-0.011456773616373539,
-0.013398204930126667,
0.052370112389326096,
-0.020068109035491943,
-0.026022614911198616,
-0.02979200705885887,
-0.004962438717484474,
-0.00458908686414361,
0.012827454134821892,
0.06829969584941864,
-0.016820834949612617,
-0.016737958416342735,
-0.016866199672222137,
0.02228163368999958,
0.06701608002185822,
-0.0004353487747721374,
-0.0041184574365615845,
-0.02043033391237259,
-0.01789834536612034,
-0.04251331463456154,
0.00998289231210947,
0.025328638032078743,
-0.0048964000307023525,
0.006624710280448198,
-0.009948060847818851,
-0.014763892628252506,
-0.05747902765870094,
0.00514436699450016,
-0.005487462505698204,
0.07989117503166199,
0.03767487779259682,
-0.04519038647413254,
-0.009935744106769562,
0.0920221358537674,
0.05740952119231224,
-0.015548383817076683,
0.014871257357299328,
0.08335118740797043,
-0.03752417489886284,
-0.07445099204778671,
0.004550579935312271,
0.033893000334501266,
0.07099580764770508,
-0.02524052932858467,
-0.022593354806303978,
0.014987555332481861,
-0.04497312754392624,
-0.02012571692466736,
0.010715717449784279,
-0.0411870963871479,
0.0060373335145413876,
-0.0005329088307917118,
-0.04358305409550667,
0.03424053639173508,
0.036049555987119675,
-0.06991792470216751,
0.036145322024822235,
-0.047174613922834396,
-0.01486671157181263,
-0.010558124631643295,
0.021246491000056267,
0.034939635545015335,
0.03506702929735184,
-0.04946004971861839,
-0.0003065145865548402,
-0.014692896977066994,
-0.0161720123142004,
-0.022488631308078766,
-0.04840514436364174,
-0.03255563601851463,
0.03523135930299759,
0.0008487538434565067,
-0.00035784230567514896,
0.021403176710009575,
-0.008520658127963543,
0.08325455337762833,
0.007809581235051155,
-0.029133083298802376,
-0.03035038150846958,
0.06535191088914871,
0.024307267740368843,
-0.03913016989827156,
-0.0035290136002004147,
-0.015033863484859467,
0.05523300915956497,
-0.043324023485183716,
-0.0050231898203492165,
0.00011703096242854372,
-0.023073146119713783,
-0.0030012906063348055,
-0.0014926352305337787,
-0.020276498049497604,
-0.026010161265730858,
-0.02860693447291851,
-0.019445281475782394,
0.007373957894742489,
-0.03456423804163933,
0.015843821689486504,
0.0034070461988449097,
-0.028060393407940865,
-0.0020417566411197186,
0.07740432024002075,
0.03174326568841934,
0.012577318586409092,
-0.05927123501896858,
0.021781619638204575,
0.03297533094882965,
0.0108833322301507,
0.00006420815770979971,
-0.012978651560842991,
0.01764460653066635,
0.0931408479809761,
0.045098334550857544,
0.036975108087062836,
-0.021781975403428078,
-0.0053235916420817375,
-0.009004710242152214,
0.017046036198735237,
0.01791875995695591,
-0.014175196178257465,
-0.03364529088139534,
-0.018785884603857994,
-0.03323997184634209,
-0.002576059428974986,
0.021623700857162476,
-0.0936339870095253,
0.022655347362160683,
-0.004175425041466951,
0.024987395852804184,
0.05860910564661026,
-0.010441823862493038,
0.04313087463378906,
0.02236306108534336,
0.013096664100885391,
0.04519085958600044,
-0.017977360635995865,
0.011573969386518002,
0.021589962765574455,
-0.014711666852235794,
-0.026253780350089073,
0.04083767533302307,
-0.004297649022191763,
-0.00030048578628338873,
0.03896216303110123,
0.04452841728925705,
-0.008830543607473373,
-0.04599165543913841,
-0.04856165125966072,
-0.0077381194569170475,
0.01532655954360962,
-0.05261291563510895,
0.003751508193090558,
0.012959430925548077,
-0.021582087501883507,
-0.10837366431951523,
-0.02525864914059639,
-0.045273471623659134,
0.07102946937084198,
0.008108492009341717,
0.005646004807204008,
0.03291856124997139,
-0.026684923097491264,
0.002357515972107649,
0.05161387845873833,
0.0493164137005806,
0.005133836530148983,
0.0018008910119533539,
-0.02772017940878868,
-0.006766421254724264,
0.011784357018768787,
-0.030110221356153488,
0.06803789734840393,
-0.06020856648683548,
0.02662329189479351,
-0.0010852654231712222,
-0.03339316323399544,
-0.023021064698696136,
-0.02737507037818432,
0.003437150502577424,
0.033368345350027084,
0.06805140525102615,
0.031942255795001984,
0.09332986921072006,
0.0036283780355006456,
0.03512860834598541,
-0.005802559666335583,
0.06238151341676712,
-0.00561874033883214,
0.027484193444252014,
-0.07062066346406937,
-0.0415470264852047,
0.07967260479927063,
-0.04458719864487648,
-0.034070584923028946,
0.03265387937426567,
0.0007611866458319128,
-0.0026271913666278124,
0.0184464193880558,
-0.044688060879707336,
0.003376913024112582,
0.0423719622194767,
-0.007012912537902594,
-0.03852368891239166,
0.0200507789850235,
0.03950424864888191,
0.025841910392045975,
-0.03883139044046402,
-0.006163771729916334,
-0.0348694734275341,
0.011534747667610645,
-0.016764884814620018,
0.024637790396809578,
0.030436506494879723,
0.07068852335214615,
-0.03387204557657242,
-0.0231711957603693,
0.015961818397045135,
0.051251523196697235,
0.005394794978201389,
0.009989609941840172,
-0.0012103905901312828,
-0.033147528767585754,
0.030284414067864418,
0.026408057659864426,
0.07088957726955414,
0.018355630338191986,
-0.03127460554242134,
-0.0018252611625939608,
0.03105355054140091,
0.014552160166203976,
-0.04686088487505913,
-0.0216835867613554,
-0.0005506959278136492,
-0.003828824497759342,
0.00011996714601991698,
0.00610688328742981,
0.011659870855510235,
-0.018521152436733246,
0.018074573948979378,
-0.06916558742523193,
-0.036488063633441925,
0.08450360596179962,
-0.05118141695857048,
-0.04714522883296013,
0.014491364359855652,
-0.01157982088625431,
0.021898068487644196,
-0.01718052476644516,
-0.08856254070997238,
0.016844814643263817,
0.0004206899320706725,
0.06978633254766464,
-0.03834790736436844,
-0.06339763849973679,
0.0049283262342214584,
-0.03873257339000702,
0.020670969039201736,
-0.015035511925816536,
-0.025933798402547836,
0.07243034988641739,
-0.024177225306630135,
0.027938835322856903,
0.009569637477397919,
-0.06093364581465721,
0.012728139758110046,
0.0245406124740839,
0.00997235719114542,
0.019629018381237984,
0.0019897236488759518,
0.001638605841435492,
-0.003185198875144124,
0.0220625177025795,
0.0072020720690488815,
0.07599339634180069,
-0.0006465862388722599,
-0.0914505273103714,
0.048457931727170944,
0.0680290162563324,
-0.0276848953217268,
0.035470589995384216,
0.01248316653072834,
0.05350254848599434,
0.06198504939675331,
0.0384337455034256,
-0.04971222206950188,
0.011135807260870934,
0.012378554791212082,
-0.046385880559682846,
-0.025503987446427345,
0.022762320935726166,
0.05163821578025818,
-0.05185171961784363,
-0.008609259501099586,
-0.003094688057899475,
0.005915519315749407,
0.0036768915597349405,
0.02084006927907467,
-0.01929107867181301,
-0.024562077596783638,
-0.0788668841123581,
-0.06459973752498627,
-0.008443678729236126,
0.008790992200374603,
-0.0028857507277280092,
-0.055374037474393845,
-0.02118697762489319,
-0.05428667366504669,
0.003751060226932168,
-0.03260033577680588,
-0.019224470481276512,
-0.018764730542898178,
-0.005358101800084114,
-0.03736334666609764,
-0.01983405277132988,
0.048558030277490616,
-0.00399165041744709,
0.013888068497180939,
-0.05151056870818138,
-0.029480168595910072,
-0.03360491245985031,
-0.0018218569457530975,
0.057375818490982056,
-0.05467868968844414,
-0.06752485781908035,
0.024005969986319542,
0.03135095164179802,
0.010261564515531063,
0.012873830273747444,
-0.012811866588890553,
0.0156968105584383,
0.007367084268480539,
0.012655895203351974,
-0.006835888605564833,
0.03537062555551529,
0.008376484736800194,
0.05877574160695076,
0.0017233124235644937,
0.028519179672002792,
-0.016254819929599762,
-0.054054636508226395,
0.03397519513964653,
0.02539960853755474,
-0.023172199726104736,
0.021947743371129036,
-0.007864481769502163,
0.022133992984890938,
0.009147543460130692,
-0.033775847405195236,
0.02501775696873665,
-0.04258063808083534,
0.0395805686712265,
0.015165308490395546,
-0.03870264068245888,
-0.06975282728672028,
-0.00765234837308526,
0.03927072882652283,
-0.014302590861916542,
0.04204323887825012,
0.003615924157202244,
0.037907857447862625,
0.01057735737413168,
0.04205720126628876,
0.042188968509435654,
0.0127736646682024,
0.040843416005373,
0.018055327236652374,
-0.01936214417219162,
-0.013649229891598225,
0.026620766147971153,
0.010792193934321404,
-0.032038286328315735,
-0.005074918270111084,
0.026200169697403908,
0.004284183029085398,
0.012234068475663662,
0.03335662931203842,
-0.032535724341869354,
-0.008413424715399742,
-0.05925614386796951,
-0.0025832115206867456,
0.04106771573424339,
-0.040660589933395386,
-0.04374619945883751,
0.0386759378015995,
0.04074444994330406,
-0.021311769261956215,
0.0737505704164505,
-0.014721541665494442,
-0.08171064406633377,
-0.07102182507514954,
0.05130461975932121,
-0.006771278101950884,
-0.013989158906042576,
0.0038204945158213377,
0.0008884895360097289,
-0.030006825923919678,
0.014439873397350311,
0.002164173638448119,
0.06849607825279236,
-0.037663888186216354,
0.016141315922141075,
-0.0222800113260746,
0.01719485968351364,
0.04416455328464508,
0.07043422013521194,
0.013347969390451908,
-0.023854531347751617,
-0.04463502764701843,
0.004825342912226915,
0.005034319125115871,
-0.03452618792653084,
0.01427549496293068,
-0.055697180330753326,
0.006913440302014351,
-0.04731704667210579,
0.05330635979771614,
-0.02053908072412014,
0.03453288972377777,
0.02678786776959896,
-0.0010763122700154781,
-0.011129879392683506,
-0.002506563439965248,
-0.012684425339102745,
0.05885039642453194,
0.024154582992196083,
-0.0554480105638504,
0.043988943099975586,
0.014752242714166641,
-0.0637945607304573,
-0.030240269377827644,
0.012335030362010002,
-0.00451459176838398,
0.040490444749593735,
-0.0174078568816185,
-0.04103608801960945,
-0.027127141132950783,
-0.007082635071128607,
-0.015691448003053665,
-0.0810447707772255,
0.0070239584892988205,
-0.0005696288426406682,
-0.048924144357442856,
0.013586594723165035,
0.010476014576852322,
-0.10812699049711227,
0.005809098482131958,
-0.044080015271902084,
-0.0031941961497068405,
0.04579606652259827,
-0.013172512874007225,
-0.0006752682966180146,
-0.023459959775209427,
-0.01499674841761589,
0.008938238024711609,
0.04579352214932442,
0.03535742685198784,
0.0025370388757437468,
-0.039234839379787445,
0.008604563772678375,
-0.01802949793636799,
-0.02580948919057846,
0.05883976072072983,
0.029320433735847473,
0.044682323932647705,
-0.017654145136475563,
-0.052779898047447205,
0.010382892563939095,
-0.05318804085254669,
0.03517362102866173,
0.05137498676776886,
0.012440444901585579,
0.030853718519210815,
0.0033012940548360348,
0.037327785044908524,
0.022815657779574394,
-0.055492110550403595,
0.05103774741292,
-0.015678001567721367,
-0.042753346264362335,
0.019543452188372612,
-0.030225049704313278,
0.026180114597082138,
0.02003895491361618,
0.06848085671663284,
0.09104803204536438,
0.03319287300109863,
-0.016386106610298157,
0.04151385650038719,
0.031601808965206146,
0.016901960596442223,
0.024898866191506386,
0.023435216397047043,
-0.03994639962911606,
0.027827223762869835,
-0.02040594257414341,
-0.03671957552433014,
-0.018950190395116806,
-0.049270614981651306,
0.03666871413588524,
0.01370492298156023,
0.03314889222383499,
0.0018163491040468216,
0.015747636556625366,
-0.00537411542609334,
-0.061655256897211075,
-0.09017316997051239,
0.048834577202796936,
0.005260346457362175,
-0.027816934511065483,
-0.06636539101600647,
0.0063941506668925285,
-0.009813525713980198,
-0.030128836631774902,
0.0029227843042463064,
-0.06332600861787796,
0.007420273497700691,
0.03934859856963158,
0.043882325291633606,
-0.07756312191486359,
-0.012375907972455025,
-0.02917066588997841,
0.014629315584897995,
0.004471922293305397,
0.058132901787757874,
0.017226187512278557,
0.008909699507057667,
0.03434295952320099,
0.03408288583159447,
-0.02338390238583088,
-0.05918363109230995,
-0.02752518840134144,
-0.05768463760614395,
0.051632046699523926,
0.00361693580634892,
-0.012254633009433746,
-0.0035920210648328066,
0.00051716627785936,
0.040226928889751434,
-0.0014647006755694747,
-0.0019363479223102331,
-0.018735911697149277,
0.0008634374826215208,
-0.023598380386829376,
0.0005373041494749486,
0.008163833059370518,
0.008524013683199883,
0.01002218946814537,
-0.009347094222903252,
-0.002186266938224435,
-0.014377734623849392,
-0.03424301743507385,
-0.001583512406796217,
0.037634994834661484,
0.012338629923760891,
0.027686432003974915,
-0.048700541257858276,
-0.033759988844394684,
-0.00401712954044342,
-0.01880660094320774,
-0.0852009505033493,
-0.025357602164149284,
-0.03444166108965874,
-0.04199473187327385,
0.04698459804058075,
0.018703032284975052,
-0.04031630977988243,
-0.062258124351501465,
0.02267746441066265,
-0.05712778866291046,
0.04151127487421036,
-0.014972914010286331,
-0.00833127461373806,
0.007333388552069664,
0.029640469700098038,
0.0034215787891298532,
-0.01746741496026516,
-0.022153563797473907,
0.017972642555832863,
0.054368555545806885,
-0.023027850314974785,
-0.025128066539764404,
-0.03297200798988342,
-0.02367185801267624,
0.043510038405656815,
-0.045490775257349014,
0.025839580222964287,
-0.0214559156447649,
0.01426173560321331,
0.002870425581932068,
-0.008821931667625904,
0.03192194551229477,
-0.012496700510382652,
0.017502596601843834,
0.004069599788635969,
0.03360699862241745,
0.04362111911177635,
0.014396332204341888,
0.06760479509830475,
0.03723503276705742,
-0.007075711619108915,
0.0025919550098478794,
-0.028205757960677147,
0.027815772220492363,
0.04481115564703941,
0.0037334973458200693,
-0.03417989984154701,
0.021404575556516647,
-0.023645207285881042,
0.03215106949210167,
-0.0019834486301988363,
-0.01483653113245964,
0.08047402650117874,
0.007843566127121449,
-0.008991560898721218,
-0.05790069326758385,
-0.012236131355166435,
-0.022291388362646103,
0.03712636977434158,
0.025147633627057076,
0.02825733833014965,
-0.01332277525216341,
-0.023137258365750313,
-0.08100641518831253,
-0.011860464699566364,
0.013976451940834522,
-0.03140433132648468,
-0.08825305104255676,
0.008188888430595398,
0.018475444987416267,
-0.0027285416144877672,
0.005839613266289234,
0.00934330653399229,
-0.038307782262563705,
-0.02148880437016487,
0.02592625468969345,
0.04428684711456299,
0.020449094474315643,
-0.0028992195148020983,
-0.02540605142712593,
-0.025568321347236633,
0.00014513832866214216,
-0.019336286932229996,
0.0018302388489246368,
0.017358338460326195,
0.07424269616603851,
-0.03285444527864456,
0.0806073471903801,
-0.0679006278514862,
0.0176335908472538,
0.022115975618362427,
-0.030045198276638985,
0.030881712213158607,
-0.019635898992419243,
0.009506968781352043,
0.07798727601766586,
0.06101209670305252,
-0.021484849974513054,
0.014646662399172783,
-0.05649863928556442,
0.04061141237616539,
-0.058705247938632965,
0.00766973989084363,
-0.0407847985625267,
0.006124824285507202,
-0.02436254732310772,
-0.013033377006649971,
0.014648462645709515,
0.0671476274728775,
0.014473679475486279,
-0.04781248793005943,
0.008761878125369549,
-0.0009414131636731327,
-0.009322380647063255,
0.07060199975967407,
0.053751517087221146,
-0.013396783731877804,
-0.0016940409550443292,
0.008865012787282467,
0.008561856113374233,
-0.06369180232286453,
-0.022651366889476776,
-0.01755833812057972,
-0.018599119037389755,
-0.00021121134341228753,
0.0021350972820073366,
-0.015772901475429535,
-0.059851985424757004,
0.05116218328475952,
-0.007806513458490372,
0.027134500443935394,
-0.05147319287061691,
-0.05022326856851578,
0.055019911378622055,
0.013494962826371193,
-0.009418207220733166,
0.015461910516023636,
0.03654893860220909,
-0.026859678328037262,
-0.029860811308026314,
-0.024559661746025085,
-0.07878303527832031,
-0.04342924803495407,
0.028009699657559395,
-0.0659138634800911,
-0.012363165616989136,
-0.02197377197444439,
0.017006821930408478,
0.06649579107761383,
-0.06199490278959274,
0.014740494079887867,
-0.04987749457359314,
0.07696758955717087,
-0.012367655523121357,
0.005260414909571409,
-0.020292429253458977,
-0.04768209159374237,
0.037915509194135666,
-0.007494472898542881,
-0.033505477011203766,
-0.024566391482949257,
0.00840485468506813,
-0.04371936619281769,
-0.0064138141460716724,
-0.00344950333237648,
-0.022312194108963013,
0.048375099897384644,
0.03969544544816017,
-0.030829336494207382,
0.024610653519630432,
0.07121092081069946,
-0.037133943289518356,
0.0008459046366624534,
0.008609498851001263,
-0.005802932195365429,
0.01512067299336195,
0.026041945442557335,
0.05217060074210167,
0.045297395437955856,
-0.015171188861131668,
-0.07596733421087265,
-0.026345524936914444,
-0.025187579914927483,
0.013164058327674866,
-0.061622150242328644,
0.04306458309292793,
0.05459015443921089
] |
<p>Non-commutative (sometimes called "fuzzy") black holes are solutions of Einstein's equations obtained with a previous basic assumption of non-commutativity of the coordinates $[x^{\mu},x^{\nu}]=i\, \theta^{\mu\nu}$. This assumption is considered helpful in the sense that removes the singularity in $r=0$. See <a href="http://arxiv.org/abs/0807.1939" rel="nofollow">this link</a> for a review, even though there have been more recent developments.</p>
<p>My question regards the possibility of extending this black hole solution to a time-dependent one, in order to describe an evaporating or accreting case.</p> | g4740 | [
-0.017060615122318268,
0.04220617935061455,
0.0020713761914521456,
0.035682301968336105,
0.01055376697331667,
-0.025325382128357887,
0.010696006007492542,
-0.0016679215477779508,
-0.02047024294734001,
0.03975404426455498,
0.04176788032054901,
-0.03531933203339577,
0.021706940606236458,
0.050157785415649414,
-0.054180730134248734,
0.045110270380973816,
0.0037920167669653893,
-0.03396572545170784,
-0.015013638883829117,
0.049227986484766006,
0.05435904487967491,
0.058552466332912445,
0.08118239790201187,
-0.01545646507292986,
0.04334408789873123,
-0.0022663846611976624,
0.07021107524633408,
-0.01803770661354065,
-0.037965793162584305,
-0.03930168226361275,
0.061173927038908005,
0.012408753857016563,
-0.008173540234565735,
0.0017321709310635924,
-0.0018243684899061918,
-0.00217728060670197,
0.05616092309355736,
-0.04879146069288254,
0.06161808222532272,
0.0022777575068175793,
-0.002759006107226014,
0.023618662729859352,
-0.0030493377707898617,
-0.0012200343189761043,
-0.008066877722740173,
-0.012037308886647224,
0.044517453759908676,
0.030126694589853287,
0.015210623852908611,
-0.006899949163198471,
0.010990509763360023,
0.050665482878685,
0.0768236294388771,
-0.022621745243668556,
-0.026679063215851784,
0.005038715433329344,
0.042220648378133774,
0.04544924572110176,
0.030102116987109184,
0.07180586457252502,
-0.09357025474309921,
-0.02799774520099163,
0.043733056634664536,
0.0002832752070389688,
0.018069930374622345,
-0.04388918727636337,
-0.05285569652915001,
-0.04155506193637848,
-0.09664132446050644,
-0.010315639898180962,
0.035093389451503754,
0.04083288088440895,
-0.010460412129759789,
0.04121217504143715,
-0.024669073522090912,
0.052004385739564896,
-0.005445653572678566,
-0.0033226630184799433,
0.02872483991086483,
-0.042011409997940063,
-0.06869053095579147,
0.010165179148316383,
0.03301344811916351,
-0.021262837573885918,
0.050638534128665924,
-0.008764837868511677,
-0.004585308022797108,
0.002562853042036295,
0.06306125223636627,
-0.03001689724624157,
-0.013169439509510994,
-0.0292048342525959,
0.03617381677031517,
-0.004919272847473621,
0.03630003333091736,
0.008516738191246986,
-0.019677963107824326,
0.02690962888300419,
0.006789444480091333,
0.027264000847935677,
0.0009184183436445892,
0.04867984727025032,
0.04700368642807007,
-0.0038241909351199865,
0.041432008147239685,
-0.047883354127407074,
-0.018808601424098015,
0.03864966332912445,
-0.010755125433206558,
0.02781669795513153,
-0.016780495643615723,
-0.05641000717878342,
-0.016800545156002045,
-0.019002720713615417,
-0.015459505841135979,
0.010423502884805202,
-0.05809115245938301,
0.02615404687821865,
-0.018750064074993134,
-0.01909041218459606,
-0.026863643899559975,
0.004395612981170416,
0.02266305312514305,
0.056091390550136566,
-0.02524626813828945,
-0.011425650678575039,
-0.06448917835950851,
-0.015785781666636467,
0.01848967932164669,
0.006894400343298912,
0.003248135093599558,
-0.010523660108447075,
0.01793537475168705,
0.06409739702939987,
-0.03200814127922058,
0.0050507839769124985,
0.024984795600175858,
-0.02009532041847706,
0.01356340292841196,
0.018455803394317627,
0.017310993745923042,
-0.02795170061290264,
0.03696011006832123,
0.0368700735270977,
0.007537877187132835,
-0.04350235313177109,
-0.08075833320617676,
-0.06795357912778854,
0.02456483617424965,
0.018659695982933044,
-0.03920703008770943,
0.1153583899140358,
-0.05661721155047417,
-0.028083644807338715,
-0.009179752320051193,
0.021312091499567032,
-0.006641853600740433,
-0.006517905741930008,
-0.0417085662484169,
-0.024905338883399963,
0.0639059767127037,
-0.008310277946293354,
0.013855965808033943,
0.08636163175106049,
0.004563282709568739,
0.04786534979939461,
-0.0028569092974066734,
-0.020698586478829384,
-0.01921119913458824,
-0.045764923095703125,
-0.029261739924550056,
0.025139370933175087,
-0.006254984997212887,
-0.02706287056207657,
0.012531336396932602,
-0.01539192721247673,
-0.009759243577718735,
-0.04002118110656738,
-0.02578282728791237,
0.013231031596660614,
-0.01797657087445259,
-0.02418004907667637,
-0.017166277393698692,
-0.019999735057353973,
0.06996403634548187,
0.014833088032901287,
0.03870432823896408,
0.04044824838638306,
-0.016936255618929863,
0.03367352485656738,
-0.020160499960184097,
0.005005661863833666,
0.047402989119291306,
0.06447546929121017,
-0.01357257179915905,
0.0325506366789341,
0.008147685788571835,
0.06670389324426651,
0.05150452256202698,
0.05564697086811066,
0.0057311453856527805,
0.013376248069107533,
0.016643114387989044,
0.03368080407381058,
0.031727615743875504,
-0.04246938228607178,
-0.013662779703736305,
-0.0029839251656085253,
0.020519694313406944,
-0.0006944700726307929,
0.061408884823322296,
-0.0485239177942276,
-0.01779065653681755,
-0.012674118392169476,
-0.024995408952236176,
-0.024954451248049736,
-0.013977008871734142,
0.001533161848783493,
-0.0003990656405221671,
-0.010252499021589756,
-0.028210757300257683,
0.009520423598587513,
0.02451615408062935,
-0.024654608219861984,
0.00682626711204648,
0.04981746897101402,
-0.012857445515692234,
-0.03741592541337013,
0.010192442685365677,
-0.0024402306880801916,
0.0040346127934753895,
0.02927255444228649,
0.023602329194545746,
0.009326276369392872,
0.018213558942079544,
0.023754864931106567,
0.027700921520590782,
0.0292343907058239,
0.02891436778008938,
0.033296700567007065,
0.054372016340494156,
0.011030664667487144,
-0.013572409749031067,
-0.021307960152626038,
0.026329174637794495,
0.0029758636374026537,
0.020145481452345848,
-0.02946990542113781,
0.01443471759557724,
-0.044314946979284286,
-0.008186434395611286,
-0.06683426350355148,
-0.031222818419337273,
-0.026679420843720436,
-0.018306901678442955,
-0.0143720218911767,
0.045344676822423935,
-0.002246089745312929,
-0.08141184598207474,
-0.03817516192793846,
0.032009534537792206,
-0.036511655896902084,
0.021105090156197548,
0.04115612432360649,
-0.015586018562316895,
-0.029721934348344803,
-0.019687145948410034,
-0.0030191587284207344,
-0.028511755168437958,
0.050087276846170425,
-0.050852078944444656,
-0.052465200424194336,
0.051157861948013306,
0.06556089222431183,
-0.023184077814221382,
0.0010254902299493551,
-0.07007098197937012,
0.03992476686835289,
0.023047540336847305,
0.046347178518772125,
0.011814630590379238,
0.030175454914569855,
-0.07949130982160568,
0.020248815417289734,
0.008673364296555519,
-0.058320220559835434,
0.04466920718550682,
0.023535000160336494,
0.028416985645890236,
0.003486062167212367,
0.02738053724169731,
0.001854167552664876,
-0.01806447096168995,
0.05015420913696289,
-0.04687858000397682,
0.07733041793107986,
-0.04303532838821411,
0.014324408955872059,
-0.04989228397607803,
0.03744832053780556,
0.04517080634832382,
0.03581218793988228,
-0.004563536029309034,
0.03044278547167778,
0.02429339475929737,
0.006668526213616133,
-0.023643143475055695,
-0.010918582789599895,
0.04238644987344742,
-0.06801928579807281,
-0.039768267422914505,
0.044790416955947876,
0.0033364398404955864,
0.053177062422037125,
0.03433004394173622,
-0.019458703696727753,
-0.02499818243086338,
-0.0056780180893838406,
-0.0022260360419750214,
-0.015770699828863144,
-0.014049445278942585,
0.0401734784245491,
-0.02567928098142147,
-0.02694978192448616,
0.058943718671798706,
0.054975882172584534,
-0.006398465484380722,
-0.055688921362161636,
-0.0967598408460617,
0.04932044818997383,
-0.06250667572021484,
-0.002081718062981963,
-0.01851714588701725,
-0.009953230619430542,
-0.04059479385614395,
-0.047855131328105927,
0.016124870628118515,
0.008404786698520184,
0.03455033153295517,
0.011081450618803501,
-0.007720828987658024,
-0.03038596175611019,
0.05568483844399452,
0.04117593169212341,
0.00048271738342009485,
0.038190361112356186,
0.027389878407120705,
0.017584731802344322,
0.002713741036131978,
0.005275270901620388,
0.06780184060335159,
-0.02002655528485775,
0.09945421665906906,
-0.010633491910994053,
0.006261998321861029,
0.08183977752923965,
0.025358952581882477,
0.007503071799874306,
0.024860570207238197,
0.025643955916166306,
-0.008216350339353085,
-0.042591214179992676,
0.02131705917418003,
0.019654929637908936,
0.04029890522360802,
-0.007686573546379805,
0.0631326213479042,
-0.002926889341324568,
0.006069480907171965,
-0.022756854072213173,
0.05747172236442566,
0.03379954770207405,
0.06221985071897507,
-0.010890748351812363,
-0.007406850811094046,
-0.02651219815015793,
0.05358356237411499,
-0.015597873367369175,
0.05665652081370354,
-0.0030431190971285105,
-0.029137244448065758,
-0.004126991145312786,
0.028069432824850082,
-0.049473755061626434,
0.0035415843594819307,
0.03548058122396469,
-0.022148460149765015,
-0.04227843135595322,
-0.030704006552696228,
-0.049212247133255005,
0.05278347060084343,
0.048418160527944565,
0.02138596773147583,
-0.07722389698028564,
-0.0055800192058086395,
0.03893124684691429,
-0.011215384118258953,
-0.05663357675075531,
0.0015905973268672824,
-0.01638244092464447,
0.08227396011352539,
0.0006803451105952263,
0.023458058014512062,
-0.012783329002559185,
-0.013495049439370632,
0.008281813003122807,
0.028381353244185448,
-0.03737778216600418,
-0.010692915879189968,
-0.04245985671877861,
-0.03568805754184723,
-0.0493827685713768,
-0.04599715769290924,
0.036698732525110245,
0.02975485660135746,
-0.030435219407081604,
0.019466791301965714,
0.015117421746253967,
-0.04387935250997543,
0.014360575936734676,
0.004408547189086676,
-0.05914079397916794,
-0.04785832762718201,
0.02675691992044449,
-0.0025475849397480488,
0.02496429532766342,
-0.033401474356651306,
0.0443076491355896,
-0.0456523522734642,
0.0279565267264843,
-0.041453100740909576,
-0.0016311171930283308,
-0.03299380838871002,
-0.02531537227332592,
-0.04087186977267265,
0.018933678045868874,
-0.039257414638996124,
0.024532632902264595,
-0.011699412949383259,
-0.015169824473559856,
0.06175300478935242,
-0.004140034317970276,
0.0038095004856586456,
-0.027932841330766678,
-0.00021978806762490422,
0.0002878922678064555,
0.0048902505077421665,
-0.020561950281262398,
-0.01533169113099575,
0.0012846325989812613,
-0.027030905708670616,
0.04152512550354004,
0.006706241983920336,
-0.025545118376612663,
-0.05910297483205795,
-0.03596330061554909,
-0.016291789710521698,
-0.028409965336322784,
-0.013403790071606636,
0.05081911012530327,
-0.016327522695064545,
-0.016358070075511932,
0.033640507608652115,
0.044580210000276566,
-0.0052273948676884174,
0.007313812617212534,
-0.07588814198970795,
-0.0697861760854721,
0.00008647381037008017,
0.004355066455900669,
-0.024950474500656128,
0.050899285823106766,
0.01456319447606802,
0.05691758170723915,
-0.01228983886539936,
-0.0039809769950807095,
0.04365310072898865,
-0.03731786459684372,
-0.005212678108364344,
-0.00444144057109952,
-0.054554615169763565,
-0.01805569790303707,
0.03625006228685379,
0.04384385049343109,
0.06834050267934799,
0.057306841015815735,
-0.03973790630698204,
0.0035896801855415106,
0.009951501153409481,
0.0010692967334762216,
0.027850547805428505,
0.014697917737066746,
0.031110256910324097,
-0.00014525956066790968,
-0.024825341999530792,
-0.033262964338064194,
-0.06640264391899109,
-0.02320306934416294,
-0.014979871921241283,
-0.0068999058566987514,
-0.07566267251968384,
0.0011136890389025211,
0.026034394279122353,
-0.007845335640013218,
-0.004131973721086979,
0.01817903481423855,
0.014473754912614822,
-0.03909463435411453,
-0.008496859110891819,
0.04856418818235397,
0.015115965157747269,
0.005211268085986376,
0.0074127777479588985,
0.010506266728043556,
0.0625520721077919,
-0.06055794283747673,
-0.00889300461858511,
-0.05317241698503494,
0.0001364864583592862,
-0.021678289398550987,
-0.015613557770848274,
-0.006974852178245783,
-0.031815625727176666,
0.043223656713962555,
0.02846372500061989,
0.020926345139741898,
-0.04639486223459244,
-0.13200803101062775,
0.039229389280080795,
0.0293973870575428,
-0.0033961301669478416,
-0.029634587466716766,
-0.010461377911269665,
-0.0011935647344216704,
0.02030699886381626,
0.01961391046643257,
-0.03259055316448212,
-0.0079390499740839,
0.020101837813854218,
-0.02629178948700428,
-0.04107466712594032,
-0.0004513378953561187,
0.03636419400572777,
-0.010031873360276222,
-0.0056792376562952995,
-0.008607529103755951,
-0.06371801346540451,
0.05058342218399048,
-0.052569080144166946,
-0.00036754520260728896,
-0.07364293932914734,
-0.02827993594110012,
-0.00827711820602417,
0.01675579696893692,
0.04640590026974678,
-0.006560259964317083,
-0.0052072713151574135,
-0.0039497553370893,
-0.017045065760612488,
-0.04645995795726776,
0.007904880680143833,
-0.02363472245633602,
0.010871768929064274,
0.024287240579724312,
-0.000514721090439707,
-0.035274624824523926,
0.009305475279688835,
0.012116973288357258,
0.04486275836825371,
-0.017142431810498238,
-0.03893623128533363,
0.048401445150375366,
-0.035812780261039734,
0.007117424160242081,
-0.04014228284358978,
-0.07024283707141876,
-0.005900050979107618,
0.00934342760592699,
0.026585670188069344,
0.005409711506217718,
-0.043794624507427216,
-0.026575477793812752,
0.05293315276503563,
-0.04870270565152168,
-0.007510819006711245,
-0.02894776500761509,
-0.005989071913063526,
0.09071096777915955,
-0.039708174765110016,
-0.004368387162685394,
-0.02538992278277874,
0.04751267656683922,
0.05402359366416931,
-0.018580064177513123,
-0.02153971418738365,
0.06190238520503044,
-0.05046767741441727,
-0.009848003275692463,
0.006970567163079977,
-0.07678677141666412,
-0.06941183656454086,
0.03180713579058647,
-0.0024764961563050747,
0.02523818425834179,
-0.029240932315587997,
0.05042935162782669,
-0.06526588648557663,
0.023371266201138496,
0.040711693465709686,
-0.020194528624415398,
-0.012730089947581291,
0.049252551048994064,
0.03225719928741455,
-0.008344112895429134,
0.009203583933413029,
-0.009475940838456154,
0.01528247632086277,
-0.006289408542215824,
0.022156523540616035,
-0.042698975652456284,
0.03314073383808136,
0.023735614493489265,
0.009940777905285358,
0.021918579936027527,
-0.010004070587456226,
0.031895995140075684,
-0.01764220930635929,
-0.0341709665954113,
0.031535517424345016,
0.004333368502557278,
-0.0013973880559206009,
0.022693641483783722,
-0.018076179549098015,
-0.008610283024609089,
-0.07610047608613968,
0.03074219450354576,
-0.07466129958629608,
-0.018451133742928505,
-0.01260655838996172,
-0.013069461099803448,
-0.04287663847208023,
-0.03975122049450874,
0.006768116727471352,
-0.026632733643054962,
0.004418587777763605,
0.05934293195605278,
-0.0006507229409180582,
0.036969952285289764,
-0.07196783274412155,
0.048782844096422195,
0.07382439821958542,
-0.04178022965788841,
-0.05221538245677948,
0.031289439648389816,
-0.05741143599152565,
-0.04288925603032112,
-0.08553263545036316,
0.014309326186776161,
-0.019600749015808105,
0.007519467733800411,
-0.04238240420818329,
-0.03794145956635475,
-0.03303530812263489,
0.021846113726496696,
0.0018984918715432286,
0.023762932047247887,
0.0831032246351242,
-0.035041097551584244,
0.04533037915825844,
-0.03720913454890251,
0.02292066439986229,
-0.07169168442487717,
-0.08182885497808456,
-0.06846608966588974,
-0.10579153150320053,
-0.03179508075118065,
-0.01500745303928852,
0.03971628099679947,
0.009423780255019665,
0.04666366055607796,
0.05182107165455818,
0.000519436551257968,
-0.007713233586400747,
-0.001340787042863667,
-0.09190933406352997,
0.03441789001226425,
0.010835723951458931,
0.003563811769708991,
0.08751579374074936,
0.029517801478505135,
-0.03313824161887169,
0.0224427692592144,
0.06531289964914322,
0.04328469559550285,
0.0006618531187996268,
0.007026298902928829,
0.025349510833621025,
0.023025067523121834,
0.03647551313042641,
-0.03957871347665787,
-0.018075546249747276,
-0.002305490430444479,
-0.0676700547337532,
-0.04358634352684021,
-0.03258801996707916,
-0.04791168496012688,
-0.027988705784082413,
0.005726612638682127,
-0.02120683342218399,
0.02469845674932003,
0.03774908557534218,
0.00869870837777853,
-0.02684776298701763,
-0.0016744587337598205,
-0.02903863601386547,
-0.04145365580916405,
-0.025786681100726128,
-0.011282658204436302,
-0.030956238508224487,
-0.03863293677568436,
-0.012294627726078033,
-0.004216478671878576,
-0.07471064478158951,
-0.06984381377696991,
0.017559591680765152,
0.014360439032316208,
-0.06280968338251114,
0.016692740842700005,
-0.007135386578738689,
0.014247703365981579,
-0.015989556908607483,
-0.03720278665423393,
-0.02726944163441658,
-0.00660385936498642,
0.04964293912053108,
-0.020409559831023216,
-0.022529374808073044,
0.007901775650680065,
0.000670627923682332,
-0.03844578564167023,
-0.01032058335840702,
-0.004503688309341669,
0.026768596842885017,
-0.025441419333219528,
0.052787359803915024,
-0.03324069082736969,
-0.000030700164643349126,
-0.02348291501402855,
0.06772565096616745,
0.042895615100860596,
0.01932643912732601,
0.0562652125954628,
-0.03515462577342987,
-0.012173077091574669,
0.013644098304212093,
-0.019736338406801224,
0.0005182100576348603,
0.005168414209038019,
-0.008766721934080124,
0.002316611586138606,
-0.045412831008434296,
-0.01969718746840954,
0.0006649779970757663,
-0.02648601308465004,
0.006234097294509411,
0.027504518628120422,
0.045685067772865295,
0.028337588533759117
] |
<p>I am building a computational model of ellipsoidal cell network formation and I would like to use a particle order parameter to study my model's behavior. I have come across this article <a href="http://prb.aps.org/abstract/PRB/v28/i2/p784_1" rel="nofollow">Steinhardt, Nelson, Ronchetti, PRB (1983)</a>, that was apparently the one that started everything, but the math is quite exotic for me. I have found that the formula:</p>
<p>$$
S = 1/3<cos^2θ - 1>
$$</p>
<p>is the order parameter for a 3-D system. This is convenient as S = 0 means no order, while S = 1 means complete alignment. A colleague at the univ has mentioned that for a 2-D particle system the previous equation for S becomes:</p>
<p>$$
S = cos2θ
$$</p>
<p>but I don't think this can be right, as in the following example: 2 particles have a 90 degree angle between them, so they are completely unaligned. <code>cos2θ = cos2*90 = -1</code> which would imply they are completely aligned, which is wrong. Also, the range is [-1:1] instead of 0 < S < 1.</p>
<p>I would really appreciate it, if anyone could point me to the right direction. </p> | g4741 | [
0.013847777619957924,
0.008235875517129898,
-0.01802057959139347,
0.0016547903651371598,
0.0815896987915039,
0.009784742258489132,
0.017417462542653084,
-0.021322352811694145,
-0.02105206623673439,
0.03471347689628601,
-0.004036004189401865,
0.05021229013800621,
0.05273428186774254,
-0.028747262433171272,
-0.05390224605798721,
0.029484109953045845,
0.03444410860538483,
0.0684940367937088,
-0.034042831510305405,
0.038453731685876846,
0.005670049227774143,
-0.013914539478719234,
-0.002413884038105607,
-0.027016209438443184,
0.007783935870975256,
0.02117302268743515,
-0.036000680178403854,
-0.07786282151937485,
-0.07488034665584564,
0.001432972028851509,
0.01563280262053013,
0.034361831843853,
0.041121236979961395,
-0.026912705972790718,
-0.05973115563392639,
-0.020945820957422256,
0.03845493122935295,
-0.01830992102622986,
0.016008127480745316,
-0.006736068520694971,
0.009920327924191952,
-0.015911731868982315,
0.03553933650255203,
-0.037547092884778976,
0.021924065425992012,
-0.023481575772166252,
-0.035474225878715515,
0.05345387011766434,
-0.03390182927250862,
-0.012694458477199078,
-0.043870434165000916,
0.07950560003519058,
0.01609278842806816,
-0.027596380561590195,
-0.04353753849864006,
0.06251750141382217,
0.0387633740901947,
-0.011978141963481903,
0.07793731242418289,
0.0651702731847763,
-0.005936220288276672,
0.03934313356876373,
0.02652648463845253,
-0.07344190031290054,
0.039632536470890045,
0.005221283063292503,
-0.012559660710394382,
0.02018720842897892,
-0.0032778687309473753,
-0.027279218658804893,
-0.01050434447824955,
-0.029330050572752953,
0.036816325038671494,
-0.03752494975924492,
-0.04505303129553795,
0.008294287137687206,
-0.02137920819222927,
-0.047269176691770554,
0.005162070505321026,
-0.025433188304305077,
-0.03664751723408699,
0.03930223733186722,
0.01084152515977621,
-0.007385747041553259,
0.046929627656936646,
0.007647510152310133,
0.011313325725495815,
-0.03668050840497017,
-0.03146381303668022,
0.020158525556325912,
-0.06337027996778488,
0.04094216972589493,
-0.013938012532889843,
-0.009632105007767677,
0.015480692498385906,
-0.035150956362485886,
-0.03984355926513672,
0.01392301358282566,
-0.008563702926039696,
0.0013026942033320665,
-0.015076566487550735,
0.01689034141600132,
-0.0016137942438945174,
0.02160198800265789,
-0.04056073725223541,
0.018189789727330208,
0.05585506185889244,
0.03804387152194977,
0.006492077372968197,
-0.05617642030119896,
-0.02698584645986557,
0.027265656739473343,
0.014224584214389324,
-0.017385631799697876,
-0.0015510068042203784,
0.01701473817229271,
0.07120935618877411,
-0.024020884186029434,
0.07947982102632523,
0.04539991170167923,
0.10588130354881287,
-0.013405167497694492,
-0.0032239665742963552,
0.0878332331776619,
-0.04320754110813141,
-0.00858707632869482,
0.014392001554369926,
0.04437900707125664,
0.06686221808195114,
0.008690407499670982,
-0.010781400837004185,
-0.03755900636315346,
-0.0003985286457464099,
0.024934493005275726,
-0.02516523003578186,
0.004780541639775038,
-0.05238303542137146,
-0.02860785275697708,
0.00454839738085866,
-0.022321751341223717,
-0.04175470024347305,
-0.03038669563829899,
0.05780637636780739,
-0.05086405202746391,
-0.025746049359440804,
-0.016225097700953484,
0.0439206026494503,
-0.006010449957102537,
0.027954835444688797,
0.04343109577894211,
-0.0049293749034404755,
0.026244575157761574,
-0.018331609666347504,
-0.05792435258626938,
-0.06461692601442337,
0.009198728017508984,
0.06346947699785233,
-0.016560520976781845,
0.007983433082699776,
0.007698778063058853,
0.054378435015678406,
0.021804798394441605,
0.008049235679209232,
-0.021874956786632538,
-0.07590175420045853,
-0.01465704943984747,
-0.03400292992591858,
-0.03158232942223549,
0.0005668372614309192,
-0.023295123130083084,
-0.03212064877152443,
0.01684711128473282,
0.04103086143732071,
0.03601537644863129,
-0.010685382410883904,
0.10880205780267715,
0.023972101509571075,
-0.006573505233973265,
0.0811363160610199,
0.012499350123107433,
-0.000179108974407427,
0.039841312915086746,
0.011352881789207458,
0.03977068141102791,
-0.04939884692430496,
-0.027780652046203613,
0.020352911204099655,
0.05327456444501877,
-0.0166937205940485,
0.006984571926295757,
0.026355814188718796,
0.02557941898703575,
-0.05660649761557579,
-0.011374308727681637,
0.03697490692138672,
0.04652227461338043,
0.060906149446964264,
-0.016263648867607117,
0.010364209301769733,
-0.02883576788008213,
-0.0090235136449337,
0.036043450236320496,
0.03920293599367142,
0.025255069136619568,
0.031017426401376724,
-0.0675785169005394,
0.03393663093447685,
-0.010740101337432861,
-0.007462298963218927,
0.017896998673677444,
-0.047133877873420715,
0.051185257732868195,
-0.041130390018224716,
0.023517195135354996,
0.013149048201739788,
-0.04077624902129173,
0.01075155008584261,
0.02906343899667263,
-0.05675026774406433,
0.01484294980764389,
-0.06164192035794258,
-0.06510835886001587,
0.04520168900489807,
-0.02391950972378254,
0.01900848001241684,
-0.013295376673340797,
-0.01756792888045311,
-0.02766960673034191,
0.010397374629974365,
0.029331615194678307,
-0.07910184562206268,
0.009797901846468449,
-0.008797735907137394,
-0.048023369163274765,
0.05151188001036644,
0.022384507581591606,
-0.03357856720685959,
-0.00877702422440052,
0.04358164221048355,
0.0025945210363715887,
-0.01951497234404087,
-0.039876848459243774,
-0.04911915585398674,
0.034878913313150406,
0.03925751522183418,
-0.04035285487771034,
0.11144731938838959,
0.00735495425760746,
-0.048625651746988297,
0.025821778923273087,
0.018157193437218666,
-0.02010905183851719,
-0.025282731279730797,
0.022292321547865868,
0.034113090485334396,
-0.0392642468214035,
-0.0300629660487175,
0.036531899124383926,
-0.016253549605607986,
-0.021677158772945404,
-0.01829848438501358,
-0.043062612414360046,
-0.010332062840461731,
-0.00565693061798811,
-0.030379701405763626,
-0.051867928355932236,
0.01015650574117899,
-0.09719609469175339,
0.03735831752419472,
-0.002437561983242631,
0.014322428032755852,
0.046141285449266434,
0.019269218668341637,
0.042528070509433746,
-0.016295572742819786,
0.047188613563776016,
-0.008591328747570515,
-0.04467621073126793,
0.006958764512091875,
0.0064039332792162895,
0.0030387258157134056,
-0.003343300661072135,
0.005842992570251226,
0.037786588072776794,
0.04140212759375572,
-0.03247854486107826,
-0.0020093778148293495,
0.0322958305478096,
0.004002938512712717,
0.025981329381465912,
0.002392645925283432,
0.06749624013900757,
-0.02274206653237343,
-0.005691940430551767,
0.019084705039858818,
-0.014185602776706219,
0.025889039039611816,
-0.052132509648799896,
0.02230473980307579,
0.038557443767786026,
-0.016057930886745453,
0.024227086454629898,
-0.015872279182076454,
-0.03358298912644386,
-0.05308201536536217,
0.006363832391798496,
-0.024609193205833435,
-0.0015332052716985345,
0.016358984634280205,
-0.017961634323000908,
-0.03268511965870857,
-0.0071415225975215435,
0.014740191400051117,
-0.00803299993276596,
0.018191443756222725,
0.02959061600267887,
0.015072708018124104,
0.03114309534430504,
0.003552457317709923,
0.01726180501282215,
-0.05142541229724884,
-0.023322846740484238,
0.0048288507387042046,
-0.018234865739941597,
0.02514609508216381,
0.039352331310510635,
-0.0020532335620373487,
-0.015123381279408932,
-0.04084467515349388,
-0.011995842680335045,
0.008995268493890762,
-0.034635525196790695,
0.0955641120672226,
-0.0019621143583208323,
-0.0008231750107370317,
-0.06499411165714264,
-0.04572103172540665,
-0.028797626495361328,
0.029398037120699883,
-0.014914599247276783,
-0.02205311693251133,
0.0015439027920365334,
-0.024124830961227417,
0.0013273946242406964,
-0.04186653345823288,
-0.012091523967683315,
0.010921616107225418,
-0.01109488308429718,
0.004072097130119801,
-0.030348341912031174,
0.017682204023003578,
-0.05129871517419815,
-0.03286455199122429,
-0.013326596468687057,
0.015247912146151066,
0.006014915183186531,
0.04146121069788933,
0.02725355327129364,
0.028857003897428513,
0.06390021741390228,
0.031162038445472717,
-0.07341555505990982,
-0.036702509969472885,
0.028814632445573807,
0.004792562685906887,
0.003505473490804434,
-0.04019404947757721,
0.04700341448187828,
0.00576699199154973,
-0.028808653354644775,
-0.017949828878045082,
-0.004057408310472965,
0.0024914159439504147,
-0.01720193773508072,
0.051446255296468735,
0.008147506974637508,
-0.04590196907520294,
0.010328030213713646,
-0.0340040884912014,
0.028887826949357986,
-0.03315779194235802,
-0.028937119990587234,
-0.03515459597110748,
0.007821740582585335,
-0.04097769409418106,
0.07196007668972015,
-0.0036900986451655626,
-0.0004626096342690289,
-0.07087107747793198,
0.02917015552520752,
0.06370137631893158,
-0.011369619518518448,
-0.023513540625572205,
-0.0344424843788147,
0.021251186728477478,
-0.0224300529807806,
0.030800990760326385,
0.004614224657416344,
0.0036692835856229067,
-0.00092269730521366,
-0.01386463362723589,
-0.04879876971244812,
-0.028603384271264076,
-0.049567218869924545,
0.03600793704390526,
-0.017138520255684853,
-0.02772899717092514,
0.0013083054218441248,
-0.023188035935163498,
0.03470310568809509,
0.009164799936115742,
0.04867297783493996,
0.052487995475530624,
-0.02083463780581951,
0.0680156722664833,
0.04681006073951721,
-0.039364080876111984,
-0.02389032207429409,
0.004040077328681946,
0.0075036087073385715,
0.013028242625296116,
0.04480930045247078,
0.0167374424636364,
-0.061991818249225616,
-0.00979919359087944,
0.0555562898516655,
0.014381215907633305,
-0.025688601657748222,
-0.07573021948337555,
0.02058054320514202,
0.006314782425761223,
0.04953166842460632,
0.008640113286674023,
-0.012016214430332184,
-0.05056121200323105,
0.007317009381949902,
-0.049860790371894836,
-0.007542910519987345,
0.04147142171859741,
0.04003892466425896,
-0.02205836959183216,
0.03374846279621124,
0.05548989400267601,
-0.07307210564613342,
0.02693292126059532,
0.009330054745078087,
-0.01654961332678795,
-0.026905527338385582,
-0.027551786974072456,
-0.024127153679728508,
0.04468896612524986,
0.009053226560354233,
-0.031183941289782524,
0.011627924628555775,
-0.04917480796575546,
-0.004547308199107647,
-0.038723643869161606,
0.009138349443674088,
-0.02860015630722046,
0.006946677342057228,
-0.03410163149237633,
-0.008907095529139042,
-0.002331734402105212,
-0.009611856192350388,
0.05615691840648651,
0.010432236827909946,
-0.029983408749103546,
-0.009586699306964874,
-0.08145319670438766,
-0.007569444831460714,
-0.01757604442536831,
0.03891290724277496,
0.011209985241293907,
0.06702007353305817,
0.022285517305135727,
-0.0392143689095974,
-0.009652401320636272,
-0.018633460626006126,
-0.002711240202188492,
-0.019460396841168404,
-0.03681490197777748,
-0.010027570649981499,
0.019796675071120262,
-0.0019009803654626012,
-0.00013234723883215338,
0.007494685705751181,
0.04620623216032982,
0.02060171216726303,
0.04168487712740898,
0.039983123540878296,
0.04228648170828819,
0.010439828038215637,
0.023947132751345634,
-0.002338168676942587,
0.019373789429664612,
-0.04684196412563324,
0.02998386323451996,
-0.07083048671483994,
0.015973197296261787,
0.02726133167743683,
-0.07248922437429428,
0.019361792132258415,
-0.021042756736278534,
0.01042814739048481,
-0.02154354751110077,
0.07499668747186661,
0.05246037617325783,
-0.03965070843696594,
0.010783776640892029,
-0.020683234557509422,
0.0011700118193402886,
-0.011943754740059376,
0.05885904282331467,
0.029021315276622772,
-0.04873460903763771,
0.006084624212235212,
-0.006017595995217562,
0.06459970027208328,
-0.04003957659006119,
-0.01943298801779747,
0.04406977817416191,
0.05069602280855179,
-0.024659613147377968,
-0.0654299333691597,
0.010340157896280289,
-0.03570852801203728,
-0.04687817022204399,
-0.009869327768683434,
0.07318524271249771,
-0.008941694162786007,
-0.0268266424536705,
0.023074433207511902,
-0.046754881739616394,
0.053996630012989044,
-0.004528345540165901,
-0.10373946279287338,
-0.04224931821227074,
0.05438852682709694,
0.041137587279081345,
-0.06041004881262779,
-0.05574626848101616,
-0.013356422074139118,
-0.0065977685153484344,
0.024081913754343987,
-0.053115397691726685,
0.005204709712415934,
0.016844576224684715,
0.016277644783258438,
0.010646510869264603,
-0.02756335958838463,
-0.03263675048947334,
0.024728046730160713,
0.015586749650537968,
-0.028691712766885757,
-0.01700044423341751,
0.07060189545154572,
-0.01724148727953434,
-0.01971675083041191,
-0.006808482576161623,
-0.024389684200286865,
-0.021659452468156815,
0.0011256578145548701,
0.033897679299116135,
0.03702894225716591,
-0.05125772953033447,
0.00596597557887435,
-0.045101191848516464,
0.04179133102297783,
0.01148897409439087,
0.03681594505906105,
0.03629779443144798,
-0.037934135645627975,
0.005712780635803938,
0.0861990824341774,
0.01779519021511078,
0.01095438003540039,
-0.05725586786866188,
-0.054792799055576324,
-0.002942918334156275,
0.03345305845141411,
-0.020868662744760513,
0.05458584055304527,
-0.014917874708771706,
0.05852695554494858,
-0.02176268771290779,
0.028718197718262672,
-0.0020579134579747915,
0.021439285948872566,
0.06844217330217361,
-0.006375287659466267,
-0.02051311545073986,
-0.04693768545985222,
-0.04843636229634285,
0.027211567386984825,
-0.001770567731000483,
0.03442368283867836,
0.02278819866478443,
0.07453892379999161,
-0.047963112592697144,
-0.002071711467579007,
0.01398096326738596,
0.02526557445526123,
0.05871620029211044,
-0.019334226846694946,
0.07394595444202423,
-0.005173107609152794,
-0.02544306218624115,
0.08705682307481766,
-0.019235868006944656,
0.03311970457434654,
-0.036208439618349075,
0.022804683074355125,
-0.015377665869891644,
0.01066721323877573,
0.032160546630620956,
-0.06351412087678909,
-0.010777054354548454,
0.017764586955308914,
-0.030385730788111687,
-0.04562719538807869,
0.02714976668357849,
-0.025784505531191826,
-0.04660424217581749,
-0.05381566286087036,
0.01999439112842083,
0.009706220589578152,
-0.02031438611447811,
-0.006902833469212055,
-0.006205876357853413,
0.012583163566887379,
-0.018880346789956093,
-0.08300710469484329,
0.016183821484446526,
0.006041414570063353,
0.02813839167356491,
-0.020798809826374054,
-0.02730000950396061,
0.04474272206425667,
0.011469103395938873,
0.07611440867185593,
-0.04047749191522598,
0.014476705342531204,
0.09688163548707962,
-0.034630753099918365,
-0.08076846599578857,
0.008166653104126453,
-0.0055305142886936665,
0.009380723349750042,
-0.06005657836794853,
0.026045721024274826,
0.009366603568196297,
-0.04094061255455017,
-0.03336087241768837,
0.05210043862462044,
-0.009285450913012028,
0.007653599139302969,
-0.0034595930483192205,
0.011747341603040695,
0.06540577858686447,
0.02252408303320408,
-0.029853858053684235,
-0.0042289551347494125,
-0.008419561199843884,
-0.007452844176441431,
-0.06438577175140381,
0.027858376502990723,
-0.005049661733210087,
-0.012264387682080269,
0.0013559362851083279,
-0.020883023738861084,
-0.002140645869076252,
0.00993693619966507,
-0.08102784305810928,
0.04013483226299286,
-0.015941133722662926,
-0.005046695005148649,
0.01227456983178854,
-0.013930651359260082,
0.043738674372434616,
0.022519651800394058,
0.11066319793462753,
0.021593865007162094,
0.027262672781944275,
-0.015597086399793625,
-0.022409936413168907,
0.028050003573298454,
-0.017355812713503838,
0.026266103610396385,
-0.022868607193231583,
0.021724358201026917,
-0.011055964976549149,
0.03834068402647972,
-0.08350515365600586,
-0.09679872542619705,
-0.02289706841111183,
0.018740959465503693,
0.050355441868305206,
0.044720083475112915,
0.04383239522576332,
0.01464981772005558,
0.07669280469417572,
-0.028958292677998543,
-0.05057197064161301,
0.03940704092383385,
0.032827164977788925,
-0.02508479543030262,
-0.021502992138266563,
-0.007836446166038513,
-0.019568856805562973,
-0.03176387399435043,
-0.02114972285926342,
0.0010737251723185182,
0.050363872200250626,
-0.0011486844159662724,
0.03408323600888252,
-0.022714264690876007,
-0.022162236273288727,
0.03679218515753746,
-0.013246431946754456,
-0.01280895434319973,
-0.09239182621240616,
0.0015185853699222207,
0.00264175608754158,
-0.041264016181230545,
0.00757094519212842,
-0.015247808769345284,
-0.03717585280537605,
0.013720056973397732,
0.01215563714504242,
0.045083239674568176,
-0.0022563685197383165,
0.009112447500228882,
-0.023290513083338737,
0.03799287602305412,
0.015177534893155098,
-0.026021430268883705,
-0.020029470324516296,
-0.029764380306005478,
-0.056808196008205414,
-0.00550055131316185,
-0.03290419653058052,
-0.014130312949419022,
0.043454330414533615,
-0.12331398576498032,
0.010973385535180569,
0.003658741246908903,
-0.007726652082055807,
0.047982051968574524,
0.031216347590088844,
-0.018067574128508568,
-0.02268388494849205,
0.03934679925441742,
0.03075588308274746,
0.012068682350218296,
0.02272738888859749,
-0.030401561409235,
0.03050149604678154,
-0.031698811799287796,
-0.027501370757818222,
-0.05002620071172714,
-0.05183352902531624,
-0.036217719316482544,
0.00951435137540102,
0.04721603915095329,
-0.0017697440925985575,
-0.009051977656781673,
-0.04308275505900383,
0.030815182253718376
] |
<p>Here I cite part from Sidney Coleman's lectures on Quantum Field Theory:</p>
<blockquote>
<p>It is a phenomenal fluke that relativistic kinematic corrections for the Hydrogen atom work. If the Dirac equation is used, without considering multi-particle intermediate states, corrections of $O \big(\frac{v}{c}\big)$ can be obtained. This is a fluke caused by some unusually low electrodynamic matrix elements.</p>
</blockquote>
<p>What is the fluke about? Also, how can one justify the usage of Pauli-Schrodinger type equations that comes from first quantization of Dirac's equation? Schrodinger's equation is universal postulate valid for any quantum theory, and is equation for wave functionals in field theory. Could one go from non-relativistic QED field theory and then justify the usage of Pauli equation in which $\psi$ is interpreted as "wave function" in certain kinematical conditions (approximation)?</p> | g4742 | [
0.026314442977309227,
-0.01158199179917574,
-0.03450716659426689,
0.039207592606544495,
0.06506182998418808,
-0.00575254438444972,
0.03786177560687065,
0.06636077165603638,
-0.04283011704683304,
-0.007687828503549099,
-0.0532209537923336,
0.03374140337109566,
0.022238655015826225,
0.04125003516674042,
0.01129855401813984,
-0.04198755323886871,
0.04850951209664345,
0.005911812651902437,
0.0064827315509319305,
0.004805080592632294,
-0.0039263563230633736,
-0.012462180107831955,
-0.017206167802214622,
-0.031262610107660294,
0.043757785111665726,
-0.01875462383031845,
0.041205380111932755,
-0.015521079301834106,
-0.045157283544540405,
-0.0007874219445511699,
0.04547235369682312,
-0.022352933883666992,
0.021137993782758713,
-0.07932630926370621,
-0.020492054522037506,
0.02137697860598564,
0.060553062707185745,
0.0205893125385046,
0.050253793597221375,
0.0054519521072506905,
-0.006660854909569025,
-0.004514330066740513,
0.03019176423549652,
-0.06786204129457474,
0.02830851450562477,
-0.038590170443058014,
0.02140394039452076,
0.02108541876077652,
-0.02812296152114868,
0.03000851534307003,
0.013369831256568432,
0.010840003378689289,
0.08260269463062286,
0.040782880038022995,
0.024844033643603325,
0.06870799511671066,
0.047618769109249115,
-0.03569614887237549,
0.060810431838035583,
0.039358220994472504,
0.015057418495416641,
-0.01389039121568203,
0.03693799674510956,
-0.018656359985470772,
0.06585481017827988,
0.006892923731356859,
-0.040918152779340744,
0.02033713273704052,
-0.007960130460560322,
0.04424740746617317,
0.024949578568339348,
-0.08268039673566818,
-0.04397100955247879,
-0.002663644263520837,
0.039753690361976624,
0.04426746070384979,
-0.00457531725987792,
-0.04004989191889763,
0.02896537445485592,
-0.01621590368449688,
-0.06293211132287979,
-0.03093714267015457,
0.03486494719982147,
0.011007241904735565,
0.05388757959008217,
0.019250953570008278,
0.027356771752238274,
0.022637829184532166,
-0.004151636268943548,
0.010297227650880814,
-0.031251776963472366,
-0.03424739092588425,
0.013500458560883999,
-0.016705481335520744,
-0.021390283480286598,
-0.040576301515102386,
-0.03184450790286064,
0.06231134757399559,
-0.0188189297914505,
-0.001533166621811688,
-0.043815162032842636,
0.04261711984872818,
0.030165227130055428,
0.033321280032396317,
0.007419063244014978,
0.035299286246299744,
-0.049639347940683365,
0.02182486653327942,
0.04184015095233917,
0.0008225456112995744,
-0.026628240942955017,
-0.04275752231478691,
0.017322944477200508,
-0.07884684950113297,
-0.038754697889089584,
-0.018297262489795685,
-0.021159252151846886,
-0.060809411108493805,
-0.024487478658556938,
0.03371395543217659,
-0.04045352712273598,
0.013484210707247257,
0.08443517982959747,
0.04013218358159065,
-0.014356404542922974,
-0.017745306715369225,
-0.06422831118106842,
0.022761577740311623,
-0.00257845688611269,
-0.050568610429763794,
0.0025454512797296047,
0.023031463846564293,
0.05812454596161842,
0.01234395056962967,
0.01799788884818554,
-0.027892133221030235,
-0.027375031262636185,
-0.028805850073695183,
-0.03205261006951332,
-0.03839337080717087,
0.04392881691455841,
-0.027835287153720856,
0.02696644514799118,
0.0009031081572175026,
0.0027987570501863956,
-0.038749899715185165,
-0.05645393207669258,
0.008452805690467358,
0.031912438571453094,
-0.01763704977929592,
0.018997784703969955,
0.019937606528401375,
-0.003398470114916563,
0.03479418158531189,
0.019914433360099792,
0.049446504563093185,
0.000053247316827764735,
-0.002415988827124238,
-0.03654344007372856,
0.006768655031919479,
0.061939019709825516,
-0.017987411469221115,
0.008869828656315804,
0.01709694229066372,
0.015664923936128616,
0.011740452609956264,
0.007557909470051527,
-0.03537056967616081,
-0.004027240443974733,
-0.037464965134859085,
-0.012518119066953659,
0.011615636758506298,
0.0022922330535948277,
0.03940628841519356,
-0.038603100925683975,
0.06797139346599579,
-0.01288947369903326,
-0.04760383814573288,
-0.02493361383676529,
0.01224417332559824,
-0.024783391505479813,
-0.03423546999692917,
0.029023552313447,
-0.004876764491200447,
-0.010355240665376186,
0.008145988918840885,
-0.019439950585365295,
0.06362028419971466,
-0.03759343922138214,
-0.03245878592133522,
0.013621392659842968,
-0.06206360086798668,
0.014712701551616192,
-0.003110873280093074,
0.041900184005498886,
0.05470747500658035,
-0.027167590335011482,
-0.026334451511502266,
-0.03371164947748184,
0.025355856865644455,
-0.013949887827038765,
0.048230212181806564,
-0.010301942005753517,
-0.047147102653980255,
0.03492116183042526,
0.028373178094625473,
-0.020865868777036667,
-0.0073343259282410145,
0.01457306370139122,
-0.015315257012844086,
0.09348975121974945,
-0.0004397815791890025,
-0.01825270988047123,
0.036790281534194946,
-0.02338075451552868,
-0.0122766038402915,
-0.006025207228958607,
-0.0531134270131588,
0.005868253763765097,
-0.004840368404984474,
-0.04969486966729164,
-0.04265996441245079,
0.035881999880075455,
0.05097813904285431,
0.0158584825694561,
0.03622930124402046,
-0.019086558371782303,
-0.06779206544160843,
-0.03446262702345848,
0.004595095291733742,
-0.013661321252584457,
0.026302015408873558,
-0.02290209010243416,
0.005788370501250029,
0.030737005174160004,
0.040001653134822845,
0.016596149653196335,
-0.03487536311149597,
0.07530435174703598,
0.010301996022462845,
-0.011958325281739235,
-0.009927232749760151,
-0.0833970457315445,
-0.02510329894721508,
0.020086731761693954,
0.01189030334353447,
0.030098114162683487,
-0.026232687756419182,
-0.042018938809633255,
0.007220630533993244,
0.020954573526978493,
-0.012525828555226326,
-0.06995167583227158,
0.018791403621435165,
0.013476537540555,
-0.03551692143082619,
0.015121718868613243,
0.09905359148979187,
-0.03552055358886719,
-0.019932979717850685,
-0.020820675417780876,
0.024964002892374992,
-0.020485976710915565,
0.05044577643275261,
0.004192968364804983,
0.040518272668123245,
0.020395297557115555,
0.01930725947022438,
0.010974434204399586,
0.03452231362462044,
-0.024733582511544228,
0.06858202069997787,
0.017285717651247978,
0.008190808817744255,
0.010410783812403679,
-0.051873963326215744,
-0.0428013913333416,
0.014356086030602455,
-0.0007313943933695555,
-0.0019526208052411675,
-0.07108663767576218,
0.006824331358075142,
-0.047564797103405,
0.03803953155875206,
0.0418134443461895,
-0.053764715790748596,
-0.016715193167328835,
-0.04030389338731766,
-0.024659868329763412,
-0.013117967173457146,
-0.030127838253974915,
0.06961008161306381,
0.05361822620034218,
0.060147568583488464,
-0.007673454005271196,
-0.045177023857831955,
0.027508288621902466,
-0.027672728523612022,
-0.03961367532610893,
0.05441845580935478,
-0.010913077741861343,
-0.022062065079808235,
-0.018306821584701538,
0.018541865050792694,
0.03322141245007515,
-0.00649345014244318,
-0.013414974324405193,
-0.02953927218914032,
-0.02212240733206272,
-0.03372538834810257,
-0.014232848770916462,
0.03708998113870621,
-0.03839018568396568,
-0.008309229277074337,
-0.0474662221968174,
-0.03301423415541649,
0.038329336792230606,
0.015272403135895729,
0.03555342182517052,
-0.008074483834207058,
-0.003768081311136484,
-0.06527537852525711,
-0.01087132841348648,
0.04528312385082245,
0.07122763246297836,
0.10066378116607666,
-0.03972640633583069,
0.020550018176436424,
-0.033544231206178665,
-0.01544031873345375,
0.03506782278418541,
-0.006758779752999544,
0.0287995133548975,
0.011077561415731907,
-0.08918807655572891,
-0.07511810213327408,
-0.04839545488357544,
0.0832519680261612,
0.02003137581050396,
-0.07183031737804413,
-0.04221193119883537,
-0.051529765129089355,
-0.03717832639813423,
0.05290811136364937,
0.021225038915872574,
-0.001924683223478496,
0.015451316721737385,
0.0022337138652801514,
-0.02887948788702488,
0.00797099620103836,
-0.007091721519827843,
-0.022995103150606155,
-0.028180953115224838,
0.015845606103539467,
-0.027938134968280792,
0.0042431894689798355,
0.06337355077266693,
0.04222050681710243,
0.029974328354001045,
0.02827271819114685,
-0.030331511050462723,
-0.0002767505357041955,
-0.004139227326959372,
0.05987025424838066,
-0.008461741730570793,
-0.03574676066637039,
-0.018629854544997215,
0.022341342642903328,
0.007453403435647488,
-0.0768328607082367,
-0.043351538479328156,
0.01670023798942566,
-0.002978426171466708,
-0.0067027248442173,
-0.05094822123646736,
-0.04014938324689865,
0.00856334250420332,
0.006147732958197594,
-0.07882823795080185,
0.03149982541799545,
0.006265710107982159,
0.03894495218992233,
0.017227903008461,
0.026666009798645973,
-0.004170059692114592,
0.01643395610153675,
-0.06694158911705017,
-0.017138231545686722,
0.007401084527373314,
0.008773216977715492,
-0.031690679490566254,
-0.02754874713718891,
-0.030525628477334976,
0.0355832539498806,
-0.0008181927260011435,
0.0096743730828166,
0.06904186308383942,
-0.026023628190159798,
0.006190971937030554,
0.06609974801540375,
-0.02313968352973461,
-0.06994320452213287,
0.05072426795959473,
0.006802672054618597,
-0.008309507742524147,
-0.0035181979183107615,
0.008799639530479908,
-0.005821933038532734,
0.023825068026781082,
-0.007055777590721846,
0.012272610329091549,
-0.022652778774499893,
0.00800030305981636,
-0.08671335875988007,
-0.014713920652866364,
-0.03488800302147865,
0.026721181347966194,
-0.0556415319442749,
0.028955187648534775,
0.015915827825665474,
0.006396538112312555,
0.04565533995628357,
0.048338983207941055,
0.009003286249935627,
0.08679323643445969,
0.028063351288437843,
-0.0025836408603936434,
0.002074178773909807,
0.05132204666733742,
-0.08202052116394043,
0.02680267207324505,
-0.03368119150400162,
-0.04839019104838371,
0.05776461958885193,
-0.06584540009498596,
-0.0007552814786322415,
0.0026989481411874294,
0.07415148615837097,
-0.055367037653923035,
0.06657446920871735,
0.08805655688047409,
0.038597602397203445,
-0.005892208311706781,
0.027659019455313683,
0.015025214292109013,
0.019336896017193794,
-0.05257118493318558,
-0.029931994155049324,
-0.06610040366649628,
-0.037985529750585556,
0.01972825452685356,
-0.0013256820384413004,
-0.006996141746640205,
0.03015872836112976,
0.07724872976541519,
-0.036426275968551636,
-0.07305605709552765,
0.05416363850235939,
0.043672531843185425,
0.013139933347702026,
-0.03267643228173256,
0.03246576711535454,
-0.011949463747441769,
0.04659565910696983,
0.043377913534641266,
-0.010841756127774715,
-0.01001206785440445,
-0.029647648334503174,
-0.09716903418302536,
0.03064410760998726,
0.010502408258616924,
0.006209062412381172,
0.014797021634876728,
-0.04578579589724541,
-0.008983149193227291,
-0.0064699966460466385,
-0.05825372412800789,
0.004418323747813702,
-0.028213832527399063,
-0.025864435359835625,
0.03725408762693405,
-0.05102265253663063,
0.027952834963798523,
0.0393526591360569,
-0.042117465287446976,
-0.018293730914592743,
-0.007082829717546701,
-0.0031997174955904484,
-0.021921833977103233,
-0.059009213000535965,
0.03713853657245636,
0.06464988738298416,
0.018795723095536232,
-0.007155771367251873,
0.036576028913259506,
0.11026055365800858,
0.01878778263926506,
-0.006007746327668428,
0.010591239668428898,
0.03528004139661789,
-0.05440334603190422,
0.026472406461834908,
0.047831978648900986,
-0.016306249424815178,
0.009824826382100582,
0.0024641421623528004,
0.05172179639339447,
0.02228061482310295,
-0.018056662753224373,
-0.02783651277422905,
0.023115243762731552,
-0.014274105429649353,
0.0022588667925447226,
-0.01848546974360943,
0.01784561574459076,
-0.03957837074995041,
0.00045764687820337713,
-0.0004000460321549326,
-0.026389217004179955,
-0.05461568385362625,
0.04108124598860741,
-0.025853415951132774,
-0.02183881774544716,
0.016485709697008133,
0.000554003519937396,
0.004654422402381897,
-0.01934625394642353,
-0.027757015079259872,
-0.010583579540252686,
0.029752615839242935,
-0.02065802924335003,
-0.02177458256483078,
0.08797638863325119,
0.06356929987668991,
0.028634587302803993,
0.0258577149361372,
-0.0017108269967138767,
0.028289087116718292,
0.024769363924860954,
0.0256175734102726,
0.025595225393772125,
-0.024692129343748093,
0.04409858584403992,
0.005011305678635836,
-0.032218948006629944,
-0.03059094399213791,
-0.0651799887418747,
0.024451809003949165,
0.009632675908505917,
-0.08434465527534485,
-0.013978179544210434,
-0.013487722724676132,
-0.023399898782372475,
-0.03654864430427551,
0.002419726923108101,
0.013291006907820702,
-0.03560802340507507,
-0.04279710352420807,
-0.029782993718981743,
0.010619722306728363,
0.02459537237882614,
-0.02366453967988491,
0.07069927453994751,
0.044390808790922165,
0.03876510635018349,
-0.011965193785727024,
-0.044718340039253235,
-0.03099413588643074,
-0.0034958594478666782,
-0.022095585241913795,
-0.05248495563864708,
0.05271005257964134,
-0.0382993221282959,
0.02064863219857216,
0.026741867884993553,
-0.02742442674934864,
0.029272427782416344,
-0.02790834940969944,
-0.04051731526851654,
0.02965608797967434,
-0.02137683518230915,
0.017413103953003883,
0.03304200619459152,
-0.07886885106563568,
-0.03566226363182068,
-0.0042895302176475525,
-0.044251494109630585,
0.024735206738114357,
0.09349492937326431,
0.04514216259121895,
-0.05848037078976631,
-0.001063097850419581,
-0.03206748515367508,
-0.027842765673995018,
-0.0011482752161100507,
0.005073995795100927,
-0.02416195720434189,
-0.048836663365364075,
-0.05888455733656883,
0.0392262265086174,
0.0027552922256290913,
0.04394618421792984,
-0.006905240472406149,
0.0351005494594574,
0.045309633016586304,
0.03686732426285744,
-0.08847253024578094,
-0.015093904919922352,
0.014896323904395103,
0.008804385550320148,
0.025714876130223274,
0.027522562071681023,
-0.03546026721596718,
-0.04495323821902275,
-0.040190763771533966,
-0.007471348159015179,
-0.01858040876686573,
0.030657395720481873,
-0.03316938877105713,
-0.03493974730372429,
0.03858568146824837,
-0.07596743851900101,
0.00048510057968087494,
-0.02138957381248474,
-0.0012489083455875516,
0.03046541102230549,
-0.0014639272121712565,
-0.005809627007693052,
0.03674106299877167,
0.005290938075631857,
-0.03724318742752075,
-0.0010383129119873047,
0.021922722458839417,
0.048635613173246384,
-0.0304772537201643,
0.023105742409825325,
-0.03616686537861824,
0.018284419551491737,
0.06944500654935837,
0.015978360548615456,
-0.03610483929514885,
-0.015504143200814724,
0.04664909467101097,
-0.06487677246332169,
-0.030255788937211037,
-0.017461881041526794,
0.05531284585595131,
0.07480011880397797,
-0.11752312630414963,
-0.006517303641885519,
0.023159507662057877,
0.027214815840125084,
0.0012672623852267861,
0.015466040000319481,
-0.021650515496730804,
-0.03960639238357544,
-0.0006091097020544112,
0.028902512043714523,
-0.008068682625889778,
-0.08363837748765945,
-0.015766581520438194,
-0.033796198666095734,
0.03595530241727829,
-0.009077840484678745,
0.03202925622463226,
0.025714952498674393,
-0.024958115071058273,
-0.04182223975658417,
0.003409694880247116,
0.027987172827124596,
-0.013908795081079006,
-0.04492182284593582,
-0.009152284823358059,
0.0023156004026532173,
-0.028983836993575096,
-0.037483688443899155,
0.02019248716533184,
0.061422400176525116,
-0.08086101710796356,
-0.017611520364880562,
-0.004226228687912226,
0.03207160159945488,
0.05301307514309883,
-0.03362829610705376,
-0.05025659129023552,
-0.015952810645103455,
-0.003049083985388279,
-0.0029564984142780304,
-0.03802512586116791,
-0.017264511436223984,
0.035702284425497055,
-0.03538341075181961,
0.014942510984838009,
0.012172252871096134,
0.0371580570936203,
-0.005314547102898359,
0.010206110775470734,
0.03729890286922455,
0.016251692548394203,
-0.002465670695528388,
-0.01814626343548298,
-0.023618405684828758,
0.017603890970349312,
0.06060865521430969,
0.01614450104534626,
0.037662796676158905,
-0.003783962456509471,
-0.01374023500829935,
-0.009102148935198784,
0.01761443354189396,
-0.01985950954258442,
-0.013552379794418812,
0.01680758409202099,
0.07403116673231125,
0.02768486924469471,
-0.05238752439618111,
-0.010134397074580193,
0.03325894474983215,
0.03873056173324585,
-0.014656572602689266,
0.022373905405402184,
-0.0046430230140686035,
-0.022875245660543442,
-0.017922114580869675,
0.005437173880636692,
-0.011369544081389904,
-0.029145468026399612,
-0.0271283145993948,
0.016365868970751762,
-0.025680823251605034,
-0.019293028861284256,
0.03866122290492058,
-0.04483189806342125,
0.053874824196100235,
-0.035829056054353714,
0.04931400716304779,
-0.012803681194782257,
-0.022004753351211548,
0.02363629639148712,
0.030323445796966553,
0.013185986317694187,
0.004285542294383049,
0.003324432997033,
0.002473092870786786,
-0.05124787241220474,
-0.01845555193722248,
-0.0199758131057024,
0.019722798839211464,
-0.012325034476816654,
0.007576724048703909,
-0.0011516180820763111,
0.058483630418777466,
-0.06204463541507721,
0.0244591124355793,
0.04806315898895264,
-0.03270455822348595,
0.0010599762899801135,
0.02421518787741661,
0.030038977041840553,
0.025529544800519943,
-0.01201277133077383,
-0.023354118689894676,
0.01163451187312603,
-0.006744631566107273,
0.026482582092285156,
-0.04153020679950714,
-0.05430081486701965,
-0.011439469642937183
] |
<p>Suppose there are <strong>two <a href="http://en.wikipedia.org/wiki/Charged_black_hole" rel="nofollow">charged black holes</a></strong> which <strong>collide to form a bigger black hole</strong>. </p>
<p>But when they combine, a lot of potential energy of the system is lost/gained depending on their charges (the opposite or the same). <strong>Will it manifest as an increase/decrease in mass of the big black hole</strong>?</p>
<p><em>If the mass were to come down (+ve ,+ve collision) will the resultant black hole shrink in size?</em></p> | g4743 | [
0.055571381002664566,
0.02192213013768196,
0.019333813339471817,
0.012440821155905724,
0.04145281761884689,
0.03734617680311203,
-0.03652328997850418,
0.020205169916152954,
-0.027566004544496536,
-0.012644714675843716,
0.01586221531033516,
-0.0048991115763783455,
0.00043029713560827076,
-0.010759719647467136,
-0.03881794586777687,
-0.006016567815095186,
0.08474241942167282,
-0.05010396987199783,
-0.025009892880916595,
0.0184408500790596,
-0.047903746366500854,
0.0016721580177545547,
-0.007259956561028957,
-0.03653371334075928,
-0.018321873620152473,
0.031196407973766327,
0.045564718544483185,
0.027786608785390854,
-0.0668802261352539,
-0.03672434762120247,
0.04486015811562538,
0.05009964853525162,
-0.012835195288062096,
0.018036186695098877,
-0.018335949629545212,
0.01652001030743122,
0.06832049041986465,
-0.04120803624391556,
-0.05151165649294853,
-0.000353874231223017,
0.06620264798402786,
-0.03278319910168648,
0.04522506520152092,
-0.0037023727782070637,
-0.02706681750714779,
-0.05055302754044533,
0.05713891237974167,
-0.0021853717043995857,
0.023877568542957306,
0.008431822061538696,
0.027391599491238594,
0.022311950102448463,
0.004460019059479237,
-0.00034289679024368525,
0.07790715992450714,
0.04267740994691849,
0.0174716766923666,
-0.03046547994017601,
-0.008835426531732082,
0.041057832539081573,
-0.0438651405274868,
0.04587961360812187,
-0.0013226628070697188,
0.0373014397919178,
0.06976701319217682,
-0.02630639262497425,
-0.07681284844875336,
-0.020800817757844925,
0.00971168838441372,
-0.00034757558023557067,
-0.00981481745839119,
0.02018268033862114,
-0.026295673102140427,
-0.06417665630578995,
0.033052992075681686,
0.005985412746667862,
0.0032891323789954185,
-0.04070229083299637,
-0.023636173456907272,
0.004653227049857378,
-0.04988231137394905,
-0.03392306715250015,
0.08792845159769058,
-0.003734864993020892,
0.03559941425919533,
-0.013084729202091694,
-0.0056682308204472065,
0.04420454800128937,
-0.03519876301288605,
0.044229552149772644,
0.055803537368774414,
-0.01641828753054142,
0.07185467332601547,
0.017543697729706764,
0.00201556459069252,
0.0017476401990279555,
0.008930237032473087,
0.02953958883881569,
0.020328842103481293,
-0.008432158268988132,
-0.03253266215324402,
0.02074594795703888,
-0.0015999345341697335,
-0.012609151192009449,
0.01856890879571438,
-0.0049015250988304615,
-0.0004480728239286691,
0.012552027590572834,
0.006412298884242773,
0.045431505888700485,
-0.009260446764528751,
-0.15771272778511047,
-0.027174953371286392,
-0.08495956659317017,
-0.0629880428314209,
-0.02476743422448635,
0.02044794149696827,
0.004728618077933788,
-0.05288216844201088,
0.01946011558175087,
-0.00823103729635477,
-0.037588246166706085,
0.0026093823835253716,
0.010864980518817902,
0.0020277404692023993,
-0.004980832803994417,
-0.015243960544466972,
0.03254372999072075,
0.01947268471121788,
-0.01758083887398243,
0.002400606172159314,
-0.0067365108989179134,
0.015498964115977287,
0.025847548618912697,
-0.022448725998401642,
-0.00010029409895651042,
0.014362906105816364,
0.02382510155439377,
-0.022288156673312187,
0.0029548080638051033,
0.03926359489560127,
-0.008759994991123676,
-0.0017357872566208243,
0.02555740624666214,
-0.022346552461385727,
-0.011443470604717731,
-0.006938941311091185,
-0.04645182564854622,
-0.013544092886149883,
0.033096954226493835,
-0.008962036110460758,
0.021873315796256065,
-0.0362464040517807,
-0.055597495287656784,
0.014657756313681602,
0.04388275370001793,
0.007506522350013256,
0.035044316202402115,
-0.013500699773430824,
-0.02346760407090187,
0.015582498162984848,
-0.02998497150838375,
0.03337709605693817,
0.0195879228413105,
-0.019096102565526962,
-0.0032139234244823456,
0.06846998631954193,
-0.02755916491150856,
0.00497574033215642,
-0.012215101160109043,
0.03247237950563431,
-0.007050940301269293,
0.024638930335640907,
0.045136887580156326,
0.018792225047945976,
0.008013526909053326,
0.02027537301182747,
-0.025937296450138092,
0.019657786935567856,
-0.011449430137872696,
-0.06690336018800735,
0.025213755667209625,
-0.014544625766575336,
-0.030230069532990456,
0.06444384157657623,
-0.017572972923517227,
0.01497432217001915,
0.10954993963241577,
-0.014844894409179688,
0.009341266006231308,
-0.08545328676700592,
-0.02687736041843891,
0.015306812711060047,
-0.005881961900740862,
0.016134198755025864,
0.020619060844182968,
0.0439375638961792,
0.016755223274230957,
-0.01488554198294878,
0.014610592275857925,
-0.05971246957778931,
0.05520963668823242,
0.051675938069820404,
0.02009936422109604,
0.03714793175458908,
0.03589455038309097,
0.007096361834555864,
-0.011143400333821774,
0.03102908469736576,
-0.001331526436842978,
0.003437604056671262,
-0.0022122429218143225,
-0.030341941863298416,
-0.012164405547082424,
-0.027103198692202568,
0.007821650244295597,
-0.017772316932678223,
0.05976962298154831,
-0.025453047826886177,
0.022083589807152748,
-0.06098606064915657,
-0.0025784149765968323,
-0.019498208537697792,
-0.03743760287761688,
0.009229423478245735,
0.015012509189546108,
-0.0024193425197154284,
-0.038819681853055954,
0.006317885126918554,
-0.009788718074560165,
-0.004410249181091785,
0.08678045868873596,
0.02846962958574295,
-0.026958512142300606,
0.026143450289964676,
0.040312062948942184,
-0.0033961108420044184,
-0.00018002252909354866,
0.015233425423502922,
0.015217302367091179,
0.036358438432216644,
-0.026822684332728386,
0.013246456161141396,
-0.006645962130278349,
0.03392354026436806,
-0.036037977784872055,
-0.013913838192820549,
0.005934066604822874,
0.0026552595663815737,
0.01520849671214819,
-0.014037046581506729,
-0.01772071048617363,
-0.000181215102202259,
0.02032512053847313,
-0.017353909090161324,
0.027559202164411545,
-0.021460361778736115,
0.032989501953125,
-0.016036128625273705,
-0.02185368537902832,
0.021479051560163498,
0.012888872064650059,
-0.027063149958848953,
0.06022484228014946,
-0.07401405274868011,
-0.016023848205804825,
-0.004709235858172178,
-0.04650574177503586,
0.014385148882865906,
0.03520495444536209,
-0.003786111483350396,
0.04745401069521904,
0.048309966921806335,
0.010478368028998375,
0.03636473789811134,
0.017775263637304306,
-0.02772202156484127,
-0.006134720519185066,
0.05657583847641945,
-0.05490867793560028,
-0.023020705208182335,
0.05349789187312126,
-0.036283187568187714,
0.013872255571186543,
0.02800551988184452,
-0.030591262504458427,
-0.020170189440250397,
-0.01664668694138527,
-0.0507795624434948,
0.02919793128967285,
-0.017396559938788414,
0.03654376044869423,
0.11168880015611649,
0.028905676677823067,
0.015024949796497822,
0.020986313000321388,
0.01537189818918705,
-0.009409047663211823,
-0.05073225498199463,
-0.02751026675105095,
0.028426390141248703,
-0.02921322174370289,
-0.067268505692482,
0.004252818878740072,
0.02509501203894615,
0.08891098946332932,
-0.05544998496770859,
0.005262407474219799,
0.004770539700984955,
-0.031466927379369736,
-0.027311181649565697,
-0.012832852080464363,
0.029845567420125008,
0.024155573919415474,
-0.050611842423677444,
-0.03791120648384094,
0.09210119396448135,
0.01696551963686943,
-0.00012301505194045603,
0.008348717354238033,
-0.020066101104021072,
-0.03440456837415695,
-0.01239204965531826,
-0.022543825209140778,
0.008077254518866539,
0.04548287391662598,
-0.0315358005464077,
-0.03531477227807045,
0.004520438611507416,
0.04954899474978447,
-0.06178664788603783,
0.009424028918147087,
0.00594757404178381,
0.03196129575371742,
-0.02818826586008072,
0.004610187374055386,
0.014644943177700043,
-0.011330286972224712,
0.02504880353808403,
0.023204531520605087,
0.034554146230220795,
-0.01563771441578865,
-0.020490018650889397,
-0.005572695750743151,
0.006480116862803698,
0.05279231444001198,
0.02110699564218521,
-0.03918568789958954,
0.023781387135386467,
-0.0768541470170021,
0.04644186049699783,
-0.05898682400584221,
0.04791068285703659,
0.00949887279421091,
0.0009024729952216148,
-0.06568241864442825,
-0.021339550614356995,
-0.008595364168286324,
-0.00895453616976738,
0.03174975514411926,
-0.010915379971265793,
-0.03876836970448494,
-0.0020538917742669582,
0.008792677894234657,
-0.032056476920843124,
-0.0028480926994234324,
-0.04766789823770523,
-0.02550109662115574,
-0.008502787910401821,
-0.02517310157418251,
-0.02845204994082451,
0.03265761584043503,
-0.030574532225728035,
0.021597053855657578,
-0.0003975244762841612,
-0.047382861375808716,
0.05528387799859047,
0.029592782258987427,
0.011997317895293236,
-0.034500718116760254,
0.06001622974872589,
-0.011871985159814358,
0.01947740465402603,
-0.012936708517372608,
-0.036014389246702194,
-0.04231536388397217,
-0.0014564978191629052,
-0.054570939391851425,
-0.0025232979096472263,
-0.030960215255618095,
-0.03455100581049919,
-0.029648488387465477,
-0.0052758497186005116,
-0.008548914454877377,
0.026873024180531502,
0.012302509509027004,
0.010236773639917374,
-0.061755791306495667,
0.011129279620945454,
0.02524550072848797,
-0.014937782660126686,
0.03949528932571411,
-0.00560294184833765,
-0.014952605590224266,
0.04179011285305023,
-0.039308156818151474,
0.03241254761815071,
0.02648795209825039,
-0.029540637508034706,
-0.0459374375641346,
0.04222651198506355,
-0.04749618470668793,
-0.013354009948670864,
-0.030951285734772682,
0.014407684095203876,
-0.022076448425650597,
0.009520095773041248,
0.012560783885419369,
-0.0035627365577965975,
0.0319843553006649,
-0.02164606936275959,
0.01568692736327648,
0.006877952255308628,
0.07482723891735077,
-0.07435549795627594,
-0.005211247596889734,
-0.02601531706750393,
-0.011134205386042595,
-0.05060998722910881,
0.027844231575727463,
0.04530371353030205,
0.023603562265634537,
-0.01903463900089264,
-0.019954539835453033,
-0.06066254526376724,
0.0933590680360794,
-0.012198900803923607,
-0.001181360799819231,
0.017192712053656578,
0.07317735999822617,
0.05573562532663345,
0.015797941014170647,
-0.01650361530482769,
-0.03518633916974068,
0.005793933756649494,
0.06092226132750511,
-0.006434663198888302,
0.010660967789590359,
0.017260031774640083,
-0.07470720261335373,
-0.054818328469991684,
-0.022766007110476494,
0.002901113126426935,
-0.06340282410383224,
-0.005863618571311235,
0.04978586360812187,
-0.0358571857213974,
0.03181019052863121,
-0.006999220699071884,
-0.01589212194085121,
-0.001965880859643221,
0.015021238476037979,
0.06663733720779419,
0.004586349707096815,
0.00042300717905163765,
-0.1038142666220665,
-0.026692751795053482,
-0.010070030577480793,
-0.03058970533311367,
0.003159146523103118,
-0.08949635922908783,
0.012682746164500713,
0.020274868234992027,
0.05076976493000984,
-0.02806112729012966,
-0.00637971144169569,
-0.0342865027487278,
-0.04769560322165489,
0.04275793209671974,
-0.040892113000154495,
0.014079517684876919,
-0.01909925416111946,
0.026883259415626526,
-0.038580652326345444,
0.005635389126837254,
0.08197228610515594,
-0.015827154740691185,
0.07117585092782974,
0.06184481456875801,
-0.009723919443786144,
0.018405446782708168,
-0.0015351100591942668,
0.0013475504238158464,
0.026664353907108307,
-0.02534724958240986,
0.0224774070084095,
-0.016568033024668694,
-0.019267739728093147,
-0.01240015309303999,
0.054250892251729965,
0.02045305259525776,
-0.019715094938874245,
-0.005047070328146219,
-0.005057895556092262,
0.0027219837065786123,
0.02891640178859234,
0.02251286618411541,
-0.021141156554222107,
0.03398915380239487,
0.060837071388959885,
-0.08009959012269974,
0.0749756321310997,
0.05308036506175995,
0.04001468047499657,
0.01309814490377903,
-0.02457818016409874,
-0.03795190900564194,
0.022420261055231094,
0.006525802426040173,
-0.05170417204499245,
0.033450040966272354,
-0.036738839000463486,
0.0282945204526186,
0.000641476595774293,
0.024557912722229958,
-0.010865404270589352,
-0.01932499185204506,
0.01914403960108757,
0.017345478758215904,
0.025622308254241943,
0.021319156512618065,
-0.016548719257116318,
0.032078418880701065,
0.00555171025916934,
0.0021490806248039007,
0.01866970956325531,
-0.021595444530248642,
0.0319032296538353,
0.03251741826534271,
-0.0009044109610840678,
0.011616387404501438,
0.018445134162902832,
-0.033040329813957214,
0.10189862549304962,
0.07546073943376541,
-0.032846346497535706,
-0.07001922279596329,
-0.02878936566412449,
0.03735562786459923,
-0.02072717808187008,
-0.06679807603359222,
-0.02516254410147667,
-0.04672161862254143,
0.024916110560297966,
-0.0133891636505723,
0.024279210716485977,
0.0427832305431366,
-0.021521560847759247,
0.0168863907456398,
-0.03509911522269249,
0.017825772985816002,
-0.06428690254688263,
-0.04461047053337097,
-0.023450074717402458,
0.009659419767558575,
-0.07921336591243744,
0.041127827018499374,
-0.016581661999225616,
0.0639306902885437,
0.028396889567375183,
-0.0031837644055485725,
-0.021161919459700584,
0.03703901544213295,
-0.04446043446660042,
0.021895021200180054,
0.016935864463448524,
-0.030740022659301758,
0.022667119279503822,
0.003973625600337982,
-0.07742615044116974,
0.06409462541341782,
-0.05225415155291557,
0.049481820315122604,
-0.054263219237327576,
0.016004502773284912,
-0.004852090030908585,
-0.03354743868112564,
0.004997408948838711,
0.027410296723246574,
0.022097738459706306,
0.012050649151206017,
0.023080555722117424,
0.060556795448064804,
-0.03637877479195595,
-0.0847291350364685,
-0.02434973232448101,
-0.03982355445623398,
-0.027152985334396362,
-0.01612890139222145,
-0.0040855444967746735,
-0.03207649663090706,
0.07522496581077576,
0.060513705015182495,
-0.011611592955887318,
-0.005206455010920763,
0.03720315173268318,
-0.04868395999073982,
0.0036999317817389965,
0.03506552428007126,
0.009129063226282597,
0.009596765041351318,
-0.010362989269196987,
0.025693031027913094,
0.000589358271099627,
0.013396668247878551,
-0.003277901094406843,
0.04100549593567848,
-0.010882058180868626,
-0.008464205078780651,
-0.006853799801319838,
0.0033880951814353466,
-0.0645928829908371,
-0.002917003585025668,
0.013928066939115524,
-0.01954691670835018,
0.0398535393178463,
-0.02787628397345543,
0.008032293058931828,
0.06128118187189102,
0.008132430724799633,
0.01995190419256687,
0.03593452274799347,
-0.005487219430506229,
0.019773202016949654,
0.0489438995718956,
0.0932331308722496,
-0.005120062734931707,
-0.008638382889330387,
-0.011639176867902279,
-0.03443038463592529,
0.01885160245001316,
0.008419291116297245,
0.004381292033940554,
0.04774755984544754,
-0.026917589828372,
0.029661357402801514,
0.0162513367831707,
-0.014813144691288471,
-0.03407568857073784,
0.00899090152233839,
-0.009186021983623505,
0.0019547368865460157,
-0.038849376142024994,
-0.0021100621670484543,
-0.07624436914920807,
-0.014700571075081825,
-0.048872578889131546,
-0.018604665994644165,
0.028603622689843178,
0.0010332216043025255,
0.013450924307107925,
-0.04028357192873955,
-0.08120249211788177,
-0.019764134660363197,
0.052653372287750244,
0.030600247904658318,
0.02297927439212799,
-0.027010854333639145,
-0.01448073796927929,
-0.015332060866057873,
-0.015817414969205856,
-0.03720971941947937,
-0.10082924365997314,
-0.002787541365250945,
-0.02378939650952816,
-0.07985719293355942,
0.0036208350211381912,
-0.0008917676750570536,
0.019665051251649857,
0.02629045955836773,
0.056703899055719376,
-0.006427211221307516,
0.007056368049234152,
0.06224628910422325,
-0.018585512414574623,
0.03877869248390198,
-0.08895411342382431,
0.059432607144117355,
0.02897530607879162,
0.03505285456776619,
-0.027248304337263107,
-0.033797286450862885,
0.001194274751469493,
0.03923099860548973,
-0.006474034395068884,
-0.012298349291086197,
0.03138308972120285,
0.031238902360200882,
-0.045631177723407745,
-0.00817074440419674,
-0.014117683283984661,
0.038246843963861465,
-0.017222533002495766,
-0.02360120415687561,
-0.04493563249707222,
0.06590188294649124,
-0.03600384667515755,
-0.0338144451379776,
-0.024292806163430214,
-0.026792554184794426,
0.04439666494727135,
0.018983595073223114,
-0.0019351036753505468,
-0.03300239518284798,
-0.006443774793297052,
-0.031881462782621384,
0.014936602674424648,
-0.0040476368740201,
-0.007817110978066921,
0.015410691499710083,
-0.0234221201390028,
-0.017205897718667984,
0.0033470354974269867,
-0.08157534897327423,
-0.04445887729525566,
-0.05999614670872688,
0.010338443331420422,
0.05393322557210922,
-0.03393947705626488,
0.004764838609844446,
-0.06896365433931351,
-0.0240369513630867,
-0.018851114436984062,
-0.02131733112037182,
0.06994444131851196,
-0.02536240592598915,
0.00690151983872056,
0.06376180052757263,
-0.05447355657815933,
0.007618135306984186,
-0.03273940086364746,
-0.09598207473754883,
0.015193277969956398,
-0.01596822403371334,
0.014644076116383076,
-0.008358274586498737,
0.018432749435305595,
0.06267692893743515,
0.07571288198232651,
-0.011330670677125454,
0.03096039779484272,
-0.05541341379284859,
-0.00858247373253107,
0.04016833007335663,
0.06208307296037674,
0.02271503023803234,
-0.04877457395195961,
-0.016266342252492905,
-0.13316455483436584,
-0.005586258601397276,
0.03030894137918949,
-0.016435818746685982,
-0.013107330538332462,
-0.08639088273048401,
0.01685512624680996,
-0.06420665979385376,
-0.00873484741896391,
0.038536205887794495
] |
<p>How does the heat energy from the Sun reach us on the Earth? Since the kinetic energy of an atom is the amount of heat energy and there is no matter in space, how does heat from the Sun reach us? </p> | g4744 | [
0.07660956680774689,
0.037431877106428146,
0.008679729886353016,
0.0393417663872242,
-0.058344170451164246,
0.035347387194633484,
-0.009111528284847736,
0.04279142618179321,
-0.04898838326334953,
-0.027683075517416,
0.01991523988544941,
0.050299469381570816,
0.04129396006464958,
-0.013408295810222626,
0.031829800456762314,
-0.01739019714295864,
0.08173474669456482,
-0.022898999974131584,
0.01946639083325863,
0.09460121393203735,
-0.007147172931581736,
-0.045239340513944626,
0.03633894771337509,
-0.05997500196099281,
-0.07346288114786148,
-0.03593475744128227,
0.007820827886462212,
0.003500684630125761,
-0.04568721726536751,
-0.042437318712472916,
0.07162488996982574,
-0.00807842705398798,
0.03079463355243206,
-0.08212029188871384,
-0.04679661989212036,
0.006107173394411802,
0.002848571864888072,
0.013503198511898518,
0.019263410940766335,
-0.05206279084086418,
0.004652936942875385,
-0.01649109274148941,
-0.0012211875291541219,
0.02966848574578762,
0.014488412998616695,
-0.016771476715803146,
-0.01199085358530283,
0.03375411778688431,
0.03802906721830368,
0.04964761063456535,
-0.012373111210763454,
0.03869341313838959,
0.018668070435523987,
0.022601405158638954,
-0.01297406479716301,
-0.028352580964565277,
-0.004593866411596537,
-0.07978884130716324,
0.0819079652428627,
0.03634560853242874,
0.12385501712560654,
-0.004763746168464422,
0.04162130877375603,
0.0002957864780910313,
0.021008668467402458,
-0.0032167620956897736,
-0.03553237020969391,
0.05333105847239494,
-0.020745854824781418,
-0.03690491244196892,
0.010756433010101318,
-0.025385266169905663,
-0.04464445263147354,
-0.03297277167439461,
0.024093884974718094,
-0.05604442209005356,
0.03797231987118721,
-0.04201130568981171,
0.01537526585161686,
0.05368423089385033,
-0.020647156983613968,
-0.019643252715468407,
-0.01682562194764614,
-0.0994592234492302,
-0.001209559035487473,
-0.04429048299789429,
-0.024091172963380814,
0.011046644300222397,
-0.08692797273397446,
0.007763424888253212,
-0.03074343129992485,
0.04436497390270233,
0.11345597356557846,
0.015898164361715317,
-0.03397582098841667,
-0.027204718440771103,
-0.026614157482981682,
0.003930066712200642,
-0.041695088148117065,
-0.04898156225681305,
-0.058526989072561264,
-0.0022986859548836946,
0.034401752054691315,
0.013283563777804375,
0.060224007815122604,
0.003049045568332076,
-0.055236246436834335,
0.01631089486181736,
0.0018272536108270288,
0.01666945219039917,
-0.00031153913005255163,
-0.0310130026191473,
0.016374174505472183,
-0.018489915877580643,
-0.04940112680196762,
-0.020046519115567207,
0.03594350069761276,
-0.06150587648153305,
0.02721034549176693,
0.0681278333067894,
0.019330525770783424,
0.06857199221849442,
0.022322721779346466,
0.07707967609167099,
-0.023471280932426453,
0.023779230192303658,
-0.010851971805095673,
-0.04478539526462555,
-0.032082054764032364,
-0.015171815641224384,
-0.00983175728470087,
0.03912431746721268,
-0.03139312565326691,
0.00563080096617341,
0.007253516465425491,
-0.016591837629675865,
-0.003555439179763198,
0.020534973591566086,
-0.01739971712231636,
0.0072031631134450436,
0.02111195959150791,
0.00058344891294837,
0.05788023769855499,
-0.030281374230980873,
-0.05319464951753616,
0.03352146968245506,
-0.025794481858611107,
-0.011622179299592972,
0.018797384575009346,
0.00959273986518383,
-0.006803910247981548,
0.033779922872781754,
0.05879030004143715,
-0.061242058873176575,
0.013426492922008038,
-0.05110035464167595,
0.03749217465519905,
-0.02327727898955345,
0.010837601497769356,
0.0018122064648196101,
0.04195975884795189,
-0.024409405887126923,
0.04384180158376694,
0.004227622412145138,
-0.0001392077683703974,
-0.02501305378973484,
-0.00244309869594872,
-0.029208514839410782,
0.011596102267503738,
0.017364129424095154,
0.00006477228453150019,
-0.018616599962115288,
-0.02994161657989025,
-0.032267432659864426,
-0.04207776486873627,
0.036714520305395126,
0.05054580420255661,
0.01682909019291401,
-0.04224909842014313,
-0.037522681057453156,
0.0011984877055510879,
-0.05230134353041649,
0.06869282573461533,
-0.04885951057076454,
-0.027849046513438225,
-0.00316793960519135,
-0.05915619060397148,
-0.02362816035747528,
0.04384562373161316,
-0.019021051004529,
-0.021464912220835686,
-0.0669805034995079,
0.05212993919849396,
-0.03979656472802162,
0.033362165093421936,
0.023990239948034286,
-0.022301241755485535,
-0.05508618429303169,
-0.02364952117204666,
-0.0016615779604762793,
0.019122278317809105,
0.04190733656287193,
-0.007811139803379774,
-0.011607999913394451,
0.06787730008363724,
-0.021573098376393318,
0.01929500512778759,
0.01781451888382435,
0.01933983340859413,
-0.02154717408120632,
0.034375566989183426,
-0.049766894429922104,
0.0165418554097414,
-0.008837812580168247,
-0.01461252011358738,
0.04665449634194374,
-0.030417881906032562,
-0.05466455966234207,
-0.01688045635819435,
-0.042307451367378235,
-0.026714516803622246,
0.03982377052307129,
-0.015008537098765373,
-0.011043023318052292,
-0.003667270066216588,
0.06947113573551178,
-0.046459078788757324,
-0.06793855130672455,
0.01947173848748207,
0.0894564539194107,
-0.08406498283147812,
0.012697143480181694,
0.003817871445789933,
-0.001215748954564333,
0.0002752596337813884,
0.014329325407743454,
-0.004775162320584059,
0.006781986448913813,
-0.033944614231586456,
0.06506454944610596,
-0.02108536660671234,
-0.06245977804064751,
-0.036680202931165695,
0.06614828109741211,
0.07296352833509445,
-0.005575674585998058,
0.03268303722143173,
0.003334833774715662,
-0.04276842623949051,
-0.034977395087480545,
0.10173369944095612,
0.004660879261791706,
-0.07464566081762314,
0.0039382451213896275,
-0.0055102212354540825,
-0.03622323274612427,
-0.051514044404029846,
0.024106424301862717,
-0.0536496676504612,
-0.060625091195106506,
-0.0032390588894486427,
-0.04342987760901451,
0.0024939936120063066,
0.042318470776081085,
-0.03484135866165161,
-0.050832267850637436,
-0.05075936019420624,
0.001724793459288776,
0.026951804757118225,
-0.0056996154598891735,
0.008456426672637463,
0.08232276886701584,
-0.00778977619484067,
0.004155137110501528,
0.01720684953033924,
-0.021740831434726715,
0.020125290378928185,
-0.018596423789858818,
0.015011962503194809,
-0.05211002752184868,
0.020756004378199577,
0.06624628603458405,
-0.0067690275609493256,
-0.023726075887680054,
0.03883294016122818,
-0.0565187893807888,
-0.027036238461732864,
0.04715393856167793,
0.06877128034830093,
-0.06996601819992065,
0.03759755939245224,
0.013437075540423393,
0.03694983571767807,
0.018750376999378204,
-0.013691212981939316,
-0.01708739809691906,
0.05803943797945976,
0.006927797570824623,
-0.04251619055867195,
-0.015486151911318302,
0.010607428848743439,
-0.03294243663549423,
-0.024158582091331482,
-0.004417811054736376,
-0.028744636103510857,
-0.005853505339473486,
-0.047122515738010406,
-0.03998730704188347,
0.009510484524071217,
-0.029816586524248123,
0.029164345934987068,
-0.0067018247209489346,
0.014489586465060711,
0.055325012654066086,
-0.01335824839770794,
-0.006822156719863415,
-0.0688949003815651,
-0.020079879090189934,
0.07079527527093887,
-0.0038453545421361923,
0.019883474335074425,
-0.005538544151932001,
-0.059509243816137314,
0.03970005363225937,
-0.01850920170545578,
0.001047774450853467,
0.023148469626903534,
-0.05915997922420502,
-0.050890058279037476,
-0.012024951167404652,
-0.046143461018800735,
0.06884579360485077,
-0.053694047033786774,
-0.010242471471428871,
-0.018472198396921158,
0.0013898623874410987,
-0.05630675330758095,
0.00803398061543703,
0.04186387360095978,
0.08183780312538147,
-0.021382475271821022,
0.018215462565422058,
-0.028377847746014595,
-0.0007106377161107957,
-0.03227786347270012,
0.03782595694065094,
-0.011361217126250267,
-0.003785933367908001,
-0.05856223404407501,
0.0005392993334680796,
0.030068855732679367,
-0.004190757870674133,
-0.03846064582467079,
-0.010815165005624294,
-0.06247512623667717,
0.03638611361384392,
-0.012577933259308338,
0.04917009174823761,
-0.007641015108674765,
0.008424736559391022,
0.053667668253183365,
0.029334379360079765,
0.0712323859333992,
0.016144022345542908,
-0.014100025407969952,
-0.03288041055202484,
0.023857248947024345,
0.002036365447565913,
0.0937337800860405,
0.007153461221605539,
-0.0389045849442482,
-0.02237444557249546,
-0.018516162410378456,
-0.005655959714204073,
0.02779393643140793,
-0.031175198033452034,
0.047329965978860855,
-0.017241420224308968,
-0.054676566272974014,
0.02767564356327057,
-0.02591457962989807,
0.008761582896113396,
0.04418204352259636,
-0.0019354335963726044,
0.05928359925746918,
0.003658613422885537,
-0.053446266800165176,
-0.02405736595392227,
-0.042296990752220154,
-0.038603998720645905,
0.01341507863253355,
-0.0639972984790802,
-0.01497420109808445,
0.042759545147418976,
-0.002770564751699567,
-0.02540292590856552,
0.05299839749932289,
0.05999542772769928,
-0.02837773971259594,
-0.0010768006322905421,
0.023654337972402573,
0.0426299013197422,
0.02914164774119854,
-0.006630242336541414,
0.020762605592608452,
0.058182042092084885,
-0.016531560570001602,
-0.03747577220201492,
-0.06531880050897598,
-0.012474446557462215,
0.04283539950847626,
0.048677314072847366,
-0.023652883246541023,
-0.018002288416028023,
-0.006408218760043383,
-0.017129935324192047,
-0.01400409359484911,
-0.006855944637209177,
0.009324818849563599,
-0.01292075589299202,
-0.04942325875163078,
-0.01708444394171238,
0.02329845167696476,
-0.016374045982956886,
0.015160832554101944,
0.1307867467403412,
0.027324242517352104,
-0.011012994684278965,
0.02104131132364273,
0.013757900334894657,
-0.04678257182240486,
-0.003095433348789811,
0.029015205800533295,
0.06982384622097015,
-0.026391366496682167,
0.028569519519805908,
0.017865190282464027,
-0.001735470606945455,
0.010452457703649998,
-0.009742259979248047,
0.09944379329681396,
0.08248576521873474,
-0.012977252714335918,
0.02415383979678154,
-0.020073408260941505,
0.03487352654337883,
0.042987290769815445,
-0.06247040256857872,
-0.050265196710824966,
-0.016326846554875374,
0.024746548384428024,
-0.004983307793736458,
-0.018933692947030067,
0.050034571439027786,
-0.025019483640789986,
0.05393603816628456,
-0.08739914000034332,
-0.006263768300414085,
-0.005423662252724171,
0.0634218230843544,
-0.036968767642974854,
0.031071675941348076,
0.02914692647755146,
0.040501970797777176,
-0.0059265755116939545,
-0.028004543855786324,
0.002064332365989685,
-0.006187638733536005,
-0.04846038296818733,
-0.001285610836930573,
0.009328453801572323,
0.02451951615512371,
-0.019908074289560318,
0.029529277235269547,
0.017081251367926598,
-0.0011879621306434274,
0.014088320545852184,
-0.05786474421620369,
0.018399154767394066,
-0.0713292583823204,
0.012591132894158363,
0.03715704008936882,
-0.009951840154826641,
0.02681601792573929,
-0.04447624087333679,
0.032017700374126434,
-0.01839037984609604,
0.036932382732629776,
-0.0056737978011369705,
-0.001532973488792777,
-0.037567369639873505,
0.005625493824481964,
-0.01940292865037918,
-0.02703806199133396,
-0.03284550458192825,
0.019459756091237068,
-0.0233602374792099,
-0.00013069240958429873,
0.06947055459022522,
0.04093971475958824,
0.029313933104276657,
0.04262242093682289,
-0.026658881455659866,
-0.0028061866760253906,
0.055964063853025436,
0.0166781023144722,
0.07377323508262634,
0.026248814538121223,
-0.005153621546924114,
0.028192708268761635,
0.034190911799669266,
-0.026307934895157814,
-0.013769194483757019,
0.029124366119503975,
0.0019054264994338155,
-0.030239993706345558,
0.037782687693834305,
-0.01949983648955822,
0.024802835658192635,
0.02611105516552925,
-0.007850260473787785,
-0.004108392633497715,
-0.004663514904677868,
0.017117034643888474,
0.0398649200797081,
0.000513701990712434,
-0.060711801052093506,
0.011929492466151714,
-0.028893450275063515,
0.0594530813395977,
-0.04377421364188194,
0.051698386669158936,
-0.00857885554432869,
-0.005388075951486826,
0.010761174373328686,
0.004461741540580988,
-0.0015026533510535955,
-0.020377276465296745,
0.0007111752638593316,
0.013468989171087742,
-0.006391188129782677,
-0.05780477449297905,
0.009302223101258278,
0.004892235156148672,
0.051183272153139114,
0.013510297983884811,
-0.027991948649287224,
0.023087510839104652,
0.02599325031042099,
-0.014155632816255093,
0.00027225870871916413,
0.0363926999270916,
0.04770465940237045,
-0.002828410593792796,
0.005335936322808266,
0.00905665010213852,
0.018197515979409218,
-0.028965722769498825,
-0.032379526644945145,
-0.027075357735157013,
0.02385704219341278,
0.035522956401109695,
0.04964251071214676,
-0.01782945916056633,
0.0344792976975441,
-0.035221341997385025,
0.0024895723909139633,
-0.07710269093513489,
0.0037599762436002493,
-0.025466151535511017,
0.00917503610253334,
-0.009233253076672554,
0.003528079716488719,
-0.02848302386701107,
0.008601000532507896,
-0.00955908466130495,
-0.034222930669784546,
-0.01821158453822136,
-0.08673927187919617,
-0.05943121016025543,
0.0163265448063612,
0.05202619358897209,
-0.02216891199350357,
-0.030514465644955635,
-0.015405639074742794,
0.016442393884062767,
-0.02699046954512596,
-0.012596922926604748,
0.10102911293506622,
-0.006455885246396065,
-0.016893833875656128,
-0.014289230108261108,
0.012856517918407917,
-0.007525404449552298,
-0.04762023687362671,
-0.05165400728583336,
0.03526415303349495,
0.007515372708439827,
0.038617897778749466,
0.07283337414264679,
-0.0063928356394171715,
0.00444503640756011,
0.01928301900625229,
-0.048326216638088226,
0.05093854293227196,
0.015127052552998066,
0.013846027664840221,
-0.007602004334330559,
0.01730876788496971,
-0.010508807376027107,
-0.0018371430924162269,
0.012175062671303749,
0.016486376523971558,
-0.007589924149215221,
-0.01749567687511444,
0.006137557327747345,
-0.028069688007235527,
-0.03618798777461052,
0.05011611804366112,
-0.01950817182660103,
-0.04547092318534851,
-0.0039352187886834145,
0.016358941793441772,
-0.01060948520898819,
0.03794274106621742,
-0.0043799071572721004,
-0.03962286561727524,
0.05405721813440323,
0.017994500696659088,
-0.007695626001805067,
-0.03161866217851639,
-0.005931135267019272,
-0.027224963530898094,
0.06629117578268051,
0.026993731036782265,
-0.014130238443613052,
0.02806556038558483,
-0.023000109940767288,
-0.018240265548229218,
0.010080228559672832,
-0.04334166273474693,
-0.015959540382027626,
0.006136468145996332,
0.012390214018523693,
-0.03586045280098915,
-0.02067171223461628,
-0.011613022536039352,
-0.02680915966629982,
-0.04281941428780556,
-0.00483367033302784,
-0.007528042886406183,
-0.05068352445960045,
-0.015442227944731712,
0.035293933004140854,
0.020047543570399284,
0.0515904575586319,
-0.0363985113799572,
0.018017912283539772,
-0.014049834571778774,
-0.06294882297515869,
0.049370475113391876,
0.006778424140065908,
0.009799273684620857,
0.027171140536665916,
0.02664106711745262,
0.02714705839753151,
0.007596224080771208,
-0.008402977138757706,
0.023234618827700615,
0.022022794932127,
-0.016302967444062233,
-0.01126868836581707,
-0.027993137016892433,
0.036941781640052795,
-0.02969232201576233,
-0.00028077210299670696,
-0.027543893083930016,
-0.008214017376303673,
-0.015998931601643562,
-0.052077677100896835,
0.016634203493595123,
0.01942809857428074,
0.011807125061750412,
0.011075994931161404,
0.05607984960079193,
0.02612011879682541,
0.011312812566757202,
0.03262043744325638,
0.01191325206309557,
0.05713186785578728,
0.007679223082959652,
0.03391662612557411,
-0.0029232967644929886,
-0.04251326248049736,
0.016078727319836617,
-0.042923443019390106,
0.010873835533857346,
-0.018421657383441925,
0.022471200674772263,
0.0026662417221814394,
0.001492018112912774,
-0.00794126745313406,
0.06806840002536774,
-0.011971833184361458,
0.0276656337082386,
0.004896782338619232,
0.04343746230006218,
-0.008734253235161304,
-0.03384095057845116,
-0.0510835200548172,
0.06763744354248047,
0.03019709885120392,
0.02109733410179615,
0.07877223193645477,
0.006968771573156118,
-0.006751101929694414,
-0.03997431695461273,
-0.007626554928719997,
0.02343742921948433,
-0.0404689759016037,
0.007085827179253101,
-0.03431873768568039,
0.011978937312960625,
-0.015416919253766537,
-0.019291257485747337,
0.05134885758161545,
-0.0183267779648304,
-0.07009655982255936,
0.010559407994151115,
-0.03948080912232399,
0.043738074600696564,
0.04809717461466789,
-0.014715516939759254,
-0.04143522307276726,
-0.021999966353178024,
0.009172632358968258,
0.007483819965273142,
-0.08828073740005493,
0.08250950276851654,
-0.015385658480226994,
-0.022346779704093933,
-0.033853087574243546,
0.0010268884943798184,
-0.02713298425078392,
0.010468369349837303,
-0.0348648801445961,
-0.07578589767217636,
0.03446066007018089,
0.025565918534994125,
-0.01912805624306202,
-0.0018346544820815325,
0.030921725556254387,
-0.021049605682492256,
0.00543232960626483,
-0.01985284499824047,
-0.054286252707242966,
-0.005592184141278267,
-0.0005792042938992381,
-0.05367431044578552,
0.013642611913383007,
0.009346649050712585,
-0.042627062648534775,
0.017895538359880447,
0.002929442562162876,
0.02834167331457138,
-0.04011711850762367,
-0.004381121601909399,
-0.026889093220233917
] |
<p>How do scientists measure the distance between objects in space? For example, <a href="http://en.wikipedia.org/wiki/Alpha_Centauri" rel="nofollow">Alpha Centauri</a> is 4.3 light years away.</p> | g4745 | [
0.0056598675437271595,
0.0027517122216522694,
-0.021504275500774384,
-0.053068771958351135,
0.0055665019899606705,
0.05103272572159767,
-0.036661796271800995,
0.0197015218436718,
-0.03464275971055031,
-0.055665258318185806,
0.011105128563940525,
-0.01181085780262947,
0.02547866478562355,
0.0115251075476408,
0.04859108105301857,
-0.0022731455974280834,
0.06940115243196487,
-0.04711372032761574,
0.048329513520002365,
0.006936416495591402,
0.1115977019071579,
-0.01470818929374218,
0.015130138024687767,
-0.031211739405989647,
-0.017266731709241867,
-0.0436314158141613,
-0.01660894975066185,
0.002922212239354849,
-0.0518471859395504,
0.003375980071723461,
0.024363631382584572,
-0.002702227560803294,
0.056140899658203125,
-0.040171388536691666,
0.04417843371629715,
-0.019139546900987625,
-0.034454263746738434,
0.03035428375005722,
0.027320193126797676,
0.016318779438734055,
-0.03807935491204262,
0.001324156066402793,
0.026108834892511368,
-0.018238626420497894,
0.09102742373943329,
0.0020448772702366114,
-0.058514561504125595,
-0.034030284732580185,
0.05101333558559418,
0.016594581305980682,
-0.011405927129089832,
0.044614918529987335,
0.0026724778581410646,
0.07272779196500778,
0.022277384996414185,
0.008721784688532352,
0.0185451228171587,
-0.05397024378180504,
0.10603217035531998,
-0.01498022023588419,
-0.008264251984655857,
-0.013366363942623138,
0.020097646862268448,
-0.0034787023905664682,
0.06665489077568054,
-0.011985012330114841,
0.016591554507613182,
0.03488653898239136,
-0.005887689534574747,
0.0025924094952642918,
0.004411831498146057,
-0.016917424276471138,
-0.007294067181646824,
0.0027603688649833202,
-0.09874455630779266,
0.03583782538771629,
0.023651041090488434,
0.017728228121995926,
0.036983657628297806,
0.0766739770770073,
-0.008784095756709576,
-0.004880900960415602,
0.011715861037373543,
-0.006464201025664806,
0.06473221629858017,
0.001828791224397719,
-0.028780531138181686,
-0.020670060068368912,
0.00849096942692995,
-0.002049434930086136,
0.008872760459780693,
0.02337084338068962,
0.048220861703157425,
-0.01890834979712963,
-0.003650408936664462,
-0.015639275312423706,
-0.03849314525723457,
0.0080540357157588,
-0.014374980702996254,
-0.02683883160352707,
-0.05785788223147392,
0.053515590727329254,
0.013615422882139683,
-0.005612414330244064,
0.04461789131164551,
0.023761054500937462,
0.01466083712875843,
-0.015271725133061409,
-0.0024115387350320816,
-0.0063537838868796825,
-0.06051585450768471,
-0.03829726204276085,
0.02133181318640709,
-0.023162957280874252,
0.02066560834646225,
-0.04955989867448807,
0.04465092718601227,
-0.003387071890756488,
0.040001485496759415,
0.006302539259195328,
-0.02617967315018177,
0.0402807891368866,
0.03367822989821434,
0.02118654176592827,
-0.05874185264110565,
-0.0016874046996235847,
0.0339801199734211,
-0.01771278865635395,
0.02176247350871563,
0.004693083930760622,
-0.03566212207078934,
0.03107590228319168,
0.009425442665815353,
-0.010828796774148941,
-0.05401855707168579,
0.02577374503016472,
0.008069487288594246,
-0.01850380375981331,
-0.046473514288663864,
0.052128866314888,
0.030533142387866974,
-0.06666058301925659,
0.03187630698084831,
-0.05659520626068115,
-0.01394687034189701,
-0.04438707232475281,
-0.028347017243504524,
0.0012870668433606625,
0.025553908199071884,
-0.00019646610599011183,
0.00918383989483118,
0.08656517416238785,
0.056387752294540405,
0.01707947999238968,
0.0195073913782835,
-0.021895790472626686,
-0.005363983102142811,
0.016516998410224915,
-0.025922849774360657,
-0.02466166391968727,
0.04800355061888695,
-0.052074093371629715,
0.01671820692718029,
0.005423212423920631,
-0.05606875941157341,
0.022645622491836548,
0.025065220892429352,
-0.05859340727329254,
0.03273025155067444,
-0.06948975473642349,
-0.07500328123569489,
-0.011165727861225605,
0.0604870431125164,
0.011135369539260864,
-0.02413315698504448,
0.07689055055379868,
-0.04056144133210182,
-0.01069718413054943,
0.0050916532054543495,
-0.009983465075492859,
-0.0004211598716210574,
-0.039606723934412,
0.05608376860618591,
0.037748951464891434,
-0.030441995710134506,
-0.00024979241425171494,
-0.004901408683508635,
-0.05946267768740654,
-0.0044397106394171715,
0.06455554068088531,
0.012424865737557411,
-0.023352427408099174,
0.022273916751146317,
-0.03257221356034279,
0.014361741952598095,
0.012734993360936642,
0.03721601888537407,
-0.04281088337302208,
-0.025233162567019463,
0.0153527045622468,
-0.04240315780043602,
0.011626589111983776,
-0.005021854769438505,
0.019881146028637886,
0.038275882601737976,
-0.05092167109251022,
0.012800644151866436,
-0.04771493002772331,
0.0060737282037734985,
0.0016929926350712776,
-0.010808863677084446,
0.02167128585278988,
-0.020252138376235962,
-0.024366263300180435,
-0.06713451445102692,
0.02022712677717209,
0.011644306592643261,
0.003958211746066809,
-0.008180215954780579,
0.024289116263389587,
0.007433110382407904,
-0.002139708725735545,
0.09463202208280563,
-0.06550922989845276,
0.03807255998253822,
0.026385942474007607,
-0.038291413336992264,
0.04554639756679535,
0.015532080084085464,
0.03390815481543541,
-0.05336853861808777,
-0.02809278666973114,
-0.05123260244727135,
0.007328884210437536,
0.0897475853562355,
0.043580736964941025,
0.01689428836107254,
0.013588287867605686,
-0.02837369777262211,
0.07962281256914139,
0.0511704683303833,
-0.07531921565532684,
-0.0437064953148365,
0.0072198533453047276,
0.006600440479815006,
-0.023692235350608826,
0.019648287445306778,
-0.009220731444656849,
-0.0774674192070961,
-0.015760092064738274,
0.04789808765053749,
0.038137033581733704,
-0.008955028839409351,
-0.005974626634269953,
-0.01467616856098175,
-0.02068050019443035,
-0.04457303136587143,
0.03605009987950325,
-0.09385069459676743,
-0.021052507683634758,
-0.005024716258049011,
-0.031004318967461586,
0.05153443291783333,
-0.06360512226819992,
0.024008339270949364,
-0.036917805671691895,
-0.05777003616094589,
0.003199799684807658,
-0.019295411184430122,
-0.01310655102133751,
-0.032839179039001465,
0.03105614334344864,
0.06947719305753708,
-0.026928329840302467,
-0.04559064656496048,
0.023038901388645172,
0.02127833291888237,
0.012991022318601608,
0.0514870248734951,
0.006773411296308041,
0.014581135474145412,
0.03329738974571228,
-0.05834133177995682,
-0.012364072725176811,
-0.02978266030550003,
-0.022329170256853104,
0.015389587730169296,
0.04967755079269409,
-0.013721761293709278,
-0.03181957080960274,
0.04012937471270561,
-0.02611217275261879,
0.01910066045820713,
-0.024129614233970642,
0.002127148909494281,
0.03937803581357002,
0.0773824006319046,
0.06916577368974686,
0.029476195573806763,
-0.024494944140315056,
-0.011301586404442787,
-0.027418067678809166,
0.022728215903043747,
-0.017652565613389015,
-0.002072725910693407,
-0.045473940670490265,
-0.004573776852339506,
-0.06947247684001923,
-0.021039661020040512,
-0.015415612608194351,
0.03135760501027107,
0.0030367730651050806,
0.013591092079877853,
0.01810629293322563,
0.009067968465387821,
-0.058672428131103516,
-0.010968947783112526,
0.039321474730968475,
0.051336538046598434,
0.03382931277155876,
0.04036155343055725,
-0.062350645661354065,
-0.02297781966626644,
-0.019619928672909737,
0.00804995372891426,
-0.025853553786873817,
-0.017058828845620155,
-0.008766749873757362,
-0.0333310104906559,
-0.03244289010763168,
-0.022105664014816284,
0.030506880953907967,
-0.005268750712275505,
-0.05968897417187691,
-0.0476849302649498,
-0.0265981312841177,
-0.028959494084119797,
0.05544328689575195,
0.01725165732204914,
0.0449099987745285,
-0.005929108709096909,
-0.04433535784482956,
-0.02934279665350914,
0.0009998624445870519,
0.02164875902235508,
0.06300655752420425,
0.03962814062833786,
0.03219205513596535,
0.0022238248493522406,
-0.06676026433706284,
-0.02166149578988552,
0.021835703402757645,
-0.00002816322012222372,
-0.05406063050031662,
0.049168139696121216,
0.017530515789985657,
-0.01908155158162117,
-0.0025966884568333626,
0.010191951878368855,
-0.031075414270162582,
0.0520486943423748,
0.02408825233578682,
-0.025070851668715477,
-0.0015080907614901662,
-0.014394272118806839,
-0.03751005977392197,
0.010877490043640137,
0.011415735818445683,
0.0981740802526474,
-0.011085951700806618,
0.0043195397593081,
0.01368929073214531,
0.03279881924390793,
0.004905328620225191,
0.027825040742754936,
-0.04856039956212044,
0.02884235419332981,
-0.04306446760892868,
-0.02580851875245571,
0.02149083837866783,
0.007332347333431244,
0.07028523087501526,
-0.002633294789120555,
-0.0788855031132698,
0.017043061554431915,
-0.010749892331659794,
-0.059396892786026,
-0.02479209005832672,
0.0009683624375611544,
-0.07751989364624023,
-0.006773676723241806,
-0.04397590458393097,
-0.04049289599061012,
-0.04249207675457001,
0.01734660565853119,
-0.03747328370809555,
0.02417115867137909,
0.02004738338291645,
-0.030400540679693222,
0.03125523775815964,
-0.043605078011751175,
0.027300525456666946,
0.0006386892055161297,
-0.0054478878155350685,
-0.03385470435023308,
-0.03698529303073883,
0.0028039684984833,
0.011309636756777763,
-0.048773400485515594,
0.027482768520712852,
-0.005020710173994303,
0.017812730744481087,
0.007308881264179945,
-0.08353504538536072,
0.02463110350072384,
-0.02314506471157074,
0.008279366418719292,
-0.030445320531725883,
-0.004489957820624113,
0.051738373935222626,
-0.028363054618239403,
0.011787455528974533,
0.008946838788688183,
0.017742767930030823,
-0.0016020622570067644,
0.06937275826931,
0.006217199843376875,
0.03574857488274574,
0.01663970947265625,
0.03923855349421501,
0.02396123670041561,
0.0230050440877676,
0.03593970835208893,
0.05900031700730324,
-0.07632793486118317,
0.022101106122136116,
0.02386949025094509,
0.016711300238966942,
0.051836080849170685,
-0.04079459607601166,
-0.00006447959458455443,
0.0365130640566349,
0.0032845160458236933,
-0.03861644119024277,
-0.017209846526384354,
0.09986372292041779,
-0.01222245767712593,
-0.027114391326904297,
-0.019420508295297623,
0.021846657618880272,
-0.007207013200968504,
0.009825333952903748,
-0.08017921447753906,
0.011850510723888874,
0.014528952538967133,
-0.013890613801777363,
0.00839485414326191,
0.021412326022982597,
0.0391579195857048,
-0.001560671254992485,
-0.05088827759027481,
-0.02085203491151333,
-0.014393262565135956,
-0.003340762574225664,
0.015428576618432999,
0.00657547265291214,
0.006083603948354721,
-0.045840077102184296,
-0.04684535413980484,
0.006214440334588289,
0.0010742032900452614,
0.017927195876836777,
-0.03398570790886879,
0.027032937854528427,
-0.06482183933258057,
0.037205733358860016,
-0.012972668744623661,
0.045010246336460114,
0.004140596371144056,
-0.023367276415228844,
-0.006953992880880833,
-0.0017479968955740333,
0.0025047529488801956,
-0.02466658130288124,
0.00041371231782250106,
0.04583554342389107,
-0.06524341553449631,
0.0073418887332081795,
0.010171364061534405,
0.0335063673555851,
-0.03553135693073273,
-0.02966926619410515,
-0.0027387284208089113,
-0.04499723017215729,
-0.07135450094938278,
-0.0286558847874403,
-0.0005520522245205939,
0.022917313501238823,
-0.00015483662718906999,
-0.009027943946421146,
-0.017014816403388977,
0.04560672864317894,
0.006126159802079201,
-0.0132373608648777,
-0.008101549930870533,
0.06992510706186295,
0.04554405063390732,
-0.02567070908844471,
0.0367577001452446,
0.02630745805799961,
0.020124394446611404,
0.01790793053805828,
-0.005983980372548103,
0.032487232238054276,
-0.013015327043831348,
-0.012430981732904911,
0.0048780543729662895,
0.05997039005160332,
-0.029116112738847733,
-0.014841701835393906,
-0.025279570370912552,
-0.0216607004404068,
0.030540162697434425,
0.018213460221886635,
0.018435485661029816,
-0.030256403610110283,
-0.030185703188180923,
-0.0017335269367322326,
0.03556450083851814,
0.009999818168580532,
-0.01892220973968506,
-0.0101869972422719,
-0.00043993486906401813,
-0.003809837158769369,
0.00002178265458496753,
-0.03687478229403496,
-0.0025471264962106943,
0.013331194408237934,
0.03789190202951431,
-0.044366803020238876,
-0.01895391009747982,
0.008906051516532898,
-0.02556765452027321,
0.0639665350317955,
0.001675776788033545,
-0.0281948484480381,
0.023797951638698578,
0.00513248797506094,
0.07416149973869324,
-0.06130854785442352,
0.008101597428321838,
-0.02840285934507847,
0.062187690287828445,
0.025152217596769333,
0.028993306681513786,
0.0044922782108187675,
0.049666307866573334,
-0.041253332048654556,
-0.06483602523803711,
-0.006708316970616579,
0.03250653296709061,
-0.020512524992227554,
0.007974312640726566,
0.008978818543255329,
0.014631080441176891,
-0.10718542337417603,
-0.014118008315563202,
-0.013616223819553852,
0.07989674806594849,
0.027154816314578056,
-0.011983441188931465,
-0.05118144303560257,
0.006089883856475353,
-0.04363960772752762,
0.018206315115094185,
0.02580968663096428,
-0.00292946002446115,
-0.0011222882894799113,
-0.07605704665184021,
0.023895414546132088,
0.003037509508430958,
0.0037799570709466934,
0.06184530258178711,
-0.025352032855153084,
-0.009091169573366642,
0.05830993503332138,
0.03927016258239746,
-0.017247913405299187,
0.04833441227674484,
-0.054188720881938934,
0.029330793768167496,
-0.06778419762849808,
-0.012353645637631416,
-0.04860999435186386,
-0.08077867329120636,
0.0028349938802421093,
-0.019643275067210197,
0.036784473806619644,
-0.0206209197640419,
0.04463791474699974,
-0.03318437561392784,
-0.018996838480234146,
0.07111117243766785,
0.03972743824124336,
0.037368789315223694,
0.0329856313765049,
-0.05431068688631058,
0.010715845040977001,
0.032598577439785004,
-0.07452672719955444,
-0.03939821943640709,
0.06232260912656784,
-0.0026544304564595222,
0.022823503240942955,
-0.013883859850466251,
0.024615062400698662,
0.02498769573867321,
-0.07856185734272003,
-0.049526240676641464,
0.04115217179059982,
0.007500618230551481,
-0.01918497122824192,
-0.026650192216038704,
0.01036414410918951,
0.020973077043890953,
0.02081504836678505,
-0.018627474084496498,
-0.03683656454086304,
0.010804429650306702,
0.0105725834146142,
-0.008425725623965263,
-0.024795226752758026,
0.05058578774333,
0.06306448578834534,
0.02711227536201477,
0.022551173344254494,
-0.029228970408439636,
0.04316717013716698,
0.062460094690322876,
0.04795648530125618,
0.024056676775217056,
0.004192092921584845,
0.03837495297193527,
-0.002091790549457073,
-0.02975129708647728,
-0.02833566628396511,
-0.026848260313272476,
0.03710302338004112,
-0.05683862417936325,
-0.013952733017504215,
0.01454724371433258,
-0.038804635405540466,
0.01323556900024414,
0.00873470026999712,
-0.02266933023929596,
0.08399149775505066,
0.003111959435045719,
-0.011923272162675858,
-0.011946486309170723,
-0.030118681490421295,
-0.010145558975636959,
-0.03946855291724205,
-0.007752557750791311,
0.008572885766625404,
0.013563341461122036,
0.012742161750793457,
-0.030859332531690598,
-0.07029809802770615,
0.0013990633888170123,
-0.016822371631860733,
-0.008678454905748367,
-0.011003421619534492,
-0.06377624720335007,
-0.026797952130436897,
-0.02784026972949505,
0.018536288291215897,
0.026556216180324554,
-0.04485660046339035,
-0.03450814634561539,
-0.011030652560293674,
0.035694777965545654,
0.03011508472263813,
0.004018609412014484,
-0.017416220158338547,
-0.020467586815357208,
0.06088078022003174,
-0.05143314599990845,
0.017520742490887642,
0.05345272272825241,
-0.04700535908341408,
-0.0313519723713398,
0.04165450856089592,
-0.0649394765496254,
-0.09120391309261322,
0.028216049075126648,
-0.014991198666393757,
0.058494068682193756,
0.03085928037762642,
0.0044499835930764675,
-0.045042917132377625,
0.0013098259223625064,
-0.022770842537283897,
0.09910856932401657,
-0.01221510674804449,
0.05956851691007614,
-0.029434163123369217,
-0.027304980903863907,
0.07475635409355164,
-0.029931282624602318,
-0.02897893823683262,
0.007339646108448505,
0.05583668500185013,
-0.004427045118063688,
-0.018129577860236168,
0.014752143062651157,
0.028016801923513412,
0.02062729001045227,
0.012721268460154533,
-0.00018425412417855114,
-0.025592634454369545,
0.06080366298556328,
-0.05735483393073082,
0.05297400429844856,
-0.031076449900865555,
-0.0017767256358638406,
0.03647633641958237,
0.03769003972411156,
-0.03498475253582001,
0.0431765578687191,
-0.051824212074279785,
-0.010445167310535908,
0.056553471833467484,
-0.036827605217695236,
0.01692628674209118,
-0.056357242166996,
0.011674863286316395,
0.009455928578972816,
-0.04706132784485817,
-0.016202053055167198,
0.008759754709899426,
-0.00798678770661354,
0.025105850771069527,
0.016213854774832726,
-0.006852251477539539,
0.005601018201559782,
-0.07121381163597107,
0.011625919491052628,
0.05524187907576561,
0.019486136734485626,
-0.03560565039515495,
0.05554720386862755,
0.05517222359776497,
0.02402900904417038,
-0.020512307062745094,
0.007049353327602148,
-0.03437301889061928,
-0.003349434118717909,
-0.022895073518157005,
-0.016583193093538284,
-0.02794307842850685,
0.035203274339437485,
0.008505395613610744,
-0.004681429360061884,
0.061547428369522095,
-0.09045235067605972,
-0.033704400062561035,
-0.03681221604347229,
-0.00997148733586073
] |
<p>On one hand, in the classical electrodynamics polarization of transparent media yields in lowering the speed of light by the factor of $n=\sqrt{\epsilon_r \mu_r}$ (refractive index).
On the other, in the quantum field theory the vacuum polarization does not decrease the speed of light. The thing it does is increase of strength of electromagnetic interaction. Why is it so?</p>
<p>My two guesses are the following:</p>
<ul>
<li>In principle the vacuum polarization does decrease speed of light ($\rightarrow 0$) but we implicitly put on-shell renormalization to keep $c$ constant.</li>
<li>For some reason the process is completely different from polarization of transparent media.</li>
</ul> | g4746 | [
0.05051605403423309,
-0.007668580859899521,
0.00396408885717392,
0.0046163080260157585,
0.06979402899742126,
0.06383249163627625,
-0.004854144528508186,
0.017166703939437866,
0.025953663513064384,
0.002536054700613022,
0.014648603275418282,
0.027114536613225937,
-0.028847958892583847,
0.06685150414705276,
-0.0007419834146276116,
0.00906754843890667,
0.06369175016880035,
-0.038579702377319336,
0.05762573704123497,
-0.019696323201060295,
-0.04867791384458542,
0.012622418813407421,
0.0008552385843358934,
-0.05837210640311241,
-0.03033316507935524,
0.028766578063368797,
0.027984872460365295,
0.012964162044227123,
0.0013103829696774483,
-0.007092706859111786,
0.02270565740764141,
0.0018361835973337293,
0.024469399824738503,
-0.03898530825972557,
-0.0031992103904485703,
-0.03349420055747032,
0.04507984220981598,
0.06923084706068039,
-0.000816020998172462,
0.0011815038742497563,
-0.014201191253960133,
0.016291795298457146,
0.02238943800330162,
0.03833945840597153,
0.008421995677053928,
-0.06935767829418182,
-0.032692406326532364,
0.012951909564435482,
-0.035123832523822784,
-0.009521408937871456,
0.0062841190956532955,
0.0053299665451049805,
0.0534239299595356,
-0.018192684277892113,
0.02571183443069458,
0.004244269337505102,
-0.05202460289001465,
-0.04876360669732094,
0.05322980508208275,
0.023710044100880623,
0.01843302696943283,
-0.05002110078930855,
0.056073807179927826,
0.002066618762910366,
0.06224493309855461,
-0.017014693468809128,
-0.018815606832504272,
0.017647773027420044,
-0.0024223520886152983,
0.025265933945775032,
-0.04085993766784668,
-0.012605397962033749,
-0.043837327510118484,
-0.03518638759851456,
0.0028682237025350332,
-0.014461133629083633,
0.011818376369774342,
-0.05602801591157913,
0.020671069622039795,
-0.011797926388680935,
0.013806895352900028,
-0.01991656795144081,
-0.03720897436141968,
0.021189264953136444,
0.0016711871139705181,
-0.0434977263212204,
0.028463957831263542,
-0.029829947277903557,
-0.04178820922970772,
0.015267225913703442,
0.008974766358733177,
-0.058212269097566605,
0.0033271941356360912,
0.05914727598428726,
0.001989357639104128,
0.004525086842477322,
0.005453983321785927,
0.046122316271066666,
-0.01517555769532919,
-0.012138503603637218,
-0.03706006333231926,
-0.013422396034002304,
0.04213796928524971,
-0.036126598715782166,
0.026246538385748863,
0.01740790531039238,
-0.026360109448432922,
-0.006577903870493174,
-0.010936865583062172,
0.05476496368646622,
-0.059965524822473526,
-0.06445085257291794,
-0.0738791897892952,
-0.055934395641088486,
0.008726894855499268,
-0.057506125420331955,
0.053606919944286346,
-0.023056529462337494,
-0.007061996031552553,
0.024575255811214447,
0.020419487729668617,
0.036697592586278915,
0.010420440696179867,
-0.03389188274741173,
-0.00827035866677761,
0.0031555236782878637,
-0.003129013581201434,
-0.02460624650120735,
0.030002465471625328,
-0.021212507039308548,
0.00499883433803916,
-0.018437393009662628,
-0.009575679898262024,
0.04690093547105789,
-0.015578292310237885,
0.03833494335412979,
0.010464818216860294,
-0.02885628119111061,
-0.006113503128290176,
-0.05873655155301094,
-0.029727816581726074,
0.0204016100615263,
-0.026942480355501175,
-0.017210768535733223,
-0.028533125296235085,
-0.01116752065718174,
0.07111527025699615,
0.024141445755958557,
0.016236720606684685,
-0.01958969421684742,
0.07342137396335602,
0.08006314188241959,
0.001001022639684379,
-0.004614199046045542,
-0.054527126252651215,
0.026198258623480797,
0.06358025968074799,
-0.015483800321817398,
0.008242746815085411,
0.03557807207107544,
0.06120294705033302,
0.013378226198256016,
0.0003851157962344587,
-0.015386853367090225,
-0.019014915451407433,
0.0205533504486084,
0.035255350172519684,
-0.017076902091503143,
-0.003614873392507434,
-0.08340462297201157,
-0.051151346415281296,
0.05087863281369209,
0.002570785814896226,
0.1023203581571579,
0.0037352037616074085,
0.04791337996721268,
0.039742328226566315,
0.017118949443101883,
-0.051664937287569046,
0.01901930384337902,
-0.018729081377387047,
-0.03018573857843876,
-0.008553274907171726,
-0.047971129417419434,
0.04593987390398979,
-0.0356384702026844,
0.016752565279603004,
0.01694354973733425,
-0.12817183136940002,
-0.004910726565867662,
0.009351606480777264,
-0.005392390303313732,
-0.021313151344656944,
0.031662244349718094,
-0.05387912690639496,
-0.003895979840308428,
0.018824592232704163,
-0.018988139927387238,
-0.013393922708928585,
0.016775866970419884,
-0.08543775975704193,
0.03803631663322449,
0.029902061447501183,
0.01865520142018795,
0.02380920946598053,
-0.01031304057687521,
-0.006297719664871693,
-0.015149394981563091,
0.01781449094414711,
0.0020634611137211323,
0.03450101241469383,
0.018122849985957146,
-0.026061998680233955,
-0.013242598623037338,
0.019267290830612183,
0.07487230002880096,
0.020825795829296112,
0.01274407934397459,
-0.0038970850873738527,
0.024730319157242775,
-0.029708249494433403,
-0.014402209781110287,
-0.017404580488801003,
-0.0052262041717767715,
-0.06321479380130768,
-0.09391646087169647,
-0.055584926158189774,
0.0511990562081337,
0.02862829715013504,
0.05366566404700279,
-0.05634654313325882,
0.02143203280866146,
-0.03799818456172943,
0.06342466175556183,
0.016303470358252525,
0.01587555557489395,
-0.057273805141448975,
-0.022340409457683563,
0.07918111979961395,
0.04360281676054001,
0.0008434029296040535,
-0.007444026414304972,
-0.04473381116986275,
0.03831344470381737,
-0.002226754557341337,
-0.023343117907643318,
-0.014165743254125118,
-0.07451041787862778,
-0.014658339321613312,
0.05120619758963585,
0.025966735556721687,
0.06776417046785355,
0.0300629623234272,
-0.01647673361003399,
0.012234589084982872,
-0.021982289850711823,
-0.0428093783557415,
0.04651093855500221,
-0.045923490077257156,
0.005900694523006678,
-0.0031358564738184214,
0.017607752233743668,
0.02317289263010025,
0.02198796719312668,
-0.03367197886109352,
0.04403005540370941,
-0.028794126585125923,
0.10037224739789963,
0.04311079904437065,
0.016332222148776054,
-0.056206390261650085,
0.08661681413650513,
-0.0351470448076725,
0.013022609986364841,
0.013096772134304047,
-0.02103530615568161,
0.05819953978061676,
-0.01539414282888174,
0.05149749666452408,
-0.04101831465959549,
-0.07724390923976898,
-0.020226091146469116,
-0.03856188803911209,
-0.025812700390815735,
-0.006174696143716574,
-0.09180496633052826,
0.0125332185998559,
0.01242948416620493,
-0.03105444647371769,
0.03468438610434532,
0.0041374871507287025,
0.07936418801546097,
-0.012545416131615639,
-0.01382418442517519,
0.020757537335157394,
0.015079043805599213,
0.07331673800945282,
-0.03307413309812546,
-0.03380274027585983,
0.019180387258529663,
-0.013656568713486195,
-0.021462900564074516,
-0.047179847955703735,
0.04015583172440529,
0.03935280442237854,
-0.0016389705706387758,
-0.03768596053123474,
-0.03216332197189331,
0.0012056283885613084,
0.02102530375123024,
-0.005143214017152786,
0.011304457671940327,
-0.012694024480879307,
-0.0036248271353542805,
-0.05283833295106888,
0.01604912057518959,
0.026976266875863075,
0.013470270670950413,
0.05739782005548477,
0.07137513160705566,
0.010304092429578304,
-0.024774493649601936,
0.013938289135694504,
-0.024223048239946365,
0.026796190068125725,
-0.03568580001592636,
0.011872826144099236,
0.051744747906923294,
0.03583858534693718,
0.005917521193623543,
0.0415167473256588,
0.010015850886702538,
0.0010789873776957393,
-0.024770645424723625,
-0.09530646353960037,
0.03527010977268219,
-0.0842619314789772,
0.05458829179406166,
0.04214392974972725,
-0.022548405453562737,
0.013249489478766918,
-0.024181539192795753,
-0.04667157307267189,
0.07649736851453781,
0.013396671041846275,
0.02722741663455963,
-0.003791195573285222,
-0.04221855849027634,
-0.028234796598553658,
0.0405859500169754,
0.025714443996548653,
0.00995547790080309,
0.024892335757613182,
-0.014707984402775764,
-0.09198548644781113,
0.019984465092420578,
0.004606446251273155,
0.06102913245558739,
0.06163973733782768,
-0.06660595536231995,
0.012660795822739601,
-0.029464423656463623,
0.02356111630797386,
-0.052336953580379486,
-0.058687418699264526,
-0.016936661675572395,
-0.010099410079419613,
0.007702167145907879,
-0.04102344065904617,
0.0597318559885025,
-0.00542698847129941,
-0.017177842557430267,
-0.027859069406986237,
0.06661555916070938,
0.024827318266034126,
0.040636081248521805,
-0.03617936372756958,
0.036736249923706055,
-0.06531370431184769,
0.024652991443872452,
0.03861135244369507,
-0.003652033396065235,
-0.002457680879160762,
0.028503911569714546,
0.0028997461777180433,
0.029385767877101898,
-0.08047912269830704,
0.003810379421338439,
-0.009908143430948257,
-0.03746972233057022,
-0.028361080214381218,
0.05281619727611542,
-0.03428519144654274,
-0.003391449572518468,
-0.02791251614689827,
-0.006734250579029322,
0.0441281795501709,
0.005708595272153616,
0.02850918658077717,
-0.032747723162174225,
0.02437736466526985,
0.012558995746076107,
-0.008070235140621662,
0.03534051030874252,
-0.00498002115637064,
0.008511857129633427,
0.009927812963724136,
0.021355710923671722,
-0.0003867864143103361,
-0.06239382550120354,
0.004028212279081345,
-0.005581294652074575,
-0.058688536286354065,
-0.032017916440963745,
0.0010447767563164234,
0.040253352373838425,
-0.002113304566591978,
-0.014985192567110062,
0.0074551827274262905,
-0.02853343077003956,
0.04228599742054939,
-0.0023326727095991373,
-0.031009119004011154,
0.034730616956949234,
-0.03327908366918564,
0.06336948275566101,
0.06446189433336258,
-0.005266367457807064,
0.0017768966499716043,
-0.07186585664749146,
0.041243601590394974,
0.016315722838044167,
-0.02099541202187538,
0.032389163970947266,
-0.03371141478419304,
0.05184539034962654,
-0.014972792007029057,
0.0493791401386261,
-0.0012908501084893942,
0.028064904734492302,
0.09820832312107086,
-0.024813007563352585,
0.0218659657984972,
-0.05694759637117386,
-0.005096483509987593,
0.06976805627346039,
-0.028552349656820297,
-0.012190435081720352,
-0.010794970206916332,
-0.020799271762371063,
-0.012718228623270988,
0.03429670259356499,
0.020937016233801842,
-0.029398910701274872,
0.0006438982090912759,
-0.019193602725863457,
-0.05770287662744522,
0.06199385225772858,
0.0867265984416008,
0.001156393438577652,
-0.06627235561609268,
0.06951526552438736,
-0.0025240140967071056,
-0.0015981737524271011,
0.04602993279695511,
-0.0019097811309620738,
-0.0060982052236795425,
-0.003412440186366439,
-0.08703576028347015,
0.010339468717575073,
-0.020031074061989784,
-0.013265742920339108,
0.018467245623469353,
0.008440176025032997,
-0.026921335607767105,
-0.02036307193338871,
-0.03362702205777168,
-0.008220763877034187,
-0.01365646906197071,
-0.058880630880594254,
-0.0083840973675251,
-0.03642214834690094,
0.04560761898756027,
-0.028077948838472366,
-0.06119047850370407,
0.030916349962353706,
-0.05110383778810501,
0.09328682720661163,
-0.04806240648031235,
-0.07673977315425873,
0.004041779786348343,
0.008811943233013153,
-0.034290071576833725,
-0.03026130609214306,
-0.0030535294208675623,
0.04675593599677086,
0.054067257791757584,
-0.006140303798019886,
-0.02689790166914463,
-0.012838446535170078,
-0.0751069039106369,
-0.0354466438293457,
-0.020365431904792786,
-0.016551978886127472,
-0.028368337079882622,
-0.027298372238874435,
0.029629504308104515,
0.02219351939857006,
0.02673679031431675,
0.05143424868583679,
0.0060050529427826405,
-0.027486324310302734,
0.01232867781072855,
0.02285878360271454,
0.003136485582217574,
0.01063651405274868,
-0.017973771318793297,
0.002632601885125041,
0.011642423458397388,
-0.04060334712266922,
0.006588358897715807,
0.0026499787345528603,
-0.03569885343313217,
-0.037665702402591705,
0.018008749932050705,
0.02800348401069641,
-0.05352910980582237,
0.0027268293779343367,
0.028164179995656013,
-0.007702302187681198,
0.03386051580309868,
0.05855058133602142,
0.03718225657939911,
-0.022802473977208138,
-0.022009721025824547,
0.007011440582573414,
0.041391000151634216,
-0.01013603713363409,
-0.01564052887260914,
0.017817441374063492,
-0.0415763221681118,
0.03192766755819321,
-0.0014667054638266563,
0.09490972757339478,
0.05814381688833237,
-0.005312503781169653,
0.0012599925976246595,
-0.057338908314704895,
0.025248490273952484,
-0.035353366285562515,
-0.012689994648098946,
-0.024478288367390633,
-0.019968312233686447,
0.057169247418642044,
-0.034851010888814926,
0.01666153222322464,
0.04198557510972023,
-0.039046354591846466,
-0.04344839230179787,
-0.0303423460572958,
0.06197585538029671,
-0.0006187256658449769,
0.01613866537809372,
-0.03540586307644844,
-0.0006035228143446147,
-0.08694085478782654,
0.05667341127991676,
-0.0015776079380884767,
0.03882666304707527,
0.006994078867137432,
-0.010880399495363235,
0.039490796625614166,
0.008772926405072212,
-0.020580090582370758,
0.001615613349713385,
0.025009077042341232,
-0.018608028069138527,
-0.05846259742975235,
-0.050975486636161804,
-0.011252766475081444,
0.06057015806436539,
-0.01310477964580059,
0.03531702980399132,
-0.06976518034934998,
-0.015023610554635525,
0.0018188671674579382,
-0.05593814328312874,
0.014132124371826649,
0.08756003528833389,
-0.01742289401590824,
-0.01773594506084919,
0.015620457008481026,
0.017138265073299408,
-0.050506241619586945,
-0.028594205155968666,
-0.007585674989968538,
-0.03521919250488281,
-0.02301187813282013,
-0.031613972038030624,
0.03560129925608635,
0.009862539358437061,
-0.05178818106651306,
0.031162811443209648,
0.008683758787810802,
-0.012172943912446499,
0.006114149931818247,
-0.012241827324032784,
-0.044997263699769974,
0.04235274717211723,
0.03018968738615513,
0.037330977618694305,
0.045680079609155655,
-0.06854218989610672,
0.018390074372291565,
-0.007553078234195709,
-0.03429396077990532,
-0.02259807102382183,
0.023460092023015022,
-0.013033026829361916,
0.0433887355029583,
0.03020472638309002,
-0.06723807007074356,
-0.028920937329530716,
-0.0028029640670865774,
0.02930220030248165,
0.0455213338136673,
-0.059830158948898315,
-0.023563148453831673,
0.05320824310183525,
0.022886091843247414,
0.04043341800570488,
-0.04180463030934334,
-0.011168163269758224,
0.061441097408533096,
0.04033774137496948,
-0.020329438149929047,
-0.027230534702539444,
-0.031055914238095284,
-0.00676029222086072,
-0.03391614556312561,
0.021517084911465645,
0.005804446060210466,
0.0982714295387268,
0.03272252529859543,
-0.027454284951090813,
0.0485856719315052,
-0.009772132150828838,
-0.009157265536487103,
-0.018968859687447548,
0.008293645456433296,
0.0037472122348845005,
0.021420292556285858,
-0.0034703726414591074,
0.02772713266313076,
0.026610221713781357,
-0.005964223295450211,
-0.042981747537851334,
-0.009381513111293316,
0.0022943583317101,
-0.028853965923190117,
-0.020154660567641258,
-0.05229944735765457,
0.0035670967772603035,
-0.009738095104694366,
0.022897513583302498,
0.015532867051661015,
-0.054790038615465164,
-0.04666357487440109,
0.03239012509584427,
-0.01005842536687851,
0.020079316571354866,
-0.04759201779961586,
0.013980627059936523,
0.014867810532450676,
0.022549841552972794,
-0.008519158698618412,
-0.02386379987001419,
0.02364768274128437,
-0.007278121076524258,
0.00468447944149375,
-0.008598116226494312,
0.034709203988313675,
-0.022933853790163994,
-0.03808201476931572,
-0.0013419577153399587,
0.0492166168987751,
-0.0591355636715889,
0.03627278283238411,
-0.00862513855099678,
0.00824862252920866,
0.058152973651885986,
-0.05979103222489357,
-0.0590694323182106,
0.06082252040505409,
0.024731971323490143,
-0.0033057911787182093,
-0.0022965725511312485,
0.0003600802447181195,
0.016028687357902527,
-0.013148320838809013,
-0.042674675583839417,
-0.04095534235239029,
0.004281463101506233,
-0.008902710862457752,
-0.005209609400480986,
-0.0071152132004499435,
-0.02048281766474247,
-0.01245995331555605,
-0.01284847967326641,
0.05188218876719475,
0.03869852051138878,
-0.005558800883591175,
0.041722629219293594,
0.03392648696899414,
0.01704852655529976,
-0.053017664700746536,
-0.0326082669198513,
-0.009267191402614117,
-0.015154016204178333,
-0.009954961016774178,
-0.009112483821809292,
0.008096788078546524,
-0.0022487605456262827,
-0.055277757346630096,
-0.022116174921393394,
0.025303106755018234,
0.007572366390377283,
-0.07202482223510742,
-0.01746988669037819,
0.014960166066884995,
0.04618894308805466,
0.009641731157898903,
-0.022937918081879616,
-0.01111761573702097,
-0.04224726930260658,
0.05087614059448242,
-0.04827496036887169,
0.02112947776913643,
0.012509212829172611,
0.004796364810317755,
-0.02075980044901371,
-0.04908019304275513,
-0.004852223675698042,
0.042453180998563766,
0.033168986439704895,
-0.021216267719864845,
-0.027958247810602188,
0.014944125898182392,
0.002259146887809038,
0.04834356531500816,
-0.01461328100413084,
-0.001962808659300208,
-0.029837466776371002,
0.029364218935370445,
0.062154579907655716,
-0.046232398599386215,
0.010401671752333641,
-0.05224809795618057,
0.02686752937734127,
-0.033473845571279526,
0.007848575711250305,
-0.06614649295806885,
0.007988495752215385,
-0.006267705000936985,
-0.027742817997932434,
0.002251001074910164,
-0.00455954484641552,
0.019806481897830963
] |
<p>It is true for fermions in the same potential that the total wavefunction of two particles must be antisymmetric with respect to exchange of electrons. Which means the spin wavefunction is given by </p>
<p>$\chi=\frac{1}{\sqrt{2}}[\chi_+ (1)\chi_- (2)-\chi_+ (2)\chi_- (1)] $</p>
<p>which looks very much like the bell state, </p>
<p>$\beta_{11}=\frac{1}{\sqrt{2}}[ |01\rangle - |10 \rangle]$. </p>
<p>So, can we call those fermions, entangled states, as long as they are within the potential or there is something fundamentally special about entangled states (e.g. difference in measurement statistics) which makes them more unique?</p>
<p>Apologies if the question is too simple for the level of this website. However, apparently it has made a lot of confusion for many people!</p> | g4747 | [
-0.01350089069455862,
0.01778465323150158,
0.00741926534101367,
-0.015140353702008724,
0.11228924244642258,
-0.04491782188415527,
-0.008031690493226051,
0.04505240172147751,
0.06490158289670944,
0.02831064537167549,
-0.03887608274817467,
0.02280666120350361,
-0.009322627447545528,
-0.003273462411016226,
0.01496496144682169,
0.019581815227866173,
0.06449916958808899,
0.02914092130959034,
0.01887882500886917,
0.008978131227195263,
-0.014650315046310425,
0.029907941818237305,
0.0042591397650539875,
0.006286401767283678,
-0.015166224911808968,
-0.033589139580726624,
-0.038504764437675476,
0.004336176440119743,
-0.012464656494557858,
0.016002601012587547,
-0.031180188059806824,
-0.03704322129487991,
0.05907457694411278,
-0.019050048664212227,
0.013415200635790825,
-0.021536853164434433,
0.04799317568540573,
-0.024754727259278297,
0.0326397530734539,
0.01037162821739912,
-0.00167768110986799,
0.016889743506908417,
-0.037440985441207886,
-0.010826059617102146,
0.023702790960669518,
0.009259474463760853,
0.015346418134868145,
0.03457383066415787,
0.005618190858513117,
-0.01419431809335947,
0.03814467787742615,
0.000017322654457530007,
0.10575416684150696,
0.05627038702368736,
0.04738961532711983,
0.03599794581532478,
0.015483756549656391,
-0.008277191780507565,
0.07053771615028381,
0.0365699864923954,
0.008481472730636597,
-0.0012276916531845927,
0.02393614687025547,
0.03117961622774601,
0.027670644223690033,
0.033118654042482376,
-0.05065183714032173,
0.031751587986946106,
-0.006510275881737471,
-0.023521536961197853,
-0.00473876902833581,
-0.0775507390499115,
0.005810757167637348,
-0.04804733395576477,
0.04834979400038719,
0.019260205328464508,
0.010539575479924679,
-0.0665101557970047,
0.01124351006001234,
-0.0069290404208004475,
-0.031305041164159775,
-0.0603509284555912,
0.020521538332104683,
-0.00035577808739617467,
0.10352163761854172,
-0.027255462482571602,
-0.022659387439489365,
0.016929827630519867,
-0.006316134240478277,
0.035254254937171936,
-0.01704629510641098,
-0.09931930154561996,
0.049855392426252365,
0.025182750076055527,
-0.04027839004993439,
-0.020405679941177368,
0.003250075038522482,
-0.018784785643219948,
-0.009451319463551044,
0.005871788132935762,
-0.0279264897108078,
0.019584549590945244,
0.060306742787361145,
0.012676679529249668,
0.033195167779922485,
-0.04215399548411369,
-0.01533211674541235,
-0.01128197181969881,
0.025641538202762604,
-0.01187986135482788,
0.0018679441418498755,
0.037515752017498016,
-0.02072296291589737,
-0.011709700338542461,
-0.048337772488594055,
0.06765636056661606,
0.08749929815530777,
-0.061160314828157425,
-0.07584337890148163,
0.03976838290691376,
-0.04308389127254486,
0.027837546542286873,
0.038857996463775635,
0.07243253290653229,
0.011962308548390865,
0.04673255234956741,
-0.0033309701830148697,
-0.003960754256695509,
0.012719899415969849,
0.0017330091213807464,
0.012561682611703873,
0.010693720541894436,
0.008318175561726093,
-0.023288119584321976,
-0.001320953480899334,
0.02546566165983677,
0.01550228800624609,
0.00020274589769542217,
-0.011462384834885597,
-0.02098473161458969,
-0.04084088280797005,
-0.041913460940122604,
0.026504939422011375,
-0.030521972104907036,
-0.002586321672424674,
-0.03712359443306923,
-0.018316948786377907,
-0.01900649629533291,
-0.03266625478863716,
0.05345927178859711,
0.03260781615972519,
0.017904017120599747,
-0.009180935099720955,
-0.029276631772518158,
-0.028914662078022957,
-0.03712393715977669,
0.023257190361618996,
0.014802861027419567,
-0.02323443815112114,
0.03199462965130806,
0.018646256998181343,
0.019632704555988312,
-0.02512175776064396,
0.0326097346842289,
-0.038574498146772385,
-0.007739109452813864,
-0.02492641471326351,
-0.0560804083943367,
-0.0109945023432374,
-0.04854128509759903,
-0.058846041560173035,
0.011718477122485638,
-0.07305973768234253,
0.0671391487121582,
0.04110275208950043,
-0.005167027469724417,
-0.08782661706209183,
-0.046417441219091415,
0.014572602696716785,
0.018866952508687973,
-0.02609061636030674,
0.03375967592000961,
0.0015054611722007394,
0.027850201353430748,
-0.03131023421883583,
-0.007043506950139999,
0.02409413829445839,
0.02913322113454342,
-0.07744549214839935,
-0.0051431842148303986,
0.0022048926912248135,
-0.014267664402723312,
0.005759598687291145,
-0.01275800634175539,
0.03430682420730591,
0.024165267124772072,
0.013277225196361542,
0.0026541559491306543,
-0.009758153930306435,
-0.0197560153901577,
-0.02262169122695923,
0.05796414986252785,
0.043759722262620926,
-0.01884697936475277,
0.03021923638880253,
0.015450610779225826,
-0.003040487878024578,
0.0087603023275733,
0.04585017263889313,
-0.02335488423705101,
0.018675576895475388,
-0.06273235380649567,
-0.008129458874464035,
0.050906792283058167,
-0.018681515008211136,
-0.030795203521847725,
0.005050429608672857,
0.020706461742520332,
-0.027124371379613876,
0.0029587275348603725,
0.031157495453953743,
-0.04515071213245392,
0.058512132614851,
0.027491692453622818,
0.0038711782544851303,
0.023416854441165924,
-0.04795360937714577,
0.02404102496802807,
-0.021613674238324165,
0.03879483789205551,
-0.05984443053603172,
-0.031274668872356415,
0.018731767311692238,
-0.07232051342725754,
-0.018475228920578957,
-0.0024220701307058334,
-0.018599102273583412,
0.062491852790117264,
-0.021781472489237785,
-0.016889136284589767,
0.00545874098315835,
0.017677700147032738,
-0.06945913285017014,
0.05047088488936424,
0.052644308656454086,
0.057984817773103714,
-0.02132187969982624,
-0.008895273320376873,
0.026850907132029533,
0.020803280174732208,
0.028960397467017174,
0.0038643949665129185,
-0.0815650075674057,
0.007422337774187326,
0.003878426505252719,
-0.0729699358344078,
0.04712902754545212,
0.02798483893275261,
-0.001247418811544776,
-0.04073261469602585,
-0.011563668958842754,
-0.015025601722300053,
0.012046939693391323,
-0.015504248440265656,
0.010746839456260204,
0.054721854627132416,
0.007663150783628225,
0.005257389973849058,
-0.05961306393146515,
0.010329038836061954,
-0.0249747596681118,
0.07279674708843231,
-0.008760947734117508,
0.03982242941856384,
-0.03404266759753227,
-0.07230209559202194,
-0.0187166016548872,
0.01593989133834839,
-0.0010409858077764511,
-0.06538067758083344,
-0.0732329934835434,
0.06265483796596527,
-0.027849433943629265,
0.04487505182623863,
0.06350143253803253,
-0.06610224395990372,
0.005891631357371807,
-0.06395894289016724,
0.030760005116462708,
0.008501304313540459,
0.008951817639172077,
0.01275034248828888,
0.058524999767541885,
-0.0071275196969509125,
-0.03960336744785309,
0.01615804061293602,
-0.021377556025981903,
-0.048484936356544495,
-0.03340878710150719,
0.08380572497844696,
0.014072263613343239,
0.009262943640351295,
0.010717219673097134,
0.02578757144510746,
0.06818459182977676,
-0.008862915448844433,
-0.058792389929294586,
0.006690798327326775,
-0.06756297498941422,
-0.042727675288915634,
-0.02917138859629631,
0.07087823748588562,
-0.020723244175314903,
-0.012223114259541035,
-0.0329052098095417,
0.003776249708607793,
-0.02240651845932007,
-0.0008777353214100003,
0.022175684571266174,
-0.02140774577856064,
-0.02818952314555645,
-0.0034169540740549564,
-0.007263071369379759,
0.004292869009077549,
0.0727459192276001,
0.0202763844281435,
-0.07045001536607742,
0.007325557991862297,
-0.13905350863933563,
-0.0855531170964241,
0.03227689489722252,
-0.018596157431602478,
-0.006326319649815559,
-0.003986642230302095,
-0.06152559444308281,
-0.04190296679735184,
-0.003390262136235833,
-0.007601525168865919,
0.031313519924879074,
0.01232925895601511,
-0.013472438789904118,
0.012107769027352333,
-0.03904810547828674,
0.031995661556720734,
0.021182473748922348,
-0.011795837432146072,
-0.048219233751297,
-0.00010737856791820377,
0.03148603066802025,
0.012900341302156448,
-0.032335296273231506,
0.07805739343166351,
0.06711734086275101,
0.014043387956917286,
-0.051423802971839905,
-0.03296119347214699,
0.04936922341585159,
-0.011086835525929928,
0.023428788408637047,
0.06348002701997757,
0.08588861674070358,
-0.025224490091204643,
0.049484722316265106,
-0.03709769248962402,
-0.027472976595163345,
-0.014676153659820557,
-0.05314158275723457,
-0.026752514764666557,
0.04604768380522728,
-0.02433573268353939,
-0.051379814743995667,
0.010719944722950459,
0.01692308485507965,
-0.03472340852022171,
0.03466123715043068,
-0.041267599910497665,
0.01756453327834606,
-0.012330209836363792,
-0.047864556312561035,
-0.052107132971286774,
-0.006653404328972101,
0.008426107466220856,
0.07395730167627335,
0.01391309779137373,
-0.002887505805119872,
-0.003450840013101697,
-0.0046663591638207436,
0.00545133650302887,
-0.04258766025304794,
-0.0017873488832265139,
0.039078082889318466,
-0.01847000978887081,
-0.03143392503261566,
-0.0336124412715435,
0.043932728469371796,
0.028736328706145287,
0.030030712485313416,
-0.10044856369495392,
-0.007366974372416735,
0.07436056435108185,
-0.07799465209245682,
-0.03213591128587723,
-0.008402790874242783,
-0.04758080840110779,
0.03272887319326401,
-0.033173881471157074,
0.019846338778734207,
-0.032030511647462845,
-0.013851985335350037,
-0.04109162092208862,
-0.028619347140192986,
0.05913852900266647,
0.06813022494316101,
0.011364700272679329,
0.007794240955263376,
-0.022917980328202248,
-0.021527085453271866,
-0.10140883177518845,
-0.003590999636799097,
-0.023537157103419304,
0.060493312776088715,
0.06161637231707573,
0.010775684379041195,
0.03700736165046692,
0.036503568291664124,
0.032459624111652374,
0.02138780616223812,
0.03022291511297226,
-0.05457363650202751,
-0.06706885248422623,
0.015236071310937405,
-0.0021579016465693712,
-0.0346209742128849,
0.0369129478931427,
-0.05813392251729965,
-0.03540152683854103,
-0.10524582117795944,
-0.023081982508301735,
0.04143821820616722,
0.029529068619012833,
0.01813003420829773,
0.005793512333184481,
-0.07322091609239578,
0.021144265308976173,
0.05974623188376427,
0.013845180161297321,
-0.02671075612306595,
-0.009343999437987804,
-0.03385164216160774,
-0.02079215832054615,
-0.05333186313509941,
0.01657404564321041,
-0.014067540876567364,
-0.03266073763370514,
0.004784435033798218,
-0.038802146911621094,
0.008408933877944946,
-0.026497818529605865,
-0.019698146730661392,
-0.03622213751077652,
-0.06314363330602646,
-0.011651496402919292,
0.013554557226598263,
-0.011487536132335663,
-0.0035408411640673876,
-0.012851482257246971,
-0.03536779060959816,
0.007012976333498955,
-0.039905909448862076,
0.012409252114593983,
0.012953176163136959,
-0.012391330674290657,
0.03088589943945408,
0.002805216470733285,
0.0307048000395298,
0.0016630163881927729,
-0.009462250396609306,
0.011865794658660889,
-0.031846385449171066,
-0.027341336011886597,
-0.024567831307649612,
-0.022831277921795845,
-0.011679913848638535,
0.008311733603477478,
0.018007773905992508,
0.010574324987828732,
0.0018526645144447684,
0.029018303379416466,
-0.027825769037008286,
-0.04021308198571205,
0.024161778390407562,
0.013987877406179905,
-0.0359041653573513,
-0.00831944216042757,
0.06772281974554062,
-0.014184852130711079,
0.031715407967567444,
-0.024987537413835526,
-0.025751275941729546,
0.026302611455321312,
-0.014505206607282162,
0.027850471436977386,
0.014775398187339306,
0.042886678129434586,
0.009712867438793182,
0.03719130530953407,
0.06622685492038727,
0.0023370187263935804,
-0.06647540628910065,
-0.10031067579984665,
0.0028137352783232927,
-0.03243834525346756,
0.012890743091702461,
-0.012531601823866367,
-0.006474539637565613,
0.060550592839717865,
-0.011876309290528297,
0.013829091563820839,
0.0649300143122673,
-0.057542797178030014,
0.009196307510137558,
0.05185864493250847,
0.01934165321290493,
-0.02627144381403923,
-0.004558285232633352,
-0.0515761598944664,
-0.019151756539940834,
-0.01320694014430046,
0.034796737134456635,
0.04742802679538727,
0.02144293487071991,
0.02148296870291233,
0.07550118118524551,
-0.010427188128232956,
-0.0005099077825434506,
-0.03892543166875839,
-0.05110355094075203,
0.025585399940609932,
0.005706241354346275,
0.04057975858449936,
0.01071621011942625,
-0.0281031746417284,
0.031221903860569,
0.035373203456401825,
-0.06563101708889008,
-0.03801840543746948,
-0.004829053301364183,
-0.03164716437458992,
0.009136195294559002,
-0.025223754346370697,
-0.01976509764790535,
0.004834306426346302,
-0.03341052681207657,
-0.053695984184741974,
0.028400173410773277,
0.029340365901589394,
0.007578667253255844,
-0.01128935907036066,
-0.004451826214790344,
-0.0454188734292984,
-0.021058185026049614,
0.01717560365796089,
0.061757735908031464,
0.011307028122246265,
-0.029326925054192543,
-0.03519148379564285,
-0.05917813256382942,
-0.03875042498111725,
0.02093091420829296,
0.006213041488081217,
0.00889501255005598,
-0.010537628084421158,
-0.038100697100162506,
-0.012201660312712193,
-0.034805163741111755,
-0.017503919079899788,
-0.01712900400161743,
-0.0023572815116494894,
0.014423977583646774,
-0.029149549081921577,
-0.017485361546278,
0.011748713441193104,
0.029432574287056923,
-0.008914126083254814,
-0.023764105513691902,
0.07696577906608582,
-0.009078241884708405,
-0.002427450381219387,
-0.026664404198527336,
0.04349471628665924,
-0.0389748215675354,
-0.003268699860200286,
-0.03997358679771423,
0.0160345621407032,
0.05171113833785057,
0.01803821139037609,
-0.020178871229290962,
-0.02422250248491764,
-0.05918196588754654,
0.0408065989613533,
0.05520188808441162,
-0.005410891026258469,
0.014208933338522911,
0.04004418104887009,
0.012365131638944149,
0.04107002168893814,
0.009061175398528576,
0.04870166257023811,
-0.02016008272767067,
-0.008922240696847439,
-0.006041662767529488,
-0.04195887967944145,
-0.03156500682234764,
-0.024578973650932312,
-0.008127780631184578,
-0.06657479703426361,
-0.00446803355589509,
0.031582050025463104,
-0.05509041249752045,
0.024605512619018555,
0.04688418656587601,
0.024130085483193398,
-0.028357038274407387,
-0.048821527510881424,
0.042210500687360764,
0.06845369935035706,
-0.007681700866669416,
0.03555195406079292,
0.07227065414190292,
0.0021075201220810413,
0.03218667581677437,
0.019018569961190224,
0.044040095061063766,
0.03260576352477074,
-0.03863837197422981,
0.018897710368037224,
-0.010520705953240395,
-0.0036119327414780855,
0.0620015487074852,
0.018020786345005035,
0.019143380224704742,
0.07951977849006653,
0.06374883651733398,
0.028437579050660133,
-0.039018262177705765,
0.0387822650372982,
0.03989731892943382,
-0.029974590986967087,
0.003357643261551857,
0.027231885120272636,
0.02197488211095333,
-0.0015845699235796928,
-0.04277445748448372,
-0.011395213194191456,
-0.030605779960751534,
-0.052126891911029816,
0.0409286729991436,
0.033189259469509125,
0.04476425424218178,
-0.07454622536897659,
-0.00046968902461230755,
0.0010694843949750066,
-0.02875809371471405,
-0.00047088137944228947,
0.019833222031593323,
0.005828711204230785,
-0.015698501840233803,
-0.017051734030246735,
-0.016041003167629242,
-0.06440705060958862,
-0.016066310927271843,
-0.05604930594563484,
-0.02919190376996994,
-0.0021665527019649744,
-0.0014304725918918848,
-0.013622891157865524,
-0.006619381718337536,
0.034862883388996124,
-0.034436874091625214,
-0.025427168235182762,
0.04246446490287781,
0.033509161323308945,
0.0064100767485797405,
0.031518515199422836,
-0.006043441127985716,
0.04397035762667656,
0.005168308038264513,
-0.031816788017749786,
0.01709110289812088,
-0.009233269840478897,
0.02487044967710972,
-0.007223845459520817,
0.014698733575642109,
-0.017887946218252182,
-0.062185563147068024,
0.017039986327290535,
0.049326613545417786,
0.026378704234957695,
0.023000987246632576,
0.02662748657166958,
0.015767555683851242,
0.045585956424474716,
-0.021113848313689232,
0.007679472677409649,
0.06208294257521629,
-0.04247541353106499,
-0.010155705735087395,
-0.03675075247883797,
-0.03953829035162926,
0.014885589480400085,
0.03417879715561867,
0.02681700512766838,
0.03476148843765259,
0.022783976048231125,
0.002628923859447241,
0.0021472631487995386,
-0.023345887660980225,
0.011981041170656681,
0.00832321122288704,
-0.01927264966070652,
0.04008561372756958,
0.025288645178079605,
-0.01748400740325451,
-0.007948745973408222,
-0.0226046834141016,
-0.07001355290412903,
0.030458645895123482,
0.031337883323431015,
0.03516845032572746,
0.031715113669633865,
-0.0025347773917019367,
0.04112526774406433,
-0.04078847914934158,
0.014455421827733517,
-0.0433398112654686,
0.033426109701395035,
0.01763324998319149,
0.035404451191425323,
-0.006995219271630049,
0.00686910143122077,
0.031701620668172836,
0.022052135318517685,
0.04116556793451309,
-0.060189805924892426,
-0.030812088400125504,
0.013971627689898014,
-0.041938792914152145,
-0.011777431704103947,
0.027451450005173683,
0.01664438284933567,
-0.04357471317052841,
-0.00983397290110588,
-0.04826617240905762,
0.09620977193117142,
0.05375111475586891,
0.005596032366156578,
0.02350248023867607,
-0.0028536778409034014,
0.020700553432106972,
0.03640973940491676,
-0.019993118941783905,
-0.008024992421269417,
-0.06470108777284622,
0.03457484766840935,
-0.029973341152071953,
-0.01043578889220953,
-0.013786044903099537,
0.007047789636999369
] |
<p>In the Standard Model of Particle physics the $SU(2)_{EW}$ symmetry and the $SU(2)$ isospin symmetry are broken. What about $SU(3)_C$? Is it broken too?</p>
<p>if YES, what breaks the symmetry?</p>
<p>If NO, what are the consequences? Anything like "all baryons have almost the same mass"?</p> | g4748 | [
0.034140538424253464,
0.016548478975892067,
0.017274631187319756,
-0.03142489865422249,
0.0519777312874794,
0.03442007303237915,
-0.028868569061160088,
0.025947876274585724,
-0.03953733295202255,
0.008649900555610657,
-0.04202744737267494,
-0.04425309598445892,
-0.03202812001109123,
0.0057100108824670315,
0.008313098922371864,
0.06622855365276337,
0.057387374341487885,
-0.026161054149270058,
-0.037520911544561386,
0.04024238884449005,
-0.03420959413051605,
-0.0134253716096282,
-0.01583940163254738,
-0.02197105810046196,
0.06353899091482162,
-0.0022113968152552843,
0.05272030830383301,
-0.0372525155544281,
-0.0542600192129612,
0.05786285549402237,
0.015428053215146065,
0.020654158666729927,
0.020259546115994453,
-0.05625338852405548,
-0.002872722689062357,
-0.07542671263217926,
0.05620525777339935,
0.010774323716759682,
-0.007136726751923561,
-0.004735937342047691,
0.028469016775488853,
0.03473125770688057,
0.03678349405527115,
-0.0025965317618101835,
-0.04081378132104874,
-0.01450123731046915,
0.024360215291380882,
0.018288880586624146,
-0.035468850284814835,
-0.04623284563422203,
0.036523230373859406,
-0.02051374688744545,
0.05331166833639145,
0.02253865823149681,
-0.0036597331054508686,
-0.034255124628543854,
0.04130066558718681,
-0.06293594092130661,
0.030848225578665733,
0.06145903468132019,
-0.010366507805883884,
0.06394274532794952,
-0.0018358422676101327,
-0.0062756529077887535,
0.007296083495020866,
0.002119417069479823,
-0.012044894509017467,
0.02294199913740158,
0.0031472400296479464,
-0.00514220492914319,
0.022607706487178802,
-0.01738400012254715,
0.004067052621394396,
-0.043289486318826675,
-0.04690706357359886,
-0.011426104232668877,
0.0191239845007658,
0.02216293290257454,
-0.044397205114364624,
-0.024246077984571457,
-0.041955288499593735,
-0.006428354419767857,
-0.03749439865350723,
-0.024547670036554337,
0.02249297872185707,
-0.0645672157406807,
-0.024100683629512787,
0.047227200120687485,
-0.0238227266818285,
-0.0036999632138758898,
-0.043199118226766586,
0.0023157759569585323,
-0.008977346122264862,
-0.00514814630150795,
-0.024310598149895668,
-0.0022560073994100094,
0.08159688115119934,
0.06683278828859329,
-0.05445852875709534,
0.0389135479927063,
-0.019641080871224403,
-0.022816084325313568,
-0.009869995526969433,
0.048849303275346756,
0.008793928660452366,
0.0037555950693786144,
0.08269393444061279,
-0.0027515480760484934,
0.044069014489650726,
0.017407454550266266,
-0.022631291300058365,
-0.00001338633956038393,
0.0010137635981664062,
0.05722324177622795,
-0.05495769530534744,
-0.023075813427567482,
0.03539125621318817,
-0.032743871212005615,
0.01779262162744999,
0.04696815088391304,
0.06243009865283966,
0.0005956703680567443,
-0.04005224257707596,
0.03189420700073242,
-0.037786804139614105,
-0.02030998095870018,
0.010908612050116062,
0.007334680296480656,
-0.011458844877779484,
-0.012849345803260803,
-0.007306415122002363,
0.036910153925418854,
-0.048267021775245667,
0.013532761484384537,
0.0355231836438179,
0.034781236201524734,
0.013674061745405197,
0.033507589250802994,
0.007372164633125067,
-0.014327888377010822,
-0.010140764527022839,
0.020639512687921524,
-0.013286132365465164,
0.035427358001470566,
-0.03088543377816677,
-0.0492972657084465,
-0.022700637578964233,
0.022430112585425377,
-0.04677613079547882,
0.05812026560306549,
-0.044683344662189484,
0.05766959860920906,
0.005025101359933615,
0.00984345842152834,
-0.039308492094278336,
-0.013914626091718674,
-0.023366861045360565,
0.024163473397493362,
0.01758798025548458,
-0.017363861203193665,
0.04138296842575073,
-0.03266828507184982,
0.0030612468253821135,
-0.00851219892501831,
-0.04335771128535271,
0.009254829958081245,
-0.019564788788557053,
-0.01582804135978222,
-0.00405257660895586,
0.00723509443923831,
-0.1093960776925087,
0.06568396091461182,
-0.01614614576101303,
0.041603751480579376,
-0.018366055563092232,
0.014028464443981647,
-0.0872829481959343,
-0.04161227494478226,
0.0149092311039567,
0.0053528351709246635,
-0.07658423483371735,
0.015571891330182552,
-0.01592247188091278,
-0.0022241564001888037,
-0.02404968999326229,
0.039304304867982864,
0.013595758005976677,
-0.009123547933995724,
0.010513515211641788,
0.06661010533571243,
-0.0614788644015789,
0.04726436361670494,
0.006532369181513786,
0.06216869875788689,
0.003189720446243882,
0.000017881551684695296,
-0.013738995417952538,
0.03274183347821236,
-0.050711739808321,
-0.02128434367477894,
0.027348259463906288,
0.028204333037137985,
-0.020351650193333626,
-0.036761075258255005,
0.013202373869717121,
-0.008318902924656868,
0.012921594083309174,
-0.023449299857020378,
0.03978857025504112,
-0.01351966429501772,
0.03842506930232048,
-0.009705506265163422,
0.0484105721116066,
-0.012564265169203281,
0.005896576680243015,
-0.006049157585948706,
-0.0010995749616995454,
0.0018467846093699336,
-0.005524899810552597,
-0.045840777456760406,
-0.07354655861854553,
-0.020691363140940666,
0.06489247828722,
-0.027197232469916344,
0.022014085203409195,
0.0097673200070858,
-0.08715515583753586,
-0.011456071399152279,
0.042703840881586075,
-0.03995689004659653,
-0.01546020433306694,
0.044699776917696,
-0.0022079094778746367,
-0.04385857284069061,
-0.003933844156563282,
0.01667802967131138,
-0.011634038761258125,
-0.06238361820578575,
0.0882718563079834,
-0.06575734168291092,
0.03366018086671829,
-0.031847625970840454,
-0.07901905477046967,
0.0067675355821847916,
0.07024521380662918,
-0.030929725617170334,
0.04406110942363739,
-0.011923044919967651,
-0.013713983818888664,
0.02409781515598297,
-0.02839324064552784,
0.06793826818466187,
-0.048584360629320145,
0.0013078084448352456,
0.012768732383847237,
-0.0178763996809721,
0.019470658153295517,
0.04961859807372093,
-0.06650711596012115,
-0.056180089712142944,
0.021402040496468544,
-0.034366071224212646,
0.015077324584126472,
-0.017600934952497482,
-0.022142620757222176,
0.02626553550362587,
0.03670589625835419,
0.02108985371887684,
0.015493584796786308,
0.027095990255475044,
-0.03445913642644882,
0.03436305373907089,
0.0284072607755661,
0.02203194797039032,
0.004723167046904564,
0.032634515315294266,
0.002701850375160575,
-0.08966711163520813,
0.024940481409430504,
-0.10574152320623398,
-0.06710677593946457,
0.037472810596227646,
0.018805591389536858,
0.0066316984593868256,
0.05255662649869919,
-0.018986986950039864,
-0.07735190540552139,
-0.05184953659772873,
-0.03061365894973278,
0.06832950562238693,
-0.016280189156532288,
-0.006237391848117113,
0.06412705779075623,
0.02188766561448574,
0.0519312359392643,
0.051131561398506165,
-0.02389623410999775,
-0.009201668202877045,
-0.09517045319080353,
-0.0082356296479702,
0.004186962265521288,
0.04104797914624214,
-0.03506183996796608,
0.008719225414097309,
-0.036255236715078354,
-0.0049226912669837475,
-0.011029071174561977,
-0.00020133345969952643,
0.03834085538983345,
-0.047311872243881226,
0.011524676345288754,
0.05076498165726662,
0.01689714938402176,
-0.019417813047766685,
-0.03292824327945709,
0.0182817205786705,
-0.038428742438554764,
0.0305594801902771,
0.010987745597958565,
-0.04202986881136894,
-0.08772264420986176,
-0.004847292322665453,
0.025440238416194916,
-0.05681002885103226,
-0.00202848669141531,
0.030242890119552612,
0.03922278434038162,
-0.047537773847579956,
-0.0497610904276371,
-0.03913481533527374,
-0.011284942738711834,
-0.04841622710227966,
0.024579506367444992,
0.028751756995916367,
-0.018202703446149826,
-0.001754948403686285,
0.03589114919304848,
-0.008710105903446674,
0.0095199691131711,
-0.00488416850566864,
0.044678058475255966,
0.0009240475483238697,
-0.027611620724201202,
-0.01039829384535551,
0.027128683403134346,
0.0030650461558252573,
0.027308722957968712,
-0.044200967997312546,
0.029048670083284378,
0.00581635907292366,
0.011653262190520763,
0.06643570959568024,
-0.011477217078208923,
-0.018282417207956314,
-0.04121481999754906,
-0.01453009806573391,
0.013584804721176624,
0.034224122762680054,
0.020142696797847748,
-0.020886996760964394,
-0.00017276566359214485,
0.0011021203827112913,
0.0634257048368454,
0.03262672573328018,
-0.07752534002065659,
0.020439885556697845,
0.0162874236702919,
0.013049868866801262,
0.03341558575630188,
-0.018611714243888855,
-0.005648913327604532,
-0.04742646962404251,
0.008242946118116379,
-0.052403200417757034,
0.07098404318094254,
0.024810532107949257,
0.04470926895737648,
-0.01182518806308508,
-0.08099251985549927,
-0.003009315114468336,
0.05669737979769707,
0.003161564702168107,
-0.003568363143131137,
-0.0055699897930026054,
0.01835872232913971,
-0.021953511983156204,
-0.06509136408567429,
-0.01869896613061428,
-0.09030109643936157,
-0.002888790098950267,
0.006200500298291445,
0.021810878068208694,
-0.007498457096517086,
0.03609355911612511,
0.02596598118543625,
-0.03312518447637558,
-0.006792903412133455,
-0.03568871691823006,
0.009452717378735542,
0.010225891135632992,
-0.023418869823217392,
0.005143887363374233,
0.007539620157331228,
-0.014154286123812199,
0.03817583620548248,
0.002829816658049822,
0.03619485720992088,
0.003581552766263485,
-0.0003760316758416593,
0.02531594969332218,
0.04099414497613907,
0.005742455366998911,
0.07946471869945526,
-0.054505605250597,
0.004106986336410046,
-0.010054636746644974,
-0.0027770018205046654,
-0.02765130065381527,
0.014675045385956764,
-0.01304294541478157,
-0.021721066907048225,
0.035216812044382095,
-0.018847627565264702,
0.032288048416376114,
0.00532251363620162,
0.016036381945014,
0.07362837344408035,
-0.026576967909932137,
-0.036782167851924896,
0.019056247547268867,
0.03262992948293686,
0.02187446504831314,
0.0038523494731634855,
0.020457491278648376,
0.009068746119737625,
0.018421608954668045,
0.006968263536691666,
0.0022845149505883455,
-0.09189245849847794,
0.04987930878996849,
0.11323689669370651,
0.03962499275803566,
-0.015995707362890244,
-0.0028629901353269815,
0.027085697278380394,
-0.013500417582690716,
-0.00008711464033694938,
-0.03754480183124542,
-0.01092023216187954,
0.009835601784288883,
-0.0022162101231515408,
0.03040597029030323,
-0.030431494116783142,
-0.017887847498059273,
-0.05504177138209343,
-0.028987044468522072,
0.008115372620522976,
0.041366152465343475,
0.005618803668767214,
-0.00913123320788145,
-0.05768100917339325,
-0.07597768306732178,
0.03222086280584335,
-0.003811224829405546,
0.04812927171587944,
-0.027652112767100334,
-0.07951861619949341,
0.008598453365266323,
-0.015816494822502136,
-0.02026386186480522,
-0.008699222467839718,
0.04071476683020592,
-0.022450115531682968,
0.03861096128821373,
0.016137482598423958,
0.021473251283168793,
-0.03660951927304268,
-0.013400869444012642,
-0.019820569083094597,
0.0027206563390791416,
0.026394417509436607,
-0.04624851420521736,
-0.00823930837213993,
-0.046117644757032394,
-0.011143776588141918,
0.0008142506703734398,
-0.055492717772722244,
0.025446388870477676,
-0.013685328885912895,
0.0025869496166706085,
0.027484185993671417,
0.05759448930621147,
-0.008658557198941708,
-0.03875723108649254,
0.015039014630019665,
0.03347340226173401,
0.033286046236753464,
-0.019937733188271523,
-0.029424749314785004,
0.027852999046444893,
0.004543484188616276,
0.018943291157484055,
0.06647271662950516,
-0.00927269272506237,
0.020277580246329308,
0.02616025134921074,
0.03022824600338936,
-0.008719272911548615,
-0.032648880034685135,
-0.07172369956970215,
0.03563698008656502,
-0.06012234464287758,
0.03991786018013954,
-0.01185254193842411,
-0.02538292296230793,
0.08784347027540207,
-0.02350473403930664,
-0.017561636865139008,
-0.008209791965782642,
-0.10094449669122696,
-0.036971040070056915,
-0.02245611697435379,
-0.00782583374530077,
-0.01827094703912735,
0.007197314407676458,
-0.057659316807985306,
-0.07331040501594543,
0.010075115598738194,
0.0120555954053998,
0.0057012587785720825,
0.021044399589300156,
-0.010133814066648483,
0.048309434205293655,
0.021756494417786598,
0.03444284945726395,
-0.05816023424267769,
-0.006771539803594351,
-0.027083992958068848,
-0.0069083343259990215,
0.03528767451643944,
-0.004994308575987816,
-0.05140845105051994,
0.04334074631333351,
0.018105726689100266,
-0.04587116464972496,
0.006691673304885626,
-0.04446778818964958,
0.0005243846098892391,
0.009963681921362877,
-0.029095694422721863,
0.006072604097425938,
0.03501613810658455,
-0.03682633116841316,
0.004125441424548626,
0.008832776919007301,
0.04119142144918442,
-0.008928164839744568,
-0.02127397432923317,
-0.018160944804549217,
-0.04234333336353302,
-0.026472358033061028,
-0.009370094165205956,
0.04043976590037346,
0.021843889728188515,
0.049123648554086685,
-0.04684780165553093,
-0.05194973573088646,
0.005445418879389763,
0.05368300527334213,
-0.0015118016162887216,
0.009465252980589867,
0.11148563772439957,
0.06730546057224274,
-0.01919216848909855,
0.006126638036221266,
-0.04685040935873985,
-0.009603826329112053,
0.030935632064938545,
0.026665467768907547,
-0.04953613877296448,
0.006312231067568064,
-0.03359603136777878,
0.005631805397570133,
-0.005744440946727991,
-0.018105801194906235,
0.03872803971171379,
-0.005025149788707495,
0.028292354196310043,
0.08533425629138947,
0.03962373360991478,
-0.037342656403779984,
-0.04514256492257118,
-0.04759163036942482,
0.06536171585321426,
-0.01074317004531622,
0.03905465081334114,
-0.016706885769963264,
-0.0169382207095623,
-0.03383203595876694,
0.009666523896157742,
0.04740172624588013,
0.046376656740903854,
0.018495187163352966,
0.028549781069159508,
0.00738045247271657,
0.04965515062212944,
0.014787688851356506,
-0.001867796527221799,
-0.005945895798504353,
0.030920865014195442,
-0.029186883941292763,
-0.0315399095416069,
0.0037742473650723696,
0.035084232687950134,
-0.05371873453259468,
-0.07569897174835205,
-0.01810353994369507,
-0.06175560876727104,
-0.08828208595514297,
-0.015136943198740482,
0.0022479859180748463,
0.012578889727592468,
0.0036707709077745676,
-0.03383255377411842,
0.022796502336859703,
0.05518576130270958,
0.03725850582122803,
0.05399392545223236,
0.030084483325481415,
-0.006269674748182297,
0.021161936223506927,
0.007550312206149101,
0.04166397452354431,
-0.008966540917754173,
-0.07299423217773438,
-0.04996129125356674,
-0.018667234107851982,
-0.003695688908919692,
-0.013502882793545723,
0.02552458643913269,
0.008315281011164188,
0.02947004698216915,
0.02288074418902397,
-0.03022504225373268,
-0.0572771318256855,
0.023256903514266014,
0.07013960927724838,
0.01520400121808052,
-0.033479899168014526,
-0.0013709940249100327,
0.016873275861144066,
0.03540211170911789,
0.01159121934324503,
0.01743904873728752,
0.033879347145557404,
-0.012796278111636639,
-0.000513711420353502,
-0.02812039479613304,
0.0255203265696764,
-0.02584846131503582,
-0.029581796377897263,
0.013960322365164757,
-0.009793845005333424,
0.005169309675693512,
0.026064030826091766,
-0.020699599757790565,
-0.014843308366835117,
-0.051078833639621735,
0.016791310161352158,
0.0006330010364763439,
-0.031185593456029892,
-0.044655002653598785,
-0.07717300951480865,
-0.04996557906270027,
0.04855044186115265,
-0.014340005815029144,
-0.020565174520015717,
0.03391615301370621,
-0.02041587047278881,
-0.02147017978131771,
0.007913214154541492,
0.048959460109472275,
-0.022237777709960938,
0.03751356527209282,
-0.013417770154774189,
0.0662686750292778,
-0.0162932388484478,
0.012346608564257622,
-0.006544135510921478,
0.04600604623556137,
0.04852157086133957,
0.00284432340413332,
-0.01824779435992241,
-0.029190005734562874,
-0.05499901622533798,
0.03431219607591629,
-0.014748185873031616,
0.06286876648664474,
0.021083317697048187,
-0.007327156141400337,
0.013585138134658337,
0.019352316856384277,
0.004798634443432093,
-0.04159509018063545,
0.08080990612506866,
-0.011833442375063896,
-0.03551324084401131,
-0.0012183224316686392,
-0.036682892590761185,
0.0017332860734313726,
-0.018688054755330086,
0.07304780930280685,
0.02822927199304104,
0.00003996289524366148,
0.07638244330883026,
0.010088198818266392,
-0.046952202916145325,
-0.0012763645499944687,
0.07845371961593628,
0.007931217551231384,
-0.045304249972105026,
0.020298264920711517,
-0.035201746970415115,
-0.015751605853438377,
-0.040155548602342606,
-0.051522284746170044,
0.026235833764076233,
-0.020132919773459435,
0.06987274438142776,
0.04044470563530922,
-0.018452977761626244,
0.0649382621049881,
-0.014792387373745441,
0.014452013187110424,
-0.04338042810559273,
0.0712428018450737,
0.049611952155828476,
-0.02417757734656334,
-0.02226589433848858,
0.024803470820188522,
-0.03678121417760849,
-0.030649913474917412,
0.015236585400998592,
-0.042543020099401474,
-0.019256852567195892,
0.019836315885186195,
0.009983625262975693,
-0.051336757838726044,
0.0026718899607658386,
0.006312408018857241,
0.06017640233039856,
0.03709585219621658,
-0.027154333889484406,
0.08488115668296814,
0.04317076504230499,
-0.05659783259034157,
0.020805275067687035,
-0.02409120462834835,
-0.05247625708580017,
0.02037893608212471,
0.02960290014743805,
0.011647122912108898,
0.02103564143180847,
-0.028706956654787064,
-0.002603030065074563,
-0.006925756577402353,
-0.011378083378076553,
0.047115590423345566
] |
<p>I'm guessing this isn't a great physics question, but I just can't find an answer with Google.
If the galactic plane is perfectly horizontal at what angle and rotation will the ecliptic plane of our Solar System be?</p> | g4749 | [
0.03302256762981415,
0.030586378648877144,
0.018847674131393433,
-0.01298485416918993,
0.03825975954532623,
0.008536090143024921,
0.023735027760267258,
-0.03598236292600632,
-0.05076923593878746,
-0.05322575941681862,
0.03923259675502777,
0.014220086857676506,
-0.004163112957030535,
-0.05220549926161766,
0.04750669747591019,
-0.021290035918354988,
-0.03853340819478035,
0.022303607314825058,
0.017635028809309006,
0.059391871094703674,
0.006877608131617308,
-0.05720726028084755,
0.016223514452576637,
-0.027194133028388023,
0.025784116238355637,
-0.010587011463940144,
-0.030590703710913658,
-0.034886252135038376,
-0.013505729846656322,
0.016622021794319153,
0.004341894295066595,
0.003816465614363551,
0.036386508494615555,
-0.04585260525345802,
-0.021649854257702827,
-0.03947346657514572,
0.005338242743164301,
0.05158264562487602,
0.07124298065900803,
-0.06166620925068855,
-0.01542693842202425,
-0.01146591268479824,
-0.03837538883090019,
0.039773646742105484,
0.00040970477857626975,
-0.020121321082115173,
0.01684277318418026,
0.03632407262921333,
0.013176590204238892,
0.04960491880774498,
-0.07637131959199905,
0.018798429518938065,
0.015100699849426746,
-0.06868863105773926,
-0.032833393663167953,
0.025684427469968796,
0.06785035878419876,
-0.04240929335355759,
-0.020164621993899345,
0.009435554966330528,
-0.029887624084949493,
-0.04884738102555275,
0.01101012248545885,
0.028239499777555466,
0.0009642101358622313,
-0.03168732300400734,
-0.012618161737918854,
0.043767496943473816,
-0.022644013166427612,
-0.0012753650080412626,
0.027660807594656944,
-0.05379969999194145,
0.009045837447047234,
-0.048459820449352264,
-0.023781519383192062,
0.008349202573299408,
0.04006776586174965,
0.002153827575966716,
0.001899638446047902,
0.005028402898460627,
0.013617823831737041,
-0.015421717427670956,
-0.01291825994849205,
0.009439380839467049,
0.05175744369626045,
-0.041872717440128326,
0.0064030783250927925,
-0.03997829183936119,
-0.03125118464231491,
0.011940029449760914,
0.025885988026857376,
0.0006546585937030613,
0.019022146239876747,
0.01638607308268547,
-0.009437110275030136,
-0.044505774974823,
-0.009069889783859253,
0.024898147210478783,
-0.02839534357190132,
0.021167226135730743,
-0.054120611399412155,
-0.022386251017451286,
0.021218664944171906,
-0.04995027557015419,
0.06328259408473969,
0.03291263431310654,
0.020373191684484482,
0.018515152856707573,
0.006196962203830481,
-0.060513682663440704,
-0.01394977979362011,
-0.002617466263473034,
-0.01360685471445322,
0.015084406360983849,
-0.05944380164146423,
0.02874521166086197,
0.038398001343011856,
0.007170975208282471,
0.12346940487623215,
0.08045297861099243,
0.0748562216758728,
0.008202669210731983,
-0.0530378632247448,
0.1297537386417389,
-0.05219738930463791,
-0.04313824698328972,
-0.03813831880688667,
0.017530884593725204,
-0.017683401703834534,
-0.0033576046116650105,
-0.018859490752220154,
-0.003993301652371883,
-0.052061889320611954,
0.0314815491437912,
0.07942048460245132,
-0.0171127300709486,
-0.004781937226653099,
-0.016431773081421852,
0.025860484689474106,
0.018442407250404358,
-0.023137101903557777,
0.02507362700998783,
0.036143992096185684,
0.015826130285859108,
-0.032634712755680084,
-0.028645364567637444,
0.01948242448270321,
0.029072314500808716,
0.06982367485761642,
0.020555902272462845,
-0.016336340457201004,
0.04261704161763191,
0.02989990822970867,
-0.039922285825014114,
-0.042632367461919785,
-0.03639305382966995,
-0.009240848012268543,
0.009409110061824322,
0.05615093186497688,
0.07193999737501144,
0.03816448524594307,
-0.012338588945567608,
-0.008142372593283653,
-0.019176656380295753,
-0.039954252541065216,
0.0032320476602762938,
-0.09318899363279343,
-0.025817932561039925,
0.02556862123310566,
0.01788107119500637,
-0.04171540588140488,
0.019398469477891922,
0.013463916257023811,
0.015675347298383713,
0.04134177416563034,
0.06860210001468658,
0.013612155802547932,
0.016094038262963295,
0.02611377090215683,
0.044843435287475586,
-0.006384561304003,
-0.031186101958155632,
-0.013965378515422344,
0.020961089059710503,
-0.06490486860275269,
-0.04460286349058151,
0.04775485396385193,
-0.05719434842467308,
-0.003936456050723791,
0.019028853625059128,
0.02236788719892502,
0.0382239930331707,
-0.012210340239107609,
0.006559024099260569,
0.03176194429397583,
0.0021410949993878603,
0.03408672660589218,
0.006691196002066135,
-0.03676379472017288,
0.08772533386945724,
0.0012138368329033256,
0.0690932348370552,
0.08828169107437134,
0.057522017508745193,
-0.007096812129020691,
-0.0019185018027201295,
0.028139455243945122,
-0.00023966183653101325,
0.03160344436764717,
0.023220738396048546,
-0.033963777124881744,
0.023022320121526718,
0.012485851533710957,
0.04071882739663124,
0.05812321603298187,
0.02256922237575054,
-0.0025920949410647154,
-0.014105032198131084,
-0.01430119015276432,
-0.024596434086561203,
-0.022241372615098953,
-0.005212826654314995,
-0.025765251368284225,
-0.010837745852768421,
0.03224646672606468,
-0.044025372713804245,
-0.061513662338256836,
-0.020518431439995766,
0.027287712320685387,
-0.0067197890020906925,
0.015360836870968342,
-0.04476255923509598,
0.04726571962237358,
-0.009665366262197495,
-0.0029893568716943264,
0.04381851479411125,
-0.01090165413916111,
0.014560266397893429,
0.026100095361471176,
-0.0019519770285114646,
-0.008151580579578876,
0.02268110401928425,
-0.0029384964145720005,
-0.005639585200697184,
0.03849232569336891,
-0.03910163417458534,
0.06948748975992203,
-0.03850797191262245,
0.023314261808991432,
0.05775594711303711,
0.03657321631908417,
-0.010445496998727322,
-0.056275878101587296,
0.06307122856378555,
-0.033270273357629776,
0.0127141447737813,
-0.011831206269562244,
0.0348513163626194,
-0.06476014107465744,
-0.008224035613238811,
-0.014695925638079643,
-0.08001719415187836,
-0.04331652820110321,
0.005649274680763483,
-0.038045089691877365,
-0.027920816093683243,
-0.03431406989693642,
0.029511354863643646,
0.06970038264989853,
0.021422475576400757,
0.03975486382842064,
0.06429719924926758,
-0.002980158431455493,
0.0403008870780468,
-0.029589818790555,
-0.05380580946803093,
0.0635417029261589,
-0.013471041806042194,
-0.05259270220994949,
0.013513797894120216,
0.010328338481485844,
-0.0035079997032880783,
0.01544258464127779,
0.06327636539936066,
0.008107272908091545,
0.028129249811172485,
-0.04730558395385742,
0.06854868680238724,
-0.04382281377911568,
0.03694736585021019,
-0.0403352789580822,
0.0037826893385499716,
0.03231460601091385,
-0.029935529455542564,
0.0013092742301523685,
0.010703351348638535,
0.015328977257013321,
0.026573490351438522,
-0.015693439170718193,
-0.0292756836861372,
-0.036461640149354935,
0.004213819745928049,
-0.002687399508431554,
0.012860901653766632,
-0.073774054646492,
0.07642320543527603,
0.01479841023683548,
-0.02913905866444111,
-0.011833847500383854,
0.024898573756217957,
-0.08018915355205536,
0.048028383404016495,
-0.02123798243701458,
0.07299507409334183,
-0.03558135777711868,
-0.02703075110912323,
-0.01774659752845764,
-0.016218455508351326,
-0.02945832535624504,
0.06834333389997482,
-0.0629785880446434,
-0.04556465148925781,
-0.07728355377912521,
-0.005166288465261459,
0.019808176904916763,
0.021155094727873802,
0.011590038426220417,
0.014877605251967907,
-0.053314659744501114,
0.03042914904654026,
0.022656137123703957,
0.04450909420847893,
-0.010905548930168152,
0.05510514974594116,
0.05036681145429611,
0.03724345192313194,
0.006102130748331547,
-0.06244368478655815,
0.022679928690195084,
0.018189508467912674,
-0.023544900119304657,
0.0038930035661906004,
0.031157221645116806,
-0.060467638075351715,
-0.035186491906642914,
-0.028621168807148933,
0.003219569567590952,
-0.06799564510583878,
0.040586233139038086,
0.014097734354436398,
0.03314966335892677,
-0.013516077771782875,
-0.007158557418733835,
-0.0524563305079937,
0.03680321201682091,
0.038248252123594284,
0.0028034888673573732,
0.038975100964307785,
-0.026627695187926292,
-0.01620440185070038,
-0.04931051284074783,
-0.07118140161037445,
0.01327156089246273,
-0.0055755386129021645,
0.04914307966828346,
-0.022374819964170456,
-0.02616143599152565,
-0.00027981933089904487,
0.00965106301009655,
-0.0010187712032347918,
-0.01731160655617714,
0.04249167814850807,
0.035402651876211166,
-0.05002246052026749,
0.005350067280232906,
0.0004913102020509541,
0.014305578544735909,
-0.04368945211172104,
-0.0353720560669899,
0.015202525071799755,
0.0245503019541502,
-0.02199268713593483,
0.050018325448036194,
0.01995845139026642,
-0.01417506393045187,
0.08876869827508926,
-0.004798157140612602,
0.018352970480918884,
0.016222771257162094,
-0.010817272588610649,
0.04798005893826485,
-0.03901942819356918,
0.03735237941145897,
-0.033387329429388046,
-0.010088092647492886,
-0.04296020790934563,
0.03931591659784317,
0.012202750891447067,
-0.01722031459212303,
0.0040410892106592655,
0.04899398237466812,
0.031320542097091675,
0.05608202889561653,
0.017463117837905884,
0.019820701330900192,
0.018048331141471863,
-0.017744755372405052,
-0.0007168151787482202,
0.037660203874111176,
-0.0295987781137228,
0.08101637661457062,
0.004787116777151823,
0.009895882569253445,
-0.003386818803846836,
0.07748248428106308,
0.02853826992213726,
-0.05004212632775307,
0.008045974187552929,
0.040008094161748886,
-0.004546567797660828,
0.006065091583877802,
0.0401906780898571,
-0.0007609519525431097,
-0.03243276849389076,
-0.0009814874501898885,
0.0825178474187851,
0.03367004916071892,
-0.051215458661317825,
0.0245099775493145,
0.003687448101118207,
-0.004173665773123503,
-0.034915219992399216,
0.023731207475066185,
-0.0032233227975666523,
-0.02732137404382229,
0.012112257070839405,
0.003075452521443367,
0.031557317823171616,
-0.015140844509005547,
-0.015852756798267365,
0.00867532379925251,
0.0021370756439864635,
0.034479573369026184,
-0.0018462389707565308,
-0.05943011865019798,
0.06315567344427109,
0.0037664351984858513,
-0.06142518296837807,
0.016633471474051476,
-0.06993090361356735,
0.009805412963032722,
-0.03965449705719948,
0.012267233803868294,
0.046468283981084824,
-0.08665649592876434,
-0.025267744436860085,
-0.07870787382125854,
0.024551229551434517,
0.003963742405176163,
0.028315141797065735,
-0.03311142697930336,
0.011476698331534863,
0.031195931136608124,
-0.000574717007111758,
0.07343598455190659,
0.029856139793992043,
-0.023390745744109154,
-0.021814290434122086,
-0.05541958287358284,
0.02243334986269474,
-0.032850779592990875,
0.0017173957312479615,
0.04503099247813225,
0.049859751015901566,
-0.008105003274977207,
-0.0018031025538221002,
-0.00780616095289588,
-0.03435003384947777,
0.014561099000275135,
-0.014660428278148174,
-0.062486447393894196,
-0.03242243826389313,
0.02813642844557762,
0.025247909128665924,
-0.025838034227490425,
0.007696522865444422,
-0.006794038228690624,
-0.02652749978005886,
0.0026564691215753555,
0.02405223436653614,
-0.0260334350168705,
-0.03815029188990593,
-0.00547347217798233,
-0.03980926796793938,
-0.010048964060842991,
-0.026728590950369835,
-0.08824574202299118,
-0.08463447540998459,
0.00944054126739502,
0.002927863271906972,
-0.027933189645409584,
0.04988251253962517,
-0.00199807807803154,
0.024562684819102287,
0.007010515313595533,
0.06023066118359566,
0.03749953955411911,
-0.032694827765226364,
-0.027492402121424675,
0.07245030254125595,
-0.03261559456586838,
-0.06138363853096962,
0.0027540400624275208,
0.03413581848144531,
-0.02487017773091793,
-0.02887657843530178,
0.0005920686526224017,
0.05926894396543503,
0.008548536337912083,
0.02373785898089409,
-0.019492018967866898,
0.003453722922131419,
-0.04335962235927582,
-0.010383917018771172,
0.015964217483997345,
-0.04495793581008911,
0.027925580739974976,
0.033455539494752884,
0.04554479569196701,
0.030932186171412468,
0.012737831100821495,
-0.0072365072555840015,
0.020672908052802086,
-0.018185244873166084,
0.036869537085294724,
-0.03507263958454132,
0.009226106107234955,
-0.031482476741075516,
0.07691376656293869,
0.005786409601569176,
-0.04242812842130661,
0.011032572947442532,
0.013651406392455101,
0.014955207705497742,
-0.021232709288597107,
0.021234020590782166,
-0.03450436145067215,
0.03445584699511528,
-0.019803104922175407,
0.00173178780823946,
-0.02249794267117977,
0.05656713247299194,
-0.010834774002432823,
-0.005208185873925686,
-0.08351325988769531,
0.032454848289489746,
-0.02077312394976616,
-0.011165902018547058,
0.025731904432177544,
-0.014959788881242275,
0.04014912247657776,
-0.02555408701300621,
0.001523642335087061,
0.006938128732144833,
0.038214799016714096,
-0.026781845837831497,
-0.008736359886825085,
-0.03300090134143829,
0.09182946383953094,
-0.0185588076710701,
-0.022163566201925278,
-0.03019833005964756,
-0.04005683213472366,
0.04915725067257881,
0.07907640188932419,
-0.026035644114017487,
-0.05612083151936531,
-0.009084806777536869,
-0.0639791190624237,
0.03082992322742939,
0.03027256578207016,
-0.0008654982666485012,
-0.0057456172071397305,
-0.017727617174386978,
-0.01696891337633133,
0.01218361034989357,
-0.03390181437134743,
0.022471396252512932,
-0.019582852721214294,
0.011090440675616264,
0.014440404251217842,
0.008060429245233536,
-0.009024707600474358,
0.04547211155295372,
-0.02423788234591484,
-0.01835089549422264,
0.07232989370822906,
0.024184750393033028,
0.011309601366519928,
-0.022685466334223747,
0.032901961356401443,
0.011585090309381485,
0.05003733932971954,
0.0007398460293188691,
0.016608189791440964,
-0.0357331782579422,
0.04296647384762764,
0.08900773525238037,
0.013621872290968895,
-0.020005008205771446,
0.019212499260902405,
-0.01720931939780712,
0.054709844291210175,
-0.045361634343862534,
0.014593594707548618,
-0.06597030162811279,
0.04110235348343849,
-0.02558058500289917,
-0.03520464897155762,
0.0033201812766492367,
-0.03653622791171074,
0.0097951116040349,
-0.052870284765958786,
-0.031220251694321632,
-0.05095415562391281,
-0.033111993223428726,
-0.01966772973537445,
0.019874125719070435,
0.021193699911236763,
-0.020668119192123413,
0.022304445505142212,
0.025775721296668053,
0.00246590469032526,
0.03441266342997551,
0.059744417667388916,
-0.007551621180027723,
-0.1037701964378357,
0.0014488404849544168,
-0.006442848592996597,
0.012107833288609982,
0.04161497950553894,
-0.0028861400205641985,
0.0022445174399763346,
-0.05825520306825638,
-0.053492471575737,
-0.024705298244953156,
-0.03186271712183952,
-0.08009488880634308,
-0.03386741504073143,
-0.02583843283355236,
-0.004998357035219669,
-0.05122974142432213,
-0.016131149604916573,
0.005570163019001484,
-0.03339780494570732,
0.010776343755424023,
0.015549978241324425,
0.010897034779191017,
0.012879522517323494,
-0.005178631283342838,
0.01231594942510128,
0.010444577783346176,
-0.008471956476569176,
0.017582252621650696,
-0.04822447896003723,
-0.0374990776181221,
0.014702587388455868,
0.007003879174590111,
-0.02129594422876835,
-0.016410768032073975,
-0.027234859764575958,
-0.02202296443283558,
-0.03207742050290108,
0.02263077348470688,
-0.018711933866143227,
0.023612618446350098,
-0.036979980766773224,
-0.0880294069647789,
0.058702342212200165,
0.0011795974569395185,
-0.039283350110054016,
0.04204326868057251,
-0.029410259798169136,
0.07398253679275513,
-0.05790112912654877,
-0.07348721474409103,
0.0018433600198477507,
-0.06129557639360428,
-0.03426414355635643,
-0.046306200325489044,
-0.017392702400684357,
0.013801787048578262,
-0.032091014087200165,
-0.02465822361409664,
-0.018132904544472694,
0.011129769496619701,
-0.004281689412891865,
0.028826728463172913,
-0.017078448086977005,
-0.060429319739341736,
-0.006800683215260506,
-0.007843506522476673,
0.012515525333583355,
0.030756376683712006,
0.03010696917772293,
-0.04625970497727394,
-0.024504540488123894,
-0.006015080492943525,
-0.07354097813367844,
-0.005217059049755335,
0.04411575198173523,
0.02385946735739708,
0.046062927693128586,
-0.003114053513854742,
-0.019365200772881508,
0.01124113705009222,
-0.012161992490291595,
0.005951286293566227,
-0.03768165409564972,
0.006292612291872501,
-0.012387788854539394,
-0.02438555471599102,
0.019209925085306168,
-0.03512930870056152,
0.01917307823896408,
0.029120929539203644,
-0.008596732281148434,
-0.04507158696651459,
0.08275973796844482,
-0.0569886714220047,
0.010183566249907017,
0.07001503556966782,
-0.003560429671779275,
-0.03740660846233368,
0.00387706165201962,
0.010285190306603909,
-0.025198454037308693,
-0.05813424661755562,
-0.032428089529275894,
-0.003460588864982128,
0.011525045149028301,
-0.02494654804468155,
-0.039984721690416336,
-0.038009170442819595,
0.05676442012190819,
0.04179016128182411,
0.02248615399003029,
0.013716244138777256,
0.02595914527773857,
-0.003634619526565075,
0.0010668975301086903,
0.044684749096632004,
0.01462817844003439,
-0.005377192050218582,
0.031018422916531563,
-0.026848554611206055,
0.04135676845908165,
-0.03884026035666466,
-0.030861876904964447,
-0.016801146790385246,
0.022023439407348633,
-0.017475558444857597,
0.026045868173241615,
-0.06450746953487396,
-0.00021938873396720737,
-0.04670436307787895,
-0.053277984261512756,
0.05825594440102577
] |
<ol>
<li><p>Photons, where do they come from?</p></li>
<li><p>What exactly is a photon? </p></li>
<li><p>I've certainly heard how they get produced, but it doesn't seem to make sense that some sort of particle should need to be produced just to mediate the interactions of electrons. I have yet to take quantum mechanics, can someone give a brief discussion of the conservation, creation and destruction of photons, and how we know they exist? </p></li>
<li><p>And furthermore why it makes sense to have a quantized bit of energy called a "photon"?</p></li>
</ol> | g4750 | [
0.04590681940317154,
-0.00460410350933671,
-0.019725952297449112,
-0.012459313496947289,
0.04260318726301193,
0.021064402535557747,
-0.028035108000040054,
0.04782286286354065,
0.024815773591399193,
-0.03279911354184151,
0.006625678855925798,
0.0012830159394070506,
0.004704383201897144,
0.0052509792149066925,
-0.012172396294772625,
-0.02912050113081932,
0.03690569847822189,
-0.009361160919070244,
0.0353923961520195,
0.04916723817586899,
-0.031583886593580246,
-0.024020491167902946,
0.029247865080833435,
-0.02832002565264702,
-0.019961001351475716,
0.0051440224051475525,
0.015829019248485565,
-0.031059516593813896,
0.02551444061100483,
-0.05355482175946236,
0.004667726345360279,
-0.022627733647823334,
0.038091473281383514,
-0.05549243092536926,
0.003523212159052491,
-0.03880713880062103,
0.04769667610526085,
-0.0012869950151070952,
0.019315695390105247,
0.04271732643246651,
-0.0019208660814911127,
-0.019343551248311996,
0.011171631515026093,
-0.041973359882831573,
0.0014332056744024158,
0.016720211133360863,
-0.004299829248338938,
-0.0006632636650465429,
0.007872823625802994,
-0.033875465393066406,
0.017911095172166824,
0.01597452536225319,
0.054782796651124954,
0.035719361156225204,
0.056285321712493896,
-0.017882870510220528,
0.011827795766294003,
0.005050919950008392,
0.0576201006770134,
-0.015808377414941788,
0.002240449422970414,
0.0013497387990355492,
-0.007720047142356634,
0.0641980767250061,
0.03815681114792824,
-0.03299329802393913,
-0.028790676966309547,
-0.01719038374722004,
0.017688162624835968,
0.03506898880004883,
0.029877806082367897,
-0.02653757855296135,
-0.022836387157440186,
0.022982655093073845,
0.06446407735347748,
0.017370814457535744,
0.0033166606444865465,
0.011113089509308338,
0.009633304551243782,
0.022618882358074188,
-0.011198807507753372,
-0.03090086206793785,
0.011922270990908146,
-0.08105956017971039,
0.05341880023479462,
-0.0026795940939337015,
-0.025476502254605293,
-0.05122490972280502,
-0.026837827637791634,
0.0024196505546569824,
0.050610221922397614,
-0.01511843129992485,
0.07777220010757446,
-0.015841767191886902,
-0.051384005695581436,
-0.0002378482895437628,
-0.023462925106287003,
0.03500884771347046,
-0.03272978216409683,
-0.008121134713292122,
-0.007156535517424345,
-0.04160035401582718,
0.04470575973391533,
0.01437130942940712,
0.08719084411859512,
0.0611199252307415,
0.009692368097603321,
-0.04978753626346588,
0.05594164878129959,
0.013171880505979061,
-0.028852790594100952,
0.042180247604846954,
-0.05220130458474159,
-0.05415826290845871,
-0.012887384742498398,
0.020380757749080658,
0.0467672236263752,
0.02616448886692524,
0.06021685153245926,
0.07784484326839447,
0.023790495470166206,
0.07491496205329895,
0.029440928250551224,
-0.03253545984625816,
0.031001098453998566,
0.011639963835477829,
0.03134297579526901,
-0.01301729865372181,
0.023228906095027924,
0.03453126922249794,
0.04203556850552559,
0.0002696490555536002,
-0.07871856540441513,
-0.007232470903545618,
0.05630025640130043,
0.06085296720266342,
0.0011849211296066642,
0.001924911281093955,
-0.00022683778661303222,
-0.0027296803891658783,
0.020772479474544525,
0.01726062223315239,
-0.0054774233140051365,
-0.0426512286067009,
-0.0006053249817341566,
0.018118927255272865,
-0.025723837316036224,
-0.027973227202892303,
-0.0012135934084653854,
0.05492275580763817,
0.08039585500955582,
0.05688821151852608,
0.013775364495813847,
-0.05962323024868965,
0.054101116955280304,
0.000006862796453788178,
0.029029086232185364,
-0.03568504750728607,
-0.05308200418949127,
0.0071497769095003605,
0.05520166829228401,
-0.028626699000597,
-0.01878749392926693,
-0.013968013226985931,
-0.022136881947517395,
-0.012200534343719482,
-0.03489425405859947,
-0.07297225296497345,
0.003120043547824025,
0.024357303977012634,
0.024380572140216827,
-0.002360848942771554,
-0.03777367249131203,
0.047897279262542725,
-0.06300406157970428,
0.08268453180789948,
0.011187445372343063,
-0.03653768450021744,
0.013024833053350449,
-0.020237522199749947,
-0.006729273125529289,
-0.06464925408363342,
0.026474416255950928,
-0.03966554254293442,
0.04221542924642563,
0.0034263068810105324,
-0.036596715450286865,
0.015050270594656467,
0.01048603467643261,
-0.003729334333911538,
-0.03974449262022972,
-0.002720803255215287,
0.05162335932254791,
-0.05355620011687279,
-0.03127521649003029,
-0.0225505493581295,
-0.03534117713570595,
-0.0639725998044014,
0.015073565766215324,
-0.03289289399981499,
-0.06599093973636627,
0.018666964024305344,
-0.03774252161383629,
0.006313869263976812,
0.00047002709470689297,
0.014603656716644764,
-0.03909144178032875,
0.01981869339942932,
-0.019569190219044685,
0.0011679416056722403,
0.013353565707802773,
-0.08247663080692291,
0.037902142852544785,
0.012618029490113258,
-0.03335699439048767,
-0.02020409144461155,
-0.022984648123383522,
0.05625060573220253,
-0.010121266357600689,
-0.0030468017794191837,
-0.004817991517484188,
-0.002756723901256919,
0.043996412307024,
-0.002850464079529047,
-0.049814604222774506,
0.030357999727129936,
-0.03670176863670349,
-0.024534471333026886,
-0.04915471747517586,
0.06642485409975052,
-0.06026700511574745,
0.02922358177602291,
-0.007601288612931967,
-0.02189548686146736,
0.0063896700739860535,
0.06911123543977737,
-0.055563148111104965,
-0.018383225426077843,
-0.0022752878721803427,
-0.010578010231256485,
0.018667010590434074,
0.026854712516069412,
0.001099070068448782,
0.019817519932985306,
0.003601593431085348,
-0.05635472387075424,
0.06491638720035553,
0.004819005262106657,
-0.061449289321899414,
-0.05190979689359665,
0.024441400542855263,
-0.02652200497686863,
-0.0040640439838171005,
-0.03282909095287323,
-0.01578081212937832,
-0.06957848370075226,
0.03499789908528328,
0.0753069594502449,
-0.04118996858596802,
0.0005815019831061363,
-0.006412610411643982,
-0.03799640014767647,
-0.049049168825149536,
-0.03450554236769676,
-0.03744520992040634,
-0.025260698050260544,
0.011763573624193668,
-0.029154010117053986,
0.0069446684792637825,
-0.03010205738246441,
-0.060438644140958786,
0.024008234962821007,
0.023137010633945465,
-0.01592825911939144,
0.055511076003313065,
-0.04342157021164894,
-0.001791659975424409,
-0.0011776912724599242,
0.00964035652577877,
-0.07055502384901047,
0.037618447095155716,
-0.004847810138016939,
-0.05288204550743103,
-0.04829707369208336,
0.034681081771850586,
-0.03720901161432266,
-0.006864537484943867,
-0.01129683293402195,
0.029724031686782837,
-0.051622338593006134,
-0.04704449325799942,
-0.011190571822226048,
-0.018731802701950073,
-0.02033332549035549,
-0.014875532127916813,
-0.01682562753558159,
-0.009307211264967918,
-0.016572333872318268,
-0.12818756699562073,
0.012361765839159489,
0.0018820051336660981,
-0.029991986230015755,
0.05319511517882347,
-0.022420911118388176,
0.0323011688888073,
0.03700902312994003,
-0.051998574286699295,
-0.02330259047448635,
-0.0155403483659029,
-0.016247885301709175,
-0.017966177314519882,
0.05036404728889465,
0.021948199719190598,
0.05931825563311577,
-0.05255064740777016,
0.015639226883649826,
0.007595006842166185,
-0.0026473619509488344,
0.03419932723045349,
-0.04375861585140228,
-0.0636497363448143,
0.008172579109668732,
0.034327853471040726,
-0.032664988189935684,
0.02915806509554386,
0.0418272390961647,
-0.027151376008987427,
-0.025938689708709717,
-0.00839430931955576,
-0.02526908367872238,
-0.0037981460336595774,
-0.013139946386218071,
-0.033516496419906616,
0.025855671614408493,
-0.010343975387513638,
-0.03807402774691582,
-0.048700001090765,
-0.025264455005526543,
0.048897091299295425,
-0.0023254863917827606,
0.034710418432950974,
0.04721979796886444,
-0.0008787115220911801,
0.03680826351046562,
0.018601352348923683,
-0.01210546400398016,
-0.018824182450771332,
-0.02548406831920147,
0.008892986923456192,
-0.040988098829984665,
0.06071716547012329,
-0.0053267087787389755,
-0.0036302804946899414,
0.004453915636986494,
-0.01974761113524437,
0.03756290301680565,
-0.01601298712193966,
0.06734282523393631,
0.08291245251893997,
-0.04224613308906555,
0.0023595120292156935,
-0.020267104730010033,
0.116531603038311,
-0.02705501578748226,
-0.019592605531215668,
-0.00843118131160736,
0.0175100639462471,
-0.01909005269408226,
0.042942315340042114,
0.0000910557500901632,
0.0026387274265289307,
0.03524356335401535,
-0.03893771022558212,
0.0023046182468533516,
-0.018727721646428108,
-0.049629516899585724,
0.02977728098630905,
0.004996350035071373,
-0.07639031112194061,
-0.01865052431821823,
-0.04052331671118736,
-0.006931069307029247,
0.050207603722810745,
-0.00020145447342656553,
0.07614969462156296,
0.029248496517539024,
-0.030054984614253044,
0.061585210263729095,
-0.03332807868719101,
-0.00005158468775334768,
0.015951208770275116,
-0.045545075088739395,
-0.021865876391530037,
-0.04767996072769165,
0.04775867983698845,
0.05185043811798096,
0.026508251205086708,
-0.032761115580797195,
0.002449651947245002,
0.020674819126725197,
0.013086837716400623,
0.07199108600616455,
0.05339251458644867,
-0.04641951620578766,
0.012856178916990757,
0.0543750636279583,
0.04093896225094795,
-0.05413888022303581,
0.04755248874425888,
-0.007252079900354147,
0.020037442445755005,
0.026933135464787483,
0.02807001955807209,
-0.01587115414440632,
-0.014260513707995415,
0.02616608887910843,
-0.0178934708237648,
-0.005808661226183176,
0.022873885929584503,
0.029839130118489265,
-0.02907797507941723,
-0.00952098984271288,
0.06408534198999405,
-0.012239916250109673,
0.03393549472093582,
0.10020523518323898,
0.006042757537215948,
-0.025454092770814896,
-0.05452908203005791,
-0.0606766939163208,
0.07743547856807709,
0.03050284832715988,
0.008218198083341122,
-0.01240023598074913,
-0.03679481893777847,
-0.017793525010347366,
-0.06558432430028915,
0.03504869341850281,
0.02561625838279724,
0.043957777321338654,
0.10467493534088135,
-0.014737162739038467,
0.0529712438583374,
-0.004646875895559788,
0.04973730817437172,
0.0013975121546536684,
-0.061588820070028305,
-0.0030879718251526356,
-0.021720780059695244,
-0.04422466456890106,
0.027693336829543114,
0.020727364346385002,
-0.007353431079536676,
-0.05277349054813385,
0.014604762196540833,
0.0012371418997645378,
0.004963451996445656,
-0.018687831237912178,
0.017112204805016518,
0.02211059257388115,
-0.059054698795080185,
-0.027503835037350655,
0.0320233516395092,
0.02332575060427189,
0.02815687283873558,
-0.034819893538951874,
-0.03011055663228035,
0.02927517332136631,
-0.0733218640089035,
-0.05288887768983841,
-0.015025305561721325,
-0.0004928358248434961,
0.046538081020116806,
-0.006831471808254719,
0.030829235911369324,
-0.03358187526464462,
-0.067625030875206,
-0.03983931988477707,
-0.014223800040781498,
-0.04024624451994896,
0.04834975674748421,
-0.029599038884043694,
-0.03415926918387413,
0.0029863074887543917,
-0.005603548604995012,
0.006090875249356031,
-0.036343976855278015,
-0.020986124873161316,
-0.0002576578699517995,
-0.030548660084605217,
-0.05043546110391617,
-0.01726635731756687,
0.012359345331788063,
-0.005723313428461552,
-0.011624262668192387,
-0.004078018479049206,
-0.008045854046940804,
0.01054928358644247,
0.0120223518460989,
0.006977761164307594,
-0.0071425423957407475,
-0.0043826657347381115,
-0.04720888286828995,
-0.02945808321237564,
-0.03515356406569481,
-0.03749513998627663,
0.042856015264987946,
-0.016969382762908936,
-0.003907628823071718,
-0.01559639535844326,
-0.03176159784197807,
-0.016494637355208397,
-0.04817836731672287,
0.003942445851862431,
0.060807738453149796,
0.01771165058016777,
0.022363455966114998,
0.039475977420806885,
0.04271947219967842,
0.030444229021668434,
-0.06695994734764099,
-0.03338097780942917,
0.008166267536580563,
-0.014526363462209702,
0.06522814929485321,
0.015319687314331532,
-0.0545465312898159,
0.000351881084498018,
0.056819990277290344,
0.017070183530449867,
-0.0017558292020112276,
-0.01198437437415123,
0.03689536452293396,
0.04950028285384178,
-0.01960938796401024,
-0.013754893094301224,
-0.0007597394287586212,
0.029352592304348946,
0.045498691499233246,
0.042223211377859116,
-0.019423967227339745,
-0.031791746616363525,
-0.017545929178595543,
0.0725877583026886,
0.08017601817846298,
0.027150139212608337,
0.05940139293670654,
0.017566511407494545,
0.011715318076312542,
-0.023377420380711555,
0.012408262118697166,
-0.00932813249528408,
0.07653266936540604,
-0.011879867874085903,
-0.020682796835899353,
-0.0008322222274728119,
0.013146358542144299,
0.009846113622188568,
-0.02196810580790043,
-0.03522656857967377,
0.032875992357730865,
0.040753960609436035,
-0.02241550385951996,
-0.016819588840007782,
0.023857785388827324,
0.007887940853834152,
0.025486337020993233,
-0.03843114525079727,
-0.004747385159134865,
0.06030868738889694,
0.04077531024813652,
0.04134342446923256,
-0.029217995703220367,
0.03366559371352196,
0.034193068742752075,
0.009079407900571823,
0.015336812473833561,
-0.007422095164656639,
-0.09506354480981827,
-0.02011086605489254,
0.07599984109401703,
0.0415039137005806,
-0.016952218487858772,
-0.05037492513656616,
-0.02616143226623535,
0.014061675406992435,
0.02958713471889496,
-0.004147211089730263,
0.03337269276380539,
0.022774845361709595,
0.014539957977831364,
0.005274365656077862,
-0.0012600405607372522,
-0.022052433341741562,
0.042693376541137695,
-0.008028102107346058,
0.02670997381210327,
-0.05382508784532547,
-0.010940640233457088,
-0.009881619364023209,
-0.022557245567440987,
-0.01645803079009056,
-0.047436464577913284,
0.010252906940877438,
0.03416978567838669,
-0.02509380131959915,
-0.010507368482649326,
0.029356442391872406,
-0.003682853188365698,
0.034281231462955475,
-0.0449218787252903,
-0.00038227991899475455,
-0.05262918025255203,
-0.010083615779876709,
-0.0023793953005224466,
-0.07170730084180832,
-0.03503188118338585,
0.051916275173425674,
0.0029639550484716892,
0.03175497055053711,
-0.015184481628239155,
-0.048801954835653305,
-0.005572854075580835,
-0.020487679168581963,
0.031953807920217514,
0.06098141893744469,
-0.012747480534017086,
0.043706972151994705,
0.037263423204422,
-0.010013599880039692,
-0.030429890379309654,
-0.040668655186891556,
0.019541066139936447,
0.024441147223114967,
-0.03600803017616272,
0.04609265923500061,
-0.047975677996873856,
-0.05314396321773529,
0.04722243547439575,
-0.04883802682161331,
0.01790759153664112,
-0.0015442768344655633,
0.14096380770206451,
0.031988322734832764,
-0.04039890691637993,
0.06331150233745575,
0.026509519666433334,
-0.016503384336829185,
-0.052524883300065994,
0.010990455746650696,
-0.037193406373262405,
0.000013515763384930324,
-0.0058587160892784595,
-0.01723710261285305,
0.048697054386138916,
0.029867229983210564,
-0.035889070481061935,
0.005392946768552065,
-0.021714305505156517,
-0.07002758234739304,
-0.01060804259032011,
-0.06117228418588638,
-0.007567611522972584,
-0.016579020768404007,
0.016137631610035896,
0.012115848250687122,
-0.033337607979774475,
-0.016436085104942322,
0.017557967454195023,
-0.026877386495471,
-0.040773820132017136,
-0.06647200137376785,
-0.011038337834179401,
0.012482400983572006,
-0.05084628984332085,
0.029060618951916695,
-0.010298902168869972,
0.0898827463388443,
-0.03898675739765167,
-0.03741960972547531,
-0.035051725804805756,
0.04362774267792702,
-0.08201607316732407,
-0.07018440961837769,
-0.009078281931579113,
-0.011168353259563446,
-0.007175988983362913,
-0.01759248599410057,
-0.01690385676920414,
-0.002030373318120837,
-0.01650235615670681,
-0.021871889010071754,
-0.01015978492796421,
-0.019465697929263115,
0.0022376300767064095,
-0.03507145494222641,
0.053932495415210724,
-0.007257062941789627,
0.011030997149646282,
0.06739041954278946,
-0.0010906871175393462,
-0.06695571541786194,
0.01302964985370636,
-0.015359397977590561,
-0.006529614329338074,
0.01793399639427662,
-0.005258533172309399,
0.008184757083654404,
-0.016607418656349182,
0.026017457246780396,
0.0017062786500900984,
-0.030720988288521767,
0.005498122423887253,
0.007230278104543686,
0.01348649151623249,
-0.007575962692499161,
0.009035148657858372,
0.07009474188089371,
0.017270388081669807,
0.027015812695026398,
0.032170455902814865,
0.018948139622807503,
-0.02002561464905739,
-0.008119232952594757,
0.02423267252743244,
-0.009722109884023666,
0.08027654141187668,
-0.012151126749813557,
-0.003075480693951249,
0.02833569049835205,
-0.008327977731823921,
0.02685275487601757,
0.021650519222021103,
-0.0059899925254285336,
0.004130924586206675,
0.03406786918640137,
-0.0020061309915035963,
-0.04980306327342987,
0.009076075628399849,
0.032508619129657745,
0.030409807339310646,
-0.06338130682706833,
-0.009932504035532475,
-0.048035748302936554,
-0.012065292336046696,
-0.043032433837652206,
-0.033834848552942276,
0.0361483134329319,
-0.01497404370456934,
0.009512481279671192,
-0.021051602438092232,
0.08067763596773148,
0.007020199671387672,
0.08146431297063828,
0.08796445280313492,
-0.06785368919372559,
-0.001617913949303329,
0.03593248873949051,
0.022864095866680145,
-0.026637008413672447,
-0.03375688195228577,
0.0025411818642169237,
0.0567457489669323,
0.019530298188328743,
-0.035292379558086395,
-0.019712772220373154,
-0.045934829860925674,
-0.005405952222645283
] |
<p>I googled How to calculate the air requirements of pneumatic conveying and found a clue to what might be a correct equation (<a href="http://uk.ask.com/question/pneumatic-conveying-calculation" rel="nofollow">http://uk.ask.com/question/pneumatic-conveying-calculation</a>). </p>
<p>Here is my attempt at running the calculation: </p>
<p>Tube diameter: 200mm<br>
Tube raduis: 100mm
Tube length : 1675 meters<br>
Weight of internal mail cannister: 1000kgs<br>
Total cylinder volume: 1.76×10^6<br>
Maximum velocity mail cannister velocity: 50m/s</p>
<p>Steps followed in an attempt to find the answer:<br>
square the radius of the cylinder<br>
$100 \times 100 = 10000$
multiply the result by $\pi$</p>
<p>$10000 * \pi = 31415.9265359$
then divide the force require by the area of the cylinder face (I have just calculated the area of a circle for this part of the equation.)</p>
<p>$31415.93/5102 = 6.15757154057$ I am Assuming this answer liter's of air? and it should be multiplied by the volume of the tube in order for me to arrive at the answer I require?</p>
<p>forced required calculation<br>
mass (kg)= 1000kgs/9.8 = 102.04 kgs<br>
if $force$ = $mass$ $\times$ $acceleration$ ($F=ma$) then..<br>
$102.04 \times 50m/s = 5102$ $Newtons$ required </p>
<p>Am I googling in the right direction or should I be looking towards fluid dynamics equations like control volume analysis?</p> | g4751 | [
0.008594401180744171,
0.03284046798944473,
-0.010253844782710075,
0.016191598027944565,
-0.007594869937747717,
0.02251064032316208,
0.039286959916353226,
0.01958124153316021,
-0.07675455510616302,
-0.014958522282540798,
-0.03220630809664726,
-0.01825169287621975,
-0.0074018207378685474,
0.015671903267502785,
0.0518987812101841,
0.02069873921573162,
0.05614902824163437,
-0.035006482154130936,
0.0025814261753112078,
-0.006829878780990839,
0.04776697978377342,
0.009249692782759666,
-0.022078458219766617,
-0.0665082335472107,
-0.018751079216599464,
-0.0313091054558754,
0.012091134674847126,
0.01578146405518055,
-0.07626140862703323,
-0.037070777267217636,
0.027846060693264008,
-0.00554688461124897,
-0.010252820327877998,
-0.03512498363852501,
-0.030207596719264984,
-0.008479396812617779,
-0.00152018282096833,
-0.011398080736398697,
-0.009858149103820324,
-0.052604157477617264,
0.004612282384186983,
-0.05869494751095772,
-0.012572155334055424,
0.06456353515386581,
0.0025843374896794558,
0.005804511718451977,
-0.03331078216433525,
-0.024043967947363853,
-0.03346630558371544,
-0.028969911858439445,
0.024959275498986244,
-0.014629046432673931,
-0.052144136279821396,
-0.03612939640879631,
-0.02950458973646164,
0.0628155916929245,
0.03890884667634964,
-0.026983210816979408,
0.026867030188441277,
-0.030113790184259415,
-0.03684169054031372,
-0.023423707112669945,
-0.0021614502184093,
0.0009382724529132247,
0.07129811495542526,
0.007917987182736397,
-0.007540812250226736,
-0.035744357854127884,
0.020997589454054832,
0.047976814210414886,
-0.005582402925938368,
-0.055682361125946045,
0.060791000723838806,
-0.03232097998261452,
-0.005910930689424276,
-0.01892770454287529,
-0.011527624912559986,
-0.038236308842897415,
0.01803855039179325,
-0.002983118174597621,
-0.004083753097802401,
0.030317112803459167,
0.04690377786755562,
-0.024284467101097107,
0.044863373041152954,
-0.049162715673446655,
-0.035116154700517654,
0.009010913781821728,
-0.03383393585681915,
-0.004004036076366901,
-0.06199325993657112,
0.053193122148513794,
0.036200061440467834,
0.0004401243932079524,
0.0357016921043396,
-0.04137678071856499,
-0.06667677313089371,
0.03827229142189026,
-0.005697082728147507,
0.019191380590200424,
-0.012315455824136734,
-0.015681784600019455,
0.010759866796433926,
-0.03771108388900757,
0.008240151219069958,
-0.03598039224743843,
0.04016668722033501,
0.07509339600801468,
0.01654794253408909,
-0.03542039915919304,
-0.04113061726093292,
-0.027282819151878357,
-0.047655485570430756,
-0.03474048897624016,
0.002449388150125742,
-0.04788120463490486,
0.03907884284853935,
-0.019753949716687202,
-0.0021013705991208553,
0.09496928751468658,
-0.0459916926920414,
0.03644051402807236,
0.031917206943035126,
0.015222156420350075,
-0.04925452172756195,
-0.05844266340136528,
0.009942800737917423,
-0.007543193642050028,
-0.021764788776636124,
-0.0019465091172605753,
0.06005369871854782,
-0.0318276546895504,
0.028534596785902977,
-0.014429129660129547,
-0.017944814637303352,
-0.020099030807614326,
-0.09956755489110947,
0.002348030684515834,
-0.01967676728963852,
-0.004934005439281464,
0.030159842222929,
0.0037131262943148613,
0.01751585118472576,
0.037093061953783035,
-0.02878153696656227,
-0.013461723923683167,
-0.04600266367197037,
0.02845860831439495,
0.0018414121586829424,
-0.01595301739871502,
-0.029208039864897728,
0.05529521778225899,
0.030680447816848755,
-0.018340755254030228,
-0.00009180900815408677,
0.0006332769989967346,
0.04307990521192551,
0.03378942608833313,
0.01831878535449505,
-0.025133999064564705,
0.07298804819583893,
0.013252927921712399,
0.043306369334459305,
-0.008012477308511734,
-0.05174849554896355,
0.031300485134124756,
-0.058729562908411026,
-0.001353139290586114,
-0.027263004332780838,
-0.03730009123682976,
-0.07690583914518356,
-0.024070264771580696,
-0.013137204572558403,
0.0441071055829525,
-0.0012528051156550646,
-0.020626908168196678,
0.10825959593057632,
0.05715508759021759,
-0.04487939178943634,
-0.032613664865493774,
0.06758785992860794,
-0.04899273067712784,
0.03225051984190941,
-0.030664870515465736,
-0.06293681263923645,
0.005344942677766085,
0.023275576531887054,
0.04981083795428276,
-0.02572520263493061,
-0.006311534903943539,
0.003855618182569742,
0.046549078077077866,
0.009983278810977936,
0.023699255660176277,
-0.04668720066547394,
0.03786430135369301,
0.03151119127869606,
-0.11557126045227051,
0.0029101604595780373,
-0.017504867166280746,
0.042740557342767715,
0.006922371219843626,
0.039209604263305664,
0.028325041756033897,
0.01833326369524002,
0.010795289650559425,
-0.023413697257637978,
0.023857776075601578,
-0.006567110773175955,
0.04395870119333267,
0.04430153965950012,
-0.017201660200953484,
-0.0017437291098758578,
0.02314787171781063,
-0.035496242344379425,
0.013754095882177353,
0.019707394763827324,
0.028288917616009712,
-0.040174391120672226,
0.029196498915553093,
0.05609360337257385,
0.0009503335459157825,
0.0018012949731200933,
-0.011542419902980328,
-0.07332021743059158,
0.004512243904173374,
0.06564494222402573,
-0.04966389015316963,
0.012346524745225906,
0.004673748277127743,
-0.011999852955341339,
0.017946915701031685,
-0.05097084119915962,
-0.004116218537092209,
0.01263338141143322,
0.0424627922475338,
-0.018722504377365112,
0.02273046225309372,
-0.023326091468334198,
-0.004989474080502987,
0.04747934266924858,
-0.016210203990340233,
-0.00020263047190383077,
-0.020337525755167007,
-0.03935389220714569,
0.02401651069521904,
0.009381882846355438,
-0.0377897247672081,
-0.02020326815545559,
0.03525129333138466,
-0.060412514954805374,
-0.005258417688310146,
-0.009095746092498302,
0.046377647668123245,
-0.006375335156917572,
0.004316162783652544,
-0.021499302238225937,
-0.015460006892681122,
-0.033082738518714905,
0.016903385519981384,
0.01603500172495842,
0.006186771206557751,
0.017835306003689766,
0.04778444766998291,
-0.07976679503917694,
0.02123403176665306,
-0.04180152341723442,
0.02180289849638939,
0.05884569138288498,
0.027229778468608856,
-0.019193893298506737,
0.01874588057398796,
-0.04993399232625961,
-0.013025213964283466,
0.02499985694885254,
-0.07076923549175262,
0.091361403465271,
-0.015104593709111214,
0.028051400557160378,
0.05641615390777588,
0.027157001197338104,
-0.006743988487869501,
-0.019208015874028206,
0.04416544362902641,
-0.010893279686570168,
-0.07799360901117325,
0.06712640076875687,
0.0265265591442585,
0.021190505474805832,
-0.01321442611515522,
-0.018469126895070076,
0.044364310801029205,
-0.06366931647062302,
0.00042549913632683456,
0.0016847376246005297,
0.1396673619747162,
0.023647837340831757,
-0.03270565718412399,
0.03929488733410835,
-0.029102060943841934,
-0.06104383245110512,
-0.018305307254195213,
0.016329525038599968,
0.03194768354296684,
-0.03717045485973358,
-0.0038612671196460724,
-0.03828759118914604,
-0.09239576756954193,
-0.05300603434443474,
0.010113765485584736,
0.008971438743174076,
0.01594952680170536,
0.019441833719611168,
-0.026883741840720177,
-0.026362275704741478,
-0.05608745664358139,
0.09166847914457321,
-0.049778953194618225,
-0.04783529415726662,
0.042960941791534424,
-0.012996308505535126,
-0.0953613743185997,
-0.018387842923402786,
0.03871621564030647,
0.018804417923092842,
0.03955233469605446,
0.01321667991578579,
0.019268721342086792,
0.017572803422808647,
-0.04374327138066292,
0.03576761856675148,
0.05202221870422363,
-0.03218346834182739,
-0.012309118174016476,
-0.02992408350110054,
-0.021879728883504868,
0.0076686968095600605,
0.02465684525668621,
0.0001965704868780449,
0.0020703182090073824,
-0.0133928582072258,
-0.039580266922712326,
-0.018844425678253174,
-0.011736753396689892,
0.0036170517560094595,
-0.002734455978497863,
0.029251238331198692,
0.06523491442203522,
0.023343345150351524,
-0.021866358816623688,
0.05815698951482773,
-0.004955403506755829,
0.04659057408571243,
-0.05925171449780464,
-0.008607333526015282,
0.03521156311035156,
0.05248870700597763,
-0.027759548276662827,
-0.009289996698498726,
0.008925621397793293,
-0.010176582261919975,
-0.02872289903461933,
-0.022847086191177368,
0.059686385095119476,
0.0395035445690155,
-0.04602647200226784,
0.022545883432030678,
0.031419653445482254,
-0.035330623388290405,
-0.004296319559216499,
-0.04717756435275078,
-0.08111074566841125,
-0.03321273252367973,
0.004246717784553766,
0.035692937672138214,
-0.032058294862508774,
0.006745470687747002,
0.006085135508328676,
-0.019892308861017227,
0.05744302272796631,
0.06920468807220459,
0.03469241410493851,
-0.03480244800448418,
-0.014753629453480244,
-0.03570808470249176,
-0.011548061855137348,
0.00012980627070646733,
0.019560489803552628,
0.03306146338582039,
-0.039057932794094086,
-0.056334756314754486,
-0.06116393208503723,
-0.06327266991138458,
-0.015909258276224136,
0.03287661448121071,
-0.014524564146995544,
0.02449270337820053,
-0.015400589443743229,
-0.059958744794130325,
0.024171868339180946,
0.06527185440063477,
-0.011632549576461315,
0.041284456849098206,
0.06376675516366959,
-0.03131616860628128,
0.06102047488093376,
0.024841276928782463,
0.007668073754757643,
0.046378735452890396,
0.0312887504696846,
0.02660704217851162,
0.03717964515089989,
-0.009686463512480259,
-0.04474093019962311,
0.01363989245146513,
-0.021951787173748016,
-0.06278920918703079,
0.022175222635269165,
-0.004733594600111246,
0.0004007004026789218,
0.0178515687584877,
-0.0026973343919962645,
-0.03777822479605675,
-0.011695419438183308,
0.048968005925416946,
0.06056314334273338,
0.028812505304813385,
-0.03676747903227806,
0.02091672457754612,
-0.017808346077799797,
-0.03807514160871506,
-0.013161536306142807,
-0.025172309949994087,
0.03657730668783188,
0.0460054874420166,
0.05208935961127281,
0.04570622742176056,
0.012569676153361797,
0.04490247741341591,
-0.03570780158042908,
0.02199978567659855,
0.006354698445647955,
-0.0033766250126063824,
-0.03726309537887573,
0.00767237413674593,
-0.0027788477018475533,
-0.022520409896969795,
-0.054341282695531845,
0.059494536370038986,
0.009931163862347603,
0.0053099351935088634,
-0.037518393248319626,
0.06460606306791306,
-0.03274393454194069,
-0.03269675374031067,
0.05808652192354202,
-0.003924270626157522,
-0.03663716837763786,
0.006124340463429689,
0.023609232157468796,
-0.027835024520754814,
0.04884030297398567,
-0.00441172206774354,
0.023724788799881935,
0.013475248590111732,
0.00841718353331089,
-0.030900441110134125,
0.028884965926408768,
-0.0014475204516202211,
-0.06768324971199036,
-0.004531952552497387,
-0.014436919242143631,
0.003641239134594798,
-0.02990228869020939,
-0.042937640100717545,
0.043831922113895416,
-0.05600261315703392,
0.0011975275119766593,
0.03853137046098709,
-0.04244076833128929,
-0.003547260072082281,
0.037797294557094574,
0.01180643867701292,
0.03182917460799217,
0.04258298501372337,
-0.004013473633676767,
-0.020084001123905182,
-0.01959923841059208,
-0.006094076205044985,
-0.021228881552815437,
0.02598476968705654,
0.07115636020898819,
0.00039259015466086566,
-0.043974798172712326,
-0.060058414936065674,
-0.006266484502702951,
0.04638706147670746,
-0.03277316316962242,
-0.00673431484028697,
0.018140755593776703,
-0.05176892876625061,
-0.017699791118502617,
0.009898917749524117,
0.008869939483702183,
-0.028891218826174736,
-0.04547937586903572,
-0.013448791578412056,
0.05834292620420456,
0.005361583549529314,
0.09732744842767715,
0.10208160430192947,
0.045649051666259766,
0.026343954727053642,
-0.00929373037070036,
-0.021594997495412827,
-0.01731959544122219,
-0.006303954403847456,
-0.03696011006832123,
0.0006467123748734593,
0.002646638546139002,
0.045034557580947876,
0.033566106110811234,
0.04426364600658417,
-0.003523178631439805,
-0.05293266102671623,
0.030941292643547058,
-0.030649524182081223,
-0.023119082674384117,
-0.036180902272462845,
0.0014752274146303535,
-0.046812448650598526,
-0.030768806114792824,
0.03973807394504547,
-0.01486402191221714,
-0.06784079223871231,
-0.01916811242699623,
0.06571444869041443,
0.0034154714085161686,
0.05894105136394501,
-0.016803501173853874,
0.015030968934297562,
-0.003859560703858733,
-0.044505637139081955,
0.057532671838998795,
0.06939594447612762,
0.005053602159023285,
-0.011691367253661156,
0.02930593304336071,
0.022052595391869545,
0.013639564625918865,
-0.013222748413681984,
0.04740826040506363,
-0.010116933844983578,
-0.01691765896975994,
0.05785006284713745,
0.012854044325649738,
0.03602695092558861,
-0.03183231130242348,
0.025057146325707436,
-0.039452265948057175,
0.02837453968822956,
0.009777363389730453,
-0.005898080300539732,
0.0012754667550325394,
-0.026536839082837105,
-0.06346029788255692,
-0.03112911805510521,
0.035678986459970474,
0.029468674212694168,
0.0172274187207222,
-0.010356636717915535,
-0.036183785647153854,
-0.06502251327037811,
-0.04565555602312088,
0.05939700827002525,
0.04602443054318428,
-0.02396310865879059,
-0.026587510481476784,
0.022800711914896965,
0.09578489512205124,
-0.0037128503900021315,
0.007274576462805271,
0.003167735179886222,
-0.018730180338025093,
-0.03987294062972069,
0.005585609469562769,
-0.009460880421102047,
-0.008524260483682156,
-0.0010815998539328575,
-0.05038665235042572,
-0.0112405801191926,
-0.05323660373687744,
-0.00485937250778079,
-0.04782005771994591,
-0.06576322019100189,
-0.01077316328883171,
0.0072418032214045525,
-0.03425288200378418,
0.03921421244740486,
0.05097593739628792,
0.03884191811084747,
0.12088475376367569,
0.017607299610972404,
-0.06704223155975342,
0.014064686372876167,
0.005981261841952801,
0.034256692975759506,
-0.013421909883618355,
-0.03426707163453102,
-0.02725931629538536,
0.01048953179270029,
0.03274368494749069,
0.053566716611385345,
0.04454199969768524,
0.03485424071550369,
-0.0052365087904036045,
0.028687957674264908,
0.02110946923494339,
0.04131929948925972,
-0.06719556450843811,
0.017235321924090385,
0.06366284191608429,
0.046934373676776886,
0.000561403576284647,
0.02719748392701149,
0.05438128113746643,
-0.05132456496357918,
0.023193541914224625,
0.03493703156709671,
-0.0597657710313797,
0.05706686154007912,
-0.004522531293332577,
-0.055341850966215134,
-0.004007658921182156,
0.032712820917367935,
0.031226474791765213,
0.020341908559203148,
0.029153019189834595,
0.0347609668970108,
0.045602694153785706,
-0.0015372075140476227,
-0.004396373871713877,
-0.025368714705109596,
0.04829505458474159,
-0.03032670170068741,
-0.057478345930576324,
0.013550642877817154,
0.007555621210485697,
-0.023182107135653496,
-0.03404957428574562,
-0.023553213104605675,
-0.012327255681157112,
-0.04418526589870453,
0.04050545021891594,
-0.02000805176794529,
-0.014426060952246189,
-0.01677772030234337,
-0.01547415554523468,
0.005799917504191399,
-0.028863009065389633,
-0.034443680197000504,
-0.059058740735054016,
-0.004441310651600361,
0.02407274767756462,
0.0034936617594212294,
0.03276768699288368,
-0.029237572103738785,
0.008852419443428516,
0.01987624354660511,
-0.06584476679563522,
0.022717153653502464,
0.04102817550301552,
-0.019071519374847412,
0.01653224043548107,
0.017337962985038757,
-0.03753781318664551,
0.011852787807583809,
-0.042121198028326035,
-0.009958906099200249,
0.017448794096708298,
-0.012535731308162212,
0.013476742431521416,
-0.053322359919548035,
0.003022699151188135,
0.02968653291463852,
-0.02050832472741604,
0.0010050118435174227,
0.013425947166979313,
-0.00044815277215093374,
-0.004323538392782211,
0.03088333085179329,
0.03188324719667435,
0.01752496510744095,
0.012023904360830784,
-0.02779407612979412,
0.03481552004814148,
0.0587029904127121,
0.0034333018120378256,
0.049977049231529236,
-0.011917573399841785,
0.016297705471515656,
0.004155747126787901,
0.0015225898241624236,
0.0373062826693058,
0.009581105783581734,
0.0058367615565657616,
-0.010334381833672523,
0.04961583390831947,
-0.02646602876484394,
0.08181393146514893,
0.01967017352581024,
-0.014374366030097008,
0.005559761077165604,
0.029497558251023293,
0.019580550491809845,
0.010325048118829727,
-0.05345802754163742,
0.007114299573004246,
0.02468295767903328,
-0.059893686324357986,
0.005601900164037943,
0.04310501739382744,
0.008127018809318542,
-0.046353522688150406,
-0.07497680932283401,
-0.03663782775402069,
-0.019246986135840416,
-0.023431992158293724,
-0.06704548001289368,
0.010496948845684528,
0.0033441390842199326,
-0.02190583385527134,
0.008303811773657799,
0.015267468988895416,
-0.012711485847830772,
-0.045035213232040405,
0.023534106090664864,
0.012882763519883156,
-0.007005760911852121,
0.0219491608440876,
-0.0066492934711277485,
-0.021986525505781174,
0.008037283085286617,
0.016622619703412056,
-0.012554989196360111,
-0.08012532442808151,
-0.042645566165447235,
0.029553234577178955,
0.03189702332019806,
0.01180263515561819,
0.018489733338356018,
-0.010090735740959644,
0.025669051334261894,
-0.04956119507551193,
-0.025104273110628128,
-0.06649133563041687,
-0.010222125798463821,
0.02189723029732704,
-0.03622861206531525,
-0.030599605292081833,
-0.021597307175397873,
0.04259953275322914,
0.0499967485666275,
-0.028119118884205818,
-0.0011168355122208595,
-0.012198294512927532,
-0.025500278919935226,
-0.005409691482782364
] |
<p>I have read many questions which ask whether there can be photons at speed other than the speed of light and all of them are answered no!</p>
<p>But when the photon is created for ex during electron transition from higher to lower energy level, it cannot simply be at initial speed $c$!</p>
<p>Why it cannot be at $c$:
It would not suffice momentum conversation. Suppose one electron releases a photon, then the photon will need to have momentum of $\frac{h}{\lambda}$ and so would the electron in opposite direction, but that would push the electron towards the nucleus which would then again take it to (though unstable) lower energy state which would result in another photon. Since this does not happen, initial momentum cannot be $\frac{h}{\lambda}$</p>
<p>Since initially photon cannot be at speed $c$ it must reach the speed of light, may it be in unmeasurable less time and thus go through all the speeds between $\text{0}$ and $c$</p>
<p>Am I right? If I am right, why are all the questions answered no, then answered no? If I am wrong, where and why am I wrong?</p> | g159 | [
0.03607909753918648,
0.029724666848778725,
0.010490569286048412,
-0.020473843440413475,
0.09200102090835571,
0.021649958565831184,
0.03519812226295471,
0.022380448877811432,
-0.06848971545696259,
0.013884888961911201,
0.0072105443105101585,
0.01709619164466858,
-0.047199465334415436,
0.029880279675126076,
-0.03961418196558952,
-0.016763966530561447,
0.14336943626403809,
-0.04524833336472511,
0.0448208786547184,
0.04337969422340393,
-0.06148511916399002,
0.00532445777207613,
-0.028517553582787514,
-0.05037592723965645,
-0.030002674087882042,
0.039368774741888046,
-0.016689598560333252,
-0.07378436625003815,
-0.009226309135556221,
0.009649842046201229,
-0.009143264964222908,
-0.06077404320240021,
0.006328143645077944,
0.0031667619477957487,
0.017504947260022163,
-0.02140931226313114,
0.02296273596584797,
-0.02108408883213997,
0.016348395496606827,
0.0015594282886013389,
-0.014618773944675922,
-0.030261632055044174,
0.006870517507195473,
-0.04739265888929367,
0.029544783756136894,
0.04509681090712547,
0.03070700541138649,
0.0649198368191719,
0.0038248589262366295,
-0.022828558459877968,
0.013854295015335083,
0.06581658124923706,
-0.011650036089122295,
0.0001684135786490515,
0.0034109654370695353,
0.0209958478808403,
0.010251917876303196,
0.012279768474400043,
0.06550775468349457,
0.014147822745144367,
-0.009808960370719433,
-0.027125302702188492,
0.053156644105911255,
-0.013305626809597015,
0.021798286586999893,
-0.004542364738881588,
0.014727815985679626,
-0.04029575735330582,
0.015818806365132332,
-0.01368789654225111,
-0.0010815811110660434,
-0.027128862217068672,
-0.03689773753285408,
-0.015462865121662617,
0.018514886498451233,
-0.024813612923026085,
0.034022118896245956,
-0.09263690561056137,
-0.0002528009645175189,
0.00786548014730215,
-0.0391799621284008,
0.003775096731260419,
0.021304991096258163,
-0.029362929984927177,
0.023194586858153343,
0.02285258285701275,
-0.005004386883229017,
0.016977505758404732,
0.01276960875838995,
-0.018737265840172768,
0.04989728704094887,
-0.06854437291622162,
0.04218969866633415,
-0.020289959385991096,
-0.024965913966298103,
0.016844715923070908,
-0.012963918969035149,
0.054758865386247635,
-0.010143348947167397,
-0.06401616334915161,
-0.011418694630265236,
-0.0027196756564080715,
0.028802530840039253,
0.020747793838381767,
-0.023993078619241714,
-0.025746943429112434,
-0.016257312148809433,
-0.018450917676091194,
-0.0014410180738195777,
-0.030301662161946297,
0.01726006716489792,
-0.010058925487101078,
-0.07449079304933548,
-0.04022126644849777,
-0.09477376192808151,
-0.06425555795431137,
0.02275596372783184,
0.007288740016520023,
-0.0052091884426772594,
0.054890602827072144,
0.10144919902086258,
-0.02087579295039177,
-0.014906219206750393,
0.020801657810807228,
0.002342458814382553,
-0.0024249705020338297,
0.012191182933747768,
0.002606314606964588,
0.06049703061580658,
-0.0002122795704053715,
-0.054539039731025696,
0.04765620082616806,
-0.020583953708410263,
0.035095203667879105,
-0.01942390762269497,
-0.02951505407691002,
0.04514996334910393,
0.018971197307109833,
0.03834869712591171,
0.0063923937268555164,
0.03186008334159851,
-0.01081851776689291,
0.033582694828510284,
-0.02238532528281212,
-0.04567847400903702,
0.022828346118330956,
0.0014217013958841562,
0.05089903995394707,
0.01785493642091751,
0.03153329715132713,
0.008923779241740704,
0.021370327100157738,
-0.02850387617945671,
0.00919648539274931,
0.016200507059693336,
0.01344251912087202,
0.05472368001937866,
0.049311354756355286,
-0.03357512503862381,
0.0493416003882885,
0.05028747767210007,
0.017674950882792473,
-0.07921504229307175,
-0.03250119462609291,
-0.013439430855214596,
-0.003019963391125202,
-0.005935624707490206,
-0.04857094958424568,
-0.08783148974180222,
-0.07479299604892731,
-0.033447615802288055,
-0.001527181128039956,
-0.0034156707115471363,
0.01056880597025156,
0.01336036715656519,
-0.01768305152654648,
0.03319753333926201,
-0.008599610067903996,
-0.04153526946902275,
0.02410092204809189,
-0.04685620218515396,
-0.04027954116463661,
-0.022535668686032295,
-0.02386578731238842,
0.037103403359651566,
-0.0005617127171717584,
-0.0014829881256446242,
0.04951563850045204,
-0.023987911641597748,
-0.023077035322785378,
-0.02004948817193508,
0.010796302929520607,
-0.038801159709692,
-0.00796997919678688,
-0.038689691573381424,
-0.0287562757730484,
0.02844550833106041,
-0.049411360174417496,
0.0035960220266133547,
0.03816283494234085,
0.007520515937358141,
0.03410449996590614,
-0.03235338255763054,
-0.01388490479439497,
0.02587026171386242,
0.004784822463989258,
0.00034251308534294367,
-0.023237209767103195,
0.038129162043333054,
-0.007431461941450834,
0.051869917660951614,
-0.04746045544743538,
-0.023579172790050507,
0.04199831932783127,
0.01208212785422802,
-0.04280927777290344,
-0.0005656154244206846,
0.0369705893099308,
0.006155224982649088,
0.00852511078119278,
-0.049523405730724335,
-0.010181646794080734,
-0.0035752668045461178,
-0.015481877140700817,
-0.07370277494192123,
-0.02034260705113411,
-0.07805638015270233,
-0.021628674119710922,
-0.02545636147260666,
0.05140106752514839,
-0.032065704464912415,
0.04153808578848839,
-0.010074782185256481,
-0.04897472634911537,
0.030611494556069374,
0.028038613498210907,
-0.026424061506986618,
-0.03450780734419823,
0.005130196921527386,
-0.012005484662950039,
-0.008957873098552227,
-0.019686585292220116,
-0.025749295949935913,
-0.015757150948047638,
-0.017610806971788406,
-0.0995480865240097,
0.04322377219796181,
-0.047599002718925476,
-0.028903210535645485,
-0.0324002169072628,
0.03252986818552017,
-0.02223343960940838,
-0.015163324773311615,
-0.022366024553775787,
-0.05895182117819786,
-0.04505731910467148,
0.026692893356084824,
0.07406561821699142,
-0.10320749133825302,
-0.029386160895228386,
-0.01146266981959343,
-0.006370241753757,
-0.03396615758538246,
-0.06851617246866226,
-0.07179568707942963,
0.005286619998514652,
-0.022162435576319695,
0.020547177642583847,
-0.017900582402944565,
-0.012177098542451859,
-0.09693959355354309,
0.027349311858415604,
0.03528296947479248,
-0.019045501947402954,
0.016733763739466667,
-0.06617400050163269,
-0.0011794371530413628,
-0.02954861707985401,
0.039561301469802856,
-0.011329553090035915,
-0.02287043258547783,
0.031071877107024193,
-0.03891376033425331,
-0.007375214248895645,
0.01114998385310173,
-0.08056465536355972,
0.028094498440623283,
0.006440185941755772,
-0.030618755146861076,
0.008634660392999649,
-0.04674326255917549,
0.016605645418167114,
0.01994495280086994,
0.03445780277252197,
0.051576584577560425,
0.0717826634645462,
0.022092297673225403,
-0.03757691755890846,
-0.08079066872596741,
-0.037607692182064056,
0.0341462567448616,
-0.039420563727617264,
-0.04415102303028107,
0.007097174879163504,
0.05453799292445183,
-0.011716450564563274,
-0.0547543428838253,
-0.004415879491716623,
-0.04946434870362282,
0.002937468932941556,
0.028194067999720573,
0.07688624411821365,
-0.06270582973957062,
0.023106830194592476,
-0.04892821982502937,
-0.0022682410199195147,
0.00795576348900795,
0.05175643414258957,
0.010553571395576,
0.026647409424185753,
-0.013852125033736229,
0.027753906324505806,
-0.022792084142565727,
-0.03737642988562584,
0.01514415629208088,
0.023683253675699234,
0.026517361402511597,
-0.007039995864033699,
-0.05989769473671913,
-0.007335799280554056,
0.074003666639328,
-0.007356720510870218,
0.012461367063224316,
-0.000291473203105852,
-0.011402484029531479,
-0.024434365332126617,
0.027027808129787445,
0.01765334978699684,
0.07628896832466125,
0.011294696480035782,
0.024302979931235313,
0.04437682777643204,
-0.05703449249267578,
0.06830750405788422,
0.005888381507247686,
-0.002595447236672044,
-0.040015242993831635,
0.0007861850899644196,
-0.048495277762413025,
-0.02574111334979534,
0.028770701959729195,
0.010798274539411068,
-0.01654844544827938,
0.0038112022448331118,
-0.057567693293094635,
0.05813483148813248,
0.0006836068350821733,
0.04065569117665291,
0.012224300764501095,
-0.024372342973947525,
0.029194854199886322,
-0.00869506411254406,
0.09940974414348602,
0.03180650249123573,
-0.020845018327236176,
0.019855154678225517,
-0.04181135445833206,
0.06183921545743942,
0.02319680154323578,
0.03118901513516903,
-0.00020576945098582655,
-0.05486439913511276,
-0.00439093541353941,
0.05904419720172882,
-0.025146013125777245,
-0.04270089790225029,
0.0204683355987072,
0.01683717966079712,
-0.017423128709197044,
0.0493432879447937,
-0.02247900329530239,
-0.0758599266409874,
0.04234983026981354,
-0.009084205143153667,
0.02073623798787594,
0.07199608534574509,
-0.021812373772263527,
-0.006177677307277918,
-0.013748623430728912,
0.013165480457246304,
0.013129137456417084,
-0.050684165209531784,
0.0020404334645718336,
0.04181244224309921,
0.02930621989071369,
0.05976972356438637,
0.0308441910892725,
-0.08160997927188873,
0.011056696064770222,
0.0004020597552880645,
-0.01899518072605133,
-0.01528762374073267,
-0.030994191765785217,
-0.0015566428191959858,
-0.015049397014081478,
0.05190526321530342,
0.04509967565536499,
0.001422722591087222,
-0.01762452907860279,
-0.016511324793100357,
0.006893763318657875,
0.00914460327476263,
-0.008023125119507313,
-0.0173186007887125,
-0.019778437912464142,
0.011824888177216053,
-0.0037921415641903877,
-0.02953394316136837,
0.007378530688583851,
0.012979496270418167,
0.02610498107969761,
0.040501758456230164,
0.08176333457231522,
0.0434880293905735,
0.07566317170858383,
0.082084059715271,
0.08748805522918701,
-0.007829972542822361,
-0.005309898406267166,
0.017382148653268814,
0.05160808563232422,
-0.008937761187553406,
0.00821855291724205,
0.011544721201062202,
-0.008872779086232185,
0.05512360483407974,
0.023722203448414803,
0.008688356727361679,
0.0075210873037576675,
0.039950594305992126,
0.03616606071591377,
-0.009104641154408455,
0.07871966063976288,
0.03214971348643303,
-0.004472929984331131,
0.0357433520257473,
-0.03875933215022087,
-0.01363429520279169,
-0.024805549532175064,
-0.07148865610361099,
-0.006786436308175325,
0.027147632092237473,
-0.03200658783316612,
-0.02142937108874321,
-0.05659383162856102,
-0.012442067265510559,
-0.016822699457406998,
0.02948993630707264,
-0.016539575532078743,
0.0340549536049366,
-0.027308952063322067,
0.04822618514299393,
0.07730010896921158,
-0.045415617525577545,
0.09051518887281418,
-0.009876621887087822,
-0.03048698417842388,
0.008378807455301285,
-0.050599537789821625,
-0.04305423051118851,
0.020567825064063072,
-0.022175194695591927,
0.010249569080770016,
0.010061562992632389,
0.012372436933219433,
0.006144242826849222,
-0.019355209544301033,
0.023292727768421173,
-0.024839431047439575,
-0.029785608872771263,
-0.009670640341937542,
-0.014999360777437687,
0.007652629166841507,
-0.008131887763738632,
-0.027502192184329033,
-0.019053088501095772,
-0.022880205884575844,
0.0371098667383194,
0.013620449230074883,
-0.045661989599466324,
-0.01108035072684288,
0.0004609445750247687,
-0.05031643807888031,
-0.013865458779036999,
0.0247920211404562,
0.07313298434019089,
0.06053498759865761,
-0.0017061751568689942,
0.007624322548508644,
-0.016150545328855515,
-0.03842366486787796,
-0.0035997426602989435,
-0.04169027507305145,
-0.03821905329823494,
0.016149111092090607,
-0.014385306276381016,
0.06918033957481384,
0.00948597677052021,
-0.01596476323902607,
0.022188836708664894,
-0.012675832957029343,
0.03354077413678169,
0.009670945815742016,
-0.034985847771167755,
0.04888950288295746,
-0.04469288885593414,
0.0011779341148212552,
-0.03740721195936203,
0.05286112055182457,
-0.05431090295314789,
0.001294212299399078,
-0.0301287192851305,
0.03157204017043114,
-0.02669306844472885,
0.03849632665514946,
-0.02070401795208454,
-0.020803457126021385,
-0.04523610696196556,
0.02463604509830475,
0.029572637751698494,
0.07960963994264603,
-0.012111522257328033,
0.04446347802877426,
-0.016052233055233955,
-0.06238361820578575,
-0.05545046180486679,
0.014239625073969364,
-0.0009390650666318834,
0.0011462727561593056,
-0.04751405119895935,
-0.023743705824017525,
-0.05813378840684891,
-0.017796121537685394,
0.12173696607351303,
0.02991783618927002,
0.0027451668865978718,
-0.017111919820308685,
-0.02153896726667881,
-0.03113655187189579,
-0.024022694677114487,
0.032661061733961105,
0.03381955623626709,
-0.03863239288330078,
0.009545485489070415,
-0.044656671583652496,
0.053613677620887756,
-0.0019487050594761968,
0.032905302941799164,
-0.03789851814508438,
-0.031687792390584946,
0.03476953133940697,
0.028499357402324677,
0.07163798063993454,
0.04096944257616997,
-0.015484161674976349,
-0.0581878162920475,
-0.004422083962708712,
-0.024012316018342972,
0.02543831244111061,
0.02090606652200222,
0.010650078766047955,
0.024885933846235275,
-0.02413669042289257,
0.02364061400294304,
0.021137885749340057,
-0.010540706105530262,
0.05546152591705322,
0.009146175347268581,
-0.06631544232368469,
-0.04382142424583435,
-0.002912803553044796,
0.04080333560705185,
-0.01577582396566868,
0.006507778074592352,
-0.002485013334080577,
0.038551196455955505,
-0.010019689798355103,
0.015939584001898766,
0.03616352006793022,
-0.019306980073451996,
-0.01803523674607277,
0.02471017651259899,
-0.013277159072458744,
-0.039011456072330475,
0.001288384897634387,
0.00461952481418848,
-0.014193491078913212,
-0.04385700821876526,
-0.05088802054524422,
0.03548353537917137,
0.008789444342255592,
-0.0011707372032105923,
0.03435812145471573,
0.0005348097183741629,
-0.030336348339915276,
0.11110042780637741,
0.0051335119642317295,
0.020933452993631363,
0.04181463643908501,
0.02652888186275959,
-0.011886569671332836,
-0.010783938691020012,
0.0011575223179534078,
-0.04337112233042717,
-0.04398607090115547,
-0.03974573686718941,
0.0028530065901577473,
0.003655839478597045,
-0.02899387665092945,
0.04145750030875206,
0.05901411920785904,
-0.031702399253845215,
-0.01075351145118475,
-0.018548624590039253,
0.033867910504341125,
0.06270013749599457,
-0.0007919045747257769,
0.08371325582265854,
0.0358237586915493,
0.05350896343588829,
0.027887677773833275,
-0.03680373355746269,
-0.03262639790773392,
0.04610098898410797,
0.020927470177412033,
0.031070919707417488,
-0.011692032217979431,
0.024342352524399757,
0.004350201226770878,
-0.0677323192358017,
0.07711955159902573,
-0.018785830587148666,
0.004482149612158537,
0.0009517826256342232,
-0.0004952797316946089,
0.042252328246831894,
0.012080141343176365,
-0.006032668519765139,
-0.038353368639945984,
-0.00540022412315011,
-0.02428620122373104,
0.0011178971035405993,
-0.03169334679841995,
0.00525851221755147,
0.06582200527191162,
-0.03161546215415001,
-0.0582834854722023,
0.024181276559829712,
-0.03376778960227966,
-0.04035041481256485,
-0.03518969193100929,
-0.03289148956537247,
0.030365165323019028,
0.013068503700196743,
0.016330070793628693,
0.011346735991537571,
0.0037113407161086798,
-0.07913273572921753,
-0.030789868906140327,
-0.031026121228933334,
0.04137047380208969,
-0.07114709168672562,
-0.04710042476654053,
-0.02804984338581562,
-0.015491615980863571,
0.03769254311919212,
0.010855203494429588,
0.07198448479175568,
-0.02855842560529709,
-0.06295843422412872,
-0.018502335995435715,
0.047584161162376404,
0.011198069900274277,
0.024668890982866287,
0.0011111001949757338,
0.04657129570841789,
-0.012436716817319393,
0.01065028365701437,
-0.010421700775623322,
-0.024330442771315575,
-0.017011811956763268,
-0.020646050572395325,
0.02411978878080845,
-0.019442304968833923,
-0.019496753811836243,
-0.011028312146663666,
-0.014468245208263397,
0.0022896593436598778,
-0.019498471170663834,
0.019587349146604538,
-0.04211273044347763,
-0.031042611226439476,
0.018711013719439507,
0.005443982779979706,
-0.01969117857515812,
0.05094803124666214,
-0.03509847819805145,
-0.00010106465924764052,
0.0022167223505675793,
-0.03001648560166359,
0.009719902649521828,
0.028448810800909996,
-0.060866110026836395,
0.013589677400887012,
0.004350899253040552,
-0.08319523185491562,
0.010010238736867905,
0.015631288290023804,
-0.011236715130507946,
-0.01418597437441349,
0.028005871921777725,
-0.00926124956458807,
-0.05058831349015236,
0.021908845752477646,
-0.0005694847204722464,
0.011972988024353981,
0.04717504233121872,
0.013854371383786201,
-0.020886480808258057,
0.01851046085357666,
-0.023753702640533447,
0.017817620187997818,
-0.0019417551811784506,
-0.014457796700298786,
-0.03685079887509346,
0.02232859656214714,
0.020963924005627632,
0.0008261982002295554,
0.022007998079061508,
0.011525277979671955,
-0.04922864958643913,
-0.04165619611740112,
-0.0016371688107028604,
0.0369538813829422,
0.014636347070336342,
-0.04389948770403862,
0.021350430324673653,
0.058265652507543564,
0.026705197989940643,
-0.021497996523976326,
0.00840788520872593,
0.0640433058142662,
0.013284619897603989,
0.08026772737503052,
0.07051418721675873,
-0.04994245991110802,
0.024715982377529144,
0.011144299991428852,
0.01843750663101673,
-0.026712100952863693,
-0.01371772401034832,
-0.0035241886507719755,
0.05892743542790413,
-0.027364380657672882,
0.049021631479263306,
-0.0202877689152956,
-0.012703980319201946,
-0.030137361958622932
] |
<p>What happens to the deflection of the magnetic compass if it is surrounded by south poles and north poles in alternating direction of a magnet around it in a circular pattern. Will it be deflected in any particular direction ?</p>
<p><img src="http://i.stack.imgur.com/MHqqH.jpg" alt="enter image description here"></p> | g4752 | [
0.014629215002059937,
-0.05303295701742172,
0.01383046992123127,
0.013633168302476406,
0.05193287506699562,
0.04863817244768143,
0.04236339405179024,
-0.024244215339422226,
-0.0012608920224010944,
0.011002179235219955,
-0.02583666332066059,
0.0005876790382899344,
-0.004614642355591059,
-0.017804479226469994,
0.04990793764591217,
0.0069726272486150265,
-0.014096911996603012,
0.028934387490153313,
0.02039482817053795,
0.027409011498093605,
0.020061174407601357,
0.0036338965874165297,
0.002757434034720063,
0.011023718863725662,
-0.03153306245803833,
-0.009435336105525494,
0.003977483604103327,
-0.04165521264076233,
-0.024592965841293335,
0.0016345728654414415,
0.04064232110977173,
0.028038086369633675,
0.0075817955657839775,
-0.02507147192955017,
-0.024330904707312584,
0.01800146885216236,
-0.026399463415145874,
0.019214631989598274,
0.019984658807516098,
-0.036442503333091736,
-0.01136602833867073,
0.010824350640177727,
-0.012742355465888977,
-0.038854293525218964,
-0.008862686343491077,
0.00517941964790225,
-0.013775703497231007,
-0.0012410858180373907,
-0.035050101578235626,
0.007262556813657284,
-0.04044703021645546,
-0.061581388115882874,
0.03209422156214714,
0.0034246896393597126,
0.010782288387417793,
0.01974235288798809,
0.06898632645606995,
-0.07074051350355148,
0.004827439785003662,
0.017069010064005852,
-0.01077836100012064,
0.07489095628261566,
-0.04197801649570465,
-0.006274067796766758,
-0.03438559174537659,
-0.023729819804430008,
-0.023152433335781097,
0.05541633814573288,
0.037108130753040314,
0.0403924398124218,
0.005915103014558554,
-0.03454995155334473,
-0.014595688320696354,
-0.07195789366960526,
-0.028268825262784958,
0.05697371065616608,
0.06450122594833374,
-0.00021808844758197665,
0.020852603018283844,
0.01667119562625885,
-0.08729857951402664,
0.037120137363672256,
-0.0586775466799736,
0.024624383077025414,
0.04429524391889572,
0.020490873605012894,
0.011935784481465816,
0.04030650854110718,
-0.06407089531421661,
-0.018101295456290245,
0.012629259377717972,
-0.042442597448825836,
0.004598133731633425,
0.00811096467077732,
0.0099144596606493,
-0.005347539205104113,
0.05280664190649986,
-0.033047910779714584,
-0.03500805422663689,
0.039896924048662186,
-0.019181061536073685,
-0.021576566621661186,
-0.0057915737852454185,
-0.027225427329540253,
0.01796332187950611,
-0.03958625718951225,
0.05641653761267662,
0.044145163148641586,
-0.02317316085100174,
0.03244816139340401,
-0.033105649054050446,
-0.04353998228907585,
-0.021263718605041504,
0.04251343011856079,
-0.030193282291293144,
-0.027214255183935165,
0.07776143401861191,
0.026443133130669594,
0.04990529641509056,
0.038481246680021286,
0.059766728430986404,
-0.02512383460998535,
0.02161003090441227,
0.04905712977051735,
-0.023217977955937386,
-0.0029004618991166353,
-0.0357382595539093,
-0.024705925956368446,
0.03862639516592026,
-0.02495088055729866,
0.04396256431937218,
-0.01822609268128872,
0.03858484327793121,
-0.018022524192929268,
-0.012823766097426414,
-0.010055769234895706,
0.06298506259918213,
-0.01940377801656723,
-0.01722743734717369,
-0.02740209549665451,
0.015002567321062088,
-0.00928876455873251,
0.06938333064317703,
0.013261849991977215,
0.037532586604356766,
-0.026670046150684357,
0.03530290722846985,
-0.04586934298276901,
0.02089453861117363,
0.034241121262311935,
0.026024548336863518,
0.005229676142334938,
-0.010938192717730999,
-0.002196449786424637,
-0.018823878839612007,
0.03381560370326042,
-0.015944063663482666,
0.06479548662900925,
0.005689528305083513,
-0.03303329646587372,
0.0542423278093338,
-0.03226228430867195,
-0.008026042953133583,
-0.012160686776041985,
-0.027759432792663574,
-0.0045809498988091946,
0.053549278527498245,
0.022891713306307793,
0.05889607593417168,
0.0014883300755172968,
-0.01194989774376154,
0.030122868716716766,
0.023824824020266533,
0.04438556358218193,
0.01612430438399315,
0.06844853609800339,
-0.011164593510329723,
-0.026489796116948128,
0.0662015900015831,
0.04800494760274887,
-0.007433858700096607,
0.06806556135416031,
0.03409041464328766,
0.013949111104011536,
-0.06208817660808563,
0.01749805361032486,
-0.007929879240691662,
0.009051588363945484,
-0.006669917143881321,
-0.029446985572576523,
0.0579804927110672,
0.011816492304205894,
-0.03010101057589054,
0.007239987142384052,
-0.0012392045464366674,
-0.0641777440905571,
0.018369033932685852,
0.026252226904034615,
-0.04888536408543587,
0.013887321576476097,
0.05209089443087578,
0.022221283987164497,
0.0991414338350296,
0.03153231367468834,
-0.04766456410288811,
-0.020816320553421974,
0.0017104955622926354,
0.021821439266204834,
0.05710642412304878,
-0.014146937988698483,
0.016640683636069298,
0.03512274846434593,
-0.03988369181752205,
0.030583078041672707,
-0.021583963185548782,
0.02609194628894329,
-0.04256977140903473,
0.05672870948910713,
-0.003197531681507826,
0.00011541245476109907,
-0.02644653432071209,
-0.0016219724202528596,
-0.018372010439634323,
-0.01462794654071331,
0.013933706097304821,
-0.015488479286432266,
-0.055712275207042694,
-0.051574740558862686,
0.029810180887579918,
-0.0023915735073387623,
-0.006259276065975428,
-0.08034822344779968,
0.027688056230545044,
-0.03720517084002495,
0.0252225324511528,
0.02985747531056404,
0.03431368246674538,
-0.010721306316554546,
0.029163824394345284,
-0.04623182862997055,
0.041583284735679626,
0.009290696121752262,
0.023553837090730667,
-0.03524629399180412,
0.03559478744864464,
0.014665978029370308,
0.08068978786468506,
0.019197074696421623,
0.005114607512950897,
0.0302607212215662,
0.047092512249946594,
-0.013064876198768616,
0.02522999979555607,
0.018903173506259918,
-0.011421525850892067,
0.061604052782058716,
-0.03026317059993744,
-0.003947969526052475,
-0.04269952327013016,
-0.03867822140455246,
-0.043042734265327454,
-0.0736168697476387,
0.038296591490507126,
-0.006661617662757635,
-0.05312025919556618,
-0.03339210897684097,
0.01812238246202469,
-0.006136404350399971,
0.0027836093213409185,
-0.021126938983798027,
-0.04559919238090515,
0.058608680963516235,
0.0371941477060318,
0.0800199806690216,
-0.06682489067316055,
-0.025867922231554985,
0.01142832450568676,
0.03709818422794342,
-0.014783713966608047,
0.06308524310588837,
0.003275172086432576,
0.002000858774408698,
0.004882529377937317,
0.010382742621004581,
0.050771284848451614,
0.0377039834856987,
-0.046277329325675964,
0.010427366942167282,
-0.06261452287435532,
-0.019465697929263115,
-0.0977964922785759,
-0.07186395674943924,
0.05230075865983963,
-0.031583741307258606,
0.04331709071993828,
0.035232458263635635,
0.012352686375379562,
0.011964130215346813,
-0.022247647866606712,
0.024634497240185738,
0.02456820383667946,
0.005216503515839577,
-0.03451422601938248,
0.01699839159846306,
-0.011974829249083996,
-0.008223100565373898,
0.00004497060217545368,
-0.07941128313541412,
0.008992999792098999,
0.019368937239050865,
-0.07152567058801651,
0.0029093872290104628,
0.01838897354900837,
-0.0074333627708256245,
0.011607733555138111,
0.05335468798875809,
-0.006074350327253342,
0.029822219163179398,
0.028089212253689766,
-0.0035578906536102295,
-0.04756557568907738,
-0.05807369574904442,
-0.04165845736861229,
0.02541230618953705,
0.03420853242278099,
-0.02275017648935318,
0.04718036204576492,
0.0011570926290005445,
-0.010871605016291142,
0.011203639209270477,
-0.03380633890628815,
-0.0072418092750012875,
-0.026224981993436813,
-0.016388962045311928,
-0.034652501344680786,
0.05725618079304695,
0.03452946990728378,
0.007361544296145439,
-0.03121340461075306,
-0.009588412940502167,
0.0871407762169838,
-0.033759571611881256,
0.007432316429913044,
-0.08217298984527588,
0.0452045239508152,
0.03597252070903778,
-0.0052407123148441315,
0.010641335509717464,
0.005081068258732557,
0.049752477556467056,
0.05281709134578705,
0.01213738601654768,
0.014087353833019733,
0.007744359318166971,
0.034324631094932556,
0.03916344791650772,
0.0006915740668773651,
0.047043461352586746,
-0.023225832730531693,
0.0056247403845191,
0.05899365246295929,
0.007331781554967165,
-0.014707869850099087,
0.02427240088582039,
-0.021090589463710785,
0.025686047971248627,
0.034423813223838806,
0.008795507252216339,
0.013135959394276142,
-0.0265143234282732,
0.021651241928339005,
0.007607394363731146,
-0.06859450042247772,
0.00937401782721281,
0.00460917828604579,
-0.025219038128852844,
0.031529027968645096,
0.04187251254916191,
-0.015467153862118721,
0.000025560191716067493,
-0.026021571829915047,
0.030940284952521324,
-0.010647534392774105,
-0.0370960459113121,
-0.031825121492147446,
0.03410455211997032,
0.07005076855421066,
0.010501556098461151,
-0.036275774240493774,
0.02573159523308277,
-0.022318677976727486,
0.019719501957297325,
0.061504874378442764,
0.0070184520445764065,
0.03412364423274994,
0.008344536647200584,
-0.04159543663263321,
-0.0043688612058758736,
-0.0423259511590004,
-0.010378752835094929,
0.061220310628414154,
0.029346805065870285,
-0.03762548044323921,
-0.008969323709607124,
0.03389718756079674,
-0.08479346334934235,
-0.03012959100306034,
-0.0032014488242566586,
-0.03534287214279175,
-0.011348634958267212,
0.02781492844223976,
-0.03421866521239281,
-0.028270931914448738,
-0.03372983634471893,
0.12316884100437164,
0.05380933731794357,
0.037955500185489655,
0.08328495919704437,
0.0018229772103950381,
-0.03408621624112129,
-0.020003613084554672,
0.07278691977262497,
-0.03799805790185928,
0.010337918996810913,
-0.08107485622167587,
0.009759251028299332,
-0.002326206536963582,
-0.0229179710149765,
-0.033338118344545364,
-0.02796899527311325,
-0.017218628898262978,
0.0061497194692492485,
0.011349501088261604,
-0.01508264895528555,
-0.08029703050851822,
0.023738883435726166,
-0.04173349216580391,
0.023898504674434662,
0.07254703342914581,
-0.003739799838513136,
-0.049129992723464966,
0.026037029922008514,
0.04629315435886383,
-0.004997480195015669,
-0.0830375924706459,
0.01917683146893978,
-0.006396227050572634,
-0.003476045560091734,
0.03520222380757332,
-0.06014597415924072,
-0.03943656384944916,
0.01629318855702877,
-0.07137278467416763,
-0.03959588706493378,
0.016492977738380432,
-0.019302429631352425,
-0.026280734688043594,
0.050524499267339706,
0.023259101435542107,
-0.025475742295384407,
-0.00048758002230897546,
-0.04780377820134163,
0.02033521793782711,
-0.04437147453427315,
-0.05618414655327797,
0.029044030234217644,
0.021090464666485786,
-0.05552179738879204,
0.0007231362978927791,
0.005054158624261618,
-0.0047083767130970955,
0.0773221105337143,
0.0015253069577738643,
-0.018002131953835487,
0.03566715121269226,
-0.005385144613683224,
0.02271139621734619,
-0.028656357899308205,
-0.022418832406401634,
-0.02866959571838379,
-0.052065566182136536,
0.00003088002267759293,
0.004029531963169575,
-0.01101671252399683,
0.025404807180166245,
-0.02098650299012661,
0.038515854626894,
-0.03869549557566643,
0.010079652070999146,
-0.03294624388217926,
0.00465406384319067,
0.030498426407575607,
-0.045926567167043686,
-0.06270018965005875,
0.01713588461279869,
-0.04141080379486084,
-0.06474613398313522,
-0.015841148793697357,
-0.02136114053428173,
-0.07595162093639374,
0.021315831691026688,
-0.04662901908159256,
-0.020186850801110268,
0.03599388524889946,
-0.025234336033463478,
0.0832570418715477,
0.005451589822769165,
-0.03839487582445145,
0.030178282409906387,
0.024485241621732712,
-0.052564557641744614,
-0.05127435177564621,
0.00814038421958685,
0.025518475100398064,
0.06489434093236923,
-0.034323520958423615,
-0.07749981433153152,
-0.016442688181996346,
-0.003994948696345091,
-0.009248394519090652,
0.013130245730280876,
0.018587835133075714,
0.023463550955057144,
-0.022134916856884956,
0.0638999342918396,
-0.03080732747912407,
-0.0415068045258522,
0.06461741775274277,
0.050953563302755356,
0.025862708687782288,
0.03506004437804222,
-0.009313119575381279,
-0.007580014877021313,
0.002660906407982111,
0.021413419395685196,
-0.04346621409058571,
0.0388227216899395,
-0.06469400227069855,
0.03190825507044792,
0.05439693480730057,
-0.021207526326179504,
-0.026838267222046852,
0.05993645638227463,
0.05865420028567314,
-0.044364914298057556,
-0.04006412625312805,
-0.004663556814193726,
-0.006757752504199743,
-0.03233204782009125,
-0.0019388601649552584,
-0.0723688080906868,
0.04185464605689049,
-0.013787336647510529,
-0.038612980395555496,
-0.04290471598505974,
0.008723564445972443,
-0.07531801611185074,
-0.019486194476485252,
0.05762912705540657,
-0.05301444232463837,
0.03797614574432373,
-0.057749707251787186,
0.025672491639852524,
-0.018344899639487267,
-0.015221750363707542,
-0.02314678765833378,
-0.0012704834807664156,
-0.026957286521792412,
0.07366311550140381,
0.06446652859449387,
0.037738118320703506,
-0.017906244844198227,
0.0011489818571135402,
0.037163086235523224,
0.10786731541156769,
0.0040992870926856995,
-0.04112965986132622,
-0.017762072384357452,
-0.011678175069391727,
0.014170684851706028,
0.03461199626326561,
0.05241813510656357,
-0.020604997873306274,
-0.00740752462297678,
0.0012708387803286314,
0.08103467524051666,
-0.055071089416742325,
0.028493132442235947,
0.02820996753871441,
-0.03440835326910019,
-0.03935902193188667,
-0.060284245759248734,
-0.020061451941728592,
0.0219968780875206,
-0.08871949464082718,
-0.028627417981624603,
-0.010700536891818047,
0.06961482763290405,
0.012303932569921017,
-0.003311347449198365,
-0.012984250672161579,
-0.037919413298368454,
0.05421922728419304,
-0.014567567966878414,
0.0019093428272753954,
0.0030169859528541565,
0.03666377067565918,
0.00009950508683687076,
0.014910949394106865,
-0.01287013478577137,
0.015675757080316544,
0.012851173989474773,
-0.03422287479043007,
0.011756699532270432,
0.0017890154849737883,
-0.012476248666644096,
-0.01347760297358036,
-0.08044248819351196,
-0.04652053117752075,
0.006249895319342613,
-0.036366406828165054,
-0.03698902949690819,
-0.07637969404459,
-0.035152897238731384,
-0.036237601190805435,
0.011118396185338497,
0.021741868928074837,
-0.004285049624741077,
-0.004402814898639917,
0.030439477413892746,
0.008844979107379913,
0.015993298962712288,
-0.014594251289963722,
0.015282181091606617,
0.01363514643162489,
0.014353555627167225,
-0.04777732491493225,
-0.016452128067612648,
0.030825112015008926,
0.017708320170640945,
-0.03296758607029915,
0.013661468401551247,
0.012227918021380901,
-0.04193689301609993,
-0.034756679087877274,
-0.0013698786497116089,
0.01516285352408886,
-0.005677283275872469,
0.01984378695487976,
0.04920267313718796,
-0.00293052033521235,
-0.018171492964029312,
-0.02730083465576172,
0.022865675389766693,
-0.018402883782982826,
-0.022298453375697136,
0.010579041205346584,
-0.00897239800542593,
0.030358117073774338,
-0.003446307498961687,
-0.04546428471803665,
-0.036524053663015366,
-0.07977050542831421,
-0.021691827103495598,
0.007041651755571365,
-0.011840835213661194,
0.04075722396373749,
-0.03141573816537857,
-0.007048932835459709,
0.000516762665938586,
-0.056701354682445526,
-0.003966614603996277,
-0.025287402793765068,
-0.02104453556239605,
0.014003502205014229,
-0.0223159808665514,
-0.0376029908657074,
-0.08708000183105469,
0.037050217390060425,
0.01868017390370369,
0.0030642258934676647,
-0.033085502684116364,
0.02457026019692421,
-0.020069938153028488,
-0.03190883994102478,
-0.005300125572830439,
0.012795168906450272,
0.041823308914899826,
0.054394908249378204,
-0.030985873192548752,
-0.01795840449631214,
0.03753089904785156,
0.030167311429977417,
-0.025272171944379807,
-0.029897242784500122,
0.01922178827226162,
0.0223037451505661,
0.03732532262802124,
-0.00026510327006690204,
0.0199186522513628,
0.008582928217947483,
0.06543330103158951,
-0.008275303989648819,
0.008196518756449223,
0.07882270216941833,
-0.012265082448720932,
-0.0490335188806057,
0.04027356207370758,
-0.00519517669454217,
0.006794337183237076,
0.06702989339828491,
0.04082644358277321,
0.02381683886051178,
-0.017952775582671165,
-0.039617735892534256,
0.034651122987270355,
-0.02877022512257099,
0.010798824019730091,
-0.01210745982825756,
0.04084841161966324,
-0.055308252573013306,
0.014949258416891098,
-0.00033937778789550066,
-0.029585769400000572,
-0.07775174081325531,
-0.01787223108112812,
0.003791196271777153,
0.04654198884963989,
0.04001423716545105,
-0.0315319299697876,
0.05818522348999977,
-0.011508839204907417,
-0.026459822431206703,
-0.014127405360341072,
-0.014295942150056362,
-0.00819321908056736,
-0.038580991327762604,
-0.08678875863552094,
0.018616126850247383,
-0.026920869946479797,
0.005024884827435017,
-0.01730080135166645,
-0.012301048263907433,
-0.07251264899969101,
-0.0366051159799099,
0.033513933420181274,
0.02240893989801407,
0.007506954949349165,
0.010019119828939438,
0.006060722284018993,
0.014051060192286968,
-0.0066122678108513355,
0.020118044689297676,
-0.047045037150382996,
-0.013199963606894016,
-0.009442313574254513,
-0.03787495940923691,
-0.058661170303821564,
0.0544416606426239,
-0.01960129290819168,
0.032159946858882904,
-0.049072470515966415,
-0.030483538284897804,
-0.011170309036970139,
-0.002976004732772708,
0.02188420109450817,
-0.05464332923293114,
0.0687410905957222
] |
<p>I cannot manage to find any journal papers about the applicability of zinc nitride as active layer of an light emitting diode (LED). But certain papers got mention that zinc nitride with a direct bandgap can be fabricated with potential applications in optoelectronics.</p>
<p>Can anyone give me some opinions on this subject?</p> | g4753 | [
0.0400405116379261,
-0.00584971159696579,
-0.009187593124806881,
0.04158691689372063,
-0.03210829943418503,
-0.02671143040060997,
0.007697069086134434,
-0.0016767180059105158,
0.08767534792423248,
-0.0797937735915184,
0.11167512834072113,
-0.004366185981780291,
0.027935780584812164,
0.01683235913515091,
-0.011992321349680424,
0.0025768999475985765,
0.030787602066993713,
0.025152286514639854,
0.022042160853743553,
-0.021475041285157204,
-0.03695545345544815,
-0.012226775288581848,
-0.010726306587457657,
-0.0384761281311512,
0.001642085611820221,
0.05501040443778038,
0.02331700548529625,
-0.04654531180858612,
-0.017150577157735825,
-0.017350144684314728,
0.025655530393123627,
-0.05254318192601204,
0.04299585893750191,
0.03695379197597504,
-0.05567639693617821,
0.014332318678498268,
0.02415292337536812,
0.027972660958766937,
0.05663299560546875,
0.020990518853068352,
-0.03057495318353176,
0.03421849384903908,
-0.02683069370687008,
-0.0530131533741951,
-0.0007677231333218515,
0.02386532723903656,
0.019054805859923363,
-0.016041049733757973,
0.011883925646543503,
-0.020305301994085312,
0.03566398471593857,
-0.023424020037055016,
0.03461572527885437,
-0.04201709106564522,
-0.033368948847055435,
-0.03836637735366821,
-0.037510890513658524,
0.0528486929833889,
0.029942525550723076,
0.022017670795321465,
-0.03781085088849068,
0.03483138233423233,
-0.024611104279756546,
-0.04891212284564972,
0.05750047788023949,
-0.007511061616241932,
-0.030743246898055077,
-0.008062731474637985,
0.035766493529081345,
0.005976138170808554,
0.05266296863555908,
0.021168183535337448,
0.009953073225915432,
-0.020891090855002403,
0.006709716748446226,
-0.0053215064108371735,
-0.07815079391002655,
0.006255405489355326,
-0.00023384441738016903,
0.05723334848880768,
0.008358334191143513,
-0.037645068019628525,
0.011638055555522442,
0.04701819643378258,
0.012268933467566967,
-0.04093443229794502,
-0.014080027118325233,
-0.03485024347901344,
-0.00514535466209054,
-0.0006552001577802002,
0.02651284635066986,
0.020385432988405228,
0.02008640766143799,
0.007822951301932335,
-0.02311335690319538,
-0.009347815997898579,
0.0164264515042305,
-0.0011017528595402837,
0.05220761150121689,
0.00767701119184494,
0.02052760124206543,
-0.06858295947313309,
-0.003959947731345892,
0.09216348081827164,
0.010181129910051823,
-0.028405236080288887,
0.00719083659350872,
0.02084030583500862,
-0.04367898404598236,
0.04632551595568657,
-0.04097624123096466,
0.03271758183836937,
0.006997651420533657,
-0.014832244254648685,
-0.04853951558470726,
0.05786726623773575,
0.009461944922804832,
-0.012179505079984665,
-0.004754533059895039,
-0.004784545861184597,
0.06730897724628448,
-0.030010012909770012,
-0.04078853502869606,
0.022363023832440376,
0.028507288545370102,
0.004437884781509638,
-0.04366322234272957,
-0.013947635889053345,
-0.016040094196796417,
-0.014206002466380596,
0.04989517480134964,
0.0541556254029274,
-0.044412873685359955,
0.011454209685325623,
0.07338748127222061,
0.0008130433270707726,
0.01828611269593239,
-0.03173147141933441,
-0.044680267572402954,
0.021219460293650627,
0.057146672159433365,
-0.0419912151992321,
-0.023158760741353035,
-0.01498622726649046,
0.03517432510852814,
0.010668144561350346,
-0.043483857065439224,
0.05806965008378029,
-0.05004756897687912,
0.03959783539175987,
-0.01555398665368557,
0.02673504501581192,
0.01521927397698164,
-0.09182853996753693,
-0.0180509053170681,
-0.008802752010524273,
0.05105637386441231,
-0.039474762976169586,
-0.06978239864110947,
-0.012835095636546612,
-0.010375709272921085,
0.06885577738285065,
0.04242313280701637,
-0.04488321766257286,
-0.018842367455363274,
-0.03889590874314308,
0.012050485238432884,
-0.05048948526382446,
-0.030076876282691956,
0.01727563515305519,
-0.01244084257632494,
0.051084235310554504,
-0.012395710684359074,
0.06948846578598022,
0.02528281696140766,
-0.055799614638090134,
0.03165440261363983,
0.024724973365664482,
0.000968095613643527,
-0.013800593093037605,
-0.0208533126860857,
-0.009215166792273521,
-0.07739029079675674,
0.02771836891770363,
-0.0383945107460022,
-0.0034395428374409676,
0.024512136355042458,
-0.12999914586544037,
-0.03192280977964401,
0.023364869877696037,
-0.015912896022200584,
0.04479198902845383,
0.05664720758795738,
0.030651094391942024,
-0.038254376500844955,
-0.012160946615040302,
-0.017817210406064987,
-0.01774032600224018,
0.06234259903430939,
-0.0017299181781709194,
-0.005054790992289782,
-0.018830206245183945,
-0.05862021446228027,
-0.01069575548171997,
0.020831255242228508,
0.032995689660310745,
-0.026133347302675247,
-0.002238089218735695,
-0.013896632008254528,
-0.0011835743207484484,
0.007557097356766462,
0.0450570285320282,
0.05250566080212593,
-0.020132454112172127,
0.055510539561510086,
0.006806531455367804,
-0.03446567431092262,
0.05213729292154312,
0.004846653435379267,
0.05791021138429642,
0.04545065388083458,
-0.020527923479676247,
-0.0018659369088709354,
-0.041029077023267746,
0.0004213786742184311,
-0.020177625119686127,
-0.02259407564997673,
0.03518512845039368,
0.04075935482978821,
0.01640281267464161,
0.006231615785509348,
-0.0659526139497757,
-0.009057639166712761,
-0.0018639820627868176,
0.0454317145049572,
0.017231088131666183,
-0.04032912105321884,
0.015284846536815166,
0.0009226182010024786,
0.013195915147662163,
-0.03904994949698448,
-0.048310764133930206,
-0.00045539322309195995,
-0.0017502811970189214,
-0.054107069969177246,
-0.04569387063384056,
-0.04500643536448479,
0.018920443952083588,
-0.024763546884059906,
-0.022300979122519493,
0.0196885596960783,
-0.05417094752192497,
-0.026736535131931305,
0.045435547828674316,
0.010616077110171318,
-0.011340993456542492,
0.0009022466256283224,
-0.018965521827340126,
-0.017851995304226875,
0.0015160928014665842,
0.04541745409369469,
-0.07014133036136627,
-0.0028747094329446554,
-0.00860406830906868,
0.0646248534321785,
-0.017063643783330917,
-0.009430255740880966,
-0.028197523206472397,
-0.030779389664530754,
0.03759928420186043,
-0.019005587324500084,
-0.011842542327940464,
-0.010125312022864819,
-0.009408804588019848,
0.05960046872496605,
-0.00009842334839049727,
0.03109084628522396,
-0.014662914909422398,
0.037112705409526825,
0.036966316401958466,
-0.003415211569517851,
-0.0356021523475647,
-0.03119080141186714,
-0.005399608518928289,
0.04663383960723877,
0.017603052780032158,
0.0030651777051389217,
-0.09954667091369629,
-0.013972972519695759,
0.007246613502502441,
0.01845221035182476,
-0.06129371002316475,
-0.014957607723772526,
-0.004315248224884272,
-0.002339801285415888,
-0.038176171481609344,
0.02709871716797352,
0.06979620456695557,
0.006503385957330465,
-0.01667453721165657,
-0.0015912591479718685,
0.0024305437691509724,
0.04944149777293205,
-0.015326786786317825,
0.06382089853286743,
0.0033589256927371025,
-0.08432739973068237,
0.060049910098314285,
0.044275831431150436,
-0.027982858940958977,
-0.005225838627666235,
-0.006210558582097292,
-0.005982693750411272,
0.028597578406333923,
-0.034200429916381836,
0.08337585628032684,
0.0024559875018894672,
-0.016135770827531815,
0.034097131341695786,
0.007022470701485872,
0.007482545450329781,
0.06554138660430908,
-0.05795696750283241,
0.010895454324781895,
0.019835738465189934,
-0.009119831956923008,
0.06868219375610352,
-0.0015939692966639996,
0.05027665197849274,
0.006794742774218321,
0.029580894857645035,
-0.03125382214784622,
-0.07336967438459396,
-0.002090307418256998,
0.010557394474744797,
-0.04083118215203285,
-0.045625150203704834,
0.048603858798742294,
0.02669006586074829,
0.047052547335624695,
-0.0180641058832407,
-0.05309800058603287,
-0.04632660746574402,
-0.02500215172767639,
0.0709681287407875,
-0.010278353467583656,
-0.015527067705988884,
-0.045876696705818176,
-0.07624459266662598,
0.013438223861157894,
-0.013959789648652077,
-0.019422199577093124,
-0.07616876810789108,
0.0049833869561553,
0.0453081876039505,
0.02323211543262005,
0.010226305574178696,
0.015900591388344765,
-0.004904772620648146,
-0.02774060145020485,
-0.006794069427996874,
0.04276729375123978,
-0.000842260371427983,
-0.00937658455222845,
-0.04283428564667702,
-0.03633107617497444,
-0.00571124441921711,
0.0022207549773156643,
0.0052336836233735085,
0.020313618704676628,
-0.001171147101558745,
0.03790136054158211,
-0.0064237709157168865,
-0.006995139177888632,
0.04485390707850456,
-0.03451765701174736,
-0.04681411385536194,
0.008563303388655186,
-0.01617671363055706,
0.013675287365913391,
-0.03468237444758415,
-0.022885417565703392,
0.05714166909456253,
0.03506779298186302,
0.03294861689209938,
-0.043865423649549484,
-0.016684433445334435,
0.007509854156523943,
-0.0017457077046856284,
0.0007466215756721795,
-0.019472230225801468,
-0.024268396198749542,
0.03129415586590767,
-0.0023933034390211105,
-0.06431005895137787,
-0.05476141348481178,
-0.06985766440629959,
0.006648814771324396,
0.05798768252134323,
0.02051389031112194,
0.010231902822852135,
0.0033903615549206734,
0.01636723056435585,
-0.011088404804468155,
-0.015558644197881222,
0.03331339731812477,
0.01997789926826954,
-0.050692368298769,
-0.01825944148004055,
-0.02560335397720337,
-0.013530571013689041,
0.02598724141716957,
-0.020179979503154755,
0.020669542253017426,
-0.02846730500459671,
-0.037304557859897614,
0.016700569540262222,
-0.040224332362413406,
-0.0007446585805155337,
0.013906789943575859,
-0.024875950068235397,
0.050223663449287415,
-0.026717741042375565,
-0.019367463886737823,
-0.006751194130629301,
0.07054097950458527,
0.01792500540614128,
-0.06508073955774307,
0.03783174976706505,
0.04783081263303757,
0.032314952462911606,
-0.008540189824998379,
0.044850658625364304,
-0.013034023344516754,
-0.02069726772606373,
0.03424287214875221,
0.03522159531712532,
-0.031228939071297646,
0.01413405779749155,
-0.02691246010363102,
0.02968662790954113,
-0.019222108647227287,
0.02058648131787777,
0.022455083206295967,
0.0012932143872603774,
-0.01189415156841278,
-0.04541350156068802,
-0.00130521843675524,
-0.022052019834518433,
-0.026654774323105812,
0.006678066682070494,
-0.05443030595779419,
-0.03195194527506828,
-0.0320950411260128,
0.020543623715639114,
-0.01613406091928482,
-0.059311069548130035,
-0.05297182500362396,
0.008482048287987709,
0.059189919382333755,
0.048432789742946625,
0.018364597111940384,
-0.027229130268096924,
0.029288513585925102,
0.047148820012807846,
-0.02767176367342472,
-0.036200519651174545,
-0.01364894863218069,
-0.0218757763504982,
-0.02553349919617176,
0.0052088224329054356,
0.038547296077013016,
0.01335850078612566,
0.04848085716366768,
0.005880407523363829,
-0.11086137592792511,
0.05716210603713989,
0.006764575839042664,
0.04668382182717323,
-0.01267043687403202,
-0.01804172992706299,
-0.0884852334856987,
0.020082222297787666,
-0.013923753052949905,
0.043415285646915436,
-0.02296639233827591,
-0.05998177453875542,
-0.0034755393862724304,
0.021902069449424744,
-0.03046930581331253,
0.03825266286730766,
-0.061387576162815094,
-0.084324911236763,
-0.04662558063864708,
-0.02294926531612873,
0.03579004108905792,
-0.00030874554067850113,
0.04005058482289314,
-0.04800764471292496,
0.0359199158847332,
0.05572059005498886,
-0.027623014524579048,
-0.010948223061859608,
-0.08789361268281937,
-0.015223725698888302,
0.017596758902072906,
0.0056138779036700726,
-0.00994280818849802,
-0.04238124564290047,
-0.07393471896648407,
-0.0086888512596488,
-0.05229392647743225,
-0.022246524691581726,
0.034602150321006775,
-0.009955985471606255,
-0.03169252350926399,
-0.015186832286417484,
-0.04475799575448036,
-0.029140833765268326,
0.028549550101161003,
-0.02660336345434189,
0.016262590885162354,
-0.027657711878418922,
-0.01952720247209072,
0.05741775408387184,
0.009178295731544495,
0.04781795293092728,
0.06800646334886551,
-0.01596113108098507,
-0.08104352653026581,
0.04212689399719238,
0.015402095392346382,
0.00018590479157865047,
-0.04850884526968002,
-0.0632578432559967,
-0.003275320865213871,
-0.013083232566714287,
0.0431949608027935,
-0.03404807671904564,
0.025737568736076355,
0.01676032692193985,
-0.02287476696074009,
0.027885936200618744,
-0.018594255670905113,
0.02561068721115589,
0.025804730132222176,
0.01405312493443489,
0.010855378583073616,
-0.010775040835142136,
0.021134328097105026,
0.0589081235229969,
0.04260265827178955,
-0.10778055340051651,
0.034678179770708084,
0.04018653929233551,
0.011326078325510025,
0.005632820539176464,
-0.008428027853369713,
0.008200534619390965,
0.009847194887697697,
0.08185535669326782,
0.06278175860643387,
-0.05131024867296219,
-0.016159044578671455,
0.006854686886072159,
0.018352065235376358,
0.0017915598582476377,
0.040356650948524475,
-0.0036406342405825853,
-0.0077293734066188335,
-0.00200210721231997,
-0.018845735117793083,
0.06145774573087692,
0.06189996004104614,
-0.045758653432130814,
0.017642296850681305,
0.08123183250427246,
0.015296563506126404,
0.011391738429665565,
0.00049663643585518,
0.0023459536023437977,
0.043931763619184494,
0.019724449142813683,
0.05136501416563988,
0.014500635676085949,
-0.01852523162961006,
-0.0025955112650990486,
0.03393925353884697,
-0.057662054896354675,
-0.05962083488702774,
0.055640432983636856,
0.024756737053394318,
0.03438177332282066,
0.005248404107987881,
-0.04411971941590309,
0.009920919314026833,
0.027201171964406967,
0.010612300597131252,
-0.007709808647632599,
0.043569184839725494,
0.004418279975652695,
-0.033848345279693604,
-0.044823527336120605,
-0.031255245208740234,
0.009257864207029343,
0.06873267143964767,
0.025985347107052803,
0.019068114459514618,
0.04063062369823456,
-0.04656873270869255,
0.015074159950017929,
-0.008256850764155388,
0.037794217467308044,
0.007438089232891798,
0.02929086983203888,
-0.07665809988975525,
0.0004280731955077499,
-0.03300780430436134,
0.005057997535914183,
0.035035308450460434,
-0.029383691027760506,
-0.004704308696091175,
-0.05632999166846275,
-0.007823359221220016,
-0.024342617020010948,
0.03684990480542183,
-0.06005209684371948,
0.04881460964679718,
0.02824360877275467,
0.03071584925055504,
-0.06091681495308876,
0.007681217510253191,
0.06359928101301193,
0.024803422391414642,
0.027803944423794746,
0.0036538594868034124,
-0.003627319587394595,
-0.07344894856214523,
0.014065738767385483,
-0.019336847588419914,
-0.10063070803880692,
0.03850828483700752,
0.018065184354782104,
0.0431227907538414,
0.03186403587460518,
0.03977684676647186,
0.00024306266277562827,
0.04769795015454292,
-0.013923510909080505,
0.0324132926762104,
-0.01664888486266136,
-0.055397115647792816,
0.00681395223364234,
0.02282685413956642,
0.029205376282334328,
0.05755050480365753,
-0.01952667534351349,
-0.010222130455076694,
-0.005704786628484726,
-0.023586992174386978,
0.008783455938100815,
-0.005639676004648209,
0.023035362362861633,
-0.03226194158196449,
-0.02354373224079609,
-0.0967869833111763,
0.03813198208808899,
0.06169751659035683,
-0.008164414204657078,
0.0092919347807765,
-0.027208372950553894,
-0.05945369973778725,
0.001637033186852932,
-0.025409340858459473,
-0.07317806035280228,
0.023108698427677155,
-0.07149927318096161,
0.015706289559602737,
0.00020876929920632392,
0.000010894807019212749,
-0.04830397665500641,
0.020939134061336517,
-0.025111405178904533,
-0.02214161865413189,
-0.0035602867137640715,
-0.0011720636393874884,
-0.006923750974237919,
-0.053501274436712265,
0.051993001252412796,
0.0130024878308177,
0.02026396617293358,
-0.0654383972287178,
0.0070174275897443295,
-0.020176149904727936,
0.0038847248069941998,
0.07576117664575577,
-0.007996268570423126,
0.020488174632191658,
0.005906373728066683,
0.00992864090949297,
0.0363394170999527,
-0.02938150241971016,
0.02281324937939644,
-0.040448080748319626,
-0.034083567559719086,
0.02087852917611599,
-0.0273616723716259,
0.08985109627246857,
-0.04691486433148384,
-0.04353996738791466,
0.02314753830432892,
0.02502528950572014,
0.03377962484955788,
0.04404744505882263,
-0.020098967477679253,
0.05295543745160103,
-0.008501634001731873,
0.0220161322504282,
-0.041778165847063065,
0.06632256507873535,
0.06365876644849777,
0.012274383567273617,
0.01016036607325077,
0.016821669414639473,
-0.05067218467593193,
-0.010863461531698704,
-0.025446919724345207,
0.030370697379112244,
0.04064839333295822,
-0.0451691709458828,
0.09574782103300095,
0.020083565264940262,
-0.02678731456398964,
-0.04615991935133934,
-0.011233357712626457,
-0.03689197078347206,
0.03589096665382385,
-0.0012506546918302774,
0.01825377531349659,
0.04066416248679161,
0.008631820790469646,
-0.0008969885529950261,
0.021086089313030243,
-0.01934683322906494,
-0.00829345639795065,
0.005264502950012684,
-0.020504403859376907,
-0.004220164846628904,
-0.017773453146219254,
0.03678995743393898,
-0.06659756600856781,
0.02348984219133854,
0.03718767315149307,
-0.011107497848570347,
0.034265194088220596,
-0.006263458635658026,
-0.014031780883669853,
-0.02451208233833313,
0.00527371559292078,
0.014170035719871521,
0.004390283953398466,
0.028032802045345306,
-0.009627078659832478,
-0.007400089409202337,
0.018137091770768166,
-0.004967524204403162,
0.003973252605646849,
-0.0005969091434963048
] |
<p>Friends, this is a numerical homework problem. I tried my best to solve it but my answer is not matching with the one given at the back of the text book. Please help me out:
A motor car moving at a speed of 72 km/h can come to a stop in 3 seconds, while a truck can come to a stop in 5 seconds. On a highway, the car is positioned behind the truck, both moving at 72 km/h. The truck gives a signal that it is going to stop at emergency. At what distance the car should be from the truck so that it doesn't collide with the truck. The typical human response time is 0.5 sec.</p>
<p>My logic and answer: since car can decelerate to a stop much faster than the truck, it only need to worry about human response time which is 0.5sec. car would cover 10m in 0.5seconds at a speed of 72 km/h. so it just need to be 10m behind the truck minimum.</p>
<p>but the answer in the book is 1.25 m</p>
<p>How is this possible?</p> | g4754 | [
0.05611409991979599,
-0.02463548071682453,
0.014744008891284466,
0.027275674045085907,
0.020013779401779175,
0.0034098599571734667,
-0.0003895008994732052,
-0.0012812254717573524,
-0.08131730556488037,
-0.010592985898256302,
-0.006450737360864878,
-0.006428641267120838,
0.011076566763222218,
-0.02445106767117977,
0.019474921748042107,
0.02019438147544861,
0.04990546405315399,
0.011325826868414879,
-0.05679847300052643,
0.020421765744686127,
0.01059489231556654,
0.025345459580421448,
-0.05364811792969704,
-0.03671795502305031,
-0.05476440116763115,
-0.02397666685283184,
-0.01886298879981041,
0.027496153488755226,
-0.03867490962147713,
0.05355021357536316,
0.002276523970067501,
-0.025314275175333023,
0.0047265952453017235,
-0.056775182485580444,
-0.08915580809116364,
-0.0016665455186739564,
0.005016790237277746,
-0.04844936728477478,
0.0011900060344487429,
0.05043464154005051,
0.027868594974279404,
-0.05734817311167717,
0.04292063042521477,
-0.042029086500406265,
-0.041332513093948364,
-0.009867864660918713,
-0.0056668538600206375,
-0.02663356252014637,
0.04303605109453201,
0.043348997831344604,
-0.06708341836929321,
-0.0033730564173310995,
-0.008269503712654114,
0.01739954575896263,
0.006297545041888952,
0.009547005407512188,
0.01703743077814579,
0.004889155272394419,
-0.003247777232900262,
-0.0008934345096349716,
-0.026130225509405136,
-0.018142754212021828,
-0.010792220942676067,
-0.06117261201143265,
0.08998969197273254,
-0.060046058148145676,
-0.033410895615816116,
0.016754359006881714,
0.05074342340230942,
0.008483022451400757,
-0.03450971096754074,
-0.027920298278331757,
-0.03414479270577431,
-0.019120968878269196,
-0.004046113695949316,
-0.027401015162467957,
0.012893255800008774,
0.016666673123836517,
0.04561016336083412,
0.06492066383361816,
-0.03938881307840347,
0.06817808747291565,
-0.04574628919363022,
0.002961418591439724,
-0.02010071650147438,
0.019329706206917763,
-0.03125298395752907,
0.005112907383590937,
-0.0524727888405323,
-0.035128314048051834,
0.004456512164324522,
0.0013167279539629817,
0.06216566264629364,
0.021153099834918976,
-0.001950711477547884,
-0.011547615751624107,
-0.030711928382515907,
0.03605714067816734,
0.03490694984793663,
-0.039094846695661545,
-0.024838104844093323,
-0.07044056057929993,
-0.008376657962799072,
0.010047554969787598,
-0.016501162201166153,
-0.03986693173646927,
0.02394324727356434,
0.01584029383957386,
-0.05619001388549805,
-0.06644681096076965,
-0.0215300265699625,
-0.08752933889627457,
-0.04957858473062515,
-0.05735496059060097,
0.007170838303864002,
0.00795893743634224,
0.06821496039628983,
0.02894529327750206,
0.00489852437749505,
-0.013306532055139542,
-0.004207877907902002,
0.013394967652857304,
0.008391807787120342,
0.053703680634498596,
0.021342113614082336,
-0.02679143287241459,
-0.05960908904671669,
0.058708369731903076,
0.051802877336740494,
0.044407639652490616,
-0.03788476437330246,
0.0020003230310976505,
0.030980000272393227,
0.002258098917081952,
-0.027569890022277832,
0.01846541091799736,
-0.011017235927283764,
0.02529984898865223,
0.026305584236979485,
0.04788145422935486,
0.014768038876354694,
0.01427975669503212,
0.016842544078826904,
-0.011239884421229362,
-0.04657798632979393,
0.018206914886832237,
-0.06424061954021454,
0.004797816276550293,
0.005217859987169504,
0.025484919548034668,
-0.027855392545461655,
0.030383972451090813,
0.008119751699268818,
0.005499761085957289,
0.019595308229327202,
0.026672830805182457,
0.0234536100178957,
0.0016621918184682727,
-0.03613542765378952,
0.0020568587351590395,
0.07405471056699753,
-0.03648807853460312,
-0.07360635697841644,
0.051824238151311874,
-0.04661105200648308,
0.04580336809158325,
-0.04516468942165375,
0.01693107560276985,
0.01619877479970455,
0.028644878417253494,
-0.06180170550942421,
-0.041336655616760254,
0.06532731652259827,
0.042018525302410126,
0.0028832026291638613,
-0.011444143019616604,
0.03505880758166313,
-0.05025583878159523,
-0.03349439799785614,
0.016844818368554115,
0.024033835157752037,
-0.02747855708003044,
0.01974019780755043,
0.05537589639425278,
-0.005969759076833725,
-0.016958512365818024,
0.01658320613205433,
0.05928126350045204,
-0.07101528346538544,
-0.017375187948346138,
-0.03529419004917145,
0.0024895130190998316,
0.03618362173438072,
0.0011116598034277558,
-0.06862355768680573,
0.0011942782439291477,
0.012353088706731796,
0.0032504696864634752,
-0.01461558137089014,
-0.05274675786495209,
0.028893964365124702,
0.017472317442297935,
0.03905383497476578,
0.06176801398396492,
-0.009348053485155106,
-0.0444302074611187,
-0.029170533642172813,
0.019167711958289146,
0.012226513586938381,
-0.04321102425456047,
0.014527118764817715,
0.042415883392095566,
-0.03630215302109718,
-0.012473727576434612,
-0.009299284778535366,
-0.035621270537376404,
0.0011713700369000435,
0.0019689644686877728,
-0.057285457849502563,
0.02476590685546398,
0.006938162259757519,
-0.02459041029214859,
0.027985982596874237,
-0.08102700114250183,
-0.05015349015593529,
0.004728336352854967,
-0.03285848721861839,
-0.08142915368080139,
0.02922292985022068,
-0.010821428149938583,
0.0162730123847723,
0.008110666647553444,
-0.0024026979226619005,
-0.07450710237026215,
0.03125461935997009,
0.06035672873258591,
0.0352054089307785,
0.0625932514667511,
0.05428328365087509,
-0.006054970435798168,
0.020330525934696198,
0.01849387399852276,
0.036692582070827484,
0.02696266584098339,
0.010072775185108185,
-0.06323425471782684,
0.012458075769245625,
-0.011010945774614811,
-0.0034195634070783854,
0.03356650099158287,
-0.01352723129093647,
-0.023817265406250954,
-0.05369893088936806,
-0.0274095106869936,
0.015737634152173996,
-0.06174340471625328,
-0.01729765720665455,
0.03151677921414375,
-0.029587317258119583,
0.04443775862455368,
-0.04921295493841171,
0.05524840205907822,
0.019944308325648308,
-0.02891514264047146,
-0.04623939469456673,
-0.017696265131235123,
-0.039286743849515915,
0.01760450005531311,
0.021571997553110123,
-0.040014397352933884,
-0.02203112281858921,
-0.009553276002407074,
0.016236351802945137,
0.010582990944385529,
-0.026731641963124275,
-0.02089303359389305,
0.020728744566440582,
-0.05458149313926697,
-0.0014045217540115118,
0.01120303850620985,
-0.060926683247089386,
-0.035639818757772446,
0.010183758102357388,
-0.0028216014616191387,
0.03463650494813919,
-0.010812325403094292,
-0.01950172707438469,
0.09033796191215515,
-0.08388365805149078,
-0.01648804359138012,
-0.07063417881727219,
0.01687774248421192,
0.03220462054014206,
0.08981234580278397,
0.049437977373600006,
0.08604900538921356,
0.044592104852199554,
0.01221296563744545,
0.03741807863116264,
-0.06092522293329239,
-0.005930091720074415,
-0.05937482789158821,
0.010989301837980747,
0.006575176492333412,
0.02807679958641529,
-0.01263389177620411,
0.015348009765148163,
0.007540425285696983,
-0.029577653855085373,
-0.03314065933227539,
0.008037600666284561,
0.019838782027363777,
0.008528373204171658,
-0.03676604479551315,
-0.03638618439435959,
0.012919152155518532,
-0.02600291557610035,
0.005323858465999365,
0.03489649295806885,
0.061384882777929306,
0.007981045171618462,
-0.10765861719846725,
-0.009563453495502472,
-0.0004913111915811896,
0.028500521555542946,
0.06863860040903091,
-0.013142303563654423,
0.018968623131513596,
-0.0030851908959448338,
-0.017404688522219658,
0.0025255903601646423,
0.059538811445236206,
-0.005228431895375252,
-0.04977643862366676,
-0.011754185892641544,
-0.061652299016714096,
0.01289353333413601,
0.04187377542257309,
0.07308569550514221,
0.02423679642379284,
0.02915465459227562,
0.016496295109391212,
0.0007098912610672414,
-0.013838793151080608,
0.007457089144736528,
0.007978740148246288,
-0.03433597832918167,
0.04530914127826691,
-0.009473470970988274,
-0.020951462909579277,
0.0051366910338401794,
0.014029930345714092,
-0.03759782388806343,
-0.053044743835926056,
0.0038165710866451263,
0.03911733254790306,
-0.0499960221350193,
0.02412848360836506,
-0.012790822423994541,
0.01518571563065052,
0.03215847909450531,
0.013353481888771057,
0.014779179356992245,
0.08059625327587128,
0.048067688941955566,
-0.013856921344995499,
-0.019813314080238342,
0.06004304066300392,
0.05119673162698746,
0.00012328186130616814,
0.008362521417438984,
-0.009714020416140556,
-0.009306279942393303,
0.01597210206091404,
0.047810789197683334,
-0.03814205527305603,
0.026199208572506905,
0.002728466410189867,
0.003416543360799551,
0.0414884127676487,
0.010958680883049965,
0.0274953655898571,
0.017861362546682358,
-0.05803438276052475,
0.05892518162727356,
-0.048152126371860504,
-0.03359389305114746,
-0.05251938849687576,
0.03315842151641846,
0.012944475747644901,
0.023961590602993965,
-0.07678981125354767,
-0.03021448478102684,
-0.03482033312320709,
0.02311663143336773,
0.039622269570827484,
-0.024203920736908913,
0.03888815641403198,
-0.0206363033503294,
0.0439641997218132,
0.03335290029644966,
0.01011072751134634,
-0.010310770943760872,
0.015084433369338512,
-0.024227261543273926,
-0.016536550596356392,
0.01121840626001358,
-0.015924913808703423,
-0.00010632254998199642,
-0.007539312820881605,
-0.04866141825914383,
-0.03567309305071831,
-0.08291929215192795,
-0.00026142052956856787,
0.04939538612961769,
0.04491748288273811,
0.02411234751343727,
0.06864820420742035,
0.013883642852306366,
0.027530116960406303,
-0.005409179721027613,
0.028616251423954964,
-0.03353771194815636,
-0.030595816671848297,
-0.012009236961603165,
0.017493005841970444,
0.01215242687612772,
0.011673343367874622,
0.028587771579623222,
0.07300423830747604,
0.07488371431827545,
0.03682876378297806,
-0.05662280693650246,
0.04758882895112038,
-0.03622720018029213,
0.019974499940872192,
-0.00490250950679183,
0.020051997154951096,
0.06321905553340912,
0.027971643954515457,
-0.022300921380519867,
0.04208263009786606,
0.010981732979416847,
0.02944728545844555,
-0.04746202751994133,
0.06058018282055855,
-0.07614390552043915,
-0.07666173577308655,
0.02354992926120758,
-0.012917392887175083,
-0.0056546516716480255,
0.03407890349626541,
-0.003150567412376404,
0.048629116266965866,
0.010354782454669476,
-0.01513907965272665,
-0.005288589745759964,
-0.048717718571424484,
0.04024314135313034,
0.042582716792821884,
0.01181884203106165,
0.03108849935233593,
0.026200100779533386,
-0.028877371922135353,
0.028517374768853188,
0.04291772097349167,
0.05021735653281212,
0.006430651992559433,
0.0023802523501217365,
-0.002121632918715477,
-0.016341686248779297,
-0.009328733198344707,
0.0023273038677871227,
-0.028959419578313828,
0.06414619088172913,
0.02227994054555893,
-0.0033148829825222492,
0.06078965216875076,
0.09005329012870789,
0.0005038087256252766,
0.00811636820435524,
-0.01463404018431902,
-0.02428511530160904,
0.027392661198973656,
0.048778973519802094,
-0.01591523177921772,
-0.02112504094839096,
0.026298100128769875,
0.05529126524925232,
-0.05291879549622536,
0.03765295818448067,
0.0058020795695483685,
-0.08575662225484848,
-0.010809333994984627,
-0.010394610464572906,
-0.04853677749633789,
0.018164142966270447,
0.02013302966952324,
-0.024748407304286957,
-0.03829296678304672,
-0.02251293510198593,
-0.002674676710739732,
-0.02040400542318821,
-0.010503365658223629,
-0.010485817678272724,
0.04746688902378082,
0.07218780368566513,
-0.008223517797887325,
0.0056134979240596294,
0.05574841797351837,
0.017569852992892265,
0.05414324998855591,
0.02463577501475811,
-0.04193449020385742,
-0.05145169422030449,
-0.05951869115233421,
-0.0010414880234748125,
0.019650312140583992,
0.023623943328857422,
0.0344652496278286,
0.054767124354839325,
-0.009570930153131485,
0.03201322630047798,
-0.02077687345445156,
-0.039144303649663925,
-0.04808790981769562,
-0.03368368744850159,
-0.06150851771235466,
-0.05561208724975586,
0.03207044303417206,
0.054630257189273834,
0.007995427586138248,
-0.03227190300822258,
-0.012194554321467876,
-0.04899173229932785,
0.0019825573544949293,
0.027020316570997238,
-0.06984314322471619,
0.06001250073313713,
-0.008434091694653034,
-0.031215941533446312,
-0.0006525245844386518,
0.03495116904377937,
0.02084883116185665,
-0.008238148875534534,
0.012012874707579613,
-0.011193059384822845,
-0.0032303661573678255,
-0.03173002228140831,
-0.05039540305733681,
0.014678195118904114,
-0.0033063229639083147,
-0.0487288162112236,
-0.01814219355583191,
-0.0168962050229311,
0.006769890896975994,
0.0076683987863361835,
0.02525019831955433,
0.013158561661839485,
-0.04785092920064926,
0.020092487335205078,
-0.0059466115199029446,
-0.023150745779275894,
0.013360685668885708,
0.030907955020666122,
-0.028296753764152527,
-0.0014483918203040957,
0.07783655822277069,
0.02789195440709591,
0.0017253629630431533,
0.029413599520921707,
-0.053481388837099075,
0.05497562885284424,
0.0228082574903965,
0.05571329966187477,
0.0010668961331248283,
0.02811286970973015,
0.013193733058869839,
-0.05592780187726021,
0.024893032386898994,
-0.014621926471590996,
-0.01702357828617096,
0.017821161076426506,
-0.048127949237823486,
-0.01894688419997692,
0.01609177328646183,
-0.027517886832356453,
-0.03436974808573723,
0.030015194788575172,
-0.013393780216574669,
0.011098173446953297,
-0.019839998334646225,
-0.001603531651198864,
-0.04542503133416176,
0.03752991929650307,
-0.09499689936637878,
0.0328206904232502,
0.04534555971622467,
-0.04407275840640068,
0.06759563088417053,
-0.007080825511366129,
0.0173498447984457,
0.014833041466772556,
0.014496716670691967,
-0.0194297656416893,
0.0014607410412281752,
0.016662167385220528,
0.011400799266994,
0.05396820232272148,
-0.044914983212947845,
0.027581464499235153,
0.052789777517318726,
0.05939894914627075,
0.06532235443592072,
-0.0583357959985733,
0.014830189757049084,
-0.019871244207024574,
-0.003909120336174965,
-0.00576368160545826,
-0.0246308334171772,
0.018753860145807266,
0.0036708221305161715,
0.021527154371142387,
-0.03533613309264183,
0.00397601630538702,
-0.01196994073688984,
-0.01231707725673914,
-0.012522262521088123,
0.07591669261455536,
0.0038367470260709524,
0.040504008531570435,
-0.0734848603606224,
0.029385104775428772,
0.006728398147970438,
-0.015324576757848263,
-0.02350551076233387,
-0.0011753049911931157,
0.05823058634996414,
0.03456679731607437,
0.025758283212780952,
0.05116359144449234,
-0.015070362016558647,
-0.012329296208918095,
0.0388166718184948,
-0.03271134942770004,
-0.03824138268828392,
0.06462930142879486,
-0.00771054532378912,
-0.015212398953735828,
0.00377542688511312,
0.02827153168618679,
-0.008818945847451687,
0.02644720859825611,
0.02124832570552826,
-0.009510216303169727,
0.014082781039178371,
0.01581168919801712,
0.012459672056138515,
0.04390312358736992,
0.029681814834475517,
0.01186163816601038,
-0.022610900923609734,
-0.0018306764541193843,
0.0006238083587959409,
-0.022960243746638298,
0.02430836670100689,
-0.00922548770904541,
-0.09548880904912949,
-0.03903784230351448,
-0.04168951138854027,
-0.01866336539387703,
-0.025441739708185196,
-0.02792338840663433,
-0.02857423759996891,
0.03931641951203346,
0.06581369787454605,
-0.006924156565219164,
0.011920531280338764,
0.030656160786747932,
-0.05146007239818573,
0.07461827248334885,
-0.03826265409588814,
-0.049884650856256485,
-0.043148308992385864,
0.03297707438468933,
0.024381883442401886,
-0.017604531720280647,
-0.01938466913998127,
0.06654196977615356,
-0.035170428454875946,
-0.006137941963970661,
0.009375124238431454,
0.02526886761188507,
-0.05819356441497803,
0.00027252890868112445,
-0.02834244631230831,
-0.0408756360411644,
0.0018629749538376927,
-0.021078987047076225,
0.005746513605117798,
0.048874396830797195,
-0.0070772115141153336,
0.0658293142914772,
0.07370509952306747,
-0.024661220610141754,
0.004737067501991987,
-0.025961896404623985,
-0.00032351171830669045,
-0.03894098475575447,
-0.010365073569118977,
0.00883337203413248,
0.0387200191617012,
-0.037533823400735855,
-0.012821679003536701,
-0.0030953625682741404,
-0.02933988720178604,
0.008433161303400993,
-0.0360187329351902,
0.03560294210910797,
0.02123327925801277,
0.005170167423784733,
-0.029769640415906906,
0.027264345437288284,
-0.05001929774880409,
-0.016056841239333153,
-0.071019247174263,
-0.032157693058252335,
-0.015110315755009651,
0.014612850733101368,
-0.01806507259607315,
0.00783669762313366,
-0.007095605134963989,
-0.02533121593296528,
-0.007170712575316429,
0.026414645835757256,
-0.0651843473315239,
-0.03159639611840248,
-0.01679731160402298,
-0.03466612473130226,
0.032447706907987595,
-0.05345137417316437,
-0.02403593435883522,
-0.016662150621414185,
0.06822329759597778,
0.020939644426107407,
-0.05643737316131592,
0.0027655577287077904,
0.07615851610898972,
0.055470630526542664,
-0.03154971823096275,
-0.027555160224437714,
-0.017672035843133926,
-0.058798979967832565,
-0.004914266988635063,
0.07957328110933304,
-0.03522651642560959,
-0.008562197908759117,
-0.0010187274310737848,
-0.04457313194870949,
-0.02868512272834778,
-0.03366606682538986,
0.007294389419257641,
-0.04018489643931389,
-0.006964803207665682,
0.03559105098247528,
-0.023002302274107933,
-0.0651644617319107,
-0.03296812251210213
] |
<p>What is more effective for travel in outer space ignoring all other factors like air radiation etc. I have a 10 kg bag of rice would I travel faster throwing the whole bag at once or throwing a grain at a time compounding my tiny acceleration or would they end up being equal?</p> | g4755 | [
0.039061158895492554,
0.07780087739229202,
0.03861772641539574,
0.015803230926394463,
0.004318724386394024,
0.00789082795381546,
-0.01335613988339901,
0.00561320036649704,
-0.05708456411957741,
-0.011906842701137066,
0.06445728987455368,
0.022516215220093727,
-0.021379204466938972,
0.05003152787685394,
0.0011377730406820774,
-0.009141746908426285,
0.11751406639814377,
-0.027005717158317566,
-0.05866224318742752,
0.017829997465014458,
0.004403586965054274,
-0.027953557670116425,
-0.030947387218475342,
-0.031750258058309555,
-0.024356849491596222,
0.0057777706533670425,
-0.0056157344952225685,
-0.022761259227991104,
-0.06201336532831192,
-0.02920662611722946,
0.07249082624912262,
-0.07642647624015808,
-0.03385061398148537,
-0.04729899391531944,
-0.05075964331626892,
-0.0003849640488624573,
-0.009333821944892406,
0.023644020780920982,
-0.03858349844813347,
-0.03923880681395531,
-0.03490927070379257,
-0.03221958130598068,
-0.005152189638465643,
0.01454139780253172,
0.018070818856358528,
0.08624624460935593,
0.025402283295989037,
0.01981452666223049,
-0.020202696323394775,
-0.007061609532684088,
-0.07585818320512772,
-0.022570814937353134,
-0.022645488381385803,
0.0024949219077825546,
-0.022192757576704025,
0.0024761867243796587,
-0.032460201531648636,
-0.009129655547440052,
0.0519612692296505,
0.004584003239870071,
-0.012205197475850582,
0.014624292962253094,
-0.03336961567401886,
-0.052684083580970764,
0.05938900634646416,
0.001998908119276166,
-0.013138197362422943,
0.034221384674310684,
0.012087700888514519,
-0.06168346107006073,
0.0669524073600769,
-0.07092271745204926,
-0.007128816097974777,
-0.0478312186896801,
-0.03953119367361069,
-0.009995643049478531,
0.018635813146829605,
0.031399842351675034,
-0.007688060402870178,
0.05819612741470337,
-0.003142124740406871,
0.0049176448956131935,
0.026377975940704346,
-0.030170824378728867,
0.04754844680428505,
-0.03468570113182068,
-0.022972702980041504,
-0.026508210226893425,
-0.0191420279443264,
-0.040003035217523575,
-0.02891518361866474,
0.006631212309002876,
0.0017056063516065478,
0.04815332591533661,
0.016569750383496284,
0.042673204094171524,
-0.025845231488347054,
0.08673406392335892,
0.011926799081265926,
0.03684313967823982,
0.02389860525727272,
0.026616599410772324,
0.041744720190763474,
0.04650743305683136,
0.00572934141382575,
-0.08548349142074585,
0.035995252430438995,
0.008864988572895527,
-0.03828943893313408,
-0.028483938425779343,
0.025450965389609337,
0.016605762764811516,
-0.017297646030783653,
0.0006021872977726161,
-0.013724712654948235,
0.011031690053641796,
0.0672372430562973,
0.0010640586260706186,
0.03255637735128403,
0.0001497183839092031,
-0.03981161117553711,
0.034024931490421295,
0.02270224131643772,
-0.046529266983270645,
-0.045979201793670654,
-0.02917015738785267,
0.025032639503479004,
-0.030043622478842735,
-0.025480739772319794,
-0.001500757527537644,
-0.03259091451764107,
-0.011503634043037891,
-0.04534093663096428,
-0.012746221385896206,
-0.02084208093583584,
-0.018104974180459976,
-0.05184213072061539,
-0.004095188342034817,
0.010793894529342651,
-0.055151402950286865,
-0.023761095479130745,
-0.039479199796915054,
-0.014325679279863834,
0.015727421268820763,
-0.08941176533699036,
0.028786703944206238,
0.016351887956261635,
0.044378310441970825,
0.006014291662722826,
0.05018310993909836,
0.021862594410777092,
0.05824734643101692,
-0.021372197195887566,
0.006127507891505957,
-0.015115623362362385,
0.02450099214911461,
0.06515110284090042,
0.000888082489836961,
0.015583517029881477,
-0.0024479972198605537,
-0.011665060184895992,
0.014510569162666798,
0.0034899823367595673,
-0.006692534312605858,
-0.06318239122629166,
0.02484266273677349,
0.06038365885615349,
0.020752547308802605,
0.03710855916142464,
-0.049828317016363144,
-0.07469353824853897,
-0.03180297836661339,
0.09311513602733612,
-0.004215369001030922,
0.016503650695085526,
0.0308334082365036,
0.05178004503250122,
0.009135620668530464,
-0.052307095378637314,
-0.00555519899353385,
0.022714829072356224,
-0.01261439360678196,
-0.07265264540910721,
0.002239348366856575,
-0.004290343727916479,
-0.02898671291768551,
0.07666803896427155,
0.051352400332689285,
-0.09432640671730042,
-0.002928958972916007,
-0.02454999089241028,
-0.03761900216341019,
-0.043569620698690414,
0.016406163573265076,
-0.05771089345216751,
-0.008600256405770779,
0.03699882701039314,
-0.04271048679947853,
-0.04718196764588356,
0.04231450706720352,
-0.04430976137518883,
0.04420115053653717,
0.014113565906882286,
-0.0020039218943566084,
0.016441943123936653,
0.00808672420680523,
-0.003506995039060712,
-0.010999660938978195,
0.013005811721086502,
-0.06780970096588135,
0.020451167598366737,
0.0022088757250458,
0.01612679660320282,
0.023571860045194626,
0.006445880047976971,
0.0056035565212368965,
-0.002184151904657483,
0.02277921512722969,
-0.04304948449134827,
-0.009810279123485088,
0.0071141985245049,
-0.018869012594223022,
0.032447561621665955,
-0.03594522923231125,
0.006785260047763586,
-0.02112865447998047,
0.008984925225377083,
-0.03806702420115471,
0.0005413660546764731,
0.016048511490225792,
-0.02893422357738018,
0.0214211568236351,
0.019516674801707268,
-0.023529602214694023,
0.0681912824511528,
0.013967993669211864,
0.004340512212365866,
0.004846916068345308,
-0.04104212671518326,
0.012130950577557087,
-0.017376238480210304,
0.033808499574661255,
-0.06479515880346298,
-0.04820508509874344,
0.03009393811225891,
-0.03613385930657387,
0.029758619144558907,
-0.06055523082613945,
0.024478048086166382,
-0.007851380854845047,
-0.02234700880944729,
0.04869375750422478,
-0.06164355203509331,
-0.021059656515717506,
-0.033336903899908066,
0.027390019968152046,
-0.034376416355371475,
0.010050679557025433,
-0.018559608608484268,
0.07004319876432419,
-0.028293997049331665,
0.032632458955049515,
-0.010892496444284916,
-0.0069166067987680435,
-0.01632874831557274,
-0.0010350869270041585,
-0.03500303626060486,
0.008969823829829693,
0.011206556111574173,
0.038169823586940765,
-0.006000628229230642,
-0.016146661713719368,
0.0246419720351696,
-0.0062618921510875225,
0.0026982584968209267,
-0.01681564934551716,
0.04611135274171829,
-0.007418087683618069,
0.020874712616205215,
-0.031042007729411125,
0.012739628553390503,
-0.013491309247910976,
-0.0024957244750112295,
0.001340182265266776,
0.008805549703538418,
-0.02306024357676506,
0.061982277780771255,
0.05647609010338783,
-0.038724176585674286,
0.02044081874191761,
-0.06550196558237076,
0.06779555976390839,
0.06380323320627213,
0.036381691694259644,
0.04028942435979843,
0.11213387548923492,
0.04893117770552635,
-0.015445969998836517,
-0.024412432685494423,
-0.06753452122211456,
0.05795348063111305,
-0.020712347701191902,
0.004736851900815964,
0.013109805062413216,
-0.07207334786653519,
0.05991194769740105,
-0.035424042493104935,
-0.057112403213977814,
-0.03877592086791992,
-0.018151387572288513,
-0.015545462258160114,
0.05513221025466919,
-0.023678213357925415,
0.06154396012425423,
-0.030590327456593513,
-0.061444178223609924,
0.007902245037257671,
0.038112934678792953,
0.03646591305732727,
0.014847628772258759,
0.03837092965841293,
-0.024531394243240356,
-0.07433648407459259,
-0.041347436606884,
-0.04351969063282013,
0.05149282142519951,
0.03552903234958649,
-0.028002755716443062,
-0.0015051158843562007,
-0.025916270911693573,
-0.024195430800318718,
0.03871341422200203,
-0.02855745516717434,
0.010964004322886467,
-0.07949423789978027,
-0.002038138685747981,
-0.02220647968351841,
0.03183285892009735,
-0.021597709506750107,
0.049999039620161057,
-0.06162675470113754,
0.032764945179224014,
0.00694556487724185,
0.0051114195957779884,
0.05142422765493393,
0.043965116143226624,
-0.0029732389375567436,
-0.0017849486321210861,
-0.01952851563692093,
-0.028584498912096024,
0.06787489354610443,
0.014834788627922535,
-0.04187522456049919,
-0.015137103386223316,
-0.03548767790198326,
-0.03715983033180237,
-0.014675970189273357,
0.05340658873319626,
0.0245954729616642,
0.0035633458755910397,
-0.014508436433970928,
-0.0020179743878543377,
-0.025349436327815056,
0.02988542802631855,
-0.02599368989467621,
0.03765628859400749,
0.03313400223851204,
0.033493850380182266,
-0.0497862845659256,
0.03422879800200462,
-0.00392001261934638,
0.010110708884894848,
-0.03543800115585327,
-0.020447110757231712,
0.04939494654536247,
-0.008781025186181068,
0.03732190281152725,
-0.009417857974767685,
0.0069313994608819485,
0.008080122992396355,
0.016031615436077118,
0.025373077020049095,
0.06289046257734299,
-0.0024871230125427246,
-0.008711746893823147,
-0.0035637684632092714,
0.021105077117681503,
0.006717817857861519,
-0.03789705038070679,
0.018074434250593185,
-0.006348767317831516,
-0.05850311741232872,
-0.020753705874085426,
0.0023912081960588694,
0.0032427210826426744,
0.00245892396196723,
0.013119097799062729,
-0.015081282705068588,
0.002466992475092411,
0.05205408111214638,
-0.003534971736371517,
0.02878001518547535,
0.02467874251306057,
0.005755182821303606,
-0.007636400405317545,
-0.04007065296173096,
0.020966872572898865,
-0.03714774176478386,
-0.0453701876103878,
0.00811722595244646,
0.01042508240789175,
0.012334282509982586,
0.026687568053603172,
-0.005831465590745211,
-0.004203413147479296,
0.02852562442421913,
-0.028446141630411148,
0.07171829789876938,
-0.00309035275131464,
0.003358423011377454,
0.02886427938938141,
0.04414413496851921,
0.001930341823026538,
-0.04321906715631485,
-0.007210946176201105,
0.06848937273025513,
0.021599339321255684,
0.06390495598316193,
0.02324630506336689,
0.055830903351306915,
-0.017398957163095474,
0.025341084226965904,
-0.013100727461278439,
0.04820212349295616,
-0.05906696990132332,
0.03537321835756302,
0.005885377526283264,
0.03259831666946411,
0.10633072257041931,
0.013959788717329502,
0.05314195901155472,
0.019818350672721863,
-0.021817779168486595,
0.04724603146314621,
0.007197389844805002,
0.05131763964891434,
-0.0078169209882617,
-0.06754393875598907,
0.004001823253929615,
-0.019682014361023903,
0.0191623754799366,
0.010118041187524796,
-0.059031348675489426,
-0.03243712708353996,
0.004955715034157038,
0.03433787822723389,
-0.06071808189153671,
-0.013116780668497086,
0.10363715142011642,
0.01951339840888977,
-0.041082169860601425,
0.07726402580738068,
0.024721777066588402,
-0.03614412248134613,
-0.00679593812674284,
0.031610652804374695,
0.0003697968786582351,
-0.05701940134167671,
-0.03447122871875763,
0.03446200489997864,
0.028386998921632767,
-0.03328804671764374,
-0.03923529013991356,
-0.003831372829154134,
0.024506649002432823,
0.0017012968892231584,
-0.010577565990388393,
-0.01648026891052723,
-0.04001361504197121,
-0.006120538804680109,
-0.02786370739340782,
-0.03698981553316116,
-0.003485420485958457,
-0.02992391586303711,
0.04175364598631859,
0.010145784355700016,
-0.06785645335912704,
-0.04670471325516701,
0.06945041567087173,
-0.04020143300294876,
0.0409395806491375,
-0.0038964098785072565,
-0.021370070055127144,
-0.0514635369181633,
-0.03517340496182442,
0.01994553580880165,
0.004526629578322172,
-0.08202124387025833,
-0.009947754442691803,
0.0026195384562015533,
-0.014478598721325397,
-0.03231952711939812,
-0.000054045478464104235,
0.05768011882901192,
-0.021102359518408775,
-0.07363244891166687,
0.021474773064255714,
0.03201571851968765,
-0.0007442719652317464,
0.020997045561671257,
0.016637198626995087,
0.05713389813899994,
-0.06133866682648659,
-0.03226112946867943,
0.00387006439268589,
0.002513529034331441,
-0.0012003447627648711,
-0.00015921358135528862,
0.04640175774693489,
-0.07549326121807098,
0.02297228015959263,
0.007954740896821022,
0.019280914217233658,
0.04504192993044853,
0.020500613376498222,
0.018855297937989235,
-0.07856966555118561,
0.02305184304714203,
0.04988769069314003,
-0.01418285071849823,
0.051151521503925323,
-0.045989058911800385,
0.07544393837451935,
0.03062835894525051,
-0.011508608236908913,
0.01479171309620142,
0.05997138470411301,
0.07321422547101974,
0.012260951101779938,
-0.048491209745407104,
-0.10534781217575073,
-0.010339188389480114,
-0.0015403410652652383,
0.007097191642969847,
0.050009891390800476,
-0.02741529606282711,
-0.0594879686832428,
0.014321109279990196,
0.0681120827794075,
0.054747749119997025,
0.004413070622831583,
-0.008811207488179207,
-0.005709468387067318,
-0.05634767562150955,
0.02982781082391739,
0.08052308857440948,
-0.017146866768598557,
-0.03752357140183449,
-0.02275657281279564,
-0.03312871232628822,
-0.00709178252145648,
0.04296239838004112,
-0.0029520972166210413,
-0.060904305428266525,
-0.017208009958267212,
-0.062352295964956284,
0.016267362982034683,
-0.04320252314209938,
0.0024624522775411606,
0.0004530545847956091,
0.00017921990365721285,
0.020764177665114403,
-0.01955476775765419,
0.044167131185531616,
0.015021677128970623,
-0.029874088242650032,
0.017657557502388954,
-0.060516733676195145,
-0.07042878866195679,
0.028973203152418137,
0.0014542712597176433,
-0.022819362580776215,
-0.030628230422735214,
-0.003895059460774064,
0.0049299984239041805,
0.009950912557542324,
-0.01414196565747261,
-0.010731900110840797,
0.07954291254281998,
-0.0378098301589489,
-0.0199455413967371,
-0.03381591662764549,
0.016153855249285698,
0.026209136471152306,
-0.07882191240787506,
-0.014705843292176723,
-0.029718030244112015,
-0.016354767605662346,
-0.04744967073202133,
-0.005360760726034641,
-0.004656102508306503,
0.039615049958229065,
0.07203088700771332,
-0.043311718851327896,
0.010659391060471535,
0.02656509540975094,
-0.01573803834617138,
-0.03639911860227585,
0.031117048114538193,
0.01878548599779606,
0.016717752441763878,
0.010625491850078106,
0.03224610164761543,
0.03958284854888916,
-0.014224505051970482,
0.015043017454445362,
-0.00436429725959897,
-0.0347643680870533,
0.06088894233107567,
-0.01720605604350567,
0.023427918553352356,
-0.022658759728074074,
-0.03165101632475853,
-0.062222324311733246,
0.0038809399120509624,
0.0055552455596625805,
-0.013887094333767891,
0.037146229296922684,
0.007314920425415039,
-0.046831417828798294,
-0.002846864750608802,
0.012013335712254047,
0.03811653330922127,
-0.010265394113957882,
-0.0008884434937499464,
-0.04241226613521576,
0.0019759242422878742,
0.05530061572790146,
-0.04887416213750839,
-0.00021673965966328979,
-0.037695590406656265,
0.03317803144454956,
0.0022736822720617056,
0.007482761982828379,
-0.020153833553195,
0.032432038336992264,
0.0016868331003934145,
-0.01125611923635006,
0.051217854022979736,
-0.02854335680603981,
0.013851536437869072,
-0.05374351516366005,
0.0026704526972025633,
-0.031283143907785416,
-0.03078433685004711,
-0.019651053473353386,
0.026384538039565086,
0.05332650616765022,
0.020369073376059532,
-0.006700028199702501,
-0.05037381872534752,
-0.05171072483062744,
-0.002927783876657486,
0.042670998722314835,
-0.02523120306432247,
0.023093702271580696,
-0.02735595405101776,
-0.015819033607840538,
-0.009925316087901592,
0.006479851435869932,
0.007160400040447712,
-0.02010600082576275,
-0.05470028147101402,
0.001867417711764574,
0.07078853249549866,
-0.030133100226521492,
-0.04049096629023552,
-0.011520356871187687,
-0.008916235528886318,
0.05684250593185425,
0.04929612949490547,
-0.06267371773719788,
0.0452994741499424,
0.04412129893898964,
0.00865071453154087,
0.017661932855844498,
-0.01931069791316986,
-0.014460896141827106,
0.06624256074428558,
-0.03880593180656433,
0.013755147345364094,
-0.012009027414023876,
0.007454672362655401,
0.009445680305361748,
-0.03753539174795151,
0.04526586830615997,
0.014987809583544731,
-0.015566988848149776,
-0.00880005955696106,
-0.01192520186305046,
-0.0688459500670433,
0.043433912098407745,
0.04680454730987549,
0.0084110451862216,
0.005710162688046694,
0.04220402613282204,
0.035112135112285614,
0.03734350576996803,
-0.04204648733139038,
-0.019553808495402336,
0.007573633920401335,
-0.0002836347557604313,
-0.00368157378397882,
0.00047747112694196403,
-0.03178166598081589,
0.01843884587287903,
-0.009768318384885788,
-0.010275943204760551,
0.05565840005874634,
0.057347673922777176,
0.038558632135391235,
0.029908185824751854,
0.005211910232901573,
-0.01825711876153946,
-0.014722627587616444,
-0.08615060895681381,
0.0023483396507799625,
-0.00647046510130167,
0.005421457812190056,
-0.026689259335398674,
0.05814175307750702,
-0.05490296334028244,
-0.03943614661693573,
0.004265181254595518,
-0.006403161678463221,
-0.000643423234578222,
0.044431786984205246,
-0.04399716481566429,
-0.04073389247059822,
0.08487123996019363,
-0.008343452587723732,
0.07333250343799591,
-0.05989129841327667,
0.02410549484193325,
-0.05212588608264923,
-0.0007878478500060737,
0.009944774210453033,
0.0523628368973732,
0.0339571014046669,
-0.026478836312890053,
0.020304420962929726,
-0.0037381413858383894,
-0.007190176285803318,
0.019432494416832924,
0.01739889569580555,
0.010067886672914028,
-0.005373876076191664,
-0.0006007549818605185,
0.025741038843989372,
-0.007632707245647907,
0.023994384333491325,
-0.011761842295527458,
0.02866300940513611,
-0.009067964740097523,
-0.017398659139871597,
-0.029307382181286812,
0.04082908481359482,
-0.042012881487607956
] |
<p>So, I remember in college physics the prof using liquid nitrogen in a demonstration. When he was done, he threw the container of LN at the front row, and of course it evaporated (or whatever) before it got to the students.</p>
<p>I am watching a cooking show now and they are using LN -- if they touched that, what would happen? Would it be possible for the chefs to pour the LN onto their skin accidentally, or would it evaporate before it reached their skin?</p> | g4756 | [
0.056331779807806015,
0.02501489967107773,
0.03335192799568176,
-0.04284316673874855,
-0.0023789312690496445,
0.037120770663022995,
-0.017992893233895302,
0.02058413065969944,
-0.023793939501047134,
-0.054900143295526505,
-0.036095939576625824,
0.04867001995444298,
0.006455297116190195,
0.06710249185562134,
0.0294853076338768,
0.019797923043370247,
0.022440265864133835,
-0.04985569790005684,
-0.015821050852537155,
0.0058800033293664455,
-0.023150380700826645,
-0.017279403284192085,
-0.03387635573744774,
-0.06349973380565643,
-0.09192918241024017,
-0.08078981190919876,
0.0014141577994450927,
0.03860238939523697,
-0.037408363074064255,
-0.0344991572201252,
-0.019955558702349663,
-0.010704241693019867,
-0.06220134347677231,
-0.0279591903090477,
-0.07194840162992477,
-0.03156815469264984,
-0.015110014006495476,
0.0026958310045301914,
-0.011344566009938717,
-0.0020233618561178446,
0.03474320471286774,
0.04273120313882828,
0.028694214299321175,
-0.016282744705677032,
-0.016351062804460526,
0.1252240538597107,
-0.039983611553907394,
-0.033043861389160156,
0.009719310328364372,
-0.019505606964230537,
-0.015572614036500454,
-0.020429814234375954,
-0.058246757835149765,
-0.0028786701150238514,
-0.021075092256069183,
-0.007276874501258135,
0.012273564003407955,
-0.013949631713330746,
0.06670348346233368,
0.07806363701820374,
-0.03385407105088234,
0.002818103414028883,
-0.052524663507938385,
-0.037747714668512344,
0.0016800516750663519,
-0.007844824343919754,
-0.01720450632274151,
0.0714813768863678,
0.06877736002206802,
0.020838920027017593,
-0.011595436371862888,
0.013307482935488224,
0.02604098804295063,
0.0009093710104934871,
0.013218280859291553,
0.0362008735537529,
-0.040533386170864105,
0.038918666541576385,
0.0007831992697902024,
0.03535450994968414,
-0.0909041240811348,
0.0115461191162467,
-0.011205150745809078,
0.006066987290978432,
0.019170712679624557,
-0.007212768774479628,
-0.004056661389768124,
-0.027054909616708755,
0.00558431725949049,
0.07541277259588242,
0.08641592413187027,
-0.02616875059902668,
0.017968766391277313,
0.047995675355196,
-0.005826444365084171,
-0.01020890660583973,
0.043647002428770065,
0.01761123351752758,
-0.01832626387476921,
-0.07572291791439056,
0.0025347317568957806,
-0.03359278291463852,
-0.01338147558271885,
-0.01798384077847004,
-0.019482042640447617,
0.039982590824365616,
0.11921340972185135,
-0.0039043640717864037,
-0.0038095475174486637,
-0.012010648846626282,
0.002396502299234271,
-0.026954438537359238,
-0.04787306487560272,
0.04968888685107231,
0.017878541722893715,
0.042101457715034485,
0.02420642413198948,
0.025001613423228264,
0.01221957616508007,
0.01627831533551216,
0.052637383341789246,
0.06372008472681046,
0.02170383557677269,
0.026782851666212082,
0.025598570704460144,
-0.006922800559550524,
-0.008324741385877132,
0.015472671948373318,
-0.0039454237557947636,
0.009672543965280056,
-0.03224185109138489,
0.06959804892539978,
-0.004800251219421625,
-0.026688633486628532,
0.038019221276044846,
0.040323637425899506,
-0.02326188050210476,
0.012037351727485657,
-0.014109733514487743,
-0.08891990780830383,
0.07847615331411362,
-0.0417572483420372,
-0.03140698000788689,
0.024909501895308495,
-0.024705583229660988,
-0.00541162583976984,
-0.038786113262176514,
0.020888851955533028,
-0.002823903691023588,
0.02811904437839985,
-0.01202140748500824,
0.014671138487756252,
0.023652879521250725,
-0.029261521995067596,
0.04233141988515854,
0.03146951273083687,
0.02789393998682499,
-0.04843463748693466,
0.04680753871798515,
-0.003925846423953772,
0.022637680172920227,
0.014141889289021492,
0.0481165274977684,
-0.02148517407476902,
-0.11096585541963577,
-0.003015282331034541,
-0.021715788170695305,
-0.03194618970155716,
0.04421978443861008,
0.01444927230477333,
-0.07853931188583374,
0.012560209259390831,
0.005637738853693008,
0.02280610427260399,
-0.021624023094773293,
0.05877523496747017,
0.0026214257813990116,
0.028311507776379585,
0.04031864181160927,
-0.040130600333213806,
-0.01368511188775301,
-0.016477305442094803,
0.01047979574650526,
-0.03338485211133957,
0.0513516329228878,
0.0025888090021908283,
0.010132398456335068,
0.028163868933916092,
-0.013561246916651726,
-0.04381275549530983,
-0.046758756041526794,
0.026014944538474083,
-0.008974001742899418,
-0.036949630826711655,
-0.03048904798924923,
-0.024181604385375977,
-0.012109380215406418,
-0.02017963118851185,
0.024831632152199745,
-0.0061274985782802105,
-0.03534262999892235,
-0.05664711445569992,
0.03413458541035652,
0.051817867904901505,
-0.03409213200211525,
-0.0036291610449552536,
-0.04754220321774483,
0.002163113094866276,
0.0019519857596606016,
-0.03983350470662117,
0.01601005718111992,
0.011276794597506523,
0.01198557484894991,
0.006549933925271034,
-0.038108523935079575,
0.046233851462602615,
-0.057255856692790985,
-0.00861444603651762,
-0.01739608310163021,
0.04047543928027153,
-0.024396467953920364,
-0.03359350562095642,
0.030751517042517662,
-0.04070320352911949,
0.019979963079094887,
-0.017937785014510155,
-0.014958697371184826,
-0.03553245589137077,
-0.05697266757488251,
0.016934562474489212,
-0.030633332207798958,
-0.02729070372879505,
-0.024831967428326607,
-0.007234652526676655,
0.008963904343545437,
-0.010215737856924534,
0.007467045448720455,
0.011205536313354969,
-0.013048193417489529,
-0.015546065755188465,
-0.010370421223342419,
-0.038243189454078674,
-0.026409607380628586,
0.01890917681157589,
0.0447726845741272,
-0.027531733736395836,
0.013679088093340397,
-0.014000725001096725,
0.013802247121930122,
-0.007409647107124329,
-0.03129523992538452,
0.019908025860786438,
-0.03126576542854309,
0.026036256924271584,
0.0020916960202157497,
0.05064353719353676,
-0.011958562768995762,
0.010366136208176613,
-0.01613909751176834,
-0.02820330113172531,
0.01046845968812704,
-0.015437399968504906,
-0.006138916127383709,
0.00599207729101181,
-0.036438487470149994,
0.01847161166369915,
-0.06862776726484299,
0.019043412059545517,
0.031917404383420944,
0.04815376177430153,
0.004152317997068167,
0.005302746314555407,
0.022316573187708855,
0.03187897056341171,
0.008038529194891453,
0.026988493278622627,
-0.03385789319872856,
-0.011747665703296661,
0.03914019465446472,
-0.03716050460934639,
-0.05473409593105316,
0.025476528331637383,
-0.021751126274466515,
-0.004449677653610706,
0.06743228435516357,
-0.0320480614900589,
-0.0337241031229496,
-0.021018136292696,
-0.01717626117169857,
-0.017277412116527557,
-0.008518118411302567,
-0.03677228093147278,
0.024002455174922943,
0.017706625163555145,
-0.0176315288990736,
0.03127923980355263,
0.055056922137737274,
0.01672379858791828,
-0.01921243779361248,
-0.020453957840800285,
0.025298696011304855,
-0.04884839057922363,
-0.007430397439748049,
0.051017362624406815,
0.007464522495865822,
0.011813810095191002,
-0.06393830478191376,
0.03301415219902992,
0.0953250527381897,
-0.07008963078260422,
-0.09919077157974243,
0.050020162016153336,
-0.05023098364472389,
0.038408853113651276,
-0.005176946055144072,
0.00492394482716918,
0.03306589648127556,
0.034540966153144836,
0.07202847301959991,
-0.0606723427772522,
0.009454126469790936,
0.01400870643556118,
0.0022032640408724546,
-0.03860790655016899,
0.010850584134459496,
-0.02337818592786789,
0.04640495032072067,
0.004136752802878618,
-0.006467048078775406,
-0.0376594252884388,
0.010606818832457066,
0.0381610281765461,
-0.03243204951286316,
-0.038414087146520615,
0.05786493793129921,
0.08369757980108261,
-0.07458913326263428,
0.021032532677054405,
0.012657904997467995,
0.03203629329800606,
0.01101517491042614,
-0.020280785858631134,
0.03694356605410576,
-0.021395741030573845,
0.1170334443449974,
-0.0014730250695720315,
0.023342348635196686,
-0.06074145808815956,
-0.047575563192367554,
-0.017238453030586243,
0.1100701242685318,
-0.00021525894408114254,
-0.04157907888293266,
-0.026047242805361748,
0.015807105228304863,
0.008149133995175362,
0.06245419383049011,
-0.01526005007326603,
0.032872121781110764,
0.0026209282223135233,
-0.05190696567296982,
-0.029523810371756554,
-0.002868134528398514,
0.011525017209351063,
-0.026543237268924713,
0.016134807839989662,
0.0493822805583477,
0.07942307740449905,
0.022829055786132812,
0.04988746717572212,
0.00726963160559535,
-0.024697555229067802,
-0.022305095568299294,
0.011313687078654766,
-0.04235228896141052,
0.00779997231438756,
-0.01637198030948639,
0.02173725701868534,
-0.03942888230085373,
0.07264416664838791,
-0.025057950988411903,
-0.005976440384984016,
0.013739562593400478,
-0.017075270414352417,
0.06284156441688538,
0.04032612591981888,
0.0405806340277195,
-0.009276230819523335,
0.0090507622808218,
-0.05317449942231178,
-0.006438018754124641,
-0.061449844390153885,
0.024758784100413322,
-0.0024813851341605186,
-0.002728678286075592,
-0.015291530638933182,
0.033809710294008255,
0.004442461766302586,
0.04026360437273979,
0.0181447621434927,
-0.018386254087090492,
0.03588026762008667,
-0.004447911400347948,
-0.02743363566696644,
-0.0209837406873703,
0.03817643225193024,
0.021364277228713036,
-0.01456098910421133,
0.0051574548706412315,
-0.0029282071627676487,
0.009395069442689419,
0.0015264272224158049,
-0.04251924902200699,
-0.01816995069384575,
-0.05743849650025368,
-0.025132251903414726,
0.006156925577670336,
0.03916797414422035,
-0.07365357875823975,
0.017994295805692673,
-0.011505436152219772,
0.028520934283733368,
0.016529349610209465,
-0.014200711622834206,
-0.045610327273607254,
0.0016665594885125756,
0.0914989709854126,
0.04944879561662674,
0.00932605005800724,
-0.0496259368956089,
-0.014209162443876266,
0.0356401726603508,
-0.00837553758174181,
0.03577606752514839,
0.010378478094935417,
0.04051520675420761,
-0.05510811135172844,
-0.009630901739001274,
0.0779133066534996,
0.0965738594532013,
-0.005513597745448351,
-0.007953718304634094,
-0.002153356559574604,
-0.035411056131124496,
0.013090739957988262,
0.010430177673697472,
0.03417802229523659,
-0.0659504234790802,
-0.018515875563025475,
0.044213294982910156,
-0.04190605506300926,
-0.0070537058636546135,
-0.026146939024329185,
0.0036481120623648167,
-0.02569245733320713,
0.011470946483314037,
0.038823727518320084,
-0.05754873529076576,
-0.030076172202825546,
-0.009550130926072598,
-0.01063541416078806,
0.035528432577848434,
0.0008071277406997979,
0.0010829075472429395,
0.023141145706176758,
-0.04074578359723091,
0.020552821457386017,
-0.028464430943131447,
0.00026510015595704317,
-0.012306313030421734,
0.017646750435233116,
0.00654879305511713,
0.06444845348596573,
0.10048270970582962,
0.0393800288438797,
-0.03327104076743126,
0.036191970109939575,
0.05312114208936691,
-0.010790876112878323,
-0.03754842281341553,
-0.02379104122519493,
0.014334456995129585,
-0.01412193477153778,
-0.021342415362596512,
-0.021682370454072952,
-0.020049504935741425,
-0.04016590863466263,
0.020091207697987556,
0.02061695046722889,
0.013689200393855572,
0.00829130969941616,
-0.01773696206510067,
0.0063570705242455006,
0.04566783457994461,
-0.02550380490720272,
0.006424469407647848,
-0.01050901785492897,
0.014761409722268581,
0.040227651596069336,
-0.020422857254743576,
-0.03961416706442833,
0.031077533960342407,
-0.03318193927407265,
-0.05050354450941086,
0.005051055457442999,
0.01307960320264101,
-0.04950200766324997,
-0.05926971882581711,
-0.03926815092563629,
0.009563206695020199,
0.03555261343717575,
0.08393805474042892,
-0.045622434467077255,
0.024347873404622078,
0.04846811294555664,
-0.005062458571046591,
-0.05354248732328415,
-0.04744163528084755,
-0.054803650826215744,
0.030543304979801178,
-0.01493929885327816,
0.035671692341566086,
0.013028153218328953,
0.05266827717423439,
-0.006062493193894625,
-0.004033122677356005,
-0.05069325864315033,
-0.020954739302396774,
-0.02998899295926094,
0.00894272979348898,
-0.009649599902331829,
0.044817566871643066,
-0.04573623463511467,
0.03684430196881294,
-0.008824070915579796,
-0.007660595700144768,
0.00026261937455274165,
-0.011808700859546661,
-0.0039010231848806143,
0.02311134710907936,
-0.03243252635002136,
-0.028183341026306152,
-0.01579453982412815,
0.0697045773267746,
0.03534073010087013,
0.007766232825815678,
0.02376471646130085,
0.04785100370645523,
0.015333849005401134,
0.03396580368280411,
-0.04352530092000961,
0.02632039226591587,
0.004099558107554913,
0.013474831357598305,
0.07375318557024002,
-0.002698492258787155,
-0.01754751056432724,
-0.023425854742527008,
0.019808005541563034,
-0.01741609536111355,
0.030674699693918228,
-0.007271521259099245,
0.06621350347995758,
-0.017995385453104973,
0.011135089211165905,
0.004209785722196102,
-0.02502775564789772,
0.022583644837141037,
0.0006623985827900469,
0.01457953080534935,
-0.00222192844375968,
-0.013215301558375359,
0.00030530765070579946,
-0.06012445688247681,
0.01799064129590988,
0.036674562841653824,
0.059427205473184586,
-0.04009845852851868,
-0.002264185808598995,
-0.033864691853523254,
-0.055285029113292694,
-0.04640306159853935,
-0.030845776200294495,
-0.04771201312541962,
-0.051085054874420166,
0.013788015581667423,
0.017970431596040726,
0.018758205696940422,
0.04356599226593971,
-0.026161475107073784,
-0.05107441172003746,
-0.07405600696802139,
0.007960265502333641,
0.040935318917036057,
0.001087118755094707,
0.019394787028431892,
0.009029198437929153,
-0.009314128197729588,
-0.044644854962825775,
0.08480500429868698,
0.06358839571475983,
0.00745715806260705,
-0.016288159415125847,
-0.05593852326273918,
-0.09910736978054047,
0.07551233470439911,
0.05977776274085045,
0.02486257441341877,
0.04635348916053772,
-0.013935618102550507,
-0.0005021984688937664,
0.010239752009510994,
0.03502504155039787,
-0.04390893876552582,
0.055779751390218735,
-0.05644528195261955,
0.02215421572327614,
-0.03129582107067108,
-0.022639455273747444,
-0.0026101921685039997,
-0.010316667146980762,
-0.031322430819272995,
0.00945167988538742,
-0.039403632283210754,
-0.023500613868236542,
0.011155092157423496,
-0.027965372428297997,
0.014628252014517784,
0.017883308231830597,
0.03627818822860718,
0.010031966492533684,
-0.027404755353927612,
0.017529483884572983,
-0.018596850335597992,
-0.021488819271326065,
0.043810371309518814,
-0.0028961817733943462,
-0.03823883831501007,
0.05043942108750343,
0.04140008985996246,
-0.013680006377398968,
-0.0029517090879380703,
0.004769877530634403,
0.059445444494485855,
-0.013655347749590874,
0.06228462606668472,
-0.014980931766331196,
0.02667924575507641,
-0.028506213799118996,
-0.011303356848657131,
-0.0024614683352410793,
-0.04201364144682884,
-0.01699869893491268,
0.0027585288044065237,
-0.040942367166280746,
0.015172460116446018,
-0.022427018731832504,
0.03049580752849579,
-0.029492774978280067,
-0.028952954337000847,
-0.08326267451047897,
-0.06368634849786758,
0.03267064690589905,
-0.040560223162174225,
0.0030560195446014404,
-0.0020456986967474222,
0.034090545028448105,
-0.022230245172977448,
0.051766738295555115,
-0.04420148953795433,
0.010034087114036083,
-0.08317448198795319,
-0.05351285636425018,
0.006480408366769552,
0.04075473174452782,
-0.01776830293238163,
0.05127502605319023,
-0.016420215368270874,
-0.0014775103190913796,
0.07442503422498703,
0.010021043941378593,
0.042802877724170685,
0.009079108014702797,
-0.04720267653465271,
-0.030805932357907295,
-0.012117928825318813,
0.02128775231540203,
0.04151343181729317,
0.0056128911674022675,
-0.027101989835500717,
0.00378044112585485,
0.0045876456424593925,
0.03380347043275833,
0.025909749791026115,
-0.019253920763731003,
-0.04260293394327164,
0.003185717388987541,
0.012289442121982574,
0.023859063163399696,
0.02036016434431076,
0.013044117949903011,
-0.018784988671541214,
-0.02778879925608635,
0.0032929780427366495,
0.021182166412472725,
0.048753924667835236,
-0.013263413682579994,
0.026606788858771324,
-0.05507110431790352,
-0.0681024044752121,
-0.00727233849465847,
0.06695881485939026,
0.09430214762687683,
0.07028727978467941,
0.042045872658491135,
0.058994609862565994,
-0.018451690673828125,
-0.032056309282779694,
-0.0058398740366101265,
0.03518024459481239,
-0.004940649960190058,
-0.005033470690250397,
-0.021726422011852264,
0.0017654986586421728,
-0.03236854448914528,
-0.014158159494400024,
-0.0045823026448488235,
-0.008056389167904854,
-0.046915363520383835,
-0.005418021697551012,
0.004067034926265478,
-0.031006701290607452,
-0.0024358087684959173,
-0.037214040756225586,
-0.016429323703050613,
-0.06542392820119858,
0.007121631875634193,
-0.014597932808101177,
0.05514651536941528,
0.0004816381260752678,
0.015208504162728786,
-0.019373470917344093,
0.00634640222415328,
-0.03922288492321968,
0.07718382775783539,
-0.011900280602276325,
-0.039762645959854126,
-0.005660219583660364,
-0.010573075152933598,
0.000987526262179017,
-0.019570380449295044,
0.01452280580997467,
0.018341030925512314,
0.05760537460446358,
0.04234575107693672,
-0.07123380899429321,
-0.08163794875144958,
0.0015114833367988467,
0.00015347583394031972,
-0.0014489738969132304,
-0.07234028726816177,
-0.033200785517692566,
0.001580185373313725,
-0.0016908616526052356,
-0.057806309312582016,
-0.0125500513240695,
0.0164541807025671,
-0.0039118933491408825
] |
<p>I must apologize, I was a little bit excited when I began understanding some of this, I can not say I can compete with professionals, and words are still difficult concepts.</p>
<p>In (<a href="http://arxiv.org/abs/gr-qc/9409013" rel="nofollow">1</a>) S.H. et al. it is discussed that in extremal cases of charged black holes in a euclidean space, there is a topological change as compared to the non extremal case. This is viewed as a discontinuity by (<a href="http://arxiv.org/abs/0901.0931" rel="nofollow">2</a>) who attempts a similar calculation in AdS. </p>
<p>The notion of charge being associated with topology comes from some versions (<a href="http://rads.stackoverflow.com/amzn/click/0071498702" rel="nofollow">3</a>,<a href="http://rads.stackoverflow.com/amzn/click/0521831431" rel="nofollow">4</a>) of the calculation performed in (<a href="http://arxiv.org/abs/hep-th/9601029" rel="nofollow">5</a>). Where the "charges are Q1 and Q5 are generated by wrapping a number Q1 of D1-branes around the circle $x^5$ and a number Q5 of D5-branes around the five circles..." and N is the momentum around the circle $x^5$ (<a href="http://rads.stackoverflow.com/amzn/click/0521831431" rel="nofollow">4</a>). Since the entropy calculation relies on those charges, it should follow that the number of string states is also dependent on the topology.</p>
<p>So in (<a href="http://rads.stackoverflow.com/amzn/click/0071498702" rel="nofollow">3</a>, <a href="http://rads.stackoverflow.com/amzn/click/0521831431" rel="nofollow">4</a>, <a href="http://arxiv.org/abs/hep-th/9601029" rel="nofollow">5</a>), the calculation is done on a supersymmetric extremal black hole. In (<a href="http://arxiv.org/abs/gr-qc/9409013" rel="nofollow">1</a>) the calculation is not on a supersymmetric extremal black hole, but there is difference in topology at the extremal limit, which is implied in (<a href="http://arxiv.org/abs/0901.0931" rel="nofollow">2</a>) to be discontinuous. In both case the change in topology is related to their being two event horizons that do connect to each other, implying a toroidal shape. In (<a href="http://arxiv.org/abs/gr-qc/9409013" rel="nofollow">1</a>) the second horizon extends to infinity, causing the change in topology, in (<a href="http://rads.stackoverflow.com/amzn/click/0071498702" rel="nofollow">3</a>), the two horizons are described as meeting at the same radius. This suggests some sort of degeneration of the torus, implying a change in topology.</p>
<p>My initial query is whether we should think of these changes in topology as discontinuous (assuming that what I described isn't horribly flawed), or possibly a smooth transitions due to quantum effects, such as uncertainty and tunneling, where the change only occur discontinuously at a microscopic level so that it appears smooth at a macroscopic level?</p>
<p>The second part of the question is that charges are described as being dependent on topology, and they are also related to symmetries. So it seems natural to think that symmetries are dependent on topology. </p>
<p>Although we live in a relativistic world, in our every day life, we still think in non-relativistic terms, and most of our theories have non-relativistic roots, so is it natural to think of there being some sort of low energy topological state (I don't know, something like Ball-3 x Real). That low energy state would apparently have certain symmetries that are dependent on that topology and would make it distinct from other possible topologies. Is that possible?</p>
<p><a href="http://arxiv.org/abs/gr-qc/9409013" rel="nofollow">1</a>- <a href="http://arxiv.org/abs/gr-qc/9409013" rel="nofollow">Entropy, Area and Black Holes</a></p>
<p><a href="http://arxiv.org/abs/0901.0931" rel="nofollow">2</a>- <a href="http://arxiv.org/abs/0901.0931" rel="nofollow">Extremal Limits and Black Hole Entropy</a></p>
<p><a href="http://rads.stackoverflow.com/amzn/click/0071498702" rel="nofollow">3</a>- <a href="http://rads.stackoverflow.com/amzn/click/0071498702" rel="nofollow">String Theory Demystified</a></p>
<p><a href="http://rads.stackoverflow.com/amzn/click/0521831431" rel="nofollow">4</a>- <a href="http://rads.stackoverflow.com/amzn/click/0521831431" rel="nofollow">A First Course in String Theory</a></p>
<p><a href="http://arxiv.org/abs/hep-th/9601029" rel="nofollow">5</a>- <a href="http://arxiv.org/abs/hep-th/9601029" rel="nofollow">Microscopic Origin of Bekenstein-Hawking Entropy</a></p>
<p>Further reference (pg 355 in <a href="http://books.google.com/books?id=LFakv848R2oC&lpg=PA355&ots=rNq7UjGfvC&dq=loop%20at%20each%20point%20of%20sphere&pg=PA355#v=onepage&q=loop%20at%20each%20point%20of%20sphere&f=false" rel="nofollow">Group Theory: An intuitive approach</a> by R Mirman):</p> | g4757 | [
0.012903394177556038,
0.01585965044796467,
-0.015209894627332687,
0.00012005373719148338,
0.07930239289999008,
-0.0355067141354084,
0.06289499253034592,
0.022081680595874786,
-0.029868436977267265,
0.04852529987692833,
-0.03770583122968674,
0.00919195543974638,
0.024897560477256775,
0.03335057571530342,
-0.0501956045627594,
-0.004662269726395607,
-0.017962560057640076,
0.014264519326388836,
0.024753209203481674,
-0.06891029328107834,
-0.013931655324995518,
-0.01833551935851574,
0.024647599086165428,
-0.06305361539125443,
-0.022918712347745895,
0.03044348768889904,
0.04874451458454132,
0.023935379460453987,
-0.07428133487701416,
-0.014545443467795849,
0.03450493514537811,
0.005273548886179924,
0.029133044183254242,
-0.002082780236378312,
-0.052188072353601456,
-0.062088366597890854,
0.060675397515296936,
-0.0061666956171393394,
0.007448387332260609,
-0.00015235260070767254,
0.0509505569934845,
-0.0393257662653923,
0.013286729343235493,
-0.028331780806183815,
-0.08791764080524445,
-0.022221650928258896,
0.026324767619371414,
0.04390571266412735,
0.053083792328834534,
0.017605507746338844,
0.024797020480036736,
0.0654812753200531,
-0.009096215479075909,
0.026631208136677742,
0.05288362875580788,
0.04160316288471222,
0.03975267335772514,
0.04212551563978195,
0.03613850101828575,
0.013268678449094296,
-0.038360968232154846,
0.025741051882505417,
0.016232462599873543,
0.06950885057449341,
0.060878582298755646,
-0.0016880944604054093,
-0.06786809861660004,
-0.06343000382184982,
-0.0695408284664154,
-0.01917058415710926,
-0.016418365761637688,
-0.03903999552130699,
-0.0016776648117229342,
-0.007349120453000069,
-0.00017328205285593867,
0.0678553506731987,
0.008172250352799892,
0.007060828153043985,
-0.029445277526974678,
0.027718134224414825,
-0.027845636010169983,
-0.047605883330106735,
0.017573071643710136,
0.034535445272922516,
0.06382635980844498,
-0.023538317531347275,
-0.006908891722559929,
-0.01546388864517212,
0.025162894278764725,
0.05106574296951294,
0.02031528763473034,
-0.02095063030719757,
0.02960968017578125,
-0.012328924611210823,
-0.022127296775579453,
0.020729992538690567,
-0.00564780505374074,
0.04088389128446579,
0.04051999747753143,
-0.02377880923449993,
-0.05412697419524193,
0.011134672909975052,
0.012786203064024448,
0.008518836461007595,
-0.005275904666632414,
-0.02380654774606228,
-0.012514704838395119,
0.03588905185461044,
0.0015982926124706864,
0.030810780823230743,
0.005010094493627548,
-0.06465882062911987,
-0.04532726854085922,
-0.03223036974668503,
-0.06218278408050537,
-0.005284289363771677,
0.0883195549249649,
-0.06678496301174164,
-0.0443146750330925,
0.009025043807923794,
0.0174137894064188,
-0.008669160306453705,
0.03395101800560951,
0.06590934842824936,
0.014504513703286648,
-0.0001275067770620808,
-0.05208160728216171,
-0.05258853733539581,
0.046893633902072906,
-0.006177674047648907,
-0.004486127756536007,
-0.03573363646864891,
0.04030900076031685,
0.10371427983045578,
-0.04839988797903061,
0.0168202705681324,
-0.0057367621921002865,
0.02188008464872837,
0.01751863770186901,
-0.04202011227607727,
-0.016087360680103302,
-0.062044188380241394,
0.021232878789305687,
-0.04269018396735191,
-0.0003752683405764401,
-0.019958632066845894,
-0.01139925792813301,
-0.0678124949336052,
0.017649076879024506,
-0.012665269896388054,
-0.013950718566775322,
0.011803855188190937,
-0.0018948673969134688,
-0.0033627082593739033,
-0.031693484634160995,
0.047477204352617264,
0.0872882679104805,
0.030986731871962547,
0.014213688671588898,
0.03370457887649536,
0.0558893121778965,
0.008350403048098087,
0.009012723341584206,
0.02339780516922474,
-0.047987550497055054,
-0.04208321124315262,
0.0887582004070282,
-0.039507362991571426,
0.031649746000766754,
-0.06108276918530464,
-0.03118983656167984,
0.026106949895620346,
0.02435033954679966,
0.003754722187295556,
0.01261028740555048,
0.04402528703212738,
-0.016341309994459152,
0.012005828320980072,
0.006665351800620556,
-0.013207662850618362,
-0.06848602741956711,
0.05751964449882507,
0.023740725591778755,
0.0012329549062997103,
0.0050811381079256535,
0.05613037198781967,
-0.007656352128833532,
0.03335985541343689,
-0.02078183926641941,
-0.048439256846904755,
-0.05562670901417732,
-0.007759854197502136,
-0.005109192803502083,
0.05622610077261925,
-0.008565490134060383,
0.03449472412467003,
0.05207109451293945,
0.005530233960598707,
-0.004271453712135553,
-0.004267877899110317,
0.01404300332069397,
0.016693629324436188,
0.017654407769441605,
0.038477152585983276,
0.04159028083086014,
0.029062744230031967,
-0.052443064749240875,
-0.035175345838069916,
0.0026628572959452868,
-0.003794573014602065,
0.03514552488923073,
-0.020484188571572304,
-0.018090583384037018,
0.00936909206211567,
0.008841396309435368,
-0.005416300147771835,
-0.017623623833060265,
-0.024984754621982574,
-0.03616747632622719,
-0.008575056679546833,
-0.008414474315941334,
-0.015253410674631596,
0.08217418193817139,
0.050122976303100586,
-0.04300704598426819,
-0.060489390045404434,
-0.0027479820419102907,
-0.055774200707674026,
-0.015853751450777054,
-0.01473947148770094,
-0.00022575969342142344,
0.004737336188554764,
0.009148583747446537,
-0.021458394825458527,
0.004118423443287611,
0.04431025683879852,
0.0034090157132595778,
-0.04205181822180748,
0.029016299173235893,
-0.018621062859892845,
0.03304192051291466,
-0.022869961336255074,
-0.05708647146821022,
0.027762828394770622,
0.019590463489294052,
-0.03895730525255203,
0.017442230135202408,
0.006157150492072105,
-0.0667833462357521,
0.022691700607538223,
0.02455120161175728,
-0.05430690944194794,
-0.029023783281445503,
0.005294948350638151,
-0.014859327115118504,
-0.0383673794567585,
0.028513949364423752,
0.0010215388610959053,
-0.012964005582034588,
-0.07318579405546188,
-0.016240768134593964,
0.006186358164995909,
0.014989146031439304,
0.02682024985551834,
-0.07881317287683487,
-0.020231006667017937,
-0.019848745316267014,
-0.0046233320608735085,
-0.040691036731004715,
0.0028028017841279507,
-0.03997378423810005,
0.04056701064109802,
0.03928900510072708,
0.012809489853680134,
0.049694906920194626,
0.05030760541558266,
-0.033864643424749374,
0.029917366802692413,
-0.0012877668486908078,
-0.020372722297906876,
-0.0025923524517565966,
0.033888332545757294,
-0.008304732851684093,
0.05290296673774719,
0.020155850797891617,
-0.02188185602426529,
0.024052385240793228,
0.06785492599010468,
-0.032873883843421936,
0.009558332152664661,
-0.0014893598854541779,
0.011947153136134148,
0.03195745497941971,
-0.016575947403907776,
0.013029283843934536,
0.048764459788799286,
-0.007861003279685974,
-0.05840063467621803,
0.0006950970855541527,
0.03080087900161743,
-0.01415025070309639,
-0.015311789698898792,
0.006717816460877657,
0.06277231127023697,
-0.002165823010727763,
0.06355482339859009,
-0.05854373425245285,
-0.05308687314391136,
0.010890509933233261,
-0.0032443946693092585,
-0.018857408314943314,
-0.018742918968200684,
0.028505995869636536,
0.0492636002600193,
0.007254431024193764,
0.018246980383992195,
0.023774590343236923,
0.012489108368754387,
0.008733476512134075,
0.013382228091359138,
-0.029981935396790504,
0.0019681276753544807,
-0.004221668932586908,
-0.0001490606664447114,
0.045141108334064484,
0.06129450723528862,
-0.03849600628018379,
-0.02190256305038929,
-0.08510839939117432,
0.009076794609427452,
0.003215653356164694,
0.009661792777478695,
0.02318335324525833,
-0.0016148320864886045,
-0.07675457745790482,
-0.054848793894052505,
-0.0014698858140036464,
-0.005979536101222038,
0.04248170182108879,
0.011328600347042084,
-0.025509456172585487,
-0.027292417362332344,
-0.011277204379439354,
0.002513798186555505,
-0.0013617725344374776,
0.03745809942483902,
-0.010731587186455727,
-0.01136031560599804,
-0.05285283923149109,
-0.012612883001565933,
0.014062128961086273,
-0.023263324052095413,
0.07713712751865387,
0.003594436449930072,
-0.009700211696326733,
0.03694620728492737,
0.016986845061182976,
-0.008088323287665844,
-0.03991089388728142,
-0.006177292671054602,
0.032127220183610916,
-0.028627345338463783,
-0.011482086032629013,
-0.06700728833675385,
0.0058294362388551235,
0.06876982003450394,
-0.006020805332809687,
-0.032440509647130966,
-0.035620857030153275,
-0.03643828630447388,
0.013477973639965057,
-0.01108322199434042,
-0.02688019722700119,
-0.0027041977737098932,
0.013019503094255924,
-0.028368990868330002,
0.05381883308291435,
0.05631858482956886,
0.036133814603090286,
-0.017616210505366325,
0.01677829585969448,
-0.01180118415504694,
0.035010963678359985,
-0.06408236920833588,
0.015266655012965202,
0.03056551143527031,
-0.03324740752577782,
-0.03818123787641525,
-0.026726985350251198,
-0.03634875267744064,
-0.07639015465974808,
0.032316580414772034,
0.021474897861480713,
-0.06559348106384277,
-0.017321059480309486,
0.006166174542158842,
0.028288381174206734,
-0.05589801073074341,
-0.0028540713246911764,
0.04926019534468651,
0.04601118341088295,
-0.05446913465857506,
-0.04962741583585739,
-0.011305022053420544,
0.010387561284005642,
-0.046900343149900436,
0.030851412564516068,
0.014535482972860336,
0.03146321326494217,
-0.09196826815605164,
0.008207987993955612,
-0.012930414639413357,
0.036697663366794586,
-0.04381812363862991,
0.04267006739974022,
0.005965893622487783,
-0.02434713952243328,
-0.054040323942899704,
-0.04667406156659126,
0.04470719397068024,
0.023210808634757996,
0.022814083844423294,
-0.007147169206291437,
-0.005604404956102371,
0.036203764379024506,
0.012125742621719837,
0.005627989303320646,
0.04573572054505348,
0.009574640542268753,
0.0288844034075737,
-0.002263152739033103,
0.0555477999150753,
-0.0798967033624649,
0.023193279281258583,
-0.056948449462652206,
0.03629676252603531,
-0.09628559648990631,
0.06236767768859863,
0.0037473763804882765,
-0.025716010481119156,
0.045820362865924835,
0.0063488418236374855,
-0.03978295251727104,
-0.05900963023304939,
-0.022179830819368362,
0.012349599041044712,
-0.03355826810002327,
0.06316525489091873,
-0.014764249324798584,
-0.011587883345782757,
-0.09722677618265152,
-0.0008482775301672518,
0.061790648847818375,
-0.05790818855166435,
0.014267023652791977,
-0.06766951829195023,
-0.014015702530741692,
-0.00861835666000843,
0.0005677660228684545,
-0.0005254608113318682,
-0.07221970707178116,
-0.02397354692220688,
0.017644114792346954,
-0.0002257708110846579,
0.018086271360516548,
-0.007706163916736841,
-0.07057246565818787,
0.008837156929075718,
0.014091822318732738,
-0.025779319927096367,
-0.0004919172497466207,
0.013926159590482712,
-0.0076144989579916,
-0.03622809424996376,
-0.024489836767315865,
0.049296461045742035,
0.03584888577461243,
-0.041281312704086304,
-0.04377790540456772,
0.0022728785406798124,
-0.030300717800855637,
0.0074843671172857285,
0.012058712542057037,
0.0428350530564785,
-0.007706659846007824,
0.06445637345314026,
-0.024985764175653458,
-0.013011625967919827,
0.00015284787514247,
0.10075059533119202,
0.008506386540830135,
-0.023973634466528893,
0.015886450186371803,
0.03873761370778084,
-0.0055087292566895485,
-0.00396820530295372,
0.037305351346731186,
0.02630375511944294,
-0.015974735841155052,
0.030921319499611855,
0.0005058978567831218,
0.03448963165283203,
0.013400228694081306,
0.005057849921286106,
-0.029262570664286613,
0.04166406765580177,
0.08521132171154022,
-0.0036209130194038153,
0.019637860357761383,
0.05988439545035362,
-0.01715259812772274,
0.06690942496061325,
-0.027141012251377106,
0.025842349976301193,
0.05163979530334473,
0.03805235028266907,
-0.03786688297986984,
-0.001557805109769106,
-0.0037790529895573854,
-0.05151558294892311,
0.02304544486105442,
0.026239611208438873,
0.028540411964058876,
-0.02203822322189808,
0.06153963506221771,
0.017785098403692245,
-0.005108048673719168,
-0.07114894688129425,
0.022311709821224213,
0.07770434021949768,
-0.009799614548683167,
0.02369844913482666,
-0.0267427209764719,
0.0032158440444618464,
-0.02127721719443798,
-0.04524650052189827,
0.04101795330643654,
0.001072000595740974,
0.07374506443738937,
-0.017491329461336136,
0.009443460032343864,
-0.025909336283802986,
-0.0017475491622462869,
0.035464685410261154,
0.036269787698984146,
-0.05312207713723183,
-0.06446685642004013,
-0.01632358692586422,
-0.02873511239886284,
-0.04542364925146103,
-0.04625279828906059,
0.01057326141744852,
-0.01840413548052311,
0.03482355177402496,
-0.02036888524889946,
-0.0016305355820804834,
0.00565184373408556,
-0.05294007062911987,
-0.07053621858358383,
-0.04955435171723366,
0.0423867292702198,
0.030824916437268257,
0.03134771063923836,
0.048562947660684586,
0.03202829137444496,
-0.06569720804691315,
0.015313687734305859,
-0.042943187057971954,
0.03313435614109039,
0.022317182272672653,
0.018484001979231834,
-0.031107893213629723,
-0.021372750401496887,
0.0003378734108991921,
0.013247392140328884,
-0.01609094813466072,
-0.016403598710894585,
-0.03682367131114006,
-0.0014626813353970647,
-0.014820567332208157,
-0.032117072492837906,
-0.07170411199331284,
0.10718344151973724,
-0.07126668095588684,
-0.0004074648313689977,
0.028950506821274757,
-0.03117559663951397,
0.004518789239227772,
-0.015659719705581665,
-0.023656584322452545,
0.010871748439967632,
0.03728324547410011,
-0.0105465492233634,
0.01588497683405876,
-0.02994898334145546,
0.0012647329131141305,
-0.03472250699996948,
-0.06693552434444427,
-0.01084033865481615,
-0.0017007655696943402,
-0.040458593517541885,
-0.00029556770459748805,
0.010443253442645073,
-0.01645171269774437,
-0.025247231125831604,
0.06156422942876816,
-0.020023567602038383,
0.006465698126703501,
-0.002506404649466276,
0.010252265259623528,
0.012486746534705162,
0.018847642466425896,
-0.02925168164074421,
0.035122014582157135,
0.002430702792480588,
0.014531165361404419,
-0.056212980300188065,
-0.01287882775068283,
-0.009378629736602306,
0.017368081957101822,
0.0007554828771390021,
0.0026813067961484194,
-0.019147418439388275,
0.04596763104200363,
0.05955757945775986,
0.06379081308841705,
-0.0033071234356611967,
0.030746212229132652,
0.004464076831936836,
0.07930726557970047,
-0.0021375345531851053,
0.006694902665913105,
-0.018030811101198196,
0.07351856678724289,
0.01445819716900587,
0.0437215119600296,
-0.030945518985390663,
-0.0013444192009046674,
0.018772346898913383,
0.02235196717083454,
0.032868891954422,
-0.023735301569104195,
0.022697515785694122,
0.01519744098186493,
0.00694311736151576,
-0.07221362739801407,
-0.022753426805138588,
0.05208190158009529,
0.0027731729205697775,
0.023735681548714638,
0.01850571297109127,
-0.01912950910627842,
-0.004093762952834368,
0.013579442165791988,
-0.017537498846650124,
-0.024842116981744766,
-0.045879777520895004,
-0.012616184540092945,
-0.006659722421318293,
-0.06681018322706223,
-0.02280055545270443,
0.0680728331208229,
0.007926478050649166,
-0.03880641981959343,
-0.004034040495753288,
0.023666389286518097,
0.05093257501721382,
-0.037537604570388794,
-0.020360838621854782,
-0.0799911692738533,
-0.01978345587849617,
0.0025613056495785713,
-0.043810226023197174,
-0.022946173325181007,
-0.031895410269498825,
-0.019689003005623817,
0.025847215205430984,
0.06900718063116074,
-0.00978999212384224,
0.06077783182263374,
0.08201915770769119,
-0.011494518257677555,
0.028467556461691856,
0.02267361618578434,
-0.05493221804499626,
0.035101305693387985,
-0.0668460950255394,
0.03959974646568298,
0.039082448929548264,
0.05247539281845093,
-0.026401452720165253,
0.004230919294059277,
-0.03293986618518829,
0.021478373557329178,
-0.017111944034695625,
0.06417816877365112,
0.035277027636766434,
-0.0011288444511592388,
0.009102209471166134,
-0.07404207438230515,
0.019581468775868416,
-0.0001678981789154932,
-0.006758860778063536,
-0.023365085944533348,
0.01229132805019617,
0.03454612195491791,
-0.04101994261145592,
-0.018930798396468163,
-0.02925136871635914,
0.022476259618997574,
0.019658247008919716,
-0.022300146520137787,
0.007636241149157286,
-0.023659123107790947,
-0.014551131054759026,
-0.02479974925518036,
0.06885828822851181,
-0.03334230184555054,
-0.024937829002738,
0.047337863594293594,
-0.08523199707269669,
-0.02886078506708145,
-0.0008378037018701434,
-0.055133137851953506,
-0.0606505312025547,
-0.04049661383032799,
0.023367498070001602,
-0.01101774349808693,
0.008126604370772839,
0.015685144811868668,
-0.04562441259622574,
-0.014742755331099033,
-0.01027018390595913,
-0.02669139765202999,
-0.039915647357702255,
0.02711348608136177,
0.05610663443803787,
0.04052605852484703,
0.048228465020656586,
-0.06739117205142975,
-0.013638697564601898,
-0.00862918607890606,
0.06270863860845566,
-0.01680929958820343,
-0.010306606069207191,
0.04214516282081604,
0.024631442502141,
0.0382961742579937,
0.06075179576873779,
0.03869243338704109,
0.016248218715190887,
-0.0480697825551033,
0.0126480832695961,
-0.012021180242300034,
-0.026142576709389687,
-0.010307003743946552,
-0.015141830779612064,
-0.0040993038564920425,
-0.004302990157157183,
-0.024355322122573853,
-0.03884073719382286,
0.0006999575416557491,
0.018291931599378586,
-0.029252033680677414,
-0.0021606592927128077,
-0.04655391722917557,
-0.010233855806291103,
0.014621973969042301
] |
<p>Lets assume we have a wire that has $10V$ across and $1$ $Amp$ flowing, now if this conductor is introduced to a changing magnetic field, $-EMF$ is induced, can we control our voltage to increase it and allow current to be stable at $1 Amp$?
Thus more power is required correct?</p>
<p>Generally, in any situation we can keep the current stable at the same value by increasing the voltage?</p> | g4758 | [
-0.0055680666118860245,
0.00320557807572186,
-0.0027610280085355043,
-0.01543776411563158,
0.0567912794649601,
0.007509924005717039,
-0.002923742402344942,
-0.007401036098599434,
-0.03141266852617264,
0.01887403428554535,
-0.07858897000551224,
0.051081474870443344,
-0.05356767401099205,
0.06869427859783173,
0.04733600094914436,
0.04676919803023338,
0.06706966459751129,
-0.03738948702812195,
0.032373033463954926,
-0.03816153481602669,
-0.003344839671626687,
-0.022749297320842743,
0.06633512675762177,
-0.026853252202272415,
0.017402568832039833,
0.0027019691187888384,
0.01144466269761324,
-0.030777582898736,
0.019227327778935432,
-0.016378212720155716,
-0.01176412682980299,
0.0504470095038414,
0.047402217984199524,
0.009642001241445541,
-0.0370488204061985,
-0.03126455843448639,
0.030482329428195953,
0.008312405087053776,
0.029131608083844185,
-0.02007746882736683,
0.006776546128094196,
-0.007408530451357365,
0.03154527768492699,
-0.010743336752057076,
-0.04215525463223457,
-0.06567452102899551,
-0.019306456670165062,
-0.055835869163274765,
-0.03595120087265968,
-0.013867538422346115,
-0.03013467788696289,
-0.016598723828792572,
0.024001603946089745,
-0.0024896806571632624,
-0.01657879538834095,
-0.05766531452536583,
-0.022830335423350334,
-0.033558014780282974,
-0.009122845716774464,
0.012723878026008606,
-0.03235946595668793,
-0.016786620020866394,
0.018325641751289368,
0.03051707334816456,
-0.03563157096505165,
-0.010879668407142162,
-0.06284604221582413,
-0.032306622713804245,
-0.01632755994796753,
0.02691100724041462,
-0.035692472010850906,
-0.061915475875139236,
-0.029755648225545883,
0.021552348509430885,
0.09534669667482376,
0.01790740340948105,
0.046669360250234604,
-0.02362198568880558,
0.035902298986911774,
-0.04197893291711807,
0.007015267852693796,
0.030222132802009583,
0.03407701849937439,
-0.03677855059504509,
0.009378137066960335,
-0.017394231632351875,
0.042321689426898956,
0.029796790331602097,
-0.00927229505032301,
-0.0038624268490821123,
0.02387971431016922,
0.02062767557799816,
0.018071763217449188,
0.01858133263885975,
0.05103067681193352,
0.009432637132704258,
-0.009450994431972504,
0.016435157507658005,
0.01951322704553604,
0.026249295100569725,
-0.05246134102344513,
-0.023092148825526237,
0.026465101167559624,
0.010771293193101883,
-0.08674310892820358,
0.048930246382951736,
0.012604539282619953,
0.019314130768179893,
0.005375957582145929,
-0.007542741950601339,
-0.005308302119374275,
-0.06685847789049149,
-0.002212942810729146,
0.030228085815906525,
-0.04126092791557312,
-0.032983604818582535,
0.005241024307906628,
0.0301984753459692,
-0.023268019780516624,
0.05816386267542839,
0.0245842132717371,
-0.038006801158189774,
0.03176267817616463,
0.02359713986515999,
-0.011004631407558918,
0.0004862431960646063,
-0.05433028191328049,
0.055302396416664124,
0.05273454263806343,
-0.041001129895448685,
-0.024152634665369987,
-0.031529031693935394,
0.0186875332146883,
-0.019213970750570297,
-0.0004055813478771597,
0.02671201527118683,
-0.014029820449650288,
0.02074439637362957,
-0.0039032024797052145,
0.013694779947400093,
0.04863995313644409,
-0.05416623502969742,
0.003458350198343396,
-0.033039819449186325,
-0.018474334850907326,
0.05154472216963768,
0.0040757376700639725,
0.022411726415157318,
0.07114099711179733,
0.0263527762144804,
0.053171854466199875,
0.05721690133213997,
-0.05023711174726486,
-0.03730824962258339,
0.03282107040286064,
0.02934572845697403,
0.02555258572101593,
0.0017469394952058792,
-0.00182235985994339,
-0.035557545721530914,
0.05806225910782814,
0.026116980239748955,
-0.0015609293477609754,
-0.0255491491407156,
-0.0020608031190931797,
-0.0007226875750347972,
0.05553601309657097,
0.03640684485435486,
-0.030647674575448036,
-0.03333079814910889,
-0.01568102091550827,
-0.02986198477447033,
0.05829288810491562,
0.01686270348727703,
-0.004463052377104759,
0.014001603238284588,
-0.00023843339295126498,
-0.025182755663990974,
0.021143730729818344,
-0.0023689153604209423,
-0.07570269703865051,
-0.007957089692354202,
0.021404113620519638,
-0.054083168506622314,
-0.01520219910889864,
0.010416957549750805,
-0.06863874942064285,
0.03845430910587311,
-0.09211871027946472,
-0.012973294593393803,
-0.10760881751775742,
0.030504921451210976,
-0.009211909957230091,
0.053145550191402435,
-0.021079298108816147,
-0.003742088796570897,
0.0086487652733922,
-0.0798143520951271,
0.0018679717322811484,
0.020542733371257782,
-0.018988849595189095,
0.06721533834934235,
0.07653582841157913,
-0.033103786408901215,
0.008204660378396511,
-0.008995098993182182,
-0.0017635658150538802,
-0.03908321261405945,
0.06854750216007233,
-0.04509954899549484,
0.09772462397813797,
-0.0012345705181360245,
0.011197935789823532,
0.012570650316774845,
-0.03893888369202614,
-0.017158709466457367,
0.055058129131793976,
-0.0020655954722315073,
-0.039103440940380096,
-0.020514866337180138,
-0.006396148819476366,
-0.011502539739012718,
0.0732579231262207,
0.021994775161147118,
-0.12396495789289474,
-0.06111445277929306,
-0.01798771694302559,
0.001060540322214365,
-0.0031016715802252293,
-0.053419895470142365,
-0.03620290756225586,
0.08501923829317093,
-0.02316492795944214,
0.02081219106912613,
0.015444806776940823,
0.035561952739953995,
-0.008894079364836216,
0.06688769161701202,
-0.017416534945368767,
-0.018039779737591743,
-0.0019765060860663652,
0.0032794708386063576,
0.04423384740948677,
0.007316221483051777,
-0.03412362560629845,
-0.0415857657790184,
-0.006246249191462994,
0.05956690013408661,
-0.00036960496800020337,
0.00125315657351166,
0.058749258518218994,
-0.08091754466295242,
0.04802456498146057,
0.04133857786655426,
-0.08526860922574997,
-0.06112736091017723,
-0.060682207345962524,
0.11047231405973434,
-0.004609859082847834,
-0.0030904458835721016,
0.03242696076631546,
0.014674635604023933,
0.0288353580981493,
0.0719694122672081,
-0.033362504094839096,
0.021505193784832954,
-0.041389644145965576,
-0.06168695166707039,
-0.01669122464954853,
0.016413938254117966,
-0.005268101580440998,
0.04405174031853676,
-0.04922978952527046,
0.05061030015349388,
0.010699243284761906,
-0.015904532745480537,
0.03618079051375389,
0.0007050832500681281,
0.0634029358625412,
-0.019451025873422623,
-0.02777223475277424,
-0.022047189995646477,
-0.023267516866326332,
-0.022291986271739006,
-0.05596191808581352,
-0.040666017681360245,
0.055179789662361145,
-0.08314236253499985,
-0.02532951533794403,
-0.005088004749268293,
-0.04815000295639038,
-0.004847451578825712,
0.06952432543039322,
-0.024338390678167343,
-0.020488964393734932,
-0.02084704302251339,
0.005398537497967482,
-0.046053431928157806,
-0.01921221613883972,
0.00029526063008233905,
-0.003315682988613844,
-0.0354049913585186,
-0.04964428395032883,
-0.01401466503739357,
0.020529070869088173,
0.021203797310590744,
-0.014322543516755104,
-0.008518146350979805,
0.039784323424100876,
0.015694500878453255,
-0.009093300439417362,
0.024459676817059517,
-0.013779216445982456,
-0.01779927685856819,
-0.08886617422103882,
0.017455626279115677,
-0.01703111082315445,
-0.010680832900106907,
0.026156678795814514,
-0.045124202966690063,
-0.033427491784095764,
-0.03605937212705612,
-0.0186754260212183,
-0.0030054727103561163,
0.028557205572724342,
0.01374818105250597,
-0.0004004357033409178,
0.006955210119485855,
-0.041164398193359375,
-0.01220605056732893,
0.017237931489944458,
-0.00777275487780571,
-0.0014921741094440222,
-0.004797004163265228,
0.020522037521004677,
-0.018906323239207268,
0.0574626699090004,
0.010109414346516132,
0.0366944819688797,
0.011331225745379925,
0.013451004400849342,
-0.024038732051849365,
-0.045794371515512466,
0.00048397251521237195,
0.029452838003635406,
0.07071682065725327,
0.02399458736181259,
0.03276568651199341,
0.036222223192453384,
-0.017036406323313713,
0.05536133050918579,
-0.008398524485528469,
0.02413949742913246,
-0.012677445076406002,
0.011428016237914562,
-0.04129790514707565,
-0.01709224097430706,
0.03856439143419266,
-0.07452352344989777,
-0.015547060407698154,
-0.06265466660261154,
-0.012906362302601337,
0.019566036760807037,
0.01059972308576107,
-0.019704075530171394,
0.03478836640715599,
0.01930399052798748,
0.04863963648676872,
-0.028430292382836342,
-0.02688227966427803,
-0.008405787870287895,
-0.03203018754720688,
-0.031107623130083084,
0.012555748224258423,
0.017191780731081963,
0.0019282296998426318,
0.03036748245358467,
0.02864227257668972,
-0.004128029569983482,
0.04103173688054085,
-0.007116282358765602,
0.016534151509404182,
-0.05647047609090805,
-0.00010306909098289907,
-0.06638696789741516,
0.005873842164874077,
0.0011857732897624373,
0.0157565176486969,
-0.020793842151761055,
-0.008564812131226063,
0.013637800700962543,
-0.014733321964740753,
0.03841959312558174,
-0.050940170884132385,
-0.019342748448252678,
-0.0010376379359513521,
-0.048708200454711914,
-0.04496630281209946,
0.052049774676561356,
0.03021365776658058,
0.0736883357167244,
0.0077256797812879086,
-0.023782780393958092,
0.032620351761579514,
0.04620283469557762,
-0.02113068290054798,
0.047111380845308304,
-0.002326185582205653,
-0.02767479233443737,
-0.038789037615060806,
0.010301560163497925,
-0.0028611067682504654,
-0.012537810951471329,
-0.05872591957449913,
0.011012573726475239,
0.0315774604678154,
0.0445580892264843,
-0.016558926552534103,
0.04684143140912056,
-0.0302553940564394,
0.030217157676815987,
0.023804951459169388,
-0.01782827079296112,
-0.02308790758252144,
-0.013751651160418987,
0.009361742064356804,
0.02911101095378399,
-0.056371599435806274,
0.017455551773309708,
-0.003755436511710286,
-0.03243070840835571,
0.05064710974693298,
0.00802359264343977,
-0.06414281576871872,
-0.03379041701555252,
0.04111713916063309,
-0.008345670998096466,
-0.03145688399672508,
0.00853066984564066,
0.03975460305809975,
0.071369469165802,
0.004136373288929462,
-0.01956608146429062,
-0.03889128938317299,
-0.019369840621948242,
-0.008772335946559906,
-0.010536055080592632,
0.01730269566178322,
0.054774209856987,
-0.016048600897192955,
-0.02266574092209339,
0.011001011356711388,
0.02533804625272751,
-0.011935058981180191,
0.04273369535803795,
-0.005541482474654913,
-0.02639230154454708,
-0.028159458190202713,
0.0027122378814965487,
-0.024042950943112373,
-0.04054080694913864,
0.013330161571502686,
0.0036831561010330915,
0.07544397562742233,
0.016027428209781647,
-0.014798448421061039,
-0.0012502270983532071,
-0.08521036058664322,
-0.0642782673239708,
0.025604741647839546,
0.010132095776498318,
0.03840649127960205,
-0.003197604790329933,
-0.009035984054207802,
0.04422600939869881,
-0.038985490798950195,
-0.02008349634706974,
-0.03511998802423477,
-0.025362983345985413,
-0.08264761418104172,
-0.03091956302523613,
0.007852704264223576,
0.008805441670119762,
0.06668027490377426,
-0.00752629479393363,
-0.03497474268078804,
-0.018485158681869507,
0.03965659439563751,
0.02706228755414486,
-0.03308458626270294,
-0.006630508229136467,
0.06867866963148117,
0.06170725077390671,
0.014039711095392704,
0.0049557918682694435,
-0.03747553378343582,
-0.006678602658212185,
-0.024862507358193398,
-0.018993588164448738,
-0.004669162444770336,
-0.0038927083369344473,
-0.02334105223417282,
-0.04547782614827156,
-0.052778881043195724,
-0.013117114081978798,
0.027343397960066795,
-0.05785679072141647,
-0.019295139238238335,
-0.04648755490779877,
0.012301141396164894,
-0.05271520838141441,
0.03594718500971794,
0.057134874165058136,
0.013857102021574974,
0.04545443505048752,
-0.006606066599488258,
-0.04574093595147133,
0.01142387930303812,
-0.033713534474372864,
0.004082357976585627,
0.07644132524728775,
0.01457408256828785,
-0.004139311145991087,
-0.012507530860602856,
0.0023897832725197077,
0.07840480655431747,
-0.043974097818136215,
0.002322773914784193,
0.025417711585760117,
0.05009851232171059,
0.08091188222169876,
0.04510905221104622,
-0.04109417647123337,
-0.025288091972470284,
0.009218074381351471,
0.026921654120087624,
0.058617740869522095,
0.0225195474922657,
-0.05100024491548538,
0.0716138705611229,
0.018329059705138206,
-0.019557300955057144,
0.06279941648244858,
0.07263939082622528,
0.021687321364879608,
-0.03182803466916084,
-0.015270664356648922,
-0.022170402109622955,
0.010975111275911331,
-0.05134269595146179,
-0.018096625804901123,
-0.01763373240828514,
-0.025643249973654747,
0.02535986341536045,
0.026120435446500778,
0.011735827662050724,
-0.010022553615272045,
-0.008825077675282955,
0.025921529158949852,
-0.03218744695186615,
0.023807864636182785,
-0.05069312825798988,
-0.008106096647679806,
-0.02208278328180313,
-0.004639090038836002,
-0.012490964494645596,
0.024568693712353706,
0.011974118649959564,
0.026399904862046242,
0.027013175189495087,
-0.016835350543260574,
-0.01363210566341877,
0.004641461186110973,
0.00334209599532187,
0.025004997849464417,
-0.015131471678614616,
-0.07035843282938004,
-0.04731017351150513,
0.00282233371399343,
-0.017309876158833504,
-0.06725984811782837,
0.015252813696861267,
0.010406342335045338,
-0.07595933973789215,
-0.012959836982190609,
0.017599282786250114,
-0.03879297524690628,
0.0419611893594265,
0.061568889766931534,
-0.015694158151745796,
-0.023105759173631668,
0.03382398560643196,
0.05477870628237724,
0.004071118775755167,
-0.002576350700110197,
0.05090611055493355,
-0.04963143169879913,
0.0295614805072546,
0.039190854877233505,
0.09223993122577667,
0.02499583177268505,
0.027157053351402283,
0.017731528729200363,
0.03325703740119934,
0.007656491827219725,
0.04622587561607361,
0.01986795850098133,
0.036153193563222885,
-0.023208165541291237,
-0.010385737754404545,
0.0704873725771904,
-0.12405063956975937,
0.007163220550864935,
-0.012908831238746643,
-0.0330628901720047,
0.016315892338752747,
0.023234285414218903,
0.007121177855879068,
0.032593466341495514,
0.07562113553285599,
-0.034215446561574936,
-0.03043213300406933,
0.019284754991531372,
0.02100396528840065,
-0.004851910751312971,
0.0027543725445866585,
0.004167389590293169,
0.00006417201802833006,
0.0624043345451355,
-0.018577035516500473,
-0.04338894411921501,
0.037677425891160965,
-0.0533243753015995,
0.00859595462679863,
0.03729943186044693,
-0.0025618458166718483,
0.042775869369506836,
-0.04541141167283058,
0.0048948186449706554,
0.016732513904571533,
-0.027920346707105637,
0.02236991375684738,
0.026710528880357742,
0.0551283173263073,
-0.00786450132727623,
-0.029066119343042374,
-0.004613411147147417,
0.024248039349913597,
-0.017072368413209915,
0.07774458080530167,
0.04305678606033325,
-0.016081765294075012,
-0.07171628624200821,
0.009551855735480785,
-0.030060086399316788,
-0.005703667178750038,
0.017031030729413033,
0.028496796265244484,
0.018076162785291672,
0.04409835860133171,
0.09121666103601456,
0.021150682121515274,
-0.009806059300899506,
-0.0093080447986722,
0.05971970036625862,
0.0002460850519128144,
-0.02931784652173519,
-0.020613161846995354,
0.0014231984969228506,
0.015453102067112923,
-0.00802664179354906,
-0.05722525343298912,
0.012202919460833073,
-0.026667030528187752,
-0.009878508746623993,
-0.04870462790131569,
-0.002846665680408478,
0.06729158014059067,
0.05038466304540634,
0.03238630294799805,
0.003464015433564782,
-0.013501585461199284,
0.035587701946496964,
-0.05737223103642464,
-0.014287545345723629,
-0.04514200985431671,
-0.02724139206111431,
0.0180344320833683,
-0.010484899394214153,
0.002675549127161503,
-0.005033460445702076,
0.014181100763380527,
0.03962547332048416,
0.0364697240293026,
-0.05496673285961151,
0.024664634838700294,
-0.0360870286822319,
-0.00405089370906353,
0.05459053814411163,
-0.008830109611153603,
0.0438045933842659,
0.0049319821409881115,
-0.009848402813076973,
0.03351952135562897,
0.008951456286013126,
-0.0022264556027948856,
-0.017845312133431435,
-0.06355129182338715,
-0.09057498723268509,
0.021453198045492172,
-0.011901561170816422,
0.020587880164384842,
0.01679629646241665,
0.027364680543541908,
0.033071357756853104,
0.008680115453898907,
-0.03158765658736229,
-0.021070200949907303,
0.034353677183389664,
0.04200664535164833,
-0.03365986794233322,
0.011982469819486141,
-0.040496814996004105,
-0.01650412753224373,
-0.0012791238259524107,
-0.02314596436917782,
0.018399003893136978,
-0.02018051967024803,
-0.02790212258696556,
0.00027617215528152883,
-0.025759825482964516,
-0.08366497606039047,
-0.003584925550967455,
-0.05783927068114281,
-0.035053860396146774,
-0.018331188708543777,
-0.023970158770680428,
-0.001865946687757969,
0.008375626988708973,
0.02188842184841633,
0.01188624557107687,
-0.04887520894408226,
-0.0107935331761837,
0.014139818958938122,
0.0038339069578796625,
0.05003686249256134,
0.0011042208643630147,
0.041796423494815826,
0.06142144277691841,
-0.007238753605633974,
0.010435378178954124,
-0.018507706001400948,
-0.07526938617229462,
-0.0072687589563429356,
0.04287101700901985,
-0.0006550000398419797,
-0.030255494639277458,
-0.03506289795041084,
-0.052822548896074295,
0.05097440630197525,
-0.04911620169878006,
0.002213873900473118,
-0.03919433429837227,
-0.06385977566242218,
-0.005302450153976679,
0.01704961061477661,
-0.0109251094982028,
0.02148260362446308
] |
<p>The atmospheric pressure is 101325 Pa,which is good enough to get our bones crushed.But why aren't we crushed due to it?</p> | g160 | [
0.07019931823015213,
0.07806731760501862,
-0.0044923448003828526,
0.00553444167599082,
0.014960769563913345,
0.029188115149736404,
0.021433085203170776,
0.06686034053564072,
-0.055932823568582535,
0.005199580918997526,
0.029253819957375526,
-0.030439872294664383,
-0.03959529101848602,
-0.018809398636221886,
0.00007018038013484329,
0.007002709433436394,
0.00444295397028327,
0.012775982730090618,
0.028339844197034836,
0.020439598709344864,
-0.05078088864684105,
-0.05477814003825188,
0.04574147239327431,
-0.028130942955613136,
-0.034301403909921646,
0.015946388244628906,
0.007804133929312229,
0.007063834462314844,
-0.044074416160583496,
0.02256113477051258,
0.02816479653120041,
-0.011054798029363155,
-0.044941697269678116,
-0.04349929094314575,
0.01631738990545273,
-0.06634698808193207,
0.01433299295604229,
-0.026898078620433807,
0.0289164949208498,
-0.07647302746772766,
-0.039829760789871216,
-0.08919383585453033,
0.022773658856749535,
0.04002254083752632,
-0.05169842019677162,
0.015919778496026993,
-0.020115865394473076,
-0.05165135860443115,
-0.006612285040318966,
0.01699802093207836,
0.024415655061602592,
-0.03892139345407486,
0.019875165075063705,
-0.010133038274943829,
-0.011542542837560177,
-0.0650835633277893,
0.057988375425338745,
0.004397260490804911,
-0.024081489071249962,
-0.011754442006349564,
-0.03101157955825329,
0.03333215042948723,
0.025777403265237808,
0.011641385965049267,
-0.0003608092956710607,
-0.03809983655810356,
-0.037905119359493256,
-0.002642775885760784,
0.07707908004522324,
0.05184989422559738,
0.028190389275550842,
-0.04694569855928421,
-0.04546435922384262,
-0.0060601322911679745,
-0.017472853884100914,
0.01845075748860836,
-0.018984012305736542,
0.008787780068814754,
0.027238398790359497,
0.0277258288115263,
0.01157654169946909,
0.013514554128050804,
0.024739615619182587,
-0.017645277082920074,
-0.0012913132086396217,
-0.0704064890742302,
0.005865767132490873,
-0.022195685654878616,
-0.00713067501783371,
0.027958815917372704,
0.04164856672286987,
-0.03602582588791847,
0.06376022845506668,
0.024786483496427536,
0.041108448058366776,
-0.008088302798569202,
-0.002707888837903738,
0.06767133623361588,
-0.07254160195589066,
-0.006793205160647631,
0.000830410688649863,
-0.0009565100190229714,
0.010125741362571716,
-0.017415856942534447,
-0.0005054516950622201,
0.002396802883595228,
0.027263926342129707,
0.004002413712441921,
-0.0018712932942435145,
-0.03366164118051529,
0.07393151521682739,
0.07508368045091629,
-0.023347340524196625,
0.02270953729748726,
-0.013366135768592358,
-0.03776055946946144,
0.0678345113992691,
-0.019811337813735008,
-0.020035557448863983,
0.05457400158047676,
0.019914550706744194,
0.026001418009400368,
0.040832050144672394,
-0.001801984733901918,
-0.021924106404185295,
0.018880609422922134,
0.052380599081516266,
0.0031117675825953484,
0.030114997178316116,
-0.07327892631292343,
-0.00616876594722271,
0.03986494615674019,
-0.037662044167518616,
0.0027782930992543697,
0.029160436242818832,
0.07571667432785034,
-0.04465872049331665,
0.002699480624869466,
-0.038352955132722855,
0.04880451411008835,
0.012109587900340557,
0.10747770965099335,
0.05476480722427368,
0.023289384320378304,
-0.0036963021848350763,
-0.0020427927374839783,
-0.03665829077363014,
0.030445324257016182,
0.025982318446040154,
0.06851087510585785,
-0.06664341688156128,
0.022412098944187164,
0.03326653316617012,
-0.012715985998511314,
-0.016446078196167946,
-0.01732461526989937,
0.0337439589202404,
0.003743254579603672,
0.016484852880239487,
0.07813278585672379,
0.06941507011651993,
0.01996265910565853,
-0.05797356739640236,
0.04137799143791199,
-0.03129919245839119,
0.03543706610798836,
-0.02210393361747265,
0.052279118448495865,
0.038315385580062866,
0.025308577343821526,
-0.02169180102646351,
0.011312349699437618,
0.008035453036427498,
0.06654958426952362,
-0.0351702906191349,
-0.007300160825252533,
-0.017727427184581757,
0.014266165904700756,
0.015227781608700752,
-0.022886069491505623,
0.05611341819167137,
0.0009863515151664615,
0.02260483242571354,
-0.06255575269460678,
-0.026820305734872818,
-0.002752969041466713,
-0.03362509608268738,
0.015453580766916275,
-0.03487486392259598,
0.017919259145855904,
-0.003357671434059739,
-0.03172890841960907,
-0.029678527265787125,
0.02629592828452587,
0.022410577163100243,
0.007697965018451214,
-0.0009182235226035118,
-0.03886708244681358,
-0.017046594992280006,
0.06979655474424362,
0.0276471134275198,
0.06108260154724121,
0.009864326566457748,
-0.04584886506199837,
-0.015797989442944527,
0.04158758744597435,
-0.045862164348363876,
0.0350601002573967,
0.05175405368208885,
0.005457335151731968,
-0.02429009974002838,
-0.011819783598184586,
0.02231716923415661,
0.03244956582784653,
-0.07708942145109177,
0.004533277824521065,
-0.02388022281229496,
0.039600223302841187,
-0.07681064307689667,
0.010375117883086205,
0.021039653569459915,
0.01918056793510914,
-0.018802011385560036,
0.0019675057847052813,
-0.012144692242145538,
-0.04780162498354912,
-0.06773006916046143,
-0.04256020858883858,
0.008613619953393936,
-0.07419238984584808,
-0.027262087911367416,
0.008114908821880817,
-0.019780149683356285,
0.023241955786943436,
-0.037623465061187744,
0.036690812557935715,
0.028307951986789703,
0.012433208525180817,
-0.005629974417388439,
0.05708954483270645,
0.020972594618797302,
-0.0689283013343811,
-0.060427334159612656,
-0.005183135159313679,
0.031833499670028687,
0.008105089887976646,
-0.04411502182483673,
0.016194118186831474,
0.007371141109615564,
0.04202341288328171,
0.0016129788709804416,
0.0028715324588119984,
-0.043547093868255615,
-0.03863353282213211,
0.02565312199294567,
-0.05706382542848587,
0.03380974009633064,
0.039990924298763275,
0.009963038377463818,
-0.07278876006603241,
-0.006579004693776369,
-0.04036471247673035,
-0.010458976961672306,
-0.0518767312169075,
-0.10287561267614365,
0.021399570629000664,
-0.024695100262761116,
-0.009890913031995296,
0.0449795126914978,
-0.019537605345249176,
0.042766787111759186,
0.006318597123026848,
0.01254119910299778,
0.05790019407868385,
0.012993794865906239,
-0.016737328842282295,
0.026773206889629364,
-0.021629346534609795,
-0.03839511796832085,
-0.05770657956600189,
0.0025457381270825863,
0.059223052114248276,
-0.016350846737623215,
0.004370841197669506,
0.019451722502708435,
-0.025436023250222206,
-0.009396257810294628,
0.007664173375815153,
0.0006591384881176054,
-0.015646355226635933,
0.053997479379177094,
0.0022464527282863855,
0.013059976510703564,
0.05577095225453377,
-0.0037222779355943203,
0.08720728009939194,
0.06802842766046524,
-0.0555168017745018,
-0.038863904774188995,
0.0365491546690464,
0.00181133474688977,
-0.03191683813929558,
0.014431014657020569,
0.0028973252046853304,
-0.05356329679489136,
0.018164359033107758,
0.011820962652564049,
-0.013635292649269104,
-0.01842406950891018,
-0.00010895050218096003,
-0.007310936693102121,
0.05886393412947655,
0.02981625124812126,
0.04229949042201042,
-0.09165210276842117,
-0.03219709172844887,
-0.040553126484155655,
-0.03824688866734505,
0.060607511550188065,
-0.010540160350501537,
-0.0192307997494936,
-0.00346681522205472,
-0.028032878413796425,
-0.03977496549487114,
0.022109271958470345,
0.0349559411406517,
0.017841443419456482,
-0.010559452697634697,
-0.02572472393512726,
-0.03857831284403801,
-0.005759582854807377,
0.00028284036670811474,
-0.03420324996113777,
-0.02307971380650997,
-0.07438696920871735,
0.02155376225709915,
0.058295320719480515,
0.0003187347901985049,
0.05175282433629036,
0.01187529694288969,
-0.04736960306763649,
-0.044124405831098557,
-0.0161304771900177,
-0.027512097731232643,
-0.020505735650658607,
0.0031353069934993982,
0.020248662680387497,
0.03878771886229515,
0.017734471708536148,
-0.0023852086160331964,
0.03694869577884674,
-0.013480668887495995,
0.016163790598511696,
-0.04130808636546135,
0.017511745914816856,
0.025313647463917732,
0.056761376559734344,
0.02529679238796234,
-0.02721322700381279,
-0.025251343846321106,
0.06752628087997437,
0.08375679701566696,
0.03378564864397049,
0.010966829024255276,
0.005573831964284182,
0.004842527210712433,
-0.03481646627187729,
-0.005362857598811388,
0.016614552587270737,
0.010424236766994,
0.011105013079941273,
-0.027098219841718674,
-0.03833308070898056,
0.007909733802080154,
0.02851155400276184,
-0.039577994495630264,
0.0473833829164505,
0.026843419298529625,
-0.020802371203899384,
-0.021852931007742882,
0.03854318708181381,
-0.039837710559368134,
-0.017743736505508423,
0.036407649517059326,
-0.06123115494847298,
0.030773526057600975,
-0.017011843621730804,
0.043091218918561935,
-0.04854189231991768,
-0.0021953717805445194,
0.013504506088793278,
-0.05268413573503494,
0.006215773057192564,
0.006406637839972973,
-0.03306732326745987,
-0.03978278115391731,
-0.02615317329764366,
-0.03508395701646805,
-0.03886565938591957,
-0.01787516288459301,
0.03484257310628891,
0.012752296403050423,
0.03821320831775665,
0.017937416210770607,
-0.018613675609230995,
0.04672975465655327,
0.027423445135354996,
-0.03204616159200668,
-0.02894056774675846,
-0.011826349422335625,
0.02594638057053089,
0.02141215093433857,
0.009395940229296684,
-0.052631277590990067,
0.0751519426703453,
0.01823480986058712,
-0.028026176616549492,
-0.0017594409873709083,
0.07042162865400314,
0.012844573706388474,
-0.05896027386188507,
0.030867919325828552,
0.017959795892238617,
-0.025764552876353264,
0.02700589783489704,
0.0464366115629673,
-0.007373649626970291,
-0.043258748948574066,
0.012573079206049442,
-0.07558807730674744,
0.02706347219645977,
0.009817652404308319,
-0.002596541540697217,
-0.007195431739091873,
0.01874895952641964,
0.052792344242334366,
-0.020229555666446686,
0.013726618140935898,
0.024022722616791725,
0.037425145506858826,
0.015173038467764854,
-0.004060438368469477,
0.030265888199210167,
0.03309932351112366,
-0.003146965755149722,
0.058760661631822586,
0.06888779252767563,
-0.034663792699575424,
0.013099987991154194,
-0.0074048093520104885,
0.01096163410693407,
-0.04122225567698479,
0.006150777451694012,
-0.05303126573562622,
0.019620534032583237,
-0.006187036633491516,
-0.018245067447423935,
0.0056924945674836636,
-0.05562713369727135,
0.12179751694202423,
-0.07548778504133224,
-0.04055549204349518,
-0.015783021226525307,
-0.020042860880494118,
-0.02722112275660038,
-0.004331766162067652,
-0.050306592136621475,
-0.015179852955043316,
-0.0416172593832016,
-0.006672744173556566,
-0.026644423604011536,
-0.07641562819480896,
-0.03719877451658249,
0.024738507345318794,
-0.03042668290436268,
0.12434026598930359,
-0.008612684905529022,
-0.022736523300409317,
0.016475623473525047,
-0.11729659885168076,
0.04861766844987869,
0.04084903374314308,
-0.05323415622115135,
0.0332583412528038,
-0.038352467119693756,
-0.002516295528039336,
-0.05358769744634628,
0.007052171975374222,
-0.04164303466677666,
-0.0011210453230887651,
-0.03250312805175781,
0.016199590638279915,
0.028237875550985336,
-0.0141102634370327,
-0.0026333665009588003,
-0.028786664828658104,
-0.04679110646247864,
0.02523679845035076,
0.021382540464401245,
-0.023435944691300392,
-0.03982976824045181,
-0.0421021468937397,
0.0015488832723349333,
-0.0269025731831789,
0.0701201781630516,
0.013534622266888618,
0.06274621933698654,
0.015956005081534386,
0.049498721957206726,
0.008671227842569351,
0.05819609761238098,
-0.05188683792948723,
0.058864641934633255,
0.0006403008592315018,
0.039626553654670715,
0.008795108646154404,
-0.002855563536286354,
0.022307027131319046,
0.009661832824349403,
-0.02826583944261074,
-0.020469050854444504,
0.00485805282369256,
0.07518742978572845,
-0.006335940677672625,
0.009922849014401436,
-0.0009156087762676179,
0.005091299768537283,
-0.03802339360117912,
-0.011189760640263557,
-0.002365210559219122,
-0.006471693981438875,
-0.06438114494085312,
0.06606268882751465,
-0.03258052468299866,
-0.004696147050708532,
0.013705609366297722,
0.0219026580452919,
0.03487997129559517,
0.052862007170915604,
-0.048914846032857895,
-0.016077371314167976,
-0.010068368166685104,
0.006338774226605892,
0.06283441931009293,
0.013603048399090767,
0.067462258040905,
-0.06123388186097145,
-0.001478073070757091,
-0.03808894753456116,
0.020691780373454094,
0.01296935323625803,
0.011018991470336914,
-0.01915493607521057,
-0.014075336046516895,
0.022106744349002838,
-0.012645456939935684,
-0.0010053579462692142,
-0.027519183233380318,
-0.02654131129384041,
-0.043017227202653885,
0.010045841336250305,
0.02286837436258793,
-0.02336285449564457,
0.017206352204084396,
0.06959253549575806,
-0.053065404295921326,
0.001665641670115292,
-0.014951017685234547,
0.009471316821873188,
-0.03528396785259247,
-0.03775829076766968,
0.025767698884010315,
0.0659346655011177,
0.03608359396457672,
-0.0017433472676202655,
0.05266305059194565,
-0.034704871475696564,
0.05573120713233948,
0.020237315446138382,
-0.051632191985845566,
0.0031122032087296247,
-0.04463578760623932,
0.034774716943502426,
-0.051374029368162155,
0.03517945483326912,
-0.005635244306176901,
-0.025092925876379013,
0.014795377850532532,
0.07639160007238388,
0.018347959965467453,
0.03397984430193901,
-0.0009604173246771097,
-0.013017870485782623,
-0.06154836341738701,
-0.034680284559726715,
-0.04339294508099556,
0.04042467102408409,
-0.005569730419665575,
-0.025108296424150467,
-0.04308683052659035,
0.053400468081235886,
0.0342782586812973,
0.026822872459888458,
-0.027228502556681633,
0.01632441207766533,
-0.0018121147295460105,
-0.004315110854804516,
0.027262844145298004,
-0.01851613074541092,
0.0067603569477796555,
-0.09332368522882462,
0.03302348032593727,
-0.01292654499411583,
0.03574516996741295,
0.021693047136068344,
-0.03652600198984146,
0.02508285827934742,
0.0016191600589081645,
-0.024410033598542213,
0.016236161813139915,
-0.011925112456083298,
0.03884809464216232,
-0.025743883103132248,
-0.059614166617393494,
0.01689048297703266,
-0.045177143067121506,
-0.0026186418253928423,
-0.017548833042383194,
0.024732962250709534,
0.0014730828115716577,
-0.026841895654797554,
-0.003974824212491512,
0.008487822487950325,
0.014302113093435764,
-0.03136971592903137,
0.018747752532362938,
-0.048727840185165405,
0.00010921234206762165,
-0.020961618050932884,
-0.017518525943160057,
0.06469064950942993,
-0.01949496380984783,
0.012698397040367126,
-0.017035407945513725,
-0.05637865513563156,
0.04239200800657272,
0.017288966104388237,
-0.011632254347205162,
-0.0548890046775341,
-0.010450082831084728,
-0.0008994592353701591,
-0.02522408217191696,
-0.016928713768720627,
0.018655411899089813,
-0.02013549953699112,
-0.03176899999380112,
0.003532732604071498,
0.008581921458244324,
0.004776190500706434,
0.019796760752797127,
0.021416764706373215,
-0.023165760561823845,
0.0006952615221962333,
0.03970956802368164,
-0.015691770240664482,
0.02015303634107113,
0.03490151837468147,
-0.07182636111974716,
0.0481906495988369,
0.056600961834192276,
-0.00319867511279881,
-0.006469522137194872,
-0.07156775891780853,
-0.05331123620271683,
0.016040431335568428,
0.037491753697395325,
0.017632560804486275,
-0.050932276993989944,
0.04290129989385605,
0.01936545968055725,
0.03454222157597542,
0.049051593989133835,
0.01634858548641205,
-0.029079146683216095,
0.03714746981859207,
-0.03594435006380081,
-0.01733439415693283,
0.03085908107459545,
-0.027549928054213524,
0.07079572230577469,
0.0033532013185322285,
0.014099783264100552,
-0.01299159787595272,
0.01987244002521038,
-0.047622889280319214,
-0.03569090738892555,
0.032057251781225204,
0.000870896503329277,
-0.07307165861129761,
-0.04190478101372719,
-0.039973169565200806,
-0.030559469014406204,
0.0014476192882284522,
-0.003331354819238186,
-0.004549380857497454,
0.01071967277675867,
0.009347296319901943,
0.05676776170730591,
-0.028671128675341606,
-0.026582403108477592,
0.029535390436649323,
0.07067680358886719,
0.020251240581274033,
-0.018682757392525673,
0.04216473549604416,
0.00036155892303213477,
-0.0038634203374385834,
-0.011842882260680199,
0.022492269054055214,
-0.04839818552136421,
0.03575953096151352,
-0.055175960063934326,
-0.009889769367873669,
-0.03907579928636551,
-0.021593360230326653,
-0.01642756350338459,
0.08872867375612259,
-0.04129358008503914,
0.03292417526245117,
-0.02031659334897995,
-0.044148437678813934,
0.038756150752305984,
-0.030577247962355614,
0.0036053236108273268,
-0.016181521117687225,
-0.039671048521995544,
0.003578408621251583,
0.0711231455206871,
-0.002135663293302059,
0.015517346560955048,
-0.061937589198350906,
-0.0008168659987859428,
-0.03928300365805626,
-0.0022737085819244385,
-0.00011713587446138263,
-0.004379356745630503,
-0.039595115929841995,
0.0077424547635018826,
0.014644516631960869,
0.013842592015862465,
0.021925993263721466,
0.0118616484105587,
-0.031209487468004227,
0.023484621196985245,
-0.034551069140434265,
-0.031256064772605896,
0.010646898299455643,
-0.000730537052731961,
0.006429098546504974,
-0.09096124768257141,
0.006588901858776808,
-0.02474140375852585,
0.07484589517116547,
-0.009127423167228699,
0.02045224793255329,
-0.025891706347465515,
-0.015643928200006485,
-0.05898568406701088
] |
<p>I'm looking for an originally German introduction to quantum mechanics. Is there such a canonical book used in German QM undergraduate courses?</p> | g4759 | [
0.059044577181339264,
-0.0577985979616642,
0.014716917648911476,
-0.035967323929071426,
-0.023276755586266518,
0.040933746844530106,
-0.021403543651103973,
-0.01346914004534483,
-0.021715862676501274,
0.038005147129297256,
0.02674766629934311,
0.03346337750554085,
0.009633858688175678,
-0.0020500237587839365,
-0.027120692655444145,
-0.021062107756733894,
-0.004434374626725912,
0.06664154678583145,
-0.003943687304854393,
-0.028849022462964058,
0.021705262362957,
0.011085531674325466,
0.017819155007600784,
-0.04071154445409775,
-0.026790812611579895,
-0.021265758201479912,
-0.0731685608625412,
-0.0367555171251297,
0.012862684205174446,
-0.011347419582307339,
-0.05740111321210861,
-0.04699501767754555,
0.05827932432293892,
-0.07532619684934616,
-0.005547576118260622,
0.02791689895093441,
0.02878926880657673,
-0.04364823177456856,
-0.009240915067493916,
-0.01741894520819187,
0.021714046597480774,
-0.05112312734127045,
0.029277915135025978,
-0.001556269358843565,
0.018676798790693283,
0.022747673094272614,
0.03784177824854851,
-0.024915562942624092,
-0.005635814741253853,
0.04592317342758179,
-0.03264084830880165,
0.03188788890838623,
0.07264015078544617,
-0.005147809628397226,
0.011408595368266106,
0.04758916050195694,
-0.04856036975979805,
0.059145793318748474,
-0.015034249983727932,
0.027173705399036407,
0.03394350782036781,
0.030542263761162758,
0.04188636317849159,
-0.003773256205022335,
0.004074785392731428,
-0.027675848454236984,
0.02764742821455002,
-0.011040285229682922,
0.0013143119867891073,
0.005306523758918047,
0.0083067137748003,
-0.056471191346645355,
-0.02375110425055027,
0.049672938883304596,
0.05964834988117218,
0.024609703570604324,
0.019600510597229004,
-0.035775281488895416,
0.060912467539310455,
0.0012296647764742374,
-0.10763976722955704,
-0.009787307120859623,
0.10653103142976761,
-0.015271326526999474,
0.13062015175819397,
-0.031028205528855324,
-0.039177875965833664,
-0.031955696642398834,
-0.03252498432993889,
-0.05740560218691826,
0.013033252209424973,
-0.03902311623096466,
0.023868320509791374,
-0.01230255700647831,
-0.022861039265990257,
-0.014009813778102398,
-0.03333421051502228,
0.014855312183499336,
-0.032496076077222824,
-0.004583945032209158,
-0.024180825799703598,
0.02700684405863285,
0.026710018515586853,
0.004956813994795084,
-0.05533422529697418,
-0.003362529445439577,
0.015122982673346996,
-0.03136157989501953,
0.008158959448337555,
0.03444351255893707,
0.015069615095853806,
-0.010817822068929672,
-0.035070180892944336,
-0.008215089328587055,
-0.016903486102819443,
0.03086477518081665,
0.07241516560316086,
0.01345683541148901,
0.0201103575527668,
0.038064561784267426,
-0.007070396561175585,
0.02481945790350437,
0.04011894017457962,
0.02421773225069046,
0.020639454945921898,
-0.011058988980948925,
-0.025629332289099693,
-0.038158118724823,
0.04693329334259033,
-0.006307777017354965,
0.06333894282579422,
0.00042041437700390816,
-0.07019271701574326,
-0.018982185050845146,
0.023928426206111908,
0.038154132664203644,
0.029745500534772873,
0.01851312629878521,
0.06043916568160057,
0.009174393489956856,
0.01173215638846159,
-0.03139270097017288,
-0.00852044764906168,
-0.003806407330557704,
0.013829723931849003,
-0.050150174647569656,
0.05591945722699165,
0.0004689113993663341,
-0.021524984389543533,
-0.005670446902513504,
0.0029478135984390974,
-0.023565318435430527,
-0.006590737029910088,
0.02405703254044056,
-0.008391566574573517,
0.009563887491822243,
0.039273783564567566,
-0.018846942111849785,
-0.024246279150247574,
-0.03154096007347107,
0.034045565873384476,
-0.03406798094511032,
-0.02517509087920189,
0.035673003643751144,
-0.031601376831531525,
0.06715191155672073,
-0.017046887427568436,
-0.07461186498403549,
0.0291980542242527,
-0.09212915599346161,
-0.008610040880739689,
0.005020461976528168,
-0.003368537174537778,
0.02725180983543396,
-0.07575743645429611,
0.03027174435555935,
0.01731996238231659,
-0.02149832993745804,
-0.02139396034181118,
-0.007445244118571281,
-0.013701189309358597,
-0.002821051049977541,
0.03650151938199997,
-0.028631221503019333,
-0.06962709128856659,
0.06676362454891205,
0.010533985681831837,
0.06670792400836945,
-0.008343334309756756,
0.02855493687093258,
-0.007869914174079895,
0.05208311602473259,
0.049870479851961136,
-0.02335130050778389,
0.07022009789943695,
-0.007843474857509136,
-0.0036694498267024755,
0.029671959578990936,
0.002192650455981493,
0.025140438228845596,
0.016676079481840134,
0.05338841304183006,
0.05035105720162392,
0.018546003848314285,
0.009105749428272247,
0.007245549466460943,
0.03276366367936134,
-0.029383694753050804,
0.07203671336174011,
-0.04491721838712692,
-0.02496263198554516,
0.05949984863400459,
0.030217168852686882,
0.015539721585810184,
-0.01215365156531334,
-0.01282232441008091,
-0.006269591860473156,
0.041114822030067444,
-0.027960270643234253,
0.06304983049631119,
-0.03270704299211502,
0.031619202345609665,
0.040327321738004684,
-0.008328506723046303,
0.0005090467748232186,
0.02417324297130108,
0.0023947556037455797,
-0.028951358050107956,
-0.01862405240535736,
0.021457167342305183,
-0.12810605764389038,
-0.06227906048297882,
-0.04435715079307556,
-0.010426696389913559,
0.0363294892013073,
0.07977776229381561,
0.011995973065495491,
0.007730669341981411,
0.025764627382159233,
0.035686541348695755,
0.07458492368459702,
-0.011182301677763462,
0.0029389632400125265,
0.0162776131182909,
-0.005693730898201466,
-0.013323981314897537,
-0.027503855526447296,
0.01708686351776123,
0.02286776341497898,
-0.016723215579986572,
0.0039304094389081,
-0.07761230319738388,
-0.07239773869514465,
-0.02122076414525509,
-0.014646903611719608,
-0.006444431841373444,
-0.037024158984422684,
-0.00788070447742939,
-0.001957576023414731,
0.052271585911512375,
0.026601366698741913,
0.0012119841994717717,
0.008284621872007847,
0.013090166263282299,
-0.00894587766379118,
-0.016212917864322662,
-0.0017592298099771142,
-0.02998758852481842,
-0.05163602903485298,
-0.04439953342080116,
-0.047154750674963,
0.10275816917419434,
-0.02361798658967018,
0.004853836726397276,
0.006080312188714743,
0.01755347289144993,
-0.035448819398880005,
-0.0038304703775793314,
0.005668201018124819,
-0.045892730355262756,
0.00450702803209424,
-0.009343708865344524,
-0.01558156032115221,
0.019779669120907784,
0.027498139068484306,
-0.01944940909743309,
0.021848557516932487,
0.055996838957071304,
0.029508644714951515,
-0.06127974018454552,
0.011637294664978981,
0.024429935961961746,
0.009130695834755898,
0.03603332117199898,
-0.05456789210438728,
0.010999379679560661,
-0.01423968467861414,
-0.005913227796554565,
-0.006245567463338375,
0.049290575087070465,
-0.02617589943110943,
-0.01752726547420025,
0.014012676663696766,
0.03037133440375328,
0.03311992809176445,
-0.0006479104049503803,
0.01173306629061699,
-0.02440953627228737,
0.0003407237818464637,
-0.004371328745037317,
-0.04975581914186478,
-0.02213987708091736,
-0.004907688591629267,
0.054889824241399765,
-0.03574800118803978,
-0.016925018280744553,
-0.045610520988702774,
-0.013704126700758934,
-0.007086093071848154,
-0.060038771480321884,
-0.04610047489404678,
-0.06635721027851105,
0.07640943676233292,
-0.059014201164245605,
0.0813787505030632,
0.03977452591061592,
-0.024278918281197548,
0.012684638611972332,
0.005313163157552481,
-0.040571000427007675,
0.0287662073969841,
-0.014040753245353699,
0.008884640410542488,
0.0036492401268333197,
-0.014046352356672287,
-0.053667254745960236,
-0.01884845830500126,
-0.02260115183889866,
0.024680674076080322,
-0.011308129876852036,
0.03426480293273926,
0.009642520919442177,
0.02452792041003704,
0.011640440672636032,
0.0042000929825007915,
-0.052460506558418274,
-0.05901843681931496,
-0.01044924184679985,
0.03461809083819389,
0.007872332818806171,
-0.0008712062845006585,
0.07214462012052536,
0.008695337921380997,
0.04539291188120842,
0.017190156504511833,
0.011482667177915573,
0.02502639777958393,
-0.0011228551156818867,
0.01470489613711834,
-0.034232452511787415,
0.032919254153966904,
-0.041237279772758484,
0.02209407649934292,
0.030189553275704384,
-0.037745401263237,
-0.03867695480585098,
-0.022228261455893517,
0.03218235448002815,
0.023469891399145126,
0.027706429362297058,
-0.06071680784225464,
-0.007512188516557217,
0.004431487061083317,
-0.017713362351059914,
-0.0155715337023139,
-0.043191682547330856,
0.033513143658638,
0.023682279512286186,
-0.10958309471607208,
-0.017030617222189903,
-0.03741531819105148,
0.004678203258663416,
0.008041837252676487,
0.052771881222724915,
0.04162965342402458,
0.04505394026637077,
0.029187263920903206,
-0.0032963892444968224,
0.04224801063537598,
0.02897140569984913,
-0.007222210522741079,
-0.03455197066068649,
-0.014487238600850105,
0.03671609237790108,
-0.01156669482588768,
0.04450167715549469,
0.04983231797814369,
0.01195789035409689,
0.00951374601572752,
0.021611519157886505,
-0.03537597879767418,
0.016085663810372353,
-0.01701156422495842,
0.02646470069885254,
-0.008347515016794205,
0.00759901711717248,
-0.004373676609247923,
-0.03820206969976425,
-0.002699243603274226,
-0.025596577674150467,
-0.0009429717320017517,
-0.020255718380212784,
0.0011246332433074713,
0.016646329313516617,
0.029987700283527374,
0.013099662028253078,
0.0333336740732193,
-0.07281814515590668,
0.015566649846732616,
0.014245465397834778,
-0.020845286548137665,
0.029250459745526314,
0.00962899625301361,
0.0003073998959735036,
0.02944372035562992,
0.024294905364513397,
-0.011898721568286419,
0.04942163825035095,
0.007964514195919037,
-0.029771598055958748,
-0.0057334513403475285,
-0.027537649497389793,
0.018366439267992973,
0.040316980332136154,
-0.013223851099610329,
-0.0010180758545175195,
0.0006835666135884821,
-0.0359066016972065,
-0.013640781864523888,
0.016807999461889267,
0.02954152226448059,
0.014161130413413048,
0.008341232314705849,
-0.0011074839858338237,
-0.04181084409356117,
0.0560515820980072,
-0.016822051256895065,
-0.040306612849235535,
0.019346758723258972,
-0.07768671214580536,
-0.006438096985220909,
-0.0025991902220994234,
-0.02244342863559723,
0.012647793628275394,
-0.029008954763412476,
-0.03821665048599243,
-0.030025027692317963,
0.014186731539666653,
0.029811710119247437,
0.05964129418134689,
-0.02581392042338848,
0.03758525848388672,
0.006444459315389395,
0.03217997029423714,
-0.059307537972927094,
-0.027814896777272224,
-0.07691124081611633,
0.08753827959299088,
-0.017007656395435333,
-0.056316178292036057,
0.026777472347021103,
-0.026817433536052704,
0.023850910365581512,
0.0020646289922297,
0.021063944324851036,
-0.024381235241889954,
0.02577854134142399,
-0.10533641278743744,
0.007498434279114008,
-0.056845348328351974,
0.019799113273620605,
0.000015278863429557532,
0.005720523186028004,
0.027967480942606926,
-0.010586346499621868,
-0.025236010551452637,
0.0395999513566494,
0.05113847181200981,
-0.013094019144773483,
-0.024994881823658943,
0.04403911530971527,
-0.059417687356472015,
0.031070392578840256,
0.0008166083134710789,
-0.049446891993284225,
0.007606742903590202,
0.0402805395424366,
-0.04236005246639252,
0.028377031907439232,
-0.0003006749611813575,
-0.02251850627362728,
-0.003691723570227623,
-0.033728815615177155,
-0.00895511731505394,
-0.0006367707392200828,
0.022020868957042694,
-0.014421289786696434,
0.03633871302008629,
-0.06753446906805038,
0.00675829267129302,
0.021301014348864555,
-0.01390142273157835,
-0.017986414954066277,
0.03142460808157921,
0.06604364514350891,
0.02596280165016651,
-0.024038875475525856,
-0.036579787731170654,
-0.0470392219722271,
-0.02844219282269478,
-0.022594604641199112,
-0.04813699051737785,
0.04141295701265335,
0.004136841278523207,
0.004225738346576691,
0.0025474131107330322,
-0.11907877773046494,
-0.00283193401992321,
-0.005979752168059349,
0.00793485902249813,
0.023875292390584946,
-0.03145597130060196,
-0.014069069176912308,
-0.020202433690428734,
0.011384271085262299,
0.08210405707359314,
-0.007311577443033457,
-0.0006649831775575876,
-0.004558286163955927,
0.06090894713997841,
-0.053923361003398895,
-0.01259281300008297,
0.020413534715771675,
-0.01881752721965313,
0.0022309047635644674,
0.039929527789354324,
0.002398549811914563,
0.012112773023545742,
0.06075495481491089,
-0.06503307074308395,
-0.04432813078165054,
-0.062209874391555786,
-0.026371926069259644,
-0.07757218927145004,
0.013289855793118477,
0.07493790984153748,
-0.052575595676898956,
-0.06462270021438599,
-0.022537661716341972,
0.05155004560947418,
0.023503558710217476,
-0.03428281843662262,
0.05343436077237129,
-0.0071459743194282055,
-0.06508690118789673,
0.0005810082657262683,
-0.0487099252641201,
-0.06239858642220497,
0.08919613063335419,
0.03526259586215019,
-0.03993650898337364,
0.0060391840524971485,
-0.00821505393832922,
-0.0037363336887210608,
0.045098207890987396,
0.03714073821902275,
-0.02832014299929142,
-0.04231027141213417,
-0.0007669145124964416,
-0.04915669187903404,
0.04262443631887436,
0.04290018975734711,
0.02641887590289116,
0.00763724884018302,
0.00473628006875515,
0.04229151830077171,
-0.03550832346081734,
0.03809582069516182,
-0.031154761090874672,
0.0345168374478817,
0.007287698332220316,
0.03740943968296051,
-0.061296503990888596,
-0.05242275819182396,
0.03679316118359566,
0.0399722158908844,
0.06570161879062653,
0.057757504284381866,
-0.0007275906391441822,
-0.07182244956493378,
-0.028408925980329514,
0.012711962684988976,
-0.016896456480026245,
0.011244278401136398,
0.0675613284111023,
0.049900978803634644,
0.052152737975120544,
-0.030215883627533913,
-0.007551637943834066,
0.016607163473963737,
-0.00931905210018158,
0.02285689301788807,
-0.09208786487579346,
-0.015854954719543457,
-0.056642938405275345,
-0.07260437309741974,
-0.0011266466462984681,
0.07901368290185928,
-0.01970049925148487,
0.00803445465862751,
0.05534913390874863,
0.026585962623357773,
0.024157026782631874,
-0.03948414698243141,
-0.006730236113071442,
0.01850711740553379,
-0.05259456858038902,
0.02663644775748253,
0.05648922175168991,
-0.03327517583966255,
-0.021516798064112663,
-0.0726262778043747,
-0.011805074289441109,
-0.032340459525585175,
-0.029806843027472496,
0.06622043997049332,
-0.0528593584895134,
-0.0363614484667778,
0.016681987792253494,
-0.025001205503940582,
-0.0007010898552834988,
-0.02508421055972576,
0.04106863960623741,
0.002116631716489792,
-0.024370575323700905,
-0.05046648159623146,
0.0013487605610862374,
-0.022410543635487556,
-0.0691789835691452,
0.02845115214586258,
0.08386513590812683,
0.03913017362356186,
-0.022292863577604294,
-0.014841353520751,
-0.01020087767392397,
0.05009637400507927,
0.09489145129919052,
0.022974858060479164,
0.03357605263590813,
-0.056714463979005814,
0.0021932260133326054,
-0.04263962805271149,
0.023064030334353447,
0.016474641859531403,
0.012286102399230003,
0.010666866786777973,
0.03526058420538902,
-0.04117647558450699,
0.04689797759056091,
0.026072010397911072,
-0.027379842475056648,
0.00518375588580966,
-0.059854064136743546,
-0.02365274541079998,
-0.01403001043945551,
0.030544329434633255,
0.03571690246462822,
0.05384088307619095,
-0.010109420865774155,
0.003922419156879187,
0.014401176013052464,
-0.008003691211342812,
-0.02149713970720768,
-0.005649232305586338,
-0.01907879300415516,
-0.022136962041258812,
0.01012152899056673,
-0.009020434692502022,
0.04573400318622589,
0.027170095592737198,
-0.04541674256324768,
-0.062447141855955124,
0.02253447286784649,
-0.04576016217470169,
0.03956069052219391,
-0.028421487659215927,
0.09398889541625977,
-0.009419328533113003,
0.033402588218450546,
-0.008610673248767853,
0.03770466521382332,
0.03704815357923508,
-0.0213865227997303,
0.03141544386744499,
0.009518016129732132,
-0.02039438858628273,
0.02872174046933651,
-0.012343103997409344,
0.01342910435050726,
-0.03950171545147896,
-0.017000632360577583,
0.040654249489307404,
0.014066816307604313,
0.014848488382995129,
0.015692031010985374,
-0.043207086622714996,
-0.0284202191978693,
0.05445457249879837,
0.020028047263622284,
0.013236510567367077,
0.0047636996023356915,
0.008923003450036049,
0.006976023782044649,
-0.02089736796915531,
-0.01789148896932602,
0.008528496138751507,
0.009201805107295513,
-0.026540931314229965,
-0.016969693824648857,
0.008541702292859554,
-0.01003393717110157,
-0.02493952587246895,
-0.010090387426316738,
0.04258568584918976,
-0.040604740381240845,
-0.006841039285063744,
-0.027326369658112526,
-0.039996303617954254,
0.016392601653933525,
0.02352946065366268,
-0.01149303000420332,
0.021418631076812744,
-0.005744672380387783,
0.04679489880800247,
-0.07967980206012726,
-0.04353943094611168,
-0.017455322667956352,
-0.03540901467204094,
0.011081094853579998,
-0.0349385030567646,
-0.04554365202784538,
-0.0009083106415346265,
0.05687014013528824,
0.010830762796103954,
-0.019550858065485954,
-0.07250578701496124,
-0.010013645514845848,
0.03922305628657341,
-0.010213091969490051,
-0.01844056136906147,
-0.02807631529867649,
-0.012059176340699196,
0.017940189689397812,
0.03281286731362343,
-0.038592785596847534,
-0.004310321528464556,
-0.000783517665695399,
0.011235330253839493
] |
<p>Given a wavefunction, $\psi(x)$, is it possible for $\psi$ to be singular at a point? Are there any rules against a wavefunctions having any singularities? For instance if </p>
<p>$$\psi(x) =\frac{\gamma(x)}{x},$$</p>
<p>where $\gamma$ is a continuous function of $x$. Is this a valid wave function?</p> | g4760 | [
0.019924750551581383,
-0.056564901024103165,
0.010102251544594765,
-0.014091656543314457,
0.04970090463757515,
0.04078948125243187,
0.022628681734204292,
0.016445336863398552,
-0.0716877281665802,
-0.005149949807673693,
0.009107793681323528,
0.01155091729015112,
-0.0034457051660865545,
-0.021112872287631035,
-0.034692395478487015,
-0.07079455256462097,
0.026848427951335907,
0.002513368846848607,
-0.014966359362006187,
0.015344318002462387,
-0.00852176547050476,
-0.021819405257701874,
0.05619620904326439,
-0.031262487173080444,
0.03930371254682541,
0.0474228709936142,
0.03120582364499569,
-0.022855961695313454,
0.038462311029434204,
0.0158704724162817,
-0.01520965900272131,
0.05690963193774223,
0.056463804095983505,
0.03341773897409439,
0.021241195499897003,
0.013265634886920452,
0.01885232888162136,
-0.031168201938271523,
0.013621049001812935,
-0.03301385045051575,
-0.01512815710157156,
0.02586279809474945,
-0.00854730885475874,
-0.031938813626766205,
-0.014240114018321037,
0.029132816940546036,
-0.025281285867094994,
0.011842925101518631,
0.013539259321987629,
-0.012677501887083054,
0.006432384718209505,
-0.023233549669384956,
-0.007999899797141552,
0.008588182739913464,
0.007440738845616579,
0.016126040369272232,
0.04938278719782829,
0.04542477801442146,
0.07949870824813843,
0.02071535587310791,
-0.018398091197013855,
0.01179380901157856,
0.09785143285989761,
0.02748771570622921,
0.006323403678834438,
-0.03936021029949188,
-0.0395757220685482,
-0.024217000231146812,
-0.04229003190994263,
-0.02017849124968052,
0.012494057416915894,
-0.05700278654694557,
-0.002442246535792947,
0.029621101915836334,
-0.029669709503650665,
0.03414975851774216,
-0.0010022965725511312,
-0.03922981396317482,
-0.04908514395356178,
0.011687500402331352,
0.007277625612914562,
-0.03753932565450668,
0.03421318903565407,
0.008504156954586506,
-0.028154201805591583,
-0.023474641144275665,
0.0017985383747145534,
-0.05571851506829262,
-0.0006678657955490053,
-0.0017240874003618956,
0.008892273530364037,
-0.0035254484973847866,
0.020791856572031975,
-0.004251615609973669,
0.028469853103160858,
-0.004664635751396418,
0.00946124829351902,
0.010366681963205338,
-0.04327045753598213,
0.028439341112971306,
0.03813673555850983,
0.019296903163194656,
0.032813213765621185,
0.04340836778283119,
-0.011406238190829754,
-0.03174611181020737,
0.004895863123238087,
0.010797030292451382,
-0.015252964571118355,
-0.08088531345129013,
0.026804247871041298,
0.02044522948563099,
-0.0192587710916996,
-0.00421973317861557,
-0.09249327331781387,
0.0062990509904921055,
0.009670790284872055,
-0.03561647981405258,
-0.0312504917383194,
0.09724609553813934,
0.01273402664810419,
0.017317814752459526,
0.01736338436603546,
0.013771302066743374,
-0.007962126284837723,
0.02823292836546898,
-0.050237931311130524,
0.026839718222618103,
0.028557932004332542,
-0.02170685864984989,
0.003863615682348609,
0.05254882946610451,
-0.0695548877120018,
-0.008659880608320236,
0.0021638439502567053,
0.004278816282749176,
0.03445752337574959,
0.011345498263835907,
0.032459408044815063,
0.0008396206540055573,
0.046018172055482864,
-0.02758774720132351,
0.012592421844601631,
0.019877813756465912,
-0.007239936850965023,
-0.05867275968194008,
0.01968858204782009,
0.009284235537052155,
0.007455895189195871,
0.023034529760479927,
-0.05757148563861847,
0.07841524481773376,
-0.017462072893977165,
-0.012056409381330013,
0.036322128027677536,
0.004263030830770731,
-0.009185729548335075,
0.04242249205708504,
-0.03019794262945652,
-0.03085615299642086,
0.03442211076617241,
0.03365270420908928,
0.04432779178023338,
0.024410968646407127,
-0.05721789225935936,
-0.01571296527981758,
-0.030270325019955635,
-0.018664946779608727,
-0.04790462926030159,
-0.059676963835954666,
-0.05890510976314545,
0.04588265344500542,
0.02471422776579857,
-0.010219239629805088,
0.07045768201351166,
-0.020195061340928078,
-0.07680381089448929,
-0.014823086559772491,
0.02223728969693184,
-0.01655443012714386,
-0.023299716413021088,
-0.04321694001555443,
-0.03729395568370819,
-0.07148710638284683,
-0.010456742718815804,
0.016543984413146973,
-0.01505542453378439,
-0.03424369543790817,
-0.10515180975198746,
0.04952017962932587,
-0.026143385097384453,
-0.013430026359856129,
-0.031836237758398056,
0.06905975192785263,
0.03138173371553421,
0.02662135474383831,
0.02643948793411255,
-0.01801619678735733,
0.013397947885096073,
0.0476231686770916,
-0.013549471274018288,
0.08570516854524612,
0.07524465024471283,
0.016965050250291824,
0.0332476906478405,
0.02406058833003044,
-0.01867498829960823,
-0.032742343842983246,
0.04818275198340416,
-0.009541506879031658,
0.05950627475976944,
-0.056371696293354034,
0.009069598279893398,
0.006867368705570698,
-0.010501171462237835,
-0.04489403963088989,
-0.04884905740618706,
-0.012855920940637589,
-0.01554842758923769,
-0.021048299968242645,
0.006026549264788628,
0.05555151775479317,
0.01254300493746996,
0.06429348140954971,
-0.004286865703761578,
-0.004637969192117453,
-0.06587516516447067,
-0.04041235148906708,
0.006701427511870861,
-0.017676644027233124,
-0.09393539279699326,
-0.030973413959145546,
0.025093378499150276,
-0.038818731904029846,
-0.0010618639644235373,
0.022152157500386238,
-0.06071968004107475,
-0.049709707498550415,
0.03991621360182762,
-0.036317791789770126,
0.002892317483201623,
-0.06507927179336548,
-0.007175331469625235,
0.007950039580464363,
0.012766350992023945,
-0.03886803239583969,
-0.048314571380615234,
0.056283872574567795,
0.01719338446855545,
-0.02157881110906601,
-0.008082887157797813,
0.0027080546133220196,
-0.03490025922656059,
0.09933042526245117,
-0.04531845077872276,
-0.0826675072312355,
-0.021754862740635872,
0.05806337296962738,
-0.041532255709171295,
-0.026455044746398926,
-0.033672165125608444,
-0.001733485609292984,
0.023365139961242676,
0.011518377810716629,
-0.016187937930226326,
0.05000414699316025,
0.004443900194019079,
0.024825775995850563,
-0.009979686699807644,
0.01696350798010826,
0.03345724195241928,
0.07558438926935196,
0.07633604854345322,
0.060388389974832535,
0.004921713378280401,
0.0002999378484673798,
0.005480749532580376,
0.012602996081113815,
0.028191814199090004,
-0.011037341319024563,
-0.08292652666568756,
-0.018452083691954613,
-0.01598956622183323,
0.005481896921992302,
0.04851740226149559,
-0.04382731765508652,
0.013923618011176586,
0.008306099101901054,
-0.001928600948303938,
-0.01833263970911503,
0.02052687481045723,
0.03919230401515961,
0.02607150189578533,
-0.0043219332583248615,
-0.02038884162902832,
-0.01627965457737446,
-0.0477919727563858,
-0.04886328801512718,
0.015899747610092163,
0.05542489141225815,
0.0712921991944313,
-0.010068138130009174,
-0.0401286818087101,
0.021417194977402687,
0.038514889776706696,
-0.007786597590893507,
-0.0289339367300272,
0.0027548044454306364,
-0.04594175145030022,
0.004164158366620541,
0.04781452938914299,
0.09006695449352264,
0.0027821462135761976,
0.002923979191109538,
-0.04891880601644516,
0.02736511453986168,
-0.0383349247276783,
-0.024563554674386978,
-0.03020923212170601,
0.038015615195035934,
-0.005195546429604292,
-0.03212255984544754,
-0.06579091399908066,
-0.0010545223485678434,
0.10190781205892563,
0.053144317120313644,
-0.02736935205757618,
0.02711901254951954,
-0.07211180776357651,
0.02941013127565384,
0.026781704276800156,
-0.03230404853820801,
0.006965166423469782,
-0.0005987251061014831,
0.01533381175249815,
0.007463449612259865,
-0.005154265556484461,
0.031687140464782715,
0.02035965397953987,
0.04812922701239586,
0.03197285532951355,
0.012831838801503181,
-0.016132716089487076,
-0.06099984049797058,
0.006469912361353636,
0.024762840941548347,
-0.0008624093607068062,
0.07346756011247635,
0.061121176928281784,
0.01195131242275238,
-0.07720626890659332,
-0.036084797233343124,
0.015901023522019386,
-0.0036782335955649614,
0.04948047176003456,
-0.04075070098042488,
0.03868535906076431,
0.014081277884542942,
-0.0019123118836432695,
-0.025282006710767746,
0.0007499628118239343,
-0.030906444415450096,
0.06364189088344574,
-0.04104600474238396,
0.011925077997148037,
-0.06793268769979477,
0.020302705466747284,
0.044863805174827576,
0.016587363556027412,
0.020405620336532593,
0.04704524204134941,
-0.004652922973036766,
0.05534273386001587,
0.0016615582862868905,
-0.026218021288514137,
-0.02310987561941147,
-0.030230656266212463,
0.0164649561047554,
-0.033873822540044785,
0.046491190791130066,
-0.013987733982503414,
-0.03450798615813255,
0.001124570262618363,
-0.04487481713294983,
-0.011727320961654186,
0.04012870788574219,
-0.03856480121612549,
-0.00142955151386559,
0.09060753136873245,
0.006932490970939398,
0.07251305878162384,
-0.05804964527487755,
-0.01616779901087284,
0.041017793118953705,
0.03170793130993843,
-0.005376191809773445,
-0.007490820251405239,
-0.0694727972149849,
-0.06886013597249985,
0.08022364974021912,
0.015238301828503609,
-0.006699192337691784,
0.003472803393378854,
-0.019638705998659134,
0.02457689680159092,
0.012824591249227524,
0.008044169284403324,
-0.007916639558970928,
0.013991814106702805,
-0.08091974258422852,
0.007580775301903486,
-0.05309423804283142,
-0.0020122311543673277,
-0.06518825143575668,
-0.039060283452272415,
-0.026200655847787857,
0.023818239569664,
-0.0667307898402214,
0.009512820281088352,
0.006688649300485849,
0.012886123731732368,
-0.043035294860601425,
0.03693877160549164,
0.022091135382652283,
0.028096001595258713,
0.04021241143345833,
0.10595019906759262,
-0.02075251005589962,
-0.04336346313357353,
0.0005621187156066298,
0.010986898094415665,
-0.025725118815898895,
-0.004215370398014784,
0.021936824545264244,
0.02076953463256359,
0.005148747470229864,
-0.0794597715139389,
-0.07211390137672424,
0.018063876777887344,
0.0219731442630291,
0.01262613758444786,
-0.02940891869366169,
0.05058698356151581,
0.015908731147646904,
-0.010225364938378334,
0.004838378168642521,
-0.061015259474515915,
-0.022106315940618515,
-0.009446460753679276,
0.009221436455845833,
-0.012919839471578598,
-0.031496092677116394,
-0.028364362195134163,
-0.053969211876392365,
0.002407838823273778,
-0.03866351395845413,
-0.032323434948921204,
-0.006838171277195215,
-0.035039033740758896,
-0.010593770071864128,
0.013894738629460335,
-0.09903686493635178,
0.011453897692263126,
0.013105284422636032,
0.03248290717601776,
0.031255804002285004,
-0.08915838599205017,
0.005582822952419519,
-0.05727511644363403,
-0.009504666551947594,
-0.01100578811019659,
0.002808873075991869,
0.031604595482349396,
0.003695241641253233,
0.010223962366580963,
-0.05018366500735283,
0.0038258570712059736,
-0.01562095619738102,
-0.04170374199748039,
-0.04323478043079376,
0.024257855489850044,
-0.06853197515010834,
-0.004188475664705038,
-0.007812783122062683,
-0.007733982056379318,
-0.033461976796388626,
-0.004459983669221401,
0.0101699223741889,
-0.019994182512164116,
-0.022596528753638268,
0.026358749717473984,
0.027446750551462173,
0.015904197469353676,
0.02964305318892002,
-0.007279089652001858,
-0.022905316203832626,
-0.005144258961081505,
-0.018281368538737297,
-0.0332372710108757,
0.016731655225157738,
-0.014375807717442513,
-0.026687799021601677,
-0.006924958899617195,
-0.016649894416332245,
0.003782637882977724,
0.0339556448161602,
0.01552970614284277,
-0.026244718581438065,
-0.027595501393079758,
0.010606751777231693,
0.019215604290366173,
-0.020854417234659195,
0.01757204346358776,
0.029295634478330612,
0.0004131921159569174,
-0.027120009064674377,
-0.04444815218448639,
-0.008595556952059269,
-0.03336176648736,
-0.07149123400449753,
0.042428359389305115,
0.012385583482682705,
-0.024179456755518913,
-0.05087241902947426,
0.04113951697945595,
0.00042511624633334577,
-0.027458656579256058,
-0.05532815679907799,
0.014250431209802628,
0.056112539023160934,
0.045815471559762955,
-0.0009739380911923945,
-0.023937204852700233,
0.0040936339646577835,
-0.06016279384493828,
-0.013213635422289371,
-0.015596636570990086,
0.0013126786798238754,
0.022578539326786995,
-0.005322115495800972,
-0.01435491070151329,
0.028897346928715706,
-0.05317002162337303,
0.037434838712215424,
-0.03129018470644951,
0.027516378089785576,
0.009304879233241081,
0.0300760455429554,
0.0074506658129394054,
-0.034029822796583176,
-0.01827206462621689,
-0.00921683106571436,
-0.09071347862482071,
-0.014471047557890415,
0.01537629310041666,
0.0425756573677063,
-0.005540996324270964,
-0.01794452965259552,
0.01340662594884634,
-0.052374765276908875,
0.0091816745698452,
-0.0022916505113244057,
0.03352201357483864,
-0.02564159221947193,
-0.025220563635230064,
-0.07261262834072113,
-0.015423016622662544,
-0.028974372893571854,
-0.020306838676333427,
0.010333696380257607,
-0.019298849627375603,
0.04265068098902702,
-0.010374129749834538,
0.011051865294575691,
-0.044851772487163544,
-0.024024175480008125,
0.025381503626704216,
0.025197351351380348,
0.018946697935461998,
-0.008826709352433681,
-0.0383831262588501,
0.1076890230178833,
0.04505768418312073,
-0.05639020353555679,
-0.029740503057837486,
0.012044212780892849,
-0.012676306068897247,
0.008892648853361607,
0.017861846834421158,
0.06826016306877136,
0.037761274725198746,
-0.03928970545530319,
-0.02349095791578293,
0.05458729341626167,
0.05383996292948723,
-0.013593805022537708,
0.001981436274945736,
0.01196938008069992,
0.0010104504181072116,
0.03504844009876251,
0.05601102486252785,
0.05099482461810112,
0.02131405659019947,
-0.003411809215322137,
-0.00542723061516881,
0.042880769819021225,
-0.01951512321829796,
0.04774579033255577,
-0.0027217718306928873,
0.024175837635993958,
0.014310596510767937,
0.0034225545823574066,
-0.023113468661904335,
-0.024740543216466904,
0.027767185121774673,
-0.08826114237308502,
0.007524183019995689,
0.033418938517570496,
-0.037617191672325134,
0.00090022012591362,
0.09224921464920044,
-0.016618525609374046,
-0.0414821095764637,
0.003413901897147298,
0.04133693128824234,
-0.011399638839066029,
0.0018542787292972207,
-0.0005199705483391881,
0.02032429166138172,
0.00589653430506587,
0.010325483977794647,
0.006557549815624952,
-0.055829428136348724,
-0.029229212552309036,
-0.05324118211865425,
0.04190468788146973,
-0.03942043334245682,
-0.06016397103667259,
0.05893053486943245,
-0.00814784038811922,
0.043919749557971954,
0.03960863873362541,
0.08189140260219574,
0.010377665981650352,
-0.07262655347585678,
0.04290049523115158,
0.04560212790966034,
0.008322757668793201,
-0.10016461461782455,
0.025535138323903084,
0.07785455137491226,
0.0071652112528681755,
-0.04695003479719162,
0.014384145848453045,
-0.02598528377711773,
0.020141467452049255,
-0.023458722978830338,
-0.04255662113428116,
-0.014025441370904446,
-0.01848376728594303,
0.06427303701639175,
0.02941960096359253,
0.01179762464016676,
-0.0019244279246777296,
0.010608866810798645,
0.05104130506515503,
0.011290228925645351,
-0.04290053993463516,
-0.04301588982343674,
-0.04900962859392166,
0.04184825345873833,
-0.013821580447256565,
-0.046408478170633316,
-0.039351917803287506,
0.007735441438853741,
-0.02971048466861248,
0.013879545964300632,
0.05192936956882477,
0.04189647361636162,
0.0064781950786709785,
-0.002019451465457678,
-0.00833650678396225,
0.006633270066231489,
0.013376990333199501,
-0.022435136139392853,
0.03137681633234024,
0.01924506016075611,
-0.0343424454331398,
-0.010438980534672737,
0.014912771992385387,
-0.015967687591910362,
-0.028299830853939056,
-0.004377357661724091,
-0.03590589389204979,
0.003128346288576722,
-0.03451316058635712,
0.06764703243970871,
0.06113024428486824,
-0.04133839160203934,
0.02490173652768135,
0.018817048519849777,
-0.002317421603947878,
0.014963604509830475,
-0.023486487567424774,
0.03643784672021866,
0.0030520432628691196,
-0.0021837831009179354,
-0.0419788584113121,
-0.009120260365307331,
0.013752121478319168,
0.06454674154520035,
-0.014849204570055008,
-0.01887626014649868,
0.06489036232233047,
0.03046228736639023,
-0.0049044168554246426,
-0.03761536255478859,
0.0027587527874857187,
0.10396868735551834,
-0.07280221581459045,
-0.021156834438443184,
0.021941406652331352,
-0.05140575394034386,
-0.025172676891088486,
0.022073056548833847,
0.026027251034975052,
0.0047149951569736,
-0.013212506659328938,
0.015481841750442982,
0.040274083614349365,
-0.03669540956616402,
0.03635924309492111,
-0.011828680522739887,
0.007975655607879162,
-0.06169101968407631,
-0.02627907134592533,
-0.0019047802779823542,
-0.029491666704416275,
0.016805652529001236,
0.03892889246344566,
-0.007903937250375748,
0.04115508869290352,
-0.024935441091656685,
-0.006745855323970318,
0.01141328178346157,
0.028895169496536255,
0.03767869621515274,
0.0007324363104999065,
0.04294908419251442,
0.030009731650352478,
0.004741281736642122,
0.05997488275170326,
0.011320743709802628,
0.061689697206020355,
-0.03689048811793327,
-0.024951985105872154,
-0.016707254573702812,
-0.007926248013973236,
0.04786928743124008,
-0.02554512396454811,
0.009586529806256294,
0.013991461135447025,
0.02378980815410614,
-0.018940644338726997,
-0.029163086786866188,
-0.023896539583802223,
0.05920366197824478,
-0.007843412458896637
] |
<p>I wonder which type of kicking may cause the ball to go a larger distance?
One way is kicking the ball when it is at rest and another is kicking a moving ball in the opposite direction.
If the ball goes farther in the second way,then what is the reason despite the fact that a moving ball will exert extra force to the player's leg?</p> | g4761 | [
0.026399970054626465,
0.0745655745267868,
-0.0018239835044369102,
0.02490893006324768,
0.021064450964331627,
0.0327904112637043,
0.03073905035853386,
0.05084287002682686,
-0.046416331082582474,
-0.02814388833940029,
-0.052212487906217575,
-0.06765024363994598,
0.025349464267492294,
-0.014946439303457737,
0.015506881289184093,
-0.02128245122730732,
0.05193740501999855,
-0.046241723001003265,
0.007515051402151585,
0.0612839013338089,
-0.013687842525541782,
0.07269575446844101,
0.047224801033735275,
-0.06721425801515579,
-0.01566142961382866,
-0.01046817097812891,
-0.029166150838136673,
-0.0007048119441606104,
-0.00385421235114336,
0.009108992293477058,
0.05862431973218918,
0.019012121483683586,
-0.01586461067199707,
-0.06199495866894722,
-0.004839966539293528,
0.01409243792295456,
0.011203395202755928,
-0.016007931903004646,
-0.012339962646365166,
0.028383975848555565,
-0.008709760382771492,
-0.041771210730075836,
-0.03372545912861824,
-0.011019706726074219,
0.026446955278515816,
-0.08180210739374161,
-0.027739787474274635,
0.03750983253121376,
-0.002505358774214983,
-0.0020977016538381577,
-0.0474373959004879,
-0.021828867495059967,
-0.0016096008475869894,
0.046402707695961,
0.030013158917427063,
0.011107134632766247,
-0.013927149586379528,
-0.03294390067458153,
0.029474405571818352,
0.012198192067444324,
-0.027648568153381348,
0.004225876182317734,
0.030222434550523758,
-0.04023221880197525,
0.004474865738302469,
-0.019217772409319878,
-0.011318587698042393,
-0.047421760857105255,
0.015847614035010338,
-0.02523346245288849,
0.0569755844771862,
-0.03949137404561043,
-0.025061100721359253,
-0.02989792637526989,
-0.005081573035567999,
-0.016534842550754547,
0.02884882315993309,
0.018233975395560265,
0.010330427438020706,
-0.047332148998975754,
0.021137824282050133,
-0.021766560152173042,
0.026320520788431168,
-0.06475905328989029,
0.04025321453809738,
0.02784198336303234,
-0.04746905341744423,
0.012595760636031628,
-0.045238833874464035,
-0.014867139048874378,
-0.03321528062224388,
-0.08593251556158066,
0.14267925918102264,
0.026129966601729393,
-0.13818229734897614,
-0.01791440322995186,
0.028618713840842247,
0.05429183319211006,
-0.008312591351568699,
-0.000007707601980655454,
-0.06169983372092247,
0.008119113743305206,
0.04067547619342804,
-0.00498982984572649,
0.014291636645793915,
-0.09584016352891922,
-0.012809610925614834,
-0.026338443160057068,
-0.06202620640397072,
0.014733992516994476,
-0.013827068731188774,
-0.04412083327770233,
-0.004959175828844309,
0.039858296513557434,
0.0018330375896766782,
-0.02882237732410431,
0.03961314260959625,
0.05711962282657623,
-0.013324996456503868,
0.015331597067415714,
-0.0038410292472690344,
-0.00843428261578083,
0.00818260945379734,
0.014210425317287445,
-0.049948498606681824,
0.03436689078807831,
-0.01088187750428915,
-0.025161975994706154,
-0.007572650909423828,
0.04262525960803032,
-0.03142702206969261,
0.06038900464773178,
-0.0013832609402015805,
-0.01871149055659771,
-0.010424789972603321,
0.008031168952584267,
-0.006241402588784695,
0.020708264783024788,
0.014185265637934208,
0.034135837107896805,
0.04598294198513031,
0.02480793371796608,
0.04347825050354004,
-0.035792022943496704,
-0.02487305738031864,
0.06252472847700119,
0.0012500440934672952,
0.02367614023387432,
-0.04430872201919556,
0.021542638540267944,
0.031194917857646942,
0.0014053127961233258,
0.004496091976761818,
0.0002157197886845097,
0.06864430755376816,
-0.023445481434464455,
-0.009843225590884686,
0.01194604579359293,
-0.03022710420191288,
0.06504928320646286,
0.033425264060497284,
-0.016414552927017212,
-0.0008351426804438233,
0.0240416768938303,
-0.032849229872226715,
0.041516341269016266,
-0.008303530514240265,
-0.007640081923455,
-0.07344452291727066,
-0.020075922831892967,
-0.057226087898015976,
-0.019071290269494057,
-0.014201425015926361,
0.029361624270677567,
0.04345174506306648,
0.01383829303085804,
0.010990428738296032,
-0.03824668005108833,
-0.0325387641787529,
-0.026564374566078186,
-0.0500214621424675,
-0.007106458302587271,
0.005538698751479387,
0.02895168401300907,
-0.00823567807674408,
-0.0033873626962304115,
0.0031872952822595835,
-0.03340477496385574,
-0.08147276937961578,
-0.015608496963977814,
0.0033137486316263676,
-0.05346711724996567,
-0.0004909758572466671,
-0.006133080925792456,
-0.006123202387243509,
-0.013130239211022854,
0.019013788551092148,
-0.025656577199697495,
-0.049636758863925934,
0.007368416991084814,
-0.08551239967346191,
-0.0017402246594429016,
-0.006093661766499281,
0.0012180767953395844,
0.0203553456813097,
-0.015312712639570236,
-0.023174308240413666,
0.028508542105555534,
0.06417705118656158,
-0.01911165378987789,
-0.012436876073479652,
-0.012253344058990479,
0.041125982999801636,
0.014594104140996933,
0.013589444570243359,
-0.013857661746442318,
-0.006501157768070698,
-0.003498911391943693,
-0.021090107038617134,
-0.0036559540312737226,
-0.014069714583456516,
0.0009877628181129694,
0.03449845686554909,
0.0000727307124179788,
-0.03150464966893196,
-0.03125699609518051,
-0.0030590028036385775,
0.0009296309435740113,
-0.03218080475926399,
0.059990882873535156,
0.006304523441940546,
-0.017887160181999207,
0.0456526018679142,
0.031461235135793686,
0.05263904482126236,
0.013804840855300426,
0.02674870751798153,
0.006305685266852379,
0.03772297874093056,
-0.0036023312713950872,
0.006026347633451223,
-0.037057504057884216,
0.048793528228998184,
-0.0503571555018425,
0.0318780355155468,
-0.021769072860479355,
0.051798105239868164,
0.005070911720395088,
0.024592259898781776,
0.024739131331443787,
0.055361002683639526,
0.05802914872765541,
-0.015338064171373844,
-0.050460878759622574,
-0.004590841941535473,
-0.03254881873726845,
-0.021522756665945053,
0.02211831696331501,
-0.05960845202207565,
-0.06099556386470795,
-0.009474091231822968,
-0.0201917365193367,
0.016495153307914734,
0.03607471287250519,
0.0032657156698405743,
0.05228209123015404,
0.007643403485417366,
0.03706112876534462,
-0.05062028765678406,
0.044003989547491074,
-0.007755584083497524,
0.07442312687635422,
-0.02397925779223442,
0.013391518034040928,
-0.011668686755001545,
0.009397665038704872,
0.03799930214881897,
-0.03580320253968239,
-0.056801460683345795,
-0.03092855028808117,
0.0052492558024823666,
0.08653930574655533,
-0.010327802039682865,
0.012561401352286339,
0.08146237581968307,
0.0006668231799267232,
0.012363246642053127,
-0.026242798194289207,
-0.026999812573194504,
-0.0482221320271492,
-0.008190781809389591,
0.005115273408591747,
0.08636859059333801,
-0.015657268464565277,
0.011718627996742725,
0.022515220567584038,
-0.03206530213356018,
-0.0377730093896389,
0.012549072504043579,
0.0022151051089167595,
0.0015602386556565762,
-0.0577910952270031,
-0.050521887838840485,
0.008247943595051765,
0.0211200974881649,
0.07241147756576538,
-0.005581554025411606,
-0.03861432522535324,
-0.02984822727739811,
0.0030791135504841805,
-0.010428410954773426,
0.036265138536691666,
-0.05981321632862091,
0.07124409079551697,
-0.04584475979208946,
-0.052979376167058945,
-0.033978819847106934,
0.06819362938404083,
0.017909694463014603,
0.02400161512196064,
-0.0029223563615232706,
-0.08857419341802597,
0.01753639243543148,
0.027256520465016365,
0.035902686417102814,
0.0560099259018898,
-0.05691695213317871,
0.007789899129420519,
-0.038801971822977066,
-0.023852776736021042,
-0.018011432141065598,
0.03739519789814949,
-0.0385284423828125,
-0.05256320908665657,
-0.025566155090928078,
0.0032061871606856585,
0.028389668092131615,
0.059069156646728516,
0.07475324720144272,
0.023382173851132393,
0.02880575880408287,
0.013517549261450768,
-0.004203294403851032,
-0.041318099945783615,
-0.03142775967717171,
0.06886927783489227,
0.003928082529455423,
0.008961389772593975,
0.0150340236723423,
0.009661935269832611,
0.00021651711722370237,
-0.05150754004716873,
0.008776157163083553,
0.0057238186709582806,
0.032295916229486465,
-0.02109583280980587,
-0.02365696243941784,
-0.021715514361858368,
-0.02151840180158615,
-0.035213910043239594,
-0.044027671217918396,
0.008807642385363579,
-0.014939253218472004,
0.015901707112789154,
-0.02983376942574978,
0.024201229214668274,
-0.03300895169377327,
-0.03554515168070793,
-0.05071497708559036,
0.0020719377789646387,
0.03698636218905449,
-0.01593038998544216,
-0.006096360273659229,
-0.000638915051240474,
0.04680626094341278,
0.03190680965781212,
0.06986255943775177,
-0.005953040439635515,
-0.051413681358098984,
0.009549010545015335,
0.021425306797027588,
0.09220892190933228,
0.024452975019812584,
0.01761271059513092,
-0.028588872402906418,
0.0198010616004467,
-0.0835554450750351,
0.033114735037088394,
0.02388901449739933,
0.004542521666735411,
0.015430937521159649,
0.015523579902946949,
-0.00849083811044693,
0.00657087005674839,
-0.02471461519598961,
0.026796353980898857,
-0.017961572855710983,
0.03690086677670479,
0.040325433015823364,
0.036504268646240234,
0.006323237903416157,
-0.017485953867435455,
-0.04245868697762489,
0.0304031353443861,
-0.07186722010374069,
-0.01855195127427578,
0.05684008076786995,
0.06904462724924088,
0.014948769472539425,
-0.01568404771387577,
-0.004672099836170673,
0.049876175820827484,
-0.03634592890739441,
-0.11400274187326431,
-0.006912983022630215,
0.03514257073402405,
-0.020355992019176483,
0.09704886376857758,
-0.042322978377342224,
0.004475418943911791,
0.03735119104385376,
-0.009444602765142918,
0.03739205002784729,
0.047776542603969574,
0.006939273793250322,
0.03246463090181351,
0.005603214260190725,
0.018933556973934174,
-0.03132552281022072,
0.016297761350870132,
-0.05875127762556076,
0.019214795902371407,
0.005297223571687937,
-0.01516421977430582,
-0.0010982365347445011,
-0.016630882397294044,
0.049839865416288376,
0.0422368049621582,
0.04325695335865021,
0.012369283474981785,
0.02428622730076313,
0.016825007274746895,
0.02420174330472946,
0.004292208701372147,
-0.01693468727171421,
0.03998501971364021,
0.011498279869556427,
-0.05775665119290352,
-0.038764942437410355,
-0.0805029347538948,
-0.00230324431322515,
0.0015605096705257893,
0.0003552598354872316,
0.00653822161257267,
0.027844494208693504,
0.015386570245027542,
-0.012928221374750137,
-0.03288019821047783,
-0.00016301835421472788,
-0.0010907091200351715,
0.012832189910113811,
-0.012512397952377796,
0.0340714231133461,
-0.011714854277670383,
0.017444156110286713,
-0.00523146940395236,
0.028317036107182503,
-0.04108976572751999,
-0.03276629373431206,
0.055555932223796844,
-0.013314316049218178,
0.04702426865696907,
0.016585934907197952,
0.05657263100147247,
0.02189544402062893,
-0.0002339156490052119,
-0.01081011351197958,
0.010980396531522274,
0.037010468542575836,
-0.08611664921045303,
-0.013811420649290085,
-0.005636506713926792,
0.0052572316490113735,
-0.07822657376527786,
-0.02193072997033596,
0.02024693228304386,
0.01572745107114315,
0.0386902280151844,
0.11175917088985443,
0.016355738043785095,
0.10376982390880585,
-0.016356205567717552,
-0.0024222168140113354,
0.018795017153024673,
-0.04576864466071129,
0.030169187113642693,
0.004252653568983078,
0.029443727806210518,
-0.010848562233150005,
-0.03297119215130806,
-0.001138351857662201,
-0.01163646299391985,
-0.0005966369062662125,
-0.04351136088371277,
0.018637225031852722,
-0.0008247586665675044,
0.0151216397061944,
-0.0029768510721623898,
-0.0644252747297287,
-0.01599186472594738,
-0.0408005565404892,
0.023042308166623116,
0.008986474946141243,
-0.04045805707573891,
0.03245332092046738,
-0.009970058687031269,
0.04400712996721268,
0.030046097934246063,
0.030448155477643013,
0.05586327612400055,
0.04849929362535477,
-0.0907152071595192,
0.029344310984015465,
-0.04642133787274361,
-0.046369001269340515,
0.02053193561732769,
-0.043746139854192734,
0.009578275494277477,
0.019123073667287827,
-0.016320420429110527,
0.01813218742609024,
0.03201702982187271,
0.07132162898778915,
0.000160402778419666,
-0.07887722551822662,
-0.07407666742801666,
-0.007502890191972256,
-0.004441994242370129,
-0.02138460800051689,
-0.07424008846282959,
0.004257614724338055,
-0.017961673438549042,
-0.0008601020090281963,
0.14973708987236023,
0.02303876355290413,
-0.02419765666127205,
-0.03371359407901764,
-0.050868529826402664,
0.07727938145399094,
-0.03233848139643669,
-0.02517799660563469,
0.05115713179111481,
-0.07210345566272736,
0.0018526245839893818,
0.004867454059422016,
0.010451902635395527,
0.0028191644232720137,
0.026632871478796005,
0.01277918741106987,
-0.048750653862953186,
-0.052928391844034195,
-0.05840776860713959,
0.02873557060956955,
-0.028136475011706352,
0.02968752197921276,
-0.0549200065433979,
-0.0440441370010376,
-0.020619096234440804,
0.05590379238128662,
0.023907901719212532,
0.007910956628620625,
-0.014562247321009636,
-0.00618892814964056,
0.06767401099205017,
0.04408257082104683,
0.01885026879608631,
0.02594837360084057,
-0.009699506685137749,
-0.04887375608086586,
0.040713150054216385,
-0.03834794461727142,
0.03370453417301178,
-0.04949966073036194,
-0.012773117050528526,
-0.0020221383310854435,
0.06067005544900894,
-0.022610269486904144,
-0.0018808894092217088,
0.05227586254477501,
-0.033726900815963745,
-0.04509945213794708,
0.010409040376543999,
-0.022242704406380653,
-0.019512513652443886,
-0.017399106174707413,
-0.0012606213567778468,
-0.0010985475964844227,
0.0007726511685177684,
-0.04651198163628578,
0.008784950710833073,
0.013927091844379902,
0.031936731189489365,
0.07275497168302536,
-0.023437228053808212,
0.027693593874573708,
0.08307615667581558,
-0.035383082926273346,
0.04373890161514282,
0.027817627415060997,
-0.0005634613335132599,
-0.049208901822566986,
0.031254880130290985,
0.0024171413388103247,
0.016449445858597755,
-0.028196463361382484,
-0.007496809121221304,
-0.003551421221345663,
-0.07113669812679291,
-0.03990267589688301,
-0.008086340501904488,
0.0037892821710556746,
-0.022718360647559166,
-0.015251880511641502,
0.015027318149805069,
0.006155151873826981,
-0.006609692703932524,
-0.039312075823545456,
0.011066940613090992,
-0.03493639826774597,
0.012089230120182037,
-0.003610041690990329,
-0.007923479191958904,
-0.045292653143405914,
0.05008210241794586,
0.008555411361157894,
-0.0044752564281225204,
-0.025117410346865654,
0.03174011781811714,
-0.02478623203933239,
0.047378651797771454,
0.0038429182022809982,
0.00301548233255744,
-0.026654042303562164,
-0.006541457027196884,
-0.0031731415074318647,
0.021495476365089417,
0.038042500615119934,
0.040240027010440826,
0.025867795571684837,
0.039715882390737534,
-0.062415916472673416,
-0.022158779203891754,
-0.06954512000083923,
0.006222615949809551,
-0.05105527490377426,
0.022239767014980316,
-0.03201930597424507,
-0.01459591370075941,
0.0007765987538732588,
0.0020331181585788727,
-0.008198553696274757,
-0.04918383061885834,
0.003932492341846228,
0.024847377091646194,
-0.016467364504933357,
0.03669898957014084,
0.005098011344671249,
-0.002829261589795351,
-0.041200537234544754,
0.023646870627999306,
0.039280228316783905,
-0.06883107870817184,
0.014045702293515205,
-0.03933871164917946,
-0.012048901058733463,
-0.022701026871800423,
0.006344708148390055,
0.012306490913033485,
-0.02646772190928459,
-0.013338712975382805,
-0.010682923719286919,
0.053982097655534744,
-0.005891166161745787,
-0.009802795015275478,
-0.03603769466280937,
-0.013542884960770607,
0.011897512711584568,
-0.017540886998176575,
-0.015633367002010345,
-0.007870125584304333,
0.04267973452806473,
-0.004335940349847078,
-0.024695690721273422,
0.08209587633609772,
0.01260287780314684,
0.02136112004518509,
-0.01372409425675869,
0.016976812854409218,
-0.00556722329929471,
-0.02761980891227722,
-0.02030579373240471,
0.009152786806225777,
0.017647767439484596,
-0.04007509723305702,
0.03157516196370125,
0.015314193442463875,
-0.016572745516896248,
0.018313439562916756,
-0.053169287741184235,
-0.03411675617098808,
0.024730781093239784,
0.009700785391032696,
0.02494669519364834,
0.028356678783893585,
-0.03077935054898262,
0.03521272540092468,
0.012603197246789932,
0.0234699584543705,
0.006151392124593258,
-0.02279062196612358,
-0.012772875837981701,
0.05053144693374634,
0.011082506738603115,
-0.05267563462257385,
-0.0718790590763092,
-0.01879841461777687,
-0.00855125579982996,
-0.002103661885485053,
-0.027777930721640587,
0.017036661505699158,
0.010004770942032337,
-0.06398674845695496,
0.0017260877648368478,
-0.023714158684015274,
-0.02282450534403324,
-0.0085286321118474,
-0.03986180201172829,
0.03339610621333122,
0.01520893257111311,
0.005911634303629398,
0.002538687316700816,
-0.018883734941482544,
0.03285510092973709,
0.02378719672560692,
0.03026529960334301,
-0.06471671164035797,
0.04156904295086861,
0.06640474498271942,
0.058261431753635406,
0.034532032907009125,
0.06061024218797684,
0.028276976197957993,
-0.038940656930208206,
0.03916112706065178,
-0.00421606469899416,
0.04594810679554939,
-0.06732606142759323,
0.03595653921365738,
-0.011520377360284328,
-0.055189043283462524,
-0.00290648709051311,
0.04618870094418526,
0.023175032809376717,
-0.06899019330739975,
0.020508695393800735,
-0.002646327717229724,
-0.059936050325632095,
-0.015506886877119541
] |
<p>I have recently just begun studying cosmology. I have a background in physics. I would like a link to download video resources on Stephan Hawking's theories on physics and/or cosmology that have not been proved wrong.</p> | g98 | [
0.03390655666589737,
0.0832396075129509,
0.005372127518057823,
0.012007737532258034,
-0.020206423476338387,
0.0386909581720829,
-0.00399760389700532,
-0.024047289043664932,
-0.012421171180903912,
-0.024378910660743713,
0.05534486100077629,
-0.05310828238725662,
0.041206251829862595,
0.058630019426345825,
-0.03400840610265732,
0.018218934535980225,
0.043353088200092316,
0.038581833243370056,
-0.023860562592744827,
0.03138498216867447,
-0.0009489951771683991,
-0.0008838502108119428,
0.05040103942155838,
-0.014211323112249374,
-0.04565069451928139,
-0.01585589349269867,
-0.018351634964346886,
-0.015641529113054276,
-0.02029978483915329,
-0.0363508015871048,
0.0422925166785717,
0.004183595534414053,
-0.02593730017542839,
-0.05681615322828293,
-0.004353146068751812,
0.010791192762553692,
0.0405857153236866,
-0.038463857024908066,
0.009240119718015194,
-0.009816033765673637,
0.02870621345937252,
-0.0356232114136219,
0.060426510870456696,
0.0179121196269989,
-0.0032920269295573235,
-0.005758842919021845,
-0.01774054579436779,
0.025119217112660408,
0.02591322548687458,
0.008024884387850761,
-0.03783508762717247,
0.05781884491443634,
0.09623850136995316,
0.008250070735812187,
-0.027292072772979736,
-0.016522448509931564,
0.02353801019489765,
-0.010186849161982536,
0.05862753093242645,
-0.016933409497141838,
0.030923228710889816,
0.047217532992362976,
0.0741189643740654,
-0.016835231333971024,
0.032041341066360474,
0.055160291492938995,
-0.02239251881837845,
-0.0038428595289587975,
0.017353657633066177,
0.013688731007277966,
0.05650939792394638,
-0.03226650878787041,
0.028823036700487137,
0.04562101140618324,
-0.03727952390909195,
0.019940348342061043,
0.01795407198369503,
0.051843415945768356,
-0.012509424239397049,
-0.00712303351610899,
-0.023785805329680443,
-0.03165280073881149,
-0.03137640282511711,
-0.05541562661528587,
0.13103073835372925,
-0.014983623288571835,
-0.05356043949723244,
0.05648089945316315,
0.017466329038143158,
-0.009827736765146255,
-0.00887981615960598,
0.0400802306830883,
0.028990978375077248,
-0.04631190001964569,
0.035898607224226,
-0.010117476806044579,
-0.06725712865591049,
0.03282102569937706,
0.0010287616169080138,
-0.002907654270529747,
-0.11275198310613632,
0.022360527887940407,
0.05159086734056473,
-0.008753828704357147,
-0.0012480560690164566,
0.005913882050663233,
0.044791724532842636,
-0.04084908962249756,
-0.004333624616265297,
0.015147916972637177,
-0.039966486394405365,
0.0006449523498304188,
0.016520913690328598,
0.05734260752797127,
-0.015427333302795887,
-0.023660870268940926,
0.05163731798529625,
0.05529880151152611,
0.0025418708100914955,
0.026310836896300316,
0.02104550413787365,
0.03893129527568817,
0.010777585208415985,
0.04631352052092552,
-0.01725033111870289,
0.014677822589874268,
-0.0010058613261207938,
-0.0633249506354332,
0.01145698968321085,
0.015026761218905449,
0.018570225685834885,
-0.018215477466583252,
-0.03804098069667816,
0.04106278344988823,
0.015261564403772354,
-0.013164474628865719,
0.05504347383975983,
0.026868803426623344,
0.01656828075647354,
-0.0135915232822299,
0.009632552973926067,
0.0030476038809865713,
0.03666868433356285,
-0.03079906292259693,
-0.0158497616648674,
-0.03058992512524128,
-0.010267806239426136,
-0.03272295370697975,
-0.03437834233045578,
-0.01830071583390236,
0.011888963170349598,
0.036793164908885956,
0.002781870076432824,
0.037160877138376236,
-0.025569235906004906,
-0.03248220682144165,
0.011563366279006004,
-0.02527557499706745,
0.02162429690361023,
0.03130064159631729,
-0.010837872512638569,
-0.028151551261544228,
-0.01103551872074604,
0.02894691750407219,
0.04043891653418541,
0.043880611658096313,
-0.006235244683921337,
-0.04713074490427971,
-0.029273314401507378,
0.004317732993513346,
-0.04924917221069336,
0.05963016301393509,
0.02999800629913807,
0.06265304982662201,
0.02699061669409275,
0.015273972414433956,
-0.013564230874180794,
0.004182871431112289,
-0.009801781736314297,
-0.01046666968613863,
0.030536066740751266,
-0.004480621311813593,
-0.0023009630385786295,
-0.002570986282080412,
0.02665591612458229,
0.0055035375989973545,
-0.014681047759950161,
-0.022555680945515633,
-0.017531944438815117,
-0.00740219047293067,
0.01181891281157732,
0.041576486080884933,
-0.0011611940572038293,
-0.023645879700779915,
0.007437246851623058,
0.017906174063682556,
0.05903399735689163,
-0.027367791160941124,
0.03379267081618309,
-0.02156284637749195,
-0.02928663231432438,
-0.022531859576702118,
0.017506849020719528,
0.01844407431781292,
-0.020498409867286682,
-0.001165485824458301,
-0.02104414440691471,
0.016369713470339775,
0.02346254326403141,
0.008089893497526646,
-0.03102375566959381,
0.0028987706173211336,
0.040034160017967224,
0.005268327426165342,
-0.02216842584311962,
0.022486452013254166,
-0.049163807183504105,
-0.007667196914553642,
-0.006886234972625971,
0.011129535734653473,
0.03856649249792099,
-0.006973969284445047,
-0.0498519092798233,
0.026057712733745575,
0.015826597809791565,
-0.03323223814368248,
-0.009771648794412613,
-0.039539508521556854,
0.008490210399031639,
0.03278626874089241,
-0.04845069721341133,
0.02293175272643566,
-0.018858367577195168,
0.011966590769588947,
0.06411052495241165,
-0.027963919565081596,
0.03481806442141533,
-0.08267851918935776,
0.03294508904218674,
-0.027099469676613808,
-0.07089678198099136,
0.00012625727686099708,
-0.06459510326385498,
-0.009991474449634552,
0.024742333218455315,
-0.060868438333272934,
0.07931447774171829,
-0.08388157188892365,
-0.012723321095108986,
-0.033173128962516785,
0.054570522159338,
0.04191817343235016,
0.005952836945652962,
0.018040906637907028,
0.009529849514365196,
0.035324495285749435,
-0.0338040255010128,
0.06433677673339844,
0.0009506180649623275,
-0.03831477463245392,
0.03879516199231148,
-0.007198987063020468,
-0.029643546789884567,
-0.012553236447274685,
-0.006601753644645214,
-0.001240310026332736,
-0.05079781636595726,
-0.01793358102440834,
-0.04158162698149681,
-0.00346484431065619,
0.05412052571773529,
0.03529595211148262,
-0.0038303739856928587,
-0.016930682584643364,
-0.04404662549495697,
0.041245926171541214,
0.004340722691267729,
0.0034198781941086054,
0.03345726802945137,
-0.0054808566346764565,
-0.00015541791799478233,
0.006580669432878494,
-0.009052437730133533,
-0.0061144279316067696,
0.019806645810604095,
-0.04267042130231857,
-0.07354574650526047,
-0.01618417166173458,
0.02187122218310833,
-0.05533280596137047,
0.040134236216545105,
0.02509072795510292,
-0.00013628840679302812,
0.05163589492440224,
-0.08117718994617462,
0.022490687668323517,
-0.00024401301925536245,
0.009822515770792961,
-0.062288813292980194,
0.03733721375465393,
0.005743639077991247,
0.007181849796324968,
0.026867583394050598,
-0.033694107085466385,
-0.0072323027998209,
0.03819458559155464,
0.029532162472605705,
-0.01749473810195923,
0.05119660869240761,
0.012405147776007652,
0.048245757818222046,
0.012748693116009235,
0.06660101562738419,
0.04060053452849388,
0.010524827986955643,
0.045027442276477814,
0.021163463592529297,
0.017695890739560127,
0.038763828575611115,
-0.010903294198215008,
-0.028946517035365105,
0.0382392592728138,
-0.04871748760342598,
-0.01566358469426632,
0.025605449452996254,
0.060831572860479355,
-0.016530903056263924,
-0.07713238894939423,
-0.009169367142021656,
-0.0037902274634689093,
-0.03886120766401291,
-0.04011233150959015,
-0.006948013324290514,
-0.020353911444544792,
-0.03407100960612297,
-0.001510071218945086,
0.005504843313246965,
0.024908559396862984,
0.0201895572245121,
-0.008367085829377174,
-0.024317795410752296,
0.0031618322245776653,
-0.09286898374557495,
0.015098773874342442,
-0.07894846051931381,
0.011475851759314537,
0.001071292208507657,
0.03570157662034035,
0.016498230397701263,
-0.044962767511606216,
0.007566177286207676,
0.042414791882038116,
0.007392761297523975,
-0.013555532321333885,
-0.05726264789700508,
0.06833088397979736,
0.06131911650300026,
0.0057012708857655525,
0.04989468306303024,
-0.01799178309738636,
-0.04422956332564354,
-0.007953032851219177,
-0.060485318303108215,
-0.017461255192756653,
-0.04661635681986809,
0.017998458817601204,
-0.015020525082945824,
-0.04875880107283592,
0.03062870353460312,
-0.02464136853814125,
0.029471183195710182,
0.013872631825506687,
0.00030098724528215826,
0.02969382517039776,
-0.0463017039000988,
-0.023478282615542412,
0.005930266343057156,
0.03544936329126358,
0.003207060042768717,
-0.02019733004271984,
0.0163859985768795,
0.024376297369599342,
0.0369715690612793,
0.034022361040115356,
-0.028874225914478302,
-0.02727968618273735,
0.03956674039363861,
0.04180360585451126,
-0.0127855921164155,
-0.03727789223194122,
0.004589846357703209,
-0.04946804791688919,
-0.00317963445559144,
0.008318411186337471,
0.014082073234021664,
-0.01859232969582081,
-0.0482080839574337,
0.033708058297634125,
0.06867081671953201,
0.02235693484544754,
0.0070766666904091835,
0.01648179441690445,
0.018563784658908844,
0.004048659931868315,
-0.014621228910982609,
0.05523880198597908,
0.026623401790857315,
-0.029519911855459213,
-0.019181707873940468,
-0.004501237068325281,
0.06909818947315216,
-0.010912960395216942,
-0.005803503096103668,
-0.03005499206483364,
0.013437177985906601,
-0.06612003594636917,
-0.034795381128787994,
-0.12100893259048462,
0.06323926150798798,
0.0183329489082098,
0.0022355003748089075,
0.0004936052719131112,
-0.002720128046348691,
-0.03938503563404083,
-0.028458159416913986,
-0.004952568560838699,
0.00032958059455268085,
0.023913096636533737,
-0.04350709915161133,
0.03112717531621456,
0.018481897190213203,
-0.029514435678720474,
-0.08146514743566513,
0.06593839824199677,
-0.044102538377046585,
0.06171320378780365,
0.029986286535859108,
-0.014763443730771542,
-0.05616029351949692,
-0.06258510798215866,
0.01894463784992695,
-0.0030191361438483,
0.010912103578448296,
-0.03148539364337921,
-0.0426265113055706,
0.08991192281246185,
0.005980071146041155,
-0.01236701849848032,
-0.0509415939450264,
-0.013940144330263138,
0.00624369690194726,
-0.004078232683241367,
-0.005163212772458792,
0.026919646188616753,
-0.012065225280821323,
-0.013257982209324837,
-0.031317438930273056,
0.05192174017429352,
-0.010498292744159698,
-0.004446073900908232,
0.025906112045049667,
0.02733932062983513,
0.0518389455974102,
0.004701767582446337,
-0.05149063467979431,
-0.028562510386109352,
-0.05270446836948395,
0.02656097151339054,
0.03952811658382416,
-0.03301269933581352,
0.02313719503581524,
-0.01792578399181366,
0.015176218934357166,
-0.014527997002005577,
-0.04015825688838959,
-0.029551872983574867,
0.04037492722272873,
-0.010369147174060345,
0.0008235160494223237,
-0.040882404893636703,
0.04229428246617317,
0.017294757068157196,
-0.02342459186911583,
0.020754238590598106,
0.018551364541053772,
0.042983751744031906,
-0.06558999419212341,
0.021925605833530426,
0.010707316920161247,
-0.04150005057454109,
-0.007215697318315506,
-0.09828998893499374,
0.028396883979439735,
-0.027426110580563545,
-0.032129544764757156,
0.006078294478356838,
-0.01124488189816475,
-0.013877583667635918,
0.02417660318315029,
0.017177464440464973,
0.019035570323467255,
-0.02735288254916668,
0.0372990258038044,
-0.018348565325140953,
-0.00927977915853262,
0.01049383170902729,
0.04332969710230827,
-0.01592973992228508,
-0.05244015157222748,
-0.029291341081261635,
-0.012997513636946678,
0.08034271746873856,
0.026204105466604233,
0.04822082072496414,
0.03269744664430618,
0.004501168616116047,
0.0168303232640028,
0.005155864637345076,
0.048207104206085205,
0.004403752274811268,
-0.024372359737753868,
0.008602308109402657,
-0.006765339989215136,
0.05084151029586792,
-0.01704523153603077,
0.011892382055521011,
-0.020290952175855637,
-0.0052723633125424385,
0.03855922818183899,
-0.008091135881841183,
-0.02362571656703949,
0.00643286993727088,
0.014957664534449577,
-0.04599186033010483,
-0.01545772049576044,
0.021413447335362434,
-0.014203764498233795,
0.016542071476578712,
-0.019195521250367165,
-0.06525225192308426,
-0.044022273272275925,
-0.02959604002535343,
0.0016001947224140167,
-0.017727093771100044,
-0.016673965379595757,
0.07270938903093338,
-0.021257344633340836,
0.017095068469643593,
0.020694661885499954,
-0.11042702198028564,
-0.07306472212076187,
-0.018984807655215263,
-0.02147933468222618,
-0.02333284728229046,
-0.022696925327181816,
0.03783918544650078,
0.01702636480331421,
0.00337054836563766,
-0.05136049538850784,
0.01481541059911251,
-0.025673145428299904,
0.013034442439675331,
0.033686310052871704,
0.02069140039384365,
-0.06761500984430313,
-0.01966300792992115,
-0.018818052485585213,
-0.07719460129737854,
0.046708788722753525,
-0.027085360139608383,
-0.04892526566982269,
0.05085781589150429,
-0.03825046122074127,
0.007094795815646648,
-0.029255682602524757,
0.007016831077635288,
-0.000627029687166214,
-0.07924386858940125,
-0.0642300620675087,
-0.017551522701978683,
0.024477519094944,
-0.00163170020096004,
0.04621509090065956,
-0.024141786620020866,
-0.002474564826115966,
-0.02757026068866253,
-0.02991766855120659,
0.03145395591855049,
-0.05957595258951187,
0.024278167635202408,
0.047882307320833206,
-0.01430737879127264,
-0.03898036107420921,
-0.11228586733341217,
-0.029944447800517082,
-0.004480530507862568,
0.055399637669324875,
-0.015606718137860298,
-0.016233859583735466,
-0.005991322919726372,
-0.07447980344295502,
-0.05765533447265625,
0.07794459909200668,
0.00647438270971179,
0.007708514109253883,
0.027157116681337357,
-0.019368479028344154,
-0.0051687234081327915,
0.03399452194571495,
0.019818700850009918,
-0.028523653745651245,
-0.02472594752907753,
-0.016184713691473007,
0.02516557089984417,
-0.025444362312555313,
0.018141333013772964,
0.008116411976516247,
0.005582126323133707,
-0.029757926240563393,
-0.05848350748419762,
0.10237081348896027,
0.02621263824403286,
0.04163992032408714,
0.01419538538902998,
-0.013357923366129398,
0.021547745913267136,
0.021238483488559723,
-0.01941671222448349,
0.04502531513571739,
0.012300455942749977,
0.009076173417270184,
-0.0364292748272419,
0.032454706728458405,
-0.009057899937033653,
-0.07126187533140182,
0.11812092363834381,
0.03349430486559868,
0.02431158348917961,
-0.0002685144718270749,
0.028106993064284325,
-0.014501272700726986,
-0.015299085527658463,
0.04125204682350159,
0.0064728958532214165,
-0.008711698465049267,
-0.04609048739075661,
-0.030780382454395294,
-0.014813966117799282,
-0.03130786493420601,
-0.027585873380303383,
-0.03942783176898956,
-0.031131921336054802,
0.007817025296390057,
0.06695008277893066,
-0.05886470526456833,
0.014842337928712368,
-0.05359696224331856,
-0.012064353562891483,
0.024419227614998817,
-0.07142647355794907,
0.015014603734016418,
0.04135718196630478,
0.03395511582493782,
-0.0025836362037807703,
-0.007710304576903582,
0.037769533693790436,
0.0010426492663100362,
-0.025434771552681923,
-0.022799959406256676,
-0.007167236413806677,
0.03408646211028099,
0.02070218324661255,
-0.048302579671144485,
0.002770892344415188,
-0.09439130127429962,
-0.010597425512969494,
-0.06275834143161774,
0.03438428044319153,
0.011103187687695026,
-0.01705259270966053,
-0.05465727671980858,
0.02301263064146042,
-0.0022135754115879536,
0.046416543424129486,
0.0014603290474042296,
0.04968687891960144,
0.04170951992273331,
-0.016142463311553,
-0.01084126252681017,
0.01980830542743206,
-0.055605340749025345,
0.00865884032100439,
-0.025208471342921257,
-0.08779444545507431,
-0.028356265276670456,
0.002856425940990448,
0.08523914963006973,
-0.029482048004865646,
0.02413148805499077,
-0.005401059985160828,
0.02107364498078823,
-0.011360437609255314,
-0.09558544307947159,
0.0179427620023489,
-0.011548702605068684,
-0.016889100894331932,
0.037223003804683685,
-0.015609554946422577,
-0.06087745353579521,
0.04188220575451851,
0.04678736627101898,
-0.029470449313521385,
0.05115734413266182,
-0.014843547716736794,
0.010579569265246391,
-0.06433720886707306,
0.013158084824681282,
0.0010073056910187006,
-0.03419385477900505,
0.00793848093599081,
0.03475312143564224,
-0.041353534907102585,
-0.015962621197104454,
-0.010382012464106083,
-0.0036457921378314495,
0.009577126242220402,
-0.01739753596484661,
0.0010580777889117599,
-0.03027644194662571,
0.04331032931804657,
0.025532850995659828,
0.04528367519378662,
0.031753916293382645,
-0.07807579636573792,
-0.07507675141096115,
0.03272387385368347,
0.003045410383492708,
-0.041931699961423874,
0.04278229922056198,
-0.04022303968667984,
0.014100803062319756,
-0.015099874697625637,
0.04549897834658623,
-0.05235762149095535,
0.015352323651313782,
-0.04379364103078842,
0.035091474652290344,
0.029218850657343864,
0.07058248668909073,
-0.05432667210698128,
0.04067784547805786,
0.06776797026395798,
0.05972934141755104,
-0.018666448071599007,
-0.029200414195656776,
-0.019231019541621208,
-0.022531146183609962,
-0.026132497936487198,
0.032617803663015366,
0.045960649847984314,
0.06464508175849915,
-0.015527449548244476,
0.051077716052532196,
0.004731884691864252,
-0.008627534843981266,
0.036770809441804886,
0.027295999228954315,
-0.05503982678055763
] |
<p>Let's have the metric for a sphere:
$$
dl^{2} = R^{2}\left(d\psi ^{2} + sin^{2}(\psi )(d \theta ^{2} + sin^{2}(\theta ) d \varphi^{2})\right).
$$
I tried to calculate Riemann or Ricci tensor's components, but I got problems with it. </p>
<p>The Ricci curvature must be
$$
R_{ij}=\frac{2}{R^{2}}g_{ij}.
$$
But when I use definition of Ricci tensor, I can't turn the expression into the expression for the metric tensor</p>
<p>Maybe, there are siome hints, which can help?</p> | g4762 | [
-0.008587823249399662,
0.0025688516907393932,
-0.025524724274873734,
-0.043067947030067444,
0.029082760214805603,
-0.011054793372750282,
0.08841928094625473,
0.006553211249411106,
-0.027156660333275795,
-0.011636017821729183,
-0.024077244102954865,
0.04213859513401985,
0.05239119008183479,
-0.028340721502900124,
0.010325606912374496,
0.008463338948786259,
0.005348698701709509,
-0.035515014082193375,
0.019425470381975174,
-0.012304786592721939,
-0.06490442901849747,
-0.045724764466285706,
0.06510507315397263,
-0.03857092186808586,
0.014653632417321205,
-0.015303359366953373,
0.09742596745491028,
0.05000095069408417,
-0.060587573796510696,
0.021443884819746017,
0.008656969293951988,
0.042045172303915024,
0.022457145154476166,
-0.022389531135559082,
0.01721910387277603,
-0.00344394170679152,
0.03720987215638161,
0.0384673997759819,
0.0013894765870645642,
-0.020117592066526413,
0.015044325031340122,
-0.04641695320606232,
0.045689959079027176,
-0.018452826887369156,
0.027344482019543648,
0.036681193858385086,
-0.01146283932030201,
0.05918385088443756,
-0.049284886568784714,
-0.0026520341634750366,
0.006189197767525911,
0.020286008715629578,
0.025800133123993874,
-0.02228124439716339,
-0.014166800305247307,
0.004895601887255907,
-0.0032533968333154917,
-0.08787944912910461,
0.033173494040966034,
0.01947016455233097,
-0.014734315685927868,
-0.041772764176130295,
-0.03921249136328697,
0.022457772865891457,
0.03121386468410492,
-0.02804386056959629,
-0.01852451078593731,
-0.013153334148228168,
0.06964832544326782,
0.026730377227067947,
0.023848311975598335,
-0.044382207095623016,
0.0788787305355072,
0.005935430061072111,
-0.05983242765069008,
-0.00673337560147047,
0.028841836377978325,
0.010844326578080654,
0.00382810365408659,
-0.011767915450036526,
0.035893894731998444,
-0.004626416601240635,
0.03887620195746422,
0.00894690677523613,
0.07933565974235535,
0.03847422078251839,
-0.002761491807177663,
-0.009060346521437168,
-0.029442859813570976,
0.031331323087215424,
-0.007459296379238367,
0.01090216264128685,
0.02079034596681595,
-0.011085939593613148,
0.02638345956802368,
-0.029954835772514343,
-0.053940124809741974,
0.022014005109667778,
-0.027876829728484154,
-0.04164520651102066,
0.032785672694444656,
0.01899869181215763,
0.05733252689242363,
0.03312114626169205,
0.04194151982665062,
0.0210349690169096,
0.02186151035130024,
0.04594758152961731,
-0.0020574515219777822,
-0.05359771475195885,
-0.014765818603336811,
0.012038066983222961,
0.002134297974407673,
-0.02402924746274948,
-0.003924015909433365,
-0.044353678822517395,
0.047917481511831284,
-0.04228690639138222,
0.0239992905408144,
0.0947430431842804,
-0.0058922846801579,
0.019514724612236023,
0.020672719925642014,
0.03583928197622299,
0.014204592444002628,
-0.010988944210112095,
-0.003305603051558137,
0.010351786389946938,
0.08396502584218979,
-0.01282098051160574,
0.058751363307237625,
0.031587280333042145,
0.010143555700778961,
-0.025665028020739555,
-0.0565042607486248,
0.06792675703763962,
-0.020604955032467842,
-0.019619034603238106,
-0.06268269568681717,
-0.05193052440881729,
0.004671236500144005,
0.026220688596367836,
0.014235679991543293,
0.0257318913936615,
-0.04192793369293213,
0.007464750669896603,
-0.009074214845895767,
-0.07071176916360855,
-0.003247104585170746,
0.00848153792321682,
-0.0012258569477126002,
0.03030458465218544,
-0.038258716464042664,
0.016670038923621178,
0.024506157264113426,
-0.00891941413283348,
-0.000221715570660308,
-0.013733877800405025,
0.0038079796358942986,
0.015185374766588211,
0.03430771082639694,
0.0104901771992445,
0.053764618933200836,
-0.009924892336130142,
-0.010803286917507648,
0.051400940865278244,
-0.01189707312732935,
-0.021169785410165787,
-0.015133279375731945,
-0.07682446390390396,
-0.06139007583260536,
-0.00991512555629015,
-0.03306758403778076,
0.0046273753978312016,
-0.00987281184643507,
0.01357290055602789,
-0.054976485669612885,
0.020401477813720703,
-0.0005864769336767495,
0.05508934333920479,
-0.018503155559301376,
-0.06373997032642365,
0.013189388439059258,
-0.019975721836090088,
-0.006234432104974985,
-0.05477360263466835,
-0.002970322035253048,
-0.050055231899023056,
-0.022366268560290337,
-0.022832505404949188,
-0.03420925885438919,
0.05865367874503136,
0.06306007504463196,
0.11987454444169998,
0.039652660489082336,
0.018083015456795692,
0.041051290929317474,
-0.049643393605947495,
-0.011284837499260902,
0.10046783834695816,
-0.033089376986026764,
-0.03618235886096954,
0.01198534294962883,
0.007262073457241058,
-0.006514102686196566,
-0.03424201160669327,
-0.04704289510846138,
-0.0030395635403692722,
0.017157992348074913,
0.02126448228955269,
0.04418162256479263,
-0.029479485005140305,
0.007514866068959236,
-0.036430176347494125,
-0.004087212961167097,
0.04101753607392311,
-0.038105692714452744,
-0.03146200254559517,
-0.03663888946175575,
-0.0028148232959210873,
-0.0397479273378849,
0.01745842956006527,
0.04414985328912735,
-0.03516994044184685,
-0.013216511346399784,
0.03755277395248413,
-0.03269992396235466,
-0.00541900098323822,
0.029540248215198517,
-0.005548187531530857,
0.0071867601945996284,
-0.02171911671757698,
0.032077863812446594,
0.02783854678273201,
0.03247201070189476,
0.025612840428948402,
-0.05333952233195305,
0.017930597066879272,
0.03290513902902603,
-0.0024306366685777903,
-0.008080978877842426,
0.016507716849446297,
0.005472264252603054,
0.005386943928897381,
0.013505404815077782,
-0.03334528207778931,
0.018578479066491127,
0.03142434358596802,
-0.0251575019210577,
0.010923285037279129,
-0.0014685840578749776,
-0.025255152955651283,
-0.07395569980144501,
0.017396990209817886,
0.018779339268803596,
-0.024390235543251038,
0.01308688335120678,
0.031664811074733734,
-0.038588717579841614,
-0.058687224984169006,
-0.07331022620201111,
-0.016859902068972588,
0.013161331415176392,
0.07373904436826706,
-0.08859694004058838,
0.004445602651685476,
0.020180614665150642,
-0.0074808550998568535,
0.02539743483066559,
0.041431427001953125,
0.0017973121721297503,
0.027138954028487206,
0.009961990639567375,
0.04194727540016174,
-0.03294665738940239,
-0.024510085582733154,
-0.03564141318202019,
-0.0037340109702199697,
-0.004805575590580702,
0.006561387330293655,
0.013379454612731934,
0.023446138948202133,
-0.009302172809839249,
0.0422140434384346,
0.023285236209630966,
-0.04982611536979675,
-0.037878669798374176,
0.019533270969986916,
-0.005938937421888113,
0.027698347344994545,
0.0417189858853817,
0.0398998036980629,
-0.006202162243425846,
-0.04265201464295387,
-0.00472084479406476,
-0.0316937230527401,
0.020281441509723663,
-0.040491584688425064,
-0.002752006519585848,
0.05838637426495552,
0.04366946965456009,
-0.0017579004634171724,
0.047441817820072174,
-0.08659059554338455,
-0.02770521678030491,
-0.022184552624821663,
-0.013487746007740498,
-0.07883552461862564,
0.029306868091225624,
-0.04353177919983864,
0.04229073226451874,
-0.023857470601797104,
0.029886698350310326,
0.010232169181108475,
-0.012122026644647121,
0.006307442672550678,
-0.02260582149028778,
-0.029100757092237473,
-0.06640652567148209,
0.029511380940675735,
-0.00391801493242383,
-0.04058971628546715,
-0.014816214330494404,
0.03345485404133797,
0.011480249464511871,
0.02946079522371292,
-0.047264453023672104,
0.031132180243730545,
-0.0009493986144661903,
-0.03856281563639641,
-0.01460203155875206,
-0.012312542647123337,
0.006539099384099245,
0.021672343835234642,
-0.07970595359802246,
-0.008841772563755512,
-0.07939828932285309,
-0.009891943074762821,
0.03254346922039986,
-0.02061491087079048,
-0.02173980325460434,
-0.006655822042375803,
-0.02288222499191761,
0.0061395009979605675,
-0.028652960434556007,
0.012681218795478344,
-0.0027425410225987434,
-0.0247721616178751,
0.014581380411982536,
-0.0016856701113283634,
-0.04182200878858566,
-0.020558495074510574,
0.021899528801441193,
-0.021199829876422882,
-0.007402325049042702,
-0.01492580957710743,
0.09341741353273392,
0.04925407096743584,
-0.056754522025585175,
-0.010057282634079456,
0.022702379152178764,
-0.04018327593803406,
-0.039519574493169785,
0.014478066004812717,
0.002492299070581794,
-0.060138437896966934,
0.06964991241693497,
0.05407632887363434,
-0.04951862990856171,
0.019362114369869232,
0.04429471865296364,
0.040938470512628555,
-0.023898452520370483,
0.07193635404109955,
-0.02996082976460457,
-0.028313543647527695,
-0.07053667306900024,
-0.05053224042057991,
0.026429805904626846,
0.003632625797763467,
-0.010255885310471058,
0.029168816283345222,
0.0015459228307008743,
-0.003132198704406619,
0.006385419052094221,
-0.03259262442588806,
0.040949806571006775,
0.0106440344825387,
0.05308648943901062,
-0.05934172496199608,
-0.016026683151721954,
-0.04265668988227844,
-0.05101703479886055,
-0.015353376977145672,
0.011137314140796661,
-0.032731372863054276,
0.027730362489819527,
0.0739557221531868,
-0.02669418230652809,
0.037149544805288315,
-0.008860326372087002,
0.01390164066106081,
0.08187924325466156,
-0.003252647118642926,
-0.008668050169944763,
0.034450456500053406,
0.007523312233388424,
-0.022446004673838615,
0.04210381582379341,
0.013908522203564644,
0.00042254195432178676,
-0.019438952207565308,
0.06398991495370865,
-0.05428218096494675,
0.0388256199657917,
-0.006378981750458479,
0.0016375285340473056,
-0.035614367574453354,
-0.03435559943318367,
0.02409766986966133,
-0.06172380596399307,
-0.05811017006635666,
0.014718323014676571,
-0.01107399445027113,
0.036943890154361725,
0.07314189523458481,
0.048561450093984604,
-0.026410171762108803,
-0.05259355530142784,
-0.04530734568834305,
0.009113759733736515,
-0.0027302836533635855,
0.0023259788285940886,
-0.0010851025581359863,
-0.049675751477479935,
0.032939936965703964,
-0.023393236100673676,
0.023562103509902954,
-0.010409889742732048,
-0.01314387284219265,
0.02243073284626007,
0.02634853683412075,
0.007855530828237534,
-0.06808245927095413,
0.020423565059900284,
0.013459051959216595,
-0.0306899081915617,
-0.06170526519417763,
-0.037249255925416946,
0.015535043552517891,
0.006952465977519751,
-0.023541435599327087,
0.011931583285331726,
-0.02133941277861595,
0.025974709540605545,
-0.002811281941831112,
-0.037586603313684464,
0.03957820311188698,
-0.05612460896372795,
-0.016795745119452477,
-0.005529184825718403,
0.005288728047162294,
-0.01651466079056263,
-0.009991590864956379,
0.021770281717181206,
-0.01788775809109211,
-0.02107740193605423,
0.05586608499288559,
0.04143762215971947,
-0.023693324998021126,
-0.007212178315967321,
0.05253976210951805,
-0.04362687095999718,
-0.07229490578174591,
0.04685747250914574,
0.04762061685323715,
-0.03144458308815956,
0.009453569538891315,
0.0015287556452676654,
-0.02913319319486618,
-0.0345851331949234,
0.023908503353595734,
-0.029244612902402878,
0.0038877951446920633,
0.030902354046702385,
-0.03276490792632103,
-0.017442487180233,
-0.028718965128064156,
-0.021726995706558228,
-0.014294513501226902,
0.021501999348402023,
0.06473253667354584,
-0.016033770516514778,
-0.013591296970844269,
0.056738439947366714,
0.06133989244699478,
0.047867629677057266,
-0.045410413295030594,
-0.026376133784651756,
0.015941714867949486,
-0.040907736867666245,
0.03839145600795746,
0.010661480017006397,
-0.007707520853728056,
0.009918536990880966,
0.06676332652568817,
0.06039970740675926,
0.019366372376680374,
0.036400023847818375,
0.07082554697990417,
0.010441990569233894,
0.012569112703204155,
0.03656243905425072,
0.018020562827587128,
0.011956819333136082,
0.04764574393630028,
0.038438014686107635,
0.05054154247045517,
0.04009650647640228,
-0.03001883067190647,
0.008040476590394974,
-0.0386369451880455,
-0.01443983893841505,
-0.036028698086738586,
0.04184230789542198,
0.04032040387392044,
-0.018672339618206024,
-0.04329172149300575,
0.05508993938565254,
-0.005245054606348276,
-0.0045146034099161625,
-0.013445485383272171,
-0.06358545273542404,
-0.014756470918655396,
0.03597404435276985,
-0.02009180374443531,
-0.02534441091120243,
-0.01987268216907978,
0.06608392298221588,
0.010868411511182785,
-0.05156191065907478,
0.014241836965084076,
0.036801014095544815,
0.02111019566655159,
-0.05855318903923035,
0.03396452218294144,
0.03053288348019123,
0.01055052038282156,
0.006477056071162224,
0.0029271061066538095,
-0.015545417554676533,
0.01039895135909319,
0.044329121708869934,
-0.037584058940410614,
0.03037882409989834,
-0.015136178582906723,
-0.0211124699562788,
-0.020544975996017456,
-0.03388441354036331,
0.010533886961638927,
0.05929228290915489,
-0.037129901349544525,
-0.011588635854423046,
0.05760005861520767,
-0.06990841776132584,
-0.08284100890159607,
0.00974900834262371,
0.023204045370221138,
0.056201279163360596,
-0.06431819498538971,
-0.02610873430967331,
0.008430637419223785,
0.014852371998131275,
0.005243724677711725,
0.04399386793375015,
0.007591166067868471,
-0.017891962081193924,
-0.024045443162322044,
0.025207137688994408,
0.007358123082667589,
0.0073574562557041645,
0.02850862592458725,
0.06133827567100525,
-0.037921931594610214,
-0.05369582772254944,
0.012482477352023125,
-0.019567031413316727,
-0.05855865031480789,
0.010997424833476543,
0.005286566913127899,
-0.0007509098504669964,
0.03847939148545265,
-0.0016524008242413402,
-0.03839386999607086,
0.010688986629247665,
-0.055538926273584366,
-0.02458382584154606,
-0.009963803924620152,
-0.006816587410867214,
0.008077857084572315,
0.012118469923734665,
-0.020466752350330353,
0.010559452697634697,
-0.009459885768592358,
0.036237072199583054,
-0.0644225999712944,
-0.08832357078790665,
-0.04168926924467087,
-0.01988406293094158,
-0.008381078019738197,
0.02022671326994896,
0.05659789219498634,
-0.002486914861947298,
0.044806864112615585,
0.023928824812173843,
-0.048735007643699646,
0.0059805396012961864,
0.0373041145503521,
-0.029175641015172005,
-0.03381531313061714,
0.06612088531255722,
0.05876084417104721,
-0.013107283972203732,
-0.07250750809907913,
0.005043751560151577,
0.000916489225346595,
0.0029162936843931675,
0.000030066987164900638,
-0.045103780925273895,
0.02577173337340355,
0.06124933809041977,
-0.06048989295959473,
-0.053886666893959045,
-0.009248212911188602,
-0.008172884583473206,
0.005478091072291136,
-0.04126276820898056,
0.031334586441516876,
0.07531865686178207,
0.05575792118906975,
0.013081845827400684,
0.0019443067722022533,
-0.03197438269853592,
-0.004234422463923693,
-0.05819441378116608,
-0.001700570690445602,
0.04638954624533653,
-0.002199549460783601,
-0.1175803393125534,
0.08731203526258469,
0.045352909713983536,
0.012530811131000519,
0.020751312375068665,
0.01164054311811924,
-0.09244973957538605,
-0.03345734626054764,
-0.02741517312824726,
0.03333541378378868,
0.0021556064020842314,
-0.07986614853143692,
-0.040561825037002563,
-0.01726098358631134,
0.019541118294000626,
0.03862207382917404,
-0.051476068794727325,
0.04408081993460655,
0.03735237196087837,
-0.008300772868096828,
0.024134935811161995,
0.001889826264232397,
-0.021686088293790817,
-0.009712864644825459,
-0.03697577863931656,
0.0007806492503732443,
-0.010337728075683117,
0.003959584049880505,
-0.01261218823492527,
-0.03725428134202957,
0.013531657867133617,
0.03294086456298828,
-0.03831195831298828,
0.0022141742520034313,
-0.030522972345352173,
-0.010320444591343403,
-0.046259187161922455,
0.004496670328080654,
-0.021765265613794327,
-0.027414437383413315,
0.03588973730802536,
0.06595581769943237,
-0.004993214271962643,
0.06697600334882736,
-0.08197616785764694,
0.051864929497241974,
-0.022185657173395157,
-0.049744173884391785,
0.0231840368360281,
0.04483060538768768,
-0.041956041008234024,
-0.019000057131052017,
0.014523521065711975,
-0.027327371761202812,
0.04841236770153046,
-0.00948353111743927,
-0.033048540353775024,
0.04906145855784416,
-0.07106681168079376,
-0.004797591362148523,
0.016703668981790543,
0.023865217342972755,
0.03901370242238045,
0.005066659767180681,
-0.03607668727636337,
-0.02464640699326992,
-0.03584444522857666,
0.02523975819349289,
-0.01905721426010132,
0.05334215611219406,
0.03024597093462944,
-0.052590612322092056,
-0.06376677751541138,
-0.011123307049274445,
0.03255264088511467,
-0.07870998978614807,
-0.03786931559443474,
-0.03997603803873062,
-0.005491869058459997,
-0.01448952965438366,
0.021502960473299026,
0.006956908386200666,
0.02603044919669628,
0.034747593104839325,
-0.016421906650066376,
0.04436728358268738,
-0.0006141205667518079,
0.027610138058662415,
0.01742052473127842,
-0.07550785690546036,
0.004346185829490423,
0.008575418964028358,
0.03343166038393974,
-0.0596470981836319,
-0.011959027498960495,
-0.025763118639588356,
-0.004315734375268221,
-0.018906669691205025,
0.026315011084079742,
0.04401963949203491,
0.07126183062791824,
-0.0012975434074178338,
-0.004455982241779566,
0.0857611745595932,
0.004450664389878511,
0.003057848894968629,
0.03360658138990402,
-0.04448629915714264,
-0.009870835579931736,
0.02966346964240074,
0.04408016428351402,
-0.01876095123589039,
0.028375348076224327,
0.010432534851133823,
-0.03312668949365616,
0.043536797165870667,
0.023390432819724083,
-0.02885308302938938,
-0.012886825948953629,
-0.003933753352612257
] |
<p>Cut, polished and etched iron meteorites have grain size about 1000 times greater than air quenched iron. The reason for the large grain size is the very slow cooling of the core of a planet or protoplanet. Check web for cross section picture Widmanstätten pattern</p>
<p>What methods can be used to grow large iron crystals on earth. What is the largest iron grain size achieved on earth? How about zone refining?</p> | g4763 | [
0.04070986062288284,
0.10386708378791809,
-0.005137466825544834,
-0.026522677391767502,
-0.01398843340575695,
0.02076168917119503,
0.022289417684078217,
0.01312659028917551,
-0.030741527676582336,
-0.024435922503471375,
0.017552699893712997,
0.019257137551903725,
0.020935552194714546,
-0.011150617152452469,
-0.009888377040624619,
0.05046788975596428,
0.03365137055516243,
-0.028076710179448128,
-0.007983033545315266,
-0.014091233722865582,
0.05778198316693306,
0.007277578581124544,
0.016255002468824387,
-0.015870992094278336,
-0.06713037192821503,
0.018726874142885208,
0.03335345536470413,
0.013379337266087532,
-0.016970736905932426,
-0.0015783092239871621,
0.035249125212430954,
0.007497837767004967,
0.0181353148072958,
0.021285658702254295,
-0.01941382698714733,
-0.050029266625642776,
-0.02233261987566948,
0.0514514334499836,
-0.0013930596178397536,
-0.06773386150598526,
-0.03609532490372658,
-0.10292764008045197,
0.02079690434038639,
0.018804024904966354,
-0.005197170656174421,
0.043656181544065475,
0.008916997350752354,
-0.001998345833271742,
0.03626502677798271,
-0.04508788138628006,
0.040855780243873596,
0.051512908190488815,
0.04542060196399689,
-0.056818652898073196,
-0.027492616325616837,
0.06567563116550446,
0.006005614530295134,
0.02211616560816765,
0.05776597186923027,
-0.06184830516576767,
-0.018488356843590736,
-0.04703224450349808,
-0.030823862180113792,
0.004048463888466358,
-0.034015197306871414,
-0.012838468886911869,
-0.03422936424612999,
0.03264925628900528,
0.04986681789159775,
0.011050994507968426,
0.012638099491596222,
-0.04102746397256851,
-0.014353069476783276,
-0.042448513209819794,
-0.06553813070058823,
0.018003012984991074,
0.02261280082166195,
0.04377895966172218,
0.04669136181473732,
0.06352759897708893,
0.016045937314629555,
-0.04295466095209122,
0.0022961751092225313,
0.012227100320160389,
-0.005310306325554848,
-0.014245955273509026,
-0.021314043551683426,
-0.04364113509654999,
-0.023840701207518578,
0.028503015637397766,
0.011736450716853142,
0.009198958054184914,
-0.02425003983080387,
-0.0022775668185204268,
-0.03131518512964249,
0.10673140734434128,
-0.016727494075894356,
0.057851437479257584,
-0.013682859018445015,
0.022006811574101448,
0.03964811563491821,
-0.01991000585258007,
0.05180535838007927,
0.02401244267821312,
0.07441627234220505,
0.009219042956829071,
0.004965831059962511,
-0.0275465939193964,
0.013200036250054836,
0.07920617610216141,
0.011768647469580173,
-0.03926374763250351,
-0.06684276461601257,
0.015778088942170143,
-0.04934404045343399,
-0.004582743160426617,
0.04647987335920334,
0.04607047513127327,
-0.01109785120934248,
0.07865827530622482,
0.0496850423514843,
-0.08833517879247665,
0.011813754215836525,
0.008801338262856007,
-0.02991497702896595,
-0.021471792832016945,
0.035413358360528946,
0.014907877892255783,
-0.0010453112190589309,
-0.03621970862150192,
-0.01198077853769064,
0.020722240209579468,
0.016954001039266586,
-0.07184119522571564,
-0.061935700476169586,
0.016500752419233322,
-0.0069099110551178455,
0.008716054260730743,
-0.011303270235657692,
-0.013599815778434277,
-0.03646048158407211,
-0.00293963891454041,
0.010361531749367714,
0.01604487933218479,
-0.0770423412322998,
0.031366657465696335,
-0.010402824729681015,
0.01008988730609417,
0.02361866645514965,
-0.0047668046317994595,
0.012308329343795776,
0.038741569966077805,
-0.010957136750221252,
-0.025231439620256424,
-0.0253301989287138,
0.005528711248189211,
0.026414543390274048,
0.006554719060659409,
0.006085497792810202,
0.005687908735126257,
-0.028455577790737152,
0.0100497305393219,
-0.0032435550820082426,
0.0011956802336499095,
0.04260679706931114,
-0.0051748682744801044,
-0.004419858567416668,
-0.01991777867078781,
-0.03070542961359024,
0.0070807854644954205,
-0.05935004726052284,
0.02456320822238922,
0.04819929972290993,
0.006198876071721315,
-0.03175082802772522,
0.01993577741086483,
0.11610721051692963,
-0.02697836048901081,
0.0017969256732612848,
-0.02860356867313385,
-0.012274347245693207,
-0.002457784488797188,
-0.045546066015958786,
0.01873726025223732,
0.007102112751454115,
0.01833481155335903,
0.04333656653761864,
-0.0257048849016428,
0.06535325944423676,
0.03384238854050636,
0.0246793981641531,
-0.05848924070596695,
-0.05481130629777908,
-0.01574186235666275,
0.03241195157170296,
-0.018650859594345093,
0.017109181731939316,
-0.03955285996198654,
-0.06937296688556671,
-0.004179826937615871,
-0.01599920354783535,
0.07506465911865234,
-0.02930317260324955,
0.01150702778249979,
0.04945847764611244,
-0.015055519528687,
-0.059716809540987015,
0.03895615413784981,
-0.034817375242710114,
0.013195768930017948,
-0.02416388876736164,
-0.032295528799295425,
-0.00336496252566576,
-0.0018834485672414303,
-0.016172362491488457,
0.010432831943035126,
-0.04417913779616356,
0.009394538588821888,
0.04237856715917587,
0.017952565103769302,
0.00003281006866018288,
-0.026514191180467606,
0.02395468018949032,
-0.03132627531886101,
0.043380800634622574,
-0.02285468950867653,
0.044975124299526215,
-0.0016822484321892262,
0.05992598459124565,
0.04881087318062782,
-0.058932993561029434,
0.008352763019502163,
-0.010505646467208862,
-0.01087450422346592,
-0.018426300957798958,
0.014000920578837395,
-0.05958530306816101,
-0.011647325940430164,
-0.08036534488201141,
0.049518875777721405,
-0.01641080714762211,
-0.01886753924190998,
-0.01724771037697792,
-0.04422323405742645,
0.011441695503890514,
-0.040082305669784546,
-0.0018915766850113869,
0.061379820108413696,
0.013874981552362442,
0.002940577454864979,
0.038962218910455704,
-0.009233467280864716,
-0.024653825908899307,
0.008563580922782421,
-0.04892567917704582,
-0.05010906234383583,
-0.013231813907623291,
0.08493755757808685,
-0.031315937638282776,
-0.005659931339323521,
-0.029071418568491936,
-0.07511790841817856,
0.050226617604494095,
0.03813353553414345,
-0.0069442796520888805,
0.025577537715435028,
-0.06541506946086884,
0.0002727338869590312,
0.022077780216932297,
0.03590092808008194,
-0.005746515467762947,
-0.008255681954324245,
0.021426774561405182,
0.039498474448919296,
-0.05635455250740051,
-0.01866009645164013,
0.055832717567682266,
-0.056842558085918427,
0.036926329135894775,
0.012817415408790112,
0.01385254692286253,
-0.025225644931197166,
0.019877031445503235,
0.05625786632299423,
0.04062899947166443,
0.026899218559265137,
-0.021625302731990814,
0.01943442039191723,
-0.024579059332609177,
0.028857653960585594,
-0.004274830687791109,
-0.007520894054323435,
-0.002729996107518673,
0.009075231850147247,
0.016946231946349144,
0.017749808728694916,
0.05266042798757553,
0.06781400740146637,
-0.030821269378066063,
0.021619131788611412,
0.03561340272426605,
-0.06581110507249832,
-0.04797028750181198,
0.033236779272556305,
0.0132190166041255,
-0.009496674872934818,
0.024952594190835953,
0.021253880113363266,
-0.08584531396627426,
-0.08638568967580795,
0.016192549839615822,
0.04392554238438606,
-0.022874895483255386,
0.024663209915161133,
-0.04406777024269104,
-0.0018887011101469398,
-0.013318167999386787,
-0.009241371415555477,
0.10659684240818024,
-0.009751427918672562,
0.0004574200138449669,
-0.01319353561848402,
0.07583322376012802,
-0.02380637265741825,
-0.00940717477351427,
0.0033559883013367653,
0.003008568659424782,
0.03802218288183212,
-0.026690036058425903,
0.001995643600821495,
-0.0371132493019104,
0.07257497310638428,
-0.08537925034761429,
0.01670026034116745,
-0.04238945245742798,
0.012895856983959675,
-0.014830275438725948,
-0.001447383314371109,
0.05340604856610298,
0.0128159299492836,
-0.09063602238893509,
0.03515692055225372,
-0.004567618016153574,
-0.05427645146846771,
0.043428048491477966,
0.024985864758491516,
-0.042414311319589615,
-0.03294612094759941,
-0.024301258847117424,
-0.01307558175176382,
0.03288552910089493,
-0.03665021434426308,
0.020865466445684433,
-0.007314190734177828,
0.002598394174128771,
0.06120123341679573,
0.012967401184141636,
0.005489604081958532,
0.04921534284949303,
-0.09110408276319504,
-0.008928410708904266,
0.03534817695617676,
-0.03263941779732704,
-0.004016582388430834,
-0.015952831134200096,
-0.009024846367537975,
0.01046335231512785,
-0.06768637150526047,
0.02522069402039051,
0.006350598763674498,
0.03494609519839287,
-0.049390532076358795,
0.024823898449540138,
0.02615407109260559,
0.03869811072945595,
0.0512235090136528,
-0.06284245103597641,
0.013935822062194347,
0.02717888168990612,
-0.045627493411302567,
0.025632517412304878,
0.025468310341238976,
0.03842887654900551,
-0.06704408675432205,
-0.04856433346867561,
-0.004963673185557127,
-0.04478389769792557,
-0.0002583876485005021,
-0.02876664325594902,
-0.029492925852537155,
0.036604851484298706,
-0.06692657619714737,
-0.02045370265841484,
0.008596766740083694,
-0.05505014583468437,
-0.04797689616680145,
0.012824545614421368,
0.018630141392350197,
0.0476745069026947,
0.001018447452224791,
-0.016176855191588402,
0.06021827086806297,
-0.013322235085070133,
0.025751259177923203,
-0.02180786244571209,
-0.048495713621377945,
0.0021382165141403675,
0.0011913643684238195,
-0.006186649203300476,
-0.009876362979412079,
0.019645938649773598,
0.0016857510199770331,
-0.01675155572593212,
-0.029421312734484673,
-0.019366035237908363,
-0.07970938086509705,
-0.0644787922501564,
-0.031173205003142357,
0.05783623084425926,
-0.06811799854040146,
-0.02508656494319439,
0.043152906000614166,
-0.01721566542983055,
-0.005409140605479479,
0.08374515175819397,
0.06436248868703842,
-0.057536780834198,
-0.0849744901061058,
-0.01899695210158825,
0.061513908207416534,
0.07695700973272324,
-0.034461963921785355,
-0.007666781544685364,
0.0012437778059393167,
0.0029641117434948683,
0.022138096392154694,
-0.002957874210551381,
0.038186684250831604,
0.028808897361159325,
-0.013042270205914974,
-0.027057670056819916,
0.03741956502199173,
0.035842787474393845,
0.07463172823190689,
0.01465605292469263,
0.03389018774032593,
-0.001766512170433998,
0.004812051076442003,
-0.015459361486136913,
0.025991646572947502,
0.016923140734434128,
0.002021827269345522,
-0.03843413665890694,
0.028885478153824806,
0.01973690092563629,
-0.05472170189023018,
-0.010233878158032894,
0.054160576313734055,
0.054255370050668716,
0.036430638283491135,
-0.026876796036958694,
-0.018881231546401978,
0.006039481610059738,
0.08986058831214905,
0.00703614205121994,
-0.002225408796221018,
-0.03595484793186188,
-0.04013444855809212,
-0.014523337595164776,
-0.030262958258390427,
-0.00388657720759511,
-0.036065880209207535,
0.017856650054454803,
0.07067719101905823,
-0.052426837384700775,
0.0005406835698522627,
-0.03651868924498558,
-0.10669887810945511,
0.07657094299793243,
0.027031797915697098,
-0.010270063765347004,
-0.011818388476967812,
0.03536941483616829,
0.021550923585891724,
-0.01271792035549879,
0.017469782382249832,
-0.060612257570028305,
-0.004783051088452339,
0.013572320342063904,
0.0078070699237287045,
-0.02782495878636837,
0.00573710398748517,
0.031203346326947212,
0.0013578328071162105,
-0.047262661159038544,
-0.043081630021333694,
0.014580574817955494,
-0.05555161461234093,
0.016507508233189583,
0.03155508637428284,
0.030636239796876907,
-0.054019466042518616,
-0.01253252662718296,
-0.017380010336637497,
0.0212079007178545,
0.023059748113155365,
0.04888930171728134,
-0.01915714330971241,
-0.00013347400818020105,
0.05980733036994934,
0.00021875242237001657,
-0.006119463127106428,
0.0036287650000303984,
-0.014568900689482689,
0.03535182401537895,
0.011231702752411366,
0.02233901247382164,
-0.0036887985188513994,
-0.0006090567330829799,
-0.06783859431743622,
-0.012476608157157898,
-0.05177619308233261,
0.0012562689371407032,
-0.015633372589945793,
0.007110325153917074,
-0.0032355713192373514,
0.020458944141864777,
-0.02916417270898819,
0.017728500068187714,
0.005406040698289871,
-0.026666291058063507,
-0.004885460715740919,
-0.017553502693772316,
0.039495546370744705,
-0.01564265415072441,
0.031217457726597786,
-0.007969747297465801,
0.03470059856772423,
-0.04198101535439491,
-0.010661226697266102,
0.053837209939956665,
0.0012414827942848206,
0.02528197318315506,
0.0021324078552424908,
0.013179491274058819,
-0.05619252473115921,
0.04966871440410614,
0.018014460802078247,
0.04101134091615677,
0.018203038722276688,
-0.04350851848721504,
-0.003176972037181258,
0.029759015887975693,
-0.06382253766059875,
-0.013607592321932316,
0.018537208437919617,
0.020159831270575523,
-0.02016904577612877,
-0.017902718856930733,
-0.03996136412024498,
-0.00846810545772314,
-0.01703427918255329,
0.02280208095908165,
-0.07095279544591904,
-0.037314523011446,
-0.05115469917654991,
-0.02420620247721672,
-0.023442337289452553,
0.042217180132865906,
0.025297321379184723,
-0.011590901762247086,
0.054505135864019394,
-0.0026401865761727095,
0.004149884916841984,
0.019343789666891098,
-0.003345947014167905,
-0.04155442863702774,
0.02445257268846035,
-0.007922093383967876,
-0.029212597757577896,
0.017369788140058517,
0.07629481703042984,
-0.03543160855770111,
0.018900983035564423,
-0.006156107876449823,
-0.01487377006560564,
-0.03166840970516205,
0.002485718810930848,
-0.012936294078826904,
-0.0320594422519207,
0.002147554187104106,
-0.018849661573767662,
-0.014981859363615513,
-0.02647233009338379,
-0.0362943671643734,
-0.06997589766979218,
-0.05501284822821617,
0.04158538207411766,
-0.05567758157849312,
-0.05703366920351982,
-0.04699825868010521,
0.06128949671983719,
0.04560951143503189,
-0.000649932655505836,
0.05843222513794899,
-0.007899618707597256,
0.013996057212352753,
0.007528148125857115,
0.04738772660493851,
0.0432162843644619,
0.05024818331003189,
0.04750556871294975,
0.015958482399582863,
-0.05302070826292038,
-0.061532847583293915,
-0.0534806102514267,
0.08838877826929092,
-0.027059337124228477,
0.04097481071949005,
0.005527152214199305,
0.0029595845844596624,
-0.022173980250954628,
-0.03590330481529236,
-0.08997493982315063,
-0.006554147228598595,
0.025718342512845993,
0.013437771238386631,
0.0042487336322665215,
0.03119940124452114,
-0.04737496003508568,
-0.028474757447838783,
0.031196855008602142,
0.0180515069514513,
0.046819496899843216,
0.005126673262566328,
0.005880562588572502,
-0.013391009531915188,
0.03865041956305504,
-0.017271876335144043,
0.03673509880900383,
-0.024183595553040504,
-0.05394142121076584,
-0.027661636471748352,
0.03822880610823631,
-0.03083023615181446,
0.016231482848525047,
-0.04150913283228874,
-0.018691865727305412,
0.043249715119600296,
-0.05117203667759895,
-0.011848179623484612,
0.014548399485647678,
-0.003190484829246998,
-0.04885663837194443,
0.027843328192830086,
0.006498165428638458,
0.036113299429416656,
0.0014405043330043554,
0.011035225354135036,
-0.020943056792020798,
0.000355524942278862,
0.04112914949655533,
0.00903265830129385,
-0.004022502806037664,
0.02508024126291275,
0.02989547699689865,
-0.03215355798602104,
0.005053401924669743,
-0.007799304090440273,
0.034633755683898926,
-0.05061258748173714,
-0.01302865520119667,
-0.00466182641685009,
0.01474242564290762,
-0.002064401749521494,
0.036910392343997955,
0.030689092352986336,
-0.0705200582742691,
0.02112165465950966,
0.013063031248748302,
-0.0015070592053234577,
0.044603366404771805,
-0.005342773627489805,
-0.02147030644118786,
0.05871637538075447,
0.014590135775506496,
-0.05331549420952797,
0.013667375780642033,
0.026674507185816765,
0.008454978466033936,
-0.01049004402011633,
0.04505975544452667,
-0.044619765132665634,
-0.012888668105006218,
0.014035080559551716,
-0.009584820829331875,
0.01908307708799839,
-0.026797227561473846,
0.05452558025717735,
-0.014986186288297176,
0.03280431404709816,
0.008086442947387695,
0.04995236545801163,
0.005243040155619383,
-0.002111049136146903,
0.016802102327346802,
0.04295434430241585,
0.09697753936052322,
0.01298681553453207,
-0.02686707302927971,
0.006572265177965164,
-0.01812710054218769,
-0.00512776430696249,
-0.005337209906429052,
0.05299042910337448,
0.03802761435508728,
0.021433334797620773,
0.004038881044834852,
0.03800061345100403,
0.010256913490593433,
-0.0019527930999174714,
0.02380231022834778,
0.02315019629895687,
-0.1119251623749733,
0.0032446198165416718,
0.025011491030454636,
0.04595084488391876,
-0.028113657608628273,
0.015569401904940605,
-0.011777445673942566,
0.047718554735183716,
-0.029309215024113655,
-0.021870944648981094,
0.022251911461353302,
-0.03878913074731827,
-0.024876900017261505,
-0.02085311897099018,
-0.03876234591007233,
-0.07184145599603653,
-0.015953266993165016,
-0.01613541878759861,
-0.001832761219702661,
-0.04676664248108864,
-0.02295839600265026,
-0.018038908019661903,
0.04521377012133598,
-0.045837584882974625,
0.060343433171510696,
-0.023778973147273064,
-0.0015171356499195099,
-0.01616801880300045,
-0.017135150730609894,
0.0024447368923574686,
-0.043389204889535904,
-0.013832365162670612,
-0.0025621408130973577,
0.03039904683828354,
0.0514066219329834,
0.02182571031153202,
-0.09040218591690063,
0.005969441030174494,
0.010940204374492168,
0.02071336843073368,
-0.007220524363219738,
0.01695188321173191,
-0.00026985094882547855,
0.009182911366224289,
-0.02377927489578724
] |
<p>Say you have a magnet that is used in a brush-less generator. If the brush-less motor was ran (by external force such as water or human interaction) for 400 years, would the magnet that was under use have a weaker magnetic field than a magnet that had not been used at all? In other words, does using a magnet decrease its strength over time?</p> | g4764 | [
0.03567744418978691,
0.007677215617150068,
0.02268495224416256,
-0.047844890505075455,
-0.010673820972442627,
0.03676780313253403,
0.014537813141942024,
0.06309370696544647,
-0.018918292596936226,
-0.0227807704359293,
-0.04885127767920494,
-0.02309463731944561,
-0.027352694422006607,
0.020324070006608963,
-0.005649104714393616,
0.029274821281433105,
-0.009548680856823921,
-0.021190283820033073,
0.02253989316523075,
0.0008974792435765266,
0.00011134843225590885,
0.001658451627008617,
0.013678392395377159,
0.013190463185310364,
-0.052596185356378555,
-0.014183508232235909,
-0.01553083211183548,
-0.04626379534602165,
0.03185560926795006,
-0.05725422874093056,
0.007453656755387783,
-0.00843084417283535,
0.013755138963460922,
-0.026199163869023323,
-0.058756355196237564,
-0.019809704273939133,
0.012640855275094509,
0.050513435155153275,
0.013805066235363483,
-0.0025859586894512177,
0.015293126925826073,
0.04459491744637489,
0.06248864158987999,
-0.010624777525663376,
0.024041807278990746,
-0.02940238267183304,
-0.01310810074210167,
-0.007767413277179003,
-0.0712941363453865,
-0.0017370611894875765,
-0.07629958540201187,
-0.057646408677101135,
0.025786904618144035,
0.013420218601822853,
0.036867693066596985,
-0.05936620756983757,
-0.004883580841124058,
-0.04368523880839348,
-0.008774942718446255,
0.002432718873023987,
-0.031007664278149605,
0.002096020383760333,
0.02733064442873001,
0.009716317057609558,
0.018004262819886208,
-0.056262847036123276,
-0.04487239196896553,
0.011820141226053238,
0.039289407432079315,
0.03523559495806694,
-0.062075261026620865,
-0.0013657789677381516,
-0.06515813618898392,
0.005087826866656542,
-0.02274813875555992,
0.04549229517579079,
0.016105255112051964,
-0.013421504758298397,
0.04110635817050934,
0.050173982977867126,
-0.032581835985183716,
0.00775334844365716,
0.00743459165096283,
0.04714394733309746,
0.08597717434167862,
0.012390879914164543,
-0.01600446179509163,
0.012732882052659988,
0.048735544085502625,
0.05846528336405754,
0.026131950318813324,
-0.01561229582875967,
0.027254274114966393,
-0.029031557962298393,
-0.02184532955288887,
0.02321702055633068,
0.025654293596744537,
0.04894141107797623,
0.007997785694897175,
0.029926050454378128,
0.0025833502877503633,
-0.04793613404035568,
0.000570468429941684,
-0.019769668579101562,
-0.023876022547483444,
-0.003568266984075308,
0.07268121093511581,
-0.02437269315123558,
-0.04381763935089111,
0.011003145016729832,
-0.02288350649178028,
-0.04650857299566269,
-0.05868469178676605,
0.020779946818947792,
0.0018986250506713986,
-0.034400541335344315,
0.029793616384267807,
0.024382036179304123,
-0.012501905672252178,
-0.013331649824976921,
0.015087001025676727,
-0.04514310136437416,
-0.04691550135612488,
-0.0032066949643194675,
-0.01378391683101654,
0.013768033124506474,
-0.009809993207454681,
0.06222376227378845,
0.04031309485435486,
-0.0103262048214674,
-0.017275555059313774,
0.020776495337486267,
0.01650782860815525,
0.011924994178116322,
0.03328773006796837,
0.01536609884351492,
0.021650725975632668,
0.013586824759840965,
0.03017055056989193,
-0.03293165937066078,
0.03801605477929115,
-0.05676386505365372,
0.012196730822324753,
-0.021922823041677475,
0.005811694543808699,
0.11200442165136337,
0.02898017317056656,
-0.0056959958747029305,
-0.0033915741369128227,
0.08030502498149872,
0.0035734798293560743,
-0.014262446202337742,
0.030854227021336555,
-0.028807364404201508,
0.0577545091509819,
-0.009200074709951878,
-0.012676388956606388,
0.02060200832784176,
-0.016661779955029488,
-0.03560265153646469,
0.0038126620929688215,
0.04364478215575218,
0.08521150797605515,
-0.0006392868817783892,
-0.048770759254693985,
0.017160454764962196,
0.03130268678069115,
0.00642248522490263,
-0.013696117326617241,
-0.01687675341963768,
0.005471361801028252,
-0.028200704604387283,
0.003065658500418067,
0.036857228726148605,
-0.016319623216986656,
0.006507699377834797,
0.0512731708586216,
-0.06897050142288208,
-0.004450901877135038,
-0.014617837965488434,
-0.009845152497291565,
-0.0057172770611941814,
0.009566577151417732,
0.01864388771355152,
-0.020164938643574715,
0.02512155845761299,
0.015442730858922005,
0.004188514780253172,
-0.09734038263559341,
-0.030594706535339355,
-0.09476124495267868,
0.0073382738046348095,
-0.002932771574705839,
0.0464043952524662,
-0.06272151321172714,
-0.03323744237422943,
-0.048995863646268845,
0.028527293354272842,
-0.011983140371739864,
-0.021794768050312996,
-0.041117776185274124,
0.04455452412366867,
0.0007001269259490073,
0.011556289158761501,
-0.016050241887569427,
-0.0822475403547287,
0.0031734721269458532,
-0.015173440799117088,
0.09031315892934799,
-0.056227292865514755,
0.038049619644880295,
0.08688894659280777,
-0.0408933162689209,
-0.03693607449531555,
-0.06038356199860573,
-0.05037050321698189,
-0.019995229318737984,
0.0061400895938277245,
-0.018045950680971146,
-0.0058771586045622826,
-0.06069546937942505,
-0.009824090637266636,
0.05231182277202606,
0.03235603868961334,
-0.024766532704234123,
-0.06379903852939606,
0.022132882848381996,
0.03671737387776375,
-0.027308156713843346,
0.033892326056957245,
-0.01395005639642477,
-0.04396269470453262,
0.01812734082341194,
-0.00944510381668806,
-0.0003601068165153265,
0.028915857896208763,
-0.00007774891128065065,
-0.04234427958726883,
0.04386892169713974,
0.012488901615142822,
0.021833758801221848,
0.009398151189088821,
-0.010015108622610569,
-0.03086371161043644,
0.07698503881692886,
-0.07344947755336761,
0.005224247928708792,
-0.0035734365228563547,
0.07794623076915741,
0.03582361340522766,
0.020025284960865974,
0.013991082087159157,
0.01958715356886387,
0.017299842089414597,
-0.035768840461969376,
0.03126112371683121,
-0.003938011825084686,
-0.01714457757771015,
-0.08494767546653748,
-0.00033382867695763707,
0.03323877602815628,
-0.03322364017367363,
0.005207400303333998,
0.05620124191045761,
0.018560905009508133,
-0.04834609851241112,
-0.05546930804848671,
-0.012541300617158413,
0.05990210175514221,
0.013255459256470203,
0.002702466445043683,
0.052051834762096405,
-0.010780040174722672,
-0.00675605796277523,
-0.015672070905566216,
-0.025947321206331253,
-0.037107910960912704,
-0.003907116129994392,
0.02041725255548954,
-0.027096200734376907,
-0.009216045960783958,
-0.04918351396918297,
-0.03552038222551346,
0.06018725410103798,
0.008327864110469818,
0.010640542022883892,
0.015064625069499016,
-0.027950210496783257,
-0.06755033135414124,
0.013554212637245655,
-0.11946666240692139,
0.03261920064687729,
0.09598793089389801,
-0.04189600795507431,
0.022528303787112236,
0.026691146194934845,
0.019510973244905472,
-0.027838997542858124,
-0.008188568986952305,
-0.018330411985516548,
0.028485920280218124,
-0.020971303805708885,
-0.0625687912106514,
-0.04210933670401573,
0.027386846020817757,
-0.03463989496231079,
-0.1097339540719986,
-0.01836078055202961,
0.018684199079871178,
-0.025538193061947823,
-0.02876746654510498,
0.032695550471544266,
0.0626029223203659,
0.04374989867210388,
-0.08496113866567612,
0.004100942052900791,
-0.007208634167909622,
0.017932340502738953,
-0.0237691942602396,
-0.017679037526249886,
0.028380151838064194,
-0.04230058193206787,
-0.001433512894436717,
-0.056870609521865845,
0.0018383899005129933,
0.049029309302568436,
0.014270997606217861,
0.032551731914281845,
-0.025568226352334023,
0.04022495448589325,
-0.025386005640029907,
0.009957922622561455,
0.0005952439969405532,
-0.018285363912582397,
-0.07612652331590652,
0.05072923004627228,
-0.04826924949884415,
-0.029219066724181175,
-0.036668580025434494,
0.019499320536851883,
0.019692014902830124,
-0.01615564152598381,
-0.025120535865426064,
0.015936989337205887,
0.00375018990598619,
0.09552612155675888,
-0.036553505808115005,
-0.019698144868016243,
-0.017542658373713493,
0.014054816216230392,
0.08343089371919632,
-0.0020868212450295687,
0.03761640191078186,
-0.018840966746211052,
-0.022351540625095367,
-0.02690686658024788,
-0.029955139383673668,
0.01623820699751377,
-0.015196169726550579,
0.02158365584909916,
-0.001055168337188661,
0.0368870347738266,
-0.038544896990060806,
-0.01017741858959198,
-0.005216016434133053,
0.08078406751155853,
-0.0039108204655349255,
0.05480275675654411,
0.014466914348304272,
-0.018667563796043396,
-0.03889314830303192,
-0.028989247977733612,
0.031165586784482002,
0.04888611286878586,
-0.03407584875822067,
0.041519686579704285,
0.1010497435927391,
0.016989562660455704,
-0.03556966036558151,
0.019603412598371506,
0.011096217669546604,
0.024347931146621704,
-0.03198457136750221,
0.035123225301504135,
-0.0302534531801939,
-0.0294802226126194,
0.002605859888717532,
0.04590318724513054,
0.03199952095746994,
0.011362317949533463,
0.0058625987730920315,
0.020843414589762688,
0.005246605258435011,
0.03933678939938545,
0.042005352675914764,
0.034660454839468,
-0.034497831016778946,
-0.047997698187828064,
0.08424562215805054,
-0.04099428281188011,
-0.0179753378033638,
0.08991008251905441,
0.006227854173630476,
0.05840745568275452,
0.006904072128236294,
-0.010212097316980362,
0.045292098075151443,
-0.000514199142344296,
0.036527834832668304,
-0.023659994825720787,
-0.018070653080940247,
-0.04799359291791916,
-0.05620447173714638,
-0.07318536937236786,
0.016832487657666206,
-0.06118452921509743,
0.06786398589611053,
0.050427380949258804,
-0.020442800596356392,
-0.016908790916204453,
0.01893468014895916,
0.018490223214030266,
-0.024463538080453873,
0.011925674974918365,
-0.06159725785255432,
-0.008382842876017094,
-0.033383965492248535,
0.0054076062515378,
0.01474830787628889,
-0.009096740745007992,
-0.012658340856432915,
0.06655304878950119,
-0.06396672129631042,
-0.014140792191028595,
0.03503039479255676,
0.01354315783828497,
-0.015403120778501034,
0.02895595319569111,
0.04939466714859009,
0.012227270752191544,
0.06360267102718353,
0.009005519561469555,
0.06818029284477234,
0.015203604474663734,
-0.03550281003117561,
0.03384478762745857,
0.0327342189848423,
0.022046303376555443,
-0.011957796290516853,
0.00044630770571529865,
-0.06747400015592575,
0.0169265978038311,
-0.017532415688037872,
-0.036593981087207794,
-0.016382839530706406,
0.004776584915816784,
-0.002631973009556532,
-0.007575376890599728,
-0.0030497980769723654,
0.025638168677687645,
-0.030707309022545815,
-0.009960558265447617,
0.004613721277564764,
0.0007975712069310248,
-0.05390939116477966,
-0.015498122200369835,
0.012430013157427311,
-0.0205853171646595,
-0.0701647475361824,
0.049810051918029785,
0.046497173607349396,
-0.05354353412985802,
0.03490276634693146,
-0.033683791756629944,
-0.026208046823740005,
-0.03221852332353592,
0.0013907499378547072,
-0.0391056053340435,
0.035512760281562805,
-0.003545415820553899,
0.018460631370544434,
-0.01848798617720604,
0.05531999468803406,
0.013246262446045876,
-0.008401555940508842,
0.001456107129342854,
-0.010862856172025204,
0.011059262789785862,
0.011981763876974583,
-0.052186813205480576,
0.03665275499224663,
0.027843313291668892,
0.023037273436784744,
-0.017642905935645103,
-0.035288255661726,
-0.0030271848663687706,
0.0073270294815301895,
-0.023140842095017433,
-0.029813552275300026,
-0.010047624818980694,
-0.05538615956902504,
0.06200152263045311,
-0.08141697198152542,
0.0008337362087331712,
0.004637712147086859,
0.022135954350233078,
0.015063849277794361,
-0.06829352676868439,
0.07095682621002197,
0.09202258288860321,
-0.04353712126612663,
0.03390675038099289,
-0.011633042246103287,
0.05241278186440468,
0.0785311609506607,
0.029294483363628387,
0.02227834239602089,
0.009977654553949833,
-0.014231236651539803,
-0.02426586113870144,
0.06323721259832382,
-0.0026353655848652124,
0.09119832515716553,
-0.009624695405364037,
-0.05661915987730026,
0.06328722834587097,
0.004912759643048048,
0.015164585784077644,
0.0005090953200124204,
0.030616356059908867,
0.06444332748651505,
0.017155826091766357,
0.004515420645475388,
-0.007942096330225468,
0.006056808866560459,
0.01090635359287262,
0.04723740369081497,
-0.010286055505275726,
-0.04134780541062355,
0.010864579118788242,
0.03257354721426964,
-0.07185038924217224,
0.05724222958087921,
-0.012758299708366394,
-0.04157146066427231,
0.022890780121088028,
-0.0413157157599926,
-0.06207910180091858,
0.010008974000811577,
-0.021108509972691536,
-0.05909814313054085,
-0.0013178556691855192,
-0.0009003237937577069,
0.079442597925663,
0.007903759367763996,
0.021806195378303528,
0.011516274884343147,
-0.0017881833482533693,
0.043137338012456894,
0.014248909428715706,
0.0050497292540967464,
-0.00655824551358819,
0.012931720353662968,
-0.02357546240091324,
0.034233398735523224,
-0.0002773333981167525,
0.011950596235692501,
-0.034492988139390945,
0.04726114496588707,
0.06505078822374344,
0.0010427029337733984,
0.017721354961395264,
-0.029501425102353096,
0.019702281802892685,
0.05248911306262016,
0.025328855961561203,
-0.05723469704389572,
-0.02181955613195896,
-0.017689643427729607,
0.03401627764105797,
-0.020003052428364754,
-0.05005223676562309,
0.0019727260805666447,
-0.0006713069742545485,
0.019317373633384705,
-0.004365983419120312,
-0.06448379904031754,
-0.01305688451975584,
0.060669466853141785,
0.024855397641658783,
0.025742046535015106,
-0.005247596651315689,
0.03377756476402283,
0.017799612134695053,
-0.0413457415997982,
0.03180989623069763,
-0.07693188637495041,
-0.013591906055808067,
0.0029941718094050884,
-0.014261259697377682,
0.01521087996661663,
0.038388658314943314,
0.03448741137981415,
-0.037557490170001984,
0.04005013406276703,
0.033400289714336395,
-0.013720281422138214,
-0.027058079838752747,
0.02617882564663887,
-0.0614449605345726,
0.028346508741378784,
0.015101243741810322,
0.010514329187572002,
-0.0049287802539765835,
0.041323594748973846,
-0.03417187184095383,
0.013329599983990192,
-0.004952022340148687,
-0.04186923801898956,
0.029407108202576637,
-0.09487201273441315,
-0.05688567832112312,
0.030128680169582367,
-0.06229061260819435,
-0.006308034062385559,
0.010126001201570034,
-0.05378986522555351,
-0.004517406690865755,
0.08608318120241165,
-0.05169154331088066,
-0.03676948323845863,
-0.03408816456794739,
-0.03685329109430313,
0.02578967995941639,
-0.006415849551558495,
0.00016823863552417606,
-0.008477400988340378,
0.020639104768633842,
0.034427251666784286,
-0.01277172937989235,
-0.023103471845388412,
0.01070395391434431,
-0.02914932742714882,
0.0323885902762413,
0.003630385035648942,
0.03672805055975914,
0.020150156691670418,
0.0436343252658844,
-0.014491108246147633,
-0.013912123627960682,
0.027593299746513367,
0.0090946638956666,
-0.023614799603819847,
-0.0469822995364666,
-0.020691223442554474,
0.05482795462012291,
0.01795070804655552,
0.023602712899446487,
0.050184912979602814,
-0.010290398262441158,
-0.025547560304403305,
-0.03630136325955391,
0.00422881543636322,
0.0008118713740259409,
0.013044539839029312,
0.03699370101094246,
0.039083532989025116,
-0.031327687203884125,
0.051281239837408066,
0.05775483325123787,
0.0067470259964466095,
-0.052824899554252625,
-0.019058341160416603,
-0.020316127687692642,
0.03332109749317169,
-0.009586500935256481,
-0.01944572478532791,
-0.02702503837645054,
0.03367679938673973,
-0.012780322693288326,
0.026410063728690147,
-0.021618790924549103,
-0.017894933000206947,
0.00610099034383893,
-0.013386251404881477,
0.04081449285149574,
-0.0734509527683258,
0.0050675999373197556,
0.06871660053730011,
-0.03265387937426567,
-0.010445504449307919,
-0.02973390556871891,
0.0002434392663417384,
0.010352449491620064,
-0.04729505255818367,
-0.05827490612864494,
0.003561564953997731,
0.01298591960221529,
0.002381587866693735,
0.0009510384406894445,
0.021879376843571663,
0.00939902663230896,
0.039031658321619034,
0.004641758278012276,
0.023940814658999443,
-0.02660181187093258,
-0.059724777936935425,
0.018798941746354103,
-0.07524242252111435,
0.037697311490774155,
-0.0376102551817894,
0.028159022331237793,
0.00860150158405304,
0.0013772643869742751,
-0.02925383858382702,
-0.02205110341310501,
-0.00019588171562645584,
-0.02986034005880356,
0.04860711097717285,
0.023941442370414734,
-0.03726230934262276,
0.01789344847202301,
-0.0028736507520079613,
-0.05075807869434357,
-0.016096891835331917,
0.054286543279886246,
-0.0072561814449727535,
0.0009674261673353612,
0.012755093164741993,
-0.01341088768094778,
-0.019345346838235855,
-0.09302869439125061,
-0.02972545474767685,
-0.028895225375890732,
-0.012688066810369492,
-0.07106215506792068,
-0.021580340340733528,
-0.002249049488455057,
-0.0419297069311142,
-0.011481610126793385,
-0.020073210820555687,
0.008580789901316166,
-0.03758072480559349,
0.05507571995258331,
-0.01661595329642296,
0.037727970629930496,
-0.015497054904699326,
0.02505180984735489,
-0.00470268540084362,
0.027063660323619843,
0.008345464244484901,
-0.0635223463177681,
0.01340506598353386,
0.014861091040074825,
0.021933428943157196,
-0.03378382697701454,
-0.002046833047643304,
0.03755534812808037,
0.023638781160116196,
-0.016990967094898224,
-0.016370754688978195,
0.034853480756282806,
0.013663611374795437,
-0.014115945436060429,
-0.05209686607122421,
-0.013621069490909576,
0.03398120775818825,
-0.015967203304171562
] |
<p>If the uncertainty principle and Copenhagen Interpretation are true, then how can a clock tick? Supposedly particles can do all sorts of things when not measured, then how can they be formed into gears that make the clock tick when not measured? </p> | g4765 | [
0.04350268095731735,
0.07176216691732407,
-0.009664873592555523,
-0.05773703381419182,
0.060750965029001236,
0.04172314330935478,
-0.024792540818452835,
-0.004998516291379929,
-0.015545293688774109,
-0.031557776033878326,
-0.07225246727466583,
-0.04722348973155022,
0.01971564255654812,
-0.036886319518089294,
-0.015695922076702118,
0.018737254664301872,
0.04771954566240311,
0.04366685822606087,
0.05922036990523338,
0.08708664029836655,
0.059225909411907196,
0.030162781476974487,
-0.02104904130101204,
-0.08133300393819809,
-0.05997678264975548,
-0.004196292255073786,
0.01879964955151081,
-0.03426385298371315,
-0.0015377408126369119,
-0.002885145368054509,
0.014952723868191242,
-0.04036727547645569,
0.023135187104344368,
-0.023661842569708824,
0.03936310112476349,
-0.04174661636352539,
0.036370083689689636,
-0.024539614096283913,
0.007007876876741648,
0.020525453612208366,
-0.044979628175497055,
-0.007185343652963638,
0.024658797308802605,
-0.00864185020327568,
-0.027509793639183044,
0.08116418868303299,
0.03202730417251587,
0.04819836840033531,
0.041935890913009644,
-0.03216924890875816,
-0.027645377442240715,
-0.005252916365861893,
0.07360225170850754,
0.06410561501979828,
0.03372088074684143,
0.04752829670906067,
0.10437916219234467,
0.03480598330497742,
0.06719020009040833,
0.0010311929509043694,
0.00003511387694743462,
-0.017368454486131668,
0.011617409065365791,
0.017103319987654686,
0.048496268689632416,
-0.0315299928188324,
-0.03273160383105278,
-0.01251195091754198,
0.02542729303240776,
0.040002211928367615,
0.044839050620794296,
-0.028174929320812225,
-0.023864775896072388,
-0.006506889592856169,
0.004452021326869726,
0.07836024463176727,
-0.017991147935390472,
0.013771187514066696,
-0.02126896008849144,
0.002744685858488083,
-0.018308386206626892,
-0.01564902439713478,
-0.013233082368969917,
-0.013197056017816067,
0.0603518933057785,
0.01848619058728218,
-0.014493197202682495,
-0.012897280976176262,
0.0527411624789238,
0.04369550943374634,
0.04234132170677185,
-0.07361315190792084,
0.05994522199034691,
-0.05254216492176056,
0.00858865212649107,
0.013011641800403595,
-0.02018854022026062,
0.0568091943860054,
-0.010352060198783875,
0.0342167429625988,
-0.05463144928216934,
0.017065750434994698,
-0.06706905364990234,
-0.02622343972325325,
-0.014285150915384293,
-0.02768723852932453,
-0.038456156849861145,
-0.02251707762479782,
0.052188724279403687,
-0.06134265661239624,
-0.012796541675925255,
-0.02241154946386814,
-0.0036901277489960194,
0.015327815897762775,
-0.00013118838251102716,
0.02103326842188835,
0.09935598075389862,
0.050709545612335205,
-0.01672256924211979,
0.010935904458165169,
0.05075525492429733,
-0.020259901881217957,
0.0034569930285215378,
0.07641807198524475,
-0.03516896814107895,
0.028640691190958023,
0.015136465430259705,
0.007079295348376036,
-0.023989081382751465,
-0.009541605599224567,
0.05517805367708206,
0.020818600431084633,
-0.03272606059908867,
0.03279632329940796,
-0.006274826359003782,
0.03835735097527504,
-0.000899895909242332,
0.009060423821210861,
-0.00041077841888181865,
-0.005346714984625578,
0.020862195640802383,
0.00375372520647943,
0.015087255276739597,
-0.07119888812303543,
0.03409580886363983,
0.02479694038629532,
0.0018397050444036722,
-0.03420739993453026,
-0.02011861279606819,
0.03671487420797348,
-0.03161140903830528,
0.04610650613903999,
0.015310230664908886,
-0.036461055278778076,
0.06508465856313705,
-0.026084190234541893,
0.05385202541947365,
0.02717571146786213,
-0.05198049172759056,
0.01627340354025364,
0.053147125989198685,
-0.0287262424826622,
0.006352665368467569,
-0.03405255451798439,
0.004357926081866026,
0.0218511912971735,
0.007725315634161234,
0.017617862671613693,
0.007127994671463966,
0.005814968142658472,
-0.057133231312036514,
-0.007456847000867128,
0.014292423613369465,
0.01499883458018303,
-0.02585061639547348,
0.04908232018351555,
-0.008597129955887794,
-0.025684989988803864,
0.007936532609164715,
-0.029504356905817986,
-0.00004368433292256668,
0.0023813825100660324,
-0.018863067030906677,
-0.03767651692032814,
-0.04286260902881622,
-0.005844756495207548,
0.0412960983812809,
-0.010713053867220879,
-0.011395304463803768,
-0.01895611546933651,
0.010448269546031952,
-0.06619366258382797,
-0.033712238073349,
0.026271704584360123,
-0.008943585678935051,
-0.03841613233089447,
-0.02121584862470627,
-0.00036724525853060186,
0.05713890865445137,
0.024544741958379745,
0.02959572523832321,
0.014668554067611694,
-0.005756433587521315,
0.0009160442859865725,
0.05018448084592819,
-0.012894919142127037,
-0.039477378129959106,
0.02009120024740696,
-0.010412732139229774,
-0.02680043876171112,
0.07030784338712692,
0.018278440460562706,
-0.02173438109457493,
0.007542867679148912,
-0.04794791340827942,
-0.02666447125375271,
0.04753884673118591,
0.010602215304970741,
0.017025340348482132,
-0.020459288731217384,
-0.03363802656531334,
-0.03258354961872101,
0.019650449976325035,
-0.017632944509387016,
0.0600476935505867,
0.017703086137771606,
-0.03477985039353371,
-0.0415918305516243,
-0.026217805221676826,
0.026678700000047684,
0.00892576202750206,
-0.04492153972387314,
-0.044146712869405746,
0.017739202827215195,
0.05240610986948013,
0.06347928941249847,
0.016686709597706795,
-0.017422417178750038,
0.07562427967786789,
0.032035715878009796,
0.026282424107193947,
-0.008483408018946648,
-0.012712053954601288,
-0.037255026400089264,
-0.04323887825012207,
-0.07184556126594543,
0.02960853837430477,
0.018380599096417427,
-0.042856041342020035,
0.031718574464321136,
0.02884100377559662,
-0.04958061873912811,
-0.047478098422288895,
-0.062246453016996384,
0.011384915560483932,
0.0009649316780269146,
0.01697659119963646,
0.06383426487445831,
-0.14245060086250305,
0.009427055716514587,
0.020596779882907867,
-0.04239911586046219,
-0.03738841786980629,
0.03433991223573685,
0.038759972900152206,
-0.03589063137769699,
-0.03710898011922836,
0.006522757466882467,
-0.042329151183366776,
-0.034207746386528015,
-0.04707610234618187,
-0.01811607927083969,
-0.00933847762644291,
0.05273223668336868,
-0.04542933404445648,
-0.009813680313527584,
-0.006658173631876707,
-0.005614068824797869,
0.06032507121562958,
-0.015119640156626701,
-0.01175790186971426,
0.059393689036369324,
-0.05063450336456299,
-0.04397610202431679,
0.04466063156723976,
-0.01739313453435898,
-0.025210482999682426,
0.004151726141571999,
-0.007948814891278744,
-0.013655681163072586,
0.008497888222336769,
0.030378956347703934,
0.04886656999588013,
0.04271528124809265,
-0.04307527467608452,
0.05389036238193512,
0.01456662081182003,
-0.004418207332491875,
-0.020513365045189857,
-0.01483395416289568,
0.042295053601264954,
-0.008641778491437435,
-0.03539900481700897,
-0.019219957292079926,
0.024817662313580513,
0.004099039826542139,
-0.03951719403266907,
-0.06652174144983292,
-0.004611494950950146,
-0.000558361760340631,
0.011319540441036224,
0.06732656061649323,
0.021728772670030594,
-0.01995852217078209,
-0.01854553259909153,
0.058452438563108444,
-0.0260196290910244,
0.045903079211711884,
0.032377954572439194,
-0.024133892729878426,
0.018538042902946472,
-0.023572027683258057,
-0.05355275422334671,
-0.07881979644298553,
0.07063121348619461,
-0.01644423045217991,
0.004050624091178179,
-0.03243805095553398,
-0.05223749205470085,
-0.015135151334106922,
0.008390069007873535,
-0.020696522668004036,
-0.003275879891589284,
0.0009735421626828611,
-0.06271626800298691,
-0.061902713030576706,
0.011817106045782566,
0.0068647293373942375,
0.006497525610029697,
0.013135598972439766,
0.0010322690941393375,
0.003856381867080927,
-0.0424540713429451,
0.03294611722230911,
-0.03805937245488167,
0.022144220769405365,
-0.010814905166625977,
-0.05104796960949898,
0.05011097341775894,
-0.040494151413440704,
0.03619091957807541,
0.02855592593550682,
0.006315399892628193,
0.04067375510931015,
0.029362592846155167,
0.03979168087244034,
0.06850075721740723,
0.0702560693025589,
0.001384295173920691,
-0.02030457928776741,
-0.019945042207837105,
0.0025573100429028273,
0.019200971350073814,
0.005975907202810049,
0.04608890414237976,
0.027623578906059265,
-0.01192894671112299,
0.08199656754732132,
0.08638184517621994,
-0.00937596894800663,
-0.07963437587022781,
0.0475807785987854,
-0.0025529488921165466,
0.015647169202566147,
0.08384592831134796,
-0.013468479737639427,
0.04804316535592079,
-0.01244899071753025,
-0.041459642350673676,
0.002570380223914981,
-0.08120384067296982,
0.018925772979855537,
0.030317753553390503,
-0.07197430729866028,
0.0603557713329792,
-0.00030294753378257155,
-0.011715167202055454,
-0.02547641471028328,
-0.0641690194606781,
-0.017846332862973213,
0.028327222913503647,
-0.0013674634974449873,
-0.025672050192952156,
-0.042669348418712616,
0.03952023386955261,
0.005837150849401951,
-0.017484480515122414,
-0.04416269809007645,
0.04265332221984863,
-0.04402286931872368,
0.05380169674754143,
0.037820395082235336,
-0.031035181134939194,
0.004840588662773371,
0.07266835868358612,
0.026937518268823624,
0.018265292048454285,
-0.06314866989850998,
0.011963730677962303,
-0.04390530660748482,
-0.0026274260599166155,
0.042668040841817856,
-0.0060050091706216335,
-0.0012916376581415534,
0.033844973891973495,
0.00039684335933998227,
0.01298428326845169,
-0.03155770152807236,
0.006654071621596813,
0.03374277800321579,
-0.02524244785308838,
0.04130189120769501,
0.052943017333745956,
0.01271782722324133,
-0.014662654139101505,
0.06726909428834915,
-0.01395548414438963,
-0.003408456454053521,
-0.06134401634335518,
-0.04379983991384506,
0.02957405336201191,
-0.028525998815894127,
0.027698572725057602,
-0.012894809246063232,
-0.050349265336990356,
0.021154191344976425,
-0.04519886523485184,
0.04329261928796768,
0.0007537893252447248,
0.043974243104457855,
0.031537678092718124,
0.010725850239396095,
0.02134702168405056,
0.03480365127325058,
-0.015888171270489693,
0.051450006663799286,
-0.006493821740150452,
-0.0061144293285906315,
0.01548739243298769,
0.030766209587454796,
-0.060446325689554214,
0.002244373084977269,
-0.09017597138881683,
-0.0113292895257473,
0.01801021210849285,
-0.013131344690918922,
-0.019028233364224434,
0.07155252248048782,
0.02209240011870861,
0.014346595853567123,
-0.07809501141309738,
-0.04684414342045784,
0.034361109137535095,
0.04961026459932327,
-0.003060710383579135,
0.03582870215177536,
-0.062408603727817535,
-0.0404788963496685,
-0.07121102511882782,
0.022049453109502792,
-0.014204747974872589,
-0.0022834837436676025,
-0.011918661184608936,
0.02417268045246601,
0.0486844964325428,
-0.05264214798808098,
-0.013885339722037315,
0.003008169587701559,
-0.006190749350935221,
-0.07125142961740494,
0.007413303013890982,
0.013032758608460426,
0.0318252332508564,
0.046080488711595535,
-0.018074465915560722,
0.010792378336191177,
-0.025283031165599823,
0.029794281348586082,
-0.01598983444273472,
-0.03681035339832306,
0.03707912564277649,
0.05042749643325806,
0.0481109581887722,
-0.061709072440862656,
0.02333809807896614,
0.0029792070854455233,
0.034359801560640335,
0.0017023123800754547,
-0.0048195980489254,
-0.020157651975750923,
-0.0420849472284317,
0.04772143438458443,
-0.07809726148843765,
0.01586320623755455,
-0.009502867236733437,
0.03569398075342178,
0.030315956100821495,
-0.029229803010821342,
0.013349926099181175,
0.022970736026763916,
-0.012480649165809155,
-0.012596944347023964,
-0.055961281061172485,
0.029633617028594017,
0.06966833770275116,
-0.0028894527349621058,
-0.0342722050845623,
-0.05272384360432625,
-0.014728267677128315,
0.021319974213838577,
-0.018808169290423393,
0.05184289067983627,
0.07433627545833588,
-0.06604864448308945,
-0.04625043645501137,
-0.030439220368862152,
-0.02205241471529007,
-0.051464296877384186,
0.006271591410040855,
0.02767348848283291,
0.029808295890688896,
0.015273435041308403,
0.04184921830892563,
0.03831944987177849,
0.021293606609106064,
0.05541734769940376,
0.030056718736886978,
-0.004872953984886408,
-0.011762028560042381,
0.003983516711741686,
0.008448007516562939,
-0.021906547248363495,
0.057588785886764526,
0.007258094381541014,
0.012031851336359978,
-0.008856937289237976,
0.015387017279863358,
0.04109444469213486,
0.009251120500266552,
-0.028703799471259117,
-0.02411423996090889,
0.06558793783187866,
0.014344844035804272,
0.0040811593644320965,
-0.07284750044345856,
-0.0013652852503582835,
0.028950538486242294,
0.007498548366129398,
-0.01560319121927023,
0.010080580599606037,
0.06848961859941483,
0.019133398309350014,
0.01306113414466381,
0.0070435237139463425,
0.04775140434503555,
0.03734665736556053,
-0.02739124186336994,
-0.011616158299148083,
0.04027644172310829,
0.08154115080833435,
0.004086049739271402,
0.056851815432310104,
-0.03340393677353859,
0.02568099834024906,
-0.07013684511184692,
0.013371562585234642,
-0.05473260581493378,
-0.0026163042057305574,
-0.0402730330824852,
-0.057510826736688614,
0.019446691498160362,
0.07483755052089691,
-0.0008428383735008538,
-0.021544627845287323,
-0.025428414344787598,
-0.0009869777131825686,
-0.007554995361715555,
0.03952229395508766,
0.030087187886238098,
0.06512202322483063,
-0.00662325881421566,
-0.010224862955510616,
-0.052565332502126694,
-0.06835146993398666,
-0.02009766921401024,
-0.049112603068351746,
0.01413060910999775,
-0.051771413534879684,
-0.010217545554041862,
-0.01571653224527836,
-0.04631685093045235,
-0.014146465808153152,
0.004744729958474636,
0.013881192542612553,
0.03784503415226936,
0.023387501016259193,
-0.04063740372657776,
-0.01279633492231369,
0.02209312468767166,
0.005858161486685276,
-0.02814101241528988,
0.015408225357532501,
0.018919391557574272,
0.006587263196706772,
-0.012696296907961369,
-0.008655287325382233,
-0.02269243821501732,
-0.003068347694352269,
-0.016509687528014183,
0.02874705195426941,
0.061947327107191086,
0.03391246497631073,
0.0333733968436718,
-0.05568684637546539,
0.04140114784240723,
-0.016384806483983994,
-0.0257027056068182,
0.003849315457046032,
0.03482937812805176,
-0.010551807470619678,
-0.043088577687740326,
-0.03811679407954216,
0.012097330763936043,
0.032371606677770615,
-0.043650202453136444,
0.010042400099337101,
-0.004717197734862566,
0.032616887241601944,
0.01486765407025814,
0.016033153980970383,
-0.0025636504869908094,
0.016535967588424683,
0.01779899187386036,
-0.020790167152881622,
-0.04743413254618645,
-0.016148032620549202,
0.04746517911553383,
-0.03939896449446678,
-0.009150166064500809,
0.02259857952594757,
-0.07090173661708832,
-0.03747109696269035,
-0.051352787762880325,
0.0268084779381752,
0.022451775148510933,
-0.013758276589214802,
0.02155366912484169,
-0.020966408774256706,
0.05011232942342758,
-0.035469502210617065,
-0.07007472217082977,
-0.06542965769767761,
0.00029555748915299773,
-0.04020499438047409,
0.0197944026440382,
-0.00464685307815671,
-0.02388501726090908,
-0.01470211148262024,
-0.021407533437013626,
-0.015373144298791885,
-0.005361154209822416,
-0.022026188671588898,
-0.0167364664375782,
-0.030614307150244713,
0.03424052894115448,
-0.0515037477016449,
-0.0315929614007473,
0.0230681411921978,
-0.0016027484089136124,
-0.0024469560012221336,
-0.005602132994681597,
-0.006944887340068817,
0.031437650322914124,
0.008266732096672058,
-0.018703211098909378,
0.00842874962836504,
0.017035212367773056,
0.02449369616806507,
-0.030261743813753128,
-0.036360643804073334,
0.010649199597537518,
0.001368008553981781,
0.020965468138456345,
-0.08411667495965958,
-0.027409756556153297,
0.012415744364261627,
0.03476874157786369,
-0.039324644953012466,
-0.01907162368297577,
-0.026237010955810547,
0.0040718065574765205,
-0.01108548790216446,
-0.004694953560829163,
0.03268036991357803,
0.032007187604904175,
-0.0024017461109906435,
-0.020940888673067093,
-0.005486480426043272,
-0.06244215741753578,
-0.06408443301916122,
0.0008017682121135294,
0.03327392786741257,
0.008696353994309902,
-0.014653271995484829,
0.005917600356042385,
-0.04359143227338791,
-0.0026644424069672823,
-0.01639842800796032,
0.03922027722001076,
0.025349915027618408,
-0.018877923488616943,
-0.020596783608198166,
-0.060993071645498276,
-0.019034478813409805,
-0.0014288771199062467,
-0.057334549725055695,
-0.008715299889445305,
0.04477611929178238,
-0.042129214853048325,
-0.040426112711429596,
-0.01834717206656933,
0.04220952093601227,
-0.05789514258503914,
0.025360241532325745,
-0.029282519593834877,
0.03457401692867279,
0.045224931091070175,
-0.01943449303507805,
-0.008338933810591698,
-0.008031015284359455,
-0.0042474474757909775,
-0.060167498886585236,
0.011735813692212105,
-0.006418256554752588,
-0.05477335676550865,
-0.04369542375206947,
-0.05543988198041916,
0.04156140238046646,
-0.03709044307470322,
0.01012502983212471,
-0.03604232519865036,
0.027736717835068703,
-0.006201001349836588,
0.01027215737849474,
0.048866115510463715,
-0.07999861985445023,
0.026224007830023766,
0.03848820552229881,
-0.015636783093214035,
-0.03657616674900055,
0.00794715154916048,
-0.009284380823373795,
0.01263139396905899,
0.024356404319405556,
-0.03682417422533035,
-0.03471587970852852,
0.008798624388873577,
-0.011126083321869373
] |
<p>I have came across two separate explanations for why atoms have a positive atomic radius (as opposed to electrons "collapsing" into the nucleus). </p>
<ol>
<li><p>The first is via Heisenberg Uncertainty Principle, where decreasing the atomic radius would raise momentum and hence kinetic energy (while potential energy decreases) - the atom would "choose" a radius that minimizes energy. </p></li>
<li><p>The second is kind of "just set-up and solve the Schrodinger equation" and obtain a certain atomic radius.</p></li>
</ol>
<p>Are these two explanations just two sides of a single coin/a matter of interpretation? I have briefly heard that there is an equivalence between "Heisenberg" and "Schrodinger" formulation of QM - is this an instance of the equivalence?</p> | g910 | [
0.019734075292944908,
0.031211670488119125,
-0.014272032305598259,
-0.039266303181648254,
0.020306475460529327,
0.04769179970026016,
-0.028507493436336517,
0.019620824605226517,
-0.012691998854279518,
0.03061940334737301,
-0.000576828490011394,
-0.028290988877415657,
0.027232669293880463,
0.01710100658237934,
0.026576152071356773,
-0.00797498319298029,
0.055228617042303085,
-0.0004326234047766775,
0.02517244778573513,
0.02573546953499317,
-0.027567723765969276,
-0.023840392008423805,
-0.06840439140796661,
-0.030075518414378166,
-0.03925545886158943,
0.030576644465327263,
-0.045501261949539185,
0.007183249108493328,
0.003532563103362918,
-0.004329183604568243,
-0.03989781066775322,
-0.011065921746194363,
0.02267399989068508,
-0.0872037336230278,
0.025418849661946297,
0.0361364521086216,
0.07114860415458679,
0.021810151636600494,
-0.0006191121647134423,
-0.04006759077310562,
0.015859797596931458,
-0.04817797988653183,
0.020246459171175957,
-0.016128119081258774,
0.037743180990219116,
-0.027324745431542397,
0.04175012931227684,
0.04102519527077675,
0.06996546685695648,
-0.04270324483513832,
-0.011164980940520763,
0.033683545887470245,
0.033534109592437744,
0.012533025816082954,
0.02421114221215248,
0.08400635421276093,
0.001636458677239716,
0.04130493104457855,
-0.009395604021847248,
-0.0004694920498877764,
0.013855413533747196,
0.004231184255331755,
-0.0111248679459095,
0.020552577450871468,
0.07015089690685272,
-0.019669048488140106,
-0.04995837062597275,
0.015212993137538433,
0.00543949892744422,
0.009487621486186981,
-0.021378662437200546,
-0.08385071158409119,
-0.0565696582198143,
0.001451698481105268,
-0.03245602548122406,
0.03788823261857033,
-0.0317019484937191,
0.020464159548282623,
0.006538763642311096,
-0.02529812604188919,
-0.08854079991579056,
-0.044543612748384476,
0.04979703202843666,
0.0013109382707625628,
-0.025504691526293755,
0.04273197427392006,
-0.0033368414733558893,
-0.02112654410302639,
0.033237557858228683,
0.057394642382860184,
-0.014396472834050655,
-0.07128880172967911,
0.07707726955413818,
-0.0356069877743721,
-0.015762798488140106,
-0.013909714296460152,
0.010626808740198612,
0.06695032864809036,
0.024223852902650833,
0.036154232919216156,
0.004983054008334875,
0.004018278792500496,
0.03348362073302269,
-0.024608269333839417,
-0.053071703761816025,
-0.02234666422009468,
-0.046936728060245514,
-0.007702333386987448,
0.039946578443050385,
0.011489888653159142,
-0.012291111052036285,
-0.018159644678235054,
-0.04426654800772667,
-0.01875993423163891,
-0.030751457437872887,
-0.0062067462131381035,
0.1018260046839714,
0.003998416475951672,
0.03049011342227459,
0.06475500017404556,
-0.0038023623637855053,
0.04111272096633911,
0.05981696769595146,
-0.05383480340242386,
-0.003850754117593169,
-0.03720627725124359,
-0.009513625875115395,
-0.015545696951448917,
0.012779933400452137,
-0.024290379136800766,
0.04675161838531494,
0.01926138997077942,
-0.04279986396431923,
0.014068390242755413,
0.03111896850168705,
0.03891995549201965,
-0.03590821102261543,
0.004439210053533316,
-0.030477916821837425,
-0.03906940296292305,
0.013274957425892353,
0.007347960490733385,
-0.030622325837612152,
-0.02324012666940689,
-0.030382631346583366,
-0.013306465931236744,
0.0028965536039322615,
0.008644383400678635,
0.010548144578933716,
0.008498082868754864,
-0.015570835210382938,
0.012653701938688755,
-0.004735888913273811,
-0.05871494859457016,
-0.05183380842208862,
-0.01443464308977127,
0.03384462371468544,
-0.02828853763639927,
0.03272107616066933,
0.027730513364076614,
0.03340952470898628,
0.0034451456740498543,
-0.017972398549318314,
-0.006982527207583189,
-0.04466167464852333,
0.03058185987174511,
0.06923636049032211,
0.0008011445752345026,
-0.013878614641726017,
-0.018114721402525902,
0.015125492587685585,
-0.032557759433984756,
0.016804194077849388,
-0.0020032154861837626,
-0.008794396184384823,
0.05283700302243233,
0.012943695299327374,
0.00028775594546459615,
0.004907956812530756,
0.012143237516283989,
-0.029379546642303467,
-0.004633422940969467,
0.06725893169641495,
-0.018220745027065277,
0.014191754162311554,
0.013612785376608372,
0.06359487771987915,
0.06488938629627228,
-0.019804377108812332,
-0.03648015856742859,
-0.006562994793057442,
-0.08800515532493591,
0.006102521903812885,
-0.028195489197969437,
-0.023255782201886177,
-0.007213824428617954,
0.0009241364896297455,
-0.01188607793301344,
-0.04190608114004135,
0.0336264967918396,
-0.02075221575796604,
-0.0027843588031828403,
-0.03757064789533615,
0.03250690922141075,
0.05716552585363388,
-0.008567998185753822,
0.0030615185387432575,
0.02461361698806286,
0.11080604046583176,
-0.0040457588620483875,
-0.023691372945904732,
-0.018664952367544174,
-0.009723026305437088,
-0.011826946400105953,
0.023533549159765244,
0.0018221789505332708,
-0.00904602650552988,
0.024660523980855942,
-0.045752037316560745,
0.01696855016052723,
-0.005085071083158255,
-0.05761997401714325,
0.023130740970373154,
-0.010005934163928032,
0.01772933639585972,
-0.013904668390750885,
-0.03556012362241745,
-0.030226849019527435,
-0.027093226090073586,
0.017575614154338837,
-0.09467432647943497,
0.05095287784934044,
-0.015839852392673492,
-0.0011230806121602654,
0.038296040147542953,
0.08385053277015686,
-0.019699376076459885,
-0.04016231745481491,
-0.006380424834787846,
-0.053965918719768524,
0.04135365039110184,
-0.034150075167417526,
-0.07570357620716095,
0.04554659128189087,
0.00521253002807498,
-0.022334691137075424,
0.028779806569218636,
-0.08846341818571091,
-0.011288058944046497,
-0.01934298686683178,
0.005303048994392157,
-0.01491082739084959,
-0.03798116743564606,
-0.07765699177980423,
-0.058640215545892715,
-0.044916462153196335,
0.004758175928145647,
0.0381932333111763,
-0.03384358063340187,
-0.031081832945346832,
-0.006542996969074011,
-0.006450593005865812,
-0.010092189535498619,
0.08232875913381577,
0.0034368187189102173,
0.0018864931771531701,
-0.05308210477232933,
0.015854772180318832,
-0.011563567444682121,
-0.005539266858249903,
-0.00579860620200634,
0.0627562552690506,
-0.07152344286441803,
0.03463384881615639,
0.008297324180603027,
-0.06626565754413605,
-0.0027857646346092224,
-0.008999117650091648,
0.04577595368027687,
-0.030419383198022842,
0.017200421541929245,
0.022899245843291283,
-0.08185204118490219,
0.01143996138125658,
0.04332846775650978,
0.021856233477592468,
0.00936019979417324,
0.03097219578921795,
0.06495797634124756,
-0.013380246236920357,
-0.012830025516450405,
0.036999963223934174,
0.018639784306287766,
0.022566623985767365,
-0.029938066378235817,
0.05153319984674454,
0.011979548260569572,
-0.012446465902030468,
-0.027291519567370415,
0.024048348888754845,
-0.059606119990348816,
0.0028389394283294678,
-0.06087912991642952,
0.034176792949438095,
0.0271663349121809,
0.06947176903486252,
-0.04054069519042969,
-0.002922919811680913,
-0.08060512691736221,
-0.024460874497890472,
-0.056269291788339615,
0.019843516871333122,
-0.016606902703642845,
0.01822429895401001,
-0.04171154648065567,
-0.02755439467728138,
-0.05609465390443802,
0.05324729159474373,
0.038222361356019974,
-0.039959605783224106,
-0.035102471709251404,
-0.061402566730976105,
-0.019270917400717735,
-0.011272044852375984,
0.012960038147866726,
0.01987253874540329,
-0.02699207328259945,
0.015996601432561874,
0.006628945469856262,
-0.016971081495285034,
0.006319497711956501,
0.0002410130255157128,
0.0021733357571065426,
0.03491751849651337,
-0.03145930916070938,
-0.0583183728158474,
-0.01177909690886736,
-0.008896331302821636,
0.020567474886775017,
0.02068583108484745,
0.026662180200219154,
-0.017535334452986717,
-0.024895284324884415,
0.028822656720876694,
-0.026682434603571892,
0.04352540150284767,
-0.0790659561753273,
-0.04485465958714485,
0.012386899441480637,
-0.07190471887588501,
0.020243944600224495,
0.05075623467564583,
0.007162198424339294,
-0.007822557352483273,
0.02048300951719284,
0.022271543741226196,
-0.018030457198619843,
0.014217447489500046,
0.027317367494106293,
0.031188825145363808,
-0.022585440427064896,
-0.026699017733335495,
0.061588045209646225,
-0.0018537990981712937,
-0.036992792040109634,
0.0032100225798785686,
0.0007662174757570028,
-0.024160750210285187,
0.010090071707963943,
-0.03949348255991936,
-0.05390958487987518,
0.004072433803230524,
0.0067694662138819695,
-0.026013201102614403,
0.052973806858062744,
-0.006800065282732248,
0.021609196439385414,
0.04518426954746246,
-0.06512200832366943,
-0.024320034310221672,
0.015846997499465942,
0.05442100390791893,
0.008592542260885239,
0.04867781698703766,
-0.024181557819247246,
-0.05031270533800125,
-0.03402136266231537,
-0.022289171814918518,
-0.029215021058917046,
-0.08346656709909439,
-0.0700186938047409,
0.021910550072789192,
-0.054223623126745224,
0.029636161401867867,
0.02870681881904602,
0.028653956949710846,
0.04457101598381996,
-0.0385822094976902,
0.012872760184109211,
0.053066667169332504,
-0.01666352152824402,
-0.02214907668530941,
-0.027745459228754044,
-0.01808411255478859,
-0.002537647495046258,
0.007997394539415836,
0.05900833383202553,
-0.002143050543963909,
-0.033695243299007416,
0.011565378867089748,
-0.042942170053720474,
0.018821848556399345,
0.03283160179853439,
0.00007668659964110702,
0.012707860209047794,
-0.01744241453707218,
-0.03378578647971153,
0.02348090335726738,
0.020935531705617905,
0.03927905112504959,
0.024455571547150612,
0.029754463583230972,
0.06185714155435562,
-0.010334798134863377,
-0.009749800898134708,
0.003671688959002495,
0.05717673897743225,
0.06298330426216125,
0.01633426733314991,
-0.01747291535139084,
0.01719844341278076,
0.06775536388158798,
0.06766818463802338,
-0.014062215574085712,
-0.042327094823122025,
0.022554593160748482,
-0.07200279831886292,
0.08232350647449493,
0.004194014240056276,
-0.0027644066140055656,
0.03303738310933113,
-0.0002971368085127324,
0.006902483757585287,
0.04287515580654144,
-0.005369745660573244,
-0.009021960198879242,
-0.043911512941122055,
0.008737334050238132,
-0.015607647597789764,
-0.030697956681251526,
-0.037893444299697876,
0.014891894534230232,
0.010196502320468426,
-0.020930377766489983,
-0.012011458165943623,
-0.0495113804936409,
-0.08436782658100128,
0.05204290896654129,
0.07753532379865646,
0.06420385092496872,
0.005151092540472746,
0.04081433266401291,
0.01806885562837124,
0.023086007684469223,
0.004889786709100008,
-0.02944207563996315,
-0.00933857075870037,
0.012260590679943562,
-0.0545986033976078,
0.019190698862075806,
-0.008861429989337921,
0.030082669109106064,
0.025235379114747047,
-0.04657593369483948,
0.05612368509173393,
-0.01205434836447239,
0.000008908488780434709,
-0.06975826621055603,
0.04550556838512421,
-0.11435441672801971,
-0.021431876346468925,
0.002501915907487273,
0.03750449791550636,
0.013968107290565968,
0.028040187433362007,
0.025133376941084862,
0.0028938830364495516,
0.0153037179261446,
0.027485694736242294,
0.012094800360500813,
0.04177907854318619,
0.030637331306934357,
0.0647190511226654,
-0.029977627098560333,
-0.00815142784267664,
-0.005527901463210583,
0.00506087439134717,
0.014034334570169449,
-0.02248351275920868,
0.011826775036752224,
-0.046739719808101654,
-0.020292330533266068,
-0.020259205251932144,
0.02053140662610531,
0.000963932485319674,
0.01901663839817047,
0.07659287750720978,
0.04717488959431648,
0.018158255144953728,
-0.0594332292675972,
-0.008984253741800785,
-0.023569531738758087,
-0.006983238272368908,
0.021671218797564507,
0.050668198615312576,
-0.05104443058371544,
-0.055886927992105484,
0.030648790299892426,
-0.0730646550655365,
0.015260512940585613,
-0.008295668289065361,
-0.032008491456508636,
0.03436732292175293,
-0.0775124728679657,
0.017387697473168373,
0.056529201567173004,
-0.03368774801492691,
0.030374230816960335,
0.03508947044610977,
0.036675479263067245,
0.05937144160270691,
-0.02750653587281704,
0.020963428542017937,
0.03482860326766968,
-0.006721540819853544,
0.05858980491757393,
-0.01303841918706894,
0.038160502910614014,
0.026344841346144676,
0.03127667307853699,
0.043193310499191284,
-0.00832783430814743,
-0.048405833542346954,
0.052370600402355194,
-0.06123173236846924,
-0.004750708118081093,
-0.040081631392240524,
0.035067569464445114,
0.011906490661203861,
-0.018335754051804543,
-0.001014044159092009,
-0.046426258981227875,
-0.06788427382707596,
0.0009627892868593335,
0.015636229887604713,
0.03844498097896576,
0.04962751641869545,
-0.016203127801418304,
-0.012731404043734074,
0.027021674439311028,
0.029123714193701744,
-0.013884643092751503,
0.020866917446255684,
0.03870023414492607,
0.06702777743339539,
0.003917775582522154,
0.0076283602975308895,
-0.007995327934622765,
0.03009181097149849,
0.08218778669834137,
-0.02246650867164135,
0.033109087496995926,
0.022571777924895287,
0.027409853413701057,
0.031139306724071503,
0.025953346863389015,
-0.01145179197192192,
-0.001976247178390622,
0.027870193123817444,
-0.0252603180706501,
0.04136333242058754,
-0.006958560552448034,
-0.03890141472220421,
-0.026043981313705444,
0.020689992234110832,
0.019003935158252716,
-0.039881475269794464,
-0.008885780349373817,
0.0411309115588665,
-0.020226243883371353,
0.005567443091422319,
0.02353827655315399,
-0.0037585177924484015,
-0.06214934214949608,
-0.017288343980908394,
0.019474321976304054,
-0.019590439274907112,
-0.11252934485673904,
-0.0744704157114029,
-0.03396857529878616,
0.03336845338344574,
0.018775388598442078,
-0.01580495573580265,
-0.0003524291096255183,
0.022002361714839935,
0.01292426697909832,
-0.004016626160591841,
-0.013663568533957005,
0.024801960214972496,
0.02300894632935524,
-0.00667441776022315,
0.08554549515247345,
-0.004700026474893093,
0.008397245779633522,
-0.002897203667089343,
-0.06757891178131104,
0.0392610989511013,
0.045991066843271255,
-0.05690496787428856,
-0.011707908473908901,
0.009923669509589672,
-0.025906354188919067,
0.028383761644363403,
-0.010002762079238892,
0.05399959534406662,
0.04235515743494034,
0.008346031419932842,
0.035170093178749084,
0.026163145899772644,
0.0004070425347890705,
-0.030762776732444763,
0.04542039707303047,
-0.007311792112886906,
0.06579381227493286,
-0.03064023144543171,
0.03312595933675766,
-0.02395184151828289,
-0.017854537814855576,
0.038321904838085175,
0.03051888570189476,
-0.016259629279375076,
-0.026836592704057693,
0.040993161499500275,
-0.00887447502464056,
-0.07907874137163162,
0.02908881939947605,
0.020923735573887825,
-0.0034224975388497114,
-0.0574786402285099,
0.03987586870789528,
0.035260558128356934,
-0.01741327904164791,
-0.0866277888417244,
0.010625789873301983,
-0.0066847410053014755,
-0.013763402588665485,
-0.0425388477742672,
0.04123803600668907,
-0.017010176554322243,
-0.07204212993383408,
0.00699032936245203,
-0.031116338446736336,
0.0031653984915465117,
-0.05407781898975372,
0.013309183530509472,
0.029209714382886887,
-0.023258399218320847,
-0.0454590804874897,
-0.03556963801383972,
-0.049681227654218674,
0.010296830907464027,
0.0017219791188836098,
-0.016619078814983368,
-0.04907391220331192,
0.002560883294790983,
0.03481088578701019,
-0.004212288651615381,
-0.04386420175433159,
-0.01633964106440544,
-0.004204426426440477,
-0.036897849291563034,
0.06622163951396942,
-0.0090682003647089,
-0.030884545296430588,
-0.04496515169739723,
0.02059498429298401,
-0.01447196863591671,
0.027238408103585243,
-0.05282654985785484,
-0.009539475664496422,
0.015622811391949654,
0.015545506961643696,
-0.011632367968559265,
0.020695742219686508,
-0.022041114047169685,
0.028919728472828865,
0.022738946601748466,
0.045170579105615616,
0.02586134523153305,
-0.02513543702661991,
-0.027018727734684944,
-0.05578096583485603,
0.026210617274045944,
0.02067045122385025,
0.05876711383461952,
0.035394854843616486,
0.014109713956713676,
0.03280351683497429,
-0.033403296023607254,
-0.055966567248106,
0.019757799804210663,
-0.02075766585767269,
0.04202202707529068,
-0.002495918422937393,
0.045227378606796265,
-0.014147115871310234,
-0.0030808113515377045,
0.07562032341957092,
0.02624293603003025,
0.0232065599411726,
0.025996815413236618,
-0.023215090855956078,
-0.00656027439981699,
-0.010500583797693253,
-0.00984007865190506,
-0.0544985830783844,
0.010625092312693596,
-0.004574381280690432,
-0.04438196122646332,
0.025957921519875526,
-0.023527631536126137,
0.015822649002075195,
-0.04148386791348457,
-0.0333201102912426,
-0.03054461069405079,
0.02488688938319683,
-0.029122235253453255,
0.02268563024699688,
-0.026998205110430717,
0.026484977453947067,
0.003098501591011882,
-0.02538502775132656,
0.033172499388456345,
-0.010189307853579521,
-0.06178228184580803,
-0.06270557641983032,
-0.03852127864956856,
0.030712397769093513,
0.038724131882190704,
-0.05698027089238167,
-0.056925415992736816,
-0.008049805648624897,
-0.04625548794865608,
0.07147025316953659,
0.06678502261638641,
-0.06044415384531021,
-0.03552156686782837,
0.06289934366941452,
-0.00753603084012866,
-0.03542787581682205,
0.017596403136849403,
0.011799131520092487,
0.03540985658764839,
-0.0012437502155080438,
0.004535332787781954,
-0.016874784603714943,
-0.03901851549744606,
0.05499860271811485
] |
<p>According to this lecture note <a href="http://www.staff.science.uu.nl/~wit00103/qft05.pdf" rel="nofollow">http://www.staff.science.uu.nl/~wit00103/qft05.pdf</a></p>
<p>page 115. Consider a Lagrangian for a massive vector field</p>
<blockquote>
<p>$$L = -\frac{1}{4} (\partial_{\mu} V_{\nu} - \partial_{\nu} V_{\mu} )^2 - \frac{1}{2} M^2 V_{\mu}^2 + ie V_{\mu} \bar{\psi} \gamma^{\mu} \psi - \bar{\psi} (\partial \!\!\!/ +m)\psi $$</p>
</blockquote>
<p>It is said </p>
<blockquote>
<p>Note that the dimension of the vector field is generically equal to 1, but since the longitudinal
component carries no derivatives in $L$, its dimension is equal to 2.</p>
</blockquote>
<p>I could not get why the dimension of the longitudinal component is 2. How to see that? </p> | g4766 | [
0.06803644448518753,
-0.01828118972480297,
-0.017955349758267403,
-0.06736145168542862,
0.036405790597200394,
0.022526858374476433,
0.08952832967042923,
0.0283588245511055,
-0.1018904522061348,
-0.01851648837327957,
-0.003570179222151637,
0.09462811797857285,
-0.014857244677841663,
-0.0010209629544988275,
0.0244962926954031,
-0.017296353355050087,
0.027933724224567413,
-0.010726002044975758,
-0.015930958092212677,
-0.05703764036297798,
-0.020991872996091843,
-0.0058103823103010654,
0.02483169175684452,
-0.008242735639214516,
0.053678516298532486,
-0.025494862347841263,
0.0598316416144371,
-0.036960747092962265,
-0.018891815096139908,
-0.012838971801102161,
0.023189084604382515,
0.004359372891485691,
0.032658450305461884,
-0.06525018811225891,
-0.004820634610950947,
-0.0010102544911205769,
0.044546570628881454,
0.07779422402381897,
0.04889119789004326,
0.00034814406535588205,
-0.025014271959662437,
-0.023876318708062172,
0.017698971554636955,
0.01745697483420372,
-0.05317910015583038,
0.05418654531240463,
-0.0434267483651638,
0.0013588586589321494,
-0.01753869839012623,
-0.028468068689107895,
0.027788156643509865,
0.012648052535951138,
0.007491007447242737,
-0.009492038749158382,
-0.004506765864789486,
0.03684224933385849,
-0.021271636709570885,
0.03169523552060127,
0.06525571644306183,
-0.004355373326689005,
0.021078480407595634,
-0.06897939741611481,
0.029063301160931587,
0.03356971964240074,
0.028074102476239204,
-0.03401580825448036,
-0.05097782239317894,
-0.06714823842048645,
0.015683414414525032,
-0.018333233892917633,
0.00937032513320446,
-0.07086444646120071,
0.047173961997032166,
0.016449954360723495,
0.022195523604750633,
-0.0037361246068030596,
0.038751084357500076,
0.0479746088385582,
0.0030454464722424746,
-0.01618957333266735,
-0.006924073677510023,
0.010759253054857254,
-0.006109990179538727,
0.07009273767471313,
0.07656082510948181,
0.019970586523413658,
0.015347075648605824,
-0.00862268265336752,
-0.019479623064398766,
0.03114270605146885,
0.004174599889665842,
0.056839365512132645,
0.04555767774581909,
0.08949830383062363,
-0.0031580235809087753,
-0.031470589339733124,
0.006422131787985563,
0.05621478334069252,
-0.044431883841753006,
-0.004726390354335308,
0.03046386130154133,
0.1125604435801506,
0.042994435876607895,
0.05240187048912048,
0.003792201867327094,
-0.006539601366966963,
0.0021163574419915676,
0.01819564960896969,
0.00015158927999436855,
-0.04181283712387085,
-0.043491166085004807,
0.013254942372441292,
-0.027890097349882126,
-0.006384839303791523,
-0.03917169198393822,
0.004824942909181118,
0.08163502812385559,
-0.052311431616544724,
-0.04170229658484459,
0.052173126488924026,
-0.002259052824229002,
0.003930564038455486,
0.025150379166007042,
0.05747770145535469,
0.04578903317451477,
0.003834119997918606,
0.018214790150523186,
0.03847232088446617,
-0.013732311315834522,
-0.02057604305446148,
-0.0020062769763171673,
0.065690778195858,
0.024895858019590378,
-0.0023339728359133005,
0.03479760140180588,
0.009253601543605328,
-0.014359555207192898,
0.015799423679709435,
-0.04546298086643219,
0.03588256984949112,
-0.054699260741472244,
0.0014661019667983055,
-0.009269886650145054,
0.01451077125966549,
-0.029024695977568626,
-0.020815933123230934,
0.04344874992966652,
-0.06803614646196365,
0.02703164890408516,
-0.04753261059522629,
-0.02376522310078144,
0.029253274202346802,
-0.01782713457942009,
-0.014142937026917934,
0.025919310748577118,
0.0353466160595417,
0.005312315188348293,
-0.052278440445661545,
-0.013048888184130192,
0.007315384224057198,
-0.012004511430859566,
0.051530689001083374,
0.014877302572131157,
-0.051759619265794754,
-0.0488177165389061,
-0.03774401918053627,
0.01525946892797947,
-0.07342790067195892,
0.016967369243502617,
-0.00495877955108881,
-0.03945118561387062,
0.01295121293514967,
0.011447167955338955,
0.0005718522006645799,
0.004667447414249182,
0.09009360522031784,
-0.0367194339632988,
-0.027698272839188576,
0.009345006197690964,
0.06618987023830414,
-0.03035229630768299,
-0.05295845493674278,
0.003481589024886489,
-0.02193445712327957,
0.0049047223292291164,
-0.056202344596385956,
-0.0067976596765220165,
0.03228462487459183,
-0.02731917053461075,
0.01093237940222025,
-0.004171290434896946,
-0.023467686027288437,
0.006164067424833775,
0.07344601303339005,
-0.009811673313379288,
0.04140414297580719,
0.006221865303814411,
-0.06632956117391586,
-0.08705230057239532,
0.039142999798059464,
-0.059017643332481384,
0.03044215403497219,
0.04552020505070686,
0.046622660011053085,
-0.007633200380951166,
-0.002596179023385048,
-0.023056592792272568,
0.004458769224584103,
-0.005774310790002346,
-0.04668235406279564,
0.04081865772604942,
-0.061059288680553436,
-0.008323213085532188,
0.016472365707159042,
0.005873429588973522,
-0.043607212603092194,
0.011796146631240845,
0.03054697997868061,
0.0017221414018422365,
0.018427405506372452,
0.021745603531599045,
-0.019844312220811844,
0.052524395287036896,
-0.06469549983739853,
0.03020121343433857,
0.035266317427158356,
0.003348201047629118,
0.029232563450932503,
-0.006569214630872011,
-0.041809070855379105,
-0.021845996379852295,
-0.01690247282385826,
-0.014753247611224651,
0.0014363167574629188,
0.0079377181828022,
0.015410715714097023,
-0.054356977343559265,
0.041066478937864304,
0.04142408445477486,
0.03237400949001312,
0.06403058767318726,
-0.027397317811846733,
0.001975388964638114,
0.003138256724923849,
0.034822847694158554,
-0.0017443380784243345,
0.05994124710559845,
0.0012694462202489376,
-0.022088157013058662,
0.03520277142524719,
-0.05217836797237396,
-0.03332315385341644,
-0.045506950467824936,
0.04642819985747337,
0.01656723953783512,
-0.014958995394408703,
0.0314260758459568,
-0.027251245453953743,
-0.028959861025214195,
-0.010336892679333687,
-0.05314381420612335,
-0.01954871043562889,
-0.0016844113124534488,
0.09360995143651962,
-0.057523488998413086,
-0.007905939593911171,
-0.021139180287718773,
0.042157672345638275,
0.044350069016218185,
-0.0033895904198288918,
0.029056061059236526,
0.06102072075009346,
0.02776625193655491,
0.001498185214586556,
-0.025546099990606308,
-0.0013207573210820556,
-0.004106482490897179,
-0.03834272548556328,
0.011117888614535332,
-0.03315964341163635,
-0.02093801274895668,
0.024105994030833244,
0.03989892452955246,
0.02451162412762642,
0.04686680808663368,
-0.0025033040437847376,
-0.04566967859864235,
0.011323513463139534,
0.0016369987279176712,
0.016676144674420357,
-0.03605896607041359,
0.018123824149370193,
-0.02948063611984253,
-0.047642115503549576,
0.015453253872692585,
0.021130116656422615,
-0.009242835454642773,
-0.043735891580581665,
-0.036254819482564926,
-0.010930195450782776,
-0.006420262157917023,
-0.009834869764745235,
0.016397159546613693,
-0.08015891909599304,
-0.008595517836511135,
-0.02366679534316063,
-0.010953420773148537,
-0.02939038909971714,
-0.01016108226031065,
-0.025695016607642174,
0.022482404485344887,
0.0038954790215939283,
0.021896136924624443,
-0.015980862081050873,
-0.07018078118562698,
-0.00547394435852766,
0.00010593250044621527,
-0.003616803092882037,
0.026980774477124214,
0.021333830431103706,
-0.04161255806684494,
-0.05350867286324501,
-0.011737307533621788,
0.05087756738066673,
-0.019826136529445648,
-0.036224622279405594,
-0.031649865210056305,
0.031458333134651184,
-0.025854704901576042,
-0.0243108868598938,
-0.03689286857843399,
-0.016831906512379646,
0.0495748370885849,
0.004114336334168911,
-0.028169021010398865,
-0.055876072496175766,
-0.08707442879676819,
0.02271803468465805,
0.00200370280072093,
-0.02857569418847561,
-0.08168318122625351,
-0.0047574532218277454,
-0.03733173757791519,
0.012893239967525005,
0.00738672586157918,
-0.08626338839530945,
-0.010714547708630562,
0.01076220441609621,
0.02394171990454197,
0.01193310134112835,
-0.05905010178685188,
-0.004627016372978687,
-0.0039608776569366455,
0.017385128885507584,
-0.013920238241553307,
0.003033837303519249,
0.05572681874036789,
0.028223756700754166,
-0.017786435782909393,
-0.0019157275091856718,
-0.001532224123366177,
-0.0617997944355011,
0.025817837566137314,
0.043174635618925095,
0.025862770155072212,
0.04797917231917381,
0.022436192259192467,
0.0009067311766557395,
-0.030734119936823845,
0.011374568566679955,
0.05983630567789078,
0.01003130804747343,
-0.014513801783323288,
0.04988691583275795,
-0.026107769459486008,
-0.034381043165922165,
-0.0015149321407079697,
-0.02050258219242096,
-0.018979530781507492,
-0.010868064127862453,
0.06096811592578888,
0.017187707126140594,
0.02763455919921398,
-0.04741596430540085,
0.012274730019271374,
-0.015067288652062416,
-0.0545818917453289,
0.03679366409778595,
-0.005928988102823496,
-0.053221769630908966,
0.03478455916047096,
0.025420531630516052,
-0.033922336995601654,
-0.011801209300756454,
-0.028006484732031822,
0.001383961527608335,
0.04217543452978134,
0.05958929285407066,
-0.01412681769579649,
0.026878999546170235,
-0.012986215762794018,
0.041945330798625946,
0.01967187598347664,
0.011410190723836422,
0.0381910465657711,
0.007657521869987249,
0.048783425241708755,
0.007386817596852779,
0.06193660572171211,
-0.01889687590301037,
-0.030720364302396774,
0.013691462576389313,
0.05637514591217041,
-0.0707613155245781,
0.04708828777074814,
-0.019099662080407143,
0.01870865747332573,
0.006763835903257132,
0.006264373194426298,
-0.04994562640786171,
0.037863750010728836,
-0.06918752193450928,
-0.01053372211754322,
-0.009282677434384823,
0.058316800743341446,
0.05707036703824997,
0.02778168022632599,
0.009577068500220776,
-0.043647315353155136,
0.040165916085243225,
-0.0070258090272545815,
0.012928641401231289,
-0.014455989934504032,
0.003622529562562704,
-0.07611697912216187,
0.007690424099564552,
-0.0847739726305008,
0.05988591909408569,
0.01968642883002758,
0.05467033386230469,
0.029771631583571434,
-0.01677786186337471,
0.04813298583030701,
-0.035494934767484665,
0.024287229403853416,
-0.02249535359442234,
-0.01774054951965809,
-0.007536797784268856,
-0.06682563573122025,
-0.00037836062256246805,
-0.009129656478762627,
-0.004977650009095669,
-0.002673504641279578,
-0.04232053831219673,
0.06860990077257156,
-0.057263635098934174,
-0.03318323567509651,
0.005899262614548206,
0.0017060484969988465,
-0.015342818573117256,
-0.006085789762437344,
0.001421567751094699,
-0.07137935608625412,
0.004267372190952301,
0.0024215360172092915,
-0.057845599949359894,
-0.036488622426986694,
0.05109115317463875,
-0.024822480976581573,
0.011981143616139889,
0.014132107608020306,
-0.024924008175730705,
-0.04358275234699249,
0.0008963600848801434,
0.027620824053883553,
0.05439665913581848,
-0.02249761112034321,
0.002585651120170951,
-0.018358994275331497,
-0.06554695963859558,
0.040298182517290115,
-0.0818791538476944,
0.035987939685583115,
0.0006050054216757417,
0.022865261882543564,
0.03130929172039032,
0.008351072669029236,
-0.034482698887586594,
0.02039959654211998,
-0.009152385406196117,
0.0032008178532123566,
0.09306129813194275,
-0.04181274399161339,
0.07148540765047073,
-0.05921023339033127,
-0.024426428601145744,
0.01862465776503086,
-0.037352580577135086,
0.003931598737835884,
0.005171199794858694,
-0.06395595520734787,
0.025943070650100708,
0.07091813534498215,
0.0013931695139035583,
0.007028374820947647,
0.06866998970508575,
0.04013308510184288,
-0.01435721293091774,
-0.019379423931241035,
0.06087777018547058,
-0.04313168302178383,
-0.07955566048622131,
0.01634521782398224,
0.02104337327182293,
0.007346000522375107,
-0.05296880379319191,
0.06967050582170486,
0.02898973599076271,
-0.005754883401095867,
-0.025537189096212387,
0.038125015795230865,
0.027709180489182472,
-0.000010425427717564162,
-0.02895243652164936,
0.005767423659563065,
0.02008536458015442,
-0.056377798318862915,
-0.05400031432509422,
-0.08105754107236862,
0.0681767612695694,
-0.00882690865546465,
0.029202120378613472,
0.011500740423798561,
-0.02786758728325367,
-0.030712688341736794,
-0.02936883643269539,
0.013977568596601486,
-0.03531849384307861,
0.00841628760099411,
-0.03329623490571976,
-0.002009254414588213,
-0.025662221014499664,
-0.014802422374486923,
0.015666954219341278,
0.001862981473095715,
-0.007451807614415884,
0.0033582302276045084,
-0.0012980039464309812,
0.055581141263246536,
-0.01664193533360958,
-0.0005614350084215403,
0.015218334272503853,
0.03885968402028084,
-0.016893818974494934,
-0.017518924549221992,
-0.033168863505125046,
0.029966481029987335,
0.019715499132871628,
-0.03853658586740494,
-0.029815537855029106,
-0.004729850217700005,
0.01742285117506981,
0.04505019634962082,
-0.060165297240018845,
-0.030954284593462944,
-0.03542365878820419,
-0.01046944409608841,
0.01139772217720747,
0.09050197899341583,
-0.015725109726190567,
-0.0008256108267232776,
0.037317581474781036,
0.009099830873310566,
0.026623394340276718,
0.03357246518135071,
0.019414281472563744,
-0.007588585838675499,
-0.03368712589144707,
-0.013672453351318836,
0.061443477869033813,
-0.026251262053847313,
-0.006792726460844278,
0.030901091173291206,
-0.05008832737803459,
0.00921973492950201,
-0.011507836170494556,
-0.02856510318815708,
-0.04698503762483597,
0.009342771954834461,
0.05560809373855591,
-0.019345883280038834,
0.0349300242960453,
-0.001572499400936067,
0.017802726477384567,
0.0216068048030138,
-0.04227478802204132,
-0.03427305817604065,
0.0368286669254303,
-0.020240847021341324,
-0.029858531430363655,
0.06317984312772751,
0.03925983980298042,
-0.01710513047873974,
-0.01919124275445938,
-0.009011968970298767,
0.015089890919625759,
-0.061273783445358276,
0.003971731755882502,
-0.03728561848402023,
0.05406710505485535,
0.03640184551477432,
0.021663229912519455,
0.004765746183693409,
0.013226673007011414,
0.039229270070791245,
-0.08211684972047806,
-0.01039207074791193,
-0.0005464939749799669,
-0.05807335302233696,
0.003821142017841339,
0.024869095534086227,
0.028582090511918068,
-0.0035030709113925695,
-0.007464547175914049,
0.0014916853979229927,
0.04722355306148529,
-0.06056078150868416,
-0.0042862375266849995,
0.0019763633608818054,
-0.004859298001974821,
0.04211001470685005,
-0.009406480006873608,
0.026370540261268616,
0.015153785236179829,
0.04402840510010719,
0.023569157347083092,
-0.07632578909397125,
0.05365074425935745,
0.0478224903345108,
0.024312715977430344,
-0.005514900200068951,
0.009086940437555313,
0.012122944928705692,
-0.015593369491398335,
-0.031694576144218445,
0.0030588400550186634,
0.01487030927091837,
0.03320103883743286,
-0.06411360204219818,
0.03454148769378662,
0.07606428116559982,
0.06217275559902191,
0.007283600978553295,
0.00373841542750597,
-0.038305215537548065,
-0.020916474983096123,
0.016565151512622833,
-0.04071127250790596,
0.013004643842577934,
-0.0041324300691485405,
-0.07963310927152634,
-0.01640518754720688,
0.013214485719799995,
-0.005682916380465031,
-0.02798420563340187,
0.0491040013730526,
0.01099875196814537,
0.012649239972233772,
0.0722813531756401,
-0.0026469652075320482,
-0.04180171340703964,
-0.05028529465198517,
-0.005340121686458588,
0.05745726823806763,
0.01573679968714714,
0.020156387239694595,
0.005408094264566898,
0.01852133683860302,
0.008905351161956787,
-0.05037396401166916,
-0.01086959894746542,
0.09434119611978531,
-0.021913113072514534,
-0.02002306468784809,
-0.09117990732192993,
-0.07551248371601105,
-0.01524372585117817,
-0.07065141201019287,
-0.003518110141158104,
0.014326254837214947,
0.012469757348299026,
0.011640802957117558,
-0.01648503914475441,
0.03232884779572487,
0.0012678244384005666,
-0.000400127173634246,
-0.023905960842967033,
0.03317105025053024,
-0.035868797451257706,
0.04617547243833542,
-0.0006258432986214757,
-0.02333694137632847,
-0.03284604102373123,
-0.015770336613059044,
0.03180016204714775,
-0.022170916199684143,
0.04657809063792229,
0.007496948353946209,
-0.055095333606004715,
-0.028626983985304832,
-0.03797044977545738,
0.049927968531847,
-0.040749479085206985,
0.030619408935308456,
0.054301973432302475,
-0.002221024828031659,
-0.007097824942320585,
0.04880228266119957,
0.04465916007757187,
-0.10250454396009445,
-0.01848657988011837,
-0.0030402459669858217,
-0.026771267876029015,
-0.06596250087022781,
-0.0369911789894104,
-0.0076990011148154736,
0.052053485065698624,
-0.008854355663061142,
0.022939614951610565,
0.015243603847920895,
-0.023239845409989357,
-0.011004338040947914,
0.004042523913085461,
0.03246268257498741,
-0.0412524938583374,
0.01699494943022728,
0.012899131514132023,
-0.046744875609874725,
0.014544681645929813,
-0.001135252765379846,
-0.033717747777700424,
0.003168284660205245,
0.0076063829474151134,
-0.011756563559174538,
-0.026095254346728325,
0.005704482086002827,
-0.05348272621631622,
0.054843876510858536,
0.009836114011704922,
-0.03340884670615196,
-0.009339962154626846,
0.01746305637061596,
-0.02307482250034809,
0.009196218103170395,
0.060138922184705734,
-0.003650820814073086,
-0.004232821054756641,
-0.04716966301202774,
0.02096184343099594,
-0.02614215575158596,
0.02670002169907093,
0.011378543451428413,
0.024373821914196014,
-0.01853821612894535,
0.02129729650914669,
-0.07350824773311615,
-0.029465634375810623,
0.04291238263249397
] |
<p>How does one calculate the capacitance of two bodies <em>with different charges</em>? I was looking at coefficients of potential, but they don't seem helpful.</p> | g161 | [
-0.014354085549712181,
0.012399360537528992,
-0.00122499477583915,
0.03150864690542221,
0.04796217381954193,
-0.0010719988495111465,
-0.009754490107297897,
0.013027280569076538,
0.01411933358758688,
0.058193814009428024,
-0.056939009577035904,
0.030403368175029755,
0.08817286044359207,
0.004993232432752848,
0.004297552164644003,
-0.004003116395324469,
0.06484054774045944,
-0.018470315262675285,
-0.013201238587498665,
0.08123534172773361,
0.007735772989690304,
-0.022206982597708702,
0.014662252739071846,
-0.0013040066696703434,
-0.0438920222222805,
-0.02895529754459858,
-0.0351024754345417,
0.01667100377380848,
-0.10660237818956375,
-0.0366603247821331,
-0.017172185704112053,
0.03400091454386711,
0.03570110723376274,
-0.03083505481481552,
-0.027821317315101624,
-0.0020961917471140623,
0.03726666793227196,
0.0018250044668093324,
-0.029854226857423782,
0.019700611010193825,
0.0319235697388649,
-0.037809599190950394,
-0.008669654838740826,
0.021915143355727196,
0.009841887280344963,
-0.05660203844308853,
0.011956922709941864,
0.025936689227819443,
-0.035629142075777054,
-0.020658884197473526,
-0.0019127653213217854,
0.058728281408548355,
0.0287260040640831,
-0.009471016004681587,
0.0397842638194561,
-0.025826772674918175,
-0.005796362180262804,
-0.02010207623243332,
0.07700101286172867,
-0.006563973147422075,
0.041330043226480484,
0.010611962527036667,
-0.03728368505835533,
0.0009690124425105751,
0.04405338689684868,
-0.02976652793586254,
-0.006591178942471743,
0.017916571348905563,
-0.00022478804748971015,
0.00604084599763155,
0.0070020901039242744,
-0.02157462202012539,
-0.024990510195493698,
-0.03451096639037132,
-0.0011422442039474845,
-0.002595017198473215,
0.028718238696455956,
-0.0064544761553406715,
0.02795981429517269,
-0.04628647118806839,
-0.009552139788866043,
-0.02216765657067299,
0.07286424934864044,
0.01690717786550522,
0.001166853355243802,
-0.009272614493966103,
0.008749604225158691,
0.041115716099739075,
-0.033720288425683975,
-0.04258016496896744,
0.04038889706134796,
-0.0024722323287278414,
0.04000438004732132,
-0.0037200613878667355,
0.05321217328310013,
-0.05605851858854294,
0.021109456196427345,
0.019372839480638504,
0.0054803877137601376,
0.006076907739043236,
-0.020739205181598663,
0.08324915170669556,
0.046693019568920135,
0.04948883503675461,
0.013076375238597393,
0.03731232509016991,
0.008323096670210361,
0.0065999822691082954,
-0.048186950385570526,
-0.02461164817214012,
-0.04530563950538635,
-0.06123815104365349,
0.03095041587948799,
-0.018355736508965492,
-0.02136596105992794,
-0.053279511630535126,
0.021986166015267372,
-0.11217288672924042,
0.014896958135068417,
0.038158807903528214,
-0.038079503923654556,
0.024382883682847023,
-0.0003844274615403265,
-0.010687571950256824,
-0.034562382847070694,
0.037234921008348465,
0.0526687391102314,
-0.0057791429571807384,
0.0439433827996254,
0.010132494382560253,
0.059040118008852005,
-0.03227344900369644,
-0.010951277799904346,
-0.044772591441869736,
0.009163126349449158,
0.06535220891237259,
0.030922165140509605,
-0.021363941952586174,
-0.01097017340362072,
0.023153752088546753,
0.03422824293375015,
-0.021344546228647232,
0.008075647056102753,
-0.0027952746022492647,
-0.04164479300379753,
0.000703114434145391,
-0.02579013630747795,
-0.05357101559638977,
0.005874243099242449,
0.06485000997781754,
0.08715654909610748,
0.04173685610294342,
0.021737493574619293,
-0.02830413356423378,
0.0364764928817749,
-0.04395424202084541,
0.05984789878129959,
0.026797698810696602,
0.02659398689866066,
0.03702905401587486,
-0.011755324900150299,
-0.001645697862841189,
0.023944560438394547,
-0.0005602070596069098,
-0.017782583832740784,
0.025264695286750793,
-0.04483897238969803,
0.01722763106226921,
-0.0020077337976545095,
-0.0653003677725792,
0.023961935192346573,
-0.07754640281200409,
0.005179607775062323,
0.043023038655519485,
0.010793707333505154,
0.0565495528280735,
-0.019171541556715965,
0.031208021566271782,
0.031927600502967834,
0.03216016665101051,
-0.02894817478954792,
0.02174530364573002,
0.03367406874895096,
-0.010132143273949623,
-0.033584389835596085,
0.010592613369226456,
0.006704085040837526,
0.07225316017866135,
-0.04205964133143425,
-0.003497356316074729,
-0.06327468901872635,
0.010720701888203621,
-0.0348113588988781,
0.01592092402279377,
0.017824605107307434,
-0.012781365774571896,
0.06469446420669556,
-0.036405209451913834,
0.01875593326985836,
-0.04054398462176323,
-0.05622408539056778,
0.04995914548635483,
0.011835559271275997,
0.05719352513551712,
0.026362404227256775,
0.00043662620009854436,
-0.008831442333757877,
-0.02747061289846897,
0.0988197773694992,
-0.006264928262680769,
-0.011682492680847645,
0.00715008145198226,
0.024113159626722336,
0.033116232603788376,
0.008163628168404102,
0.02179088443517685,
-0.044477254152297974,
-0.020698383450508118,
-0.07384967058897018,
-0.013731053099036217,
-0.002410211367532611,
0.008559245616197586,
-0.005403577815741301,
-0.010455234907567501,
-0.06925781816244125,
0.020197046920657158,
-0.013034890405833721,
0.06521538645029068,
-0.011903882957994938,
-0.011152325198054314,
-0.014265216886997223,
0.027152135968208313,
-0.0029404449742287397,
-0.015833716839551926,
-0.05946609005331993,
0.05697433650493622,
-0.011150763370096684,
-0.012871903367340565,
0.0017419580835849047,
-0.00210125045850873,
-0.014279010705649853,
-0.03783458471298218,
0.003557961666956544,
0.024962168186903,
0.027290618047118187,
0.00949560571461916,
-0.003162669250741601,
0.009298031218349934,
-0.00124284066259861,
0.018184050917625427,
-0.02619180828332901,
-0.014207882806658745,
-0.04555040970444679,
0.01649618148803711,
-0.0243669543415308,
-0.03309134021401405,
-0.011674711480736732,
-0.006727945525199175,
-0.03525300696492195,
0.007479221094399691,
-0.011737972497940063,
-0.02455078810453415,
-0.048446714878082275,
0.044470250606536865,
-0.07296217232942581,
-0.042016979306936264,
-0.02295280434191227,
-0.00808626227080822,
0.06666842103004456,
-0.029263978824019432,
-0.03528256714344025,
0.07483820617198944,
0.01565277762711048,
-0.027789117768406868,
0.020145239308476448,
-0.05716453120112419,
0.03934507817029953,
-0.050458114594221115,
0.009933224879205227,
-0.02043425850570202,
-0.012163829989731312,
-0.0007988391444087029,
-0.03245905786752701,
0.008889764547348022,
0.05972001329064369,
-0.023054450750350952,
0.03426990658044815,
0.012068669311702251,
0.037557002156972885,
-0.024240031838417053,
-0.0020540456753224134,
0.05688716843724251,
0.019134193658828735,
-0.03534728288650513,
0.04439866915345192,
0.02438732050359249,
0.09647097438573837,
-0.029900280758738518,
-0.04182439669966698,
0.01110305916517973,
0.004382709041237831,
0.046118639409542084,
0.007505586836487055,
0.018169913440942764,
0.05527269095182419,
0.034929096698760986,
-0.004572784993797541,
-0.04773624613881111,
0.10904370993375778,
0.02889050729572773,
-0.03116915188729763,
0.002143661491572857,
0.02704019844532013,
-0.019973307847976685,
-0.00005633490945911035,
0.0000722268086974509,
0.005193531047552824,
-0.015422266907989979,
-0.0027123542968183756,
-0.06483493745326996,
0.01359522808343172,
-0.10039107501506805,
0.0551111213862896,
0.0017547683091834188,
-0.008903883397579193,
0.02698611095547676,
-0.06995046883821487,
-0.013371308334171772,
0.002618347527459264,
0.012547486461699009,
0.018727991729974747,
0.054471854120492935,
0.003181991633027792,
0.008786619640886784,
-0.037251491099596024,
-0.05151919648051262,
0.09303311258554459,
0.016894780099391937,
0.015398244373500347,
0.0002789900463540107,
-0.018813347443938255,
-0.03371766582131386,
-0.023049253970384598,
-0.08280281722545624,
-0.06979644298553467,
-0.02966182678937912,
-0.0158254224807024,
0.017518848180770874,
-0.004675368778407574,
-0.04752201959490776,
0.0002289703261340037,
-0.02256906032562256,
0.02477315068244934,
0.062415413558483124,
-0.035579435527324677,
-0.006302842870354652,
0.01665920577943325,
0.02086056023836136,
-0.08244822174310684,
0.07420003414154053,
0.029784318059682846,
-0.05199723318219185,
0.010373170487582684,
0.06007999926805496,
0.04704451560974121,
-0.05062345042824745,
-0.009111267514526844,
0.05964503437280655,
-0.0030910465866327286,
-0.018872220069169998,
0.004259662237018347,
0.004771009087562561,
0.011993330903351307,
0.03847013786435127,
0.01968463696539402,
-0.04117133468389511,
-0.03681766241788864,
-0.0025793525855988264,
-0.012526853010058403,
0.006306177005171776,
0.02699190191924572,
0.013125493191182613,
0.011969665065407753,
-0.017640257254242897,
-0.024826010689139366,
0.0017584840534254909,
0.06123052164912224,
0.022038528695702553,
-0.012778363190591335,
-0.019229382276535034,
-0.01145563181489706,
-0.05204875394701958,
-0.07804673165082932,
0.008645934984087944,
0.025674672797322273,
-0.05695164576172829,
-0.013524445705115795,
-0.06433019787073135,
0.04254277050495148,
0.025304194539785385,
0.027400095015764236,
0.0034665348939597607,
0.040879905223846436,
-0.031806156039237976,
-0.04535780847072601,
-0.02306552045047283,
0.05094054713845253,
-0.026391582563519478,
0.03210590034723282,
0.021062957122921944,
-0.014458625577390194,
-0.012110159732401371,
0.06662856042385101,
-0.017579849809408188,
-0.03255898132920265,
-0.0031850452069193125,
-0.0130055733025074,
-0.012006741017103195,
0.024010784924030304,
0.05724209174513817,
-0.019615238532423973,
-0.020678941160440445,
-0.04262763634324074,
-0.013027366250753403,
0.02164641208946705,
0.01861550845205784,
0.05890520662069321,
-0.017157020047307014,
0.021985266357660294,
0.01263517141342163,
-0.008284340612590313,
0.044864777475595474,
-0.03965993598103523,
0.035928137600421906,
-0.06931092590093613,
0.06706149131059647,
-0.025842269882559776,
0.02464924193918705,
-0.016713054850697517,
0.003070644335821271,
0.08322751522064209,
-0.018361719325184822,
-0.013153587467968464,
-0.06726520508527756,
0.008243395015597343,
0.042770761996507645,
-0.026889150962233543,
-0.0421459935605526,
-0.00022772685042582452,
-0.06340858340263367,
-0.04374083876609802,
-0.01822681538760662,
-0.038091834634542465,
-0.014720356091856956,
-0.058447711169719696,
-0.01922355592250824,
0.051879677921533585,
-0.014581783674657345,
0.013193406164646149,
-0.006468215491622686,
-0.05119701102375984,
-0.015706630423665047,
-0.024258865043520927,
-0.055761080235242844,
-0.04616972804069519,
0.015048709698021412,
-0.021748464554548264,
0.011478538624942303,
0.01835618168115616,
-0.004984608851373196,
0.036699648946523666,
0.004623027052730322,
0.014973970130085945,
0.004554469604045153,
0.029650455340743065,
0.0013773476239293814,
0.0015895465621724725,
-0.012364596128463745,
-0.09790223091840744,
-0.020543372258543968,
-0.01737792417407036,
0.03220205381512642,
-0.05083638057112694,
0.03462008759379387,
-0.038503002375364304,
-0.025798767805099487,
-0.023893041536211967,
0.007967420853674412,
0.011950364336371422,
0.014388373121619225,
-0.03047078475356102,
0.03541972488164902,
0.020020317286252975,
0.023997029289603233,
0.002315514488145709,
0.060465916991233826,
0.04664875566959381,
0.020495479926466942,
-0.07380293309688568,
0.04744900390505791,
-0.0024954865220934153,
0.0174676813185215,
-0.04725344851613045,
-0.0006289234152063727,
0.023439163342118263,
0.044284604489803314,
0.0018828698666766286,
0.012601813301444054,
0.04717756807804108,
-0.017150912433862686,
0.022368239238858223,
-0.0037598549388349056,
0.07869520783424377,
0.028224097564816475,
0.0137687548995018,
0.0821547582745552,
-0.005095253232866526,
-0.04326699301600456,
-0.0054489197209477425,
0.004778714384883642,
0.07199330627918243,
0.020611288025975227,
0.03910084441304207,
-0.026171568781137466,
-0.008898275904357433,
0.010677634738385677,
0.014996168203651905,
-0.05785250663757324,
0.016768626868724823,
0.017935696989297867,
-0.0156893040984869,
0.013732166029512882,
-0.043644532561302185,
-0.01410594955086708,
0.00045776544720865786,
-0.029354749247431755,
-0.018373558297753334,
-0.018772609531879425,
-0.002668389119207859,
0.018083591014146805,
-0.002119425218552351,
-0.0071434136480093,
0.012288115918636322,
0.04523790255188942,
-0.0018571922555565834,
-0.04646676778793335,
-0.03041735291481018,
0.030665775761008263,
0.04188452661037445,
0.05065097287297249,
-0.007514419034123421,
-0.04455893486738205,
-0.009276867844164371,
-0.025645457208156586,
0.0760955885052681,
-0.026923591271042824,
0.019716031849384308,
-0.03500949591398239,
-0.022117145359516144,
0.02353372611105442,
0.09101668000221252,
-0.02587967924773693,
0.04009706526994705,
-0.011793318204581738,
-0.026145370677113533,
-0.06267683207988739,
-0.01067209243774414,
0.026104260236024857,
0.03544272482395172,
-0.02913312427699566,
-0.01805315725505352,
0.005375977605581284,
0.031408052891492844,
-0.07880520075559616,
0.022567156702280045,
0.03844963014125824,
-0.016822120174765587,
0.013111023232340813,
0.02480980195105076,
0.021174445748329163,
-0.01887262426316738,
-0.019487090408802032,
-0.0010741287842392921,
-0.021506333723664284,
-0.022204959765076637,
0.09765616804361343,
0.025637105107307434,
-0.07727201282978058,
0.06911585479974747,
-0.016255199909210205,
-0.011436465196311474,
-0.03759447857737541,
0.07909444719552994,
-0.06887668371200562,
0.0037726389709860086,
-0.03177570179104805,
0.032241541892290115,
0.001695822225883603,
0.024734074249863625,
0.07186276465654373,
0.0783889889717102,
-0.04117993265390396,
-0.015128487721085548,
-0.01595287397503853,
0.05089036375284195,
-0.026014558970928192,
-0.012206989340484142,
-0.007897032424807549,
-0.04911252483725548,
-0.012269074097275734,
-0.08095771074295044,
-0.0236817579716444,
-0.034650303423404694,
-0.016746575012803078,
-0.01815308816730976,
-0.031610384583473206,
0.031361307948827744,
0.049897659569978714,
-0.06396135687828064,
0.024286093190312386,
0.010330704972147942,
-0.013502310961484909,
0.014758544974029064,
0.013305715285241604,
0.01256203930824995,
0.037274740636348724,
-0.01572449319064617,
-0.02496550977230072,
0.00906308926641941,
-0.072189100086689,
0.008181891404092312,
0.040323130786418915,
0.07327772676944733,
0.047940317541360855,
0.01294158585369587,
0.041393544524908066,
-0.0158270001411438,
-0.047449324280023575,
-0.03343828767538071,
0.018211781978607178,
-0.004293615464121103,
0.040050070732831955,
0.04119554162025452,
0.005064225755631924,
0.0055675627663731575,
-0.007970419712364674,
0.0526217445731163,
-0.03194095939397812,
-0.04894308000802994,
0.00971482414752245,
0.006579678505659103,
-0.04599323496222496,
0.019910939037799835,
0.05103201046586037,
-0.01526156160980463,
-0.006327953189611435,
0.06014746055006981,
-0.007411914877593517,
0.01833474449813366,
-0.021677829325199127,
0.0019874072168022394,
0.023191340267658234,
0.018338721245527267,
-0.02063807286322117,
0.02378525771200657,
-0.029159806668758392,
-0.005643066950142384,
-0.06820801645517349,
0.008415943011641502,
-0.03374120965600014,
0.0007002167403697968,
-0.034492794424295425,
-0.09195315092802048,
0.04265146702528,
-0.025963710620999336,
-0.014128094539046288,
0.0019966140389442444,
-0.010532333515584469,
-0.049874771386384964,
0.02812177687883377,
0.02135538123548031,
0.0014726088847965002,
-0.030625546351075172,
-0.002464024582877755,
-0.06504376977682114,
0.01740829460322857,
0.0011581172002479434,
-0.03795388713479042,
0.02300100214779377,
0.06599380820989609,
-0.024675728753209114,
0.0007906099199317396,
-0.01704353839159012,
-0.0005073798238299787,
-0.05790223926305771,
0.023959649726748466,
-0.014271127991378307,
0.020323442295193672,
0.06897981464862823,
-0.0054108514450490475,
0.0368058905005455,
-0.06286154687404633,
0.005645571742206812,
-0.03422834351658821,
-0.04186958074569702,
-0.027338828891515732,
-0.021934879943728447,
-0.043501272797584534,
-0.023850349709391594,
-0.01962934620678425,
0.013403588905930519,
0.047802891582250595,
0.029623819515109062,
-0.020413944497704506,
-0.05871019512414932,
0.06328637152910233,
-0.043983299285173416,
0.01936892233788967,
0.04199214652180672,
0.05192393437027931,
0.004049185197800398,
-0.04283811151981354,
0.04538033530116081,
-0.06205933168530464,
-0.0044161672703921795,
-0.07705914974212646,
0.002156395697966218,
0.04675435274839401,
0.0018253660527989268,
0.005259296391159296,
0.023441631346940994,
-0.006366245448589325,
0.0050759753212332726,
-0.001111997407861054,
-0.00879230722784996,
-0.0179807860404253,
-0.042392533272504807,
0.018520906567573547,
0.05945379659533501,
-0.034625474363565445,
-0.013658746145665646,
-0.04977353662252426,
-0.01624291017651558,
-0.06342016160488129,
-0.024395210668444633,
0.009921595454216003,
-0.032535526901483536,
0.0015678415074944496,
0.09529457986354828,
-0.012146024033427238,
0.04057161137461662,
-0.05341976135969162,
-0.059407789260149,
0.04376839101314545,
0.019935326650738716,
-0.045203518122434616,
-0.0073981028981506824,
0.021486921235919,
0.01026955060660839,
0.015223064459860325,
-0.04367251694202423,
-0.019501077011227608,
-0.03473846614360809,
-0.008419958874583244,
0.02300792559981346,
-0.04939727485179901,
-0.014759126119315624,
0.0007905875099822879
] |
<p>This is a question I found in my old high-school textbook(I'm revising the topics for a course).Two blocks A and B of masses $1kg$ and $2kg$ are placed on a fixed triangular wedge by a massless in-extensible string as shown.
<img src="http://i.stack.imgur.com/vkP06.png" alt="enter image description here"></p>
<p>The pulley is massless and friction-less. The coefficient of friction between block A and wedge is $\mu _1 = 2/3$ and that between B and wedge is $\mu _2 = 1/3$ (let's neglect the difference between static and kinetic friction).The inclines are at $45 ^\circ $ with the horizontal.We need to find the frictional force exerted on each block,and the tension in the string.</p>
<p>I worked out the problem,and I thoroughly checked my steps.Since the maximum resistive(friction) force is higher than the components of weights of the bodies along the inclines,there should be a state of equilibrium.I got the equations:
$$T= \frac {10}{\sqrt2}+f_A \space .........(1)$$
$$T+f_B=\frac {20}{\sqrt 2} \space .........(2)$$
$$=> f_A +f_B = \frac {10}{\sqrt 2} \space ....(3); f_A-f_B=2T-\frac{30}{\sqrt 2} \space ....(4)$$
$$max(f_A)=max(f_B)=\frac{10\sqrt2}{3}\space .........(5)$$
(Considering $g=10 m/s^2$) Where $f_A$ and $f_B$ are frictional forces experienced by blocks $ A$ and $B$.
There seems to be no way to get exact values of $f_A$ and $f_B$.Still,the book says(only numerical answers are given in the end,no complete solution) that $$f_A=\frac {10}{3\sqrt2} , f_B=\frac{10\sqrt2}{3} and \space T= \frac{40}{3\sqrt2} $$
All I can see by looking at the book's answers is that the author simply guessed that let there exist limiting(max) friction between $B$ and the wedge,and he might have put the value $f_B= max(f_B)$ and solved.In that case,why not the friction between $A$ and the wedge be limiting and the answers be $$f_A=\frac{10\sqrt2}{3} , f_B=\frac {10}{3\sqrt2} and \space T= \frac{50}{3\sqrt2} $$
But when we look at eq$(3)$,we see that neither of the frictions needs to be limiting,their sum needs to satisfy $\frac{10}{\sqrt2}$. Any way to justify the book's answers?</p> | g4767 | [
0.023161301389336586,
0.028501909226179123,
0.005998101085424423,
-0.01194495428353548,
0.03707210347056389,
-0.008304481394588947,
0.06367573887109756,
-0.013055951334536076,
-0.021529341116547585,
0.02193780057132244,
-0.060650862753391266,
-0.005482209846377373,
0.0026301229372620583,
0.034165699034929276,
0.036457836627960205,
0.07183098793029785,
0.07119373977184296,
-0.023846479132771492,
0.01667754165828228,
-0.019860170781612396,
-0.06269658356904984,
-0.011443288065493107,
-0.036591123789548874,
0.013807317242026329,
0.026152266189455986,
-0.020344598218798637,
0.0605207160115242,
-0.023678816854953766,
-0.042385585606098175,
0.006068226415663958,
0.010692760348320007,
-0.017937619239091873,
-0.00979434885084629,
-0.01959548331797123,
-0.04226347431540489,
-0.016109392046928406,
0.09026633948087692,
-0.009119021706283092,
0.0003933120460715145,
0.021462172269821167,
0.021945582702755928,
-0.08483266085386276,
0.027387723326683044,
0.006005445029586554,
-0.03643416985869408,
-0.028306569904088974,
-0.02701554261147976,
0.011777227744460106,
-0.004142331425100565,
0.008633117191493511,
0.006069744471460581,
0.03829465061426163,
0.06852810084819794,
-0.027814777567982674,
-0.02789357490837574,
0.02240484394133091,
0.03784412145614624,
-0.053138118237257004,
-0.008183934725821018,
0.04521363228559494,
-0.05999390035867691,
-0.004706889856606722,
0.027183139696717262,
-0.046815913170576096,
0.0182389784604311,
-0.049421992152929306,
0.004265248775482178,
0.05058895796537399,
0.004834240302443504,
0.016587549820542336,
-0.0025121141225099564,
-0.018294358626008034,
0.040849845856428146,
-0.0883355513215065,
-0.07325123250484467,
-0.03399257734417915,
0.03915984183549881,
0.01751619204878807,
0.009814203716814518,
-0.04266717657446861,
-0.027032503858208656,
0.030003610998392105,
0.013977550901472569,
-0.023304065689444542,
0.0405898354947567,
-0.043889593333005905,
0.0525100901722908,
0.020637579262256622,
-0.04135247319936752,
0.04615695774555206,
0.026196813210844994,
-0.0005990470526739955,
0.07407698035240173,
0.07298015803098679,
0.002700005192309618,
-0.00716057326644659,
0.009164917282760143,
0.0826394110918045,
-0.013904974795877934,
-0.014927501790225506,
-0.019379887729883194,
-0.0184763316065073,
0.052576154470443726,
0.015897778794169426,
0.015620856545865536,
-0.05041693150997162,
0.056617192924022675,
0.050128623843193054,
-0.03110537678003311,
0.007055396214127541,
-0.06866546720266342,
0.04471711814403534,
-0.05095366761088371,
-0.09649201482534409,
-0.008303123526275158,
0.00493368785828352,
0.0111959557980299,
0.03239861875772476,
-0.006054670084267855,
-0.00014697230653837323,
-0.03570016473531723,
-0.028394877910614014,
-0.003812753362581134,
0.0612608976662159,
0.0024988166987895966,
-0.027712438255548477,
0.01870662160217762,
0.026286110281944275,
-0.001216992037370801,
-0.04445414990186691,
-0.04340260848402977,
0.028442513197660446,
0.04937480762600899,
-0.02585669979453087,
-0.0008036639192141593,
0.04880654811859131,
-0.07469682395458221,
0.021634139120578766,
0.018861476331949234,
-0.005984005052596331,
-0.060081034898757935,
0.012171238660812378,
-0.07246582955121994,
0.03300551697611809,
-0.012005378492176533,
0.044006090611219406,
-0.05440106615424156,
0.029577402397990227,
0.01549129094928503,
0.0028066644445061684,
0.012963690795004368,
0.041866570711135864,
-0.012184918858110905,
-0.013266466557979584,
0.021989887580275536,
0.0250777006149292,
0.05851783975958824,
-0.05753978341817856,
-0.053379662334918976,
0.009663045406341553,
0.027569323778152466,
-0.055575739592313766,
0.046585921198129654,
0.014288898557424545,
-0.052915289998054504,
0.031523384153842926,
-0.04981015995144844,
-0.037925463169813156,
0.03514386713504791,
-0.023907015100121498,
-0.08642764389514923,
-0.016260547563433647,
0.05443751439452171,
0.08139266818761826,
-0.054042425006628036,
0.02718282863497734,
0.06054298207163811,
-0.011598539538681507,
0.03961760550737381,
-0.016437970101833344,
0.03852372244000435,
-0.011728387326002121,
0.060876306146383286,
0.0496705062687397,
-0.04257539287209511,
0.022915702313184738,
0.03996935114264488,
0.03330065310001373,
0.00514551717787981,
-0.020324498414993286,
-0.030536724254488945,
0.0073798350058496,
0.0013602299150079489,
0.07683973014354706,
-0.0031249180901795626,
0.02847326546907425,
-0.00693495012819767,
-0.031206436455249786,
0.04869936779141426,
-0.026811040937900543,
0.01968485116958618,
0.011887389235198498,
0.023314200341701508,
-0.044082216918468475,
0.011058271862566471,
0.000026403056835988536,
0.025556115433573723,
-0.020127618685364723,
0.0038090830203145742,
-0.008547428995370865,
0.015439473092556,
0.021734554320573807,
-0.052401456981897354,
0.05905437469482422,
-0.0006006924668326974,
-0.09726867079734802,
0.0467650406062603,
-0.018816573545336723,
0.0036717632319778204,
-0.009336035698652267,
-0.01943902298808098,
-0.049792200326919556,
-0.0028689727187156677,
-0.031200282275676727,
-0.0826881155371666,
-0.059198249131441116,
-0.01300116442143917,
-0.021336203441023827,
-0.015684306621551514,
0.02640937827527523,
-0.04400914907455444,
-0.04471936076879501,
0.025100350379943848,
-0.0043418011628091335,
0.006573849357664585,
0.004272222984582186,
0.02946608141064644,
0.0038454097229987383,
0.029829449951648712,
0.019727129489183426,
0.065098337829113,
-0.04615263268351555,
-0.053431667387485504,
-0.05147435888648033,
0.05964411795139313,
-0.010663394816219807,
-0.01002421509474516,
0.06356649100780487,
0.037004634737968445,
0.0924612432718277,
-0.010631087236106396,
0.009911412373185158,
-0.05591459199786186,
0.011969420127570629,
0.0008909322787076235,
0.03616523742675781,
-0.016327153891324997,
-0.006136508658528328,
0.012575446628034115,
-0.04176557809114456,
-0.04592318460345268,
-0.019471662119030952,
0.005901772994548082,
0.0532352514564991,
-0.09613087028265,
0.04730796068906784,
-0.03284124284982681,
-0.06019706279039383,
0.026750171557068825,
0.033309631049633026,
-0.051675885915756226,
-0.04370270296931267,
-0.0012918865540996194,
0.02226444147527218,
-0.009671327657997608,
-0.02493496611714363,
0.01209093164652586,
0.01105534378439188,
-0.023759596049785614,
0.020368603989481926,
-0.004816551227122545,
0.003252508584409952,
-0.01935005933046341,
0.035819172859191895,
0.010277566500008106,
0.014948830008506775,
-0.000783531810157001,
0.01752755604684353,
-0.020105423405766487,
0.006914463359862566,
-0.029445741325616837,
0.0013005670625716448,
0.03874307498335838,
0.05029739812016487,
0.006399872712790966,
0.04561241343617439,
-0.051161788403987885,
-0.07712415605783463,
-0.016064699739217758,
-0.015293794684112072,
-0.021525107324123383,
0.0004244680458214134,
0.05376134067773819,
0.014346763491630554,
0.021061202511191368,
-0.021035900339484215,
-0.029199864715337753,
-0.0656789019703865,
0.006258894689381123,
0.007026504259556532,
-0.003159604500979185,
0.019093263894319534,
-0.0064768544398248196,
-0.012824726291000843,
-0.022477485239505768,
0.02284783497452736,
0.045841917395591736,
0.02968093566596508,
-0.025697560980916023,
-0.045161280781030655,
-0.05266691744327545,
-0.0016470958944410086,
0.03213755041360855,
-0.0013990063453093171,
0.009359663352370262,
0.016419803723692894,
-0.10718903690576553,
0.014258025214076042,
-0.06553567945957184,
-0.008948306553065777,
0.0022697383537888527,
0.03980005532503128,
0.020221158862113953,
-0.06834307312965393,
-0.008679080754518509,
-0.07035880535840988,
0.030540864914655685,
0.020168747752904892,
0.029356947168707848,
0.02850762940943241,
-0.06277932971715927,
-0.028198737651109695,
-0.025162894278764725,
0.03214030712842941,
-0.020934324711561203,
0.03679106757044792,
-0.0063094389624893665,
0.0606258399784565,
0.0003251725865993649,
0.01915440708398819,
0.05315248668193817,
-0.025750229135155678,
0.00520044332370162,
0.009821939282119274,
0.014181128703057766,
0.04068128019571304,
0.0182383693754673,
0.01759481243789196,
-0.029924867674708366,
-0.046976275742053986,
0.07284875959157944,
0.010277064517140388,
-0.008313093334436417,
0.008922263979911804,
0.03500030189752579,
-0.026448851451277733,
0.02524752914905548,
0.013812107034027576,
-0.012189614586532116,
0.02131303958594799,
0.009367807768285275,
-0.05378357693552971,
0.026229197159409523,
-0.0023726082872599363,
0.01753106154501438,
-0.07715469598770142,
0.023023923859000206,
-0.018999364227056503,
0.008462007157504559,
0.03980989381670952,
0.036763470619916916,
0.011338132433593273,
-0.04225306957960129,
0.015228426083922386,
0.025241181254386902,
0.04248550534248352,
-0.028558799996972084,
0.011480843648314476,
0.06601013243198395,
-0.02312159352004528,
-0.009286039508879185,
-0.03200511261820793,
0.009980992414057255,
0.024255746975541115,
-0.041029784828424454,
0.03780584782361984,
0.057411693036556244,
0.015299797058105469,
0.017459237948060036,
0.003989391028881073,
-0.008298145607113838,
-0.011110707186162472,
-0.025078466162085533,
0.04332121089100838,
-0.04765108600258827,
0.03316337242722511,
0.031065255403518677,
-0.009875411167740822,
0.03754285350441933,
-0.049741230905056,
0.007930540479719639,
-0.027402572333812714,
-0.029301926493644714,
-0.012536232359707355,
0.018575452268123627,
-0.004647628869861364,
-0.012209546752274036,
-0.005391830112785101,
0.01873837597668171,
-0.026163021102547646,
0.007090618368238211,
0.00417870981618762,
-0.050845660269260406,
-0.034804921597242355,
0.06405758112668991,
-0.008992061018943787,
-0.04137949272990227,
0.04961897432804108,
0.043864257633686066,
-0.033698514103889465,
-0.0051192790269851685,
0.009236892685294151,
-0.06164369359612465,
0.012419959530234337,
-0.028904680162668228,
0.05869107320904732,
0.011884585954248905,
0.0010643686400726438,
-0.01210110355168581,
0.06289838254451752,
-0.04261746257543564,
0.06327024102210999,
-0.004139392636716366,
0.01358217466622591,
0.031007230281829834,
0.01121948566287756,
0.007526602130383253,
-0.015821337699890137,
0.009583903476595879,
-0.020176254212856293,
-0.024050742387771606,
-0.0395304299890995,
0.006614869926124811,
-0.03178770840167999,
-0.021391674876213074,
-0.028527507558465004,
0.0003956999280489981,
0.06995786726474762,
-0.003100724657997489,
-0.00018853021902032197,
0.020780988037586212,
-0.050598762929439545,
0.008721234276890755,
0.01005777157843113,
-0.025955481454730034,
0.0035906187258660793,
-0.03109356202185154,
0.025925952941179276,
0.020611513406038284,
-0.00373225100338459,
0.02769063599407673,
-0.028720881789922714,
0.044328346848487854,
0.035468149930238724,
-0.022797811776399612,
0.040939077734947205,
0.021159183233976364,
0.03492042422294617,
0.050869982689619064,
-0.019403468817472458,
-0.0800749659538269,
0.024619081988930702,
-0.017946312204003334,
-0.012608801014721394,
0.006958905607461929,
-0.057248104363679886,
-0.04528077691793442,
0.0037078666500747204,
0.043879035860300064,
0.02174842730164528,
0.03636845573782921,
0.033251769840717316,
-0.05486288294196129,
0.011657494120299816,
-0.03467683866620064,
0.025652797892689705,
0.04265543445944786,
-0.011419125832617283,
0.009582954458892345,
0.02733258157968521,
-0.011302138678729534,
0.021886171773076057,
0.032524559646844864,
-0.011547193862497807,
0.02099808119237423,
0.018578307703137398,
0.027799826115369797,
-0.056642767041921616,
-0.03002832643687725,
0.026278560981154442,
-0.029478151351213455,
0.0208188034594059,
0.041518401354551315,
0.012709238566458225,
0.048144616186618805,
0.04085163772106171,
0.04470424726605415,
0.042661841958761215,
-0.052600961178541183,
0.02746005356311798,
0.044579457491636276,
-0.010445786640048027,
0.013424630276858807,
0.02479758858680725,
-0.01923285610973835,
0.010115185752511024,
-0.015925277024507523,
-0.03386818617582321,
-0.09267926216125488,
0.032855480909347534,
-0.017834050580859184,
0.004155400674790144,
-0.0036003615241497755,
-0.012142485938966274,
-0.007047141902148724,
-0.04155604541301727,
-0.005648387596011162,
-0.048079147934913635,
-0.011352254077792168,
-0.06417009234428406,
-0.011468790471553802,
-0.0443972647190094,
0.02563679777085781,
0.0073226881213486195,
-0.023033633828163147,
0.01679193787276745,
-0.07496429234743118,
-0.0663924291729927,
0.02494848147034645,
0.008467009291052818,
-0.030298639088869095,
0.05588371679186821,
-0.05307573825120926,
-0.048813629895448685,
-0.011097620241343975,
-0.0009346840670332313,
0.010332872159779072,
-0.01633198745548725,
0.001531882444396615,
-0.024080194532871246,
0.06863317638635635,
-0.02884245477616787,
0.010249439626932144,
0.032094620168209076,
-0.015162999741733074,
-0.05989088490605354,
0.004049092996865511,
0.023092826828360558,
0.0281960591673851,
0.03748894855380058,
0.0007287911139428616,
0.018049025908112526,
0.01026410423219204,
0.06985830515623093,
0.04431255906820297,
0.010059097781777382,
-0.05716946721076965,
-0.06814628094434738,
0.059495363384485245,
0.09403343498706818,
-0.07128756493330002,
0.04874163120985031,
-0.021900581195950508,
-0.020944900810718536,
-0.019123045727610588,
0.03882769122719765,
-0.07426059246063232,
-0.028944002464413643,
0.017752952873706818,
-0.04956908896565437,
-0.06519696861505508,
0.02054717391729355,
-0.02713734284043312,
0.09319660067558289,
0.0257329773157835,
0.0015591090777888894,
0.009518547914922237,
0.022996678948402405,
0.050477515906095505,
0.043758995831012726,
0.06051131337881088,
0.0514373704791069,
0.05624527111649513,
-0.0014990509953349829,
0.004951369483023882,
-0.014437170699238777,
0.002067259978502989,
0.022339288145303726,
-0.012607531622052193,
-0.000987324514426291,
0.008413220755755901,
0.055464327335357666,
0.0020571770146489143,
0.0020621479488909245,
0.04297465831041336,
0.021640796214342117,
0.01545964926481247,
-0.02715301886200905,
-0.016900600865483284,
-0.06286618113517761,
-0.013214780949056149,
0.019457567483186722,
0.05283406749367714,
-0.06445986777544022,
-0.0064575402066111565,
-0.004659813828766346,
-0.02946835197508335,
-0.0018070113146677613,
0.030411262065172195,
0.008580343797802925,
0.05433464050292969,
0.02008870430290699,
-0.003094966057687998,
0.014966384507715702,
-0.046412479132413864,
0.06005644425749779,
-0.05553644150495529,
0.0069067892618477345,
-0.015383049845695496,
0.051483750343322754,
-0.030410099774599075,
0.016582053154706955,
-0.01658158376812935,
0.04165975749492645,
0.02730926312506199,
-0.018070198595523834,
0.05864570289850235,
0.02466585859656334,
-0.0426323302090168,
0.03344034403562546,
0.02895854040980339,
-0.02240568771958351,
-0.015877628698945045,
0.007692174520343542,
-0.031171748414635658,
-0.02465948648750782,
0.008283804170787334,
-0.04915131255984306,
0.03652738407254219,
0.04515518248081207,
-0.031206117942929268,
0.019630836322903633,
0.0503753162920475,
0.0065361931920051575,
-0.031808286905288696,
0.04796900227665901,
-0.016653362661600113,
0.03245826065540314,
-0.03647565096616745,
-0.0475824773311615,
0.012448574416339397,
-0.03649701550602913,
-0.01364349015057087,
0.007798423524945974,
0.025002496317029,
0.019272569566965103,
-0.004686201456934214,
0.0041556390933692455,
-0.043188296258449554,
-0.011375309899449348,
0.03662741184234619,
-0.02908397652208805,
0.0006232720334082842,
-0.010239002294838428,
-0.043191902339458466,
0.009409031830728054,
-0.007798176258802414,
-0.00518858851864934,
-0.0067537035793066025,
0.03542756661772728,
-0.013758615590631962,
0.06968896090984344,
0.01743932068347931,
0.015443778596818447,
0.0030625530052930117,
-0.010620803572237492,
-0.07230634987354279,
0.02830205298960209,
0.022686617448925972,
-0.028385350480675697,
-0.018919767811894417,
0.006652743089944124,
-0.04604380577802658,
-0.04193723946809769,
-0.019742116332054138,
0.0022642393596470356,
-0.007985749281942844,
-0.04149724915623665,
-0.0897103101015091,
-0.0549660362303257,
0.04300975054502487,
0.043607600033283234,
-0.032798636704683304,
-0.0018890434876084328,
0.030395902693271637,
0.03395746648311615,
-0.04561854898929596,
0.027592860162258148,
0.006135434843599796,
-0.06257852166891098,
-0.0261685773730278,
-0.01227384153753519,
-0.03995627164840698,
-0.13027024269104004,
-0.07690715044736862,
-0.017284613102674484,
0.0009078453877009451,
-0.06724240630865097,
0.020315159112215042,
0.009127934463322163,
-0.011121425777673721,
-0.0553274005651474,
0.06176096573472023,
0.016721434891223907,
-0.04213475435972214,
-0.03305361419916153,
0.016253761947155,
0.006892338860780001,
-0.006769534666091204,
0.0521821603178978,
-0.01922820508480072,
-0.014607008546590805,
-0.027572711929678917,
-0.026113588362932205,
0.011987699195742607,
0.005355112720280886,
-0.017366379499435425,
0.03805502876639366,
-0.0273372121155262,
0.0038643910083919764,
0.026484621688723564,
0.003714820137247443,
-0.034579966217279434,
0.0056504360400140285,
0.055099621415138245,
-0.03138453885912895,
0.005830544047057629,
0.015094841830432415,
0.061525315046310425,
0.006077788770198822,
-0.06840141862630844,
0.0009167086100205779,
-0.03857665881514549,
-0.040656305849552155,
0.016088174656033516,
-0.06397774815559387,
0.027482440695166588,
-0.007852775976061821
] |
<p>Why doesn't the Moon, or for that matter anything rotating another larger body, ever fall into the larger body?</p> | g931 | [
0.0065011833794415,
0.0253653172403574,
-0.004298854153603315,
-0.015786124393343925,
0.0025522366631776094,
0.054071132093667984,
0.011341136880218983,
0.012254328466951847,
-0.02433151751756668,
-0.09096251428127289,
0.017007313668727875,
-0.07514466345310211,
-0.0060781207866966724,
-0.003892878070473671,
-0.004249580204486847,
-0.019145503640174866,
0.045959390699863434,
-0.02329830452799797,
0.024911634624004364,
0.046384114772081375,
-0.020595286041498184,
0.029372116550803185,
-0.0001868268591351807,
-0.010511627420783043,
-0.03386586159467697,
0.05014241859316826,
0.0019492745632305741,
-0.01432751677930355,
0.004005120135843754,
0.015904471278190613,
-0.012967978604137897,
0.021546971052885056,
0.0028864392079412937,
-0.019994882866740227,
0.04160655662417412,
-0.0349084697663784,
-0.03496041148900986,
-0.01013951189815998,
-0.02749374881386757,
0.032727502286434174,
-0.04677281901240349,
0.023516137152910233,
-0.03660120069980621,
0.031670525670051575,
0.01257441844791174,
-0.0343402735888958,
0.044842563569545746,
0.014562045224010944,
0.031855177134275436,
-0.052581045776605606,
-0.03301636129617691,
0.024825293570756912,
0.02439768984913826,
-0.03214484080672264,
0.03425266966223717,
0.015606611035764217,
0.05639003589749336,
-0.016036268323659897,
-0.0008868085569702089,
0.053725264966487885,
0.0360402911901474,
-0.049288276582956314,
-0.008624337613582611,
-0.015176973305642605,
0.014749697409570217,
-0.019223837181925774,
-0.044944413006305695,
0.0321248359978199,
0.045790694653987885,
0.003482942236587405,
0.037601083517074585,
-0.037538181990385056,
-0.008504531346261501,
0.007912705652415752,
-0.032753996551036835,
0.021175330504775047,
-0.024855036288499832,
-0.012703287415206432,
0.007820619270205498,
-0.06053324416279793,
-0.05112650990486145,
0.03995523974299431,
0.05007810518145561,
0.02303563989698887,
0.021270958706736565,
0.029003219678997993,
0.010488058440387249,
0.014213787391781807,
-0.01923184283077717,
0.04659031704068184,
0.14096397161483765,
-0.035695355385541916,
0.013826506212353706,
-0.007691496517509222,
-0.030106715857982635,
-0.032202448695898056,
0.027919089421629906,
0.03252452611923218,
-0.07426603883504868,
-0.011949838139116764,
-0.02270202897489071,
0.033916931599378586,
-0.03959375619888306,
0.04627158120274544,
0.06236742064356804,
0.020325222983956337,
0.002636036602780223,
0.009885306470096111,
0.02080351486802101,
0.008597449399530888,
0.0041742208413779736,
-0.023774001747369766,
0.03764168173074722,
0.014034660533070564,
-0.004228684119880199,
-0.01269309502094984,
0.02409430965781212,
0.02123826928436756,
-0.010416273027658463,
0.03219456598162651,
-0.020878518000245094,
-0.03155791759490967,
-0.03542041778564453,
0.024899637326598167,
-0.025794634595513344,
-0.01569725200533867,
0.043432023376226425,
-0.0025874425191432238,
0.0017914726631715894,
-0.016215413808822632,
0.00031028292141854763,
0.042052075266838074,
-0.010312668047845364,
-0.003768559778109193,
0.04612886905670166,
0.016598131507635117,
-0.016291027888655663,
-0.042351897805929184,
-0.028759758919477463,
0.023765623569488525,
-0.01385554950684309,
0.021838830783963203,
0.03901507705450058,
-0.010326467454433441,
-0.023396149277687073,
0.05362136289477348,
0.013877096585929394,
-0.008930201642215252,
-0.017610104754567146,
0.09205302596092224,
0.006407736800611019,
0.06619460135698318,
0.044057782739400864,
-0.06405399739742279,
-0.021136891096830368,
-0.0013747786870226264,
0.04681071639060974,
-0.0126534728333354,
-0.0014486756408587098,
0.03139519691467285,
0.06656400114297867,
0.0010809770319610834,
0.004205468576401472,
-0.009583553299307823,
-0.03580200672149658,
-0.014588153921067715,
-0.07324044406414032,
-0.030217530205845833,
-0.042743247002363205,
0.0037924584466964006,
-0.07030729949474335,
-0.026560211554169655,
-0.012499800883233547,
0.10027444362640381,
0.04820605367422104,
0.08341719955205917,
-0.009382160380482674,
-0.011449825018644333,
0.07635165005922318,
-0.0018715630285441875,
-0.03526190668344498,
-0.04655195027589798,
0.009054363705217838,
0.010413526557385921,
0.015412337146699429,
-0.026312632486224174,
-0.02085592783987522,
0.04145088791847229,
-0.014386155642569065,
-0.04120277985930443,
-0.002407494932413101,
-0.009815595112740993,
-0.007290954701602459,
-0.02594088576734066,
0.028172718361020088,
-0.004850440658628941,
-0.013631118461489677,
-0.06777863949537277,
-0.0892900824546814,
0.046928878873586655,
-0.012451635673642159,
-0.008647128939628601,
0.048726245760917664,
-0.037972286343574524,
-0.009190688841044903,
0.0038110229652374983,
-0.041255928575992584,
0.03702419623732567,
-0.003712807083502412,
-0.030692383646965027,
0.03064490109682083,
0.02959897369146347,
-0.015202272683382034,
-0.0004077197809237987,
-0.043496739119291306,
-0.026217669248580933,
-0.09290046244859695,
0.027507634833455086,
0.0295096505433321,
-0.016412334516644478,
0.04092587158083916,
0.01668630540370941,
0.01179986260831356,
-0.0242649856954813,
-0.02065146341919899,
0.04710712656378746,
-0.024187562987208366,
0.029687611386179924,
0.045946020632982254,
0.02474144659936428,
-0.0690307691693306,
0.021092893555760384,
-0.01391451433300972,
0.027673549950122833,
-0.02262686751782894,
0.01873258873820305,
-0.02276621386408806,
-0.03089943155646324,
-0.025692792609333992,
0.05279615521430969,
0.007759671658277512,
-0.02298041805624962,
-0.05360555648803711,
-0.039712052792310715,
0.06721074879169464,
-0.02591611072421074,
0.00045782176312059164,
-0.002441683318465948,
-0.012055223807692528,
0.06875202804803848,
-0.00962145160883665,
0.018524162471294403,
-0.07283326983451843,
-0.050752848386764526,
-0.05418537184596062,
-0.0373736172914505,
-0.022793173789978027,
0.006093956064432859,
-0.08282789587974548,
-0.03905195742845535,
-0.03285543620586395,
0.010748948901891708,
0.038338322192430496,
-0.012410556897521019,
-0.12862904369831085,
-0.02972535230219364,
-0.04525812342762947,
-0.03934412822127342,
0.003723332192748785,
-0.006174775771796703,
0.017418060451745987,
0.03655703738331795,
0.04214778542518616,
0.015147512778639793,
-0.05882430821657181,
0.046614259481430054,
-0.021833404898643494,
-0.052791666239500046,
0.03757692500948906,
-0.030375108122825623,
-0.011711513623595238,
-0.004508709069341421,
-0.024305041879415512,
0.05118599161505699,
0.028934037312865257,
0.02034163475036621,
-0.05610207840800285,
0.03668663278222084,
0.013832406140863895,
0.0015577346784994006,
-0.04478922113776207,
-0.022474415600299835,
0.0429365448653698,
0.03362661600112915,
0.060252223163843155,
0.05409082770347595,
0.009791706688702106,
0.028934672474861145,
-0.11254000663757324,
0.043996039777994156,
0.015321268700063229,
-0.005528146401047707,
0.018408745527267456,
0.02792973630130291,
0.0016609261510893703,
0.06796684861183167,
0.008163194172084332,
-0.01905849762260914,
-0.007094331551343203,
-0.025354774668812752,
0.02124144695699215,
0.057566579431295395,
-0.04439208656549454,
0.025219568982720375,
-0.05614514648914337,
0.007345867343246937,
-0.006319367326796055,
0.08269639313220978,
0.04044727981090546,
-0.015892015770077705,
0.014300323091447353,
-0.010371973738074303,
-0.045219164341688156,
-0.049814265221357346,
0.010204960592091084,
-0.043514184653759,
-0.055960703641176224,
0.041598763316869736,
0.021005475893616676,
-0.03091924823820591,
-0.03637625649571419,
0.047677651047706604,
0.010432825423777103,
-0.04124561697244644,
-0.06029818207025528,
0.07658542692661285,
0.03873560577630997,
0.03555963933467865,
0.052254024893045425,
0.011199346743524075,
-0.03174763172864914,
-0.024986183270812035,
0.022908110171556473,
-0.019677482545375824,
0.02896822802722454,
-0.004247890319675207,
-0.0008276489097625017,
-0.03685498982667923,
-0.014170082286000252,
-0.035341404378414154,
0.04581126943230629,
0.022498203441500664,
-0.02463526464998722,
-0.00888915080577135,
0.007193730212748051,
-0.015839917585253716,
0.000039120779547374696,
-0.011034763418138027,
0.014515742659568787,
-0.05285026133060455,
0.006926026660948992,
-0.01353406347334385,
-0.032363466918468475,
0.09009522199630737,
0.02388402633368969,
0.048599958419799805,
-0.021557653322815895,
0.04213970527052879,
0.00350392609834671,
-0.021443020552396774,
0.007686183322221041,
-0.008959035389125347,
-0.04441826790571213,
0.0010147580178454518,
0.013778865337371826,
-0.0404544398188591,
-0.006850048433989286,
0.03165803477168083,
0.020386064425110817,
-0.06619268655776978,
0.034725312143564224,
-0.04230783134698868,
-0.031946439296007156,
0.01329608354717493,
-0.017122766003012657,
0.014768386259675026,
-0.04896179214119911,
-0.0009586967062205076,
-0.035914745181798935,
-0.045086514204740524,
-0.010858172550797462,
-0.015551290474832058,
0.05340494215488434,
-0.027210859581828117,
0.05342612415552139,
0.017849748954176903,
-0.01579907350242138,
-0.046974003314971924,
0.007687518373131752,
-0.05710117146372795,
-0.022919461131095886,
0.034642040729522705,
-0.03866071626543999,
-0.041498132050037384,
-0.006138158496469259,
0.009178029373288155,
0.028172435238957405,
-0.005943738855421543,
-0.020379774272441864,
0.012573390267789364,
-0.00648467568680644,
0.09742490202188492,
0.03134092316031456,
-0.05474020168185234,
0.0601993128657341,
-0.00334961642511189,
-0.02306542731821537,
-0.017768342047929764,
0.0200461745262146,
0.011805458925664425,
-0.05856211856007576,
0.020411793142557144,
-0.022549796849489212,
0.027181824669241905,
0.03498176857829094,
-0.008996778167784214,
0.038229234516620636,
0.017244646325707436,
-0.010810647159814835,
0.022189265117049217,
-0.05019791051745415,
0.03856011480093002,
0.04683682695031166,
0.022880181670188904,
-0.04185668006539345,
0.036520253866910934,
-0.017736025154590607,
0.048773519694805145,
-0.05146859958767891,
0.046212565153837204,
0.024025030434131622,
-0.03225009888410568,
0.04069923236966133,
0.03508072346448898,
-0.01769608072936535,
0.04921725019812584,
0.006184295751154423,
0.009420683607459068,
0.011046810075640678,
-0.01463114283978939,
-0.026696547865867615,
-0.04465615749359131,
-0.021372254937887192,
0.013675740920007229,
-0.03299243375658989,
-0.03629313409328461,
-0.0031493655405938625,
0.029666289687156677,
-0.03330256789922714,
0.0018582851625978947,
-0.0036524434108287096,
-0.025149062275886536,
-0.01417213212698698,
-0.00720171956345439,
-0.001798949670046568,
-0.025625158101320267,
0.011981483548879623,
0.029147526249289513,
0.010199010372161865,
0.019847026094794273,
-0.06586936861276627,
0.06129218265414238,
0.016098503023386,
0.07059236615896225,
-0.020130779594182968,
0.023866605013608932,
-0.027002761140465736,
-0.07301488518714905,
0.029695255681872368,
-0.05786764249205589,
-0.0453004464507103,
-0.0407957062125206,
0.011373698711395264,
0.004711166489869356,
-0.044809743762016296,
0.04197932779788971,
-0.0594954751431942,
-0.035425398498773575,
0.012013569474220276,
0.02937956713140011,
0.016287019476294518,
-0.02322489209473133,
-0.01492228452116251,
-0.04782550409436226,
0.024594299495220184,
0.031568992882966995,
0.003082752926275134,
-0.04173706844449043,
-0.0006356214289553463,
-0.01788063906133175,
0.01066720299422741,
-0.032051388174295425,
-0.003775401972234249,
0.01186241116374731,
0.003623389173299074,
0.045164164155721664,
0.02627570368349552,
0.005234610754996538,
-0.057895760983228683,
-0.011638478375971317,
-0.025019463151693344,
-0.03109392710030079,
0.0040426673367619514,
0.045629166066646576,
-0.0007114905747584999,
-0.02602699212729931,
0.0066434419713914394,
-0.06436876207590103,
0.02133488468825817,
-0.044274937361478806,
-0.016327455639839172,
-0.03191952779889107,
0.04833761602640152,
-0.0022039159666746855,
0.01810452714562416,
0.051841236650943756,
-0.01008639670908451,
-0.04212305694818497,
-0.029461108148097992,
-0.016523737460374832,
0.048930224031209946,
-0.04191165417432785,
0.05131613463163376,
0.060640111565589905,
-0.018631042912602425,
-0.06022908166050911,
0.009347117505967617,
0.045194510370492935,
0.036741819232702255,
-0.10929815471172333,
0.018798701465129852,
-0.02294495515525341,
-0.012992695905268192,
0.0862775519490242,
0.021505506709218025,
0.0016111682634800673,
-0.02847454696893692,
0.057684846222400665,
0.027827449142932892,
0.028543440625071526,
-0.03774936497211456,
0.04838651791214943,
-0.03111095353960991,
0.04059702903032303,
-0.0158036258071661,
-0.00010054955055238679,
-0.008375821635127068,
-0.009525041095912457,
-0.037591490894556046,
-0.017346728593111038,
-0.053374867886304855,
-0.044671401381492615,
0.00336820469237864,
-0.008978597819805145,
0.05337980389595032,
-0.03932810202240944,
-0.01212912518531084,
-0.0021325084380805492,
0.03767673298716545,
0.022190136834979057,
-0.028097083792090416,
0.02162950485944748,
-0.01486554928123951,
0.02328351140022278,
0.03727639466524124,
0.02647792361676693,
-0.022842781618237495,
-0.00420389324426651,
0.006097348406910896,
-0.010241061449050903,
0.05278810113668442,
0.013728094287216663,
-0.0018081178423017263,
0.034039612859487534,
-0.010897582396864891,
0.0038007949478924274,
-0.05858926475048065,
-0.03419738635420799,
0.04714563861489296,
-0.03564395383000374,
0.005386461038142443,
0.008086993359029293,
-0.0020723959896713495,
0.008121111430227757,
-0.06778471171855927,
-0.033656638115644455,
-0.04035177826881409,
0.0017955972580239177,
-0.03786861523985863,
-0.07383434474468231,
0.002844186732545495,
-0.00483049126341939,
0.1290653645992279,
0.059983715415000916,
-0.014672868885099888,
0.011774087324738503,
-0.031914811581373215,
-0.014058406464755535,
0.062247149646282196,
0.039107080549001694,
-0.016335658729076385,
0.009991561993956566,
-0.008391250856220722,
0.006953390780836344,
-0.02965380996465683,
-0.023327700793743134,
0.026495812460780144,
0.03976788744330406,
-0.06725811958312988,
-0.02069845423102379,
0.027076655998826027,
-0.024307921528816223,
0.008004993200302124,
-0.03350828215479851,
0.014407935552299023,
-0.036520861089229584,
-0.0589144192636013,
0.019184548407793045,
0.00943274237215519,
0.02230994403362274,
0.056014806032180786,
0.019055137410759926,
-0.047807373106479645,
-0.01754026859998703,
0.05452052503824234,
0.08020039647817612,
-0.04290730506181717,
-0.005786890164017677,
0.036325376480817795,
-0.03243838623166084,
-0.05444997921586037,
0.074445441365242,
0.0005111541249789298,
0.030820723623037338,
0.00017888619913719594,
0.028390437364578247,
0.014274491928517818,
0.039880234748125076,
-0.05278307944536209,
-0.015325747430324554,
0.02074698731303215,
0.018871186301112175,
-0.010294207371771336,
0.03632006049156189,
-0.004621437285095453,
0.016530048102140427,
-0.00812741182744503,
-0.004363566637039185,
0.011384285986423492,
-0.00910300761461258,
0.025627950206398964,
0.011406311765313148,
0.011089111678302288,
0.028084972873330116,
-0.013354083523154259,
-0.025096066296100616,
-0.011694861575961113,
0.004803854506462812,
0.03404904529452324,
0.030656037852168083,
-0.009300705045461655,
0.009438729844987392,
-0.06433622539043427,
-0.017811739817261696,
0.02742423489689827,
-0.045231178402900696,
0.05139030143618584,
-0.047005545347929,
0.024804696440696716,
0.026911573484539986,
-0.012556720525026321,
0.052369456738233566,
0.02414252981543541,
0.06554167717695236,
0.0007294760434888303,
0.0068144830875098705,
0.0210732314735651,
-0.0026775894220918417,
0.010852606035768986,
0.0050423466600477695,
0.022666919976472855,
0.026795873418450356,
-0.01373840868473053,
0.03745586797595024,
-0.0626414492726326,
-0.0035752132534980774,
-0.01409969013184309,
0.01037391647696495,
0.006603718735277653,
0.04247641563415527,
0.016213173046708107,
-0.006909966003149748,
-0.049267955124378204,
-0.05690383538603783,
0.051927972584962845,
0.0918637290596962,
-0.04558517411351204,
0.029766790568828583,
-0.0690041184425354,
-0.026996241882443428,
0.028546864166855812,
0.0739753469824791,
-0.02048235572874546,
0.007390426937490702,
0.03647284582257271,
0.005528458394110203,
-0.014257006347179413,
0.038265410810709,
-0.03580549731850624,
-0.0033485691528767347,
0.023975059390068054,
0.01543961651623249,
0.0036617154255509377,
-0.0785929337143898,
-0.05540665611624718,
-0.05769113451242447,
0.02977874130010605,
-0.007388216909021139,
-0.005699151661247015,
-0.012133026495575905,
-0.013856594450771809,
0.05800074338912964,
-0.017386263236403465,
-0.09517877548933029,
-0.05769119784235954,
-0.021396955475211143,
-0.059425339102745056,
-0.04908479005098343,
-0.009411650709807873,
-0.0006509246304631233,
-0.03809273988008499,
0.004785376135259867,
0.07727538049221039,
-0.008832976222038269,
0.02077881433069706,
0.034664593636989594,
-0.007246498484164476,
0.07597576826810837,
0.0385950468480587,
-0.026552902534604073,
0.03301144018769264,
0.06893150508403778,
-0.0174406748265028,
0.03825950622558594,
0.03221890702843666,
0.01853884384036064,
-0.04002406448125839,
0.040448177605867386,
0.0006638109916821122,
0.004157713148742914,
0.01635185442864895,
0.03881295397877693,
0.00849569495767355,
-0.08290513604879379,
0.03116004355251789,
-0.011112572625279427,
-0.03388723358511925,
0.028560396283864975
] |
<p>As the earth rotates around itself, does this have any effect on the dynamics of flights?</p>
<p>Or "shouldn't" this have an effect?</p>
<p>Does flying in the direction of the rotation of earth around itself, or against, it take the same time? and if yes, why?</p>
<p>Let me try to make my question clearer one more time: once the aircraft is in the air, why don't we add the earth's speed rotation to its speed if it is moving the direction of the rotation, and why don't we deduct when it is moving in the opposite direction of the rotation, as simple logic suggests?</p> | g162 | [
0.020501460880041122,
0.053306713700294495,
0.023911094292998314,
0.0682898610830307,
0.032135847955942154,
0.019092516973614693,
0.10122035443782806,
-0.007225323468446732,
-0.026926586404442787,
-0.07023560255765915,
0.021067041903734207,
0.0008624288602732122,
-0.01651313714683056,
0.0663876160979271,
0.030649179592728615,
-0.026787981390953064,
-0.0012421616120263934,
-0.017488062381744385,
0.06390604376792908,
0.007289777975529432,
-0.006338968873023987,
-0.02961888536810875,
-0.01077456958591938,
-0.012079507112503052,
-0.012164471670985222,
-0.00318975280970335,
-0.013109582476317883,
-0.09297173470258713,
-0.03586207330226898,
-0.0030747370328754187,
0.027504419907927513,
0.04251755401492119,
-0.007920513860881329,
-0.0422784760594368,
-0.02462799847126007,
-0.007344070356339216,
-0.02719806507229805,
0.0008285754593089223,
0.04570050537586212,
-0.03617095947265625,
0.01635555736720562,
0.001208463916555047,
-0.0509776845574379,
0.018236657604575157,
0.031336814165115356,
0.04575241729617119,
-0.02413230948150158,
0.029983466491103172,
0.011695723980665207,
-0.023194892331957817,
-0.03753682225942612,
0.008309194818139076,
0.01761186681687832,
-0.0003686956479214132,
-0.006964675150811672,
-0.020215027034282684,
0.06686864793300629,
0.007154345512390137,
-0.009101293049752712,
0.012131609953939915,
-0.04902438074350357,
-0.012303141877055168,
-0.029105570167303085,
0.006726197432726622,
0.029518088325858116,
-0.04079011082649231,
-0.04878222197294235,
-0.05967535451054573,
0.04082093760371208,
0.027645695954561234,
0.0428311824798584,
-0.04152540862560272,
-0.02696393057703972,
-0.031651318073272705,
-0.012401482090353966,
-0.005124259740114212,
0.039041485637426376,
-0.024404224008321762,
0.06754633039236069,
0.0073427194729447365,
-0.03661720082163811,
0.004633309785276651,
0.009675111621618271,
-0.021781228482723236,
0.049473728984594345,
0.002878535073250532,
0.03053903393447399,
0.04433830454945564,
-0.019309384748339653,
0.017772389575839043,
0.014591814950108528,
-0.05500772222876549,
0.02899240516126156,
0.02295823022723198,
-0.07452927529811859,
-0.08670685440301895,
-0.0124554093927145,
0.06543327867984772,
-0.07582655549049377,
0.053885046392679214,
-0.03909870237112045,
0.03382273018360138,
-0.018540171906352043,
0.0029645918402820826,
0.027435120195150375,
-0.0104394955560565,
0.05807330086827278,
0.037335775792598724,
-0.018419167026877403,
-0.07551155984401703,
-0.01380845531821251,
-0.05271186679601669,
0.022876301780343056,
0.030590981245040894,
-0.0145923662930727,
-0.021481527015566826,
0.04371034353971481,
-0.04826623946428299,
0.02218722179532051,
0.04149329289793968,
0.03423193842172623,
-0.00007330913649639115,
-0.009402899071574211,
-0.01046266034245491,
0.010800143703818321,
-0.031177716329693794,
0.03159996494650841,
-0.004884596448391676,
0.02455850876867771,
0.004900685045868158,
-0.022651806473731995,
0.016842296347022057,
0.013754701241850853,
0.0620117150247097,
-0.03182872384786606,
-0.042348653078079224,
-0.01365999411791563,
0.04183608666062355,
-0.06214261054992676,
0.02656709775328636,
0.06373607367277145,
0.03503130376338959,
0.04538971930742264,
0.0012345100985839963,
-0.0706104040145874,
0.06465554237365723,
0.0064057703129947186,
-0.024298787117004395,
0.07052280008792877,
0.014584940858185291,
-0.01970723457634449,
0.02790364809334278,
-0.035773735493421555,
-0.03285848721861839,
0.04129544645547867,
0.01802331767976284,
0.02393632009625435,
0.03903427720069885,
-0.022481445223093033,
0.010182802565395832,
0.07507877796888351,
0.009026030078530312,
0.0011333008296787739,
0.03552580252289772,
-0.017473343759775162,
0.028964806348085403,
-0.004513667896389961,
-0.018601175397634506,
-0.03166503459215164,
0.05044500157237053,
0.002824750728905201,
0.006750226020812988,
0.026589790359139442,
0.011804343201220036,
0.01701207086443901,
0.05990529805421829,
0.032616257667541504,
-0.02986305020749569,
-0.009478849358856678,
0.01203254796564579,
-0.020119884982705116,
0.013826980255544186,
-0.017648527398705482,
-0.008110661059617996,
0.017468081787228584,
-0.027605779469013214,
-0.014606102369725704,
-0.024517036974430084,
-0.07706063240766525,
-0.018078792840242386,
0.02416660264134407,
-0.027207735925912857,
-0.05721723660826683,
0.008390892297029495,
-0.08854915201663971,
-0.024614039808511734,
-0.011929509229958057,
0.03719501569867134,
-0.030776672065258026,
0.05607273429632187,
0.009179321117699146,
-0.022101905196905136,
0.09441104531288147,
-0.016026118770241737,
0.012097629718482494,
-0.02034704014658928,
0.0032746947836130857,
0.02072957344353199,
0.03678544610738754,
0.022853892296552658,
0.09720182418823242,
0.04562406986951828,
0.008160112425684929,
0.05784330889582634,
0.03214510902762413,
0.030757779255509377,
-0.019255489110946655,
-0.002093356102705002,
0.014224711805582047,
-0.004767180420458317,
0.02915976569056511,
-0.01787453517317772,
-0.0010311496444046497,
-0.05370071157813072,
-0.06061499938368797,
-0.029008373618125916,
-0.059754688292741776,
-0.03195793554186821,
-0.007436003070324659,
0.04637974500656128,
-0.02705025114119053,
-0.009496862068772316,
0.013487358577549458,
-0.02030179835855961,
0.0599646233022213,
0.0115297120064497,
0.05160067230463028,
0.05748694762587547,
-0.00747390603646636,
-0.009561791084706783,
0.01905791647732258,
0.0017699399031698704,
-0.02017478458583355,
-0.0015325347194448113,
0.037523865699768066,
-0.055315736681222916,
0.03481515496969223,
-0.018642820417881012,
-0.009090358391404152,
0.04698130115866661,
0.06158177927136421,
-0.002866736613214016,
-0.0635005533695221,
0.02803369238972664,
-0.01927889697253704,
0.004919013474136591,
-0.061243936419487,
0.04294730722904205,
-0.02935241349041462,
-0.006997269578278065,
-0.0410502664744854,
-0.009266446344554424,
0.006750595290213823,
0.0011892557376995683,
-0.036884281784296036,
0.017221489921212196,
-0.02647433802485466,
0.024919597432017326,
-0.006653144024312496,
-0.007229630369693041,
-0.06937852501869202,
0.008833922445774078,
0.035606011748313904,
0.07011473178863525,
0.017949899658560753,
-0.03924701735377312,
0.017656465992331505,
-0.0018238865304738283,
-0.025478985160589218,
0.03241853788495064,
0.024182405322790146,
0.0012895604595541954,
-0.05215642601251602,
0.05079241096973419,
0.08282344788312912,
-0.013999547809362411,
-0.04862093925476074,
0.030859895050525665,
-0.04325410723686218,
0.006409395486116409,
-0.011025016196072102,
0.01939806342124939,
0.08033151179552078,
0.010465884581208229,
0.05536298081278801,
0.04114847630262375,
0.05088500678539276,
-0.062270425260066986,
-0.038725510239601135,
0.024503586813807487,
0.01926751434803009,
0.0013469915138557553,
-0.00430641183629632,
0.060556769371032715,
-0.03420840948820114,
0.041875313967466354,
-0.04326815530657768,
-0.046467334032058716,
-0.052166324108839035,
0.034851543605327606,
-0.05768176168203354,
0.04718060791492462,
-0.06342324614524841,
-0.007751201279461384,
0.01181277260184288,
-0.022183001041412354,
-0.08707348257303238,
0.017014745622873306,
0.023030875250697136,
-0.006589511409401894,
-0.04700097441673279,
-0.03246338292956352,
-0.0501599982380867,
-0.0026479715015739202,
0.00033219114993698895,
0.0350567027926445,
-0.01714242808520794,
0.002582584274932742,
-0.046722155064344406,
-0.08529176563024521,
0.018009521067142487,
0.015636272728443146,
-0.019813213497400284,
0.01696176640689373,
-0.07884339243173599,
0.006970661226660013,
0.03104448691010475,
-0.002082456834614277,
0.01738087646663189,
0.08423641324043274,
-0.040898315608501434,
-0.008267341181635857,
-0.0167384035885334,
-0.03111588954925537,
-0.017363576218485832,
-0.011828993447124958,
0.016905035823583603,
0.01895429939031601,
-0.05417764186859131,
0.036218516528606415,
0.0974951758980751,
-0.0008697196608409286,
-0.054684173315763474,
-0.04916432127356529,
0.020834991708397865,
0.011421416886150837,
0.01799612306058407,
0.029164502397179604,
-0.011934613808989525,
0.017566382884979248,
-0.03532315045595169,
-0.00031086025410331786,
-0.016532305628061295,
0.010648339986801147,
0.018840638920664787,
0.016250483691692352,
-0.02089342288672924,
0.0255208071321249,
-0.03201715648174286,
-0.006001120898872614,
0.03200116381049156,
0.06828499585390091,
-0.033526461571455,
0.005702722351998091,
0.03560870140790939,
-0.0593891404569149,
0.03925615921616554,
0.007736670318990946,
-0.0015197047032415867,
-0.022841624915599823,
0.018091892823576927,
0.013039132580161095,
0.006649705581367016,
0.007228630129247904,
0.012731092981994152,
0.028280479833483696,
-0.008008467964828014,
-0.029794318601489067,
0.006897930521517992,
-0.02145962417125702,
0.03656230494379997,
-0.021873096004128456,
0.045119546353816986,
0.00955154187977314,
0.04732504487037659,
0.0302437711507082,
-0.032616060227155685,
-0.01969308778643608,
-0.02664966695010662,
0.020022915676236153,
0.025055017322301865,
0.005841520614922047,
-0.07310228049755096,
0.018047893419861794,
-0.015715312212705612,
0.04249555990099907,
-0.0013065780512988567,
-0.0379764661192894,
-0.018712705001235008,
-0.01435778196901083,
-0.029801689088344574,
0.00649142125621438,
-0.0578216016292572,
-0.07742629945278168,
0.01919803023338318,
0.030150262638926506,
0.010046510025858879,
0.04231666028499603,
0.04651052504777908,
-0.04170463979244232,
0.0032889386638998985,
0.05774857476353645,
0.06089131161570549,
-0.015399736352264881,
-0.03512163460254669,
0.02407071739435196,
0.02951962500810623,
-0.015471242368221283,
-0.016072053462266922,
0.011715443804860115,
0.010022563859820366,
-0.013847777619957924,
-0.0035074667539447546,
0.016270916908979416,
-0.04476214945316315,
0.012364458292722702,
0.04260542243719101,
0.11190182715654373,
0.04248221218585968,
-0.04925532266497612,
0.0090913912281394,
0.01972789876163006,
0.05717163905501366,
-0.026564734056591988,
-0.01361798495054245,
0.01676875352859497,
-0.060418616980314255,
-0.030872661620378494,
-0.006899955216795206,
-0.04069116711616516,
-0.05756339058279991,
0.05176710709929466,
0.027657078579068184,
0.014795910567045212,
-0.08552272617816925,
-0.02034343220293522,
-0.033705394715070724,
-0.010336952283978462,
-0.011333733797073364,
-0.0026797575410455465,
-0.07420148700475693,
0.023987848311662674,
-0.012792768888175488,
-0.006324059795588255,
-0.06035808101296425,
0.011960916221141815,
0.004722236189991236,
-0.03871563449501991,
-0.052157845348119736,
0.010366796515882015,
0.024244854226708412,
-0.010360468178987503,
-0.05155130848288536,
0.06831693649291992,
-0.010781925171613693,
0.025364020839333534,
0.03914780542254448,
-0.008832446299493313,
-0.030891122296452522,
-0.07591409981250763,
-0.019610434770584106,
-0.03738068789243698,
0.03416501358151436,
0.02005705237388611,
-0.006140213925391436,
-0.001163483364507556,
-0.027331339195370674,
-0.04759830981492996,
0.013477517291903496,
-0.05685224011540413,
0.03682009503245354,
-0.009478929452598095,
-0.06391970813274384,
-0.07446808367967606,
-0.053949832916259766,
0.0015776650980114937,
-0.008038793690502644,
-0.03968337923288345,
-0.03840721771121025,
-0.05436788499355316,
-0.0037869890220463276,
0.0308226365596056,
-0.011430605314671993,
0.027397170662879944,
-0.024244049564003944,
0.051235031336545944,
0.09839986264705658,
-0.023983292281627655,
-0.08695394545793533,
0.04375467821955681,
-0.026438118889927864,
-0.004540930036455393,
-0.003060495713725686,
-0.011031927540898323,
0.02614135667681694,
-0.007836750708520412,
-0.018151741474866867,
-0.02082371711730957,
0.0513303168118,
-0.01782536506652832,
-0.009657456539571285,
0.04173775017261505,
-0.0032275323756039143,
-0.035531673580408096,
0.03640645369887352,
-0.03768637403845787,
-0.048729632049798965,
-0.011137801222503185,
0.025282762944698334,
0.040707867592573166,
0.03758227825164795,
-0.016561811789870262,
0.053547076880931854,
0.001041432493366301,
0.027388043701648712,
-0.04549882933497429,
-0.004394696094095707,
-0.03270348906517029,
0.035170167684555054,
0.004143576603382826,
-0.030185898765921593,
0.02134212851524353,
0.03137911483645439,
0.07508126646280289,
0.007629286032170057,
-0.0350630022585392,
-0.035427991300821304,
-0.009672661311924458,
0.02683033049106598,
0.023404134437441826,
-0.0893685445189476,
0.049381986260414124,
-0.03882042318582535,
-0.05028575286269188,
-0.06215634196996689,
0.046200230717659,
-0.010649643838405609,
0.001882700715214014,
0.0322214774787426,
-0.04678841680288315,
0.01657111756503582,
0.010362157598137856,
0.02336950972676277,
0.03203495591878891,
0.008362085558474064,
-0.0054999408312141895,
0.045593246817588806,
-0.009099546819925308,
0.0296711977571249,
0.011000940576195717,
-0.006883063819259405,
-0.0148445013910532,
-0.01258041337132454,
0.022030850872397423,
0.01556344423443079,
0.0423392578959465,
-0.020862266421318054,
-0.029723117128014565,
-0.06603407859802246,
-0.0041794609278440475,
0.0025830515660345554,
-0.03473640978336334,
0.023669781163334846,
-0.044717174023389816,
0.035980816930532455,
-0.007640047464519739,
-0.0025911659467965364,
0.02285212278366089,
0.0665513202548027,
-0.015551063232123852,
-0.038855861872434616,
-0.008759829215705395,
-0.00818807352334261,
-0.021290991455316544,
-0.014643552713096142,
-0.03422649949789047,
0.0010477157775312662,
0.01985195092856884,
0.0009075041743926704,
0.021969789639115334,
0.024331724271178246,
-0.031299006193876266,
0.14735539257526398,
-0.046138908714056015,
0.03687835857272148,
-0.007600277196615934,
-0.001955744344741106,
-0.010287443175911903,
0.028669269755482674,
-0.0003021483134943992,
-0.0034898491576313972,
0.004817445296794176,
0.033639539033174515,
0.0042723664082586765,
-0.011204375885426998,
-0.01203078031539917,
0.009031273424625397,
-0.0022835039999336004,
0.003659848589450121,
0.02918204665184021,
0.0011405893601477146,
-0.0031738101970404387,
-0.02496650069952011,
-0.03365584835410118,
0.049537401646375656,
0.013841108419001102,
-0.0683940127491951,
0.01062563806772232,
-0.0083163408562541,
0.03018108196556568,
0.04096380993723869,
0.05892522633075714,
-0.06970244646072388,
0.04312138631939888,
0.037493832409381866,
0.023314177989959717,
-0.04331478849053383,
0.050988104194402695,
-0.02997848391532898,
-0.002467749174684286,
-0.03063972480595112,
0.0420689731836319,
0.01364879310131073,
-0.00648378673940897,
-0.048433221876621246,
0.0071359118446707726,
0.05277010425925255,
-0.08945346623659134,
0.012408197857439518,
-0.013599738478660583,
-0.0005889133899472654,
-0.03938203677535057,
-0.026552114635705948,
0.040634311735630035,
0.046609796583652496,
-0.0204653050750494,
0.018489565700292587,
0.025564607232809067,
-0.0023431635927408934,
-0.024773292243480682,
-0.0249924436211586,
-0.042688265442848206,
-0.07545337826013565,
0.02268657088279724,
-0.02053009532392025,
-0.00019643999985419214,
0.018380139023065567,
0.017758812755346298,
-0.007023091893643141,
0.03908500820398331,
-0.009122719056904316,
0.018661310896277428,
-0.006390111055225134,
-0.007058137562125921,
0.0028539325576275587,
0.04129170626401901,
-0.020894696936011314,
-0.04591263830661774,
0.01603779010474682,
-0.024014988914132118,
0.024669861420989037,
0.01078756432980299,
-0.008757209405303001,
0.03734017536044121,
-0.01926015131175518,
0.02293238788843155,
0.002077083569020033,
-0.032735634595155716,
-0.056411754339933395,
-0.10988183319568634,
0.03311939164996147,
0.048440057784318924,
-0.007841735146939754,
0.019769202917814255,
-0.07921137660741806,
0.02048184722661972,
0.026864459738135338,
0.0028021240141242743,
-0.07424220442771912,
0.031046314164996147,
-0.018258489668369293,
-0.008212200365960598,
0.08109711110591888,
0.00856065098196268,
0.04176687076687813,
-0.03764715790748596,
0.02116045542061329,
0.044959794729948044,
-0.048658814281225204,
0.021968860179185867,
0.033366359770298004,
-0.02771972492337227,
0.030791791155934334,
-0.019938910380005836,
-0.024232398718595505,
-0.02423095516860485,
-0.00340656447224319,
0.009813685901463032,
-0.008697920478880405,
-0.020620178431272507,
-0.00578575674444437,
0.005356933921575546,
-0.05807465314865112,
-0.05473820120096207,
-0.008399573154747486,
0.007116278633475304,
0.02610311657190323,
-0.007770880125463009,
0.07658213376998901,
-0.0337955504655838,
0.05085182934999466,
0.03679056093096733,
0.009156975895166397,
0.035890012979507446,
-0.023838946595788002,
-0.006445229984819889,
0.01886085979640484,
0.0012745079584419727,
-0.032721322029829025,
0.01656983606517315,
-0.012750447727739811,
-0.009280864149332047,
-0.011563144624233246,
0.004161431919783354,
-0.011381319724023342,
-0.007756365463137627,
0.008556966669857502,
0.021143848076462746,
-0.02907142974436283,
-0.014112000353634357,
-0.02197067067027092,
0.029856009408831596,
-0.029503174126148224,
-0.011466962285339832,
0.020104702562093735,
0.07311053574085236,
-0.019456950947642326,
0.0026595189701765776,
0.0171080119907856,
-0.051620565354824066,
-0.011603915132582188,
0.018033092841506004,
0.021611152216792107,
-0.009248672984540462,
0.003014905611053109,
-0.08206455409526825,
-0.062619149684906,
0.09006939083337784
] |
<p><img src="http://i.stack.imgur.com/YMVBx.jpg" alt="Retarded"></p>
<p>Imagine that we have a pair of parallel plates, $A$ and $B$, separated by some distance as in Fig. $1$ above.</p>
<p>At time $t_1$ we simultaneously charge both the plates. This could be done by previously sending a light signal to a charging apparatus at each plate from a source located at the mid-point between them.</p>
<p>According to standard electromagnetic theory a retarded electric influence travels at the speed of light from $A$ to $B$ and vice-versa.</p>
<p>At time $t_2$ the electric influence from $A$ produces a force at $B$ and vice-versa. </p>
<p>There are two points that I would like to raise about this description:</p>
<ol>
<li>There are no reaction forces. It is as if a pair of boxers each punched the other on the nose simultaneously but neither felt a reaction back on their boxing glove.</li>
<li>Once the electric influences have left the charged plates at time $t_1$, and before they have produced forces on the opposite plates at time $t_2$, they must exist "somewhere". That somewhere is the electromagnetic field. </li>
</ol>
<p>Now consider the picture described in Fig $2$ below which includes both retarded and advanced interactions.</p>
<p><img src="http://i.stack.imgur.com/zBS6w.jpg" alt="Retarded and Advanced"></p>
<p>Again at time $t_1$ we simultaneously charge both the plates.</p>
<p>Now as well as a retarded electric influence that travels at the speed of light from $A$ to $B$ we also have an advanced electric influence which travels backwards in time from $B$ to $A$. Thus the force at plate $B$ at time $t_2$ is balanced by an equal and opposite force on plate $A$ at time $t_1$ (and vice-versa). </p>
<p>Now as soon as we charge the plates up we measure electric forces on them.</p>
<p>At first glance it seems that we have "action at a distance" but in fact we only have "reaction at a distance". In terms of spacetime, each plate at time $t_1$ is linked with the opposite plate at time $t_2$ in a manner that is consistent with the principle of locality provided we include advanced interactions.</p>
<p>As there is no delay between charging the plates and measuring forces then there is no time interval during which the influences could be said to be in transit in the form of an electromagnetic field.</p>
<p>Thus in this picture we have:</p>
<ol>
<li>Reaction forces</li>
<li>No electromagnetic field</li>
</ol>
<p>Could one perform such an experiment to see if charged plates immediately repel each other?</p> | g4768 | [
0.0765669047832489,
0.026847826316952705,
-0.004177591763436794,
-0.032454799860715866,
0.11651833355426788,
0.04942243546247482,
-0.0035338797606527805,
0.018680337816476822,
-0.046539437025785446,
0.018542103469371796,
0.01353487279266119,
0.05961516872048378,
-0.04476074129343033,
-0.0004782724427059293,
0.012278269045054913,
0.0182828139513731,
0.15083833038806915,
-0.056098006665706635,
0.036226850003004074,
0.05915263667702675,
-0.04533834010362625,
0.059447675943374634,
-0.03013329766690731,
-0.058478131890296936,
-0.04961477592587471,
-0.04445794224739075,
0.03351656347513199,
-0.02947775088250637,
-0.029984889551997185,
-0.06487799435853958,
-0.03868794068694115,
-0.04373457282781601,
0.05107881873846054,
-0.016724854707717896,
-0.04705236107110977,
-0.04009469971060753,
0.04669596254825592,
-0.03461696580052376,
-0.03753659501671791,
0.036898937076330185,
-0.009845837950706482,
0.03343505412340164,
0.04051302745938301,
-0.015156424604356289,
0.03254290297627449,
-0.02246028371155262,
-0.05218242108821869,
-0.001233050599694252,
0.003482030238956213,
0.010585104115307331,
-0.00703432084992528,
0.019050708040595055,
0.02073023095726967,
-0.009700401686131954,
0.0061109913513064384,
-0.0210635457187891,
0.07054337114095688,
-0.0048025306314229965,
0.022899117320775986,
0.030270976945757866,
-0.018353478983044624,
0.03900493308901787,
0.047897979617118835,
0.03898608684539795,
0.053624529391527176,
0.01201834436506033,
-0.04233570769429207,
-0.0007110960432328284,
-0.025801127776503563,
0.010138512589037418,
-0.06196409836411476,
-0.05371934175491333,
-0.04698719456791878,
0.0243707112967968,
0.0016084834933280945,
0.009772075340151787,
0.048953548073768616,
-0.0015129807870835066,
0.01957947388291359,
0.036290641874074936,
-0.03947743773460388,
-0.01074452418833971,
0.039517514407634735,
0.021679691970348358,
0.05845535174012184,
-0.04181734099984169,
0.006030634511262178,
-0.00782741792500019,
-0.04742490127682686,
-0.01325184851884842,
0.020331716164946556,
-0.043945636600255966,
0.042702242732048035,
0.012334438040852547,
-0.0025760310236364603,
-0.008731228299438953,
0.023527787998318672,
0.040928810834884644,
0.0026726380456238985,
-0.004167305771261454,
-0.04129895567893982,
0.04474128410220146,
-0.019439946860074997,
0.01791555993258953,
-0.029783714562654495,
-0.01164725050330162,
0.05614814907312393,
-0.02940976619720459,
-0.015819190070033073,
-0.02982698380947113,
-0.009997320361435413,
-0.04961755499243736,
-0.05631009861826897,
-0.007219481747597456,
-0.002627017442137003,
-0.057782046496868134,
0.0011432647006586194,
-0.020311832427978516,
-0.052283771336078644,
0.020320845767855644,
0.014090808108448982,
-0.025671184062957764,
-0.008079136721789837,
0.02463856339454651,
0.02553083561360836,
-0.011580982245504856,
-0.017754124477505684,
0.060533154755830765,
0.026636317372322083,
0.01317482627928257,
-0.008440118283033371,
0.009447308257222176,
0.0107526620849967,
0.02676255814731121,
-0.015388261526823044,
-0.01595124788582325,
0.0474080853164196,
0.026404554024338722,
-0.002341123763471842,
-0.012931369245052338,
0.03101174160838127,
0.011663313955068588,
-0.038028620183467865,
-0.035236965864896774,
0.0044861226342618465,
0.021005885675549507,
-0.009177650325000286,
-0.029779527336359024,
0.0382024422287941,
0.012533022090792656,
0.024556726217269897,
0.05642801523208618,
-0.023018037900328636,
0.05927655100822449,
-0.02238065004348755,
0.0187518447637558,
0.017217833548784256,
-0.004267998039722443,
0.00024421632406301796,
-0.02646918222308159,
0.06479846686124802,
0.0034997917246073484,
-0.0022008304949849844,
-0.061998214572668076,
0.0013823037734255195,
0.030132049694657326,
0.023367363959550858,
-0.03974740207195282,
0.03163804113864899,
-0.08462248742580414,
-0.06722267717123032,
-0.028256533667445183,
0.0009881864534690976,
0.01491539552807808,
0.032561857253313065,
0.010003112256526947,
-0.018733637407422066,
-0.09278736263513565,
0.0009903182508423924,
-0.03201331943273544,
-0.03191785514354706,
0.006865919101983309,
-0.0004253893275745213,
0.0070142922922968864,
0.0027497278060764074,
-0.005297568626701832,
-0.058811597526073456,
0.07333922386169434,
-0.08748902380466461,
-0.040806811302900314,
0.01857008971273899,
-0.004720259923487902,
-0.05584908649325371,
-0.04190404713153839,
-0.03604675456881523,
0.023037293925881386,
0.03391722962260246,
0.012304863892495632,
0.02226148545742035,
0.027415955439209938,
-0.047148238867521286,
0.025263119488954544,
0.03595035895705223,
0.019073449075222015,
-0.022516092285513878,
0.029039163142442703,
-0.0017576048849150538,
-0.04963374882936478,
0.0009671830339357257,
-0.006175302434712648,
0.03789481148123741,
-0.0031800877768546343,
0.011375805363059044,
-0.0046210684813559055,
-0.014338530600070953,
-0.041445497423410416,
-0.02921297401189804,
0.04116189107298851,
-0.015535795129835606,
0.0072288839146494865,
-0.06770653277635574,
0.0658021941781044,
-0.015503855422139168,
-0.0689718946814537,
-0.028969328850507736,
-0.034380752593278885,
0.02648126147687435,
-0.02897638827562332,
-0.06842613965272903,
0.004030674230307341,
-0.060714010149240494,
-0.00755652179941535,
-0.021859468892216682,
-0.02004576288163662,
0.0533333420753479,
0.0008419885416515172,
-0.0018192444695159793,
-0.029041172936558723,
-0.008852398954331875,
0.00780067965388298,
0.035249095410108566,
-0.040412891656160355,
-0.015688767656683922,
0.07645989954471588,
-0.036595623940229416,
-0.06928795576095581,
0.023289060220122337,
0.008062694221735,
0.02658108063042164,
0.01963643915951252,
0.04385822266340256,
-0.0013019789475947618,
0.005660812836140394,
-0.012698964215815067,
-0.004600259941071272,
-0.027791058644652367,
0.014146307483315468,
0.08353474736213684,
-0.076630137860775,
-0.08678743243217468,
-0.028211116790771484,
0.027513187378644943,
0.011139804497361183,
0.027677079662680626,
-0.052284885197877884,
-0.025629887357354164,
-0.039855241775512695,
0.043022945523262024,
0.01852327771484852,
-0.03345774486660957,
-0.049282487481832504,
0.0120804812759161,
0.06242873892188072,
-0.029014956206083298,
-0.014806129038333893,
-0.011829493567347527,
0.004558201413601637,
-0.051860127598047256,
0.012850464321672916,
0.015298774465918541,
0.03847093507647514,
-0.013693946413695812,
-0.03751884400844574,
-0.011088590137660503,
0.012899410910904408,
0.009042665362358093,
0.025459587574005127,
-0.005002948455512524,
0.004705692641437054,
-0.004588371142745018,
-0.05847855657339096,
0.020432360470294952,
0.056280460208654404,
-0.03647175431251526,
-0.0005174815887585282,
0.033129747956991196,
0.05818740278482437,
-0.08297087997198105,
-0.05660530552268028,
-0.0040975213050842285,
0.03960806876420975,
-0.06753575801849365,
0.01336801890283823,
0.03864166513085365,
0.052529145032167435,
-0.03356381505727768,
-0.034832172095775604,
-0.0609978623688221,
0.017817266285419464,
-0.000026188421543338336,
-0.007587040308862925,
0.029182609170675278,
-0.013470455072820187,
0.03129503130912781,
-0.02996458113193512,
0.012400195933878422,
0.020049432292580605,
-0.023355863988399506,
-0.0010608434677124023,
0.03180880472064018,
0.03460332006216049,
-0.019145680591464043,
-0.018744517117738724,
0.013729926198720932,
0.01282245758920908,
0.0472540445625782,
-0.060749657452106476,
0.041169073432683945,
-0.04844776168465614,
-0.00011063048441428691,
0.025783484801650047,
0.04948853701353073,
0.026252776384353638,
-0.05870585888624191,
-0.008695781230926514,
-0.037297431379556656,
0.05036016181111336,
0.07500386983156204,
0.03591266646981239,
0.0552387535572052,
0.0005818480858579278,
0.01671893708407879,
-0.024892374873161316,
-0.00429508974775672,
-0.008280186913907528,
0.014433871023356915,
0.03949896618723869,
-0.011538181453943253,
-0.06345368921756744,
-0.013922732323408127,
0.052430152893066406,
-0.0034353130031377077,
0.03149367868900299,
-0.000023847374905017205,
0.02276208996772766,
0.023060396313667297,
-0.014358017593622208,
-0.030541451647877693,
-0.024373464286327362,
-0.046062760055065155,
-0.01610078662633896,
0.01882421225309372,
-0.013858186081051826,
-0.007060736883431673,
0.04819368198513985,
0.02728334069252014,
-0.05161220207810402,
0.07520046830177307,
0.04908999428153038,
-0.026224911212921143,
0.024670345708727837,
-0.03167261555790901,
-0.015162607654929161,
0.012116296216845512,
0.039914172142744064,
-0.04732394590973854,
0.039540573954582214,
-0.009899421595036983,
-0.003950359765440226,
0.0844186395406723,
-0.0023862419184297323,
0.05448372662067413,
-0.03900572657585144,
-0.0019184912089258432,
0.08244901150465012,
0.0601835623383522,
-0.0005269337561912835,
0.012160327285528183,
-0.01330441515892744,
-0.03350832685828209,
0.046340152621269226,
-0.0018197569297626615,
-0.02064305916428566,
-0.015288956463336945,
0.0106880534440279,
-0.029664749279618263,
0.027827994897961617,
-0.03187522664666176,
0.03075561299920082,
-0.04154275730252266,
0.044486742466688156,
0.005689313169568777,
-0.030449997633695602,
0.017088517546653748,
-0.08337518572807312,
-0.03051402047276497,
0.06271117925643921,
-0.035847872495651245,
0.04020777717232704,
-0.03700970485806465,
-0.03503657504916191,
-0.06161745637655258,
-0.01902499608695507,
-0.05294536054134369,
-0.012566320598125458,
0.04479013755917549,
0.05840805545449257,
0.05392442271113396,
0.010429808869957924,
0.023272311314940453,
0.02511613257229328,
0.06566746532917023,
0.02596476301550865,
-0.05110663175582886,
0.03274501860141754,
0.0640001893043518,
0.039079152047634125,
-0.02042723074555397,
0.004525037482380867,
-0.024678083136677742,
0.022660326212644577,
0.043816592544317245,
-0.07089337706565857,
-0.029922975227236748,
-0.0356253944337368,
0.029662860557436943,
-0.008483764715492725,
0.04671051353216171,
0.05115007981657982,
0.08245141804218292,
0.05528860539197922,
-0.003754895878955722,
0.013545745052397251,
0.03488333523273468,
0.0034334175288677216,
0.0910632535815239,
-0.04601307958364487,
-0.029505819082260132,
0.02233249694108963,
-0.054468147456645966,
-0.06536462903022766,
0.02589215710759163,
-0.019803093746304512,
-0.028932925313711166,
-0.002648778958246112,
0.019571417942643166,
-0.002855622209608555,
0.001076933229342103,
0.0028583495877683163,
0.016049452126026154,
-0.011893737129867077,
-0.002425765385851264,
-0.0014449014561250806,
-0.00861893966794014,
0.004336177837103605,
-0.004100243095308542,
-0.03229136019945145,
-0.03711894154548645,
-0.06860888749361038,
0.013600819744169712,
-0.01810978166759014,
0.013938060961663723,
0.03794616088271141,
0.006710294168442488,
-0.0004894878366030753,
-0.04225454851984978,
-0.014098632149398327,
0.021141989156603813,
0.0017860422376543283,
-0.04632934182882309,
-0.008839319460093975,
-0.013881893828511238,
0.02044692635536194,
-0.004580854903906584,
-0.031084515154361725,
-0.036186929792165756,
-0.010483021847903728,
0.06612953543663025,
0.011784731410443783,
-0.03250079229474068,
-0.010985330678522587,
-0.02031247690320015,
-0.02429290860891342,
-0.015207077376544476,
0.008909279480576515,
0.0754094049334526,
-0.04066598787903786,
0.07143813371658325,
-0.04335419088602066,
-0.010664749890565872,
-0.024168794974684715,
0.058816906064748764,
0.025665685534477234,
-0.0035477932542562485,
-0.044381726533174515,
0.019406169652938843,
0.03507063165307045,
-0.01649700663983822,
-0.011952496133744717,
0.047217100858688354,
-0.08843949437141418,
0.06658016890287399,
0.01244110893458128,
0.028302395716309547,
0.01132453978061676,
0.007326334249228239,
-0.01683931052684784,
-0.014161833561956882,
-0.04286490008234978,
-0.06330253183841705,
0.07705866545438766,
-0.04201262816786766,
0.0347965769469738,
0.002968020038679242,
0.05038408190011978,
-0.03367162495851517,
-0.010226767510175705,
0.019527914002537727,
-0.0017243896145373583,
0.008553541265428066,
-0.011773419566452503,
-0.005646254867315292,
0.04376397281885147,
-0.012822873890399933,
-0.02509218268096447,
-0.027674201875925064,
0.08165811002254486,
-0.03798413649201393,
-0.0024352935142815113,
-0.04209601879119873,
0.0015509540680795908,
-0.019010238349437714,
0.04322079196572304,
0.007007061503827572,
-0.005921785719692707,
0.027000360190868378,
-0.04304557666182518,
-0.013291899114847183,
0.016797684133052826,
-0.020337054505944252,
0.05267767608165741,
-0.005362572614103556,
0.046985942870378494,
0.03373926877975464,
-0.018584927543997765,
0.007271136157214642,
-0.002476791851222515,
-0.051087141036987305,
-0.013744006864726543,
-0.03153071179986,
0.06318725645542145,
0.014248030260205269,
-0.0048734345473349094,
0.03107338771224022,
0.032522980123758316,
-0.00606783339753747,
0.024647722020745277,
-0.012052235193550587,
0.03606267273426056,
0.029172677546739578,
0.04348945617675781,
-0.020466677844524384,
0.027621639892458916,
-0.013026726432144642,
0.0336468443274498,
0.019205745309591293,
0.009654807858169079,
0.04145675152540207,
-0.07626307010650635,
-0.009373354725539684,
0.017108280211687088,
0.02329043298959732,
-0.018416326493024826,
-0.013715390115976334,
-0.04240916669368744,
0.05297571420669556,
0.0006352582713589072,
-0.029043342918157578,
0.053051844239234924,
-0.07232504338026047,
0.023103609681129456,
-0.0472852997481823,
-0.01587509922683239,
-0.06689339131116867,
-0.03283443674445152,
-0.02959846332669258,
0.015181086026132107,
0.044583845883607864,
-0.007341355085372925,
0.12553410232067108,
-0.060886792838573456,
-0.036429304629564285,
0.009894912131130695,
-0.05247609689831734,
-0.024387747049331665,
0.017813198268413544,
-0.024431928992271423,
-0.007912099361419678,
0.017261086031794548,
0.013272174634039402,
-0.04373539984226227,
-0.01646439917385578,
-0.029852380976080894,
-0.009430496022105217,
0.011072902008891106,
0.02480754442512989,
-0.042832355946302414,
-0.0024368013255298138,
-0.03746982291340828,
0.10372647643089294,
0.034798651933670044,
-0.049788180738687515,
-0.0314728207886219,
-0.00739135779440403,
0.023901183158159256,
-0.015431617386639118,
-0.04468464478850365,
0.0066302004270255566,
0.03273378685116768,
0.01694628596305847,
-0.011665291152894497,
-0.04017845541238785,
-0.012924473732709885,
0.0897621139883995,
0.016500459983944893,
0.038754452019929886,
0.029925620183348656,
0.024934856221079826,
0.02457602135837078,
-0.0161572378128767,
0.04118301719427109,
0.0052971248514950275,
0.019009478390216827,
0.0506400428712368,
0.013595020398497581,
-0.02695665881037712,
0.028507191687822342,
0.05523467808961868,
-0.029925966635346413,
0.023958545178174973,
0.015509854070842266,
-0.030185837298631668,
-0.007315291091799736,
0.026265382766723633,
-0.05934511497616768,
0.021220171824097633,
0.018731556832790375,
-0.03246017172932625,
-0.03517528623342514,
-0.019309593364596367,
-0.016225459054112434,
-0.045171212404966354,
-0.06036631762981415,
0.019100291654467583,
-0.056030791252851486,
0.010785724967718124,
-0.03250657394528389,
-0.06793473660945892,
-0.021617423743009567,
-0.025836313143372536,
0.014696687459945679,
-0.06809873878955841,
0.04186943545937538,
-0.009110151790082455,
-0.02581237070262432,
0.02263391762971878,
0.059737130999565125,
0.02227674424648285,
0.003871964057907462,
-0.038781069219112396,
-0.014395800419151783,
0.03936360031366348,
-0.009135805070400238,
-0.0025650537572801113,
-0.028416909277439117,
0.010770251974463463,
-0.017092248424887657,
-0.0055656698532402515,
-0.03021083027124405,
-0.04155578836798668,
0.010722717270255089,
0.009493223391473293,
-0.026440313085913658,
0.02141241542994976,
0.018848447129130363,
-0.02536625787615776,
0.013954568654298782,
0.006785004865378141,
-0.030596252530813217,
-0.011994301341474056,
-0.02322547324001789,
0.005317087285220623,
0.04783610627055168,
-0.03704144433140755,
-0.02780180238187313,
0.010449712164700031,
-0.04424244910478592,
0.018339572474360466,
0.0036832343321293592,
0.0019331254297867417,
0.0367087684571743,
0.09533900767564774,
-0.01916036196053028,
-0.01095480378717184,
0.0004667099565267563,
0.0159283634275198,
0.009651003405451775,
0.03928707540035248,
0.017455946654081345,
0.04961066320538521,
-0.009380267933011055,
-0.035377927124500275,
-0.012949955649673939,
-0.08146002888679504,
0.005761764012277126,
-0.015800848603248596,
0.04458606615662575,
0.005124769173562527,
0.045091696083545685,
-0.02263307012617588,
0.021650491282343864,
-0.05089835822582245,
-0.017639530822634697,
0.02125333435833454,
0.01821194775402546,
0.04635316878557205,
0.029347622767090797,
0.023370882496237755,
-0.0032224066089838743,
-0.003653945866972208,
-0.03771317005157471,
-0.07425463944673538,
-0.044180724769830704,
-0.0005244280328042805,
0.00360116851516068,
-0.027773002162575722,
-0.0011384657118469477,
0.04766056686639786,
0.015821989625692368,
0.004569801036268473,
0.02713378705084324,
-0.028158070519566536,
-0.04417964816093445,
-0.01696430705487728,
0.060688938945531845,
-0.012684978544712067,
-0.04182431474328041,
0.04736008122563362,
0.0416269414126873,
0.0015121203614398837,
-0.06161128729581833,
-0.004795684479176998,
-0.03251545876264572,
-0.03941021114587784,
0.015368929132819176,
-0.02232678048312664,
-0.02181326039135456,
-0.001029482576996088
] |
<p>In light of the well known fact that <em>magnetic forces do no work</em>,</p>
<p>In every such case that nature presents us, it is possible to find some agent which does the work while magnetic forces just give direction to it. As an example, in the case of an electromagnet lifting weights, it is the potential source that powers the electromagnet which is responsible for the actual work done.</p>
<p>In the case of friction due to <a href="http://en.wikipedia.org/wiki/Eddy_current" rel="nofollow">eddy currents</a>, specifically <em>the case of slowing down of a metal object passing through a magnetic field</em>, <strong>what is the agent which is responsible for the work done?</strong></p> | g4769 | [
0.060623109340667725,
0.04723461717367172,
-0.010946850292384624,
-0.02489805594086647,
0.0953700989484787,
0.019152997061610222,
0.028372520580887794,
0.00569427665323019,
0.0033483090810477734,
-0.007768868934363127,
0.005553406197577715,
-0.042571619153022766,
-0.028033647686243057,
-0.011288700625300407,
-0.007367870770394802,
0.07932545244693756,
0.07364687323570251,
0.0021757192444056273,
0.07517437636852264,
0.018762215971946716,
0.020289113745093346,
-0.03069412149488926,
0.03917650878429413,
-0.020542316138744354,
-0.014669175259768963,
-0.031154870986938477,
-0.015897151082754135,
-0.046285588294267654,
0.010230040177702904,
-0.0658169761300087,
0.030458467081189156,
0.006083980202674866,
0.04920361563563347,
-0.033846545964479446,
-0.02898959070444107,
-0.007901365868747234,
0.07086563110351562,
0.08392128348350525,
0.005210327450186014,
0.009302196092903614,
-0.05447854846715927,
0.00933769065886736,
-0.0037971120327711105,
-0.03532269969582558,
-0.0318305566906929,
-0.05414985865354538,
-0.04730718210339546,
0.008588163182139397,
-0.06279128789901733,
-0.04206574708223343,
0.0049442402087152,
-0.008915296755731106,
0.047411128878593445,
0.024570606648921967,
0.02704635076224804,
-0.04186907410621643,
0.04461253061890602,
-0.029270919039845467,
0.04976183548569679,
-0.00733879953622818,
-0.004523551091551781,
0.014675102196633816,
0.011711937375366688,
0.005790466908365488,
0.013664578087627888,
-0.031477004289627075,
-0.0160943903028965,
0.012545057572424412,
0.016613898798823357,
0.03808053210377693,
-0.017861686646938324,
0.026793353259563446,
-0.016986040398478508,
0.011568501591682434,
-0.03051832504570484,
0.023404724895954132,
0.02349640429019928,
0.0460817813873291,
0.04790825769305229,
-0.023207392543554306,
0.01950804702937603,
-0.00810393039137125,
0.0005799493519589305,
0.01896493509411812,
0.08791167289018631,
-0.02288629487156868,
0.03560241684317589,
0.0553545206785202,
0.0177006833255291,
0.014363713562488556,
0.05127646401524544,
-0.001479184371419251,
0.05018723011016846,
-0.003702849615365267,
0.001263096695765853,
0.016789155080914497,
0.030858024954795837,
0.026753079146146774,
-0.026930291205644608,
0.014171271584928036,
-0.05356668680906296,
-0.012438285164535046,
-0.04533420875668526,
-0.050517868250608444,
0.04864993691444397,
0.004587228875607252,
0.023979753255844116,
0.04089818894863129,
-0.04090872034430504,
0.034662142395973206,
0.006686215288937092,
-0.018339864909648895,
-0.06548792123794556,
0.03894814848899841,
0.01038907840847969,
-0.075846366584301,
0.03539489209651947,
-0.02228599041700363,
-0.01836402155458927,
0.07904756814241409,
-0.022303519770503044,
-0.01349272858351469,
-0.025410903617739677,
0.0563872829079628,
0.007697128690779209,
-0.01136801764369011,
0.014145364984869957,
0.016762293875217438,
0.008783497847616673,
-0.00429115304723382,
0.02724977396428585,
0.007421543821692467,
0.036396075040102005,
-0.012298181653022766,
-0.04383813589811325,
0.08274970948696136,
-0.057827189564704895,
0.02245245687663555,
0.035822298377752304,
0.018404928967356682,
-0.03455542027950287,
-0.03500134125351906,
0.03226042538881302,
-0.03563364967703819,
-0.005200961139053106,
-0.006679717451334,
0.003705141367390752,
0.03500691056251526,
0.042419616132974625,
0.041661251336336136,
0.04552014544606209,
0.054063595831394196,
-0.021091043949127197,
-0.04749665781855583,
0.017269285395741463,
0.03359183669090271,
-0.007543371524661779,
-0.038085728883743286,
0.000709166401065886,
0.0064005497843027115,
0.05945363640785217,
-0.03502221778035164,
0.026579834520816803,
-0.0068817888386547565,
-0.0011855813208967447,
0.021234719082713127,
0.02687724679708481,
-0.01892833225429058,
0.040202297270298004,
0.058454155921936035,
-0.08757798373699188,
0.007122068665921688,
0.018258413299918175,
0.08268038928508759,
-0.0025643992703408003,
0.0698610469698906,
0.04361025616526604,
-0.03593142703175545,
0.05284702032804489,
0.016562994569540024,
-0.01247415505349636,
-0.024629324674606323,
0.043077219277620316,
0.026133539155125618,
0.033342499285936356,
0.006468695122748613,
-0.022906456142663956,
0.06510791182518005,
-0.011728587560355663,
-0.013088436797261238,
-0.046216871589422226,
-0.022473972290754318,
0.044979579746723175,
0.03141694515943527,
-0.00590717326849699,
0.0005777416517958045,
-0.06706948578357697,
-0.019383175298571587,
-0.01421410869807005,
-0.04522420093417168,
-0.0346074104309082,
0.058182016015052795,
0.01130584441125393,
-0.016497932374477386,
0.0005942261777818203,
-0.01143092755228281,
0.011931153945624828,
0.031983762979507446,
0.05200233310461044,
-0.029164820909500122,
0.04895412176847458,
0.00575233856216073,
-0.013151263818144798,
-0.05503462627530098,
-0.049129098653793335,
-0.046556103974580765,
-0.07504961639642715,
-0.00025448811356909573,
-0.0387607179582119,
-0.01594008319079876,
-0.018671603873372078,
0.013431940227746964,
0.008458808064460754,
0.008773879148066044,
-0.08925915509462357,
-0.005840879864990711,
0.0015872458461672068,
-0.008998743258416653,
-0.034230466932058334,
-0.03502129018306732,
-0.02140672691166401,
0.036156103014945984,
0.05299258977174759,
-0.022491786628961563,
0.03741857782006264,
0.013524369336664677,
0.03079565055668354,
0.025359464809298515,
0.0007976238848641515,
0.022605087608098984,
-0.015544991940259933,
-0.02197909541428089,
-0.005705769173800945,
-0.055760402232408524,
0.03942262753844261,
-0.022023262456059456,
0.025242239236831665,
0.017603799700737,
0.01748250052332878,
0.04890542849898338,
0.06215168908238411,
-0.046335916966199875,
-0.02766508236527443,
0.00904189981520176,
0.005149565637111664,
0.004390519578009844,
-0.026546629145741463,
0.07039474695920944,
-0.01478514913469553,
-0.03716425225138664,
-0.012923537753522396,
0.021561728790402412,
0.06648553162813187,
0.07438363134860992,
-0.013277803547680378,
-0.03412259742617607,
-0.09275186061859131,
0.0027295618783682585,
0.02765733376145363,
0.04270599037408829,
-0.06401675939559937,
-0.02060096152126789,
-0.0006105186184868217,
-0.024691959843039513,
-0.017145447432994843,
-0.05094912275671959,
0.0194452665746212,
-0.008924741297960281,
-0.007890978828072548,
0.028085188940167427,
0.0009977830341085792,
0.011148624122142792,
0.0356859527528286,
-0.036826156079769135,
0.005111040081828833,
-0.01695634238421917,
-0.026099830865859985,
-0.06308085471391678,
-0.0004958115168847144,
-0.058299995958805084,
0.018117766827344894,
0.007160788401961327,
0.10024695843458176,
-0.01691531576216221,
-0.018231423571705818,
0.012062324211001396,
0.06502659618854523,
-0.08252546936273575,
-0.046720877289772034,
0.02309701032936573,
0.029422592371702194,
-0.029392022639513016,
-0.0005701871705241501,
0.033323805779218674,
0.060379836708307266,
0.0066180359572172165,
-0.014305495657026768,
-0.06509918719530106,
-0.018757091835141182,
-0.02286297269165516,
-0.018239708617329597,
0.07994105666875839,
-0.02709891088306904,
-0.007714024744927883,
-0.08215248584747314,
0.020144956186413765,
-0.002664326224476099,
-0.04036349430680275,
-0.006643074098974466,
-0.05102391913533211,
-0.01364398654550314,
-0.06715713441371918,
0.03325566649436951,
-0.0176357664167881,
0.03884327784180641,
0.02481694333255291,
0.03066788986325264,
0.01672114059329033,
-0.00535251060500741,
0.03181660920381546,
0.010938411578536034,
-0.0011924918508157134,
-0.04756985604763031,
-0.01029216405004263,
-0.13214898109436035,
-0.008347809314727783,
0.019925754517316818,
-0.0009873938979580998,
0.004594770260155201,
0.043296873569488525,
0.01668383926153183,
-0.034219346940517426,
-0.03997727856040001,
0.015967387706041336,
-0.019531138241291046,
0.07201096415519714,
-0.017325975000858307,
0.026796147227287292,
-0.004872972145676613,
-0.006371077615767717,
0.04646981507539749,
0.012881130911409855,
0.02002669870853424,
0.02275061421096325,
0.039984364062547684,
-0.04059307277202606,
0.034972336143255234,
0.015119865536689758,
-0.0418814942240715,
0.010731942020356655,
-0.03529072925448418,
0.047312021255493164,
-0.020586203783750534,
0.016993071883916855,
0.0017114457441493869,
0.05488443747162819,
0.031025530770421028,
0.039701271802186966,
-0.00018922427261713892,
-0.01840907707810402,
0.08725770562887192,
0.009569033049046993,
0.014051736332476139,
0.0362381748855114,
0.02055116929113865,
0.02433384396135807,
0.035019367933273315,
-0.009662499651312828,
-0.06377586722373962,
0.007022860459983349,
0.02916473150253296,
0.09895636886358261,
0.01329325046390295,
0.010171066969633102,
0.03270316496491432,
0.012148633599281311,
-0.06294014304876328,
0.049117594957351685,
-0.021665621548891068,
-0.028849253430962563,
-0.004017538856714964,
0.04308442398905754,
0.006397950928658247,
-0.003869350766763091,
0.025733504444360733,
-0.02849407121539116,
0.008618091233074665,
-0.023427098989486694,
0.05653645470738411,
-0.023730209097266197,
0.06619704514741898,
0.04835350811481476,
-0.01758117415010929,
0.05761154741048813,
0.03439909592270851,
0.03358960524201393,
-0.01737559586763382,
-0.036408498883247375,
-0.010434063151478767,
-0.03560592606663704,
-0.010351382195949554,
-0.02752443216741085,
-0.03330416977405548,
0.014659592881798744,
0.03861147537827492,
-0.02319086343050003,
-0.01870063878595829,
0.07909741252660751,
0.032560933381319046,
-0.04165129363536835,
0.03457128256559372,
0.053182292729616165,
0.022741125896573067,
0.02232332155108452,
-0.04213101789355278,
0.048227131366729736,
-0.005046055652201176,
0.013968116603791714,
-0.010602721013128757,
-0.03967234492301941,
-0.04988642781972885,
0.02458198368549347,
-0.03598479926586151,
-0.040895044803619385,
-0.057592831552028656,
0.03086480125784874,
0.003583837067708373,
0.03417063131928444,
0.04237425699830055,
0.06189454346895218,
0.0008103219443000853,
0.0542101226747036,
0.006114802323281765,
-0.005483638495206833,
-0.04990960657596588,
0.0425274483859539,
-0.008685938082635403,
-0.016556289047002792,
-0.04504669830203056,
-0.048204969614744186,
-0.037997566163539886,
-0.015315834432840347,
-0.06425102055072784,
-0.04956319183111191,
0.004147191531956196,
0.04278332367539406,
0.025264106690883636,
-0.05976376682519913,
-0.009726137854158878,
-0.014278647489845753,
0.00243920530192554,
-0.06039100140333176,
-0.005007329396903515,
0.0348559133708477,
-0.0669839084148407,
-0.011720121838152409,
0.006643679924309254,
-0.010218624025583267,
-0.04671581834554672,
0.018997548148036003,
0.029466737061738968,
0.02870345488190651,
-0.02299094758927822,
0.04421917349100113,
0.0414571575820446,
-0.05843273922801018,
0.03633519634604454,
-0.048488955944776535,
-0.032033298164606094,
0.0003685261181090027,
0.005024575162678957,
0.04726378247141838,
-0.0014000170631334186,
-0.02457217499613762,
-0.016926748678088188,
0.02105622924864292,
-0.03473226726055145,
0.049233801662921906,
0.04456733167171478,
-0.010448026470839977,
0.019950224086642265,
0.04485096037387848,
0.0014021508395671844,
-0.0915171355009079,
-0.09410174936056137,
0.019534625113010406,
-0.018998360261321068,
0.059052616357803345,
-0.003779413877055049,
-0.025682222098112106,
-0.01500554010272026,
-0.0424225777387619,
-0.032921504229307175,
0.029085759073495865,
-0.010547038167715073,
0.01168275997042656,
0.06180697679519653,
-0.04057051241397858,
0.030708294361829758,
0.008505734615027905,
-0.0469910204410553,
-0.0016655594808980823,
0.01695183478295803,
0.015258467756211758,
0.0036027575843036175,
0.04130154475569725,
-0.004192578140646219,
0.0026502208784222603,
-0.017976723611354828,
0.03266799822449684,
0.014239024370908737,
0.047995373606681824,
0.0432659350335598,
-0.05837711691856384,
-0.0076896571554243565,
0.014815106056630611,
-0.04634236544370651,
0.032280050218105316,
0.022650597617030144,
0.04383394494652748,
0.02902943082153797,
0.018211882561445236,
0.0075984494760632515,
-0.02380685694515705,
0.016096753999590874,
-0.06659229099750519,
0.11069946736097336,
-0.03226723149418831,
-0.06394041329622269,
-0.0034494642168283463,
0.009204605594277382,
-0.019913889467716217,
0.04616269841790199,
0.05400175601243973,
-0.0685003474354744,
-0.017775364220142365,
-0.029679346829652786,
-0.02128295972943306,
0.0304257795214653,
-0.06988875567913055,
-0.04435603320598602,
0.033905062824487686,
-0.02258218079805374,
-0.016420451924204826,
-0.030229531228542328,
-0.00854773260653019,
-0.006354866549372673,
-0.012571951374411583,
-0.003907403443008661,
-0.0723215863108635,
0.03233962878584862,
0.01349604781717062,
0.045110464096069336,
-0.002806286793202162,
0.006101640406996012,
-0.012936873361468315,
-0.017160654067993164,
0.038279347121715546,
0.02661326713860035,
0.056874245405197144,
-0.04587993025779724,
0.012520245276391506,
-0.03823843225836754,
0.04087444022297859,
0.05897423252463341,
0.0075855134055018425,
-0.02845941111445427,
-0.055350180715322495,
-0.04744090139865875,
0.028392033651471138,
0.037041373550891876,
0.004898310173302889,
0.005165437236428261,
-0.020902955904603004,
-0.013373157940804958,
0.014820283278822899,
-0.09547939151525497,
-0.025737598538398743,
0.0484284833073616,
-0.012686032801866531,
-0.006844665855169296,
0.04020315408706665,
-0.039959318935871124,
0.004733653273433447,
-0.06381947547197342,
-0.01580359973013401,
-0.025172485038638115,
0.007397388108074665,
-0.009920292533934116,
0.05885421112179756,
-0.02121124416589737,
0.0008743288926780224,
0.020721513777971268,
0.04210080951452255,
0.02530921809375286,
-0.027473580092191696,
-0.004542514216154814,
0.016010615974664688,
-0.029206806793808937,
-0.023720644414424896,
-0.017129139974713326,
0.021163461729884148,
-0.05090911686420441,
-0.013726417906582355,
-0.0010985323460772634,
-0.009113174863159657,
-0.058261364698410034,
-0.055130280554294586,
-0.05003228411078453,
-0.02916599251329899,
-0.04094887152314186,
-0.07440564781427383,
0.02696388214826584,
-0.041478175669908524,
0.016085010021924973,
0.003569595981389284,
-0.0680835172533989,
-0.03434539958834648,
0.017742637544870377,
-0.0005756578175351024,
0.01778355985879898,
0.029393011704087257,
-0.005472332704812288,
0.0030583541374653578,
-0.07281485944986343,
-0.0033034521620720625,
-0.015176353976130486,
-0.020532865077257156,
0.04479735344648361,
0.041769757866859436,
-0.0503896027803421,
0.04015599936246872,
-0.036869749426841736,
0.022632040083408356,
-0.034539349377155304,
-0.03097390942275524,
-0.0029659755527973175,
0.05278049409389496,
-0.03795403614640236,
0.011916243471205235,
0.0008721655467525125,
-0.04559395834803581,
-0.010073701851069927,
-0.0049464586190879345,
-0.02657541260123253,
0.005413018632680178,
-0.03214121609926224,
0.02742808498442173,
0.003622853895649314,
0.0024699510540813208,
-0.019361654296517372,
0.005343662574887276,
0.016809120774269104,
0.004621373023837805,
-0.02371199056506157,
0.015934675931930542,
-0.04491350054740906,
-0.014540472999215126,
-0.020036403089761734,
0.028585050255060196,
-0.007292827591300011,
-0.10500426590442657,
-0.020251987501978874,
-0.0038915842305868864,
-0.029765892773866653,
-0.0012098558945581317,
-0.0009471192606724799,
-0.02804945595562458,
0.00789213739335537,
-0.016357067972421646,
-0.011575739830732346,
0.02998330257833004,
-0.03307223692536354,
-0.07351578772068024,
0.04326988384127617,
-0.009637929499149323,
-0.0257805697619915,
0.0257377028465271,
-0.0005791462026536465,
-0.03188963979482651,
0.009122749790549278,
0.08760538697242737,
0.013836846686899662,
-0.0014873185427859426,
0.009039988741278648,
0.004512309096753597,
0.0008157656993716955,
0.05497314780950546,
-0.01967793144285679,
0.006401740945875645,
0.01638363115489483,
-0.03869571536779404,
0.0069225989282131195,
0.023020295426249504,
-0.013697865419089794,
-0.012753940187394619,
-0.008387683890759945,
0.007442442700266838,
0.012544196099042892,
0.013646090403199196,
-0.009516098536550999,
0.04119032621383667,
0.02198086306452751,
-0.02771138772368431,
0.017147621139883995,
0.07190586626529694,
-0.030568927526474,
0.024625515565276146,
0.0712493509054184,
0.024196580052375793,
0.0373598076403141,
0.007766540627926588,
-0.04219822585582733,
-0.06687325239181519,
-0.024297606199979782,
-0.002031055511906743,
-0.008042226545512676,
-0.0189242884516716,
-0.005322218406945467,
-0.008401619270443916,
0.017820285633206367,
-0.058285459876060486,
-0.015192138962447643,
-0.005249944049865007,
-0.05462361499667168,
-0.0731593519449234,
0.005340231582522392,
-0.024480212479829788,
0.03136928007006645,
-0.0193730890750885,
-0.038753241300582886,
-0.06557878851890564,
-0.020273935049772263,
-0.005652762949466705,
0.004697435535490513,
-0.007650424726307392,
-0.04129616916179657,
0.03851323574781418,
-0.01568896882236004,
0.013133798725903034,
0.015972042456269264,
0.06617698818445206,
-0.06074220687150955,
-0.04698534682393074,
-0.015093764290213585,
-0.019054261967539787,
-0.006912565790116787,
0.044128794223070145,
0.04104536399245262,
0.03388719633221626,
-0.032361261546611786,
-0.032338060438632965,
-0.041773390024900436,
0.003418286330997944,
-0.021038956940174103,
0.017589082941412926,
-0.037905771285295486,
0.03174448013305664
] |
<p>"Field" is a name for associating a value with each point in space. This value can be a scalar, vector or tensor etc. I read the wikipedia article and got that much, but then it goes it into more unfamiliar concepts. </p>
<p>My question is how to interpret a basic field. Lets say there is a field with momentum and energy. Does that mean, that any "object" which can interact with that field, can borrow that momentum and energy from that field and give back to it as well. Much like an electron in some (not its own) electromagnetic field, right? Now how do I extend this understanding to concepts like:</p>
<blockquote>
<p>$U_\lambda$ is the radiation energy density per unit wavelength of a thermodynamic equilibrium radiation field trapped in some cavity."</p>
</blockquote>
<p>Does that mean, that the "numbers" that make up the field in each point in space stay constant with temperature or time (or both, I'm not sure.) And if there are object is that field which can interact with it, for example electrons, then they can take energy from that field or lose energy to that field. Then the author calls this field a "photon gas" without explanation. So does that mean a bag of photons in cavity is mathematically equivalent to specifying some numbers in space? Or something else. </p> | g4770 | [
0.042899809777736664,
0.01893429271876812,
0.007048862986266613,
-0.0034683519043028355,
0.03005588799715042,
0.019712883979082108,
0.0032953722402453423,
0.02901177480816841,
-0.034808967262506485,
-0.05772693455219269,
0.002051984891295433,
0.01062400545924902,
0.025162789970636368,
-0.017726419493556023,
0.0014216331765055656,
-0.030270498245954514,
0.059538889676332474,
-0.01712951250374317,
0.04177664965391159,
-0.0030171575490385294,
-0.011723865754902363,
0.056751150637865067,
-0.005208259914070368,
-0.037721164524555206,
-0.07637530565261841,
0.003454674733802676,
0.0487639494240284,
-0.017328625544905663,
-0.00792908389121294,
-0.08046479523181915,
0.002909096423536539,
-0.010490049608051777,
0.043729543685913086,
-0.04984642192721367,
-0.0572168193757534,
-0.05307881161570549,
0.06219624727964401,
0.03452560678124428,
0.036470476537942886,
0.019567793235182762,
-0.0014021574752405286,
-0.03889657184481621,
0.02304667793214321,
0.057081904262304306,
-0.027358343824744225,
0.03848224878311157,
-0.044167499989271164,
-0.047873564064502716,
0.05634617432951927,
0.0004916501347906888,
-0.03201939910650253,
0.0303649865090847,
-0.020081697031855583,
0.01915670745074749,
0.04578468203544617,
0.010989842936396599,
0.03464499115943909,
-0.001785098691470921,
0.06327448785305023,
-0.017962273210287094,
0.028279414400458336,
-0.022579796612262726,
-0.04980836808681488,
-0.0026379385963082314,
0.06774011999368668,
0.024946024641394615,
-0.05030553787946701,
-0.01958964578807354,
-0.052392445504665375,
-0.04751395061612129,
0.05590429902076721,
-0.007064766250550747,
-0.03516313061118126,
-0.04183746501803398,
-0.009546110406517982,
-0.009465763345360756,
-0.013473737984895706,
-0.009175796061754227,
0.046650297939777374,
-0.0027400399558246136,
-0.02776470221579075,
-0.044745177030563354,
0.03979223966598511,
-0.0008946935413405299,
0.06612542271614075,
-0.03143490105867386,
-0.02190568670630455,
-0.0315648578107357,
-0.008299254812300205,
-0.014231803826987743,
-0.008474813774228096,
0.08541975170373917,
0.06492231786251068,
0.02361699379980564,
-0.006279774475842714,
0.048110753297805786,
-0.005722654052078724,
0.040765851736068726,
-0.018723448738455772,
-0.022794751450419426,
-0.009874665178358555,
0.007697391323745251,
0.002873771358281374,
0.011845720931887627,
-0.029451165348291397,
0.017850777134299278,
-0.026161078363656998,
0.039969321340322495,
0.004158346448093653,
0.01403859630227089,
-0.07703185826539993,
0.014399118721485138,
-0.06779997050762177,
-0.07149669528007507,
-0.07540272921323776,
-0.07105918228626251,
0.07028599828481674,
-0.007780906744301319,
0.0023829443380236626,
0.045126620680093765,
0.011199633590877056,
0.033271946012973785,
0.02777356095612049,
0.04436959698796272,
0.0181169081479311,
-0.03947172313928604,
-0.021282998844981194,
-0.032720696181058884,
0.00019987046835012734,
-0.0074625336565077305,
0.017342478036880493,
-0.017650220543146133,
-0.029877254739403725,
0.03699247166514397,
-0.031634457409381866,
0.024041056632995605,
0.026539601385593414,
0.008404016494750977,
0.049031756818294525,
0.007852261886000633,
0.0302483681589365,
-0.031770918518304825,
-0.01913784071803093,
-0.0021568064112216234,
-0.01385574508458376,
-0.02414878085255623,
0.00009901240991894156,
-0.010556352324783802,
0.071661576628685,
0.027828747406601906,
0.03477521240711212,
0.09723558276891708,
-0.059242937713861465,
-0.016401683911681175,
0.05045802891254425,
0.010751745663583279,
-0.0075995177030563354,
0.013105540536344051,
-0.01667471043765545,
0.01951911486685276,
0.05997581407427788,
0.042764291167259216,
0.025113169103860855,
-0.0007885193917900324,
-0.04907458275556564,
-0.07205574959516525,
0.03433385491371155,
-0.10276953130960464,
-0.02248220704495907,
-0.031354647129774094,
-0.0016095496248453856,
0.008345188573002815,
-0.07635937631130219,
0.034940868616104126,
-0.01842389442026615,
0.03586264327168465,
0.051925983279943466,
0.02255410887300968,
-0.005122276488691568,
0.0036692984867841005,
-0.04908880963921547,
-0.04436737298965454,
0.05965219810605049,
-0.03949499502778053,
-0.01563115231692791,
0.0476909838616848,
-0.01140145305544138,
0.03214576840400696,
-0.04791776090860367,
0.0026944673154503107,
-0.04685847833752632,
-0.056646257638931274,
0.019175570458173752,
0.06342430412769318,
-0.016069602221250534,
0.025477854534983635,
0.047392092645168304,
-0.007705527823418379,
-0.03881936892867088,
-0.017551425844430923,
-0.018564388155937195,
0.00018202255887445062,
-0.028465373441576958,
0.06789766997098923,
0.0769021213054657,
0.03699116408824921,
-0.04303192347288132,
0.02990078181028366,
0.009866134263575077,
0.0013949834974482656,
0.07364378869533539,
-0.05938185006380081,
0.029338888823986053,
0.1315421313047409,
-0.0290316641330719,
-0.033800818026065826,
-0.010809879750013351,
-0.010773428715765476,
0.017080552875995636,
-0.02120964229106903,
-0.04873701184988022,
-0.02340857870876789,
0.02744450606405735,
0.005963534116744995,
0.005269390065222979,
0.014577987603843212,
-0.027925778180360794,
0.022094395011663437,
0.035118427127599716,
0.030961422249674797,
-0.09936584532260895,
0.04716051369905472,
0.022013487294316292,
-0.027243826538324356,
0.04255145788192749,
0.03002302348613739,
-0.058068256825208664,
0.01796814426779747,
-0.016937224194407463,
0.04312549903988838,
0.010920532047748566,
0.02279643714427948,
-0.051653653383255005,
0.014995889738202095,
0.007386426907032728,
-0.02407149225473404,
0.031592559069395065,
-0.017045054584741592,
-0.0302099771797657,
0.007002840284258127,
-0.0077925133518874645,
0.013932506553828716,
0.01953325793147087,
0.004390766378492117,
-0.01907695084810257,
-0.016745461151003838,
-0.06899627298116684,
0.02209681086242199,
-0.06159648671746254,
-0.057518813759088516,
0.040269333869218826,
-0.04279868304729462,
0.008625040762126446,
0.04787212982773781,
-0.0019288791809231043,
-0.07153557240962982,
0.011101113632321358,
0.04276324063539505,
-0.008758612908422947,
-0.06011871248483658,
-0.03454688563942909,
0.021276624873280525,
0.028708849102258682,
-0.012874102219939232,
0.03471432626247406,
-0.00853811763226986,
-0.00005404014518717304,
-0.0309420395642519,
0.016513969749212265,
-0.09430857002735138,
0.021318936720490456,
-0.014289199374616146,
-0.07995732873678207,
0.04333825036883354,
0.036497682332992554,
-0.04095881059765816,
-0.005566655192524195,
-0.006450904533267021,
-0.002320665866136551,
-0.019469140097498894,
0.009364739991724491,
0.021030066534876823,
-0.020745020359754562,
0.015093592926859856,
-0.010088433511555195,
0.049429699778556824,
0.027445312589406967,
0.014923441223800182,
0.030853787437081337,
0.060636572539806366,
0.00818862859159708,
-0.03577343747019768,
0.0024710700381547213,
-0.019342966377735138,
0.011788499541580677,
0.019472135230898857,
-0.08856900036334991,
-0.030344538390636444,
-0.0016775367548689246,
-0.0019719507545232773,
-0.05189831927418709,
0.07580673694610596,
-0.01758047379553318,
-0.01590500958263874,
-0.0849786177277565,
0.02174261026084423,
0.002708776853978634,
-0.052490413188934326,
0.012722266837954521,
-0.0554349459707737,
0.0030285955872386694,
-0.01206296682357788,
0.07527328282594681,
-0.028549347072839737,
0.037448327988386154,
0.0793495625257492,
-0.046612437814474106,
-0.03429272770881653,
-0.03446735441684723,
-0.0569036491215229,
0.0019416962750256062,
-0.029726454988121986,
-0.022497985512018204,
0.006743218749761581,
-0.01700012758374214,
-0.03352389112114906,
-0.045083124190568924,
-0.012203982099890709,
0.04167473688721657,
-0.03487228974699974,
0.010826027020812035,
-0.005046252626925707,
-0.015437762252986431,
0.018652450293302536,
0.021428046748042107,
-0.018569791689515114,
0.03441831097006798,
-0.011161699891090393,
0.013802582398056984,
0.0036124021280556917,
0.015339668840169907,
0.014385849237442017,
0.025344349443912506,
0.003088791389018297,
-0.03402192145586014,
0.045298803597688675,
0.03879455849528313,
0.02292526699602604,
-0.01757827028632164,
-0.018153294920921326,
-0.004346475936472416,
-0.02079365774989128,
0.04385129362344742,
0.00810845848172903,
-0.03267475962638855,
-0.019866904243826866,
-0.011804062873125076,
0.00865142047405243,
0.023685598745942116,
-0.02922721952199936,
0.03026438131928444,
-0.0543728731572628,
-0.03295470029115677,
-0.0007398450979962945,
-0.027182606980204582,
-0.0759657695889473,
0.05763456970453262,
-0.038351234048604965,
-0.041559848934412,
0.009263715706765652,
0.06042926758527756,
-0.020679114386439323,
0.0112296799197793,
-0.00821778830140829,
0.0134098120033741,
-0.002002692548558116,
0.0318303182721138,
0.04546041414141655,
0.03485485538840294,
0.018189165741205215,
-0.027936168015003204,
-0.033380333334207535,
-0.055160727351903915,
0.027556970715522766,
0.03219160437583923,
-0.026449698954820633,
-0.01567000523209572,
-0.023032061755657196,
-0.02177567034959793,
0.023039627820253372,
0.042021673172712326,
0.016178173944354057,
0.025780562311410904,
-0.029546894133090973,
0.036599960178136826,
0.03812103718519211,
0.10789308696985245,
-0.05882512032985687,
-0.03482649847865105,
-0.05427125468850136,
0.003567122621461749,
-0.012589129619300365,
-0.008176830597221851,
-0.04524794965982437,
0.012349609285593033,
0.030255671590566635,
0.030705269426107407,
-0.03539912402629852,
0.039493855088949203,
0.04629267007112503,
0.0164506696164608,
0.05262431874871254,
-0.0136770810931921,
-0.031677648425102234,
-0.034837253391742706,
0.016560111194849014,
0.048424433916807175,
0.021189609542489052,
-0.006278004497289658,
-0.010689006187021732,
0.018493345007300377,
0.058307401835918427,
0.0034997831098735332,
0.012678965926170349,
-0.07155060768127441,
-0.006892174948006868,
-0.0956306904554367,
0.00873206090182066,
0.0035922499373555183,
0.056813210248947144,
0.08589737117290497,
-0.013202651403844357,
0.01077269297093153,
-0.030147474259138107,
-0.01570023223757744,
0.024955827742815018,
-0.053824879229068756,
-0.00106651964597404,
-0.011987430974841118,
-0.003972529899328947,
-0.04021615535020828,
0.019375665113329887,
-0.014510728418827057,
-0.048855166882276535,
0.03338964655995369,
-0.0019633823540061712,
0.005642611067742109,
0.004358459729701281,
0.054371923208236694,
-0.005732016172260046,
-0.03889961540699005,
0.0017364420928061008,
0.03899484872817993,
0.006700920406728983,
0.048228953033685684,
-0.07293824851512909,
-0.043161313980817795,
-0.04034334793686867,
-0.05487632006406784,
-0.014545571058988571,
0.03670649230480194,
0.0015274055767804384,
0.0005634616827592254,
0.00018485092732589692,
0.028866780921816826,
-0.005961533170193434,
-0.0337776318192482,
0.00745035195723176,
-0.004357703495770693,
-0.06630989909172058,
0.0018734149634838104,
-0.009146666154265404,
0.025740189477801323,
0.04117334261536598,
-0.03933877497911453,
-0.016987647861242294,
-0.026348192244768143,
0.04605830833315849,
0.007398828398436308,
0.003433863166719675,
-0.040976300835609436,
0.0012131623225286603,
0.04659745469689369,
0.015323285944759846,
-0.05432358384132385,
-0.006638745311647654,
0.012431816197931767,
-0.03182980418205261,
-0.02953234501183033,
-0.031984843313694,
0.0009726162534207106,
0.008549202233552933,
-0.029528839513659477,
0.0066727991215884686,
-0.013170935213565826,
0.003881598124280572,
0.022636180743575096,
0.020062703639268875,
-0.0009055549162440002,
0.01663840189576149,
0.04961807653307915,
0.04056322202086449,
0.016233276575803757,
0.03478382155299187,
0.007311142049729824,
-0.02545643039047718,
-0.018137715756893158,
-0.0036547547206282616,
-0.003228965913876891,
0.019323259592056274,
0.0036442361306399107,
-0.00032428590930067003,
0.02607961744070053,
-0.045890696346759796,
0.04244956746697426,
0.009989793412387371,
0.020130908116698265,
-0.03462396189570427,
0.03880274295806885,
0.0965125560760498,
0.04195332154631615,
0.04426990821957588,
0.013306455686688423,
-0.0015846194000914693,
-0.03549295291304588,
-0.07196015864610672,
-0.04146268218755722,
0.00960183423012495,
0.05233968049287796,
0.022515520453453064,
-0.05104077607393265,
-0.02185109071433544,
-0.018157044425606728,
0.026347536593675613,
0.04392906650900841,
0.003119830973446369,
0.0036459332332015038,
-0.015171064995229244,
0.03362986445426941,
-0.014834322035312653,
-0.0014191800728440285,
0.010482567362487316,
0.02889075130224228,
-0.029110228642821312,
0.03400556743144989,
-0.0010218616807833314,
0.0220172218978405,
0.010489355772733688,
-0.022783149033784866,
-0.03960753232240677,
-0.004886150360107422,
0.07102508842945099,
-0.0005114670493640006,
-0.025614988058805466,
0.0468241386115551,
0.004530693404376507,
0.018507223576307297,
-0.14054182171821594,
0.0328984335064888,
0.019597144797444344,
0.05565308406949043,
0.035089220851659775,
-0.013313508592545986,
-0.03720012679696083,
-0.029302043840289116,
0.01964864507317543,
0.007250727619975805,
0.01689837872982025,
-0.04686751216650009,
0.034427035599946976,
0.03356551006436348,
-0.016468696296215057,
0.051418203860521317,
-0.11100394278764725,
-0.0057777478359639645,
0.030970342457294464,
-0.02936171181499958,
-0.0032558452803641558,
0.03891013190150261,
-0.0031261357944458723,
0.008119149133563042,
-0.00421294616535306,
0.008301996625959873,
0.0077158017084002495,
-0.015695160254836082,
-0.01165577583014965,
0.006940753199160099,
0.01920931041240692,
-0.03991914540529251,
0.035919226706027985,
-0.014211979694664478,
0.016603440046310425,
0.001617248635739088,
-0.023400068283081055,
0.015257569961249828,
0.07574258744716644,
-0.039817944169044495,
-0.04923143610358238,
-0.0029697909485548735,
-0.028496183454990387,
-0.0312831811606884,
0.010177699849009514,
0.0008629775256849825,
0.03602474927902222,
-0.008131641894578934,
-0.019238214939832687,
-0.0014264443889260292,
0.02780340425670147,
0.010814364068210125,
-0.008442714810371399,
0.002329000737518072,
-0.03518308326601982,
-0.02970203012228012,
-0.00047022479702718556,
0.04329807311296463,
0.00386631372384727,
-0.061938151717185974,
0.08088958263397217,
0.06321687996387482,
0.0062236725352704525,
-0.04585358873009682,
-0.01787862554192543,
0.02447599731385708,
0.010053493082523346,
-0.007825915701687336,
0.048440121114254,
-0.05396124720573425,
0.041163478046655655,
0.028968295082449913,
-0.004637749865651131,
0.05923023074865341,
-0.014775853604078293,
0.06419812887907028,
0.05031413212418556,
-0.03208547085523605,
-0.036728039383888245,
-0.021563749760389328,
0.005332266446202993,
-0.022038590162992477,
-0.00269417860545218,
-0.03691786527633667,
0.01802504062652588,
-0.017182370647788048,
0.002019118517637253,
0.001205931999720633,
0.06559232622385025,
-0.04673496633768082,
0.034513164311647415,
-0.025645099580287933,
-0.050220150500535965,
-0.018514102324843407,
-0.010461606085300446,
-0.028908848762512207,
0.025486698374152184,
-0.04259070008993149,
0.02723698876798153,
0.03841495141386986,
0.004437057767063379,
0.039746202528476715,
-0.04153957962989807,
-0.0063178399577736855,
-0.050719019025564194,
-0.06742703914642334,
0.02489754557609558,
-0.04325101524591446,
-0.00221360195428133,
-0.01498160045593977,
0.08470069617033005,
-0.008696362376213074,
-0.02534261718392372,
-0.007517325226217508,
0.08927168697118759,
-0.0021804342977702618,
0.010578667744994164,
-0.0022486781235784292,
0.036169007420539856,
-0.002895261161029339,
0.010951663367450237,
-0.036903902888298035,
-0.026676736772060394,
-0.012980963103473186,
-0.05751555413007736,
0.0020000359509140253,
-0.03056975081562996,
-0.04214504733681679,
-0.05232887715101242,
0.040198978036642075,
0.09389552474021912,
-0.005517592653632164,
-0.012064199894666672,
-0.0522443912923336,
-0.02593211643397808,
0.014753404073417187,
-0.014496291056275368,
0.03550348058342934,
-0.013419893570244312,
0.010806365869939327,
0.0034507843665778637,
-0.05080340430140495,
0.006627796683460474,
-0.0034928186796605587,
-0.0019100932404398918,
0.04009942710399628,
0.044122595340013504,
0.00576734496280551,
0.025522669777274132,
0.02859046496450901,
0.05134519562125206,
-0.021725045517086983,
0.0066163609735667706,
-0.03560305014252663,
0.004113301169127226,
-0.005516324192285538,
-0.026508495211601257,
-0.003826434025540948,
-0.011800668202340603,
-0.048074331134557724,
-0.03983834758400917,
0.01629183441400528,
-0.0065176840871572495,
-0.03473832830786705,
-0.006159535609185696,
-0.042314495891332626,
0.0018002199940383434,
0.03372090309858322,
0.08585713058710098,
0.0030333814211189747,
-0.029713494703173637,
0.015167346224188805,
-0.027789780870079994,
0.061710938811302185,
-0.025072306394577026,
0.0004642173880711198,
0.02451309934258461,
-0.0036092717200517654,
-0.02874607779085636,
-0.05393785238265991,
0.049494147300720215,
0.05624062567949295,
0.018305590376257896,
-0.02608894743025303,
0.04285714030265808,
-0.014818880707025528,
0.07372210174798965,
0.04098860174417496,
-0.09853087365627289,
-0.01921510510146618,
0.008936005644500256,
0.014458168298006058,
-0.030356666073203087,
0.016434136778116226,
0.02140665613114834,
0.013590240851044655,
-0.03475445136427879,
0.00471697049215436,
-0.04041390120983124,
-0.01570918783545494,
0.014305515214800835
] |
<p>Imposing SU(2) and U(1) local gauge invariance introduces 4 gauge bosons, two of which correspond to $W^{\pm}$ bosons. The other two gauge fields $W^{\mu}_3$ and $B^{\mu}$ however are said not to correspond to $Z$ and $\gamma$ bosons because of the incorrect chiral coupling of the $Z$ boson if this identification is made.</p>
<p>The "physical" bosons are said to be Weinberg rotated by $\sin^2\theta_W=0.23$, where the angle is obtained from experiment. This gives the observed coupling of $Z$ to both left and right chiralities and also a different mass from the $W$ brothers, again observed experimentally.</p>
<p>Why? Why do the physical $Z$ and $\gamma$ bosons have to be Weinberg rotated? (by Nature that is, not by phenomenologists) If there was no rotation, the three $W$ 's would have the same masses and would couple only to lefties. This doesn't immediately seem particularly disastrous to me.</p>
<p>I don't see how <a href="http://en.wikipedia.org/wiki/Totalitarian_principle" rel="nofollow">Gell-Mann's Totalitarian Principle</a> can save the day here, because what I'm essentially asking is why our particle detectors observe the Weinberg rotated bosons and not the "natural" ones that come out of the Lagrangian? What is it that makes particular linear combinations of bosons the physical ones? And crucially, why aren't the $W^{\pm}$ bosons rotated in a similar manner? (Or would we not notice if they were?)</p> | g4771 | [
0.02774568274617195,
-0.04211672395467758,
-0.0009451604564674199,
-0.008217576891183853,
0.05546993762254715,
0.0055715106427669525,
0.08513126522302628,
0.01029253751039505,
0.00937622506171465,
0.019380291923880577,
0.010222304612398148,
0.00003494592965580523,
-0.06395579129457474,
0.010568330995738506,
-0.010606625117361546,
-0.043748948723077774,
0.040927477180957794,
0.059764157980680466,
0.09584173560142517,
-0.02242187410593033,
-0.022879142314195633,
0.045069701969623566,
-0.05951933190226555,
-0.022002724930644035,
-0.029050815850496292,
0.0030184851493686438,
-0.010798313654959202,
-0.022800486534833908,
0.028078077360987663,
-0.011040402576327324,
0.04716339707374573,
0.010837172158062458,
0.02709132432937622,
0.03254318609833717,
0.02434668317437172,
-0.06568560749292374,
0.03744731470942497,
-0.05547591671347618,
0.02948615886271,
-0.011772374622523785,
-0.043614890426397324,
0.014301029033958912,
-0.018758822232484818,
-0.021899651736021042,
-0.01603526435792446,
0.0657418817281723,
-0.01156450342386961,
0.05403532460331917,
0.044819243252277374,
-0.019999951124191284,
-0.0054871998727321625,
-0.051743753254413605,
0.054941046983003616,
0.027070093899965286,
0.057302217930555344,
0.034198466688394547,
0.05835002288222313,
0.009657503105700016,
0.06951074302196503,
0.020245671272277832,
-0.007794990669935942,
-0.02560202032327652,
-0.028689242899417877,
-0.0018931948579847813,
0.07558032125234604,
-0.05157431215047836,
-0.016585195437073708,
0.04380522668361664,
0.026842089369893074,
0.03463643044233322,
-0.029526889324188232,
-0.01560157723724842,
-0.03324434906244278,
0.02336144633591175,
0.047627128660678864,
0.05742292106151581,
-0.03492432460188866,
-0.006226652301847935,
-0.05299712345004082,
-0.027114227414131165,
-0.018049906939268112,
-0.012482866644859314,
-0.009229699149727821,
-0.006778537295758724,
0.08620297163724899,
-0.027625570073723793,
0.03560863807797432,
0.006925965193659067,
-0.03305875137448311,
-0.014255470596253872,
0.039741672575473785,
-0.06912219524383545,
0.05075084790587425,
0.018136736005544662,
-0.03519921749830246,
0.020191093906760216,
0.002852768637239933,
0.08445333689451218,
-0.03053235448896885,
-0.013550757430493832,
-0.01708533801138401,
0.06404711306095123,
-0.03502846509218216,
0.007197442464530468,
-0.017384124919772148,
-0.03238748386502266,
0.09978985041379929,
0.060394443571567535,
-0.04704931005835533,
-0.024543020874261856,
-0.046682752668857574,
0.030576063320040703,
0.03333897143602371,
0.004523378796875477,
-0.06191733479499817,
-0.0379771813750267,
-0.01417621597647667,
-0.015900006517767906,
0.06099654361605644,
0.0894218161702156,
0.004415367264300585,
-0.06264002621173859,
-0.021508708596229553,
0.02843661792576313,
-0.02970784716308117,
-0.03427334874868393,
-0.00900349672883749,
0.00023804571537766606,
0.0015582448104396462,
-0.05156102403998375,
0.036629509180784225,
-0.024194765836000443,
-0.000532043632119894,
0.010427767410874367,
0.022316643968224525,
-0.012754842638969421,
0.031580377370119095,
0.034550875425338745,
-0.005221092142164707,
-0.000494993815664202,
-0.0028298278339207172,
-0.04204360023140907,
0.007622780743986368,
-0.010493995621800423,
-0.028551645576953888,
0.055468473583459854,
-0.022297458723187447,
-0.051058415323495865,
0.04853592813014984,
0.06662491708993912,
0.0035174968652427197,
0.13503089547157288,
0.06686798483133316,
-0.048980578780174255,
0.020717673003673553,
-0.05061325058341026,
0.026423612609505653,
-0.0014203545870259404,
0.007019720505923033,
0.026440244168043137,
0.07942637801170349,
-0.03729845955967903,
0.000009386578312842175,
-0.00004302331944927573,
-0.004179240670055151,
-0.011219584383070469,
-0.025775764137506485,
-0.03391820937395096,
-0.0019576004706323147,
-0.04627623036503792,
-0.07742950320243835,
-0.01115849893540144,
-0.056764718145132065,
-0.014086110517382622,
0.037502605468034744,
0.08101166784763336,
-0.049387894570827484,
-0.04327128082513809,
-0.0016585899284109473,
0.016646407544612885,
-0.061497047543525696,
0.03272021934390068,
0.015459274873137474,
-0.00797757226973772,
-0.04542185738682747,
-0.043991055339574814,
-0.006982689257711172,
0.06119152531027794,
0.028881708160042763,
0.0002191120875068009,
0.035420555621385574,
0.008718740195035934,
-0.02956712618470192,
-0.017816105857491493,
0.0009833363583311439,
0.025418635457754135,
-0.006427919026464224,
0.022768408060073853,
-0.011202826164662838,
0.03846398741006851,
-0.014781744219362736,
-0.009098414331674576,
0.027072029188275337,
-0.057410694658756256,
-0.03184368088841438,
-0.05599335953593254,
-0.025856439024209976,
0.005190642084926367,
0.057416029274463654,
-0.025549789890646935,
-0.029527705162763596,
-0.04101364687085152,
0.002037420403212309,
0.004194609355181456,
-0.03574186936020851,
-0.030721789225935936,
-0.041044969111680984,
0.007891802117228508,
-0.026502668857574463,
-0.04878895357251167,
-0.0020558983087539673,
-0.02059507928788662,
0.058366306126117706,
-0.018040789291262627,
0.007282419130206108,
0.007795481476932764,
-0.06437817215919495,
-0.024186698719859123,
0.010861231945455074,
-0.041677456349134445,
0.0031067293602973223,
0.047044236212968826,
0.0037420589942485094,
0.05240852013230324,
0.04707153141498566,
0.013661264441907406,
-0.03534796088933945,
0.0025787451304495335,
0.08179665356874466,
-0.0003181180509272963,
0.01997775211930275,
0.000033290642022620887,
-0.034075893461704254,
0.02085442841053009,
0.08978449553251266,
-0.014271709136664867,
0.05748217552900314,
-0.005149011965841055,
-0.05437229946255684,
0.03328283876180649,
0.015369286760687828,
-0.001094693667255342,
-0.019050028175115585,
-0.020917896181344986,
0.014210031367838383,
0.02743888832628727,
0.012748492881655693,
0.015784351155161858,
-0.08435925841331482,
-0.031152673065662384,
0.004445507191121578,
-0.04282008484005928,
0.0051282555796206,
0.03510790690779686,
0.015319759026169777,
-0.0070871105417609215,
0.06262704730033875,
0.04707004129886627,
-0.025124218314886093,
0.007398934103548527,
-0.043778207153081894,
0.028836624696850777,
0.021023685112595558,
0.017780981957912445,
-0.0033864877186715603,
-0.045251134783029556,
-0.013886602595448494,
-0.006071817595511675,
0.008487305603921413,
-0.03407933935523033,
-0.024484165012836456,
0.07309002429246902,
-0.0173090361058712,
-0.014840945601463318,
0.03594984486699104,
0.0008972885552793741,
-0.04178695008158684,
-0.049231741577386856,
-0.025391055271029472,
0.006817672401666641,
0.003049983875826001,
0.0025802699383348227,
0.06147852540016174,
0.017299626022577286,
0.04746318608522415,
-0.015520322136580944,
0.051211319863796234,
-0.012398475781083107,
-0.038325317203998566,
0.06452494114637375,
0.05161691829562187,
0.01140615064650774,
0.01956060715019703,
0.02466336451470852,
-0.019013026729226112,
-0.024407127872109413,
-0.07080838084220886,
0.016581140458583832,
-0.025020286440849304,
0.02576281875371933,
-0.04005609452724457,
0.02572507970035076,
-0.019299952313303947,
0.004503464326262474,
0.0028135795146226883,
-0.006127683911472559,
-0.0718526691198349,
0.04866544529795647,
-0.03397919982671738,
-0.00793769396841526,
-0.07257028669118881,
0.026906028389930725,
-0.012430917471647263,
-0.045267172157764435,
0.04424385353922844,
0.03115362860262394,
-0.04947575554251671,
0.0020548165775835514,
-0.010366466827690601,
-0.03275991603732109,
0.0009923117468133569,
0.026430586352944374,
0.0022594404872506857,
0.04501444101333618,
-0.08611587435007095,
0.00688968924805522,
-0.040311671793460846,
0.017686989158391953,
0.0131957046687603,
-0.0074843126349151134,
-0.010219424962997437,
-0.04091951996088028,
-0.043551910668611526,
-0.011624420061707497,
-0.012573832646012306,
0.0072536044754087925,
-0.002779441187158227,
-0.05722789838910103,
0.023868832737207413,
0.018470467999577522,
0.014811313711106777,
0.03493161126971245,
0.04708278179168701,
0.007987922057509422,
0.017775993794202805,
0.02066871151328087,
-0.018634961917996407,
0.005334315821528435,
0.04012066125869751,
-0.019846146926283836,
-0.011606445536017418,
0.030174555256962776,
-0.051371198147535324,
-0.023734675720334053,
-0.04009167477488518,
0.024648411199450493,
-0.04249686002731323,
0.01585436798632145,
0.05685155838727951,
-0.006730400957167149,
-0.036127690225839615,
-0.011214631609618664,
-0.018488727509975433,
0.008773400448262691,
0.04941784217953682,
-0.07791690528392792,
-0.03515629842877388,
0.006066702771931887,
-0.045512668788433075,
-0.0037435104604810476,
0.004555673338472843,
0.019526349380612373,
0.0061035980470478535,
0.03253580629825592,
0.023198449984192848,
0.02031681127846241,
-0.03547166660428047,
-0.0014240331947803497,
-0.03184070438146591,
-0.014812078326940536,
-0.022720303386449814,
0.002979181706905365,
0.012415874749422073,
-0.03967129811644554,
0.019975734874606133,
-0.03202926367521286,
0.015196532011032104,
0.01993449591100216,
0.03161580488085747,
-0.04968903958797455,
0.019359031692147255,
0.02888788841664791,
-0.0039641899056732655,
-0.043708521872758865,
0.0031336143147200346,
-0.005026284605264664,
-0.028077835217118263,
-0.030478158965706825,
0.07697969675064087,
-0.037303559482097626,
0.04265777766704559,
0.03655848279595375,
0.03462926670908928,
-0.0749019980430603,
0.08448652178049088,
-0.04802930727601051,
-0.035738252103328705,
-0.05975031107664108,
0.015296652913093567,
-0.008113360963761806,
-0.014802380464971066,
0.0019324596505612135,
0.047576192766427994,
-0.0002489687758497894,
0.023329854011535645,
0.06644257158041,
0.01869797706604004,
0.01708419807255268,
-0.001898858929052949,
0.0046707987785339355,
0.09829531610012054,
0.002376594813540578,
-0.03465224429965019,
-0.00964020099490881,
0.012245077639818192,
-0.03271760419011116,
-0.026587028056383133,
0.041037313640117645,
0.019346363842487335,
0.06592778861522675,
0.017959149554371834,
-0.03831892088055611,
-0.0076459175907075405,
-0.045309778302907944,
-0.03099224343895912,
0.06641105562448502,
-0.05100105330348015,
-0.01990327425301075,
-0.017959468066692352,
-0.027724865823984146,
-0.007056836038827896,
0.02695818431675434,
-0.008338036015629768,
-0.008785054087638855,
0.03543916344642639,
-0.052092183381319046,
-0.027111606672406197,
0.07341963797807693,
-0.012466935440897942,
0.002226301934570074,
-0.11499479413032532,
-0.048954568803310394,
0.007304865401238203,
-0.026658978313207626,
0.03231692314147949,
0.01672673597931862,
-0.0265180841088295,
0.03050266206264496,
-0.05278186872601509,
-0.0277260635048151,
-0.014199691824615002,
-0.01699201576411724,
0.016190649941563606,
-0.02676917240023613,
-0.009093431755900383,
0.006336847320199013,
-0.01896829344332218,
-0.013489320874214172,
-0.030733725056052208,
-0.06787798553705215,
-0.033752650022506714,
-0.0025418931618332863,
0.049449946731328964,
0.018462898209691048,
-0.018398553133010864,
-0.0045806108973920345,
-0.0463557168841362,
-0.005448606330901384,
0.030613968148827553,
0.01834266260266304,
0.06039653345942497,
-0.04117285832762718,
0.06768177449703217,
-0.04206060990691185,
-0.00243192701600492,
0.03430718183517456,
-0.04924866557121277,
-0.03754101321101189,
-0.024089675396680832,
0.001907505327835679,
-0.03953152149915695,
0.037522099912166595,
0.008204379118978977,
0.003851712215691805,
0.004432204645127058,
0.05656524375081062,
0.08651937544345856,
-0.02721564657986164,
-0.02658466435968876,
0.011667221784591675,
-0.024278851225972176,
-0.033597540110349655,
0.024527383968234062,
0.015314034186303616,
0.046750910580158234,
0.009817749261856079,
-0.02787724696099758,
-0.020617881789803505,
0.01689545437693596,
-0.09177805483341217,
0.006686776410788298,
0.04848334193229675,
-0.011066382750868797,
-0.03920016810297966,
-0.03565755486488342,
0.05167395621538162,
-0.008810553699731827,
0.0019224503776058555,
0.004491258412599564,
-0.024293726310133934,
-0.010832205414772034,
-0.013263731263577938,
0.10452816635370255,
0.025231624022126198,
0.05333123356103897,
-0.019779399037361145,
0.047361526638269424,
-0.01779540441930294,
0.02845672145485878,
0.07710041105747223,
0.03315447270870209,
-0.035052038729190826,
0.003559600794687867,
-0.005782401189208031,
0.013011271134018898,
0.02092166058719158,
0.0023635097313672304,
0.006765949539840221,
-0.0520283542573452,
0.03356359899044037,
-0.0790652483701706,
0.05235651135444641,
-0.004209696780890226,
-0.022672759369015694,
-0.00894545204937458,
-0.01635025441646576,
-0.06696152687072754,
-0.030268942937254906,
-0.06532422453165054,
-0.026086850091814995,
0.005156409461051226,
0.02342918887734413,
0.007809169590473175,
0.008496633730828762,
0.032591018825769424,
0.0045523494482040405,
0.00007793850818416104,
-0.0007896596216596663,
0.00584162212908268,
0.015949778258800507,
-0.02525760792195797,
0.05238187313079834,
0.0023475862108170986,
0.07756206393241882,
-0.0036022355780005455,
0.03527209535241127,
-0.005251564085483551,
0.00858106929808855,
-0.005145369563251734,
-0.04052729904651642,
0.04415934905409813,
0.033259306102991104,
-0.00028265445143915713,
-0.09313523024320602,
0.01550830528140068,
0.029755573719739914,
-0.036529168486595154,
-0.0010448112152516842,
0.026508843526244164,
0.0009867714252322912,
-0.03954838216304779,
0.021448306739330292,
-0.041548654437065125,
0.042372364550828934,
-0.03831292688846588,
-0.020897643640637398,
0.05834827944636345,
-0.002408896340057254,
-0.03740180656313896,
-0.09585371613502502,
0.068629689514637,
0.018957538530230522,
0.03006576932966709,
0.013431898318231106,
0.010340860113501549,
0.004372021649032831,
-0.030010828748345375,
-0.025612378492951393,
0.026705307886004448,
-0.014546522870659828,
-0.005620685406029224,
0.01073457207530737,
0.003968195989727974,
0.00895265955477953,
0.0038545499555766582,
-0.0327608548104763,
-0.009004737250506878,
0.012610239908099174,
-0.0324237197637558,
-0.011678332462906837,
0.03052685596048832,
-0.0029158582910895348,
0.02831181138753891,
-0.021916233003139496,
0.03410196676850319,
0.053000155836343765,
-0.03184260427951813,
0.02211865410208702,
0.03142973780632019,
0.0562758594751358,
-0.0025079206097871065,
0.00602707639336586,
0.01717507839202881,
0.07612094283103943,
0.012283142656087875,
-0.04114590212702751,
-0.021129650995135307,
0.020136144012212753,
0.012581855989992619,
0.03390300273895264,
0.019569285213947296,
0.03371516242623329,
0.02448686957359314,
-0.004109441302716732,
-0.028971608728170395,
0.037961993366479874,
0.019748538732528687,
-0.010524408891797066,
-0.04973790794610977,
0.024244559928774834,
0.01209512073546648,
-0.011251415126025677,
0.035421472042798996,
0.025237854570150375,
-0.07271197438240051,
-0.03221266344189644,
-0.05027902126312256,
-0.029856186360120773,
0.03309987112879753,
-0.015982240438461304,
-0.04111555218696594,
0.0038358354941010475,
-0.002159964991733432,
-0.04420953989028931,
0.0009160992922261357,
0.026418456807732582,
-0.0008150241919793189,
-0.01082644797861576,
0.05630224198102951,
0.0033963676542043686,
-0.05187226086854935,
-0.03102562017738819,
0.021719513460993767,
0.015456878580152988,
-0.07038447260856628,
-0.040781158953905106,
0.030731936916708946,
0.0016164890257641673,
-0.007250555325299501,
0.012607945129275322,
-0.0034280437976121902,
0.04562913626432419,
0.04817786440253258,
-0.010491098277270794,
-0.016620352864265442,
-0.016035454347729683,
0.0032889496069401503,
-0.01734582707285881,
-0.030012164264917374,
0.03750401735305786,
0.022610660642385483,
0.022724315524101257,
0.07838238775730133,
-0.010076218284666538,
-0.07176845520734787,
0.042580947279930115,
-0.01023672241717577,
0.05008475482463837,
-0.032393962144851685,
-0.01801067776978016,
0.021954411640763283,
-0.023408498615026474,
-0.0147069301456213,
-0.03609210625290871,
0.01712506078183651,
-0.038735512644052505,
-0.029575034976005554,
-0.0567595437169075,
-0.025026213377714157,
0.009241011925041676,
0.011071155779063702,
0.0360209159553051,
0.0970323234796524,
0.03338729590177536,
0.07930886745452881,
-0.03602439537644386,
-0.022541183978319168,
-0.017640814185142517,
-0.017601443454623222,
-0.04442932829260826,
0.00043771276250481606,
0.01569473184645176,
-0.01521387044340372,
-0.015305285342037678,
-0.026768552139401436,
-0.03454028442502022,
0.03364473208785057,
-0.02182973362505436,
0.05028281733393669,
0.020367197692394257,
-0.0925755575299263,
0.01243179477751255,
-0.03803156688809395,
0.034842975437641144,
-0.03275672346353531,
0.008049109019339085,
-0.011408479884266853,
0.031438250094652176,
-0.013488809578120708,
0.012492947280406952,
0.023927073925733566,
-0.049484189599752426,
0.01872147247195244,
-0.04003346338868141,
-0.039937518537044525,
-0.032662831246852875,
-0.011122286319732666,
0.028284259140491486,
-0.007852190174162388,
-0.013952811248600483,
0.002304744441062212,
0.006548617966473103,
-0.0368204228579998,
0.04870627820491791,
0.028986666351556778,
-0.021933935582637787,
0.08176689594984055,
-0.011447583325207233,
0.02403918467462063,
0.025711463764309883,
-0.030419031158089638,
-0.04112325981259346,
-0.03694480285048485,
0.0012876427499577403,
-0.0028901943005621433,
-0.05184806138277054,
-0.017003187909722328,
0.003006974933668971
] |
<p>I watched on TV as they where showing gold bars stored in bank vaults and I noticed that they always stack them with the narrow side down and the wide side up. Like this:</p>
<p><img src="http://i.stack.imgur.com/Mvllb.jpg" alt="Gold Bar Stacking"></p>
<p>So there has to be a mechanical reason why is that. Any ideas?</p> | g1024 | [
0.037326883524656296,
0.10742063820362091,
0.009865536354482174,
-0.02300652489066124,
0.042289700359106064,
0.04987356439232826,
0.011430713348090649,
-0.009070659056305885,
-0.03401174768805504,
0.0200488343834877,
-0.027275117114186287,
-0.007480834145098925,
0.0017460444942116737,
0.01720603182911873,
-0.025141870602965355,
-0.05556671321392059,
0.016615860164165497,
0.007731611840426922,
0.05546920374035835,
0.028599990531802177,
-0.02050669491291046,
0.007990904152393341,
-0.00861224066466093,
0.003049778286367655,
-0.036527182906866074,
0.05475207045674324,
0.02654282934963703,
0.011313916184008121,
-0.02593803033232689,
0.0008010296733118594,
0.0006935009732842445,
0.004475565627217293,
-0.016950782388448715,
0.021885499358177185,
-0.025562390685081482,
-0.007077667862176895,
0.06491968035697937,
-0.018894512206315994,
0.02569415606558323,
-0.02475130558013916,
-0.03739866614341736,
0.022062594071030617,
-0.006732007022947073,
-0.0373169369995594,
0.012133052572607994,
-0.01816062070429325,
0.00705299386754632,
0.02484256401658058,
0.048593636602163315,
-0.030337018892169,
0.008272435516119003,
0.017272569239139557,
0.0055929385125637054,
-0.03900058567523956,
0.0612449087202549,
-0.005296690389513969,
-0.05457989498972893,
0.04430314153432846,
0.056753989309072495,
0.0022387122735381126,
0.05273934826254845,
-0.009937371127307415,
0.034658774733543396,
0.022876858711242676,
0.05514688044786453,
0.02525472268462181,
0.019672716036438942,
0.02371780201792717,
0.053955137729644775,
0.004862856585532427,
0.012943549081683159,
-0.02490336261689663,
-0.010648328810930252,
-0.05196265131235123,
0.027406668290495872,
0.0367412194609642,
-0.03441585227847099,
0.06446708738803864,
-0.0062394230626523495,
0.022656956687569618,
0.0070799230597913265,
0.0016234716167673469,
-0.033270929008722305,
0.00019295199308544397,
0.005400314461439848,
0.05312107503414154,
0.008337443694472313,
-0.03747985512018204,
-0.024088693782687187,
0.059310607612133026,
-0.0099581778049469,
-0.04471511393785477,
0.03877187892794609,
0.032789453864097595,
-0.060029517859220505,
-0.053954314440488815,
-0.005998217035084963,
0.06925798952579498,
-0.010405618697404861,
0.0034046578221023083,
0.018906164914369583,
0.005064724013209343,
0.03812585771083832,
-0.005983893759548664,
0.01880532130599022,
0.000824586721137166,
0.02517738752067089,
0.04825707525014877,
-0.055113255977630615,
-0.016102636232972145,
-0.021815115585923195,
-0.012962765991687775,
-0.032734133303165436,
0.039113059639930725,
0.015009860508143902,
0.08224660158157349,
0.05456678196787834,
0.04210897907614708,
0.018122786656022072,
0.020697517320513725,
0.07719780504703522,
-0.03282599151134491,
0.014705028384923935,
-0.04822475463151932,
-0.046775564551353455,
-0.051673758774995804,
0.03299002721905708,
-0.011904149316251278,
0.05893871188163757,
-0.02995236963033676,
0.08594691008329391,
0.03816341608762741,
-0.00868972111493349,
-0.02157578244805336,
0.04367407038807869,
0.018201390281319618,
0.026290735229849815,
-0.041269127279520035,
-0.03260909393429756,
0.009460732340812683,
-0.03947798162698746,
-0.054614484310150146,
-0.005024179816246033,
0.0020782689098268747,
-0.0037885077763348818,
-0.06846185028553009,
0.034926433116197586,
0.007641876582056284,
0.001974573126062751,
-0.04619109630584717,
-0.039566561579704285,
0.004384055733680725,
0.008903507143259048,
-0.045737121254205704,
0.0028176968917250633,
-0.040823765099048615,
0.004970230627804995,
0.003985200542956591,
0.029694553464651108,
0.05984371155500412,
0.00464436924085021,
0.008555618114769459,
-0.010192696005105972,
-0.05304696783423424,
-0.08301757276058197,
0.0062582651153206825,
0.016508476808667183,
-0.043730758130550385,
0.01589757204055786,
0.01013999991118908,
0.03050791472196579,
0.03912435099482536,
-0.01699250191450119,
0.020446859300136566,
0.02421441487967968,
0.09579294174909592,
0.03589867427945137,
0.018179940059781075,
0.0322146899998188,
-0.018821556121110916,
-0.02758421190083027,
-0.011415117420256138,
0.03741610422730446,
-0.03356142342090607,
0.004052078351378441,
-0.08462034165859222,
0.02908685803413391,
0.022982703521847725,
-0.043212052434682846,
-0.04918588697910309,
0.01019516121596098,
0.023401953279972076,
-0.014226211234927177,
0.053689729422330856,
-0.026721317321062088,
-0.02765997126698494,
-0.01363998744636774,
-0.0014601601287722588,
-0.06741894781589508,
0.001209058566018939,
-0.05636022984981537,
-0.003296575043350458,
0.04969167709350586,
0.016105109825730324,
-0.07537472993135452,
-0.03859420865774155,
-0.015337657183408737,
0.04941520467400551,
0.038045018911361694,
-0.028487013652920723,
-0.06936267763376236,
0.015128707513213158,
-0.04946395009756088,
-0.05950257182121277,
0.024866251274943352,
0.019795939326286316,
0.027256986126303673,
0.02283991128206253,
0.029658105224370956,
0.02347833476960659,
-0.022989336401224136,
-0.0402228906750679,
-0.01607062667608261,
0.0021389599423855543,
0.027968116104602814,
-0.04585534334182739,
0.0011737599270418286,
-0.03231489285826683,
0.0342228002846241,
-0.014016911387443542,
-0.009596990421414375,
0.06135959178209305,
-0.007604080718010664,
-0.003491508774459362,
0.014309882186353207,
-0.013067440129816532,
-0.021165257319808006,
0.06337510794401169,
-0.035517603158950806,
-0.03826914727687836,
0.035173941403627396,
-0.045377228409051895,
0.0007052362198010087,
0.0016216521617025137,
0.03212633728981018,
-0.0328192375600338,
0.0357930064201355,
-0.0031151052098721266,
-0.0014664694899693131,
0.015524848364293575,
0.002697801450267434,
-0.03562239557504654,
-0.014959686435759068,
0.02320978417992592,
0.021035758778452873,
-0.022435683757066727,
-0.049271877855062485,
-0.05911768600344658,
0.038546930998563766,
-0.0707235112786293,
-0.008316917344927788,
0.014922523871064186,
0.02595205418765545,
-0.01899179443717003,
0.01627301797270775,
0.022308968007564545,
0.006404233165085316,
0.02641192451119423,
0.028645016252994537,
0.04047192260622978,
0.00984317809343338,
0.06533953547477722,
0.016071930527687073,
0.02478674240410328,
0.000698195886798203,
-0.048640280961990356,
-0.03305765241384506,
0.004470556043088436,
-0.015474120154976845,
-0.02121882140636444,
-0.043904051184654236,
0.020795462653040886,
-0.02023952454328537,
-0.05291452631354332,
0.02482036128640175,
0.08128674328327179,
0.011239743791520596,
0.0013183635892346501,
-0.016980241984128952,
0.002846379764378071,
-0.012960483320057392,
0.04259738698601723,
0.022030498832464218,
-0.023805251345038414,
0.0025305275339633226,
0.021305738016963005,
-0.022211933508515358,
0.006617669947445393,
-0.032954584807157516,
-0.002862675813958049,
-0.03945545852184296,
0.032146353274583817,
-0.029166141524910927,
0.018792908638715744,
-0.018237296491861343,
0.05474497750401497,
0.011798424646258354,
0.030615974217653275,
-0.021614640951156616,
-0.015841487795114517,
-0.009210817515850067,
0.04607263207435608,
0.03999237343668938,
0.02886981889605522,
-0.04087376594543457,
-0.05241101607680321,
0.03347545862197876,
0.004469611681997776,
0.006400695536285639,
0.01792694255709648,
-0.03689270466566086,
0.03717461973428726,
-0.027484003454446793,
-0.0055438438430428505,
0.006984705105423927,
0.002362708793953061,
-0.003961965441703796,
-0.009239480830729008,
0.017889035865664482,
0.008666804060339928,
0.021658848971128464,
0.04319100081920624,
-0.007808143272995949,
0.01591411978006363,
0.01653013378381729,
0.02490996941924095,
-0.011222882196307182,
-0.03614459186792374,
-0.01082635298371315,
-0.029456445947289467,
-0.009057463146746159,
0.054195478558540344,
-0.008982190862298012,
-0.031078843399882317,
-0.04767584055662155,
0.051100313663482666,
-0.01688525825738907,
0.05766347423195839,
-0.02887188270688057,
0.011641792953014374,
-0.05900253355503082,
0.04391331225633621,
0.034857116639614105,
0.014785613864660263,
-0.011553687043488026,
-0.010061998851597309,
-0.02338469959795475,
0.016156861558556557,
0.005045859608799219,
-0.018372951075434685,
-0.015929527580738068,
0.002141993260011077,
-0.00832223892211914,
-0.08942869305610657,
-0.03645804524421692,
0.030119890347123146,
-0.04497228562831879,
-0.016914725303649902,
0.027042206376791,
-0.011865200474858284,
0.00583718391135335,
0.03638225048780441,
0.01857862062752247,
-0.07436555624008179,
0.038195665925741196,
0.0033497801050543785,
-0.03367122262716293,
0.006391816306859255,
0.007537812925875187,
-0.023506619036197662,
0.04813792183995247,
-0.013252565637230873,
0.006386112421751022,
-0.0059359995648264885,
-0.0716988742351532,
-0.033998776227235794,
0.08291685581207275,
-0.022794131189584732,
0.050738781690597534,
-0.013411318883299828,
0.0006373545038513839,
0.04794447869062424,
-0.012446056120097637,
0.01028365921229124,
-0.004193102475255728,
0.026489093899726868,
0.10066525638103485,
0.027317823842167854,
-0.05083632469177246,
-0.015743758529424667,
-0.009162437170743942,
0.007318913470953703,
-0.027074597775936127,
-0.05835232511162758,
-0.03925618529319763,
0.0331965796649456,
0.014849529601633549,
-0.04417303577065468,
-0.0607219897210598,
-0.040943510830402374,
0.06128472089767456,
-0.03929505497217178,
-0.010392650030553341,
0.058627013117074966,
0.07628851383924484,
0.03949799761176109,
0.001748047536239028,
0.07913617789745331,
0.033116359263658524,
0.011732498183846474,
0.06047763302922249,
0.056774117052555084,
0.005836797878146172,
-0.05082160234451294,
-0.0021246320102363825,
0.03144100308418274,
-0.04101908206939697,
-0.011272374540567398,
-0.012776980176568031,
0.011405027471482754,
0.04610340669751167,
0.022991210222244263,
0.020602023229002953,
-0.030153706669807434,
0.0025319906417280436,
0.007210650015622377,
-0.02362646907567978,
-0.013523275032639503,
0.009095431305468082,
0.028134316205978394,
0.029881592839956284,
-0.05130860581994057,
-0.06265460699796677,
0.03168980032205582,
0.01328841783106327,
0.001099063316360116,
-0.04542488977313042,
0.050604380667209625,
0.0003012517699971795,
-0.0254643727093935,
-0.07769183069467545,
-0.009626259095966816,
0.0016067033866420388,
-0.05371168255805969,
0.03860876336693764,
-0.04144536331295967,
-0.025816703215241432,
0.014671091921627522,
0.006279687862843275,
0.03898309916257858,
-0.05320350080728531,
-0.04062649607658386,
-0.020171180367469788,
0.00961114652454853,
-0.02133280225098133,
-0.05933837965130806,
0.04273920878767967,
-0.026003843173384666,
-0.0484325997531414,
-0.00498101906850934,
-0.00364964478649199,
0.06604551523923874,
0.003383013652637601,
0.025922227650880814,
0.0616195946931839,
-0.0015496014384552836,
0.07165417820215225,
-0.026492521166801453,
-0.01811242289841175,
-0.11556687951087952,
-0.05351237952709198,
0.05004649981856346,
0.030619913712143898,
-0.003247396554797888,
-0.012515200302004814,
-0.0034793363884091377,
0.009433944709599018,
-0.028703412041068077,
-0.0001065118340193294,
0.04281128942966461,
0.03750574216246605,
-0.033916324377059937,
0.022640714421868324,
-0.07356403023004532,
-0.038713302463293076,
-0.09234023839235306,
-0.04085705429315567,
-0.03703993931412697,
0.05294513329863548,
-0.01810135692358017,
0.03252584859728813,
-0.006718129850924015,
-0.00568139785900712,
-0.026821335777640343,
0.018999889492988586,
-0.021030377596616745,
-0.0928371399641037,
-0.017572587355971336,
0.03138714283704758,
-0.02111506462097168,
-0.011997264809906483,
-0.030211739242076874,
0.03556666523218155,
-0.027907028794288635,
0.022069962695240974,
-0.03610369935631752,
-0.026694143190979958,
0.025925971567630768,
0.011866113170981407,
-0.04762951657176018,
-0.04114535078406334,
0.03931998461484909,
-0.032782528549432755,
-0.011283480562269688,
0.02707117609679699,
0.018748652189970016,
-0.04992733523249626,
-0.057579394429922104,
0.04946156218647957,
-0.003418245352804661,
0.00010161959653487429,
-0.01403858046978712,
0.09156908839941025,
0.013007660396397114,
0.013771220110356808,
0.011486785486340523,
0.05528905987739563,
0.07366441935300827,
-0.02337859570980072,
0.04803095757961273,
0.04769625887274742,
-0.040042631328105927,
-0.05950113385915756,
0.08160807937383652,
0.016216570511460304,
-0.08654599636793137,
0.020593790337443352,
-0.024541229009628296,
0.06286922842264175,
-0.015934642404317856,
0.062265753746032715,
0.07888608425855637,
-0.02431223727762699,
0.015148155391216278,
0.009882543236017227,
0.026187723502516747,
0.00739267049357295,
-0.0029876043554395437,
-0.024081554263830185,
-0.03766467794775963,
0.0042111375369131565,
0.07949464023113251,
0.024709545075893402,
0.013691185042262077,
-0.0032213616650551558,
-0.0005151340737938881,
-0.03450602665543556,
0.021376853808760643,
0.04783972352743149,
0.034424688667058945,
-0.00832882709801197,
0.022810056805610657,
0.001045488752424717,
0.03586062416434288,
0.023401878774166107,
0.028298942372202873,
-0.10682018846273422,
-0.005031564738601446,
0.034269027411937714,
-0.04911734163761139,
0.018574373796582222,
-0.0036120370496064425,
-0.013224411755800247,
-0.017038891091942787,
0.012132417410612106,
0.022230541333556175,
0.022777242586016655,
-0.03966899588704109,
-0.012319957837462425,
-0.07666496187448502,
-0.053006451576948166,
-0.01738693192601204,
0.06932070851325989,
-0.029666047543287277,
0.02087327651679516,
-0.017628297209739685,
-0.049274131655693054,
0.06738782674074173,
-0.022594526410102844,
-0.06852832436561584,
0.01257441658526659,
-0.007823264226317406,
0.06578923016786575,
0.005676561966538429,
0.0031731310300529003,
-0.033649742603302,
0.008452712558209896,
0.008794056251645088,
-0.0025683999992907047,
0.045482564717531204,
-0.005616060923784971,
0.026476850733160973,
-0.024982234463095665,
0.015369873493909836,
-0.0403873436152935,
-0.0951823964715004,
-0.008457484655082226,
0.011585256084799767,
-0.008264143951237202,
0.028690095990896225,
-0.029321156442165375,
-0.010379300452768803,
-0.030427271500229836,
0.029195504263043404,
-0.06282277405261993,
0.03280482441186905,
-0.12853021919727325,
-0.00364715326577425,
-0.012032246217131615,
-0.014269649982452393,
-0.043689582496881485,
0.041031673550605774,
-0.04535661265254021,
-0.02360987849533558,
0.00626623909920454,
-0.007785798981785774,
-0.05323612317442894,
0.035424571484327316,
-0.05879569798707962,
-0.0017941019032150507,
-0.017565906047821045,
-0.013448458164930344,
0.035548727959394455,
-0.00879182480275631,
-0.038458451628685,
0.05085701867938042,
-0.021488992497324944,
-0.04272168502211571,
-0.01205796841531992,
-0.025974566116929054,
0.027986416593194008,
0.002787682693451643,
0.022215094417333603,
-0.038931701332330704,
-0.039242230355739594,
0.026307525113224983,
0.017217112705111504,
-0.053359247744083405,
0.020045259967446327,
-0.038157492876052856,
-0.005084119271486998,
0.04713286831974983,
-0.013955471105873585,
-0.01718050055205822,
0.028230516240000725,
0.02885390818119049,
-0.002053219359368086,
-0.0013569595757871866,
-0.0374765619635582,
0.01263828668743372,
-0.04511113092303276,
-0.0031910210382193327,
0.04468497261404991,
0.01008705422282219,
0.0368761271238327,
0.07028673589229584,
-0.009133045561611652,
-0.032134898006916046,
0.006458244286477566,
0.015550438314676285,
-0.060896746814250946,
0.059861741960048676,
-0.02236110158264637,
-0.02255242131650448,
-0.01583816111087799,
0.057065755128860474,
0.04892243072390556,
0.0226886086165905,
-0.0003380067355465144,
0.016577454283833504,
0.044089604169130325,
-0.011104078032076359,
0.028712213039398193,
0.007079595699906349,
0.028403326869010925,
-0.011379933916032314,
0.017569169402122498,
0.028793586418032646,
-0.022693078964948654,
-0.044228918850421906,
0.022571628913283348,
0.009083490818738937,
-0.019905855879187584,
0.0003795925877057016,
0.02180575765669346,
-0.03773902729153633,
0.0012052311794832349,
0.05805985629558563,
-0.029683023691177368,
-0.04479432478547096,
-0.018117297440767288,
-0.046878233551979065,
0.12108860164880753,
0.03703492879867554,
0.070343017578125,
-0.005864798557013273,
-0.007222488056868315,
0.05936392769217491,
0.000003676466349133989,
-0.028406813740730286,
-0.024317249655723572,
-0.058463286608457565,
-0.01131971925497055,
-0.005690072197467089,
0.016742251813411713,
0.021796446293592453,
0.01685897633433342,
-0.019070878624916077,
-0.05825820937752724,
0.04714352637529373,
-0.04535951837897301,
-0.025665370747447014,
0.0037264639977365732,
0.029206428676843643,
-0.0067137619480490685,
-0.05904974043369293,
-0.05806737393140793,
0.01582745648920536,
-0.016751207411289215,
-0.03790288791060448,
-0.010468175634741783,
-0.0536457821726799,
-0.04166524484753609,
-0.012395817786455154,
-0.04151298478245735,
-0.030758412554860115,
0.013312183320522308,
0.007170179858803749,
0.018408017233014107,
-0.03121638484299183,
0.0062538497149944305,
-0.03969229757785797,
0.00789722241461277,
0.01632174849510193,
0.030107971280813217,
-0.003000095020979643,
0.015508849173784256,
0.009271819144487381,
0.05369937792420387,
0.056745655834674835,
0.006330907344818115,
-0.051594141870737076,
0.01748095080256462,
-0.07123136520385742,
0.021791087463498116,
-0.007628996390849352,
-0.06283256411552429,
0.021908307448029518
] |
<p>The question is very simple, but complicated to solve. I am looking for a <em>genera</em> form solution to this problem. Thus there will be no numbers, just variables. What I mean by that is often in physics you have equations like $F = ma$. I don't have the numbers to the problem yet, because that will vary based on the spaceship, its engine, the distance, etc.</p>
<p>Newtonian physics works as an approximation, however its allows the spaceship to exceed $c$ during its travels. I would like to add relativity, with the frame of reference being the spaceship. </p>
<p>I can already solve this problem in discrete time steps programatically, but it would be nice to have a general form solution that would be more accurate. (Because discrete time stepping is expensive computationally, and a general form solution would be much much faster.)</p>
<p>From my current algorithm the variables are:</p>
<ul>
<li>$M$ = base mass of spaceship in kkg (ie 1000kg)</li>
<li>$C$ = cargo space of spaceship kkg </li>
<li>$D$ = distance to be traveled in km</li>
<li>$T$ = thrust of the engines in kN</li>
<li>$F$ = fuel consumed per year in kkg/year </li>
<li>$E$ = food consumed per year in kkg/year</li>
<li>$A$ = maximum velocity you can possibly achieve {$A < c$} in m/s</li>
<li>$B$ = maximum velocity you are willing to achieve {$B <= A$} in m/s</li>
</ul>
<p>Some notes. </p>
<ul>
<li>Cargo space can be used to be store fuel and/or food.
<ul>
<li>The way I solved this problem before, was calculated fuel costs first, and then decided if there was enough food afterwards. Based on $C_{remaining} > t_{travel} * E$</li>
</ul></li>
<li>Loaded cargo adds to $M$ so $M_{total} = M + C_{fuel} + C_{food}$</li>
<li>As you fly the mass of the fuel is consumed, reducing the weight of the spaceship, allowing you accelerate faster.
<ul>
<li>Engine efficiency is not part of the equation. The engine produces $T$ thrust and consumes $F$ fuel per year. (unless I am wrong, I shouldn't have to worry about it, if it does matter, lets say 100%; its ideal.)</li>
</ul></li>
<li>The ship needs to spend fuel accelerating (to the halfway point or until B it achieved), and then spend fuel decelerating on the other end. the $t_{accelerating} \neq t_{decelerating}$ due to the change in mass during voyage. This also means less fuel will be consumed to decelerate as well.</li>
<li>As length inversely dilates with velocity, the length of the trip shrinks as the spaceship nears $c$ and expands as you decelerate as you near the destination.</li>
</ul>
<p>What I am looking for is a function that determines if the one-way trip is possible, how long it will take, and how much fuel is consumed in the process, in the form of</p>
<p>$$f(M, C, D, T, F, E, A, B) -> (isPossible, t_{total}, C_{fuel-consumed})$$</p>
<p>I realize that with B there will be conditionals.</p>
<p>As far as I can tell, there are 3 rate of change problems (more?)</p>
<ul>
<li>Mass increases as velocity increases $M_{relative} = M_{current} * \gamma$</li>
<li>Mass decreases as fuel is expended $M_{current} = M + C_{fuel} - C_{fuel-consumed}$
<ul>
<li>$C_{fuel-consumed} = F * t_{running-engines}$</li>
</ul></li>
<li>Distance decreases as velocity increases $D_{relative} = D_{base} / \gamma$</li>
<li>Am I missing something?</li>
</ul>
<p>Some references:</p>
<ul>
<li><a href="http://en.wikipedia.org/wiki/Speed_of_light#Upper_limit_on_speeds" rel="nofollow">http://en.wikipedia.org/wiki/Speed_of_light#Upper_limit_on_speeds</a></li>
<li>$\gamma = \dfrac{1}{\sqrt{1-v^2/c^2}}$</li>
<li>$a = \dfrac{T}{M_{relative}}$ Note: $a$ will change as $M_{relative}$ changes, but $T$ remains constant</li>
</ul> | g4772 | [
0.016001487150788307,
0.04472720995545387,
-0.008520317263901234,
-0.01669173687696457,
-0.013746104203164577,
-0.04673970490694046,
0.008646653965115547,
-0.008582697249948978,
-0.09235766530036926,
-0.0038838188629597425,
0.05637546628713608,
-0.011388448067009449,
0.07101380825042725,
0.052628252655267715,
0.008390648290514946,
-0.001058177906088531,
0.06312280148267746,
-0.06281108409166336,
-0.019788097590208054,
0.04583433270454407,
0.024168381467461586,
0.03269558399915695,
0.0074243443086743355,
-0.03358248621225357,
-0.0204498041421175,
-0.048630695790052414,
-0.008793331682682037,
0.03334753215312958,
-0.07285984605550766,
0.020349787548184395,
0.028516225516796112,
-0.09107010811567307,
0.04040340706706047,
-0.052333515137434006,
-0.05515342205762863,
-0.01708144322037697,
0.021302130073308945,
0.04871207848191261,
0.04920041933655739,
0.020182156935334206,
0.007941816002130508,
-0.04452412575483322,
0.04113374650478363,
0.03722276911139488,
0.005599187221378088,
-0.020521096885204315,
0.04440845176577568,
-0.04969567805528641,
0.02140701189637184,
0.0002131697110598907,
-0.030636165291070938,
0.050415776669979095,
-0.03074328601360321,
-0.05493217334151268,
-0.02060764469206333,
0.042602114379405975,
-0.06072935461997986,
-0.035216063261032104,
-0.000488735968247056,
0.00847860611975193,
-0.019756825640797615,
-0.04902542009949684,
0.011942696757614613,
-0.01921250857412815,
0.08869316428899765,
-0.03121289610862732,
-0.055995579808950424,
0.0001275896793231368,
0.020434990525245667,
-0.04437442496418953,
0.03854646906256676,
-0.03046564571559429,
-0.03661772981286049,
-0.06051480397582054,
0.0010134187759831548,
-0.01566721312701702,
-0.039648398756980896,
0.0246463343501091,
-0.029163574799895287,
0.03618858754634857,
-0.05393991246819496,
0.05622638389468193,
0.03511330485343933,
0.0035666106268763542,
-0.006743364967405796,
0.004559350199997425,
0.07273523509502411,
0.029848704114556313,
0.020051628351211548,
-0.0036993478424847126,
-0.01145096868276596,
0.0034665472339838743,
0.09253647923469543,
-0.03723864629864693,
0.0010078896302729845,
0.005369745194911957,
-0.022520041093230247,
0.02251535840332508,
0.05173492431640625,
-0.0007350838859565556,
0.06091121956706047,
0.003678010543808341,
-0.025333935394883156,
-0.02507432922720909,
-0.01078220084309578,
-0.06303846091032028,
0.06741103529930115,
0.03412414714694023,
0.0099885119125247,
-0.05077353119850159,
-0.005264805164188147,
-0.0659332275390625,
0.019601430743932724,
-0.023906011134386063,
-0.04865472391247749,
-0.0454661101102829,
0.008449723944067955,
-0.029012639075517654,
-0.013346117921173573,
0.00646020146086812,
-0.02313329465687275,
0.002617591992020607,
-0.013845285400748253,
0.038965001702308655,
0.019775889813899994,
-0.023563718423247337,
-0.05132396146655083,
0.04295971989631653,
-0.02421380952000618,
-0.008677295409142971,
-0.037730731070041656,
0.01853620819747448,
0.034565966576337814,
0.005368223879486322,
-0.028701607137918472,
0.0027316103223711252,
-0.04015650600194931,
0.08925921469926834,
-0.019507460296154022,
0.0582021065056324,
-0.05105304345488548,
-0.046763744205236435,
0.023741066455841064,
0.013024132698774338,
-0.05517367273569107,
0.06687002629041672,
-0.05092015117406845,
-0.01123905647546053,
0.019683877006173134,
0.017894195392727852,
0.003005795180797577,
0.07411496341228485,
-0.04158828780055046,
0.003955476451665163,
0.049906276166439056,
-0.0023832654114812613,
0.028064876794815063,
0.0064591714181005955,
-0.02114526368677616,
-0.06123802438378334,
0.08079755306243896,
0.04687834158539772,
-0.005485227797180414,
-0.023751195520162582,
-0.06189875677227974,
0.0801100805401802,
0.02442523092031479,
-0.010196316987276077,
-0.023243900388479233,
-0.01940692961215973,
-0.056001704186201096,
-0.03855397179722786,
0.0676988810300827,
0.06643838435411453,
0.016352500766515732,
0.016503211110830307,
0.0652916356921196,
-0.03784267231822014,
-0.05305667594075203,
0.010138379409909248,
0.004445670638233423,
-0.05736490339040756,
0.06707854568958282,
0.009015227667987347,
-0.022039486095309258,
0.007660363335162401,
0.00007570787420263514,
0.0701637715101242,
-0.07234455645084381,
-0.01717378757894039,
-0.01834275759756565,
0.005730888340622187,
0.06879841536283493,
0.010563656687736511,
-0.038178373128175735,
0.007869678549468517,
0.04071121662855148,
-0.059082288295030594,
-0.05792482569813728,
0.01702999882400036,
-0.03914385288953781,
0.04625745117664337,
-0.013606728054583073,
0.030402304604649544,
0.023848947137594223,
-0.03409959003329277,
0.009675766341388226,
-0.04258503392338753,
0.020436864346265793,
0.027660781517624855,
0.04393085092306137,
-0.00941456388682127,
-0.0309513621032238,
0.0020711717661470175,
0.016145382076501846,
-0.06484068185091019,
-0.011350749060511589,
0.015809470787644386,
-0.007365429308265448,
-0.008572946302592754,
0.05266819894313812,
-0.053637538105249405,
0.04660885035991669,
0.02275289036333561,
-0.005406100768595934,
-0.06250778585672379,
0.026326099410653114,
-0.06270788609981537,
0.05566950514912605,
0.003035560715943575,
-0.0276458989828825,
0.01976608857512474,
0.032177817076444626,
-0.08891448378562927,
0.05465751513838768,
-0.017791489139199257,
-0.02439356967806816,
0.014283537864685059,
0.013091012835502625,
0.011853596195578575,
0.06479252129793167,
0.021958068013191223,
0.0021525968331843615,
-0.01841147057712078,
0.06207329407334328,
-0.06552823632955551,
0.023926371708512306,
-0.00698124011978507,
0.0060013774782419205,
0.020637551322579384,
-0.008601449429988861,
-0.029390854761004448,
-0.0743524357676506,
0.02237561158835888,
-0.013911845162510872,
-0.027441296726465225,
-0.03682124987244606,
0.057427968829870224,
-0.03063659556210041,
-0.00930869672447443,
-0.04174939915537834,
-0.02399529702961445,
0.010487089864909649,
0.020044855773448944,
0.0007365356432273984,
0.005913199856877327,
-0.04032319039106369,
-0.022007303312420845,
0.002605229616165161,
-0.004444664344191551,
-0.0434395857155323,
-0.029266364872455597,
0.022714773193001747,
0.018792713060975075,
0.020280491560697556,
0.04357646405696869,
0.0364045687019825,
0.019909685477614403,
0.03622804954648018,
0.09283418953418732,
-0.009387162514030933,
-0.1061125248670578,
-0.04051501303911209,
0.025542132556438446,
0.025655511766672134,
-0.007173360791057348,
0.03105071373283863,
0.024899790063500404,
-0.014326964505016804,
0.00811844039708376,
-0.009071500040590763,
0.023816796019673347,
0.06255563348531723,
0.0028838736470788717,
0.035799913108348846,
0.026599640026688576,
0.029128557071089745,
0.04696076363325119,
-0.032886456698179245,
-0.10311123728752136,
0.015567663125693798,
-0.022223778069019318,
0.036624081432819366,
0.03454313799738884,
-0.015544803813099861,
0.017915092408657074,
-0.045561615377664566,
-0.0007854669820517302,
-0.003056698478758335,
0.028066614642739296,
-0.0159132182598114,
0.027436304837465286,
0.02087637223303318,
-0.0146785331889987,
-0.04705112427473068,
-0.02656107395887375,
0.00419298280030489,
-0.0331256240606308,
-0.012257306836545467,
-0.02357666566967964,
0.04230617731809616,
-0.06369655579328537,
-0.008161514066159725,
-0.024591946974396706,
-0.0010012064594775438,
0.016719603911042213,
-0.05081766098737717,
-0.006191277410835028,
-0.023174334317445755,
0.03219133988022804,
0.02581150457262993,
0.0021368185989558697,
-0.008045201189815998,
-0.01854160614311695,
-0.002128330757841468,
-0.009034129790961742,
-0.023102013394236565,
0.02737428992986679,
0.01558228861540556,
0.038673143833875656,
-0.024974355474114418,
-0.034461960196495056,
0.014433658681809902,
0.060749270021915436,
0.002965670544654131,
-0.001503415871411562,
0.0010037721367552876,
0.039600443094968796,
-0.009658768773078918,
-0.030294662341475487,
0.019161488860845566,
-0.05535314604640007,
-0.0016238301759585738,
0.004062124993652105,
0.006083339918404818,
0.04309964179992676,
0.011278251186013222,
0.020326750352978706,
0.004700424615293741,
0.020915068686008453,
-0.028633587062358856,
-0.0028003044426441193,
-0.019244058057665825,
0.034162819385528564,
0.038059357553720474,
0.03641951456665993,
0.054290059953927994,
0.013546383008360863,
0.00273694284260273,
-0.02403103932738304,
0.025377845391631126,
-0.03240751847624779,
-0.000726010650396347,
-0.021404653787612915,
0.012700957246124744,
-0.011659251525998116,
0.018764037638902664,
-0.009293599985539913,
0.01943959668278694,
0.04993828013539314,
0.02063891477882862,
0.0022511151619255543,
0.005716333631426096,
-0.0096781300380826,
0.01987621560692787,
-0.008546769618988037,
-0.05413581803441048,
-0.04240662604570389,
0.01812874525785446,
0.06376687437295914,
-0.01416473463177681,
-0.07800525426864624,
-0.03254718333482742,
0.06150076910853386,
0.0019067948451265693,
0.008684229105710983,
0.005677537061274052,
0.0018175492295995355,
-0.04330984503030777,
0.05022628977894783,
0.0236897524446249,
0.007337096147239208,
0.010145487263798714,
0.04408181831240654,
-0.05759550258517265,
0.0006426179315894842,
0.031406912952661514,
-0.02374047040939331,
-0.020209386944770813,
-0.005764048546552658,
0.021145842969417572,
0.010253461077809334,
-0.008949083276093006,
-0.014080850407481194,
-0.05558540299534798,
-0.0013588611036539078,
0.05008728802204132,
-0.024745415896177292,
0.01900792308151722,
0.014220713637769222,
0.00003592838766053319,
0.10077223181724548,
0.02126779966056347,
-0.012875471264123917,
-0.0251536276191473,
0.01954539865255356,
0.00555868586525321,
0.027128687128424644,
0.06173243746161461,
-0.007804111111909151,
-0.0018038325943052769,
0.01682777889072895,
-0.004632549826055765,
0.06597082316875458,
-0.03665779531002045,
0.0809137374162674,
0.024144208058714867,
0.025542348623275757,
0.06420735269784927,
-0.020863160490989685,
-0.0037521016784012318,
-0.016832156106829643,
0.01268403884023428,
-0.004084950778633356,
-0.020601395517587662,
0.059523921459913254,
-0.02677689678966999,
-0.08206804096698761,
-0.0033264479134231806,
0.01610628515481949,
0.024374637752771378,
0.036623746156692505,
-0.017136944457888603,
0.06519998610019684,
0.0003072342951782048,
-0.016965270042419434,
-0.03875366970896721,
0.002268614247441292,
0.10625379532575607,
0.040784817188978195,
-0.023097308352589607,
-0.0005485093570314348,
0.01548268087208271,
0.024544479325413704,
-0.00669119181111455,
-0.0038542961701750755,
-0.00029138478566892445,
0.003570779925212264,
0.019380180165171623,
0.033145368099212646,
0.01331937126815319,
0.013242739252746105,
0.015812667086720467,
-0.003409908153116703,
-0.030477426946163177,
-0.0007267212495207787,
0.0004129894368816167,
0.004090142901986837,
-0.020841939374804497,
0.010888990946114063,
-0.013932409696280956,
-0.030141526833176613,
0.008258579298853874,
0.05695590749382973,
0.05897511914372444,
0.02129080519080162,
0.012903803959488869,
-0.0726935863494873,
0.03878888115286827,
-0.060234714299440384,
0.011349453590810299,
-0.023031169548630714,
-0.006085020024329424,
-0.014535374008119106,
-0.012599998153746128,
0.017101764678955078,
-0.00030793517362326384,
-0.033937711268663406,
0.027340620756149292,
-0.055015165358781815,
-0.0605706050992012,
0.04481390863656998,
-0.0027361975517123938,
-0.021448776125907898,
-0.02903422713279724,
-0.023901699110865593,
0.038821250200271606,
0.04143992066383362,
-0.03724835440516472,
0.07240071892738342,
0.018174156546592712,
0.03200224041938782,
0.000659559853374958,
-0.04589955136179924,
-0.030623024329543114,
-0.05752453953027725,
0.027099573984742165,
0.024411339312791824,
0.025644127279520035,
-0.03982246294617653,
0.052117932587862015,
0.00475656520575285,
0.02453230880200863,
0.048017460852861404,
0.06291726976633072,
0.02248873934149742,
-0.09401098638772964,
-0.06664635986089706,
-0.0005259057506918907,
0.015635661780834198,
0.031251564621925354,
-0.03508950024843216,
-0.009256094694137573,
-0.0196047592908144,
-0.07979241013526917,
0.04778653755784035,
0.03656977042555809,
0.0038968634326010942,
0.03595501929521561,
-0.03451745584607124,
-0.010056833736598492,
-0.009265781380236149,
0.040031976997852325,
0.041904281824827194,
0.0026328070089221,
-0.031327925622463226,
-0.04794277995824814,
-0.00826637540012598,
-0.02290050871670246,
-0.04158463701605797,
-0.019598551094532013,
-0.010762211866676807,
0.03608159348368645,
-0.022813355550169945,
0.0022853012196719646,
-0.010120784863829613,
0.011474466882646084,
-0.07196119427680969,
-0.014083296991884708,
0.027598034590482712,
0.03132942318916321,
-0.01495935395359993,
0.05580826848745346,
-0.011706882156431675,
0.01347944512963295,
-0.05385226756334305,
0.01331240776926279,
0.004531223326921463,
-0.007722628768533468,
0.019592290744185448,
-0.034476593136787415,
-0.03737436980009079,
-0.021882176399230957,
-0.0022648589219897985,
0.06056107208132744,
-0.039168715476989746,
-0.000572585966438055,
-0.09528161585330963,
-0.0440651997923851,
0.01813594438135624,
-0.005163675639778376,
-0.023290380835533142,
-0.012508447282016277,
-0.033448148518800735,
-0.036300092935562134,
0.0628410056233406,
0.007313164882361889,
-0.025706220418214798,
-0.028249384835362434,
-0.05092702805995941,
-0.03446805849671364,
-0.01568697951734066,
0.01990724541246891,
-0.04977776110172272,
-0.03498493880033493,
-0.011231189593672752,
-0.042484138160943985,
-0.012581748887896538,
0.04824640229344368,
0.06222156062722206,
-0.014737255871295929,
0.03685372322797775,
0.024314837530255318,
0.0007032681023702025,
-0.03152036666870117,
0.002432604320347309,
-0.04021241515874863,
-0.01567818969488144,
0.04720746725797653,
-0.04801328480243683,
0.027824420481920242,
0.06075402721762657,
0.021729569882154465,
0.032423943281173706,
0.0008768956759013236,
-0.01699080318212509,
-0.012554279528558254,
0.04948626831173897,
0.0539565272629261,
0.022910596802830696,
-0.0034258239902555943,
-0.04875089228153229,
0.03360697999596596,
-0.06831514835357666,
0.035467103123664856,
0.011539485305547714,
-0.024495147168636322,
0.0013147643767297268,
0.06264429539442062,
-0.01278989389538765,
0.026967957615852356,
-0.02741093374788761,
-0.06428482383489609,
0.03180602937936783,
0.024321625009179115,
0.02462669275701046,
-0.0537991002202034,
0.06984501332044601,
0.04366692900657654,
0.010933362878859043,
-0.03287411481142044,
-0.035720743238925934,
-0.0021195688750594854,
0.010687570087611675,
-0.06639254093170166,
-0.03838884457945824,
0.033991266041994095,
-0.05138039588928223,
-0.014319954439997673,
0.014659818261861801,
-0.004054629243910313,
-0.030889363959431648,
-0.02592608518898487,
0.015136278234422207,
-0.035513609647750854,
-0.011903081089258194,
-0.017910663038492203,
-0.0007543287938460708,
0.07547483593225479,
-0.021667413413524628,
0.01617424003779888,
-0.038921039551496506,
0.020080070942640305,
0.03575333207845688,
0.03269394114613533,
0.0597524531185627,
0.00018442727741785347,
-0.053055115044116974,
0.004934454336762428,
-0.030442895367741585,
0.010735422372817993,
-0.0013034575385972857,
-0.06752116233110428,
0.03153815492987633,
-0.01771906390786171,
0.050087690353393555,
-0.028417082503437996,
0.007434086874127388,
0.03753848373889923,
-0.035947684198617935,
0.012070545926690102,
-0.007223178166896105,
-0.03490850329399109,
0.018473749980330467,
-0.0007873510476201773,
-0.047743476927280426,
-0.01583857834339142,
-0.008131783455610275,
0.03120574541389942,
-0.020688429474830627,
-0.014077785424888134,
0.04510916769504547,
0.04619384929537773,
0.04297441989183426,
-0.013212218880653381,
0.006136423442512751,
0.0390939936041832,
0.015729358419775963,
0.057426903396844864,
-0.007766924798488617,
-0.03462489694356918,
0.04202864319086075,
0.030103513970971107,
-0.021574106067419052,
-0.043792348355054855,
-0.00792820192873478,
-0.05188627541065216,
-0.017665838822722435,
-0.06519797444343567,
-0.00048120482824742794,
-0.037670109421014786,
0.0032676986884325743,
-0.03762736916542053,
0.028061673045158386,
-0.019612930715084076,
-0.021012496203184128,
-0.002974974922835827,
0.028403175994753838,
0.04922987520694733,
0.003299685660749674,
-0.006910622585564852,
0.02590474672615528,
-0.0073232753202319145,
-0.06907964497804642,
-0.005602201912552118,
-0.06840744614601135,
-0.048720259219408035,
-0.045533906668424606,
0.0074744150042533875,
-0.03668556362390518,
0.005649224389344454,
0.003949168138206005,
-0.03528940677642822,
0.02775479480624199,
0.06302675604820251,
-0.004654120188206434,
-0.028505757451057434,
-0.059737153351306915,
-0.00688032153993845,
0.05381933972239494,
-0.012469188310205936,
-0.10621270537376404,
0.013596741482615471,
0.03055305778980255,
0.0519709549844265,
0.030599867925047874,
-0.018710820004343987,
0.060968127101659775,
0.054583072662353516,
0.015423432923853397,
0.034572407603263855,
0.0015661827055737376,
-0.04511650651693344,
0.012322578579187393,
0.03718051686882973,
-0.008989636786282063,
0.007261924911290407,
0.016447920352220535,
-0.07161445915699005,
-0.040909599512815475,
-0.02947002649307251,
0.004970688372850418,
-0.03124394081532955,
-0.0067351749166846275,
-0.0017326525412499905,
-0.041639216244220734,
-0.008088379167020321,
0.02772040106356144
] |
<p>I'm having problems seeing the global SU(2) invariance of the QED Lagrangian.
My specific problem is seeing why
\begin{equation}
e^{-i a_i \sigma_i} \gamma_\mu e^{i a_i \sigma_i} = \gamma_\mu
\end{equation}</p>
<p>In every book i looked it up, it was written this is trivial and i couldn't find a computation, so i guess i'm missing something trivial. Any tip or reading recommendation where the global SU(2) invariance is shown explicitly would be much appreciated.</p> | g4773 | [
0.01912950538098812,
-0.047928132116794586,
-0.011258509941399097,
-0.08147701621055603,
0.007241065613925457,
0.06748569011688232,
0.08500105142593384,
0.08406765758991241,
-0.08112607896327972,
0.05687296763062477,
0.06819170713424683,
0.0689803957939148,
0.05947282165288925,
0.04962024465203285,
0.014660881832242012,
0.01212532538920641,
0.07570497691631317,
0.026013072580099106,
0.013679735362529755,
-0.020731644704937935,
-0.009326404891908169,
0.0025190110318362713,
-0.003953938838094473,
-0.014076754450798035,
0.034068763256073,
0.042476240545511246,
0.030618462711572647,
0.022753534838557243,
0.06263723224401474,
-0.020650256425142288,
-0.03950688615441322,
-0.0071844011545181274,
0.07197346538305283,
-0.0583086721599102,
-0.013279810547828674,
0.0623062327504158,
0.04232074320316315,
0.02088899351656437,
0.03682432323694229,
0.01939588412642479,
-0.01907515898346901,
0.02175026200711727,
-0.023024151101708412,
0.046601973474025726,
-0.004297703038901091,
-0.0006434153765439987,
-0.020013166591525078,
0.06090807914733887,
-0.02765520289540291,
-0.04011230543255806,
0.041203368455171585,
0.027806803584098816,
0.03176359459757805,
-0.09059055894613266,
-0.021678578108549118,
0.007920201867818832,
-0.007104030344635248,
0.039610426872968674,
0.05172567442059517,
0.007418586872518063,
0.05482727661728859,
-0.07337500154972076,
-0.0004074721073266119,
-0.004806824494153261,
0.06419453024864197,
-0.05444662272930145,
-0.039097096771001816,
-0.019656632095575333,
-0.038428980857133865,
0.020722320303320885,
-0.03356269374489784,
-0.0026817461475729942,
0.049235012382268906,
-0.01673964038491249,
0.0540008582174778,
-0.01185490470379591,
0.014025283977389336,
0.08701504021883011,
-0.03107086755335331,
-0.0070990449748933315,
-0.02661299705505371,
-0.012462107464671135,
0.0007415421423502266,
0.036259375512599945,
0.044935524463653564,
-0.031099390238523483,
0.011290843598544598,
0.03301224485039711,
-0.018872279673814774,
-0.08540654182434082,
0.021115591749548912,
0.03028605692088604,
0.01834663189947605,
0.03924902155995369,
-0.028259681537747383,
-0.024958070367574692,
-0.014832614921033382,
0.055799417197704315,
-0.025709254667162895,
0.02573411352932453,
-0.0074799545109272,
-0.015174251049757004,
-0.010408374480903149,
0.093243308365345,
-0.04241330176591873,
0.0216799508780241,
-0.0056519643403589725,
0.00962693803012371,
-0.020652001723647118,
-0.0174820888787508,
-0.08375965058803558,
0.01754753105342388,
0.023747870698571205,
0.01491331122815609,
-0.07076270878314972,
-0.004408244974911213,
0.007017797790467739,
-0.016680991277098656,
0.005632634740322828,
0.04285886138677597,
0.013316716067492962,
0.028251774609088898,
-0.009685325436294079,
-0.009628288447856903,
0.03535717725753784,
-0.01951300911605358,
-0.050270985811948776,
-0.054693713784217834,
0.02999890223145485,
0.03528083860874176,
0.015079977922141552,
-0.0030401458498090506,
-0.014385124668478966,
0.03191079571843147,
0.024394815787672997,
0.053304772824048996,
0.02726816013455391,
0.02845120243728161,
-0.0092875761911273,
-0.00946370605379343,
-0.06192028895020485,
0.012722937390208244,
0.047167908400297165,
-0.041651103645563126,
-0.03749050199985504,
0.034776512533426285,
0.02993789128959179,
-0.040462322533130646,
-0.004586306866258383,
0.022748706862330437,
0.014472311362624168,
0.040228404104709625,
-0.007221497129648924,
-0.021076848730444908,
0.023409675806760788,
-0.0501544289290905,
0.007072736509144306,
-0.03816285356879234,
0.007299735210835934,
0.045743927359580994,
0.0028760815039277077,
-0.016305675730109215,
0.029158206656575203,
-0.01600474864244461,
0.002852024743333459,
0.04967375472187996,
0.03253468871116638,
-0.03635040298104286,
-0.05668450519442558,
-0.019542541354894638,
-0.057570431381464005,
-0.001993883401155472,
0.058435507118701935,
0.020290754735469818,
-0.0017313618445768952,
0.09119833260774612,
0.02129107154905796,
-0.05889129266142845,
0.012855708599090576,
0.016791773959994316,
-0.003804026171565056,
-0.03862147405743599,
0.0022585666738450527,
0.012670355848968029,
-0.015125811100006104,
-0.0037644170224666595,
0.020065413787961006,
0.10962172597646713,
0.018959203734993935,
0.029905889183282852,
0.024211889132857323,
0.0020849064458161592,
-0.014525161124765873,
-0.01396578922867775,
0.026606110855937004,
0.024171778932213783,
0.058946359902620316,
-0.07766993343830109,
-0.04038243368268013,
0.015835106372833252,
-0.02590114250779152,
0.029816346243023872,
0.034451793879270554,
0.03942681849002838,
-0.004964838270097971,
-0.05438350886106491,
0.014790891669690609,
-0.049028366804122925,
0.04083729535341263,
-0.01740935631096363,
-0.018024200573563576,
-0.020141759887337685,
0.03588569536805153,
-0.013846918009221554,
0.046450380235910416,
0.013513472862541676,
0.00909173209220171,
0.027039000764489174,
-0.07707858830690384,
0.014312946237623692,
-0.03204253688454628,
-0.033606722950935364,
0.025783361867070198,
-0.018205685541033745,
0.01868448033928871,
0.05999785289168358,
-0.08909114450216293,
-0.060821693390607834,
-0.006765705533325672,
0.01503625139594078,
-0.053686317056417465,
0.012281936593353748,
-0.0042759147472679615,
-0.04923534020781517,
0.006419456098228693,
-0.0038299064617604017,
-0.06404200941324234,
0.013184155337512493,
0.110077865421772,
0.017233824357390404,
-0.00786728598177433,
0.0036263763904571533,
-0.04481508582830429,
0.012780584394931793,
0.04694359004497528,
0.0069695161655545235,
0.022045578807592392,
-0.003857845440506935,
-0.006276390515267849,
0.028436526656150818,
-0.006738678086549044,
-0.004331364296376705,
-0.05350634455680847,
0.027190018445253372,
0.0027341260574758053,
-0.05975993350148201,
0.001087996643036604,
0.014762934297323227,
-0.021683501079678535,
0.0390147902071476,
-0.01068955659866333,
-0.048834141343832016,
-0.0045647164806723595,
0.03946630284190178,
-0.03992880508303642,
-0.004492258653044701,
0.03500035032629967,
-0.009471544995903969,
0.06719337403774261,
-0.0231219083070755,
0.02298596128821373,
0.04705182835459709,
0.0003737143997568637,
0.017325248569250107,
0.010488942265510559,
-0.02674759551882744,
-0.023389117792248726,
-0.007616695482283831,
-0.002760960953310132,
-0.03188841789960861,
0.008848524652421474,
-0.01606551557779312,
0.011411412619054317,
0.06720636039972305,
0.05055055022239685,
-0.07249311357736588,
0.004294475540518761,
0.029437372460961342,
0.019614554941654205,
0.02882225252687931,
0.002394726499915123,
-0.026674706488847733,
-0.06136082112789154,
-0.03480067104101181,
-0.035593438893556595,
0.014568268321454525,
-0.08150991797447205,
-0.023250017315149307,
-0.006353364326059818,
-0.024628084152936935,
0.0016629161546006799,
0.0240329559892416,
0.016261080279946327,
-0.03141538426280022,
-0.04563875123858452,
0.003647470148280263,
-0.015214992687106133,
-0.020710915327072144,
-0.0487486869096756,
-0.023476969450712204,
-0.040473490953445435,
-0.0156056247651577,
0.005176938604563475,
-0.061543744057416916,
-0.013323207385838032,
0.006896950304508209,
0.008220312185585499,
0.007596232928335667,
-0.007408240810036659,
0.0051455372013151646,
-0.0014480374520644546,
-0.059178680181503296,
0.04657759144902229,
0.01926933042705059,
0.008069856092333794,
0.017945609986782074,
-0.013835527002811432,
-0.03134051710367203,
-0.03876909986138344,
0.0039675976149737835,
-0.024729056283831596,
0.00897459127008915,
0.014326997101306915,
0.03702593967318535,
0.011971458792686462,
-0.04088737815618515,
-0.10119161754846573,
-0.01765991374850273,
0.019188618287444115,
0.02640857920050621,
-0.06427296251058578,
-0.06528547406196594,
-0.06264453381299973,
0.05497526377439499,
-0.011905651539564133,
-0.07995308190584183,
0.0063946302980184555,
-0.02074747160077095,
-0.018331753090023994,
0.0015567941591143608,
-0.011594460345804691,
-0.006807412952184677,
0.004079949576407671,
-0.019704725593328476,
-0.021793879568576813,
0.038656774908304214,
0.020899731665849686,
0.008207203820347786,
-0.025370843708515167,
-0.028973832726478577,
0.0027973251417279243,
0.023159172385931015,
0.010464786551892757,
0.011446370743215084,
-0.021234584972262383,
-0.02434784732758999,
-0.006994784343987703,
-0.01696121320128441,
-0.02239968068897724,
0.03455593064427376,
0.06494905054569244,
0.0242312029004097,
-0.002715684939175844,
0.003390267724171281,
-0.026968084275722504,
-0.04090195894241333,
-0.0010502362856641412,
0.03273217752575874,
0.028094835579395294,
0.02003767527639866,
-0.0033733975142240524,
0.008826369419693947,
0.06553419679403305,
0.02181970328092575,
0.035674821585416794,
0.012069196440279484,
-0.018568813800811768,
0.06361758708953857,
-0.005760291591286659,
-0.06798651814460754,
-0.010979737155139446,
-0.04335154965519905,
-0.006998849101364613,
0.002817732747644186,
0.021608572453260422,
-0.007354613393545151,
0.016094226390123367,
0.027084019035100937,
-0.015563402324914932,
-0.016894038766622543,
-0.03235284984111786,
0.034132521599531174,
0.07717670500278473,
-0.011178427375853062,
-0.030273932963609695,
0.018918801099061966,
-0.020839188247919083,
-0.013041733764111996,
0.04921567440032959,
-0.07651148736476898,
-0.0454711839556694,
0.008950571529567242,
0.03516564518213272,
-0.0385100319981575,
-0.01061407383531332,
-0.03397220000624657,
-0.061702318489551544,
-0.059397950768470764,
-0.013929635286331177,
-0.05914780870079994,
0.08343656361103058,
-0.06617173552513123,
-0.010225780308246613,
-0.05417396500706673,
0.04502079635858536,
0.05962277203798294,
0.031012240797281265,
0.06002011150121689,
0.01198700349777937,
0.00356591260060668,
-0.021602917462587357,
-0.015016838908195496,
-0.025768181309103966,
0.028887394815683365,
-0.07608174532651901,
0.01982031762599945,
-0.02897626720368862,
0.05010214447975159,
-0.03172307088971138,
0.02681795135140419,
0.08164889365434647,
-0.04924587160348892,
0.03361028432846069,
-0.04592538997530937,
-0.01998043805360794,
0.006741155404597521,
-0.00016099931963253766,
0.016129979863762856,
-0.016581740230321884,
-0.04044359549880028,
0.03418465331196785,
-0.05827068164944649,
-0.011870060116052628,
0.019894499331712723,
-0.03700333461165428,
-0.03508984297513962,
0.00477732066065073,
0.040016692131757736,
0.004201470874249935,
0.03308232128620148,
-0.020538993179798126,
-0.08495692163705826,
-0.004360791761428118,
0.04508981853723526,
0.04961247369647026,
-0.04719676449894905,
-0.08731728047132492,
0.06120971217751503,
0.009202565997838974,
-0.04777391999959946,
0.014314539730548859,
0.03789014741778374,
-0.009688609279692173,
-0.08089732378721237,
0.011575927957892418,
0.019658658653497696,
-0.03940102458000183,
-0.002428879262879491,
-0.019091540947556496,
-0.010279560461640358,
-0.017545731738209724,
-0.04495691880583763,
0.02155880443751812,
-0.003454547142609954,
0.010630335658788681,
0.009448699653148651,
0.020743729546666145,
0.01168522983789444,
0.025279853492975235,
-0.03885793685913086,
0.022769782692193985,
0.008594929240643978,
0.02233223244547844,
0.02466772124171257,
-0.04993852600455284,
0.026898622512817383,
-0.004443389363586903,
-0.025098083540797234,
-0.011947305873036385,
-0.01330647710710764,
-0.03416374325752258,
-0.009816555306315422,
0.017781324684619904,
0.010463537648320198,
-0.007330833934247494,
0.057473987340927124,
0.08745792508125305,
-0.0154917286708951,
-0.007468758150935173,
0.06264813989400864,
0.02478358894586563,
-0.019284993410110474,
0.029800469055771828,
-0.021349042654037476,
0.04141866788268089,
0.01287861168384552,
-0.02976856753230095,
0.017055494710803032,
-0.00009138586756307632,
-0.05443454533815384,
0.05490963160991669,
0.027378695085644722,
-0.0066449446603655815,
-0.031135067343711853,
-0.015685494989156723,
0.008551941253244877,
-0.05698118358850479,
-0.011146257631480694,
0.022460004314780235,
0.027390796691179276,
0.028122004121541977,
0.021483004093170166,
-0.012790416367352009,
-0.01606295444071293,
0.056440286338329315,
-0.04104550555348396,
-0.006253368686884642,
-0.03151153773069382,
-0.02392333559691906,
0.01438971795141697,
0.01458015013486147,
-0.016604194417595863,
0.024348769336938858,
0.01715983636677265,
-0.007003005128353834,
0.0020949491299688816,
0.014768404886126518,
-0.037661660462617874,
-0.0006516058929264545,
0.017035111784934998,
-0.0004015149315819144,
0.018891610205173492,
0.020202530547976494,
0.019111284986138344,
-0.031065309420228004,
0.0022107353433966637,
0.04372093826532364,
0.01837010867893696,
-0.03321042284369469,
0.003315548412501812,
0.00955201406031847,
-0.010285574942827225,
0.06173880398273468,
-0.010942192748188972,
-0.04036813601851463,
-0.041743598878383636,
0.006948616821318865,
0.005404021590948105,
0.06335482001304626,
0.04531059414148331,
0.008970249444246292,
0.06026965752243996,
0.056104596704244614,
0.013150544837117195,
0.026640096679329872,
-0.0008216264541260898,
-0.039988428354263306,
-0.05197194591164589,
-0.0097653204575181,
-0.016086813062429428,
-0.0014063672861084342,
0.06638970226049423,
0.008247492834925652,
-0.06001858040690422,
-0.003388316836208105,
0.048832233995199203,
-0.025841090828180313,
0.006639854051172733,
0.027232343330979347,
0.050924237817525864,
0.04276305437088013,
0.008231979794800282,
-0.02724400721490383,
0.0009958213195204735,
0.052435290068387985,
-0.007582028862088919,
0.00939816515892744,
0.005153974052518606,
-0.037309251725673676,
0.0440576933324337,
0.0674419105052948,
0.007405196316540241,
-0.017499495297670364,
0.005287305451929569,
-0.008956964127719402,
0.0028342893347144127,
-0.02890029363334179,
0.004942690022289753,
0.025722267106175423,
-0.01998944953083992,
0.03630830720067024,
-0.02070033922791481,
-0.0062084197998046875,
0.003544378327205777,
0.025456931442022324,
-0.10538197308778763,
-0.017055079340934753,
0.02558894082903862,
-0.043601665645837784,
-0.038425151258707047,
0.01495899073779583,
0.03689303994178772,
-0.020950866863131523,
-0.009817459620535374,
0.02887202985584736,
0.05347910895943642,
-0.016202416270971298,
0.016018100082874298,
0.0436568446457386,
-0.04977243021130562,
0.004292300436645746,
0.006802618503570557,
0.015351866371929646,
0.0011556465178728104,
0.01944596879184246,
-0.01967550627887249,
-0.051767054945230484,
0.01339311245828867,
0.0031272510532289743,
0.07415212690830231,
-0.028053076937794685,
0.009659197181463242,
0.027867021039128304,
-0.030616862699389458,
-0.05662030354142189,
0.04548242688179016,
0.026743091642856598,
-0.003332176711410284,
-0.08393058180809021,
-0.010733931325376034,
0.05736885219812393,
0.02777322567999363,
-0.006647237576544285,
0.0077423700131475925,
-0.025866959244012833,
0.04177599400281906,
0.014292348176240921,
-0.0495382584631443,
0.014842716977000237,
-0.022320296615362167,
0.006424983963370323,
0.026284832507371902,
-0.016711348667740822,
0.03851810842752457,
-0.00014999398263171315,
0.011858954094350338,
-0.04349372163414955,
-0.058429062366485596,
0.0420713908970356,
0.04044729471206665,
-0.047552455216646194,
-0.045950889587402344,
-0.038165558129549026,
-0.00407968508079648,
-0.039443228393793106,
-0.007405870594084263,
0.0004976953496225178,
0.09004135429859161,
-0.03548813238739967,
-0.005541246850043535,
-0.013953667134046555,
0.02500392310321331,
-0.03409026190638542,
-0.006906431168317795,
-0.07463356852531433,
0.01312988344579935,
0.014788275584578514,
-0.05244220048189163,
-0.034112587571144104,
0.06206795573234558,
-0.07680399715900421,
-0.002645993372425437,
0.003129018237814307,
-0.01333039440214634,
-0.03838014602661133,
0.0015142095508053899,
0.01372059341520071,
0.03443301469087601,
0.03245595842599869,
0.03683089464902878,
0.016543257981538773,
-0.023494457826018333,
-0.02226601354777813,
-0.033725395798683167,
-0.015683813020586967,
0.0018658165354281664,
-0.025454474613070488,
-0.1005118116736412,
-0.038105130195617676,
-0.023537667468190193,
-0.027342623099684715,
0.007271908223628998,
-0.031933970749378204,
-0.007143790367990732,
0.06857750564813614,
0.004427841864526272,
-0.01952001266181469,
0.02316555380821228,
0.013325322419404984,
0.04506612569093704,
-0.017488684505224228,
0.038423068821430206,
0.03200812265276909,
-0.045862842351198196,
-0.0658591091632843,
-0.012759034521877766,
0.01041282620280981,
0.000320876861223951,
0.03970690816640854,
0.012349316850304604,
-0.022360369563102722,
0.0174920205026865,
0.012897513806819916,
0.02328476309776306,
-0.05511941760778427,
0.009677807800471783,
-0.010843982920050621,
-0.09077613055706024,
0.015639478340744972,
0.02077278308570385,
0.024513140320777893,
-0.04930233582854271,
-0.011821271851658821,
-0.023983536288142204,
-0.019000256434082985,
-0.054509084671735764,
0.030861537903547287,
-0.036512479186058044,
0.04028047248721123,
-0.02158423885703087,
0.04042990133166313,
0.03554539754986763,
0.019455580040812492,
0.03637741878628731,
0.029434753581881523,
-0.07115129381418228,
0.06237835809588432,
-0.041540488600730896,
0.023011017590761185,
0.03873312473297119,
-0.03530468791723251,
-0.028466910123825073,
-0.016093531623482704,
0.013879260048270226,
-0.012181867845356464,
-0.10389751940965652,
-0.05728746950626373,
0.030867459252476692
] |
<p>Well for example we put a ball filled with water, with a density of $1\cdot 10^3 kg/m^3$, in space.</p>
<p>How to calculate the pressure the water is exposed to?</p> | g4774 | [
0.057052064687013626,
0.0056806765496730804,
-0.01611979305744171,
-0.06702760607004166,
-0.016169540584087372,
0.0460670106112957,
0.012190822511911392,
-0.012273908592760563,
-0.029390975832939148,
0.02486264519393444,
-0.040067870169878006,
0.03231444209814072,
0.06370214372873306,
0.03276876360177994,
0.011562960222363472,
0.02385634370148182,
0.028586622327566147,
-0.02307695336639881,
-0.01236743200570345,
-0.0430297888815403,
-0.020416801795363426,
-0.06296346336603165,
0.012972703203558922,
-0.04287215694785118,
-0.0419248566031456,
-0.021867897361516953,
0.030403723940253258,
0.035630080848932266,
-0.014504418708384037,
0.0022126331459730864,
-0.017721835523843765,
0.03499028831720352,
-0.011931709945201874,
-0.04471616446971893,
0.0011569715570658445,
-0.04341209679841995,
0.0008387782727368176,
0.01607676036655903,
0.005033461842685938,
-0.0323542058467865,
0.016549568623304367,
-0.06316785514354706,
0.02069631777703762,
0.03507876768708229,
-0.03955492004752159,
0.019734913483262062,
-0.06956026703119278,
-0.012104641646146774,
-0.016470111906528473,
-0.01492198184132576,
-0.02454838901758194,
0.07322290539741516,
-0.015323162078857422,
0.014609308913350105,
-0.03457492217421532,
0.015706762671470642,
-0.014292136766016483,
-0.09612871706485748,
0.027597401291131973,
-0.03487690910696983,
-0.02284315414726734,
-0.023576973006129265,
0.011185402050614357,
0.0056158131919801235,
0.043744053691625595,
-0.0022803335450589657,
-0.04568074643611908,
-0.005027242004871368,
-0.007787431124597788,
0.0026865683030337095,
0.06054117530584335,
-0.011668646708130836,
0.024655815213918686,
-0.02229129709303379,
-0.10546651482582092,
0.012115294113755226,
0.021288514137268066,
0.04423129931092262,
-0.0067900437861680984,
-0.025827156379818916,
-0.012799238786101341,
0.014943056739866734,
0.05636793002486229,
-0.08145454525947571,
0.027461925521492958,
-0.03050186112523079,
-0.0024175383150577545,
-0.051431529223918915,
-0.01428664568811655,
-0.04654845967888832,
0.013600324280560017,
-0.01357963401824236,
0.04749104008078575,
0.0403921902179718,
0.015999505296349525,
-0.04349549859762192,
-0.03298426792025566,
0.03861704468727112,
0.030475769191980362,
-0.01988239772617817,
-0.006556064821779728,
-0.03343363106250763,
-0.011709864251315594,
0.0005401815287768841,
-0.04510435089468956,
0.012346949428319931,
0.015460980124771595,
0.04096819832921028,
-0.013653886504471302,
-0.02826634980738163,
-0.004094541538506746,
0.02550353668630123,
0.024217134341597557,
-0.007200090680271387,
0.017075875774025917,
-0.05015904828906059,
0.054194480180740356,
-0.030615245923399925,
-0.007555012591183186,
0.021939581260085106,
0.04312434047460556,
0.027607807889580727,
0.02835717983543873,
-0.0043981606140732765,
-0.011753464117646217,
0.008346044458448887,
-0.029856234788894653,
-0.00773663492873311,
0.055163655430078506,
-0.0008524354780092835,
0.017088094726204872,
0.03429670259356499,
0.005835098214447498,
-0.0009912640089169145,
0.007225855253636837,
0.056591667234897614,
-0.09834600985050201,
0.01901194639503956,
-0.02955460734665394,
0.04834834486246109,
0.032930124551057816,
0.05583540350198746,
-0.031688667833805084,
0.06542492657899857,
0.013638638891279697,
-0.009716679342091084,
0.009992600418627262,
-0.004587835632264614,
0.005361610557883978,
0.017187051475048065,
0.07048505544662476,
0.07009431719779968,
0.049719590693712234,
-0.014584279619157314,
0.052034687250852585,
-0.02351827546954155,
-0.0012213175650686026,
-0.05489148572087288,
0.03180048614740372,
0.04953114688396454,
0.05217663198709488,
-0.004806889221072197,
0.0435972698032856,
0.04362809658050537,
-0.06165698170661926,
0.030549893155694008,
0.07195232063531876,
0.00023020482331048697,
-0.016256079077720642,
0.00419215951114893,
-0.00587962893769145,
-0.015031333081424236,
0.009835486300289631,
-0.021049534901976585,
-0.038117147982120514,
0.009324832819402218,
-0.010552429594099522,
0.005682164803147316,
-0.002576440805569291,
0.010905691422522068,
0.04322556033730507,
-0.014584817923605442,
0.07293527573347092,
-0.021796489134430885,
-0.05832316353917122,
0.006565758492797613,
0.011067433282732964,
-0.04915899410843849,
-0.06768561899662018,
-0.022817786782979965,
0.004302141256630421,
0.054338373243808746,
0.01955336518585682,
0.020421089604496956,
0.03649665415287018,
-0.007704981602728367,
0.09431150555610657,
0.00593367638066411,
-0.051260072737932205,
0.017933011054992676,
-0.023472659289836884,
0.02084660902619362,
0.03491294011473656,
0.04841896891593933,
0.013111534528434277,
0.030268825590610504,
-0.009263979271054268,
0.03242192417383194,
0.02957063913345337,
0.02173777110874653,
0.004956421442329884,
-0.03679103031754494,
0.003538857214152813,
0.030172066763043404,
-0.030692236497998238,
0.059632524847984314,
-0.025903841480612755,
-0.010023397393524647,
-0.06497900187969208,
0.011864148080348969,
-0.04275685176253319,
0.03805593028664589,
0.04287467151880264,
0.06866952031850815,
-0.04387293756008148,
-0.02304002270102501,
-0.005280589684844017,
0.048068612813949585,
0.05764598399400711,
-0.006909389980137348,
-0.014839865267276764,
0.035139862447977066,
-0.055665273219347,
-0.041920118033885956,
0.009727686643600464,
0.10328211635351181,
-0.05726076290011406,
0.0400950089097023,
0.04885787144303322,
0.05913099646568298,
0.004946596920490265,
-0.0006589046097360551,
-0.0125383660197258,
-0.024213014170527458,
0.010532566346228123,
-0.011088470928370953,
0.014949163421988487,
0.011367137543857098,
0.05008798837661743,
0.051313500851392746,
-0.035175975412130356,
-0.018609628081321716,
-0.0031380660366266966,
-0.007490190677344799,
0.017710005864501,
0.03221072256565094,
-0.06595659255981445,
0.004315047059208155,
-0.03460071235895157,
-0.06309102475643158,
0.0035281863529235125,
-0.033414099365472794,
0.019333545118570328,
-0.03564568981528282,
-0.017697855830192566,
0.031954072415828705,
-0.024540064856410027,
0.032607972621917725,
0.06149512529373169,
0.03965812548995018,
-0.001641451963223517,
0.052279744297266006,
0.0005566314212046564,
0.03334856033325195,
0.012295874767005444,
-0.030159903690218925,
0.02711544744670391,
-0.011398429982364178,
0.01720796339213848,
-0.04114983230829239,
-0.014594979584217072,
0.04532516375184059,
-0.06146321818232536,
0.02674240432679653,
0.05505950003862381,
-0.0301474891602993,
0.06278075277805328,
0.025354409590363503,
0.020378457382321358,
-0.056164998561143875,
0.06882991641759872,
0.02679648995399475,
-0.009875706396996975,
0.07069236785173416,
-0.01593790017068386,
0.035607270896434784,
0.05844912678003311,
0.02165326289832592,
0.010026847943663597,
0.05544491112232208,
0.03805297985672951,
0.011499190703034401,
0.04555940628051758,
-0.008208689279854298,
-0.05110768973827362,
0.010344332084059715,
-0.0010782593162730336,
-0.038885410875082016,
-0.0073484694585204124,
-0.024263236671686172,
-0.02570325694978237,
0.05462048947811127,
0.03058505803346634,
-0.06192459166049957,
-0.030044639483094215,
-0.04821619763970375,
0.039916668087244034,
-0.027057843282818794,
0.03730844706296921,
-0.046965304762125015,
-0.03118997812271118,
-0.04394428804516792,
0.05278000608086586,
-0.000021660343918483704,
-0.038333162665367126,
0.03341332823038101,
-0.06256925314664841,
-0.028171252459287643,
-0.03114127181470394,
-0.09195590764284134,
0.017492985352873802,
-0.010099804028868675,
-0.01676042750477791,
-0.03792112320661545,
-0.07204410433769226,
-0.07457135617733002,
0.02840353175997734,
-0.0327911414206028,
-0.03702740743756294,
0.026830554008483887,
-0.0839664414525032,
-0.02681371569633484,
-0.06943707913160324,
-0.02754376456141472,
-0.052426114678382874,
0.018085412681102753,
0.04816931486129761,
0.008692320436239243,
-0.008044134825468063,
0.0106167858466506,
0.02349291741847992,
-0.03891930729150772,
0.037504736334085464,
-0.02776804193854332,
0.0089014433324337,
0.035682596266269684,
0.05408094450831413,
0.02672763541340828,
-0.025684664025902748,
-0.025277040898799896,
-0.013019012287259102,
-0.017421631142497063,
0.0034474609419703484,
0.03999574854969978,
-0.03225810080766678,
-0.010427492670714855,
0.04903731495141983,
-0.016986848786473274,
-0.03328268229961395,
0.029585635289549828,
0.014393714256584644,
-0.015913452953100204,
0.028361884877085686,
0.03494243323802948,
0.04959772527217865,
-0.07867071777582169,
-0.006099774036556482,
0.005962098482996225,
-0.043725814670324326,
-0.010276459157466888,
0.07200276851654053,
-0.010396377183496952,
0.02594495192170143,
-0.023127960041165352,
0.003616517409682274,
-0.0048642889596521854,
-0.0013728868216276169,
0.031174777075648308,
0.050757769495248795,
-0.015102463774383068,
0.02007332071661949,
-0.04914075881242752,
0.0037474744021892548,
0.056425485759973526,
0.0005287736421450973,
-0.021853897720575333,
0.013247656635940075,
0.015940891578793526,
-0.04951825365424156,
-0.01488317921757698,
0.02821912243962288,
-0.003024592064321041,
0.03291252627968788,
-0.04515409842133522,
-0.00424299668520689,
0.002855840837582946,
0.03175898641347885,
-0.0376465767621994,
-0.025333471596240997,
0.01427376177161932,
0.04306871071457863,
-0.01612250693142414,
-0.056632984429597855,
0.01352002564817667,
0.006064814981073141,
-0.009470896795392036,
-0.0003834273375105113,
0.0014114349614828825,
-0.0051416815258562565,
-0.0002652905823197216,
-0.04313218966126442,
0.013004629872739315,
-0.01562534272670746,
-0.043858852237463,
0.0031965472735464573,
0.04735250771045685,
0.053841181099414825,
0.000959325407166034,
0.042863793671131134,
-0.06319857388734818,
0.035634081810712814,
0.03206999972462654,
-0.055176347494125366,
0.04197687655687332,
0.0008199468138627708,
0.016035867854952812,
0.0005956909735687077,
-0.0228362325578928,
-0.02618129551410675,
-0.00040899639134295285,
-0.002651015529409051,
0.008772746659815311,
-0.009738828986883163,
-0.0016761493170633912,
0.03834201768040657,
0.09873302280902863,
-0.02089698240160942,
-0.04280557855963707,
-0.059028904885053635,
-0.055258024483919144,
-0.03949247673153877,
-0.015363306738436222,
-0.00460489047691226,
-0.009278564713895321,
-0.039029255509376526,
-0.0020118358079344034,
-0.03187757357954979,
-0.007429862394928932,
0.007375241722911596,
0.07875707745552063,
-0.052650414407253265,
-0.012054704129695892,
-0.03572795167565346,
-0.018730763345956802,
-0.02691851742565632,
-0.008728640154004097,
-0.07266344130039215,
0.012119085527956486,
-0.01078748982399702,
0.0012641454814001918,
0.04850805923342705,
0.007143063936382532,
-0.006238877773284912,
0.02873549982905388,
0.022171903401613235,
0.05603576824069023,
-0.015516099520027637,
0.010012532584369183,
0.09466320276260376,
-0.06191950663924217,
0.037471238523721695,
0.03655271232128143,
-0.034389302134513855,
0.0697755441069603,
0.04306373372673988,
0.0233761016279459,
-0.021938547492027283,
0.057949963957071304,
-0.00010370498057454824,
0.010861219838261604,
-0.00024924171157181263,
0.010970840230584145,
0.019591737538576126,
0.04973387345671654,
-0.07224170863628387,
-0.021838227286934853,
0.021236324682831764,
-0.038039952516555786,
0.011744149029254913,
0.007880046963691711,
-0.03583260253071785,
-0.05088101699948311,
0.00043337061651982367,
0.024791782721877098,
-0.010641815140843391,
0.03129972517490387,
0.00504517974331975,
0.006791869178414345,
0.02373393625020981,
0.04194975271821022,
0.026215553283691406,
0.03787290304899216,
0.018131040036678314,
-0.03781517222523689,
0.07956967502832413,
-0.02739395573735237,
-0.052348263561725616,
-0.003454384859651327,
-0.01886133663356304,
-0.005200864747166634,
0.014605021104216576,
-0.005801742896437645,
0.03241131827235222,
0.014741984196007252,
0.003232182702049613,
-0.016668399795889854,
-0.08065591752529144,
-0.03380068391561508,
0.019284270703792572,
-0.005107361823320389,
-0.04460061714053154,
-0.053580816835165024,
-0.016149207949638367,
-0.08007819205522537,
-0.024357764050364494,
-0.050111908465623856,
0.008114281110465527,
0.02439681440591812,
0.10938378423452377,
0.016986900940537453,
-0.041840698570013046,
-0.006730575114488602,
0.010535753332078457,
-0.01212231069803238,
-0.02635619416832924,
0.01785007305443287,
-0.07277790457010269,
-0.0008114540833048522,
0.042276013642549515,
0.016750367358326912,
0.00493493489921093,
0.05100318789482117,
-0.014448669739067554,
0.006769929546862841,
0.015287883579730988,
-0.07517775148153305,
0.0020592394284904003,
-0.0080533716827631,
-0.027609676122665405,
-0.003420233726501465,
0.05208317190408707,
0.041009992361068726,
-0.009644778445363045,
-0.0007362458854913712,
-0.023081257939338684,
-0.03331183269619942,
0.006074253469705582,
0.0014543569413945079,
0.04941421002149582,
0.017222415655851364,
-0.019528169184923172,
-0.02413381077349186,
-0.014269707724452019,
-0.0558626689016819,
0.0173385851085186,
0.0030476171523332596,
0.014488239772617817,
0.004629668779671192,
-0.016932131722569466,
0.007383511867374182,
-0.0029731562826782465,
0.04169031232595444,
0.013700404204428196,
-0.07344172894954681,
0.008678904734551907,
0.017198676243424416,
-0.03839850053191185,
-0.0670228973031044,
0.027591820806264877,
0.005002184305340052,
-0.020753219723701477,
0.010670012794435024,
-0.021736344322562218,
-0.017617037519812584,
0.030534129589796066,
-0.0014053541235625744,
-0.01987958885729313,
0.05052293837070465,
0.03324245661497116,
0.06271293014287949,
-0.014333223924040794,
0.04710961505770683,
0.02833707444369793,
-0.024798084050416946,
0.020062312483787537,
-0.06063276156783104,
0.025643054395914078,
-0.028865186497569084,
0.001667025382630527,
-0.040293268859386444,
-0.06670645624399185,
0.05383514612913132,
0.0003254359180573374,
0.03877616301178932,
0.059211697429418564,
-0.004289380740374327,
0.033446092158555984,
0.0022682875860482454,
0.01433146558701992,
-0.01733008585870266,
-0.02550029754638672,
-0.007727417629212141,
0.00023725444043520838,
-0.06210946664214134,
0.006252544466406107,
-0.03177473694086075,
-0.027156665921211243,
-0.018198976293206215,
0.009149106219410896,
-0.004019091371446848,
0.017434533685445786,
0.0020759606268256903,
-0.016350051388144493,
-0.021024947986006737,
-0.03985261544585228,
0.06315849721431732,
-0.012714000418782234,
0.058165986090898514,
0.052176035940647125,
0.03504723682999611,
0.013060291297733784,
0.023871421813964844,
-0.04887251555919647,
0.0007751245284453034,
-0.005540357902646065,
0.02191164717078209,
0.012134119868278503,
-0.03374306857585907,
-0.04109794273972511,
0.029197990894317627,
-0.003833154449239373,
-0.06618152558803558,
-0.029551684856414795,
0.0006101693725213408,
-0.035859573632478714,
0.07152062654495239,
0.03712683171033859,
0.04372341185808182,
-0.0130776297301054,
0.013481774367392063,
-0.0005324825178831816,
-0.04127383232116699,
-0.013153995387256145,
-0.03133942559361458,
-0.010136472061276436,
0.031731292605400085,
0.07400310784578323,
-0.06338111311197281,
0.02986755035817623,
-0.05345305800437927,
-0.026195751503109932,
-0.017331406474113464,
-0.060669880360364914,
0.040030337870121,
-0.05622843652963638,
0.02838326431810856,
0.008674439042806625,
0.041655104607343674,
-0.015449998900294304,
0.03634018823504448,
-0.03352498263120651,
0.03517340123653412,
-0.016104355454444885,
-0.037318311631679535,
-0.009366798214614391,
-0.0449845977127552,
0.00910230539739132,
-0.0470261387526989,
0.048914529383182526,
0.013912832364439964,
0.026112988591194153,
-0.005739078391343355,
0.007291332818567753,
-0.03931504115462303,
0.01403262559324503,
0.021252507343888283,
0.023751331493258476,
0.014636840671300888,
0.07270229607820511,
-0.010479902848601341,
-0.053411778062582016,
0.012323069386184216,
-0.024388834834098816,
-0.0706656351685524,
0.006433156318962574,
-0.07049522548913956,
-0.03317582234740257,
-0.005510048009455204,
-0.029986117035150528,
-0.016203200444579124,
0.005953947547823191,
-0.020627720281481743,
-0.0016502301441505551,
-0.02927909977734089,
0.026007315143942833,
0.016116764396429062,
-0.06702569872140884,
0.006392390932887793,
0.014431668445467949,
-0.03383254632353783,
-0.047116633504629135,
0.027250327169895172,
0.0431499220430851,
-0.01746203377842903,
0.03404092416167259,
-0.013862419873476028,
-0.048323094844818115,
-0.015696492046117783,
0.02161296084523201,
0.0547209195792675,
-0.04184001311659813,
-0.041928019374608994,
-0.0007363074691966176,
0.04249678924679756,
0.028886698186397552,
0.01641826331615448,
0.03546038642525673,
-0.04113775119185448,
0.018236126750707626,
0.09583120048046112,
-0.02394440770149231,
-0.01930692233145237,
0.01822187379002571,
-0.03407321870326996,
0.03320660442113876,
-0.03782514110207558,
-0.03439325466752052,
0.0346040278673172,
0.06884679198265076,
-0.010207864455878735,
0.09308651834726334,
-0.03949958086013794,
0.02051021158695221,
-0.014511526562273502,
-0.03287103772163391,
-0.093633733689785,
-0.021662229672074318,
-0.015061539597809315,
0.017024675384163857,
-0.08222948014736176,
-0.022803882136940956,
0.023649217560887337,
0.016035625711083412,
0.007677453104406595,
0.05267228186130524,
-0.04283997789025307,
0.01574712246656418,
-0.050387654453516006
] |
<p>It is possible to calculate the time dilation with Lorentz transformation? So with the equation $$t'=\gamma(t-\frac{x v}{c^2}) \tag{1}$$ in which $\gamma$ is the Lorentz-Factor?</p>
<p>In an exercise I have succeeded.</p>
<p>So why can be calculated with the equation $(1)$ the time dilation? What is the reason? </p> | g117 | [
0.005810420960187912,
-0.0022411809768527746,
0.0009903477039188147,
-0.013488524593412876,
0.01149698719382286,
0.01825600489974022,
0.04088114574551582,
0.024731822311878204,
-0.02505735494196415,
0.030590450391173363,
-0.0509822741150856,
0.06464555114507675,
0.015556590631604195,
0.004448933992534876,
-0.0026346982922405005,
-0.01899362914264202,
0.08106725662946701,
0.021686576306819916,
-0.0832037702202797,
0.010526269674301147,
-0.003842890029773116,
-0.01824156939983368,
0.03701532259583473,
-0.06523723155260086,
0.037303145974874496,
-0.01895509660243988,
0.005667939782142639,
0.07368098944425583,
-0.06372176110744476,
0.01533052884042263,
0.006686161272227764,
0.032874695956707,
-0.02394944243133068,
0.03764178976416588,
0.04524417966604233,
-0.02066299319267273,
0.01686920039355755,
0.01043237466365099,
0.05508426949381828,
0.023236706852912903,
-0.026429560035467148,
0.042991843074560165,
-0.004910436924546957,
0.02325519546866417,
-0.0005964221199974418,
-0.006459604017436504,
-0.02138676866889,
0.04089494049549103,
-0.03662922605872154,
-0.0005317226750776172,
-0.029946792870759964,
-0.004383467603474855,
0.03852667659521103,
-0.05196432024240494,
0.011481134220957756,
-0.00624810392037034,
0.06330132484436035,
-0.040736421942710876,
0.03724457696080208,
0.07687926292419434,
-0.009217493236064911,
-0.08371705561876297,
-0.008852958679199219,
0.029771829023957253,
0.032776784151792526,
-0.04893939197063446,
-0.02551139146089554,
-0.013488253578543663,
-0.01907995156943798,
0.03332415223121643,
-0.040677715092897415,
-0.02027219533920288,
0.01863005757331848,
0.023604029789566994,
-0.014560624957084656,
-0.009362789802253246,
0.025116534903645515,
-0.0015658452175557613,
-0.012423072941601276,
-0.06212829798460007,
0.0033942393492907286,
-0.008768332190811634,
-0.030277786776423454,
-0.051829658448696136,
0.04292118921875954,
-0.04944300651550293,
0.032459087669849396,
0.02498999610543251,
0.02560514211654663,
0.019250493496656418,
0.026827657595276833,
-0.0518917478621006,
0.09322553128004074,
0.0013338914141058922,
-0.015540588647127151,
0.006369480863213539,
-0.014675572514533997,
0.0314163938164711,
-0.019372345879673958,
-0.03690486401319504,
0.04476642981171608,
-0.0066732014529407024,
-0.04213546961545944,
0.013486196286976337,
-0.0063184574246406555,
-0.026510724797844887,
-0.010419252328574657,
-0.02375873737037182,
-0.01786252111196518,
-0.05693158507347107,
-0.05051177740097046,
-0.03814627230167389,
0.055883247405290604,
-0.023835228756070137,
-0.05908132344484329,
-0.07110276818275452,
-0.014951800927519798,
0.060142237693071365,
0.0012534564593806863,
0.03218090534210205,
0.014763877727091312,
0.007806571200489998,
0.0261684563010931,
-0.004957955330610275,
-0.015597289428114891,
-0.01966937445104122,
-0.02890271320939064,
0.006883388385176659,
0.03441726043820381,
-0.055103082209825516,
-0.02660900168120861,
0.07492909580469131,
0.06064281612634659,
0.006083363201469183,
-0.023667147383093834,
0.034735057502985,
0.010646242648363113,
0.012801319360733032,
-0.035605669021606445,
0.0020349088590592146,
0.005472313147038221,
-0.03289017453789711,
-0.018883805721998215,
0.006929201073944569,
-0.02639942057430744,
0.08868911862373352,
-0.07419227808713913,
-0.04426537826657295,
-0.00945590902119875,
-0.02640807442367077,
-0.04178815707564354,
0.021269062533974648,
0.06432449072599411,
-0.020626250654459,
0.08352696895599365,
-0.0024280850775539875,
0.027990061789751053,
-0.02535211108624935,
-0.025454087182879448,
0.0856575220823288,
0.03247517719864845,
-0.003720848122611642,
-0.029973622411489487,
-0.07026728242635727,
-0.0629483014345169,
0.04533197730779648,
0.04404347389936447,
0.00675921980291605,
-0.038184866309165955,
-0.10142195224761963,
-0.07861330360174179,
-0.024806298315525055,
-0.0030144620686769485,
-0.012266683392226696,
0.0475383959710598,
0.04586310312151909,
-0.06050175428390503,
-0.000507328484673053,
-0.10642631351947784,
-0.008910799399018288,
0.004767764825373888,
-0.026960289105772972,
0.004887028131633997,
-0.030370155349373817,
0.021530847996473312,
-0.014369931071996689,
-0.003637479618191719,
0.0005212549003772438,
-0.09722378104925156,
0.0298406220972538,
0.02813791111111641,
-0.02700725942850113,
0.009432648308575153,
-0.012710385024547577,
-0.044638488441705704,
0.03264806047081947,
0.09234357625246048,
-0.04155895859003067,
-0.010182132944464684,
0.05128573253750801,
-0.08800127357244492,
0.015736199915409088,
0.05413668602705002,
-0.01286646630614996,
0.037183064967393875,
-0.0023300230968743563,
-0.06331872940063477,
-0.02656528726220131,
0.03640374913811684,
-0.02463673986494541,
0.06670253723859787,
-0.01141131017357111,
-0.03911719471216202,
-0.000056152985052904114,
-0.05833124369382858,
-0.06870397925376892,
-0.007491960655897856,
0.02550111897289753,
-0.037419505417346954,
0.06530392915010452,
-0.008225767873227596,
0.006264765281230211,
0.021678810939192772,
-0.013592228293418884,
-0.03678267076611519,
-0.0351848267018795,
-0.0064351498149335384,
-0.027903011068701744,
0.015028619207441807,
0.0196783859282732,
-0.048660531640052795,
0.046379074454307556,
-0.040696337819099426,
-0.005919473245739937,
0.028969259932637215,
0.008849694393575191,
-0.03362879529595375,
-0.004705758765339851,
0.00803339947015047,
0.01753009483218193,
0.04642447456717491,
-0.01990860141813755,
0.009118188172578812,
-0.017943331971764565,
0.027982618659734726,
-0.006425164174288511,
0.046963658183813095,
-0.010704049840569496,
-0.011302128434181213,
-0.05660129711031914,
0.013089136220514774,
-0.05185249075293541,
-0.015352210961282253,
-0.04082416743040085,
-0.046983007341623306,
-0.0294444989413023,
-0.005960197187960148,
0.04119512438774109,
-0.050781410187482834,
-0.033086761832237244,
-0.028240468353033066,
0.0006165436934679747,
0.0001651978091103956,
0.07254813611507416,
-0.024828359484672546,
-0.010934912599623203,
-0.04847361147403717,
0.030615825206041336,
-0.0445224829018116,
-0.028808869421482086,
-0.0061596957966685295,
0.009120231494307518,
0.02610805630683899,
0.02201789990067482,
-0.07121369242668152,
-0.0537276528775692,
-0.015692465007305145,
0.029169822111725807,
0.025420300662517548,
-0.0280458927154541,
-0.030875587835907936,
0.021844087168574333,
-0.020863085985183716,
0.05337224528193474,
-0.03611486032605171,
-0.025503572076559067,
-0.03664099797606468,
0.010670249350368977,
0.006619560997933149,
0.010090597905218601,
-0.01913653500378132,
0.028949415311217308,
0.005445524118840694,
-0.05527392029762268,
0.035467494279146194,
0.012064645998179913,
0.06616063416004181,
-0.0798654779791832,
0.003069730708375573,
0.041629988700151443,
0.012811567634344101,
-0.001965828938409686,
-0.00320111564360559,
0.007453785743564367,
0.04137428477406502,
-0.03765666112303734,
-0.03155948966741562,
-0.03875325992703438,
-0.020441925153136253,
0.0047704000025987625,
-0.03745613247156143,
0.019615888595581055,
0.010985945351421833,
0.005437389016151428,
-0.0335036963224411,
0.011474546045064926,
0.027042191475629807,
-0.014972768723964691,
0.061464350670576096,
0.026178667321801186,
-0.014202837832272053,
-0.07206173241138458,
-0.05939444899559021,
0.020551130175590515,
0.020042981952428818,
-0.05653829872608185,
-0.02545899711549282,
-0.009776893071830273,
-0.05873420089483261,
-0.033537108451128006,
0.008002793416380882,
-0.01879846304655075,
0.022462978959083557,
0.004872052930295467,
0.03156164288520813,
-0.011349502019584179,
0.0000032719108276069164,
0.0646408274769783,
0.0015891658840700984,
-0.054030679166316986,
-0.043674781918525696,
-0.029277397319674492,
-0.01847471483051777,
0.07317489385604858,
0.03731720149517059,
0.007732204161584377,
0.007069090381264687,
-0.01465174276381731,
0.014342195354402065,
0.00295536988414824,
0.028363263234496117,
-0.009026332758367062,
-0.026185523718595505,
-0.023300623521208763,
0.008579226210713387,
0.03540050983428955,
0.021745899692177773,
0.04464400187134743,
-0.009699228219687939,
0.0020895397756248713,
0.0016114097088575363,
0.03249354287981987,
-0.020121943205595016,
0.006218560505658388,
-0.04995962232351303,
-0.010434222407639027,
0.002878021914511919,
0.0613093376159668,
-0.03056260198354721,
0.03344041481614113,
0.02527887001633644,
-0.02670753188431263,
0.054560281336307526,
0.039598386734724045,
-0.056036293506622314,
-0.023809237405657768,
-0.018163122236728668,
0.06338322162628174,
-0.0001925103715620935,
0.04326704144477844,
0.001030110171996057,
-0.020506098866462708,
0.025522267445921898,
0.017152614891529083,
0.022345827892422676,
-0.0022756324615329504,
-0.03246594965457916,
0.03202030807733536,
0.05033678933978081,
-0.058936502784490585,
0.012243568897247314,
0.03161264955997467,
0.011183870024979115,
0.027227234095335007,
-0.0019774038810282946,
-0.031443964689970016,
0.08725930750370026,
-0.00172968371771276,
-0.004206025507301092,
0.026751751080155373,
0.007001132238656282,
0.025349954143166542,
0.030790524557232857,
-0.01752554439008236,
-0.034649815410375595,
0.054554492235183716,
0.0625903531908989,
-0.012874442152678967,
0.03512345999479294,
-0.01317919697612524,
-0.05734661594033241,
-0.002635395620018244,
0.032906368374824524,
-0.061238039284944534,
0.018365934491157532,
-0.011750291101634502,
0.011291338130831718,
-0.04573528841137886,
0.021990546956658363,
-0.007881668396294117,
0.007782577537000179,
0.025763528421521187,
0.009731130674481392,
0.009871916845440865,
-0.04963286221027374,
0.010959555394947529,
0.09322281926870346,
0.052068084478378296,
0.002720624441280961,
-0.06621284037828445,
0.05451237037777901,
-0.006028234027326107,
-0.05259888991713524,
0.0438896007835865,
-0.03796840086579323,
0.036055952310562134,
-0.013273458927869797,
0.057309895753860474,
0.053176406770944595,
0.06120839715003967,
0.06169430539011955,
-0.06428024917840958,
0.08792360126972198,
-0.010879279114305973,
-0.02675708755850792,
0.03780828416347504,
-0.017510106787085533,
-0.05215832218527794,
-0.04500684514641762,
0.01929664984345436,
-0.021392488852143288,
0.003259341698139906,
0.001955465879291296,
0.04946247115731239,
0.04860135540366173,
-0.009123084135353565,
-0.01215851679444313,
-0.009305771440267563,
0.049307629466056824,
0.047861531376838684,
0.003459871280938387,
0.0026265301275998354,
0.0010351893724873662,
0.01825154386460781,
0.016280585899949074,
-0.03849286586046219,
0.04174817353487015,
-0.028018489480018616,
-0.01854497566819191,
0.019313568249344826,
-0.018291426822543144,
-0.025882860645651817,
-0.004535207524895668,
-0.01336416695266962,
-0.023608222603797913,
0.03287314996123314,
-0.06478323042392731,
0.0063407691195607185,
0.02157190442085266,
-0.02152412012219429,
-0.027979401871562004,
-0.02839498594403267,
-0.011664165183901787,
-0.03496178612112999,
-0.01947356015443802,
0.031909577548503876,
-0.026531429961323738,
0.03296322375535965,
0.03763739764690399,
-0.04977445304393768,
-0.024698913097381592,
0.04464727267622948,
0.061698708683252335,
-0.06414280086755753,
0.03339426964521408,
0.038603801280260086,
0.010873409919440746,
-0.021153496578335762,
0.06641070544719696,
-0.04647509753704071,
-0.05192360654473305,
0.026793455705046654,
-0.01363296713680029,
-0.03883477300405502,
-0.030105657875537872,
0.03923829272389412,
0.02426474541425705,
0.027706079185009003,
-0.047942910343408585,
0.05428127571940422,
0.02558116428554058,
0.012346356175839901,
0.018940497189760208,
0.03129581734538078,
0.013362019322812557,
-0.06057048588991165,
0.060631513595581055,
-0.0364750400185585,
0.030093949288129807,
-0.03628324344754219,
0.0201482605189085,
0.053951021283864975,
0.046189796179533005,
-0.011613138020038605,
0.01635732688009739,
0.03245198354125023,
-0.0844452977180481,
-0.05636358633637428,
0.024059347808361053,
-0.023998595774173737,
0.029721062630414963,
0.008436307311058044,
0.0013582961400970817,
0.03456061705946922,
0.018465567380189896,
-0.027871670201420784,
0.01028660498559475,
-0.047166526317596436,
-0.022331126034259796,
-0.005246064160019159,
-0.03729742765426636,
-0.018133293837308884,
0.05077178031206131,
0.04315829277038574,
0.011294260621070862,
0.015292933210730553,
-0.019982147961854935,
-0.0048577748239040375,
0.014847462065517902,
-0.005189268384128809,
0.011629484593868256,
-0.06707894802093506,
0.051173701882362366,
-0.030851755291223526,
0.007821980863809586,
0.0377032570540905,
0.008889446966350079,
0.0048225270584225655,
-0.02248327247798443,
-0.02317390777170658,
0.02857954241335392,
0.009282623417675495,
-0.03766625374555588,
0.024972641840577126,
-0.04551165923476219,
-0.07278382033109665,
0.0012815376976504922,
-0.004673931282013655,
0.03420863300561905,
0.022393427789211273,
-0.030963068827986717,
0.03030865453183651,
0.006094262003898621,
0.004236976616084576,
-0.008215091191232204,
0.012296897359192371,
0.04975619912147522,
-0.07095563411712646,
-0.061642322689294815,
-0.03775902837514877,
0.020026637241244316,
0.007349598221480846,
-0.05278726667165756,
-0.06918423622846603,
-0.03667931258678436,
0.03055940940976143,
-0.022167809307575226,
-0.03284386545419693,
-0.020194025710225105,
0.04341307654976845,
-0.021851293742656708,
0.011582189239561558,
0.004556719213724136,
-0.009123595431447029,
0.010195395909249783,
0.017935315147042274,
-0.017105700448155403,
0.01210850477218628,
0.011452684178948402,
0.028750523924827576,
0.005239933729171753,
0.038274530321359634,
0.006990768946707249,
0.04527060315012932,
0.022101394832134247,
0.00895895715802908,
-0.04215104877948761,
0.035168420523405075,
0.03977489098906517,
-0.029615849256515503,
0.05910450592637062,
0.037541162222623825,
-0.049512919038534164,
0.007913917303085327,
0.05164241045713425,
-0.03084389492869377,
0.006429379805922508,
0.02923602983355522,
-0.029271036386489868,
0.010911808349192142,
0.08562615513801575,
-0.02067115344107151,
0.012183945626020432,
0.010065248236060143,
-0.046241916716098785,
0.08655679225921631,
-0.019981948658823967,
0.01763446256518364,
0.0024590324610471725,
-0.038479771465063095,
0.06322821229696274,
-0.006441979669034481,
0.007508604321628809,
0.04609328508377075,
0.023281637579202652,
0.037899598479270935,
-0.041011691093444824,
0.014354076236486435,
0.0239206962287426,
0.04893068969249725,
-0.036309078335762024,
0.009103533811867237,
0.0018410567427054048,
-0.053578536957502365,
-0.0362069196999073,
0.03993815556168556,
0.03475894033908844,
-0.0052353935316205025,
-0.11533588171005249,
0.04945159703493118,
0.06444764137268066,
-0.00532218161970377,
-0.036322638392448425,
0.023943599313497543,
-0.01591530628502369,
-0.07019221782684326,
-0.008912300691008568,
-0.00565291428938508,
-0.04699990898370743,
-0.01940237358212471,
-0.02239745669066906,
-0.04844552278518677,
0.005904363468289375,
0.050371259450912476,
0.012622149661183357,
0.06292968988418579,
-0.00799042358994484,
0.013346625491976738,
0.06198098883032799,
-0.07512184977531433,
-0.009917759336531162,
0.020834671333432198,
-0.010366386733949184,
-0.028144586831331253,
-0.02872689813375473,
0.009590760804712772,
-0.004228854551911354,
0.01325223222374916,
-0.00830155424773693,
0.014674866572022438,
-0.07207931578159332,
-0.014176469296216965,
-0.05100535973906517,
0.005217194091528654,
-0.0257590152323246,
-0.009420299902558327,
0.020009463652968407,
-0.029791483655571938,
0.0006221280782483518,
0.003806330030784011,
-0.03630397468805313,
-0.034085605293512344,
-0.0035507555585354567,
0.02583969570696354,
-0.018212322145700455,
-0.083740234375,
0.040381330996751785,
0.019472278654575348,
-0.027630092576146126,
0.004112815484404564,
0.023771226406097412,
-0.00775790074840188,
0.01855740137398243,
0.004573928192257881,
0.026301687583327293,
0.030255883932113647,
-0.00039060995914041996,
-0.024089641869068146,
-0.04036790877580643,
-0.010007098317146301,
0.010060164146125317,
0.0022730177734047174,
-0.02420881576836109,
-0.021486559882760048,
-0.017244594171643257,
-0.001380777102895081,
0.008082890883088112,
0.017940150573849678,
0.010522531345486641,
-0.02577047608792782,
0.015102875418961048,
0.0072837043553590775,
-0.011034518480300903,
-0.04119451716542244,
-0.02240714430809021,
-0.033683814108371735,
0.011417108587920666,
-0.0597652941942215,
0.028150180354714394,
-0.03580264747142792,
0.043727580457925797,
0.007247206289321184,
-0.02131393738090992,
0.042157333344221115,
0.025541042909026146,
0.018645767122507095,
0.05712573230266571,
-0.06896810233592987,
0.014646782539784908,
0.10567211359739304,
0.014996820129454136,
0.021219074726104736,
-0.03265190124511719,
0.013948031701147556,
-0.005929526872932911,
0.003140695858746767,
-0.009247438982129097,
0.025926440954208374,
0.0314507782459259,
-0.03274541348218918,
0.03536612540483475,
0.04945752024650574,
0.04941873997449875,
0.04043162614107132,
0.019322695210576057,
-0.026969587430357933,
0.0027345730923116207,
0.02223685197532177,
0.07624480873346329,
-0.006249469239264727,
-0.007197469472885132,
0.045072343200445175,
0.004248852375894785,
0.05180559679865837,
0.012492611072957516,
-0.07919974625110626,
-0.019425857812166214,
0.0212238896638155
] |
<p>Looking for suggestions on how to approach calculating the capacitance of a capacitor where the plates have an arbitrary shape. I've seen derivations of capacitance for a few highly symmetric arrangement (eg coaxial cylinders) but nothing like a general approach to predicting the measurable capacitance of arbitrary arrangements of plates. </p>
<p>Thanks for any suggestions or references. </p> | g4775 | [
0.005699949339032173,
-0.021261822432279587,
-0.0000570593292650301,
0.0025346623733639717,
-0.0413244403898716,
-0.036321040242910385,
0.004776607267558575,
0.03091023676097393,
-0.06092217192053795,
0.016205953434109688,
-0.037856247276067734,
0.02042163349688053,
0.059814099222421646,
0.01601557433605194,
0.038110628724098206,
0.02009148895740509,
0.016725245863199234,
0.03784409910440445,
0.03390318155288696,
0.05449267104268074,
0.03222811967134476,
0.01167144626379013,
0.010272255167365074,
0.021131334826350212,
0.002116104355081916,
-0.02786444127559662,
0.008358056657016277,
-0.02609311044216156,
-0.030753672122955322,
-0.05514920875430107,
-0.02681766077876091,
-0.013928644359111786,
0.03963472694158554,
0.007600840181112289,
-0.0045377579517662525,
0.027622170746326447,
-0.006937314290553331,
0.046894751489162445,
0.023228423669934273,
-0.007344165351241827,
0.02660536952316761,
0.009181905537843704,
-0.06771483272314072,
0.04051022604107857,
-0.010658228769898415,
-0.04802745208144188,
-0.03235892578959465,
0.010311879217624664,
-0.0595918744802475,
-0.030973248183727264,
0.02416791021823883,
0.022127356380224228,
0.07308143377304077,
-0.01892896741628647,
-0.007299894001334906,
0.0035091014578938484,
0.008524728007614613,
-0.017488859593868256,
0.07041150331497192,
0.024828210473060608,
0.014510062523186207,
0.06180134788155556,
-0.05559078976511955,
-0.007480621337890625,
0.025575557723641396,
0.0024922664742916822,
0.0007244541775435209,
-0.005351420491933823,
0.0068864841014146805,
0.019954662770032883,
0.044208355247974396,
-0.019419506192207336,
0.04710398241877556,
-0.04405033588409424,
-0.02656705491244793,
-0.01632305234670639,
-0.0220657791942358,
0.001476275036111474,
0.009326229803264141,
-0.047225743532180786,
-0.027102481573820114,
-0.0018464415334165096,
0.05448056384921074,
-0.043008580803871155,
0.004650919232517481,
0.00639647152274847,
0.026646094396710396,
-0.0037181926891207695,
0.014877120964229107,
0.011644089594483376,
0.02850976027548313,
-0.03548160567879677,
0.05190633237361908,
-0.05997851863503456,
-0.03230997920036316,
-0.03413364663720131,
0.018599940463900566,
-0.01964254304766655,
-0.03396337479352951,
-0.0005031555774621665,
0.01812766306102276,
0.07489346712827682,
0.02948816865682602,
0.033098530024290085,
0.002311627147719264,
0.027709709480404854,
0.07170601934194565,
0.002320817206054926,
0.013733336701989174,
-0.0756724625825882,
-0.007646327372640371,
-0.0008127021719701588,
-0.008017057552933693,
0.02280891127884388,
0.0019871522672474384,
-0.0006900279549881816,
0.035622067749500275,
-0.06107016280293465,
0.027572212740778923,
0.08625064790248871,
0.014141222462058067,
-0.003439696040004492,
-0.030911149457097054,
0.017392726615071297,
0.01172368973493576,
0.04843246191740036,
0.007673616986721754,
-0.002715352224186063,
0.04004830867052078,
-0.03833206743001938,
0.04252249002456665,
-0.013831192627549171,
-0.011312193237245083,
0.0070713236927986145,
-0.0052423723973333836,
0.045113954693078995,
-0.02588815987110138,
-0.036172591149806976,
0.024550355970859528,
-0.003563132369890809,
0.010670932941138744,
0.014234986156225204,
-0.008359863422811031,
0.03342936560511589,
0.016151437535881996,
-0.0486760288476944,
0.0005420005181804299,
-0.07261548191308975,
-0.004593092016875744,
0.03543802723288536,
0.002817627042531967,
0.036486364901065826,
-0.007056937552988529,
-0.04707277566194534,
0.0005784128443337977,
0.02217322215437889,
0.015012936666607857,
0.005539443343877792,
0.015028764493763447,
0.04651661962270737,
-0.018697449937462807,
-0.03829408437013626,
-0.008032175712287426,
-0.07247233390808105,
-0.046073488891124725,
-0.0279947891831398,
-0.03154546394944191,
0.020905641838908195,
-0.04732620716094971,
-0.05239922180771828,
0.04157121852040291,
-0.033053893595933914,
-0.02413778193295002,
0.015918809920549393,
-0.011681132018566132,
0.00275586755014956,
0.01612459123134613,
0.029721327126026154,
0.04609314352273941,
0.01613578014075756,
0.017205631360411644,
0.023040592670440674,
0.08413431793451309,
-0.035390909761190414,
-0.0011963630095124245,
-0.02083871141076088,
0.039790984243154526,
-0.005102377384901047,
-0.02674884721636772,
0.017771994695067406,
-0.055608853697776794,
0.0016639375826343894,
0.024084098637104034,
0.026402754709124565,
-0.03633211925625801,
0.023952405899763107,
0.08635064214468002,
-0.007771466858685017,
-0.0513695552945137,
-0.0570676214993,
-0.009841516613960266,
0.020362045615911484,
-0.0011490728938952088,
0.09222692996263504,
0.013357065618038177,
0.020467005670070648,
0.02397248148918152,
-0.01678810454905033,
0.03289898857474327,
0.0406445674598217,
-0.021847238764166832,
-0.008644301444292068,
-0.03207169845700264,
0.039759647101163864,
0.037329159677028656,
0.007048715837299824,
-0.04839397966861725,
-0.03207354620099068,
-0.044724684208631516,
-0.01839166134595871,
0.05055362358689308,
-0.03874822333455086,
-0.04648604243993759,
0.016390332952141762,
-0.07603149861097336,
0.062458187341690063,
0.01456987950950861,
-0.0035206745378673077,
-0.028734872117638588,
-0.008574734441936016,
-0.037429533898830414,
0.010516687296330929,
0.006706023123115301,
-0.03767238184809685,
-0.00854409672319889,
0.024001911282539368,
-0.02753562293946743,
-0.008653504773974419,
-0.027266792953014374,
-0.027312850579619408,
-0.008010759018361568,
-0.05810508877038956,
-0.03344515711069107,
-0.021729329600930214,
-0.047333985567092896,
0.0002950826601590961,
-0.007626143749803305,
-0.009590084664523602,
0.011906434781849384,
0.0031391470693051815,
-0.021069198846817017,
-0.007162950932979584,
-0.02272598259150982,
0.0033647764939814806,
0.0012257009511813521,
-0.009179379791021347,
0.029951894655823708,
0.029107162728905678,
-0.005105250980705023,
-0.03539780154824257,
-0.03899424523115158,
-0.0613773949444294,
-0.0212476197630167,
0.00434704078361392,
-0.022686179727315903,
-0.010837250389158726,
-0.013929463922977448,
-0.03921493515372276,
0.06179482862353325,
-0.0023874270264059305,
0.0030079216230660677,
0.06632030010223389,
0.04884839057922363,
-0.029971828684210777,
0.023856259882450104,
-0.034220416098833084,
0.013235784135758877,
-0.0007775514968670905,
-0.05134347826242447,
0.0360097661614418,
0.04810260981321335,
-0.032245784997940063,
-0.01750953681766987,
0.003812630893662572,
0.05119679123163223,
0.022520359605550766,
0.05869966745376587,
-0.05566157028079033,
0.03268444538116455,
-0.004935016855597496,
-0.005742313340306282,
-0.015722166746854782,
-0.03860677778720856,
-0.08647161722183228,
0.09001041948795319,
0.05707448348402977,
0.03926130384206772,
0.02502588927745819,
-0.0025346623733639717,
0.02445622719824314,
-0.053958021104335785,
0.027517369017004967,
-0.04291662201285362,
-0.05884995684027672,
0.015213487669825554,
0.07243113219738007,
0.04520097374916077,
-0.05411893501877785,
0.032292772084474564,
0.04375045374035835,
-0.01999983936548233,
-0.010641981847584248,
-0.01589035429060459,
-0.015020559541881084,
-0.024491870775818825,
0.005651522893458605,
0.0012333488557487726,
0.020569518208503723,
-0.0802951455116272,
-0.022273967042565346,
0.05215699225664139,
-0.056246399879455566,
0.02045908011496067,
0.04946358874440193,
-0.045730821788311005,
0.03678656741976738,
-0.04881875216960907,
0.009669866412878036,
-0.015047705732285976,
0.05176073685288429,
-0.020114697515964508,
0.053249113261699677,
0.03624645620584488,
0.0063881343230605125,
-0.024869093671441078,
-0.06824889779090881,
0.04752018302679062,
0.004971619229763746,
-0.008409721776843071,
-0.020480841398239136,
0.01612260192632675,
-0.040809519588947296,
0.015661928802728653,
-0.09581530094146729,
-0.07208465784788132,
0.04531873017549515,
0.016902580857276917,
0.016529496759176254,
0.010569133795797825,
-0.02507931925356388,
0.030823592096567154,
0.02105514146387577,
0.014526925049722195,
0.02555316686630249,
-0.05281209945678711,
0.043325573205947876,
0.0023789280094206333,
0.019682317972183228,
-0.08547385782003403,
0.028855230659246445,
0.0031992706935852766,
-0.04821142554283142,
-0.0071711307391524315,
0.004402747377753258,
0.05097567290067673,
-0.05697231367230415,
0.007428762502968311,
0.04422170668840408,
0.027995705604553223,
-0.04381544888019562,
-0.004827556665986776,
-0.03477122262120247,
0.010192833840847015,
0.011502537876367569,
-0.015125581063330173,
-0.019161609932780266,
-0.06580471992492676,
0.049384135752916336,
-0.0037561822682619095,
0.02603621408343315,
-0.01683124713599682,
-0.0006932471296750009,
0.0631951093673706,
-0.015589581802487373,
-0.05689861625432968,
-0.009351687505841255,
-0.005000274162739515,
0.08799891918897629,
-0.05828152969479561,
-0.03677067533135414,
-0.007603276986628771,
-0.05960192158818245,
-0.026463888585567474,
-0.019897080957889557,
-0.03818434104323387,
-0.0674428641796112,
0.012470786459743977,
-0.006167796906083822,
0.05636775121092796,
-0.009055552072823048,
0.06472544372081757,
-0.09133929014205933,
0.04694764316082001,
0.003632586682215333,
0.015214319340884686,
-0.041828352957963943,
0.03208788111805916,
-0.04225582256913185,
0.014033420011401176,
0.000875406083650887,
0.02197110839188099,
-0.01241998840123415,
0.0719175711274147,
-0.013887358829379082,
0.014868581667542458,
-0.03373869135975838,
-0.027203230187296867,
-0.013553994707763195,
0.020541401579976082,
0.038741033524274826,
-0.022415846586227417,
0.0018125161295756698,
-0.040109120309352875,
0.00068518181797117,
0.04366649314761162,
-0.032017309218645096,
-0.008290883153676987,
-0.02237616665661335,
-0.0009783030254766345,
0.00034989690175279975,
0.041923753917217255,
-0.03164251521229744,
-0.01298637967556715,
0.015985431149601936,
-0.024013185873627663,
0.02937840111553669,
-0.02949749492108822,
0.04029347002506256,
0.002946943510323763,
-0.02197383902966976,
-0.0220860056579113,
-0.04630699008703232,
0.023902250453829765,
-0.014949571341276169,
0.014942831359803677,
0.06536032259464264,
-0.06608584523200989,
0.008568569086492062,
0.00589743023738265,
0.005059792660176754,
-0.024037091061472893,
-0.024463413283228874,
-0.04000353813171387,
0.020793873816728592,
-0.05232724919915199,
-0.042352136224508286,
0.019090361893177032,
0.0037868714425712824,
0.04560837894678116,
0.0016754129901528358,
0.0012038466520607471,
-0.008701139129698277,
-0.05121680721640587,
-0.0027676804456859827,
-0.059142664074897766,
0.06537124514579773,
-0.010496814735233784,
-0.024378960952162743,
-0.03343548998236656,
0.017755527049303055,
-0.016187399625778198,
0.03219277039170265,
0.003361365059390664,
0.023063121363520622,
-0.0013022770872339606,
0.042011603713035583,
-0.01045383233577013,
0.0007086708792485297,
-0.1250976324081421,
-0.03018353134393692,
-0.052415598183870316,
-0.004505242221057415,
0.0006040367297828197,
0.00236328924074769,
0.018202336505055428,
-0.01037526410073042,
-0.014829306863248348,
-0.0006306388531811535,
-0.03580338507890701,
0.028793198987841606,
-0.03139626234769821,
0.02273488976061344,
-0.013288930989801884,
0.01939111202955246,
-0.04504906386137009,
-0.004414408467710018,
0.022310078144073486,
-0.01661718264222145,
-0.018557731062173843,
0.014625762589275837,
-0.006027954630553722,
0.03585182875394821,
0.024345550686120987,
-0.0282276701182127,
0.004962040111422539,
0.012624482624232769,
0.0020871199667453766,
0.020428607240319252,
0.05356542393565178,
0.022427469491958618,
0.046219225972890854,
0.006625805981457233,
0.07364286482334137,
0.004189396742731333,
-0.03186462074518204,
0.0534612275660038,
-0.024278029799461365,
-0.006112208589911461,
-0.02838863804936409,
0.009047601372003555,
0.07857538014650345,
0.04175693914294243,
-0.03150233253836632,
0.0261579230427742,
-0.020007625222206116,
0.03296007588505745,
-0.013504043221473694,
-0.013827224262058735,
-0.013579065911471844,
-0.012761303223669529,
-0.01131721492856741,
0.018530072644352913,
-0.06904993951320648,
-0.022812994197010994,
-0.044898927211761475,
0.017129328101873398,
-0.005289661698043346,
0.005287660751491785,
0.05047880485653877,
-0.004225546959787607,
-0.046727463603019714,
0.05319160595536232,
0.03766321763396263,
0.06049739569425583,
-0.0027287867851555347,
-0.013521269895136356,
-0.019761864095926285,
0.06122538074851036,
0.04105473309755325,
0.03582845628261566,
-0.028162522241473198,
-0.017924007028341293,
-0.0344495065510273,
-0.001775850891135633,
0.11271818727254868,
-0.004798821173608303,
0.011710774153470993,
-0.04591355100274086,
0.03130042552947998,
-0.039441559463739395,
0.054919175803661346,
0.014932525344192982,
0.0073316958732903,
0.008373025804758072,
0.033142849802970886,
0.032965805381536484,
0.02134256437420845,
0.018566356971859932,
0.05015550181269646,
0.027436155825853348,
-0.004009174648672342,
-0.04868366941809654,
0.026501568034291267,
-0.04053232818841934,
0.02179611660540104,
-0.010171954520046711,
0.013661408796906471,
0.03054049238562584,
0.039541371166706085,
0.03805038332939148,
-0.014639366418123245,
-0.009238623082637787,
-0.0014676329446956515,
-0.025252193212509155,
-0.004342568106949329,
0.050375185906887054,
0.06278214603662491,
-0.0358780138194561,
0.038729432970285416,
-0.05403747782111168,
-0.03271738067269325,
-0.036685261875391006,
0.0523686408996582,
0.027532631531357765,
0.06944888085126877,
-0.05340884253382683,
0.08070960640907288,
0.06538545340299606,
0.022819729521870613,
0.04974191263318062,
0.023504365235567093,
-0.031144218519330025,
0.0015335436910390854,
-0.03749624267220497,
0.05547134205698967,
-0.034675609320402145,
-0.007061578333377838,
0.03679164871573448,
-0.043064095079898834,
-0.027129121124744415,
-0.028219126164913177,
0.0031821399461477995,
-0.015819847583770752,
-0.022009143605828285,
-0.020163729786872864,
-0.00854704063385725,
0.01544024609029293,
-0.007930818013846874,
-0.026904962956905365,
0.015766259282827377,
0.0268725473433733,
0.05241406336426735,
-0.056118112057447433,
-0.009984340518712997,
0.0014113100478425622,
0.02313082106411457,
0.008716332726180553,
-0.025841644033789635,
0.044288575649261475,
-0.048787109553813934,
-0.022799724712967873,
0.045669566839933395,
0.09156037122011185,
0.048246804624795914,
0.0005625832127407193,
0.01794264279305935,
-0.09009511768817902,
-0.06684689223766327,
0.04670924320816994,
0.05742805078625679,
-0.039014074951410294,
0.030202094465494156,
0.071441151201725,
0.03469071537256241,
-0.00704233767464757,
0.03844011574983597,
0.003532454604282975,
-0.015970518812537193,
-0.04279293119907379,
0.029101723805069923,
0.06620176136493683,
-0.04682815074920654,
-0.047076430171728134,
0.06996119022369385,
0.0042618256993591785,
0.007132479455322027,
0.028186772018671036,
-0.04146178439259529,
0.03524569049477577,
0.0383756086230278,
-0.027745166793465614,
-0.011802103370428085,
0.0378086231648922,
-0.04169680178165436,
0.0314900167286396,
-0.03569818660616875,
0.018619826063513756,
0.008876130916178226,
-0.018827898427844048,
-0.07174574583768845,
0.005362952593713999,
-0.031727809458971024,
-0.054866451770067215,
0.013953576795756817,
0.0033830313477665186,
-0.01656564697623253,
0.025460636243224144,
-0.04608948156237602,
-0.0424187146127224,
0.007272148039191961,
0.012019927613437176,
-0.020505646243691444,
-0.02274138480424881,
-0.026192892342805862,
-0.07928717881441116,
0.013884282670915127,
-0.03974122181534767,
-0.02630571648478508,
0.015638267621397972,
0.021042264997959137,
-0.01444387249648571,
-0.031775761395692825,
0.001165183843113482,
-0.06134481728076935,
-0.03243165463209152,
0.03411426767706871,
-0.006560139358043671,
0.04190856218338013,
0.009466372430324554,
0.030290311202406883,
0.09868210554122925,
-0.06621070951223373,
-0.04469349980354309,
-0.050710324198007584,
-0.024447623640298843,
-0.044245120137929916,
-0.014472675509750843,
-0.06609837710857391,
-0.0036546913906931877,
0.027869466692209244,
0.018033213913440704,
0.08192873746156693,
0.00928859505802393,
0.0013658471871167421,
-0.052448444068431854,
0.011782691814005375,
-0.09124680608510971,
-0.011488743126392365,
0.04946916550397873,
0.025346949696540833,
-0.05416867882013321,
-0.06838363409042358,
0.09472344070672989,
-0.03586656600236893,
0.0611974373459816,
-0.036323849111795425,
-0.030797705054283142,
0.03431614488363266,
0.0185075756162405,
0.04256710782647133,
0.060262877494096756,
0.0456993468105793,
0.041543636471033096,
0.041831567883491516,
-0.019206566736102104,
-0.011841324158012867,
0.024068649858236313,
0.022847486659884453,
0.05310898646712303,
-0.027959080412983894,
0.016871128231287003,
-0.018659450113773346,
-0.008904868736863136,
-0.039517320692539215,
-0.0034866938367486,
0.014016960747539997,
-0.01194374542683363,
-0.023479975759983063,
-0.0012350990436971188,
-0.04516968876123428,
-0.04969795048236847,
0.01675468124449253,
0.030112698674201965,
-0.04971756413578987,
-0.02682640589773655,
-0.05101750046014786,
0.039585936814546585,
-0.0033265312667936087,
0.050662074238061905,
-0.0029504920821636915,
-0.00859511736780405,
0.014782985672354698,
-0.04653231427073479,
-0.03777609393000603,
0.03960009664297104,
-0.016902361065149307,
-0.011911755427718163,
-0.07879993319511414
] |
<p>Does anyone know where I can find the solution for a spherically symmetric thin shell of timelike matter falling into a Schwarzschild black hole? The matter should be pressureless, so that each particle on the shell follows a radial geodesic. I am interested in the case where the shell is released from rest at a given Schwarzschild radius and time.</p>
<p>I think this is a special case of something called the Bondi-Tolman metric, but I'd rather not try to unpack that solution if there is a simpler way to find what I'm looking for. For null matter the answer is known (and simple), it's the Vaidya metric. </p>
<p>Edit: After thinking about this a little more I think it might be trivial; is it just Schwarzschild inside the shell with the black hole mass $M$, and Schwarzschild outside the shell with mass $M+E$, where $E$ is the energy of the wave?</p>
<p>Edit to the edit: The first edit looks wrong, I don't think it's a solution to Einstein's equations. </p> | g4776 | [
0.06843290477991104,
-0.01713959500193596,
0.01605117693543434,
-0.03396177664399147,
0.016472987830638885,
0.02719554863870144,
-0.026602115482091904,
-0.03836897015571594,
-0.07044685631990433,
-0.006846345495432615,
0.022359704598784447,
-0.027167947962880135,
0.04916065186262131,
0.05054546892642975,
-0.023764438927173615,
-0.00650044297799468,
0.048205506056547165,
-0.012042446061968803,
-0.02020707167685032,
-0.030910547822713852,
0.04674507677555084,
0.0018989667296409607,
0.02587597258388996,
-0.02757427841424942,
0.01096002385020256,
0.030598487704992294,
0.032319650053977966,
-0.010400474071502686,
-0.03033898025751114,
-0.015327438712120056,
-0.0006472792592830956,
0.04455437511205673,
0.028430579230189323,
-0.012284987606108189,
0.04060634598135948,
0.013576488010585308,
0.029289020225405693,
-0.007011090405285358,
0.04234138876199722,
0.008399500511586666,
-0.003854676615446806,
-0.04194365441799164,
0.0072230747900903225,
0.07340403646230698,
0.03496969863772392,
-0.026912478730082512,
0.021478768438100815,
0.037862420082092285,
0.003688495373353362,
-0.005978848785161972,
0.020292824134230614,
0.04959259182214737,
0.0211387537419796,
-0.08102025091648102,
-0.02980557084083557,
0.019400039687752724,
-0.0019186774734407663,
-0.020206183195114136,
0.0027963779866695404,
0.04568155109882355,
-0.022485531866550446,
-0.00842252466827631,
0.019514011219143867,
-0.053345680236816406,
0.03657094016671181,
0.018549393862485886,
-0.058517325669527054,
-0.025745829567313194,
0.008510909043252468,
-0.046579089015722275,
0.02512984909117222,
-0.00945394765585661,
-0.0009963037446141243,
-0.025558607652783394,
-0.036035582423210144,
0.049321986734867096,
0.026488520205020905,
-0.00433874037116766,
0.005991087760776281,
-0.05638379231095314,
-0.03738079592585564,
0.030310599133372307,
-0.006805329583585262,
-0.004578597377985716,
0.07233951985836029,
-0.014061973430216312,
0.04043588414788246,
-0.03691478446125984,
-0.008658457547426224,
0.035050369799137115,
-0.01387405302375555,
0.0017748713726177812,
-0.004996033851057291,
-0.07357650250196457,
0.015865864232182503,
-0.01593068242073059,
-0.02976887673139572,
0.002252254169434309,
-0.03433679789304733,
-0.029416663572192192,
0.00001839948345150333,
-0.026551632210612297,
0.017201313748955727,
-0.06591956317424774,
-0.01419605128467083,
-0.035232044756412506,
-0.01313809771090746,
0.06211737543344498,
0.009191954508423805,
-0.003959040157496929,
0.03435499221086502,
-0.09501416236162186,
-0.011362073011696339,
-0.03745192289352417,
-0.060036249458789825,
-0.0809217318892479,
0.0009099700255319476,
-0.0034404294565320015,
-0.03300189599394798,
0.10047316551208496,
-0.01236835028976202,
0.02303330972790718,
0.002418703632429242,
0.023660629987716675,
-0.017657112330198288,
-0.012423364445567131,
0.0011924483114853501,
-0.04723703861236572,
-0.02085234969854355,
0.00823274441063404,
-0.03383414447307587,
-0.026826487854123116,
0.04150605574250221,
0.00022686745796818286,
-0.05790459364652634,
0.07400760054588318,
-0.05013100430369377,
-0.0038630336057394743,
-0.026746420189738274,
-0.0396045483648777,
-0.02420755662024021,
-0.05498042702674866,
-0.004157490562647581,
0.03307141736149788,
-0.005859376396983862,
0.04227009043097496,
-0.012040060013532639,
0.006551015190780163,
0.07072847336530685,
0.023373333737254143,
-0.008007440716028214,
0.04479404538869858,
0.030756060034036636,
-0.006828607525676489,
-0.02559729665517807,
-0.02344880998134613,
-0.007435813080519438,
0.013340799137949944,
0.006324432324618101,
-0.023180952295660973,
0.04004088416695595,
0.022196177393198013,
0.0074724312871694565,
0.022883620113134384,
-0.04781060665845871,
0.07061102986335754,
-0.029048945754766464,
-0.004600075073540211,
0.039959631860256195,
-0.060536645352840424,
-0.031692251563072205,
-0.005347339436411858,
-0.02851642109453678,
0.033237554132938385,
0.017237897962331772,
-0.038709692656993866,
-0.025323715060949326,
0.0023998222313821316,
0.033792074769735336,
0.010315890423953533,
0.018044227734208107,
-0.04917342588305473,
0.004463271703571081,
-0.014317426830530167,
0.029035083949565887,
-0.04520367085933685,
0.12218534201383591,
0.011250250041484833,
-0.009913409128785133,
-0.006018738728016615,
-0.009656422771513462,
0.000603772175963968,
0.040924571454524994,
0.06290915608406067,
0.02015378698706627,
0.016021734103560448,
0.05318010225892067,
-0.03912927955389023,
-0.009428905323147774,
0.009656700305640697,
0.03147682547569275,
0.01628296636044979,
0.017530255019664764,
0.030760567635297775,
0.035419754683971405,
-0.007735620252788067,
0.012465870007872581,
-0.005023819860070944,
0.014518700540065765,
-0.008492155000567436,
-0.009416934102773666,
0.013058206997811794,
0.018156088888645172,
-0.034132566303014755,
0.011670215055346489,
0.04188665747642517,
-0.035836488008499146,
0.030337106436491013,
-0.032351911067962646,
0.021866150200366974,
-0.04616386070847511,
-0.012393687851727009,
-0.030429843813180923,
-0.052703578025102615,
0.046165622770786285,
0.03200557082891464,
-0.026397692039608955,
0.014013545587658882,
0.024813134223222733,
-0.04344994202256203,
-0.036486752331256866,
0.009218549355864525,
-0.007789372932165861,
-0.0022902570199221373,
0.05183812975883484,
-0.012231633067131042,
-0.05149073526263237,
-0.0489569827914238,
0.002261118497699499,
0.01932975836098194,
0.0041780308820307255,
0.011153237894177437,
-0.05206788331270218,
-0.05973953381180763,
0.06504741311073303,
0.022644251585006714,
0.028140438720583916,
0.025791853666305542,
0.006896197330206633,
-0.02719113789498806,
0.04346437007188797,
-0.027446558699011803,
-0.05116385221481323,
-0.038177769631147385,
0.015423748642206192,
0.022400936111807823,
-0.006311855744570494,
0.0402224138379097,
-0.01694517582654953,
-0.07192811369895935,
-0.007038034498691559,
-0.041532885283231735,
0.03161463886499405,
0.06281832605600357,
-0.042323511093854904,
0.04375092685222626,
-0.07470618933439255,
0.005432291887700558,
0.002638801233842969,
0.02174394391477108,
-0.001726718619465828,
0.029067741706967354,
0.03759908303618431,
0.05300850048661232,
-0.013724097050726414,
-0.0038590983022004366,
0.03726651147007942,
0.04621318355202675,
0.03565939888358116,
0.03717527166008949,
-0.018288705497980118,
-0.009778473526239395,
-0.02890174463391304,
0.03610797971487045,
0.0019252467900514603,
-0.08814045786857605,
0.01272657886147499,
0.03292443975806236,
0.03733082115650177,
-0.013282652013003826,
-0.00039021798875182867,
0.051181674003601074,
0.04967186972498894,
0.07481060177087784,
0.030262533575296402,
0.11770077049732208,
0.015791667625308037,
0.014313757419586182,
-0.02056880109012127,
-0.0007952715968713164,
-0.041185323148965836,
-0.029834864661097527,
0.006608875934034586,
-0.0037319702096283436,
0.0016339430585503578,
0.014679977670311928,
-0.019530583173036575,
-0.01861143670976162,
-0.012767002917826176,
-0.0064713796600699425,
0.08298441022634506,
0.0006408688495866954,
0.058408673852682114,
0.04715757817029953,
-0.06292826682329178,
0.013844630680978298,
-0.05661415681242943,
-0.0469779372215271,
0.04323999583721161,
0.014156450517475605,
-0.004104147665202618,
0.031809352338314056,
0.011069746688008308,
0.008746671490371227,
0.0366060808300972,
0.002019149949774146,
-0.049114126712083817,
-0.005545630119740963,
-0.06732628494501114,
0.007184470072388649,
-0.040745463222265244,
-0.05570824816823006,
0.07167526334524155,
0.006486716214567423,
-0.014763065613806248,
-0.010282689705491066,
-0.021822238340973854,
0.030417433008551598,
0.05528535321354866,
0.02918868139386177,
0.032092783600091934,
-0.03534222021698952,
-0.0007131652091629803,
0.027270082384347916,
-0.0575319342315197,
0.00913199596107006,
0.030989233404397964,
-0.05863402783870697,
-0.00794904213398695,
-0.008841494098305702,
0.0136080551892519,
0.048265136778354645,
0.026395471766591072,
-0.01802629791200161,
0.03513538837432861,
0.03409615904092789,
0.008275586180388927,
-0.018876509740948677,
0.07360091805458069,
-0.00588883925229311,
0.006901205517351627,
-0.07436562329530716,
-0.03662816807627678,
-0.006916663143783808,
0.03423425182700157,
-0.091483935713768,
0.047556761652231216,
-0.06964778155088425,
0.01367503684014082,
-0.012263818643987179,
0.038779642432928085,
-0.006374272517859936,
0.022003429010510445,
0.02353575825691223,
-0.030728546902537346,
-0.06875275820493698,
-0.05171925202012062,
0.015722239390015602,
-0.01656998321413994,
-0.04949858784675598,
-0.03277711197733879,
-0.012299579568207264,
0.006681713275611401,
0.028162823989987373,
0.027247441932559013,
-0.00742917787283659,
-0.0780256986618042,
-0.03703102469444275,
0.010292795486748219,
-0.0402989387512207,
0.0073295519687235355,
-0.044620826840400696,
0.00951277744024992,
-0.02904469333589077,
-0.02354039065539837,
-0.01793755404651165,
0.012245223857462406,
-0.025992143899202347,
-0.03320104256272316,
0.006953654810786247,
0.052777986973524094,
0.00509817898273468,
0.014418533071875572,
0.008915895596146584,
0.01873212493956089,
0.029508786275982857,
0.018806057050824165,
-0.026618540287017822,
0.001729730167426169,
-0.059459488838911057,
0.022032903507351875,
-0.05505391210317612,
-0.012395384721457958,
-0.009474825114011765,
0.0432128943502903,
-0.010103789158165455,
0.028867339715361595,
0.048028551042079926,
-0.028276147320866585,
0.015930458903312683,
-0.03733908385038376,
-0.06092580407857895,
0.007016397546976805,
-0.014147053472697735,
-0.01247536949813366,
-0.0474875271320343,
0.0321732796728611,
0.030536692589521408,
-0.01694171503186226,
0.07729017734527588,
-0.03429093956947327,
-0.04487127810716629,
-0.0012935553677380085,
0.014527699910104275,
-0.04061055928468704,
0.00869519542902708,
-0.010643871501088142,
-0.03766188025474548,
-0.028346380218863487,
0.03581559285521507,
0.006439014803618193,
-0.02538251504302025,
-0.004091411363333464,
-0.019475288689136505,
-0.04514560103416443,
0.08640267699956894,
0.00818188488483429,
-0.006297954358160496,
0.016415134072303772,
-0.018613915890455246,
-0.030070332810282707,
0.006837315391749144,
0.02356860600411892,
-0.04125668853521347,
-0.07324047386646271,
0.010078280232846737,
-0.024946114048361778,
0.05970758572220802,
0.044942423701286316,
0.012584059499204159,
-0.032194945961236954,
-0.016698140650987625,
0.009196325205266476,
0.017381884157657623,
-0.046488258987665176,
-0.08287636935710907,
-0.050446391105651855,
0.03847144544124603,
0.016559362411499023,
-0.015323275700211525,
-0.03108590841293335,
0.04217812791466713,
0.027067862451076508,
-0.02421608380973339,
-0.05957780033349991,
0.07433953136205673,
-0.0041166129522025585,
-0.05772025138139725,
0.01622088998556137,
-0.03822009637951851,
-0.036452800035476685,
-0.026725519448518753,
0.05767561495304108,
-0.004686417058110237,
-0.002840090775862336,
0.03812064975500107,
-0.01965387724339962,
0.01766454614698887,
0.0005168455536477268,
-0.04852179065346718,
0.02825561724603176,
-0.051302846521139145,
0.000968220760114491,
0.019135266542434692,
0.028207099065184593,
0.04550689086318016,
0.04080666974186897,
-0.013773920014500618,
-0.02431744709610939,
0.04303598403930664,
-0.08214262127876282,
0.013039040379226208,
0.033715587109327316,
0.04085240885615349,
-0.05387956276535988,
0.01165296696126461,
-0.015609548427164555,
0.049157075583934784,
0.005130165722221136,
0.037337809801101685,
0.018694264814257622,
-0.024256227537989616,
-0.025481337681412697,
0.0317811481654644,
-0.08580782264471054,
-0.036499857902526855,
-0.015322939492762089,
0.04672560095787048,
0.00744636869058013,
-0.020113741979002953,
-0.06133206561207771,
0.027608448639512062,
0.028751596808433533,
0.05338083952665329,
0.02142259106040001,
0.02195042185485363,
-0.0669357180595398,
0.014737998135387897,
0.005696667358279228,
-0.010282550007104874,
0.029434597119688988,
-0.030391033738851547,
0.04816696047782898,
-0.024950586259365082,
0.038840003311634064,
0.007023775018751621,
-0.002965505002066493,
0.053355924785137177,
0.05532148852944374,
-0.0002337773476028815,
-0.0003637801855802536,
-0.04772772267460823,
0.08195443451404572,
0.015164665877819061,
0.03865201771259308,
0.010857287794351578,
-0.032319117337465286,
0.06956575065851212,
0.03874869644641876,
-0.024097397923469543,
-0.07619404047727585,
0.05085383355617523,
-0.03227515518665314,
0.06722458451986313,
0.002127232728525996,
0.02946465089917183,
0.015954703092575073,
-0.08836215734481812,
-0.048421137034893036,
-0.04836856946349144,
-0.031340550631284714,
-0.004484199918806553,
-0.0323089174926281,
0.011097588576376438,
-0.02407715655863285,
-0.020563945174217224,
-0.054159536957740784,
-0.014035428874194622,
0.07966208457946777,
0.05163291096687317,
-0.03925153613090515,
0.02318473346531391,
0.001842960831709206,
0.03694631904363632,
0.031800225377082825,
-0.005932308267802,
0.001683039590716362,
-0.031299155205488205,
0.00013634904462378472,
0.010129125788807869,
0.020753394812345505,
-0.005487401969730854,
0.04734816774725914,
-0.04182136431336403,
0.0050667040050029755,
0.0064541045576334,
-0.04374301806092262,
-0.018025442957878113,
0.03133644163608551,
-0.003685249714180827,
-0.009150023572146893,
-0.023816728964447975,
-0.036867424845695496,
0.015329977497458458,
-0.02813035249710083,
0.037172261625528336,
-0.004686636384576559,
-0.018252480775117874,
-0.03374588117003441,
0.010382434353232384,
-0.0720936506986618,
0.034431081265211105,
0.022084061056375504,
0.06380003690719604,
-0.034756116569042206,
0.004847933538258076,
-0.030097199603915215,
0.009338371455669403,
0.028122790157794952,
-0.006965020205825567,
0.017346182838082314,
0.053839344531297684,
-0.048033636063337326,
0.013283905573189259,
0.022379538044333458,
-0.013296137563884258,
0.015040827915072441,
0.005339458584785461,
-0.031060362234711647,
-0.09043966233730316,
0.04505368694663048,
0.05442596599459648,
-0.03326132148504257,
-0.07532619684934616,
0.014395591802895069,
0.02683945558965206,
-0.017849396914243698,
0.003260197816416621,
0.006357874255627394,
0.03885185718536377,
0.05028460919857025,
-0.0028514491859823465,
-0.009450971148908138,
0.038930851966142654,
-0.011520357802510262,
0.03182109817862511,
-0.00013363000471144915,
0.03490014001727104,
0.047489043325185776,
0.011159272864460945,
0.03076213225722313,
-0.021458197385072708,
0.024843450635671616,
0.04649464040994644,
-0.09294884651899338,
0.06924264878034592,
0.009096061810851097,
0.017211932688951492,
-0.05799619480967522,
0.002283360343426466,
0.0260578952729702,
-0.01698746532201767,
-0.0494898222386837,
-0.006983418948948383,
-0.029584210366010666,
-0.05898984894156456,
-0.03366425260901451,
0.004480115137994289,
0.0003276954812463373,
-0.07051768898963928,
0.017960306257009506,
-0.01014805119484663,
-0.003173781791701913,
-0.031103648245334625,
-0.04242909699678421,
0.051017213612794876,
0.014581878669559956,
-0.02226700447499752,
0.01754702813923359,
-0.017049800604581833,
0.008269811980426311,
0.02434120699763298,
-0.06523285061120987,
-0.0011844504624605179,
-0.06775158643722534,
0.008715256117284298,
0.047199398279190063,
0.05233330652117729,
-0.02440919168293476,
-0.007415805011987686,
0.013575125485658646,
0.02540074661374092,
-0.044862113893032074,
0.0399022251367569,
-0.047797344624996185,
0.02421439252793789,
0.02892201393842697,
0.03182997554540634,
-0.03240833431482315,
0.046814244240522385,
0.043605197221040726,
0.12331360578536987,
-0.05120878666639328,
-0.007132978178560734,
-0.0073530119843780994,
-0.04318714886903763,
0.06215635687112808,
0.05334871634840965,
0.018765637651085854,
-0.017760032787919044,
-0.03686750307679176,
0.04204263538122177,
-0.018346242606639862,
0.00883449800312519,
-0.0014842122327536345,
-0.002337345853447914,
-0.09372901171445847,
-0.02141786552965641,
-0.004428976681083441,
0.05178219452500343,
0.023123368620872498,
-0.0160524882376194,
0.006989408750087023,
-0.022582346573472023,
0.026572592556476593,
-0.017667708918452263,
-0.03560271114110947,
0.062354519963264465,
-0.015406125225126743,
-0.06173161044716835,
-0.017667362466454506,
0.030053500086069107,
0.020119285210967064,
-0.032792940735816956,
0.018538082018494606,
-0.0031078029423952103,
-0.05372492969036102,
0.003571879817172885,
0.007930669002234936,
-0.03940444439649582,
-0.015343918465077877,
-0.012969267554581165,
0.006004408933222294,
0.036791298538446426,
0.022130722180008888,
-0.009943651035428047,
-0.022506793960928917,
-0.0004963912069797516,
0.013752330094575882,
-0.0031739515252411366,
0.04219415411353111,
-0.032175350934267044,
-0.043283309787511826,
-0.009537137113511562,
0.04421099275350571,
-0.012222271412611008,
-0.009401158429682255,
0.04557742550969124,
0.05391150340437889,
-0.04973288252949715,
0.03468840569257736,
0.015156352892518044,
0.024039199575781822,
0.020726798102259636,
-0.013289956375956535,
-0.0997360497713089,
0.03088296391069889,
-0.057227723300457,
-0.0227193720638752,
0.016637517139315605,
-0.03464314714074135,
-0.02785184048116207,
-0.024092013016343117,
0.031955402344465256,
0.028773941099643707,
0.008089808747172356,
0.06470126658678055,
0.0378081388771534
] |
<p>My question is little bit philosophical.
I would like to explain my ideas with a 2 dimensional universe model. </p>
<p>If we had lived in 2 dimensional universe like a plane, What could we observe when seeing a 3d object? </p>
<p>For example:
If a square pyramid that is inside full of material comes to the plane universe in right angle, what could the people who live in 2d universe observe? Firstly, we could see small square and slowly it would enlarge and then it would dissappear suddenly. If the scientists who live in the 2d universe observed such event , All scientists could get shocked and they could check their physics formulas because energy is not conversed in that event. They had believed that Energy is conserved and nobody could create energy from nothing and finally they could understand that total observed universe energy can be much more what they calculated with their formulas.</p>
<p>My questions:</p>
<ol>
<li><p>What could we see a 4d pyramid comes to our 3d universe? is it correct that Firstly we would see small cube and it would enlarge and then suddenly disappears?</p></li>
<li><p>Dark matter and Dark energy is related with such ideas? <a href="http://map.gsfc.nasa.gov/universe/uni_matter.html" rel="nofollow">http://map.gsfc.nasa.gov/universe/uni_matter.html</a></p></li>
<li><p>I know we do not observe such strange events till now but maybe scientists can get some results during micro experiments. Is there any such experimental results at least in micro universe (atomic level experiments in quantum mechanics)?</p></li>
</ol>
<p>Sorry for your time if it was asked before.</p> | g4777 | [
0.017691947519779205,
0.019707966595888138,
0.010592176578938961,
-0.026856297627091408,
-0.0011385100660845637,
0.06351469457149506,
-0.012595889158546925,
0.020167509093880653,
-0.04377872124314308,
-0.07592413574457169,
0.04584978148341179,
0.002822337904945016,
0.048472076654434204,
0.004515416454523802,
0.03030339814722538,
0.008774284273386002,
-0.007635339628905058,
-0.05578699707984924,
-0.019439807161688805,
0.017792239785194397,
-0.007047599647194147,
-0.008322970941662788,
0.00494074821472168,
-0.03651253879070282,
-0.028268152847886086,
-0.014879319816827774,
0.03104550950229168,
0.018078424036502838,
-0.0706552192568779,
-0.025667034089565277,
-0.0015608691610395908,
-0.05900187790393829,
0.049355074763298035,
-0.07332810759544373,
-0.024542542174458504,
0.002605186076834798,
0.05483347550034523,
0.021886982023715973,
0.02004171907901764,
-0.005582013167440891,
-0.043170686811208725,
-0.013311352580785751,
-0.0417785607278347,
-0.017780736088752747,
0.06437825411558151,
0.018944798037409782,
-0.015353023074567318,
-0.013129415921866894,
0.06600981205701828,
-0.061179377138614655,
-0.028856558725237846,
0.02100074291229248,
0.06499823927879333,
0.04960982874035835,
0.028896329924464226,
0.05943666771054268,
-0.004682136699557304,
-0.05143899843096733,
0.10202937573194504,
-0.005139938089996576,
-0.04353371262550354,
0.028276817873120308,
0.05144035071134567,
0.019105546176433563,
0.04210672900080681,
0.00025720824487507343,
-0.0641556978225708,
0.00481530511751771,
-0.0002897956583183259,
-0.0109096709638834,
0.061392053961753845,
-0.03068077564239502,
-0.03885357454419136,
-0.027719730511307716,
0.02530253864824772,
0.04717947915196419,
0.036369603127241135,
0.010573630221188068,
-0.021665222942829132,
0.020647525787353516,
-0.07756398618221283,
0.01073573250323534,
-0.00031543796649202704,
-0.026751717552542686,
0.08641538769006729,
-0.0069185043685138226,
-0.00005609351137536578,
-0.01885647512972355,
0.03244085609912872,
0.017413638532161713,
-0.017567021772265434,
0.0066145360469818115,
0.06016203761100769,
0.032754555344581604,
0.0007731493678875268,
-0.0043524508364498615,
-0.024520909413695335,
0.027472129091620445,
-0.03268907219171524,
0.042506143450737,
-0.04628052935004234,
-0.028445256873965263,
0.06114257127046585,
-0.01148880086839199,
0.021693799644708633,
-0.01206483319401741,
-0.001758390455506742,
0.0318562313914299,
-0.00004646516390494071,
0.005217721685767174,
-0.011563707143068314,
-0.0038600934203714132,
-0.06030803918838501,
0.015899498015642166,
0.00006984110223129392,
-0.01598401740193367,
0.059500016272068024,
-0.06190018728375435,
0.025082571431994438,
0.0525757297873497,
0.02665526047348976,
0.06275288015604019,
-0.0009563060011714697,
0.022849686443805695,
0.0018405525479465723,
0.0006936003919690847,
-0.030878383666276932,
-0.021432798355817795,
-0.01079476997256279,
-0.014447150751948357,
0.04296805337071419,
-0.0010354595724493265,
-0.02737252041697502,
0.046075791120529175,
0.00034108266117982566,
0.02515186183154583,
-0.036725156009197235,
-0.0032052595634013414,
0.03289297968149185,
-0.0018631670391187072,
-0.010025110095739365,
-0.05162859708070755,
-0.036004092544317245,
-0.021158389747142792,
-0.005674557760357857,
-0.028678186237812042,
0.01756579987704754,
0.011874904856085777,
-0.027530239894986153,
0.003752961987629533,
0.019437424838542938,
0.09057995676994324,
0.03863706812262535,
-0.05375469848513603,
-0.020751304924488068,
0.03655925393104553,
-0.040747564285993576,
-0.020345672965049744,
-0.008234988898038864,
-0.04458026587963104,
0.0597117580473423,
-0.0136577058583498,
-0.020548628643155098,
0.026721781119704247,
-0.05601353943347931,
0.02447694167494774,
0.04749765247106552,
-0.11798493564128876,
0.04542979225516319,
-0.023254426196217537,
-0.05471928045153618,
0.02112337201833725,
0.02347024343907833,
0.05214015021920204,
-0.026520203799009323,
0.045880358666181564,
0.006215356756001711,
-0.032566919922828674,
-0.008188481442630291,
0.02253832295536995,
-0.052813395857810974,
-0.024045832455158234,
-0.0017805417301133275,
-0.012289008125662804,
0.033231668174266815,
-0.03262103721499443,
0.030811510980129242,
0.06942560523748398,
0.0447806641459465,
-0.0015296973288059235,
-0.033616770058870316,
-0.06987390667200089,
-0.010576815344393253,
-0.024033768102526665,
0.0048095970414578915,
-0.03899297118186951,
0.05175714194774628,
0.011617641896009445,
-0.04121808707714081,
0.001438768464140594,
0.014924832619726658,
-0.002196874003857374,
0.03489610180258751,
0.02976234070956707,
0.04817844182252884,
0.004830572754144669,
-0.007792029529809952,
0.02235104888677597,
-0.02047153003513813,
-0.0077689168974757195,
0.03932614251971245,
-0.020188668742775917,
0.028278551995754242,
0.02675306797027588,
-0.018024055287241936,
0.038112565875053406,
0.03490985184907913,
0.006007657386362553,
-0.03252566605806351,
0.03855731338262558,
0.005281193647533655,
-0.05882817506790161,
0.027309508994221687,
-0.01941673830151558,
0.04531378671526909,
0.02398139052093029,
-0.08565454185009003,
-0.039533838629722595,
0.02494354546070099,
0.026269761845469475,
-0.06238361448049545,
0.010678550228476524,
0.021295232698321342,
0.0037836050614714622,
0.044392190873622894,
0.024523494765162468,
-0.033958401530981064,
-0.010499974712729454,
0.01853484846651554,
-0.014205384999513626,
0.02367246337234974,
-0.009480937384068966,
-0.06902814656496048,
-0.024530883878469467,
0.060688041150569916,
-0.08924667537212372,
0.0258156917989254,
0.030908312648534775,
0.038547974079847336,
-0.007773746270686388,
0.04263487830758095,
-0.0007078798371367157,
-0.04138915613293648,
-0.018826860934495926,
-0.020324693992733955,
-0.05036604031920433,
-0.02258765697479248,
0.10299315303564072,
-0.022726137191057205,
-0.09364764392375946,
0.0638057217001915,
-0.02017529308795929,
0.0013665100559592247,
0.042739879339933395,
-0.02680087275803089,
-0.05061279982328415,
-0.042928267270326614,
0.006074369885027409,
-0.04431028291583061,
0.02120727114379406,
-0.0304145198315382,
0.01602223515510559,
-0.04400515556335449,
0.036667950451374054,
-0.011250421404838562,
0.03437844663858414,
0.006089013069868088,
-0.04060914367437363,
0.0398208424448967,
-0.011539281345903873,
0.00866418331861496,
0.025769300758838654,
-0.06590742617845535,
0.04724607616662979,
0.05309831351041794,
-0.004705006256699562,
-0.07708136737346649,
-0.04030808433890343,
0.0015490740770474076,
-0.02195008285343647,
-0.030091961845755577,
0.01335607748478651,
-0.03314926475286484,
0.012965016067028046,
-0.057403720915317535,
-0.019373608753085136,
-0.023840080946683884,
-0.005271919537335634,
-0.015524830669164658,
0.03362751752138138,
-0.006098726764321327,
-0.077176034450531,
0.004422809462994337,
-0.0015720578376203775,
-0.02965722791850567,
0.04188463091850281,
0.016802286729216576,
0.004405340179800987,
0.036788031458854675,
-0.055645979940891266,
-0.02922651916742325,
0.026535898447036743,
-0.003680986585095525,
-0.003598549170419574,
-0.01322279404848814,
0.008443727158010006,
0.006965409964323044,
0.05725036934018135,
0.0066460357047617435,
-0.004889513831585646,
0.07064426690340042,
0.01562855765223503,
-0.0455988273024559,
-0.013931755907833576,
0.038805220276117325,
0.006228078156709671,
-0.021884290501475334,
-0.00924487505108118,
-0.019061023369431496,
-0.02952577918767929,
-0.0017982717836275697,
-0.018517697229981422,
-0.016574574634432793,
0.0021249933633953333,
-0.023844273760914803,
-0.004313794896006584,
-0.08172569423913956,
0.015789782628417015,
0.06398700177669525,
0.0037534283474087715,
0.0019615953788161278,
-0.002291809068992734,
-0.028747450560331345,
-0.04294750466942787,
0.04230474680662155,
-0.015482165850698948,
-0.02079351432621479,
-0.005370719823986292,
-0.009003314189612865,
-0.035043973475694656,
0.07681206613779068,
0.028142819181084633,
0.00046121422201395035,
-0.03702500835061073,
0.027151664718985558,
0.056226253509521484,
0.026338284835219383,
0.008723282255232334,
0.011917516589164734,
-0.024439165368676186,
-0.04035194218158722,
-0.034374624490737915,
0.04502185806632042,
0.0004967673448845744,
-0.013795210979878902,
-0.010316945612430573,
0.009286550804972649,
0.017277006059885025,
0.04231662303209305,
-0.008118592202663422,
0.04111120104789734,
-0.00038970253081060946,
-0.06099184229969978,
-0.052679985761642456,
0.033933743834495544,
0.019458400085568428,
0.015922602266073227,
-0.00981135480105877,
-0.03196655586361885,
-0.006679186597466469,
0.034675851464271545,
0.029513470828533173,
0.03390120714902878,
0.020154273137450218,
0.012570015154778957,
-0.014348247088491917,
-0.004396582487970591,
-0.05932425707578659,
-0.06675542891025543,
-0.034802619367837906,
0.0315195694565773,
-0.017618896439671516,
-0.014459365047514439,
-0.01737949065864086,
0.01945355348289013,
-0.06336767971515656,
-0.0064860195852816105,
0.03842925280332565,
-0.0005818363861180842,
0.0005799647769890726,
0.013646543025970459,
0.016648052260279655,
0.007499889470636845,
0.0015184652293100953,
-0.019996505230665207,
0.01832583360373974,
-0.0006098118028603494,
0.001966924639418721,
0.02002745494246483,
0.017267145216464996,
0.02366919443011284,
0.023198960348963737,
0.025475384667515755,
-0.0184114221483469,
0.002323295921087265,
-0.025717226788401604,
0.026154281571507454,
-0.021082930266857147,
0.008082068525254726,
0.024799201637506485,
0.05437900871038437,
0.06496930122375488,
-0.02880534902215004,
0.017968550324440002,
-0.006240020040422678,
0.025353608652949333,
0.010938071645796299,
-0.03164389729499817,
-0.09468905627727509,
0.027740605175495148,
0.03497052937746048,
0.021156957373023033,
-0.003452081000432372,
0.06112357974052429,
-0.006720123812556267,
-0.04862252250313759,
-0.03420412912964821,
0.04226402938365936,
-0.04541908949613571,
0.02951151691377163,
0.017585095018148422,
0.027869315817952156,
0.0013354744296520948,
0.0014253805857151747,
0.045945119112730026,
0.048756759613752365,
-0.04573475569486618,
-0.007436131592839956,
0.015412251465022564,
0.026363395154476166,
-0.062083907425403595,
0.051013946533203125,
0.018795017153024673,
-0.02936622127890587,
0.04049571231007576,
0.015122991986572742,
-0.0345008485019207,
0.06908099353313446,
-0.019027693197131157,
0.05498405545949936,
-0.06859636306762695,
0.00881692674010992,
-0.007291600573807955,
0.010501316748559475,
-0.005185355897992849,
-0.04975613206624985,
-0.09279549866914749,
0.004645554348826408,
-0.07127375155687332,
-0.013186573050916195,
-0.057341936975717545,
-0.01199458260089159,
0.0023838242050260305,
0.033970873802900314,
-0.03610001504421234,
-0.004377324134111404,
-0.0275117214769125,
-0.0014516853261739016,
0.04184657707810402,
-0.017672372981905937,
0.025157425552606583,
0.019125472754240036,
0.06000274419784546,
-0.019464338198304176,
0.047505855560302734,
0.017827901989221573,
-0.026791425421833992,
-0.0009781536646187305,
-0.02431931160390377,
-0.03887608274817467,
-0.018938560038805008,
-0.02261653169989586,
0.017383702099323273,
-0.010787388309836388,
-0.0842292308807373,
0.024316616356372833,
0.011462245136499405,
-0.03682088851928711,
-0.015495737083256245,
-0.0010449119145050645,
0.002677957294508815,
-0.010038583539426327,
0.019542019814252853,
-0.04393940791487694,
0.006246575620025396,
0.009739755652844906,
0.05243559181690216,
-0.11038269847631454,
0.013617435470223427,
0.03507573902606964,
-0.05756958946585655,
-0.04283022880554199,
0.008460796438157558,
0.06602206826210022,
-0.012640556320548058,
-0.03590986505150795,
0.034204889088869095,
0.01185531821101904,
-0.01850910857319832,
0.009676627814769745,
-0.06574275344610214,
0.002607530914247036,
0.06314398348331451,
-0.022968260571360588,
0.05472714826464653,
0.011518541723489761,
0.0026375786401331425,
0.07129180431365967,
0.058993637561798096,
0.030281443148851395,
-0.0005578125128522515,
0.03394770994782448,
-0.01408778503537178,
0.0168707687407732,
-0.009071006439626217,
-0.012167554348707199,
0.011271389201283455,
0.01200857199728489,
0.051767781376838684,
0.015533576719462872,
-0.02137661911547184,
-0.004823192022740841,
0.003957167733460665,
0.04135337844491005,
-0.015201047994196415,
-0.042234908789396286,
-0.005100175738334656,
0.03608827665448189,
0.07733459770679474,
0.0019489008700475097,
-0.030576156452298164,
0.043252136558294296,
0.025954995304346085,
0.09715019911527634,
-0.030285965651273727,
0.02058686502277851,
-0.048940643668174744,
-0.01336869690567255,
-0.03859945386648178,
-0.015833977609872818,
-0.03398964926600456,
0.07586728036403656,
0.009008312597870827,
-0.030399484559893608,
-0.029283668845891953,
-0.048140645027160645,
0.037547070533037186,
-0.013804959133267403,
0.031728677451610565,
0.010117992758750916,
-0.00044775925925932825,
0.01800762303173542,
0.015564622357487679,
0.034261588007211685,
0.017391527071595192,
-0.035360559821128845,
0.06710583716630936,
-0.02277304418385029,
-0.019749099388718605,
-0.02923263981938362,
-0.010949216783046722,
0.025008657947182655,
0.058718375861644745,
0.016286039724946022,
0.034214459359645844,
0.054349351674318314,
0.007903628051280975,
-0.01779724657535553,
-0.014574783854186535,
-0.0574122816324234,
0.002781612565740943,
0.03054838441312313,
0.018765922635793686,
0.0222660880535841,
-0.04000277817249298,
-0.051101792603731155,
-0.013554273173213005,
0.005971936043351889,
-0.062095023691654205,
0.015672262758016586,
-0.030297981575131416,
-0.06444995105266571,
-0.040944214910268784,
-0.044566810131073,
0.026249801740050316,
0.010532399639487267,
-0.052212897688150406,
-0.027871785685420036,
0.07677986472845078,
0.013631153851747513,
-0.021313326433300972,
-0.012616625986993313,
-0.010611842386424541,
0.030328599736094475,
-0.0075915795750916,
-0.08590351045131683,
0.03362127020955086,
-0.054108671844005585,
0.04051906615495682,
-0.034973978996276855,
0.01927989535033703,
-0.023882515728473663,
0.0359380729496479,
-0.04854763671755791,
0.02912639081478119,
-0.0026154988445341587,
-0.07905282080173492,
0.05148475617170334,
0.09558405727148056,
0.08754241466522217,
-0.01442673895508051,
0.007017252966761589,
0.04699663817882538,
0.08060864359140396,
0.002885273890569806,
0.013933604583144188,
-0.026305003091692924,
0.05440192669630051,
0.00934607069939375,
0.013245879672467709,
0.03018675558269024,
-0.00443675834685564,
0.038561418652534485,
-0.0018376822117716074,
-0.00431715277954936,
-0.017360875383019447,
0.01474447175860405,
0.02126503176987171,
-0.0323784202337265,
-0.03501944988965988,
-0.005480614025145769,
-0.04869841784238815,
-0.013587613590061665,
-0.03062981553375721,
-0.049551308155059814,
-0.00832186546176672,
0.0076131755486130714,
-0.005646670702844858,
-0.027781682088971138,
-0.05398610606789589,
-0.02598775364458561,
0.040886469185352325,
-0.021893145516514778,
-0.020660022273659706,
-0.05815531685948372,
0.004965552594512701,
-0.015627775341272354,
-0.052845437079668045,
-0.019687289372086525,
0.0036434608045965433,
-0.024639533832669258,
-0.032740626484155655,
-0.07598111778497696,
0.015987664461135864,
-0.04134673625230789,
-0.04971572384238243,
0.0032400283962488174,
0.005385297816246748,
0.05171535536646843,
-0.013458682224154472,
0.04026571288704872,
0.06238970905542374,
0.04257024824619293,
0.023956142365932465,
-0.04668957740068436,
0.025522993877530098,
0.011571591719985008,
-0.011421787552535534,
-0.043754275888204575,
-0.035816267132759094,
0.013639003038406372,
-0.023055491968989372,
0.023408647626638412,
-0.04253465309739113,
-0.002103209961205721,
0.0110954400151968,
0.03119625337421894,
0.06127427518367767,
-0.026593293994665146,
-0.026779821142554283,
0.0038778677117079496,
-0.00008942950807977468,
0.003933515399694443,
-0.015310162678360939,
0.016056042164564133,
-0.06005031615495682,
0.023205189034342766,
0.0006192790460772812,
-0.0330396331846714,
-0.00735949631780386,
0.0003655502514448017,
0.07477186620235443,
0.03237754851579666,
0.032283440232276917,
0.08225744962692261,
0.022401222959160805,
-0.03726314380764961,
0.005139011424034834,
0.04817413538694382,
-0.02733779512345791,
-0.09556575119495392,
-0.02819325029850006,
-0.044431544840335846,
-0.02645811066031456,
0.040721725672483444,
0.011055434122681618,
-0.011419577524065971,
-0.028380753472447395,
0.0009256982593797147,
0.04604940488934517,
0.023409174755215645,
0.07199752330780029,
0.022069541737437248,
-0.036781735718250275,
-0.02382068894803524,
0.03258504346013069,
0.023540275171399117,
0.013365332037210464,
-0.02533169649541378,
-0.053405873477458954,
0.008883518166840076,
0.0221699271351099,
0.016909155994653702,
-0.01273344922810793,
0.005594171583652496,
-0.040250904858112335,
-0.07023978978395462,
0.001231522997841239,
0.06886139512062073,
-0.032547056674957275,
-0.02951166406273842,
-0.041683852672576904,
-0.027376720681786537,
0.04642451927065849,
0.011749892495572567,
-0.03759030997753143,
0.008569653145968914,
-0.0065918113104999065,
-0.0876779854297638,
-0.042262014001607895,
0.02412782981991768,
0.04916409030556679,
-0.010098744183778763,
0.054465778172016144,
0.007148542907088995,
-0.030590735375881195,
-0.004563212860375643,
0.043707944452762604
] |
<p>I would like to estimate the Maximum power/ tension that can be, between the sky diving guider and the "tourist".</p>
<p>In this <a href="http://skykef.co.il/upload2/Image/Edit%202.jpg" rel="nofollow">picture</a> what the max tenstion will be, I think it is maximum when the parachute is opened.</p> | g4778 | [
0.0018271311419084668,
0.03472069278359413,
-0.017476988956332207,
0.03488318249583244,
-0.0370236411690712,
0.031005891039967537,
-0.001690759789198637,
0.01527728047221899,
-0.045606549829244614,
0.0308102834969759,
-0.021362395957112312,
-0.08039896190166473,
-0.05109424516558647,
0.002794853877276182,
0.04252583906054497,
0.06471336632966995,
0.04136345908045769,
-0.08610697090625763,
0.007080533541738987,
-0.040776610374450684,
-0.0020648555364459753,
-0.034002747386693954,
-0.0429321825504303,
-0.01306909415870905,
-0.01132777240127325,
0.011811730451881886,
-0.009246418252587318,
-0.0025730296038091183,
-0.10625430941581726,
-0.010203875601291656,
0.030987972393631935,
-0.021772483363747597,
-0.018469838425517082,
-0.006257527973502874,
-0.05343678966164589,
-0.013321555219590664,
0.002453260123729706,
0.015251892618834972,
-0.07477093487977982,
0.01597544550895691,
-0.018316466361284256,
-0.0402102991938591,
0.007352597080171108,
0.004331232514232397,
-0.029874414205551147,
-0.05623151361942291,
0.008328747004270554,
0.030446941033005714,
-0.03900287672877312,
0.01767835207283497,
-0.04425501823425293,
0.04733286052942276,
-0.019112367182970047,
0.0019389927620068192,
-0.028315013274550438,
-0.006030055694282055,
0.03918988257646561,
-0.017670297995209694,
0.023134099319577217,
0.023347407579421997,
-0.044780097901821136,
-0.01743835210800171,
-0.016616297885775566,
0.01325142104178667,
0.003844632301479578,
0.014731529168784618,
-0.05553489178419113,
-0.03558952361345291,
0.07601671665906906,
0.030116993933916092,
0.013597247190773487,
-0.018422622233629227,
-0.027424609288573265,
0.038068510591983795,
-0.08902442455291748,
-0.02902079001069069,
-0.025202034041285515,
0.027613988146185875,
0.00013193232007324696,
0.026631660759449005,
0.0163413193076849,
-0.0008150949142873287,
-0.04466741904616356,
-0.05377709120512009,
0.009548038244247437,
-0.006506512872874737,
0.033762987703084946,
-0.05217129737138748,
-0.014088773168623447,
0.022971997037529945,
0.029328450560569763,
-0.0008640129235573113,
0.0815347284078598,
0.007056545000523329,
0.02814295142889023,
-0.011794112622737885,
0.0115177221596241,
0.023851854726672173,
-0.022066248580813408,
-0.028316954150795937,
-0.028468424454331398,
-0.02473621442914009,
-0.0029264381155371666,
0.05163036659359932,
-0.08601655811071396,
-0.030919929966330528,
0.07218585163354874,
-0.04654056951403618,
0.031683921813964844,
-0.0359700471162796,
0.015001815743744373,
0.0025549407582730055,
-0.034926947206258774,
-0.007139118853956461,
-0.05259782448410988,
-0.07777132093906403,
-0.024173544719815254,
0.0054620844312012196,
-0.014741828665137291,
0.010897457599639893,
0.04789663478732109,
0.028003228828310966,
-0.04146687313914299,
0.023009151220321655,
0.03393271565437317,
0.03076566755771637,
0.009575157426297665,
0.04503507912158966,
-0.015470925718545914,
-0.07406007498502731,
-0.00717965979129076,
-0.07015857100486755,
0.00019029811664950103,
0.02038152515888214,
-0.023126676678657532,
0.028727492317557335,
-0.01845485158264637,
0.01593361794948578,
0.008505191653966904,
-0.016452642157673836,
-0.01600111834704876,
-0.02693861350417137,
0.044514916837215424,
0.024915648624300957,
-0.001930585247464478,
-0.030340144410729408,
0.0062266867607831955,
0.06984342634677887,
-0.005573565606027842,
-0.04684751480817795,
0.08778632432222366,
-0.011874871328473091,
-0.019534360617399216,
-0.024709636345505714,
0.00905228964984417,
0.008642243221402168,
0.02442127652466297,
-0.028987767174839973,
0.025570133700966835,
0.029167406260967255,
0.014126949943602085,
0.023413388058543205,
0.07549527287483215,
0.0021108086220920086,
-0.04276740178465843,
-0.01602557860314846,
0.05824745446443558,
0.01736321486532688,
0.0023013665340840816,
-0.056627269834280014,
-0.053480420261621475,
-0.049927446991205215,
0.00001291786611545831,
-0.05140860006213188,
0.03339852765202522,
0.021654704585671425,
0.05818172171711922,
-0.0240611732006073,
0.05846085771918297,
0.06001792103052139,
0.012384466826915741,
-0.010435400530695915,
0.026624370366334915,
-0.005447848234325647,
-0.04255117103457451,
-0.03111836686730385,
-0.024185923859477043,
-0.05276203528046608,
-0.047426141798496246,
-0.018483463674783707,
0.030395647510886192,
-0.033662181347608566,
0.028289426118135452,
0.03379261493682861,
-0.05916355550289154,
-0.034648265689611435,
0.08773509413003922,
0.005599822383373976,
0.016922686249017715,
0.0013526880647987127,
0.00902971625328064,
0.020587153732776642,
0.03564445301890373,
-0.022897008806467056,
-0.0009299960802309215,
0.005355562549084425,
-0.0000714647612767294,
0.012869986705482006,
0.023782987147569656,
0.010113392025232315,
-0.0014324322110041976,
-0.013761447742581367,
0.04440812021493912,
0.0399014838039875,
0.042337626218795776,
0.030533310025930405,
-0.027138933539390564,
0.005151186138391495,
0.038554996252059937,
-0.031132344156503677,
-0.01232330035418272,
0.09064216166734695,
0.006534322164952755,
0.018425321206450462,
-0.07212167978286743,
0.004089426714926958,
-0.015064992941915989,
-0.037008170038461685,
0.09416668862104416,
-0.009055748581886292,
-0.023889858275651932,
-0.02769206464290619,
-0.038709383457899094,
0.014161366969347,
-0.0035905675031244755,
0.0521722286939621,
0.031791817396879196,
0.04154864698648453,
0.0008094573859125376,
-0.03718516603112221,
0.024048184975981712,
0.029162520542740822,
-0.01979319378733635,
0.04532988369464874,
-0.010599876753985882,
0.013548463582992554,
-0.08088714629411697,
0.0378851555287838,
-0.014279315248131752,
0.05701654404401779,
0.004460458643734455,
-0.00525046419352293,
0.005261774640530348,
0.04663460701704025,
-0.018139077350497246,
-0.01959102973341942,
-0.019919252023100853,
0.026058658957481384,
-0.03185843676328659,
-0.041603557765483856,
0.006807259749621153,
0.003577383002266288,
0.00649182079359889,
-0.05704033374786377,
-0.054710887372493744,
-0.00813246425241232,
-0.06607053428888321,
-0.033492106944322586,
0.01933063194155693,
0.0029581673443317413,
0.0017998310504481196,
0.07331858575344086,
-0.01723354309797287,
0.07565275579690933,
-0.030300652608275414,
-0.043121736496686935,
-0.01332526933401823,
0.006244145333766937,
-0.032875288277864456,
-0.037285830825567245,
0.010820609517395496,
0.0106532983481884,
-0.014455748721957207,
0.045493584126234055,
0.024862779304385185,
-0.07880952954292297,
-0.003522522747516632,
0.028834519907832146,
-0.03077419102191925,
0.033792220056056976,
-0.02602318674325943,
0.017501359805464745,
0.06574173271656036,
0.04354189336299896,
0.013874792493879795,
-0.0005572669324465096,
0.0023890668526291847,
0.021207284182310104,
0.03376404196023941,
0.004582739435136318,
0.005760614760220051,
-0.07315026223659515,
0.021017037332057953,
-0.0037454573903232813,
-0.038529638200998306,
0.011090093292295933,
0.031140325590968132,
0.00657822797074914,
0.06345019489526749,
0.03111960180103779,
-0.06451234221458435,
0.026055844500660896,
0.07315707206726074,
-0.036169447004795074,
-0.00016739702550694346,
0.030156005173921585,
0.04029465839266777,
0.014144344255328178,
-0.061838433146476746,
-0.08059068769216537,
0.02590174414217472,
-0.019210439175367355,
0.052754271775484085,
0.024364475160837173,
-0.004007119219750166,
0.04297001659870148,
-0.03045542910695076,
0.06038779392838478,
-0.04402924329042435,
-0.031674861907958984,
0.029014702886343002,
0.006316129118204117,
0.02040751837193966,
-0.03403082489967346,
-0.017273666337132454,
0.02511417306959629,
0.03802561014890671,
0.03881265968084335,
-0.010198806412518024,
-0.006444241385906935,
-0.004257464315742254,
0.024422481656074524,
-0.04743587225675583,
0.029340052977204323,
-0.0033006726298481226,
0.01992843486368656,
-0.029466688632965088,
0.04041037708520889,
0.02283010631799698,
0.03771866112947464,
0.02368873544037342,
0.03826538845896721,
-0.019849922508001328,
0.0016056607710197568,
-0.024097533896565437,
-0.0250089131295681,
-0.010114953853189945,
0.024520061910152435,
-0.06496644765138626,
-0.013309426605701447,
0.044776830822229385,
0.06185794249176979,
0.08222763985395432,
-0.014559854753315449,
-0.010881866328418255,
-0.043636977672576904,
-0.0072352890856564045,
0.05236231908202171,
-0.06210402399301529,
-0.02944040857255459,
-0.021533800289034843,
-0.03537658601999283,
-0.014181895181536674,
0.0016680802218616009,
0.04315875470638275,
-0.04535740613937378,
0.05744021758437157,
-0.06121065840125084,
0.0466226190328598,
0.05605028569698334,
0.02846682071685791,
0.014178087934851646,
0.003122644266113639,
0.026098113507032394,
0.011382197961211205,
0.0008510443149134517,
-0.014405671507120132,
-0.024409227073192596,
0.07585904002189636,
-0.0564202181994915,
-0.0002490299812052399,
-0.09907519817352295,
-0.00613065343350172,
0.08992574363946915,
0.034509383141994476,
-0.007764052599668503,
-0.006507613230496645,
0.036573875695466995,
-0.0326058454811573,
-0.0034400566946715117,
0.0025203395634889603,
0.01873393915593624,
-0.026578258723020554,
0.047481290996074677,
-0.04702000319957733,
-0.008225571364164352,
0.0348249152302742,
0.006421683356165886,
-0.018542509526014328,
0.033682141453027725,
0.06789863854646683,
-0.024336403235793114,
-0.027466701343655586,
-0.04787716642022133,
0.02487664669752121,
0.016716143116354942,
0.0006311529432423413,
0.00403862027451396,
0.044126398861408234,
-0.003965748008340597,
0.029909741133451462,
0.04225355014204979,
0.05356493964791298,
-0.021340714767575264,
-0.031000487506389618,
-0.019693640992045403,
0.022206690162420273,
0.0077123334631323814,
-0.0077311028726398945,
-0.03101099655032158,
0.03561566025018692,
-0.017760830000042915,
-0.02671107091009617,
-0.016156163066625595,
-0.01534388866275549,
0.06580433994531631,
0.04355272650718689,
0.024728458374738693,
0.010711553506553173,
-0.01220295112580061,
-0.014478813856840134,
0.03830583021044731,
0.007804267108440399,
0.06161201745271683,
0.06720452755689621,
0.05752641335129738,
-0.0024374467320740223,
-0.04987742379307747,
-0.0011385236866772175,
-0.022069307044148445,
-0.007125209551304579,
-0.08148428052663803,
-0.011235041543841362,
-0.0007015766459517181,
-0.009637177921831608,
-0.0235414020717144,
0.018023207783699036,
-0.011338402517139912,
0.019133392721414566,
-0.025933220982551575,
-0.04394657909870148,
-0.04544408991932869,
-0.05371943116188049,
0.015993088483810425,
-0.017074037343263626,
0.03056819923222065,
-0.09932717680931091,
-0.016659529879689217,
-0.006544165778905153,
-0.041853297501802444,
-0.011614589020609856,
0.011629156768321991,
0.0009876011172309518,
0.08205615729093552,
-0.06597419828176498,
0.02549728937447071,
0.034609921276569366,
0.014595553278923035,
0.021181369200348854,
-0.02567194402217865,
-0.03045090287923813,
0.09561700373888016,
-0.08846815675497055,
0.04346581920981407,
0.004040944389998913,
0.008552281185984612,
-0.02304890565574169,
-0.030585814267396927,
0.04426546022295952,
-0.04506091773509979,
0.024493377655744553,
0.04258710518479347,
-0.01551396306604147,
-0.0000370622547052335,
-0.029471922665834427,
-0.02392316795885563,
0.01593048684298992,
0.020155148580670357,
0.01429841760545969,
0.0009173599537461996,
0.004512532148510218,
-0.0408514067530632,
-0.010009796358644962,
0.025954583659768105,
-0.01392223872244358,
0.013990060426294804,
0.0038512086030095816,
-0.004248772282153368,
0.04136066883802414,
0.08027780801057816,
-0.07914920896291733,
0.01560426875948906,
-0.01541674230247736,
-0.0026651399675756693,
0.027804194018244743,
0.0012492587557062507,
0.01806987076997757,
0.06559839099645615,
-0.05601774901151657,
0.016895446926355362,
0.06446804106235504,
-0.009157725609838963,
0.12067330628633499,
0.0006338469102047384,
-0.07095813751220703,
0.013507537543773651,
-0.01347365416586399,
0.0059654489159584045,
0.06006244197487831,
-0.04184162989258766,
-0.014884689822793007,
0.030136527493596077,
-0.055801600217819214,
-0.1189676895737648,
-0.015086854808032513,
-0.004888749215751886,
-0.003841801779344678,
0.03562992811203003,
-0.022545399144291878,
-0.0066319736652076244,
0.016935376450419426,
0.005817207507789135,
-0.035485368221998215,
0.04709495231509209,
0.042159486562013626,
0.006954093463718891,
-0.1058180183172226,
0.036776017397642136,
0.008510190062224865,
0.03784913197159767,
0.04202938824892044,
-0.011945565231144428,
-0.06600497663021088,
0.02147189900279045,
0.0788268893957138,
0.001378322602249682,
-0.0227911826223135,
0.0162944458425045,
-0.04467165097594261,
0.0011351893190294504,
0.07780127227306366,
0.026539092883467674,
0.007073607295751572,
0.011649735271930695,
-0.01119245495647192,
-0.03619913011789322,
-0.06019015982747078,
-0.016872044652700424,
0.0006568768876604736,
-0.0062162126414477825,
0.00275370548479259,
-0.03460347279906273,
0.048573561012744904,
-0.0020993631333112717,
0.03191624954342842,
-0.030926797538995743,
0.032617781311273575,
-0.028711535036563873,
0.0413614921271801,
-0.041452616453170776,
-0.03213972970843315,
0.008740289136767387,
0.0431547574698925,
-0.02551235258579254,
-0.01730896532535553,
0.03468302637338638,
-0.04808308184146881,
-0.00261148763820529,
-0.04344809055328369,
-0.010179046541452408,
0.007691374514251947,
0.013476266525685787,
0.04407978430390358,
0.0020156821701675653,
0.03526892513036728,
-0.028012331575155258,
0.024837305769324303,
-0.007440665736794472,
0.019433507695794106,
0.05154409632086754,
0.00819292664527893,
0.04809616133570671,
0.0070676300674676895,
-0.004124926403164864,
0.029548047110438347,
0.023001015186309814,
0.011857843026518822,
-0.025153782218694687,
-0.005482836626470089,
-0.01663328893482685,
-0.012759258039295673,
-0.02000570297241211,
0.017103493213653564,
0.040852561593055725,
-0.03183097392320633,
-0.00005180105654289946,
0.052624866366386414,
0.013865179382264614,
-0.0077127269469201565,
-0.04917748272418976,
0.006835381966084242,
0.00011863082909258083,
-0.016724884510040283,
-0.006975200027227402,
-0.03741304203867912,
-0.021382536739110947,
-0.0208502896130085,
-0.0404151976108551,
-0.020134085789322853,
-0.06913301348686218,
-0.007307825610041618,
0.019056281074881554,
-0.007803941611200571,
-0.017656657844781876,
-0.0009917132556438446,
0.030798127874732018,
-0.06153586134314537,
-0.029549848288297653,
0.06498654931783676,
0.03785248100757599,
0.04277510195970535,
0.030653102323412895,
-0.027039678767323494,
-0.002231790218502283,
-0.0018398170359432697,
-0.04471708834171295,
-0.019261818379163742,
0.00672438507899642,
-0.01944543980062008,
-0.03113684244453907,
0.009940038435161114,
-0.06490761041641235,
-0.015921950340270996,
0.011926309205591679,
-0.03912527859210968,
-0.0038068327121436596,
-0.041371628642082214,
-0.024112189188599586,
0.007524355314671993,
0.005406936630606651,
0.048092134296894073,
0.04932171478867531,
0.017180781811475754,
-0.07132165879011154,
-0.016198240220546722,
0.03584371134638786,
0.06464356929063797,
-0.0047925421968102455,
-0.07089385390281677,
-0.005009891465306282,
0.011174967512488365,
0.017326997593045235,
-0.026443608105182648,
-0.05255798250436783,
0.001674095168709755,
-0.013893150724470615,
-0.0174240842461586,
0.003635945962741971,
0.052217233926057816,
0.033404361456632614,
-0.009509854018688202,
-0.032404810190200806,
-0.04262193292379379,
-0.014411112293601036,
-0.00450652651488781,
0.06367651373147964,
0.011197938583791256,
-0.035531848669052124,
0.005621003452688456,
0.032724570482969284,
-0.04880303889513016,
0.07697239518165588,
0.014535726979374886,
-0.042724691331386566,
-0.03366463631391525,
0.043517157435417175,
-0.006186758633702993,
0.054726071655750275,
0.048514995723962784,
-0.006489621941000223,
-0.005068385507911444,
0.031530510634183884,
-0.02898622490465641,
0.013011793605983257,
-0.048694539815187454,
-0.022894058376550674,
0.029595952481031418,
-0.013771041296422482,
-0.015975994989275932,
0.02443637326359749,
-0.003922449890524149,
0.0410446859896183,
-0.026661759242415428,
0.026833202689886093,
0.012517603114247322,
0.029698172584176064,
-0.012671294622123241,
0.01947023533284664,
0.0271183792501688,
0.011282751336693764,
0.018580779433250427,
0.004146933555603027,
-0.017081277444958687,
-0.09549075365066528,
-0.051451995968818665,
0.05636976286768913,
-0.004334305878728628,
-0.022430535405874252,
-0.009364784695208073,
0.0021719406358897686,
-0.010546664707362652,
-0.06735216826200485,
-0.007316563278436661,
-0.050093065947294235,
-0.035631004720926285,
-0.017397210001945496,
-0.002554734004661441,
0.0034216835629194975,
-0.007955136708915234,
0.05726189911365509,
-0.006094730459153652,
-0.018187403678894043,
-0.035817794501781464,
0.006918380036950111,
0.061756860464811325,
-0.006766115315258503,
-0.01320578157901764,
0.027431299909949303,
0.05457710102200508,
-0.0034552784636616707,
0.06731610745191574,
0.008708691224455833,
0.02756665274500847,
0.03675125539302826,
-0.03306495398283005,
-0.056756842881441116,
-0.062163565307855606,
-0.04883197322487831,
0.004188550170511007,
0.001587925129570067,
-0.022975679486989975,
-0.00909313652664423,
0.010333959944546223,
-0.028864998370409012,
-0.019261209294199944,
-0.0030345204286277294,
0.049454301595687866,
0.00625208206474781
] |
<p>I did an exercise which probably is quite popular,<br>
in which you draw an electromagnetic wave and prove that it should
propagate at the speed of light $1 \over \sqrt {\mu_0\epsilon_0}$ using Farday's law and Ampere's law.</p>
<p>Basically if this is the wave: </p>
<p><br>
<img src="http://i.stack.imgur.com/SqAzU.png" alt="Electromagnetic wave"></p>
<p>Let's say the E-field (red) is in the X direction, the B-Field (blue) is in the Y direction,
and the velocity of the wave is in the Z direction.</p>
<p>You take for example for ampere's law a surface in the ZY plane with a length L
equal to the amplitude of the wave,
and a width equal to $\lambda\over 4$
You do a similar thing with Faraday's law and you get the speed of light,
assuming you know that the E-field and B-field propagate in this manner.</p>
<p>I got the right answer but I wondered about this:
Let's say I only had the E-field and I know the wave propagates at the speed of light, I assume this is enough information to draw the B-field at each point.</p>
<p>But how will I know the direction? Both Faraday's law and Ampere's law say you need a closed loop integral and the rules I've been taught say
you go over the loop in a clockwise direction for example and take the
normal to the surface according to the right hand rule etc.</p>
<p>But clockwise and counter-clockwise direction don't really give me much information in this case, so how can I determine the direction of the B-field
if I only have the E-field?</p> | g4779 | [
0.019131703302264214,
0.05794623866677284,
-0.010580111294984818,
-0.026115501299500465,
0.08323883265256882,
0.0032206473406404257,
0.0706859901547432,
-0.032734647393226624,
-0.035710323601961136,
-0.03758259490132332,
0.03759331256151199,
0.051190558820962906,
0.02893313765525818,
0.05916973575949669,
0.022580603137612343,
-0.00007599496166221797,
0.08185502886772156,
-0.02090347744524479,
0.05951811745762825,
0.008667092770338058,
0.0020018056966364384,
0.013135457411408424,
-0.036200299859046936,
0.030424300581216812,
-0.017017999663949013,
-0.05376218259334564,
-0.01807272993028164,
-0.062362100929021835,
-0.03372906520962715,
-0.033240530639886856,
-0.009506314992904663,
-0.018926037475466728,
0.06247718632221222,
-0.06451688706874847,
0.02935292199254036,
-0.0015784528804942966,
-0.004095061216503382,
0.04947279393672943,
0.01554195024073124,
0.025803321972489357,
0.0666034072637558,
-0.052159372717142105,
-0.02120581455528736,
0.003232839284464717,
0.07442162185907364,
-0.027038104832172394,
-0.042294807732105255,
-0.014162945561110973,
-0.02740815095603466,
0.01601085066795349,
-0.01040880847722292,
0.05102568492293358,
0.07042226195335388,
-0.015820903703570366,
-0.02829829230904579,
0.01799744740128517,
0.017005611211061478,
-0.06570933014154434,
0.06529134511947632,
0.025270359590649605,
0.014128814451396465,
-0.011425493285059929,
-0.016192786395549774,
0.04497165605425835,
0.036999404430389404,
0.005600675009191036,
-0.03881112486124039,
-0.01678895764052868,
-0.03421679139137268,
0.052088260650634766,
-0.010295487940311432,
-0.07713731378316879,
-0.017240360379219055,
-0.08602117002010345,
-0.007818921469151974,
-0.0186170507222414,
0.01009711716324091,
-0.012495094910264015,
-0.046583645045757294,
0.03364279121160507,
0.018331335857510567,
-0.04360007494688034,
-0.0006790889310650527,
0.010096857324242592,
0.022418584674596786,
0.03034387342631817,
0.02909059450030327,
-0.005300677847117186,
-0.041826281696558,
-0.05573563277721405,
0.03922262787818909,
-0.028321975842118263,
0.07403381913900375,
0.05036481097340584,
0.04648603871464729,
-0.035158462822437286,
-0.023655232042074203,
0.014760127291083336,
-0.031648509204387665,
0.007601287215948105,
-0.07880126684904099,
-0.0026900016237050295,
-0.020221810787916183,
-0.04151984304189682,
-0.05109088867902756,
0.05513779819011688,
0.015653511509299278,
0.01796496845781803,
-0.0022174648474901915,
-0.023891277611255646,
-0.02352735958993435,
-0.07572376728057861,
-0.06742474436759949,
-0.006796005181968212,
-0.028410639613866806,
0.023431969806551933,
0.027629617601633072,
0.004847273230552673,
-0.0002665103238541633,
0.05496660992503166,
-0.022403603419661522,
-0.02083875983953476,
0.01542012207210064,
0.0284682996571064,
0.026235956698656082,
0.02193130925297737,
-0.06213073432445526,
-0.019225668162107468,
0.03021111898124218,
0.027506910264492035,
-0.00033912426442839205,
-0.002345670945942402,
0.013816716149449348,
0.008702063001692295,
-0.044373366981744766,
-0.027622710913419724,
0.0001694140228210017,
0.03685290366411209,
0.04549205303192139,
-0.001161828520707786,
-0.02111089788377285,
-0.029953964054584503,
0.02405276522040367,
-0.04464872181415558,
-0.05912398174405098,
0.036970339715480804,
0.037993498146533966,
-0.04120543971657753,
0.037740666419267654,
-0.009546825662255287,
0.021263720467686653,
0.10147695988416672,
-0.01585005223751068,
0.0550185963511467,
0.02069755829870701,
-0.017610017210245132,
0.035288937389850616,
0.017581477761268616,
-0.0063402168452739716,
-0.03313766419887543,
0.04949590563774109,
0.01982130855321884,
-0.02061331644654274,
0.025930656120181084,
-0.030239377170801163,
-0.006280251778662205,
0.015775982290506363,
-0.03704134374856949,
-0.02922735922038555,
-0.02365158498287201,
-0.008215958252549171,
0.002942991442978382,
0.03668957203626633,
-0.0001683621812844649,
0.023800360038876534,
0.0854329764842987,
-0.022121842950582504,
0.029265889897942543,
0.046093035489320755,
-0.013759163208305836,
-0.004894875455647707,
0.010252072475850582,
0.023707259446382523,
0.02867550030350685,
-0.0009424161398783326,
0.0003046782221645117,
-0.06585997343063354,
-0.03410787507891655,
-0.04345899075269699,
-0.016364427283406258,
-0.0010616732761263847,
-0.04579015448689461,
-0.049537308514118195,
0.04227958992123604,
-0.03759193420410156,
-0.016631966456770897,
0.020573323592543602,
-0.04056534543633461,
-0.03593858331441879,
0.0484878309071064,
-0.019967880100011826,
0.0642956867814064,
0.09005629271268845,
-0.003983051050454378,
0.02652326039969921,
-0.001989820972084999,
-0.005168721079826355,
0.05333763360977173,
0.04216659441590309,
-0.010870227590203285,
0.050722405314445496,
0.011097040958702564,
0.02816690318286419,
0.03543487563729286,
0.010436633601784706,
-0.015429885126650333,
-0.04588642716407776,
0.06904743611812592,
-0.032583534717559814,
-0.020204758271574974,
0.0025089720729738474,
0.013815498910844326,
0.0036794189363718033,
-0.03242557868361473,
-0.019453376531600952,
0.03716953098773956,
-0.030978942289948463,
0.044779080897569656,
-0.004231494385749102,
0.07929724454879761,
-0.0034920135512948036,
-0.04046674072742462,
-0.015265091322362423,
-0.02780829556286335,
0.029978448525071144,
0.014114325866103172,
0.013430409133434296,
0.020775554701685905,
0.044633518904447556,
0.027518395334482193,
0.04296496510505676,
-0.01098345685750246,
0.019096169620752335,
-0.05795333907008171,
-0.01516303513199091,
-0.030186187475919724,
0.05980171635746956,
0.01029925886541605,
-0.04360048845410347,
0.020062865689396858,
0.046205900609493256,
0.04303557798266411,
-0.012825977988541126,
0.07029285281896591,
-0.02759990654885769,
0.04396430402994156,
-0.010098928585648537,
0.019595129415392876,
-0.047706007957458496,
-0.015048401430249214,
-0.024699091911315918,
0.031979598104953766,
0.053618330508470535,
0.004399302415549755,
-0.00883750431239605,
-0.019059745594859123,
-0.040990885347127914,
0.012665840797126293,
0.005133744794875383,
-0.0064656687900424,
-0.05196959525346756,
0.004818867426365614,
-0.03806563466787338,
-0.009858837351202965,
0.004374388139694929,
-0.09296894073486328,
0.04719409719109535,
-0.05321752279996872,
-0.01620958186686039,
0.02883271686732769,
0.04514503851532936,
-0.013098112307488918,
-0.039871226996183395,
-0.008334159851074219,
0.06895081698894501,
-0.05528191849589348,
0.03255051001906395,
0.01864011213183403,
-0.012420124374330044,
0.006648574490100145,
-0.03784775733947754,
-0.015664611011743546,
0.022842828184366226,
-0.00902651809155941,
-0.006087781395763159,
0.037781380116939545,
0.011575085110962391,
-0.04012330248951912,
0.0032002641819417477,
-0.013973811641335487,
0.030423562973737717,
0.010808199644088745,
0.011712489649653435,
-0.028935814276337624,
0.041906870901584625,
0.0034549583215266466,
-0.05318182334303856,
-0.07523117959499359,
0.022926587611436844,
0.028736980631947517,
0.01953020878136158,
0.02147865481674671,
0.0025332323275506496,
-0.032074782997369766,
-0.012983322143554688,
0.010664758272469044,
-0.00025254860520362854,
0.02580474503338337,
0.04222072660923004,
0.010226172395050526,
-0.044024478644132614,
0.011745216324925423,
0.03375350311398506,
0.04237008094787598,
-0.01872885413467884,
-0.048732224851846695,
0.004542386159300804,
0.019347170367836952,
-0.007333830464631319,
0.0036492887884378433,
-0.024768564850091934,
0.04275323823094368,
-0.03912770748138428,
0.0012973209377378225,
-0.0007053068839013577,
0.01114958431571722,
0.040105096995830536,
0.06534875929355621,
0.04064987972378731,
0.029916122555732727,
0.014826620928943157,
-0.00801504123955965,
-0.044014982879161835,
-0.029224243015050888,
-0.010009046643972397,
-0.03062463365495205,
-0.02433132380247116,
0.05584046617150307,
-0.017757553607225418,
-0.013318651355803013,
0.04287050664424896,
0.005540771875530481,
0.01083039678633213,
0.019407257437705994,
-0.017994439229369164,
0.07261469960212708,
0.029735352843999863,
0.032235316932201385,
0.07036864757537842,
-0.0592707023024559,
-0.016245033591985703,
0.005743834190070629,
-0.04030800238251686,
-0.0392707884311676,
-0.014118177816271782,
0.013747720047831535,
0.024234270676970482,
0.07204912602901459,
-0.015574495308101177,
-0.048812031745910645,
0.06304503232240677,
-0.057915110141038895,
-0.01200571097433567,
0.05391763523221016,
-0.056261658668518066,
-0.04645811393857002,
0.0379851870238781,
-0.006235407665371895,
-0.017232052981853485,
0.043081674724817276,
-0.02146376483142376,
0.09948906302452087,
-0.010387353599071503,
-0.005045794416218996,
-0.01419865619391203,
0.027006791904568672,
-0.018247636035084724,
-0.04047297686338425,
0.03196633234620094,
0.005877686198800802,
0.02767462655901909,
-0.07941876351833344,
-0.03755372390151024,
0.0011282949708402157,
-0.01626659370958805,
-0.03618514910340309,
-0.022050701081752777,
0.00686052767559886,
-0.04291541501879692,
0.009568903595209122,
-0.002083641244098544,
0.024476397782564163,
0.02971174195408821,
0.031609926372766495,
-0.0527786985039711,
0.0018871729262173176,
0.008447347208857536,
-0.04424867406487465,
0.045738767832517624,
-0.010634582489728928,
0.005288007203489542,
-0.011636747978627682,
-0.020272577181458473,
-0.062319330871105194,
0.04744040593504906,
0.01122241374105215,
0.03018137626349926,
-0.013378201983869076,
0.002105468651279807,
-0.0074471961706876755,
0.04060796648263931,
-0.02056441269814968,
-0.0028033561538904905,
-0.03818488493561745,
-0.06192130595445633,
0.05635487288236618,
0.06640845537185669,
-0.0399329736828804,
-0.010269707068800926,
-0.020258912816643715,
-0.06300570070743561,
0.04877996817231178,
-0.06265775859355927,
0.03492102771997452,
-0.09450972825288773,
0.0002609046350698918,
0.024291465058922768,
0.08014891296625137,
0.04782583937048912,
0.03924086317420006,
0.03351631760597229,
-0.045430008322000504,
0.006781891919672489,
-0.018275102600455284,
-0.0354594849050045,
0.04595142602920532,
-0.0732276514172554,
-0.058296363800764084,
0.004618989769369364,
-0.03391670435667038,
-0.0430322103202343,
0.03266870975494385,
-0.011346296407282352,
-0.014523726888000965,
-0.014229540713131428,
-0.009123358875513077,
-0.03794606029987335,
0.04670922830700874,
0.017633866518735886,
-0.006708923261612654,
-0.03302042931318283,
-0.02339771017432213,
0.02393457666039467,
0.00598407257348299,
0.027092644944787025,
-0.05338871106505394,
-0.037705373018980026,
-0.04353919252753258,
-0.013750463724136353,
0.023488499224185944,
0.02343420684337616,
-0.006605552509427071,
0.03976280242204666,
-0.009146993979811668,
-0.01798275113105774,
-0.010323520749807358,
-0.024869835004210472,
-0.00006359402323141694,
-0.08329477161169052,
-0.025138510391116142,
-0.07895529270172119,
0.0023871141020208597,
0.01562867872416973,
0.013297796249389648,
-0.04041643440723419,
-0.05007930472493172,
-0.014080166816711426,
0.057674214243888855,
-0.040136970579624176,
-0.052537743002176285,
-0.0008095685043372214,
0.033993061631917953,
-0.01980428583920002,
0.0003245682455599308,
-0.07238484174013138,
-0.05799277499318123,
0.02090451866388321,
-0.006581236142665148,
0.008771400898694992,
-0.04698877036571503,
-0.09156687557697296,
-0.00910798367112875,
-0.003773115109652281,
0.000030306038752314635,
-0.01817668415606022,
0.042672298848629,
0.045281391590833664,
-0.008428055793046951,
-0.025432616472244263,
-0.003052139189094305,
0.03448256477713585,
-0.012823608703911304,
-0.0053643472492694855,
-0.029114218428730965,
0.07279335707426071,
-0.027028720825910568,
-0.06667520105838776,
0.06421633064746857,
0.018827572464942932,
0.012931842356920242,
0.042039792984724045,
0.004805643577128649,
-0.018857711926102638,
-0.05502796545624733,
-0.020016007125377655,
-0.017269738018512726,
-0.10255327075719833,
-0.03217679262161255,
0.03732630982995033,
0.014458504505455494,
0.04377434030175209,
0.04038313031196594,
-0.0018507007043808699,
0.02382044680416584,
0.020639466121792793,
-0.010206450708210468,
0.06399181485176086,
-0.06574487686157227,
-0.006274169310927391,
0.033032551407814026,
0.003675550688058138,
-0.030807828530669212,
0.035763561725616455,
0.03148193284869194,
-0.017817871645092964,
-0.0013074612943455577,
-0.029417941346764565,
-0.026874499395489693,
0.028734616935253143,
0.0011250674724578857,
-0.01157542783766985,
0.013082058168947697,
0.015519936569035053,
-0.029053078964352608,
-0.05445389077067375,
0.05599766969680786,
-0.02091711014509201,
0.040413904935121536,
0.007195404730737209,
-0.008359509520232677,
0.08463135361671448,
-0.01941565051674843,
0.039897993206977844,
0.001983236987143755,
-0.029602807015180588,
-0.022634821012616158,
0.023262711241841316,
-0.000266207818640396,
0.03556017950177193,
0.06950896233320236,
-0.056665971875190735,
-0.0019981872756034136,
-0.06640691310167313,
0.04008885845541954,
0.05682123452425003,
0.028695767745375633,
0.020941928029060364,
-0.038463372737169266,
-0.022319357842206955,
0.034322965890169144,
-0.009194443933665752,
0.028579670935869217,
-0.03009403869509697,
-0.03757066652178764,
0.007801047991961241,
0.03379691392183304,
0.028033683076500893,
-0.04128790274262428,
0.06872519105672836,
-0.010103767737746239,
-0.0459468774497509,
0.04151887446641922,
-0.029888436198234558,
-0.023414671421051025,
-0.03494420275092125,
-0.028767693787813187,
0.035763535648584366,
-0.017532700672745705,
0.01195373386144638,
0.04198860377073288,
-0.009684593416750431,
-0.0695059597492218,
-0.0014558803522959352,
-0.05308469384908676,
0.04067907854914665,
0.03599666804075241,
-0.006355591583997011,
-0.005150178913027048,
0.0634162649512291,
-0.055044613778591156,
-0.012561452575027943,
-0.007357679773122072,
-0.015766343101859093,
-0.021857798099517822,
-0.03436052054166794,
0.008157670497894287,
-0.03053496778011322,
0.017650531604886055,
-0.0035589898470789194,
0.04429879039525986,
0.08254482597112656,
0.022278308868408203,
-0.042618606239557266,
0.01789774000644684,
0.008230511099100113,
0.02021726220846176,
-0.009241296909749508,
0.016774943098425865,
0.048236142843961716,
-0.0015624904772266746,
0.10883815586566925,
-0.011272304691374302,
-0.0440681129693985,
0.014722775667905807,
0.04074084758758545,
0.01204793993383646,
-0.015531100332736969,
0.026578407734632492,
-0.005572485737502575,
0.06639447063207626,
-0.010342583060264587,
0.04969945549964905,
-0.01511144544929266,
0.028130458667874336,
-0.022360781207680702,
-0.07925814390182495,
0.042825404554605484,
0.009018276818096638,
-0.03757711872458458,
-0.019038520753383636,
0.014635714702308178,
-0.0017331026028841734,
-0.07094360888004303,
0.01811227761209011,
-0.0014010382583364844,
0.04491760581731796,
0.011794066987931728,
0.04772977530956268,
-0.0672021210193634,
-0.0453636534512043,
-0.03352894261479378,
-0.06580179184675217,
0.010894681327044964,
-0.009653010405600071,
0.020456556230783463,
0.017954343929886818,
-0.06331020593643188,
0.01676393672823906,
-0.05346735194325447,
0.006879712920635939,
0.0019516028696671128,
-0.028410254046320915,
-0.006138290278613567,
0.041538652032613754,
0.004688960500061512,
0.032750822603702545,
-0.03784235939383507,
0.005935749504715204,
-0.006228177342563868,
0.003946390934288502,
-0.006830133032053709,
0.055394768714904785,
-0.055728450417518616,
-0.02462627924978733,
-0.011643415316939354,
-0.008279010653495789,
-0.060060471296310425,
0.02266308106482029,
-0.0008518663235008717,
-0.019750570878386497,
-0.045839566737413406,
-0.0030308100394904613,
-0.021853240206837654,
-0.04740399867296219,
0.00039472721982747316,
-0.014673493802547455,
0.001274718320928514,
0.027735859155654907,
-0.010187063366174698,
-0.04647789150476456,
0.030324362218379974,
-0.00474564591422677,
-0.023221679031848907,
0.006417973432689905,
0.023234058171510696,
-0.008948019705712795,
0.020554233342409134,
-0.039707209914922714,
-0.029220236465334892,
-0.04975629225373268,
-0.013105261139571667,
0.02906983159482479,
-0.011927942745387554,
0.012285793200135231,
0.02524746023118496,
0.06982483714818954,
0.015098906122148037,
0.0043742600828409195,
-0.0076147401705384254,
0.025013789534568787,
-0.01909618079662323,
0.05391469970345497,
-0.04661404713988304,
-0.04136435687541962,
0.00621926411986351,
-0.008874352090060711,
-0.017903180792927742,
0.03364843875169754,
0.041891131550073624,
-0.032955143600702286,
0.051114942878484726,
-0.026020435616374016,
-0.023288749158382416,
-0.04480966553092003,
-0.07186374068260193,
0.06490007787942886,
-0.010206797160208225,
0.0008665157947689295,
0.029194384813308716,
0.0016342654125764966,
0.03831304982304573,
-0.05044936761260033,
0.00607333006337285,
-0.049726702272892,
0.00346501381136477,
-0.004424688871949911,
0.019255468621850014,
0.006691917311400175,
0.054572902619838715,
0.007462504785507917,
0.014528554864227772,
0.03562742844223976,
-0.013594445772469044,
0.03698732703924179,
0.0011402165982872248,
-0.017392605543136597,
0.03465254232287407,
-0.06400004029273987,
0.05785126984119415,
0.018676256760954857,
-0.04402918368577957,
-0.044348541647195816,
0.03604958578944206,
-0.006766894366592169,
0.002187022939324379,
-0.024849850684404373,
-0.04292416572570801,
-0.013070165179669857
] |
<p>I've constructed such table from many different sources for my thesis introduction:
<img src="http://i.stack.imgur.com/zixNi.jpg" alt="enter image description here"></p>
<p>I'm trying to make a bit of philosophy it the thesis first chapter.</p>
<p>Are they realistic or not? Could you make any comments on the ranges presented here.</p>
<p>I'm not trying to say that physics overcomes chemistry or something like this.
These are two different and independent sciences. They study different objects.</p>
<p>The question here: are ranges correct?</p>
<p>For example for time range. It is easy to find this range in internet, but for chemistry it is not.
So, my thought were this. What is minimum time in chemistry? It should be time when the fast chemical reaction can occur/or start, it is ~ tens of femtosecond. </p>
<p>So, I've hoped that people in <a href="http://physics.stackexchange.com/">physics.StackExchange</a> will give me some comments on what I've done by so far. I've discussed this topic with some other scientists and corrected my table. But it is not enough, I need more information.</p>
<p>Please do not hesitate to swear:)</p> | g4780 | [
0.007446111645549536,
0.0188866276293993,
-0.008859447203576565,
-0.009433486498892307,
0.0333976075053215,
-0.03756370395421982,
-0.03335706889629364,
0.016687102615833282,
-0.033617742359638214,
-0.0028016623109579086,
0.015458790585398674,
-0.009845919907093048,
0.03261883929371834,
-0.020648883655667305,
-0.04291396588087082,
0.0019355544354766607,
0.05890171229839325,
-0.04894763231277466,
0.005669105798006058,
0.049517106264829636,
-0.02115018106997013,
-0.039605557918548584,
-0.03747427836060524,
-0.054640498012304306,
-0.10103268176317215,
-0.006667039822787046,
-0.0009344879654236138,
0.005814881529659033,
-0.04283875599503517,
-0.026828128844499588,
-0.030427271500229836,
0.0058908178471028805,
-0.005113358609378338,
0.03754446282982826,
-0.028365839272737503,
-0.023257555440068245,
-0.02075430564582348,
-0.002732514403760433,
0.01114693097770214,
0.023250889033079147,
0.015432829968631268,
-0.04566541314125061,
0.05802091211080551,
-0.05698597803711891,
0.014467324130237103,
0.00729760667309165,
-0.02495012991130352,
-0.02554001845419407,
0.003365123877301812,
-0.0012725336709991097,
-0.044353678822517395,
0.06372823566198349,
0.005504148080945015,
0.006007916759699583,
-0.0003574452712200582,
0.002366563305258751,
0.0061460454016923904,
0.03360568732023239,
0.04395130276679993,
-0.002705969847738743,
0.006376719567924738,
0.0009162969654425979,
-0.02893553301692009,
-0.027724245563149452,
0.09235271066427231,
0.04372043535113335,
-0.044320058077573776,
-0.019630348309874535,
0.001114550861530006,
-0.03728104010224342,
-0.051487036049366,
-0.010734615847468376,
-0.0336560383439064,
0.02948923036456108,
-0.030699472874403,
0.019666476175189018,
0.011691452004015446,
-0.022415556013584137,
0.027350008487701416,
0.03876687213778496,
-0.0895751491189003,
0.024289533495903015,
-0.02597765624523163,
-0.0384468249976635,
0.03401193395256996,
-0.017528686672449112,
-0.03676539286971092,
0.012073446996510029,
0.010700169019401073,
0.051654309034347534,
-0.0028325216844677925,
-0.010552596300840378,
0.0653529167175293,
-0.09469307214021683,
-0.0071082222275435925,
-0.01722244918346405,
-0.01653672382235527,
0.04851534217596054,
0.006419531535357237,
0.02829202637076378,
-0.019701141864061356,
0.006200790870934725,
0.01841401867568493,
0.002755444496870041,
-0.03795323148369789,
-0.03156106173992157,
0.029808664694428444,
-0.022940440103411674,
-0.04171651974320412,
-0.04479436203837395,
-0.04401861131191254,
-0.0044183372519910336,
-0.07352316379547119,
-0.027088312432169914,
-0.00785176083445549,
-0.03861843794584274,
0.007444868329912424,
0.03721615672111511,
0.033014360815286636,
0.01683797314763069,
0.03881816193461418,
0.06331264227628708,
0.04111199453473091,
0.029536869376897812,
-0.012665178626775742,
-0.08269534260034561,
-0.02858784794807434,
0.008532680571079254,
-0.012881466187536716,
-0.06891634315252304,
-0.046001795679330826,
-0.04098614677786827,
-0.052430372685194016,
0.01371326670050621,
-0.0012674611061811447,
0.03674919158220291,
0.034660495817661285,
0.01279937382787466,
-0.01821989007294178,
0.016522547230124474,
0.059214070439338684,
-0.0038691323716193438,
-0.013025912456214428,
-0.0710504949092865,
-0.05464867502450943,
0.019456619396805763,
-0.025185218080878258,
0.04111974686384201,
0.044934455305337906,
-0.010040553286671638,
0.008680833503603935,
0.06638813763856888,
-0.005443928763270378,
0.0013732912484556437,
-0.025257574394345284,
-0.019242944195866585,
0.044900521636009216,
-0.020919490605592728,
0.027275320142507553,
-0.0008374282042495906,
0.00895429402589798,
-0.027218861505389214,
-0.013842352665960789,
0.03409881517291069,
-0.023105252534151077,
0.002100131008774042,
0.043285761028528214,
-0.033926382660865784,
0.021709727123379707,
-0.006741573568433523,
-0.08198849856853485,
-0.03463815525174141,
0.03865113854408264,
0.032132696360349655,
-0.02397366613149643,
0.012197551317512989,
0.03446655347943306,
-0.01420905627310276,
-0.009230622090399265,
0.02978845313191414,
-0.013410395942628384,
-0.026243969798088074,
-0.01320970244705677,
-0.014207429252564907,
0.025934752076864243,
-0.01591581106185913,
0.017468875274062157,
0.02628200501203537,
-0.08117407560348511,
-0.0010401996551081538,
-0.03492522984743118,
-0.05729306489229202,
0.013715309090912342,
0.003648900892585516,
-0.016461046412587166,
-0.022113865241408348,
0.017571086063981056,
-0.00961863249540329,
-0.0119802076369524,
-0.005998945329338312,
-0.0032439937349408865,
0.04223159700632095,
-0.007029048632830381,
0.03965821862220764,
0.0035807203967124224,
0.009456614963710308,
0.00860127154737711,
-0.007597149349749088,
-0.0027862410061061382,
-0.03467760235071182,
0.03635049983859062,
0.058242253959178925,
-0.04097611457109451,
0.01315238606184721,
-0.030944162979722023,
-0.017198476940393448,
-0.03252191096544266,
0.024705899879336357,
0.038514960557222366,
0.04916111379861832,
0.01185003574937582,
-0.024171771481633186,
0.0145117761567235,
-0.058573219925165176,
0.001713997102342546,
-0.02215007320046425,
-0.013427887111902237,
-0.04738294333219528,
0.06234456226229668,
0.03129091486334801,
-0.03839176148176193,
0.01907583884894848,
-0.05044979974627495,
-0.1008240282535553,
0.012527412734925747,
0.05168122798204422,
0.017366280779242516,
-0.038559067994356155,
0.007971970364451408,
0.003554040566086769,
0.036255329847335815,
-0.019846810027956963,
-0.016603980213403702,
0.08418012410402298,
-0.029650695621967316,
-0.10109458863735199,
0.009826422668993473,
-0.013944583013653755,
-0.0018122931942343712,
0.04437606409192085,
0.05971270427107811,
-0.02497089095413685,
-0.04837384819984436,
0.061740804463624954,
-0.06226513162255287,
-0.030711382627487183,
0.03887632116675377,
0.03887925297021866,
-0.011628065258264542,
0.014203866943717003,
0.016655683517456055,
-0.01187690906226635,
0.02116892859339714,
-0.026936938986182213,
-0.013476031832396984,
-0.013457955792546272,
-0.06522895395755768,
0.03340132161974907,
-0.040022701025009155,
-0.013467640615999699,
-0.015083416365087032,
-0.03952363505959511,
-0.014983374625444412,
0.017620902508497238,
-0.03439396992325783,
0.016984961926937103,
0.025172539055347443,
-0.040434084832668304,
0.018124505877494812,
-0.019817784428596497,
-0.022199848666787148,
-0.033698827028274536,
-0.062434595078229904,
0.02467159554362297,
-0.006537428591400385,
-0.023683613166213036,
0.027426782995462418,
-0.007247954607009888,
-0.04769689589738846,
0.002584997797384858,
0.022397315129637718,
0.009610241279006004,
0.04074636846780777,
0.06307630240917206,
-0.04777519404888153,
0.03184867650270462,
0.04818158596754074,
-0.11902466416358948,
-0.03406025096774101,
0.053867559880018234,
0.0024126858916133642,
0.003287486732006073,
0.05450005456805229,
0.07058284431695938,
0.0160791277885437,
0.012446562759578228,
-0.03601016849279404,
0.016457797959446907,
-0.02894943580031395,
0.0020006042905151844,
0.04069517180323601,
0.04379476606845856,
0.052099477499723434,
0.026125920936465263,
-0.013027742505073547,
0.027762558311223984,
0.03144414350390434,
0.05634597688913345,
0.04662302881479263,
-0.05136733502149582,
0.015247950330376625,
-0.02374839410185814,
-0.003042457392439246,
-0.017510823905467987,
0.02950526401400566,
0.026740798726677895,
-0.03369295969605446,
-0.07646863162517548,
-0.060497164726257324,
0.017102299258112907,
0.07289091497659683,
0.05497025325894356,
-0.008057253435254097,
-0.045993342995643616,
-0.06173799932003021,
-0.069459930062294,
0.025578681379556656,
0.03822503983974457,
0.03758019581437111,
-0.03547884523868561,
-0.041741009801626205,
-0.005759829189628363,
0.00007821508188499138,
-0.012174952775239944,
0.056292250752449036,
0.013864647597074509,
-0.04241480678319931,
0.022585969418287277,
-0.02629346027970314,
-0.044210005551576614,
0.02746816910803318,
-0.025696037337183952,
-0.0018971394747495651,
-0.00011822341912193224,
0.014605632051825523,
0.0005675907013937831,
-0.029103601351380348,
0.08562532067298889,
0.027534717693924904,
0.0074570984579622746,
-0.0049171303398907185,
-0.02685648947954178,
0.035876087844371796,
0.0029030179139226675,
-0.0409577339887619,
0.04435253143310547,
-0.004071677103638649,
0.1153448224067688,
0.04018401727080345,
-0.0035210323985666037,
-0.01102832518517971,
0.014408671297132969,
0.0467899926006794,
-0.023849407210946083,
0.06091909483075142,
-0.017845474183559418,
-0.025327809154987335,
0.02389782853424549,
-0.03537745773792267,
0.056630875915288925,
0.036521490663290024,
0.04245179146528244,
0.04087349399924278,
-0.018090728670358658,
0.03861270844936371,
-0.0027819278184324503,
-0.022991562262177467,
-0.008700968697667122,
-0.05567294359207153,
-0.023431574925780296,
0.015050532296299934,
-0.026462040841579437,
-0.07142486423254013,
0.052146971225738525,
-0.0511210635304451,
-0.012677159160375595,
-0.0036207991652190685,
0.037464581429958344,
-0.008676577359437943,
0.06504299491643906,
-0.009210650809109211,
-0.0424291230738163,
-0.026292834430933,
0.022638507187366486,
-0.010529469698667526,
-0.0144508583471179,
-0.0006385542219504714,
0.03298450633883476,
0.017876340076327324,
-0.020658226683735847,
-0.03524727374315262,
-0.0072756544686853886,
-0.043715935200452805,
0.006706899497658014,
-0.005111624486744404,
0.0031488933600485325,
-0.019261721521615982,
-0.05986487492918968,
0.011342604644596577,
-0.014435439370572567,
0.05554986372590065,
0.06517300754785538,
0.0010852208361029625,
-0.018764514476060867,
-0.02069200575351715,
0.042334455996751785,
0.017140647396445274,
0.00925468374043703,
0.03670939803123474,
0.006814128253608942,
0.05080489441752434,
0.027922142297029495,
-0.03507799282670021,
-0.010869661346077919,
-0.04321935027837753,
0.04341480880975723,
0.04679623991250992,
0.015521963126957417,
-0.014980984851717949,
0.009350410662591457,
0.013952713459730148,
0.03036186657845974,
0.0055580479092895985,
0.04611806198954582,
-0.03169025853276253,
0.07596414536237717,
-0.07391371577978134,
-0.03066045232117176,
-0.018890345469117165,
-0.03661619499325752,
0.009435110725462437,
0.047389425337314606,
-0.010372316464781761,
-0.018363110721111298,
-0.002567891264334321,
-0.057228799909353256,
0.014934144914150238,
0.041180577129125595,
0.058781709522008896,
0.08179301768541336,
-0.06466910988092422,
-0.005340150557458401,
-0.03842214122414589,
-0.016747644171118736,
-0.018139254301786423,
0.03371020406484604,
0.00020850123837590218,
-0.018533801659941673,
-0.045535072684288025,
0.011485548689961433,
-0.012192497961223125,
-0.028729595243930817,
0.041325975209474564,
0.00008405510016018525,
0.02113908901810646,
-0.009022889658808708,
0.021697580814361572,
-0.012588363140821457,
-0.0012964289635419846,
0.0008630200172774494,
-0.006678991485387087,
0.07204093039035797,
0.010754515416920185,
0.026600198820233345,
0.006802848540246487,
-0.004480708856135607,
-0.0464899018406868,
-0.01302980724722147,
0.032465897500514984,
-0.010360955260694027,
0.02391642890870571,
0.025700723752379417,
0.04308373108506203,
-0.04269206523895264,
-0.0025586073752492666,
-0.01664232462644577,
0.004881711211055517,
0.015139717608690262,
-0.003692428581416607,
0.017590435221791267,
-0.05831403285264969,
0.04424721747636795,
0.014761500060558319,
0.0314030647277832,
-0.013707033358514309,
0.07192540913820267,
0.06756250560283661,
0.025645729154348373,
0.018717965111136436,
-0.0013792527606710792,
0.041915468871593475,
0.08158242702484131,
0.07144042104482651,
0.050665128976106644,
-0.038236264139413834,
-0.046189773827791214,
0.01167161762714386,
0.02418314479291439,
-0.02537703886628151,
-0.04796554520726204,
-0.004257901571691036,
-0.012470722198486328,
0.04729747772216797,
-0.0007953892345540226,
0.013778842985630035,
0.011202225461602211,
-0.03935449570417404,
-0.04148677736520767,
0.041614994406700134,
0.05955829843878746,
-0.034379396587610245,
-0.013062362559139729,
-0.06261977553367615,
0.0010254418011754751,
-0.030234690755605698,
0.029741937294602394,
-0.06647753715515137,
0.0074003636837005615,
0.018066415563225746,
-0.013094261288642883,
-0.06703358143568039,
-0.01794271171092987,
-0.01965336501598358,
-0.015432192012667656,
0.03352900967001915,
-0.03726298734545708,
0.04371532052755356,
0.008605577982962132,
0.04685021564364433,
-0.021678762510418892,
0.03521629795432091,
-0.0070723858661949635,
0.01780867949128151,
-0.05367050692439079,
0.039217352867126465,
0.07588577270507812,
-0.04711516574025154,
0.00211746571585536,
0.010687006637454033,
-0.029854614287614822,
0.024025576189160347,
0.017708322033286095,
-0.03857890143990517,
0.04901336506009102,
0.01927737332880497,
-0.03729510307312012,
-0.010434026829898357,
0.056428950279951096,
0.012989070266485214,
0.02004912681877613,
0.0148869464173913,
-0.07120631635189056,
0.01732797361910343,
-0.006218187045305967,
0.018399566411972046,
-0.008833191357553005,
0.053496260195970535,
-0.01515587791800499,
-0.017886675894260406,
-0.009171443991363049,
-0.02495158277451992,
-0.05545610189437866,
-0.06545981019735336,
-0.021136194467544556,
0.021259525790810585,
-0.03205479681491852,
0.050449009984731674,
0.05603441968560219,
-0.03705405443906784,
-0.09282892942428589,
0.00032524054404348135,
-0.016527695581316948,
0.0072975605726242065,
-0.04308576136827469,
0.012406487949192524,
-0.021820664405822754,
0.015784572809934616,
-0.04085118696093559,
-0.028278978541493416,
0.08958379179239273,
-0.02033938467502594,
-0.0005657613510265946,
0.0004548257275018841,
-0.006673265248537064,
0.017978332936763763,
0.027146723121404648,
-0.04835410788655281,
0.052845317870378494,
0.004232318140566349,
-0.012497085146605968,
-0.027278300374746323,
0.030385108664631844,
-0.004676880314946175,
0.06742003560066223,
-0.027198752388358116,
-0.06354507803916931,
0.0346379429101944,
0.027107704430818558,
-0.0413774736225605,
-0.018677271902561188,
0.033341776579618454,
0.021869409829378128,
0.05429376661777496,
-0.0005309440311975777,
-0.0018846150487661362,
0.07713556289672852,
-0.02892475016415119,
0.0700087621808052,
0.030658310279250145,
-0.019579729065299034,
0.008605861105024815,
-0.02149471454322338,
0.00298637175001204,
0.06731151044368744,
-0.05036432296037674,
0.059913184493780136,
-0.03590914234519005,
0.0058776880614459515,
0.008899911306798458,
0.054190732538700104,
0.05708160251379013,
-0.05567542091012001,
0.04304971173405647,
0.042485322803258896,
-0.0158458910882473,
-0.015970880165696144,
0.03360603377223015,
-0.0005009442684240639,
-0.0067052943632006645,
-0.021801264956593513,
0.06186138093471527,
-0.035793814808130264,
-0.07175838202238083,
0.03613567352294922,
-0.008812079206109047,
-0.014048769138753414,
0.013939682394266129,
-0.023608487099409103,
0.012671828269958496,
-0.011464929208159447,
-0.04527655243873596,
-0.03191706910729408,
0.00419978890568018,
-0.0396876260638237,
0.022489525377750397,
0.08547654002904892,
-0.01502827275544405,
-0.0561058409512043,
0.0025376081466674805,
-0.050854604691267014,
-0.011420986615121365,
-0.025975530967116356,
0.013740193098783493,
-0.020385876297950745,
0.04930562525987625,
0.03319983929395676,
-0.01956184022128582,
-0.012301173061132431,
0.033334553241729736,
0.005235281307250261,
-0.014918988570570946,
0.017131324857473373,
0.011018789373338223,
-0.0411342978477478,
-0.005980395246297121,
0.049050472676754,
-0.05299082770943642,
0.03187326714396477,
0.024330781772732735,
-0.009906906634569168,
-0.0004943580715917051,
0.0003618237969931215,
0.02784648910164833,
-0.054470933973789215,
0.03176989406347275,
-0.013301396742463112,
-0.0051082125864923,
-0.024995896965265274,
0.06139529123902321,
-0.029668886214494705,
0.05187244713306427,
-0.01396141853183508,
-0.024515558034181595,
0.009345813654363155,
-0.02730177342891693,
0.08643567562103271,
-0.01330309733748436,
0.03859834745526314,
-0.0024911456275731325,
-0.050348199903964996,
-0.0112460283562541,
0.03433073312044144,
0.018168725073337555,
-0.032582804560661316,
0.07613957673311234,
0.0036938912235200405,
-0.023890599608421326,
-0.0409197062253952,
0.01319097075611353,
0.02477782964706421,
-0.059729717671871185,
-0.03098384477198124,
-0.04888087511062622,
-0.032782070338726044,
0.009870285168290138,
0.012129506096243858,
-0.008127209730446339,
-0.013132404536008835,
-0.0011187834898009896,
0.0291067473590374,
0.003119186032563448,
-0.04847166687250137,
-0.014158327132463455,
0.05180172994732857,
-0.048192765563726425,
0.017752451822161674,
0.024999694898724556,
0.027302691712975502,
-0.09294422715902328,
0.037606578320264816,
-0.013309822417795658,
0.006389168556779623,
-0.034582965075969696,
-0.0076834470964968204,
-0.022363102063536644,
-0.004838119260966778,
-0.031184302642941475,
0.0059072403237223625,
0.06841149926185608,
-0.04152790829539299,
-0.03879591077566147,
0.04828007146716118,
-0.02681039273738861,
0.07106263935565948,
0.05405678227543831,
-0.043579425662755966,
0.026152780279517174,
0.04837736487388611,
0.07117192447185516,
0.034810300916433334,
-0.03159727901220322,
0.0037400999572128057,
0.02201453223824501,
0.028269058093428612,
-0.01822342351078987,
0.0001454337761970237,
-0.045692723244428635,
-0.05222916603088379
] |
<p><strong>Problem statement:</strong></p>
<p>A cylinder rolls without slipping down a hill. It is released from height h. What is its speed when it come down? The cylinder mass may be completely concentrated on the radius R, which is the radius of the cylinder.</p>
<p><strong>My thoughts:</strong></p>
<p>At the top(hight h) the potential energy of the cylinder is E=mgh and at the bottom(h=0) all energy has become kinetic energy since friction and air drag is neglected in this context.(I assumed this). Thus:</p>
<p>$mgh=\frac{1}{2}mv^2 \Leftrightarrow v=\sqrt{2gh}$ </p>
<p><strong>Correct answer</strong> is however $v=\sqrt{gh}$ which means that energy must have been lost,correct?</p>
<p>What have i missed?</p>
<p><img src="http://i.imgur.com/Ge3x1nu.png" alt="picture"></p> | g4781 | [
0.07809018343687057,
0.007718635722994804,
-0.00842168927192688,
0.04223687946796417,
0.037865668535232544,
0.032481275498867035,
0.07506760209798813,
0.005743572022765875,
-0.08761734515428543,
0.008409813046455383,
-0.03576066717505455,
0.021823201328516006,
0.004633454140275717,
0.025642620399594307,
-0.005485450383275747,
0.021462103351950645,
0.08510056138038635,
-0.05151667073369026,
0.04009773209691048,
-0.014366485178470612,
-0.06637237966060638,
0.017498403787612915,
-0.042254120111465454,
-0.029615510255098343,
0.03564372658729553,
-0.031054344028234482,
0.05162670835852623,
-0.028501037508249283,
-0.05906078219413757,
-0.024137472733855247,
0.014895913191139698,
-0.009901672601699829,
0.05942574888467789,
-0.049142979085445404,
-0.03062513656914234,
-0.003084934316575527,
0.06874609738588333,
-0.00219943025149405,
0.03172017261385918,
-0.05101810768246651,
0.03762686252593994,
-0.025032948702573776,
0.025225643068552017,
0.004846162628382444,
-0.005672656465321779,
-0.00953512080013752,
0.002506200922653079,
0.04296993464231491,
0.004482722375541925,
-0.02477983757853508,
0.03281274065375328,
0.036114346235990524,
0.00419885478913784,
-0.0877332091331482,
-0.01736896112561226,
0.0024752728641033173,
-0.02050931565463543,
-0.00896926037967205,
0.021695416420698166,
0.04032713919878006,
0.026332780718803406,
-0.06322149187326431,
0.012545262463390827,
-0.02000860497355461,
0.028642762452363968,
-0.055877167731523514,
-0.059985678642988205,
-0.018906783312559128,
0.0406801737844944,
0.005852486006915569,
0.022220289334654808,
-0.014511039480566978,
0.013829091563820839,
-0.06434199959039688,
-0.04465961828827858,
-0.050845276564359665,
0.02766719087958336,
-0.057073283940553665,
0.018846381455659866,
-0.054533958435058594,
-0.05766281858086586,
0.03940229117870331,
-0.00326421856880188,
0.03335225209593773,
0.046677324920892715,
0.030843492597341537,
0.023026131093502045,
0.06160154566168785,
-0.032248854637145996,
0.08005749434232712,
0.020935816690325737,
-0.02114972285926342,
0.0771041065454483,
-0.001059018773958087,
-0.0040946342051029205,
-0.020588675513863564,
-0.04542713239789009,
0.10126814991235733,
0.02103176899254322,
0.013786549679934978,
-0.01666281558573246,
-0.07475906610488892,
-0.03314986824989319,
-0.014049804769456387,
0.02498438209295273,
-0.010802543722093105,
-0.014696236699819565,
0.040113355964422226,
0.019440695643424988,
-0.0037881096359342337,
0.05679616332054138,
-0.018287839367985725,
-0.0672936663031578,
-0.06314749270677567,
-0.024520890787243843,
-0.08636479824781418,
0.0625595971941948,
-0.02423781156539917,
-0.025476474314928055,
0.03127510845661163,
-0.007543443236500025,
0.05733821541070938,
-0.002449182327836752,
0.060860034078359604,
-0.01875370182096958,
0.0018923883326351643,
-0.018832605332136154,
0.012836750596761703,
0.028562234714627266,
0.005627037957310677,
-0.038344502449035645,
-0.016733167693018913,
0.03513579070568085,
-0.0022863124031573534,
0.03680014982819557,
0.041432030498981476,
-0.0364324115216732,
0.032129738479852676,
0.009856718592345715,
0.0034454050473868847,
0.045203085988759995,
-0.016593899577856064,
0.01479008886963129,
0.010491980239748955,
-0.04945790395140648,
0.020688548684120178,
-0.016655372455716133,
0.041324108839035034,
0.0259696152061224,
-0.03547373041510582,
0.013580414466559887,
0.021353667601943016,
0.002246486023068428,
-0.09718886017799377,
0.04881013557314873,
-0.011848443187773228,
0.05077921226620674,
0.02818663977086544,
0.011318031698465347,
0.04594772681593895,
0.051016151905059814,
-0.02179025672376156,
0.019224192947149277,
0.009564505890011787,
-0.035308629274368286,
0.04533853009343147,
-0.031161697581410408,
-0.02726641297340393,
0.029703820124268532,
-0.023014111444354057,
-0.048061471432447433,
-0.025714481249451637,
0.04696805775165558,
-0.0008286663796752691,
-0.05822610855102539,
0.005261857528239489,
0.10784018784761429,
-0.027198858559131622,
-0.03240683674812317,
0.009061492048203945,
-0.006456137169152498,
-0.01841692253947258,
0.028870994225144386,
-0.019369252026081085,
0.057840436697006226,
-0.002929776906967163,
-0.010064850561320782,
0.03347400575876236,
-0.041074108332395554,
-0.03183480724692345,
-0.026814166456460953,
0.03990768641233444,
0.02166549488902092,
0.020114067941904068,
-0.05524585396051407,
0.01933968812227249,
0.04790571704506874,
-0.0407910980284214,
0.016725728288292885,
0.04570654779672623,
0.021463871002197266,
0.02703455276787281,
0.046150095760822296,
-0.010155259631574154,
0.029744984582066536,
0.0354948416352272,
0.05158119276165962,
0.0313723050057888,
-0.00881407130509615,
0.0012115240097045898,
0.03413829952478409,
0.025508573278784752,
-0.026738859713077545,
0.01263058464974165,
0.019697997719049454,
-0.05905211716890335,
-0.0286224577575922,
0.051738351583480835,
-0.032252147793769836,
-0.005038140807300806,
-0.02606922574341297,
0.0015498900320380926,
-0.0182895977050066,
-0.0015942204045131803,
-0.04925423860549927,
-0.0074898176826536655,
-0.05599801242351532,
-0.040929727256298065,
-0.0370127335190773,
-0.043042223900556564,
-0.01700642518699169,
0.03540044650435448,
-0.026516448706388474,
-0.06612171232700348,
0.033908016979694366,
0.06732864677906036,
-0.03810388967394829,
0.00583339249715209,
0.021343523636460304,
0.021843643859028816,
-0.0117800859734416,
-0.03524461016058922,
-0.0211715679615736,
-0.055971771478652954,
0.0006071694660931826,
0.027165217325091362,
0.0061864363960921764,
-0.005093824118375778,
0.02696298062801361,
0.053308624774217606,
0.022980276495218277,
-0.009222268126904964,
0.028976256027817726,
0.02047117054462433,
0.024349693208932877,
0.04019078239798546,
-0.06786283850669861,
-0.03903984650969505,
-0.02333163656294346,
-0.06933197379112244,
-0.019010500982403755,
-0.003874001558870077,
-0.007710953243076801,
0.00973791629076004,
-0.05829944834113121,
-0.0026431463193148375,
-0.035263366997241974,
-0.04601617157459259,
0.007566212676465511,
-0.015479945577681065,
-0.03722912445664406,
0.032126978039741516,
0.002040969207882881,
0.03976532444357872,
0.00011964081204496324,
-0.04973636567592621,
-0.009867694228887558,
-0.023705611005425453,
0.016734102740883827,
-0.010847803205251694,
-0.002889245515689254,
-0.012073496356606483,
-0.051950301975011826,
0.004300719127058983,
-0.00980035588145256,
-0.06667165458202362,
0.040122512727975845,
0.021486913785338402,
-0.009167837910354137,
0.04073047265410423,
-0.06303318589925766,
0.04581136256456375,
0.08806764334440231,
0.03565576300024986,
0.02007094956934452,
0.1006687581539154,
0.04674156382679939,
-0.023829923942685127,
-0.05031490698456764,
-0.07157975435256958,
-0.007019591983407736,
-0.016891371458768845,
-0.02130940929055214,
0.01884104683995247,
0.0028606329578906298,
0.00917022954672575,
0.009399423375725746,
-0.06400001794099808,
-0.038374386727809906,
-0.019688831642270088,
0.011962893418967724,
0.050940047949552536,
0.06315790116786957,
0.019280551001429558,
-0.09315163642168045,
0.023979488760232925,
-0.04165121540427208,
-0.033685069531202316,
0.010387750342488289,
0.0556439571082592,
-0.04034857079386711,
-0.06264002621173859,
-0.03567048907279968,
0.026221051812171936,
0.011065869592130184,
-0.03226527199149132,
-0.06453297287225723,
0.022626657038927078,
0.03295892849564552,
-0.0359475202858448,
-0.018002301454544067,
0.08912963420152664,
0.009971939027309418,
-0.03313814848661423,
-0.013946857303380966,
-0.03309570252895355,
-0.003036584472283721,
-0.03195851296186447,
0.04092295840382576,
-0.011665159836411476,
-0.01832900196313858,
0.019217370077967644,
-0.008725262247025967,
-0.019705763086676598,
0.003540295409038663,
0.03850708529353142,
-0.00712181068956852,
0.004898689687252045,
-0.013851753436028957,
-0.044521503150463104,
0.039754174649715424,
-0.037793129682540894,
0.03017406538128853,
-0.026372678577899933,
-0.034867171198129654,
0.03298388421535492,
-0.03905068710446358,
0.012060843408107758,
-0.018251489847898483,
0.023858556523919106,
-0.0012228001141920686,
-0.050117239356040955,
-0.0055979411117732525,
0.06846744567155838,
0.030598308891057968,
-0.042107079178094864,
-0.06263213604688644,
0.06269944459199905,
-0.01962050423026085,
0.015578833408653736,
0.007061685435473919,
-0.008344752714037895,
-0.022377029061317444,
0.01779950223863125,
0.05573899298906326,
-0.002670024521648884,
-0.017472917214035988,
0.008571191690862179,
-0.025770213454961777,
0.024376632645726204,
0.08331577479839325,
-0.03236270323395729,
-0.03335217759013176,
0.021564291790127754,
-0.010034460574388504,
-0.016478179022669792,
-0.05673854053020477,
-0.024114664644002914,
0.013666742481291294,
0.011092444881796837,
0.017833871766924858,
-0.003035240340977907,
0.009369824081659317,
0.03066117689013481,
-0.023365085944533348,
0.015622999519109726,
0.04462648555636406,
-0.0072949230670928955,
-0.028261816129088402,
0.0456729531288147,
-0.03010646067559719,
0.0034520227927714586,
-0.05374889075756073,
-0.007665765006095171,
0.017779750749468803,
0.02449517697095871,
0.05829731747508049,
-0.024269776418805122,
0.0191495418548584,
-0.010587996803224087,
0.026824384927749634,
-0.04354989901185036,
-0.03545920178294182,
-0.01810290850698948,
0.030898533761501312,
-0.01816934533417225,
-0.0006295227794907987,
0.003071195911616087,
-0.04477377608418465,
0.023043785244226456,
0.0022288847249001265,
0.027619630098342896,
-0.004830815363675356,
-0.0002990047796629369,
-0.005010336171835661,
-0.012671580538153648,
0.0424346849322319,
0.04685023054480553,
0.004573132377117872,
0.007757014129310846,
0.0035043007228523493,
-0.0061927600763738155,
-0.042825885117053986,
-0.032253436744213104,
-0.013474339619278908,
0.06839872151613235,
0.04476717859506607,
-0.013456988148391247,
0.005582977086305618,
0.06278432905673981,
0.02444511279463768,
-0.0027430469635874033,
0.003965579904615879,
0.04427444562315941,
-0.016287576407194138,
0.029810013249516487,
-0.03223853185772896,
-0.035784993320703506,
0.02333325333893299,
-0.10034864395856857,
-0.03907584398984909,
0.0018922267481684685,
0.031197737902402878,
0.043003592640161514,
-0.03615747019648552,
0.008125631138682365,
-0.055279914289712906,
-0.009184635244309902,
-0.008096306584775448,
0.006339621730148792,
0.017447134479880333,
0.03639650344848633,
0.01404427457600832,
0.023576317355036736,
-0.004237059503793716,
-0.028789525851607323,
-0.026775220409035683,
0.021964916959404945,
-0.014571750536561012,
-0.013118481263518333,
-0.003966939635574818,
-0.03331402689218521,
0.023924974724650383,
-0.032736167311668396,
-0.012619572691619396,
0.009604413993656635,
0.028815966099500656,
0.012021828442811966,
0.07585334777832031,
-0.05209836736321449,
-0.055247046053409576,
0.021230874583125114,
0.03631835803389549,
0.011291798204183578,
0.01258817221969366,
0.049417443573474884,
-0.04214067757129669,
-0.008015311323106289,
-0.0050844163633883,
-0.0029559610411524773,
0.03172674402594566,
0.042431142181158066,
-0.06511689722537994,
-0.014143713749945164,
0.02066132053732872,
0.0010493723675608635,
0.046827781945466995,
-0.012494472786784172,
-0.04962463304400444,
0.020893029868602753,
-0.05873703584074974,
-0.011580762453377247,
-0.010072404518723488,
0.012075056321918964,
-0.033117469400167465,
0.02313263528048992,
0.06086849793791771,
0.00044798830640502274,
-0.003916194662451744,
0.06531219184398651,
-0.0006837220280431211,
0.03446466103196144,
0.04010629653930664,
0.03443841636180878,
0.010514366440474987,
-0.044658925384283066,
0.01550247147679329,
0.056210339069366455,
0.020858563482761383,
0.03041437454521656,
0.05472659319639206,
0.059442613273859024,
0.044861555099487305,
-0.0360085628926754,
-0.018101878464221954,
-0.0013545836554840207,
-0.04809212312102318,
-0.024541158229112625,
-0.043808579444885254,
0.05011887848377228,
-0.00523958308622241,
-0.03853146731853485,
-0.0012508830986917019,
0.035730406641960144,
-0.008502858690917492,
-0.008822205476462841,
0.00847200769931078,
-0.03389718011021614,
0.015365255996584892,
-0.04205762967467308,
-0.030385054647922516,
0.004538541194051504,
-0.026337379589676857,
0.059506554156541824,
-0.03894755244255066,
0.018118204548954964,
-0.10415587574243546,
-0.03771807625889778,
0.04516596347093582,
-0.027270615100860596,
-0.006536321248859167,
0.0394488126039505,
-0.004266789183020592,
0.05409202724695206,
-0.031705837696790695,
0.016122646629810333,
0.04417310655117035,
-0.05526602640748024,
-0.008151886984705925,
-0.03079255484044552,
0.022662324830889702,
0.004974353592842817,
-0.014915772713720798,
0.05277986079454422,
0.0596143938601017,
-0.047095946967601776,
0.012422596104443073,
0.033915646374225616,
0.040416501462459564,
0.01992059126496315,
0.018478861078619957,
0.01448627095669508,
0.07383964955806732,
0.012859556823968887,
0.02795347571372986,
0.002111012814566493,
-0.08222118765115738,
-0.04617386311292648,
-0.007364423479884863,
-0.008345303125679493,
-0.012003346346318722,
0.004342959728091955,
0.09337206184864044,
-0.0556318573653698,
0.009614954702556133,
-0.04094359651207924,
-0.01900372840464115,
-0.030823038890957832,
0.07811561971902847,
-0.020907152444124222,
0.001415697974152863,
0.07895504683256149,
-0.02434637024998665,
-0.002183615928515792,
-0.04768899083137512,
-0.010268960148096085,
-0.02097015641629696,
-0.015173758380115032,
-0.054708097130060196,
0.009639846161007881,
-0.015722963958978653,
0.027776198461651802,
0.03913283720612526,
-0.01742228865623474,
0.025461306795477867,
0.0024246135726571083,
0.013827789574861526,
0.034010108560323715,
-0.03495820611715317,
0.014597486704587936,
-0.01353527046740055,
0.04077719897031784,
0.0031598543282598257,
0.0067445263266563416,
-0.041010599583387375,
0.004882436245679855,
0.03780621662735939,
0.03001677617430687,
0.043837789446115494,
-0.08409292995929718,
-0.012064989656209946,
0.03390112891793251,
0.07593246549367905,
-0.044599588960409164,
0.030527181923389435,
0.0048377844505012035,
-0.10221746563911438,
0.05086439102888107,
0.02449878118932247,
0.0025839293375611305,
0.04307179898023605,
0.026866672560572624,
-0.025825174525380135,
0.03450494632124901,
-0.017901089042425156,
0.03214611858129501,
-0.020789729431271553,
0.02185947448015213,
0.0538865402340889,
0.00187735166400671,
-0.00895541813224554,
0.032885510474443436,
0.0026484462432563305,
0.021085934713482857,
-0.05174874886870384,
-0.0033039848785847425,
0.024846546351909637,
-0.027744123712182045,
0.0029725730419158936,
-0.03297184407711029,
0.0014563133008778095,
0.01296925637871027,
-0.045828089118003845,
0.055958349257707596,
-0.0009710626909509301,
-0.01901886612176895,
-0.03720913454890251,
0.03992093354463577,
0.0279129259288311,
-0.06309624761343002,
-0.0185933206230402,
-0.018170002847909927,
0.02080366760492325,
0.02100437320768833,
-0.006381593178957701,
0.03603701293468475,
-0.003134381491690874,
-0.061023302376270294,
-0.012194146402180195,
-0.021845458075404167,
0.03511868044734001,
0.0000970357286860235,
-0.060939304530620575,
-0.019394490867853165,
-0.034841388463974,
-0.0041040717624127865,
0.01404216606169939,
-0.023213258013129234,
-0.03461331129074097,
0.006639382801949978,
-0.009065776132047176,
-0.00914087239652872,
0.003188114380463958,
0.008467909879982471,
-0.0023666550405323505,
0.0030277736950665712,
-0.0502028651535511,
-0.021674128249287605,
0.012629080563783646,
0.011850337497889996,
-0.0263117253780365,
0.07372894138097763,
0.04213540256023407,
-0.008097084239125252,
-0.014193910174071789,
-0.02414599061012268,
0.003856160445138812,
0.03588517755270004,
0.03754464536905289,
-0.03171899914741516,
0.025061672553420067,
0.021649368107318878,
0.013268297538161278,
0.05251212790608406,
-0.03780065476894379,
0.04458761215209961,
-0.00593958143144846,
-0.03454889729619026,
-0.05184489116072655,
0.03517879173159599,
0.03155122324824333,
0.01465841569006443,
0.014344851486384869,
0.018208105117082596,
0.052607253193855286,
0.043342288583517075,
-0.04862681031227112,
-0.023604264482855797,
0.012933045625686646,
-0.05841406434774399,
-0.026739569380879402,
-0.03221488744020462,
0.0018502927850931883,
-0.07889451831579208,
-0.036651287227869034,
-0.037174955010414124,
-0.037469394505023956,
-0.02195906639099121,
-0.024278054013848305,
-0.030801862478256226,
-0.020721742883324623,
-0.03411432355642319,
0.011723365634679794,
-0.006436015944927931,
-0.002628984162583947,
-0.049298081547021866,
0.02209540270268917,
0.03282640129327774,
-0.008482491597533226,
0.005253983195871115,
-0.05751346796751022,
-0.039577558636665344,
0.021743904799222946,
0.019548233598470688,
-0.006816189270466566,
-0.042859192937612534,
-0.05101914331316948,
0.09566357731819153,
0.021732831373810768,
-0.04755401238799095,
0.025141900405287743,
0.02050328254699707,
0.008589540608227253,
0.018349790945649147,
0.030505811795592308,
-0.048437729477882385,
0.009076480753719807,
0.024164635688066483,
-0.05248335003852844,
-0.020930254831910133,
-0.04887831211090088,
-0.01587204448878765,
0.008132128044962883,
-0.0615554004907608,
0.058638907968997955,
-0.0839485228061676,
0.016018813475966454,
0.0547652393579483
] |
<blockquote>
<p><em>A block of mass $200$kg is connected to a horizontal ceiling by four identical light elastic ropes, each having natural length $7$m and stiffness $180$N/m. It is also connected to the floor by a single light elastic rope having stiffness $80$N/m. All five ropes are stretched and vertical, and air resistance is neglected.</em></p>
<p><em>Find the tension in one of the upper ropes.</em></p>
</blockquote>
<p>I know it's just $kx$, but I don't understand why it is not $\frac{kx}{4}$ because tension is shared between four ropes. </p> | g4782 | [
0.05500234663486481,
-0.00676904059946537,
-0.009386396035552025,
0.008725042454898357,
0.02426832914352417,
0.006010335870087147,
0.019381484016776085,
-0.0036176869180053473,
-0.08396464586257935,
-0.030806850641965866,
-0.043798480182886124,
-0.01680106297135353,
-0.03710465133190155,
0.005321281496435404,
0.03422132506966591,
0.05004740133881569,
0.08449780195951462,
0.003183277091011405,
0.0490933321416378,
-0.0312933549284935,
-0.06881078332662582,
-0.015587225556373596,
0.003973584622144699,
-0.037950299680233,
0.030244246125221252,
0.015558564104139805,
0.03842299431562424,
-0.039769940078258514,
-0.07690410315990448,
0.0005457234219647944,
0.01741032861173153,
0.018756872043013573,
0.06157073378562927,
-0.03608165681362152,
-0.01590711995959282,
-0.03308553993701935,
0.056105177849531174,
-0.008527521044015884,
0.001856394694186747,
-0.039523277431726456,
-0.007314401213079691,
0.03154623135924339,
-0.08067864924669266,
0.04097941517829895,
-0.034287866204977036,
0.014663354493677616,
-0.03557808697223663,
0.0505027212202549,
0.006831520237028599,
-0.040199559181928635,
-0.012049783952534199,
0.0881551131606102,
0.0006397393299266696,
-0.04812859743833542,
0.015401260927319527,
0.04198974743485451,
0.0024966741912066936,
0.03660279139876366,
0.03561749681830406,
0.06779737025499344,
-0.03783709183335304,
-0.019506309181451797,
0.04657931253314018,
0.02164253406226635,
0.02001178450882435,
-0.025592168793082237,
0.015327949076890945,
-0.016816290095448494,
0.06769944727420807,
0.05069204419851303,
-0.006451056804507971,
-0.050157226622104645,
0.005079245660454035,
0.002023066394031048,
-0.04131881147623062,
-0.022807324305176735,
0.001542946440167725,
0.012739957310259342,
-0.037196606397628784,
-0.010048601776361465,
0.013500680215656757,
0.043178778141736984,
-0.01935628056526184,
-0.01368360873311758,
-0.008946003392338753,
0.0025243517011404037,
-0.016375793144106865,
-0.009298083372414112,
-0.031373314559459686,
-0.01733863539993763,
0.059015605598688126,
-0.022224068641662598,
0.05332871153950691,
0.015505753457546234,
-0.010677700862288475,
-0.03968483582139015,
-0.014416554011404514,
0.03915155678987503,
-0.018862618133425713,
-0.06545817106962204,
-0.010667700320482254,
-0.033585477620363235,
-0.029492301866412163,
0.01296511571854353,
-0.03765760734677315,
-0.01566634140908718,
0.01574096269905567,
0.005493395496159792,
-0.028937287628650665,
-0.045315589755773544,
-0.01829875446856022,
0.01562075037509203,
-0.05006283521652222,
-0.04796788468956947,
-0.036579594016075134,
-0.025354908779263496,
0.050380170345306396,
0.012930255383253098,
-0.003294095629826188,
-0.0012174155563116074,
-0.013555335812270641,
-0.019314240664243698,
0.03264075517654419,
-0.0038204484153538942,
-0.03614269942045212,
-0.025838427245616913,
0.07497122138738632,
0.05610564723610878,
0.011531691998243332,
-0.0451420396566391,
-0.003910160157829523,
0.01124065276235342,
0.030952520668506622,
-0.043373215943574905,
0.05268729105591774,
0.018019400537014008,
-0.040214307606220245,
-0.013304834254086018,
0.004747125320136547,
0.027795856818556786,
-0.013887382112443447,
0.012029648758471012,
-0.012554644607007504,
-0.02181856334209442,
-0.05441968888044357,
-0.01898634433746338,
-0.01518233586102724,
-0.030682004988193512,
0.03314927965402603,
-0.023760903626680374,
-0.015255366452038288,
0.05815168097615242,
-0.031137807294726372,
-0.009987695142626762,
0.0348178893327713,
-0.002936477307230234,
0.06471724808216095,
-0.018895965069532394,
0.0014776659663766623,
0.03541930392384529,
0.013573640026152134,
0.005283685866743326,
-0.011807774193584919,
-0.03562617674469948,
-0.05179107189178467,
0.02765066735446453,
0.021274618804454803,
0.01613985002040863,
0.016809016466140747,
-0.04878658056259155,
-0.05232203006744385,
-0.04868413135409355,
0.012171541340649128,
0.04332171007990837,
0.00010708814079407603,
0.0664682537317276,
0.0514209121465683,
-0.04104907438158989,
0.05352045223116875,
0.022096095606684685,
0.004317767918109894,
-0.032979536801576614,
0.05791131407022476,
-0.006999399978667498,
-0.03747019171714783,
0.04335717111825943,
0.018231552094221115,
-0.049312297254800797,
-0.035109590739011765,
-0.05695660039782524,
-0.007845374755561352,
0.022429734468460083,
0.010916709899902344,
0.04304220527410507,
0.028514795005321503,
-0.030609313398599625,
-0.027946924790740013,
0.00699864374473691,
-0.03015943244099617,
0.03288310766220093,
0.06719561666250229,
0.009120522066950798,
0.05749790370464325,
-0.021199669688940048,
0.02752086892724037,
0.060247134417295456,
-0.01168285496532917,
-0.00011892483598785475,
0.07738227397203445,
-0.03757496178150177,
-0.03745221346616745,
-0.02788870595395565,
-0.016228923574090004,
0.0428951270878315,
-0.00004617613376467489,
-0.06779735535383224,
0.043611280620098114,
0.07893379032611847,
-0.04183289036154747,
0.04403742402791977,
-0.01115963514894247,
0.02627628669142723,
-0.006390893366187811,
-0.009062095545232296,
-0.06591467559337616,
-0.0707831010222435,
-0.032885584980249405,
-0.008370579220354557,
-0.0356975756585598,
-0.03770831599831581,
-0.042952243238687515,
-0.029378794133663177,
-0.03151330351829529,
0.036972545087337494,
0.042117889970541,
0.10360420495271683,
0.017278866842389107,
0.02672756090760231,
0.0177608672529459,
-0.02845701016485691,
0.007505633868277073,
-0.060628101229667664,
-0.025993656367063522,
-0.023473292589187622,
0.05414094030857086,
0.06301995366811752,
0.04360957816243172,
-0.015612313523888588,
0.01217105146497488,
0.08030147105455399,
0.019305115565657616,
0.015250183641910553,
-0.055356454104185104,
0.028704430907964706,
0.009575924836099148,
-0.04472367465496063,
-0.00036080583231523633,
0.0024489853531122208,
-0.01000099815428257,
-0.02465211972594261,
-0.02185584418475628,
-0.06592442840337753,
0.0031333155930042267,
0.0026887848507612944,
-0.13990655541419983,
-0.018858779221773148,
-0.027136381715536118,
-0.03531714528799057,
0.033713750541210175,
0.030460873618721962,
0.012601757422089577,
0.061378758400678635,
0.005606153514236212,
0.023709071800112724,
-0.020221872255206108,
-0.0696493536233902,
0.014187987893819809,
0.035101935267448425,
-0.04781283810734749,
0.062085166573524475,
0.07810927927494049,
0.025780227035284042,
-0.0363759882748127,
0.012196888215839863,
0.03824581578373909,
-0.028260469436645508,
-0.012637763284146786,
0.03465376794338226,
0.011666461825370789,
-0.002146607032045722,
-0.0026455591432750225,
0.022675227373838425,
0.020278165116906166,
-0.007398821413516998,
0.023481523618102074,
0.026456600055098534,
-0.04907136410474777,
0.01816023327410221,
-0.05321837589144707,
0.03004269488155842,
-0.06893531233072281,
0.008391089737415314,
-0.005337701644748449,
0.025444697588682175,
0.02074863575398922,
-0.004053219687193632,
-0.013622421771287918,
-0.008044290356338024,
0.014498160220682621,
0.04353624954819679,
0.002775514731183648,
0.038446929305791855,
0.07770799100399017,
0.007891391403973103,
-0.04053405299782753,
-0.010785132646560669,
0.07493558526039124,
0.019148601219058037,
-0.008639434352517128,
-0.03846906125545502,
-0.013979344628751278,
-0.0067023588344454765,
-0.02396448887884617,
0.0008164773462340236,
-0.07816677540540695,
0.0006421190919354558,
-0.0859651193022728,
0.028132442384958267,
-0.06714437156915665,
-0.017936719581484795,
-0.030312327668070793,
-0.019313277676701546,
0.015835890546441078,
-0.056035853922367096,
-0.05251835286617279,
-0.07725086808204651,
-0.02798713743686676,
0.002644563326612115,
-0.011582490988075733,
-0.013524670153856277,
-0.06612754613161087,
0.008165596053004265,
-0.02004505693912506,
0.03522404655814171,
0.002406276762485504,
0.0029754918068647385,
-0.019238250330090523,
0.058227699249982834,
0.03925656899809837,
0.007613942492753267,
0.0060694897547364235,
0.009766546078026295,
0.002710081171244383,
0.0034463361371308565,
0.0041857496835291386,
0.05373004078865051,
0.03990250453352928,
0.02494274266064167,
-0.023439154028892517,
0.008181951940059662,
0.08774975687265396,
0.00041255896212533116,
0.04384278878569603,
-0.03812713921070099,
-0.05196857079863548,
0.023975292220711708,
0.05922309681773186,
0.07873232662677765,
0.007388474885374308,
0.03196370229125023,
0.009947416372597218,
-0.03706307336688042,
-0.030282165855169296,
-0.01695992611348629,
0.03711266070604324,
-0.022918978706002235,
0.01797381415963173,
-0.005082631483674049,
0.029367927461862564,
0.0792534127831459,
0.0803656205534935,
-0.01694323681294918,
-0.022388361394405365,
0.053125493228435516,
0.04125354439020157,
0.05977030470967293,
-0.02549511194229126,
0.024974463507533073,
0.03922712430357933,
-0.012910537421703339,
0.006380496546626091,
-0.014466463588178158,
-0.046268753707408905,
0.04521922394633293,
0.0069021801464259624,
0.0031919789034873247,
0.09465229511260986,
0.022304721176624298,
-0.08474349230527878,
0.028708379715681076,
-0.012985613197088242,
-0.011847422458231449,
-0.014755424112081528,
-0.0038106341380625963,
-0.049000415951013565,
0.026975732296705246,
0.0356864407658577,
-0.031209971755743027,
0.06559445708990097,
0.0690058246254921,
0.032338667660951614,
-0.02451072260737419,
-0.006048549432307482,
-0.06680024415254593,
0.04000205546617508,
-0.03451145440340042,
0.029184741899371147,
0.04494977369904518,
0.03889873996376991,
-0.04192040488123894,
0.019763857126235962,
0.04361918941140175,
-0.03051643632352352,
-0.022343847900629044,
0.04357273504137993,
0.045215826481580734,
0.022998085245490074,
0.04215731844305992,
0.03577684238553047,
-0.0073644001968204975,
-0.032952744513750076,
0.024325519800186157,
-0.013452669605612755,
-0.02432922273874283,
-0.04051617532968521,
0.018552720546722412,
0.04057474806904793,
0.02054606005549431,
0.005122310947626829,
0.10505169630050659,
0.029057728126645088,
0.005420352332293987,
-0.018067369237542152,
0.0038702853489667177,
0.046177517622709274,
0.009088657796382904,
-0.0413399338722229,
0.013150282204151154,
-0.04347750544548035,
0.040784068405628204,
-0.0051237414591014385,
-0.046282872557640076,
0.03455008193850517,
-0.01526699960231781,
0.030465394258499146,
-0.053283028304576874,
0.02742854133248329,
0.018547307699918747,
0.055751193314790726,
0.008246324025094509,
0.0006532000843435526,
0.007012535352259874,
-0.02887527458369732,
-0.016491197049617767,
-0.0026044747792184353,
0.01592910662293434,
-0.04833385348320007,
0.0413530170917511,
-0.02174047939479351,
0.01922176592051983,
0.012903562746942043,
0.013121604919433594,
-0.03337504342198372,
0.047297440469264984,
0.012092542834579945,
0.010061614215373993,
0.01019278448075056,
0.01988827995955944,
0.05940479040145874,
-0.08511245995759964,
0.015236864797770977,
-0.008221064694225788,
-0.06003565713763237,
-0.02196471579372883,
0.06687422096729279,
-0.0014352084835991263,
-0.017340686172246933,
-0.01958637498319149,
0.009923328645527363,
-0.019610220566391945,
0.010930853895843029,
0.04074686020612717,
-0.11478054523468018,
-0.0289311520755291,
-0.002436400391161442,
-0.03595210611820221,
-0.0009523067274130881,
0.002033207332715392,
0.030587106943130493,
-0.034573137760162354,
0.0025890409015119076,
0.030383145436644554,
0.03485391288995743,
0.04667222499847412,
-0.05018102750182152,
0.04025043919682503,
0.019109612330794334,
-0.03340981528162956,
-0.004939318168908358,
0.07660358399152756,
-0.03635644167661667,
-0.06140439584851265,
-0.033965472131967545,
0.01890883594751358,
0.03205747529864311,
-0.02339412271976471,
0.02420365810394287,
-0.050991855561733246,
-0.017465878278017044,
-0.02160092629492283,
-0.010257001966238022,
-0.017398780211806297,
0.020254064351320267,
-0.0034883026964962482,
0.023654481396079063,
-0.010623792186379433,
-0.07563814520835876,
-0.005746795795857906,
-0.013270591385662556,
0.030674191191792488,
-0.024391382932662964,
-0.019920282065868378,
0.008437560871243477,
-0.026518939062952995,
0.00016166290151886642,
-0.014211082831025124,
0.005266888532787561,
0.012777966447174549,
0.0029490417800843716,
-0.038106705993413925,
0.07094796001911163,
-0.022352809086441994,
-0.010361471213400364,
0.01110058557242155,
-0.012894978746771812,
-0.005782428663223982,
-0.044921327382326126,
-0.028213119134306908,
0.02976890280842781,
0.004040153231471777,
-0.0014144653687253594,
0.02060905657708645,
-0.059957005083560944,
-0.031987886875867844,
-0.037489645183086395,
0.017074206843972206,
0.008158345706760883,
-0.022368067875504494,
0.007421763613820076,
0.04931855946779251,
0.049094222486019135,
0.013014071621000767,
-0.027824949473142624,
0.0004908276023343205,
-0.005513338837772608,
-0.06121157482266426,
-0.05310017615556717,
0.006372166331857443,
0.0270526222884655,
0.010344714857637882,
0.03539459407329559,
0.03148326277732849,
0.025193484500050545,
0.06632529944181442,
0.04029538854956627,
0.014103060588240623,
-0.03802156820893288,
-0.04203224554657936,
-0.024352336302399635,
-0.022852150723338127,
0.0007460155175067484,
0.02023407630622387,
0.031224535778164864,
-0.045173488557338715,
0.027200423181056976,
-0.01765158772468567,
-0.033853162080049515,
-0.06993464380502701,
-0.01636107638478279,
0.014942233450710773,
-0.06515040993690491,
0.025942757725715637,
-0.03590637072920799,
0.030848437920212746,
0.012741858139634132,
0.003335854969918728,
-0.019733566790819168,
0.07312586158514023,
0.03653930872678757,
0.0347861722111702,
0.029230913147330284,
-0.02143079973757267,
0.051748525351285934,
-0.025323180481791496,
0.021074309945106506,
0.03938087448477745,
-0.007085724733769894,
-0.0017690369859337807,
-0.047967031598091125,
0.008811390958726406,
0.04243497550487518,
0.04560086131095886,
0.02108764462172985,
-0.013900668360292912,
0.0014949087053537369,
-0.07501648366451263,
0.007305514067411423,
0.01569940894842148,
-0.02356288768351078,
-0.06818930059671402,
0.024170076474547386,
-0.04015084356069565,
-0.025353815406560898,
-0.058899711817502975,
0.03236028924584389,
-0.007029533386230469,
-0.05145056173205376,
-0.02489415928721428,
-0.009362459182739258,
-0.011294897645711899,
-0.03480907902121544,
-0.012717897072434425,
-0.042573459446430206,
0.042284633964300156,
0.0013071036664769053,
0.05523538216948509,
-0.07365971058607101,
0.029103050008416176,
0.03622480109333992,
0.0254611037671566,
-0.004995167721062899,
-0.0426698662340641,
-0.013633538037538528,
0.006608300842344761,
0.012895772233605385,
-0.0698358491063118,
0.047741521149873734,
-0.03257764130830765,
-0.03482631966471672,
0.008780381642282009,
-0.021070823073387146,
0.03616948798298836,
-0.007094383705407381,
-0.003976405598223209,
-0.05202816426753998,
-0.03778381273150444,
-0.01359635777771473,
-0.027882182970643044,
0.029382051900029182,
0.03142369166016579,
-0.059310898184776306,
-0.01213998906314373,
0.0010906526586040854,
-0.018319806084036827,
-0.027834787964820862,
0.004093396011739969,
0.04929399862885475,
-0.023036299273371696,
-0.03345312550663948,
0.0043995869345963,
0.02937481552362442,
0.009658792056143284,
0.027319731190800667,
0.02758997492492199,
-0.007983379065990448,
0.007724754046648741,
0.00021270521392580122,
0.03919224813580513,
0.007941984571516514,
-0.03514140099287033,
-0.07047959417104721,
-0.00482089864090085,
-0.003756769234314561,
0.017578817903995514,
-0.01162426732480526,
0.0655762255191803,
0.024596979841589928,
-0.03645256906747818,
0.0004968448192812502,
-0.013636903837323189,
-0.004958895966410637,
0.10002340376377106,
0.018428994342684746,
-0.01450928021222353,
0.018418096005916595,
0.028491279110312462,
0.012001090683043003,
-0.031309206038713455,
0.018762163817882538,
0.014389078132808208,
-0.02454172633588314,
-0.025466199964284897,
-0.0380123071372509,
0.008013412356376648,
-0.04393548518419266,
-0.04078254476189613,
0.005968041252344847,
-0.0029376728925853968,
-0.03326999023556709,
-0.02946794591844082,
0.01740156300365925,
0.06645254790782928,
-0.041352029889822006,
0.015293142758309841,
0.0071320924907922745,
0.023054754361510277,
-0.002957887016236782,
0.03618830069899559,
0.0020284042693674564,
-0.06952181458473206,
-0.014898121356964111,
-0.024777602404356003,
-0.06716080009937286,
-0.062079329043626785,
-0.07946594059467316,
0.0027823925483971834,
0.042587462812662125,
-0.016813281923532486,
-0.029721403494477272,
0.043395377695560455,
0.0005258988821879029,
-0.009212632663547993,
0.006562692578881979,
-0.016556164249777794,
-0.009749148041009903,
0.021662145853042603,
0.02350878156721592,
0.029004767537117004,
0.023843906819820404,
0.03259475156664848,
-0.021392280235886574,
0.05820131674408913,
-0.06706466525793076,
0.015821240842342377,
0.05031736567616463,
-0.015768973156809807,
-0.09333442151546478,
0.01535372156649828,
-0.00817971769720316,
-0.020714255049824715,
-0.0008478210074827075,
0.0012104588095098734,
0.03529587388038635,
0.001703233690932393,
-0.018652375787496567,
-0.03313809260725975,
0.007785014342516661,
0.02311861142516136,
0.0069049340672791,
-0.00211157463490963,
-0.0038696685805916786,
0.02472018636763096,
-0.05804801359772682,
-0.02423088625073433,
0.02334437519311905,
-0.025093160569667816,
0.02028929628431797,
0.0685587003827095
] |
<p>I want to find out how to predict Iridium flares, but I don't know where to start. If I know Solar position, Iridium satelites' TLE and it's shape, I need a magnitude(time) function for some place on Earth. As I see now, main question is in satellite orientation (it's panels).</p>
<p>Any ideas?</p> | g4783 | [
-0.014209502376616001,
0.01091785728931427,
0.0071519664488732815,
-0.04218349605798721,
-0.006056884303689003,
-0.03466746211051941,
0.012296033091843128,
0.012277457863092422,
-0.014534548856317997,
-0.03845622390508652,
0.025636592879891396,
0.07875202596187592,
0.09562603384256363,
0.00410315440967679,
0.027599280700087547,
-0.05553818121552467,
0.06678345054388046,
0.02104775607585907,
0.06165613606572151,
0.046502746641635895,
0.05636398494243622,
-0.03336453065276146,
0.019941948354244232,
-0.017779184505343437,
-0.021643947809934616,
0.07088831067085266,
0.04585794731974602,
0.007349951192736626,
0.03347284346818924,
-0.031254034489393234,
-0.005679772701114416,
-0.0025356123223900795,
0.03789541497826576,
-0.052947115153074265,
-0.035026390105485916,
0.028961583971977234,
0.00014594016829505563,
0.03241570293903351,
0.018181338906288147,
0.009473858401179314,
0.018223248422145844,
-0.05774319916963577,
0.05466772988438606,
0.06101558357477188,
0.06789685040712357,
0.003152793273329735,
-0.02920929156243801,
0.03312145546078682,
-0.017978310585021973,
0.021864989772439003,
0.017986837774515152,
0.04551363363862038,
0.02714240737259388,
-0.04037783294916153,
0.0012229111744090915,
-0.024418599903583527,
0.03673906624317169,
-0.07019804418087006,
0.040910955518484116,
0.004219503607600927,
0.073802150785923,
-0.00663002161309123,
-0.013625819236040115,
-0.06690850853919983,
0.016494065523147583,
0.04507694020867348,
-0.0336291566491127,
-0.018356552347540855,
-0.005100480746477842,
0.03236309811472893,
0.047402091324329376,
0.04911961033940315,
0.01156234834343195,
0.000406716950237751,
-0.04412601515650749,
-0.02231304533779621,
0.02022748440504074,
0.008623754605650902,
-0.0003837718104477972,
0.05502355471253395,
0.03088749572634697,
0.0213197972625494,
0.0331248939037323,
0.0020470493473112583,
0.027388978749513626,
0.003900441573932767,
0.005534197669476271,
0.04889904335141182,
0.042196862399578094,
-0.06385453790426254,
-0.004930690862238407,
0.007680242415517569,
0.043768033385276794,
-0.034065768122673035,
0.015344724990427494,
-0.01259323488920927,
-0.0018449986819177866,
0.01393132470548153,
-0.02769966423511505,
-0.0031415936537086964,
-0.019138259813189507,
0.02508118934929371,
0.008400374092161655,
0.015829337760806084,
-0.051520586013793945,
0.04812062159180641,
-0.004123104270547628,
-0.045231904834508896,
0.08559603244066238,
-0.005940156988799572,
-0.003153187455609441,
-0.028632821515202522,
-0.009488414041697979,
-0.03861616551876068,
-0.0037369648925960064,
-0.03079182468354702,
-0.027525361627340317,
-0.07056679576635361,
-0.005517146084457636,
0.057984136044979095,
0.0951843187212944,
-0.05420585349202156,
0.02992403879761696,
0.019335195422172546,
0.00893181562423706,
0.03496364504098892,
-0.009747638367116451,
-0.019407259300351143,
-0.04082697629928589,
0.022498905658721924,
-0.025955816730856895,
-0.0042648776434361935,
-0.014816739596426487,
0.011727898381650448,
0.004429113119840622,
0.04846890643239021,
-0.0292485561221838,
-0.01431046612560749,
-0.00018642604118213058,
0.005057813134044409,
0.036520425230264664,
0.004530974198132753,
0.05034792050719261,
-0.011074221692979336,
-0.008445004932582378,
0.01977374032139778,
-0.003769542323425412,
-0.008147381246089935,
0.0428871214389801,
0.054881904274225235,
-0.007626458536833525,
0.039649445563554764,
-0.007371409330517054,
-0.062465786933898926,
0.02431124821305275,
-0.03868456929922104,
-0.008939174003899097,
-0.0010511954315006733,
0.00794175360351801,
0.014108209870755672,
-0.013023266568779945,
0.042237505316734314,
-0.008450624532997608,
-0.0032331524416804314,
0.02112734504044056,
-0.03904144465923309,
0.007984570227563381,
-0.023369155824184418,
-0.021615222096443176,
-0.0058768619783222675,
0.03575969859957695,
-0.028146373108029366,
0.0972386822104454,
-0.0011597629636526108,
-0.04353301599621773,
0.06630012392997742,
-0.005666159093379974,
0.028078680858016014,
0.06189695745706558,
0.056698936969041824,
-0.00237316288985312,
-0.029266012832522392,
0.022496413439512253,
0.03167938441038132,
-0.039897046983242035,
-0.06736475229263306,
0.025799812749028206,
-0.015747569501399994,
-0.04243381321430206,
0.08791708201169968,
-0.0030212756246328354,
-0.027141254395246506,
0.021164923906326294,
-0.008335801772773266,
0.016812656074762344,
-0.06433824449777603,
-0.006202871911227703,
-0.04066237434744835,
-0.038639962673187256,
0.04005488380789757,
-0.0013515455648303032,
-0.0027225781232118607,
0.03671672195196152,
0.045004844665527344,
-0.011604557745158672,
0.02391228824853897,
0.016696229577064514,
-0.010273110121488571,
-0.01277357991784811,
0.04495978727936745,
-0.013783443719148636,
-0.01578744873404503,
-0.0045847464352846146,
-0.007399300113320351,
0.028317579999566078,
0.014132489450275898,
-0.029057595878839493,
0.03789428249001503,
-0.013950560241937637,
-0.058218371123075485,
-0.0568123385310173,
-0.010482640005648136,
0.022355206310749054,
-0.013306130655109882,
0.03043171390891075,
0.02880866639316082,
0.013842005282640457,
0.05473419651389122,
0.02143673412501812,
-0.018558107316493988,
-0.0665099173784256,
0.009536905214190483,
0.05654173344373703,
0.029482105746865273,
0.040500838309526443,
0.013774905353784561,
0.0072434162721037865,
-0.0036627829540520906,
0.0690067708492279,
0.046543050557374954,
-0.0339946486055851,
-0.017646655440330505,
0.03509969636797905,
0.007971837185323238,
-0.006570864003151655,
-0.05493328347802162,
0.029124319553375244,
0.007679820992052555,
-0.07225028425455093,
-0.02129516936838627,
0.03779798746109009,
0.043872032314538956,
-0.05022753030061722,
0.05325612798333168,
-0.11158055067062378,
0.009204798378050327,
-0.06319528818130493,
0.01713973842561245,
-0.045175712555646896,
0.01286853477358818,
-0.030578386038541794,
-0.01400657556951046,
0.022482367232441902,
0.002989969216287136,
0.012316311709582806,
-0.08691428601741791,
-0.024885455146431923,
-0.01896691881120205,
0.023350343108177185,
0.006486281752586365,
0.0360238254070282,
0.022548457607626915,
0.09870384633541107,
0.040601618587970734,
0.002035629004240036,
0.0060052527114748955,
0.037204694002866745,
-0.01380726508796215,
-0.02021380141377449,
0.00245683453977108,
0.06475372612476349,
-0.04636019840836525,
-0.05110711604356766,
0.024680981412529945,
0.014172756113111973,
-0.006396231707185507,
0.03326050192117691,
0.13916639983654022,
-0.012439146637916565,
-0.0000232851361943176,
-0.002998684998601675,
-0.04291396960616112,
0.019413869827985764,
0.014583486132323742,
-0.04572737589478493,
-0.06350976228713989,
0.05715395137667656,
-0.019264614209532738,
0.040901537984609604,
-0.049698006361722946,
0.025136975571513176,
-0.018635712563991547,
0.010245499201118946,
-0.05043907091021538,
-0.0135780805721879,
-0.0028000182937830687,
-0.02714654803276062,
-0.0606355220079422,
0.04241371899843216,
-0.04158761352300644,
0.01571015454828739,
0.0026935823261737823,
-0.022838978096842766,
0.05031319707632065,
0.01212102547287941,
0.03320259973406792,
-0.06289277225732803,
0.04006100445985794,
0.006753925699740648,
-0.003855322254821658,
-0.027630062773823738,
-0.07109823822975159,
-0.05115879699587822,
0.050323206931352615,
0.03954967483878136,
0.03291736915707588,
0.029346799477934837,
-0.034764185547828674,
-0.058865007013082504,
0.007056511007249355,
-0.026285456493496895,
0.04900464043021202,
0.01591065526008606,
-0.043743036687374115,
0.005926917307078838,
-0.009866624139249325,
0.010616025887429714,
0.026870762929320335,
-0.0016581795644015074,
0.02544972114264965,
-0.038716334849596024,
0.0200558602809906,
-0.007669384591281414,
-0.03284996747970581,
-0.0404999740421772,
-0.03818805515766144,
-0.005472094751894474,
-0.02224961668252945,
-0.008306654170155525,
-0.022420722991228104,
0.009508315473794937,
-0.02054874785244465,
0.0019771065562963486,
-0.017712734639644623,
0.049980659037828445,
0.09262272715568542,
0.048157885670661926,
0.019435131922364235,
0.005038830917328596,
-0.009206258691847324,
-0.06593909859657288,
-0.007869837805628777,
-0.011839990504086018,
-0.01476198434829712,
0.027996918186545372,
-0.0027156739961355925,
0.008071839809417725,
0.006156363058835268,
-0.012777992524206638,
-0.019129116088151932,
0.0005819904035888612,
0.08084788918495178,
0.021563686430454254,
-0.013376324437558651,
-0.002975927432999015,
-0.022958600893616676,
-0.02031681127846241,
-0.025753332301974297,
-0.010785557329654694,
0.03534495830535889,
-0.037197574973106384,
-0.004858896601945162,
0.024023467674851418,
-0.046272676438093185,
0.05829829350113869,
0.018095189705491066,
0.004103911109268665,
0.0036252301651984453,
0.012131198309361935,
-0.02123004011809826,
0.03966338932514191,
-0.06253185123205185,
-0.03241785988211632,
-0.04191393777728081,
0.03778190538287163,
-0.029133019968867302,
0.045561179518699646,
0.048243630677461624,
-0.007490471936762333,
-0.015668343752622604,
0.03425168618559837,
-0.08144929260015488,
0.044874995946884155,
0.0016142524546012282,
-0.04583630710840225,
-0.03215140849351883,
0.002469026716426015,
-0.014473974704742432,
0.05082060396671295,
-0.049859628081321716,
0.03887050971388817,
0.061190105974674225,
0.06054886430501938,
-0.06424858421087265,
0.03548208624124527,
0.03646719828248024,
-0.00035055106854997575,
-0.006642353255301714,
0.08131598681211472,
0.028949782252311707,
-0.027524391189217567,
0.033808205276727676,
0.0366920530796051,
-0.04725119471549988,
-0.013936970382928848,
0.0315701887011528,
0.039372291415929794,
-0.044387087225914,
0.04049945995211601,
0.028089186176657677,
-0.006704074330627918,
-0.0014696139842271805,
-0.02338971011340618,
0.008576344698667526,
-0.061832599341869354,
0.006813542451709509,
0.028524691238999367,
0.015674984082579613,
-0.032021455466747284,
-0.010110432282090187,
0.025796135887503624,
0.001866799546405673,
-0.0033052421640604734,
-0.004750665742903948,
-0.025787273421883583,
0.04114386439323425,
-0.052787501364946365,
-0.0037029439117759466,
-0.05615406110882759,
-0.02613196149468422,
0.008189246989786625,
-0.007529925089329481,
-0.062263693660497665,
0.04334398731589317,
-0.02753950096666813,
-0.010054212063550949,
0.06278982758522034,
-0.003332702675834298,
0.046750351786613464,
0.02462940849363804,
0.02397080324590206,
-0.040983252227306366,
0.02342171221971512,
-0.0020306475926190615,
0.07909749448299408,
0.01565205119550228,
-0.021473444998264313,
0.006406835280358791,
-0.004749540239572525,
0.011676723137497902,
-0.05216958001255989,
0.03839173540472984,
0.04964425042271614,
-0.024233538657426834,
-0.029030878096818924,
-0.017501426860690117,
-0.05872610956430435,
-0.08187860995531082,
-0.029706226661801338,
0.060371819883584976,
-0.039935991168022156,
-0.020428301766514778,
-0.012622770853340626,
-0.029676374047994614,
-0.054256074130535126,
0.015165376476943493,
-0.005718159023672342,
0.013522369787096977,
0.030241888016462326,
-0.009400507435202599,
-0.06452609598636627,
-0.022721057757735252,
0.04670795798301697,
0.004993085283786058,
-0.07608021050691605,
-0.01576036773622036,
-0.031430136412382126,
-0.048255424946546555,
0.022407786920666695,
0.021801937371492386,
-0.004093436989933252,
0.011450674384832382,
-0.026371343061327934,
0.0443667396903038,
-0.005402717273682356,
0.013311496004462242,
0.018591633066534996,
-0.039007145911455154,
0.012234486639499664,
0.010490166023373604,
0.011178766377270222,
0.02202373743057251,
0.007829043082892895,
-0.04842865467071533,
-0.00387546862475574,
-0.04697923734784126,
-0.029775656759738922,
0.10367005318403244,
-0.0195841696113348,
0.024043215438723564,
-0.04480506852269173,
0.02424108050763607,
0.03500518947839737,
0.02341906726360321,
0.03159254789352417,
-0.06443800032138824,
-0.07901116460561752,
-0.025751275941729546,
0.04979858547449112,
-0.0251866914331913,
-0.012238400988280773,
-0.0005869304877705872,
-0.03798440843820572,
-0.04538586363196373,
0.03543941304087639,
-0.03570890054106712,
0.038575850427150726,
0.03346840292215347,
-0.012116695754230022,
-0.04533794894814491,
-0.005055973306298256,
0.058319851756095886,
-0.009329496882855892,
-0.0706406757235527,
-0.035737086087465286,
-0.04565802961587906,
-0.02633821964263916,
0.03033117763698101,
-0.00008851669554132968,
0.022940801456570625,
0.012338420376181602,
0.0358879454433918,
0.04337242618203163,
-0.057484276592731476,
0.010754893533885479,
-0.015955178067088127,
-0.022195402532815933,
0.020667897537350655,
-0.07303053140640259,
-0.008528784848749638,
0.013708994723856449,
-0.006426649633795023,
0.008849084377288818,
0.044306375086307526,
0.03490200638771057,
-0.01294835563749075,
0.002307854127138853,
-0.012775012291967869,
0.07653755694627762,
0.04835231974720955,
0.021897928789258003,
-0.0847930982708931,
0.024394206702709198,
-0.0020922133699059486,
0.011065228842198849,
-0.08628898859024048,
0.05649126321077347,
0.02507266215980053,
-0.0372726134955883,
-0.015856681391596794,
0.051410429179668427,
0.019059516489505768,
-0.0010811544489115477,
-0.03192528709769249,
0.011688443832099438,
0.054365821182727814,
-0.00162264215759933,
0.021357132121920586,
0.019476357847452164,
-0.03266094997525215,
0.014061636291444302,
-0.005313577130436897,
0.014193817973136902,
-0.01984921284019947,
-0.03264065086841583,
0.03387599438428879,
-0.07320475578308105,
0.06512956321239471,
-0.00437207892537117,
0.05272788926959038,
-0.0500783696770668,
0.017484772950410843,
0.05426422134041786,
-0.013791062869131565,
0.04978328198194504,
-0.02635796181857586,
0.00824135821312666,
0.01209232397377491,
0.015404530800879002,
-0.05961267277598381,
-0.007520731072872877,
0.026286223903298378,
-0.018670231103897095,
-0.0027556479908525944,
0.01213768683373928,
-0.04109649732708931,
0.008898686617612839,
0.05444575846195221,
0.0017208649078384042,
-0.035750824958086014,
0.02395012602210045,
-0.021616464480757713,
-0.07179386913776398,
-0.0248187854886055,
0.024383287876844406,
0.018064208328723907,
0.04308280348777771,
-0.009956659749150276,
0.023577891290187836,
-0.040434177964925766,
0.009146265685558319,
-0.01859108917415142,
-0.004761595744639635,
0.008304445073008537,
0.0037624873220920563,
-0.03265932947397232,
-0.00417172210291028,
0.01029400248080492,
-0.002672132570296526,
0.00999843142926693,
0.002655258635058999,
-0.06828039139509201,
0.0023983661085367203,
-0.0034850030206143856,
-0.03166026249527931,
-0.001929654274135828,
-0.028019459918141365,
-0.006373642943799496,
-0.018474550917744637,
-0.011762367561459541,
0.004781771916896105,
-0.08433735370635986,
-0.00823651161044836,
-0.031072214245796204,
0.07711290568113327,
0.07974789291620255,
0.014701912179589272,
-0.010197887197136879,
-0.017622211948037148,
-0.032157447189092636,
-0.0012021081056445837,
-0.040445178747177124,
-0.05547795817255974,
0.01205163449048996,
-0.009614148177206516,
0.022425677627325058,
-0.05047846585512161,
-0.06129388138651848,
0.012279357761144638,
-0.06815284490585327,
-0.05581918731331825,
-0.014028864912688732,
-0.015594839118421078,
-0.009937875904142857,
-0.042684707790613174,
0.08152391016483307,
-0.07632093876600266,
-0.05028662085533142,
-0.005437525920569897,
-0.003916718065738678,
-0.055863648653030396,
0.027754968032240868,
0.012482862919569016,
-0.03730382025241852,
-0.026126625016331673,
0.006622501648962498,
-0.0258095134049654,
-0.05560079589486122,
-0.013235076330602169,
-0.04981905594468117,
-0.03667657449841499,
0.06268374621868134,
-0.0008961670100688934,
-0.08320839703083038,
0.04298964515328407,
0.00353993964381516,
0.01379791833460331,
0.019491197541356087,
-0.025304216891527176,
0.026533063501119614,
-0.0005749099655076861,
0.022116925567388535,
0.04863649606704712,
-0.068930484354496,
-0.020096709951758385,
-0.0353170670568943,
-0.02369368076324463,
-0.027990849688649178,
0.001330140745267272,
-0.0037902777548879385,
0.03501393273472786,
0.026514528319239616,
-0.012404506094753742,
-0.009398962371051311,
-0.013935399241745472,
0.02081441879272461,
-0.026735369116067886,
0.022230012342333794,
0.012801829725503922,
-0.030054006725549698,
-0.0525355190038681,
-0.03697327524423599,
0.016528040170669556,
-0.016063537448644638,
0.006122806575149298,
0.03282604366540909,
-0.029859917238354683,
0.020572293549776077,
0.041107796132564545,
-0.03738998621702194,
0.05745577812194824,
0.05885232985019684,
-0.01609700731933117,
-0.03778490796685219,
-0.008882996626198292,
-0.018318340182304382,
-0.055412713438272476,
-0.04463416710495949,
-0.02571202628314495,
0.025255825370550156,
-0.02479005604982376,
0.004168338142335415,
-0.03421581909060478,
0.000499940593726933,
0.030132779851555824,
0.03734150156378746,
-0.061489444226026535,
0.03084990754723549,
-0.016924895346164703,
-0.04686367139220238,
-0.01685800403356552,
0.03983144834637642,
0.03771306946873665,
-0.02524556964635849,
0.0011177544947713614,
0.016323179006576538,
-0.029004963114857674,
0.020912954583764076,
0.02594004198908806,
-0.056041501462459564,
-0.016179094091057777,
-0.02189052291214466,
-0.00683765159919858,
0.058285970240831375,
0.020665127784013748,
-0.002104940125718713,
-0.03254156559705734,
-0.0027928247582167387
] |
<p>I am reading Gelfand's Calculus of Variations & mathematically everything makes sense to me, it makes perfect sense to me to set up the mathematics of extremization of functionals & show that in extremizing a certain functional you can end up with Newton's laws (i.e. you could extremize some arbitrary functional $L$ & in examining the form of Newton's laws you see that one should define $L$ as $T - V$) & this way of looking at things requires no magic, to me it seems as though you've just found a clever way of doing mathematics that results in Newton's laws.</p>
<p>However in books like Landau one must assume this magical principle of least action using the kind of thinking akin to Maupertuis, & I remember that every time I read some form of justification of this there's always a crux point where they'd say 'because it works'. I'm thinking that there may be a way to explain the principle of least action if you think of extremizing functionals along the lines Euler first did & use the method of finite differences (as is done in the chapter on the Variational Derivative in Gelfand, can't post a link unfortunately), i.e. because you're thinking of a functional as a function of n variables you can somehow incorporate the $T - V$ naturally into what you're extremizing, but I don't really know... I'm really hoping someone in here can give me a definitive answer, to kind of go through what the thought process is in this principle once and for all!</p>
<p>As far as I know, one can either assume this as a principle as in Landau & use all this beautiful theory of homogeneity etc... to get some results, or else once can assume Newton's laws & then use the principle of virtual work to derive the Euler-Lagrange equations, or start from Hamilton's equations & end up with Newton's laws, or one can assume Newton's laws & set up the calculus of variations & show how extremizing one kind of functional leads to Newton's laws - but I'm not clear on exactly what's going on & would really really love some help with this. </p> | g4784 | [
0.01839103363454342,
0.030670979991555214,
-0.006810933351516724,
0.04535702243447304,
0.06069717928767204,
-0.03116149827837944,
0.027130061760544777,
0.008436837233603,
0.038194917142391205,
-0.03393598645925522,
-0.08753880113363266,
0.003947916440665722,
0.01228727214038372,
0.051080405712127686,
-0.027656886726617813,
0.00702501880005002,
0.07087846845388412,
-0.02826669253408909,
0.04566679894924164,
-0.007048851810395718,
-0.02874205820262432,
0.03131560981273651,
0.04697137698531151,
0.008757120929658413,
-0.01931348443031311,
0.02611169032752514,
-0.03594783693552017,
0.009612095542252064,
-0.05973195657134056,
0.05147840827703476,
0.01945873163640499,
-0.022585980594158173,
0.0016477510798722506,
-0.05414704233407974,
0.023777637630701065,
-0.008708546869456768,
0.06185410916805267,
0.020089304074645042,
0.03164497762918472,
-0.024758776649832726,
-0.04715246334671974,
-0.054173439741134644,
0.01907939463853836,
0.012593423016369343,
-0.0007204705034382641,
-0.03947055712342262,
-0.00999439973384142,
-0.044048793613910675,
-0.02927318774163723,
-0.025482850149273872,
0.021591633558273315,
0.025297150015830994,
0.007303944323211908,
0.008954567834734917,
0.06596820056438446,
0.001189987058751285,
0.02493978850543499,
0.019028497859835625,
0.054086700081825256,
-0.019871758297085762,
0.05375891178846359,
-0.009352341294288635,
0.00509182782843709,
0.05578228831291199,
0.021828804165124893,
-0.04496797174215317,
-0.00719018280506134,
-0.043603017926216125,
0.017844971269369125,
-0.01776365004479885,
-0.01650307886302471,
-0.01612037979066372,
-0.023632442578673363,
-0.05954957380890846,
-0.02144267037510872,
-0.0014670689124614,
0.047378893941640854,
0.02725219540297985,
0.029377130791544914,
-0.02767772413790226,
-0.0056820642203092575,
-0.039319731295108795,
0.05979794263839722,
0.011129263788461685,
0.045555319637060165,
-0.0039728619158267975,
0.03175933659076691,
-0.016994280740618706,
-0.01388565730303526,
0.08337200433015823,
-0.01946457289159298,
0.026376985013484955,
0.0540299117565155,
0.034423962235450745,
-0.09665706753730774,
0.004291991237550974,
0.02229912579059601,
-0.028341317549347878,
-0.021619589999318123,
-0.03572056442499161,
-0.008912721648812294,
0.01571238972246647,
-0.0028613426256924868,
-0.023059910163283348,
-0.08239848166704178,
0.014296197332441807,
0.08223866671323776,
0.019132215529680252,
0.001774080446921289,
-0.005076281726360321,
-0.03994983062148094,
0.005591486115008593,
-0.04739292338490486,
-0.03872008994221687,
-0.038376469165086746,
0.00655123358592391,
0.010723002254962921,
0.008000115863978863,
-0.007114905398339033,
0.019911043345928192,
0.010672108270227909,
0.012540880590677261,
-0.018515661358833313,
0.03110410086810589,
-0.027287675067782402,
0.04546437785029411,
-0.01442061085253954,
-0.027404632419347763,
0.009550068527460098,
0.019119545817375183,
0.07455770671367645,
-0.007565952837467194,
-0.02127004601061344,
0.002754263347014785,
0.008479496464133263,
0.025697093456983566,
-0.02147255837917328,
0.031685639172792435,
-0.001684291404671967,
-0.028450993821024895,
-0.022948458790779114,
-0.057590749114751816,
-0.05518984794616699,
-0.0414295494556427,
-0.024096976965665817,
0.04640236124396324,
-0.0381058007478714,
0.019573895260691643,
0.0003752164775505662,
-0.024641815572977066,
-0.022524846717715263,
0.06995014101266861,
0.03646809980273247,
-0.02870059572160244,
0.013136150315403938,
-0.015193132683634758,
0.02805623598396778,
0.025292495265603065,
0.0024956671986728907,
-0.04666318744421005,
0.06174766644835472,
-0.027128977701067924,
0.030167914927005768,
-0.027902379631996155,
-0.0605866014957428,
0.04700631648302078,
-0.028776241466403008,
0.010211785323917866,
0.06693195551633835,
-0.060575276613235474,
-0.11332722008228302,
-0.019615434110164642,
0.02893456444144249,
0.02540939301252365,
-0.019351961091160774,
0.0312198493629694,
-0.01782071590423584,
-0.05999191105365753,
-0.021693821996450424,
0.017567673698067665,
-0.05562296137213707,
-0.035899341106414795,
-0.006373942829668522,
-0.00825016014277935,
-0.035454366356134415,
-0.0057416982017457485,
0.02137315832078457,
-0.012025930918753147,
-0.06802605837583542,
-0.03964721038937569,
-0.021626310423016548,
-0.019658047705888748,
-0.009967107325792313,
-0.038858603686094284,
-0.020146796479821205,
0.020640527829527855,
-0.015644993633031845,
-0.043719880282878876,
-0.028056949377059937,
0.03186386451125145,
0.03936580568552017,
0.027126494795084,
-0.002577264793217182,
0.005710977129638195,
-0.008043330162763596,
-0.0006239944486878812,
-0.04531962051987648,
-0.030783236026763916,
0.04786704108119011,
0.014468278735876083,
0.07110543549060822,
-0.007417457643896341,
0.004853018559515476,
0.011546168476343155,
-0.023287847638130188,
-0.03220124915242195,
0.011581438593566418,
0.0013103262754157186,
-0.012995938770473003,
-0.05216901749372482,
0.0053496211767196655,
0.026485221460461617,
0.011320172809064388,
0.03892892971634865,
-0.002153802430257201,
-0.0019728769548237324,
0.00994985643774271,
0.01885342039167881,
0.01841934584081173,
-0.005306873470544815,
-0.009824208915233612,
-0.0049848612397909164,
0.0018152616685256362,
-0.009940700605511665,
0.04421351104974747,
0.0007670517661608756,
-0.018051309511065483,
-0.05719440057873726,
0.06976664066314697,
0.08063044399023056,
-0.014626678079366684,
-0.038884490728378296,
-0.00918846670538187,
0.07172339409589767,
-0.010805448517203331,
-0.0017635672120377421,
-0.010835109278559685,
0.01778276078402996,
-0.08625848591327667,
-0.018889032304286957,
-0.003947571851313114,
-0.020205408334732056,
0.01373344101011753,
-0.06660967320203781,
0.039929550141096115,
0.036959145218133926,
-0.05332783982157707,
-0.013760702684521675,
0.012445017695426941,
0.024672260507941246,
0.036311518400907516,
0.06375271826982498,
0.030400903895497322,
0.07976504415273666,
-0.029336346313357353,
0.054311636835336685,
0.004942790605127811,
0.02699393965303898,
-0.0031293989159166813,
0.023397745564579964,
-0.032184407114982605,
0.06401436775922775,
-0.04700207710266113,
0.034708403050899506,
-0.0461803637444973,
-0.04991091042757034,
-0.02057546004652977,
-0.050229717046022415,
0.02931431494653225,
0.002409619279205799,
-0.009054883383214474,
-0.036531660705804825,
-0.0024887481704354286,
0.005075907800346613,
0.03018120303750038,
-0.013188443146646023,
0.04363584518432617,
0.010966409929096699,
-0.03461718559265137,
-0.04957570135593414,
0.02197718620300293,
-0.010122119449079037,
-0.005432869307696819,
-0.019519053399562836,
-0.06952007114887238,
0.04651402682065964,
0.0011305585503578186,
0.0012305270647630095,
-0.02592311054468155,
0.002555369632318616,
-0.0032415275927633047,
-0.014061733148992062,
-0.011381963267922401,
0.06980961561203003,
-0.046784527599811554,
0.06725737452507019,
0.0019242706475779414,
-0.03746204823255539,
-0.01892000064253807,
-0.03905736282467842,
0.026463476940989494,
0.03192868083715439,
-0.002375762676820159,
-0.04808753356337547,
0.010867739096283913,
0.0020574266090989113,
-0.015324469655752182,
0.028743596747517586,
0.027979038655757904,
0.002793320454657078,
-0.08655443042516708,
-0.10624004155397415,
0.046203192323446274,
-0.046723511070013046,
0.06389132887125015,
0.0005531456554308534,
-0.07596326619386673,
-0.02570369839668274,
0.00008083163265837356,
-0.0043972088024020195,
0.03203035891056061,
0.0021515649277716875,
-0.027019988745450974,
-0.006651687435805798,
-0.03793427720665932,
-0.03708164393901825,
-0.045126985758543015,
0.015613230876624584,
0.0912199467420578,
0.036609310656785965,
-0.004448652267456055,
0.018732493743300438,
-0.029444731771945953,
0.04083262383937836,
0.015807637944817543,
-0.052021581679582596,
0.0034679342061281204,
0.06372873485088348,
0.01545704249292612,
0.02248876914381981,
-0.005926910787820816,
-0.04678483307361603,
-0.011938764713704586,
0.01374449860304594,
0.020673103630542755,
-0.017312422394752502,
0.03917333111166954,
0.059864066541194916,
0.04360608756542206,
-0.05280621722340584,
-0.007302954327315092,
-0.03731798008084297,
-0.08450838178396225,
-0.005856400355696678,
0.015825964510440826,
0.06317087262868881,
0.007559550926089287,
0.01484790351241827,
-0.0708426907658577,
-0.0026537629310041666,
0.0609779916703701,
-0.007317321840673685,
0.06025605648756027,
0.04078269004821777,
-0.002740417141467333,
0.012586572207510471,
0.021211804822087288,
0.0266640055924654,
-0.022248363122344017,
0.00358418351970613,
0.003752762218937278,
0.02581515721976757,
0.041482437402009964,
0.0044753216207027435,
0.02108870819211006,
0.015030520968139172,
-0.07458353042602539,
0.0009225779795087874,
-0.003147170413285494,
0.05550386756658554,
-0.04419665411114693,
0.006244424264878035,
-0.02012200467288494,
-0.015742093324661255,
0.03365439549088478,
0.05505357310175896,
0.019027618691325188,
-0.012061052024364471,
-0.017760522663593292,
0.048340607434511185,
0.03493762016296387,
0.02217034064233303,
-0.01678870990872383,
0.016095958650112152,
-0.028620239347219467,
-0.07501678168773651,
0.05110112950205803,
0.01454960647970438,
0.011621338315308094,
-0.06452273577451706,
-0.02042861096560955,
-0.0490703210234642,
0.04399334639310837,
-0.02840244397521019,
0.02292587421834469,
0.013557316735386848,
0.0077523537911474705,
-0.04868146777153015,
-0.014520873315632343,
0.02466878481209278,
0.05654434859752655,
-0.0034194972831755877,
-0.04861806333065033,
0.026970162987709045,
-0.01667327620089054,
0.0646277442574501,
0.04731540009379387,
0.014893626794219017,
0.01933290995657444,
-0.043620411306619644,
-0.11568913608789444,
-0.00966530479490757,
-0.026725342497229576,
-0.008939085528254509,
-0.03816733881831169,
-0.034472234547138214,
0.06119266897439957,
0.10970690101385117,
-0.016109637916088104,
0.04447472468018532,
0.05360858142375946,
0.029944198206067085,
-0.03881217539310455,
0.013891985639929771,
-0.041680436581373215,
0.02319779060781002,
-0.0016037366585806012,
-0.0478939525783062,
0.012579996138811111,
-0.005095355678349733,
-0.029682958498597145,
0.04751491919159889,
-0.009907362051308155,
0.019963765516877174,
-0.00821892824023962,
0.01256485190242529,
-0.04905856400728226,
0.0059922486543655396,
0.05887026712298393,
-0.018438879400491714,
-0.057664986699819565,
-0.03525441884994507,
-0.0006748769083060324,
0.015811536461114883,
0.038373395800590515,
0.031369488686323166,
-0.018160708248615265,
-0.009162445552647114,
0.016667211428284645,
0.015761826187372208,
0.02903655543923378,
0.05400606989860535,
0.027044735848903656,
-0.003037080867215991,
0.023629095405340195,
-0.08066647499799728,
0.035615600645542145,
0.00975312851369381,
-0.027635563164949417,
0.018852194771170616,
-0.024004848673939705,
0.023772386834025383,
0.02339775115251541,
0.001690332661382854,
-0.0292759258300066,
-0.031450096517801285,
-0.02173302322626114,
-0.03806709870696068,
-0.04160143435001373,
-0.005701088812202215,
0.03139503300189972,
0.0035758495796471834,
0.016784222796559334,
-0.02626069076359272,
-0.03232524171471596,
-0.05333879962563515,
0.06973560154438019,
0.020538493990898132,
-0.006097586825489998,
-0.006169037893414497,
-0.059172406792640686,
0.03787057101726532,
-0.09626084566116333,
-0.01085064560174942,
-0.008205683901906013,
-0.04240620136260986,
0.05489691346883774,
-0.013869807124137878,
-0.030110392719507217,
-0.011098148301243782,
0.029211755841970444,
0.04556768015027046,
-0.03776565194129944,
-0.013614844530820847,
0.01334579847753048,
0.0100343506783247,
-0.0199747234582901,
0.00732292840257287,
0.03238846734166145,
-0.04421013593673706,
0.01895914226770401,
-0.006892425008118153,
0.015397008508443832,
-0.03353329375386238,
0.03749794885516167,
-0.011390727944672108,
-0.05327298492193222,
-0.02798599749803543,
-0.034410201013088226,
0.0469692088663578,
-0.08706682920455933,
0.01095611322671175,
0.024208849295973778,
0.014710008166730404,
-0.03610525280237198,
0.02891548164188862,
0.030346257612109184,
0.023375092074275017,
0.022067049518227577,
0.0020888429135084152,
-0.011653044261038303,
0.007599927019327879,
0.008197407238185406,
0.06122734397649765,
0.0002911725896410644,
0.004992961417883635,
-0.04218316823244095,
-0.021088920533657074,
0.0174922663718462,
-0.027801262214779854,
-0.061451468616724014,
0.012642917223274708,
-0.00498657813295722,
0.006290065124630928,
-0.01189285796135664,
0.04858063533902168,
-0.06944669038057327,
-0.06790073961019516,
-0.01446304377168417,
0.007706406060606241,
0.06241467222571373,
-0.05252400413155556,
0.007548750378191471,
-0.0042875055223703384,
-0.00009587275417288765,
-0.0266228336840868,
0.018661513924598694,
0.02935112453997135,
0.030308175832033157,
0.029277998954057693,
-0.033281855285167694,
0.009135333821177483,
0.0005792752490378916,
-0.002105477498844266,
0.07098101824522018,
0.006037456449121237,
-0.02315821312367916,
-0.08181730657815933,
-0.015405608341097832,
0.024847932159900665,
-0.009753469377756119,
-0.04307086020708084,
0.02303975634276867,
-0.015835251659154892,
-0.028694353997707367,
0.06062399223446846,
-0.007997537963092327,
-0.06981454789638519,
-0.00024163034686353058,
0.010394570417702198,
-0.011498191393911839,
0.014395673759281635,
-0.05485714599490166,
0.0269313994795084,
0.04864625260233879,
-0.028323009610176086,
0.043562475591897964,
-0.019837921485304832,
0.08577491343021393,
-0.030355174094438553,
0.010794365778565407,
0.023090191185474396,
-0.01629495806992054,
-0.030509211122989655,
-0.02611921727657318,
0.0883670449256897,
-0.025951212272047997,
0.021146507933735847,
-0.017716793343424797,
-0.018098143860697746,
-0.07237232476472855,
0.028719712048768997,
0.03139658272266388,
0.03280065581202507,
-0.028847239911556244,
-0.03463008254766464,
-0.043429456651210785,
-0.02761036530137062,
0.03194735571742058,
0.024098696187138557,
-0.023861180990934372,
0.04615326225757599,
0.02764919213950634,
-0.012542709708213806,
0.016421232372522354,
0.016388632357120514,
-0.015469634905457497,
0.002571830991655588,
0.04040154069662094,
0.005431522615253925,
0.0361301526427269,
0.038256268948316574,
0.00618869811296463,
0.031262367963790894,
-0.04359474405646324,
0.060962237417697906,
-0.0035876918118447065,
0.020232442766427994,
-0.04064047336578369,
0.0562799796462059,
-0.09499511867761612,
0.038527049124240875,
0.0408623144030571,
-0.002280187327414751,
0.020210277289152145,
0.026563122868537903,
-0.03928792476654053,
0.010631398297846317,
-0.06281193345785141,
0.012343835085630417,
0.03729933127760887,
0.011371475644409657,
-0.019679347053170204,
0.018439529463648796,
0.034087758511304855,
0.048606500029563904,
-0.01246908400207758,
-0.05499086529016495,
-0.007741686888039112,
-0.0971614196896553,
-0.0576845146715641,
-0.03713738173246384,
0.07436395436525345,
-0.005730413366109133,
0.040708959102630615,
0.04811243340373039,
0.002845887327566743,
0.010212221182882786,
-0.01242512185126543,
-0.06632640212774277,
0.013929587788879871,
-0.011973649263381958,
-0.022059688344597816,
0.04392291232943535,
0.062259189784526825,
-0.01586327515542507,
0.000034365766623523086,
0.03630739077925682,
-0.03302044793963432,
0.025260837748646736,
0.039013881236314774,
0.07635956257581711,
0.046737510710954666,
-0.005910723935812712,
-0.07003862410783768,
-0.01574869267642498,
-0.043025337159633636,
-0.02721504494547844,
-0.06455391645431519,
-0.014556837268173695,
-0.036475036293268204,
0.012723703868687153,
0.046208154410123825,
0.026294976472854614,
-0.02648339234292507,
0.08769086748361588,
0.03395857289433479,
0.015451036393642426,
0.0067075928673148155,
-0.010451436042785645,
0.029741281643509865,
-0.018338588997721672,
-0.002751483116298914,
0.005596261937171221,
0.019924983382225037,
0.0007477456820197403,
-0.01831037737429142,
-0.035336658358573914,
-0.034673888236284256,
-0.0014283685013651848,
-0.011310946196317673,
0.015209086239337921,
-0.02673410251736641,
0.038875654339790344,
0.005892863962799311,
0.018357472494244576,
0.017051391303539276,
-0.037711456418037415,
0.03385555371642113,
0.033630166202783585,
-0.0022182126995176077,
0.053361598402261734,
0.045199595391750336,
-0.1109352856874466,
-0.03877851739525795,
-0.025305883958935738,
-0.028755301609635353,
-0.0485682338476181,
-0.02356983907520771,
-0.015330308116972446,
-0.020686430856585503,
-0.05181983485817909,
0.03586792200803757,
0.0001989706070162356,
0.019972853362560272,
0.059669461101293564,
-0.012711630202829838,
-0.006917263381183147,
-0.004975233227014542,
0.0398784838616848,
-0.024874195456504822,
-0.01908440887928009,
0.003665851429104805,
0.038974225521087646,
0.0017607288900762796,
-0.012278744019567966,
0.02516147494316101,
0.001360093243420124,
0.02450084313750267,
-0.002399451332166791,
-0.010978887788951397,
0.03298070281744003,
-0.020699096843600273,
-0.0164690762758255,
0.025603387504816055,
-0.055771954357624054,
-0.006480930373072624,
0.07406880706548691,
0.041349660605192184,
0.004660916514694691,
-0.03990320488810539,
-0.03701416775584221,
-0.00060442672111094,
0.031872592866420746,
-0.007645867764949799,
-0.01535318698734045,
0.0005931417108513415,
-0.03874702379107475
] |
<p><strong>Problem statement</strong></p>
<p>A straight and homogenous stick with mass m is pressed against a wall with the force F. The stick is horizontal perpendicular against the wall. Given that the friction between the wall and the stick is μ, determine the horizontal component of F in order for the stick to not fall down.</p>
<p><strong>My thoughts</strong></p>
<p>Forces involved:</p>
<p>We have:
The gravitational force <strong>mg</strong> in the negative y-direction.
The normal force from the wall, <strong>N</strong>(negative x-dreiction).
The friction force in the positive y-direction which is <strong>f=μN</strong> and
the force <strong>F</strong> which acts in the positive x-direction. Thus:</p>
<p>$$\sum F_{x}: F-N=0 \Rightarrow F=N \\
\sum F_{y}: mg-f=mg-\mu N=0 \Rightarrow N=F=\frac{mg}{\mu }$$</p>
<p>$$\boxed{F=\frac{mg}{\mu}}$$
<img src="http://i.imgur.com/QFJq7wT.png" alt="picture"></p>
<p>*<em>Correct answer is $\boxed{F=\frac{mg}{2\mu}}$ *</em></p> | g4785 | [
0.050982117652893066,
0.04951043799519539,
-0.011413272470235825,
0.040328677743673325,
0.01597888395190239,
0.009207994677126408,
0.05242113769054413,
-0.022016266360878944,
-0.09426271915435791,
-0.037090953439474106,
-0.0021892718505114317,
-0.011372911743819714,
-0.0490635484457016,
-0.003914299421012402,
0.011749915778636932,
0.05613040179014206,
0.06602206826210022,
0.0043380847200751305,
0.0063216970302164555,
0.02993563935160637,
-0.029783807694911957,
0.023937510326504707,
0.015588544309139252,
-0.020831404253840446,
0.04068632796406746,
-0.04158449172973633,
0.03958173841238022,
0.0076965456828475,
-0.016886340454220772,
0.0076138474978506565,
0.025265013799071312,
0.012763329781591892,
0.023736145347356796,
-0.04182139411568642,
-0.019598012790083885,
0.010344498790800571,
0.029402034357190132,
0.0189126618206501,
0.03368588909506798,
-0.017396705225110054,
-0.03706773743033409,
-0.01615193858742714,
0.01945657655596733,
-0.000687290565110743,
0.0009143640054389834,
-0.03741340711712837,
0.015027821995317936,
0.006903009954839945,
-0.007853550836443901,
0.014667567797005177,
-0.009725949726998806,
0.025439269840717316,
0.05631403625011444,
-0.06074286997318268,
-0.008946718648076057,
0.019346335902810097,
0.04546508565545082,
-0.0550161711871624,
0.009879140183329582,
0.05111006647348404,
-0.01363640371710062,
-0.0002036945807049051,
0.008094452321529388,
-0.07375139743089676,
0.015637556090950966,
-0.02647116594016552,
-0.03986005485057831,
0.02758866921067238,
-0.011883561499416828,
-0.011779689230024815,
0.0017441313248127699,
-0.022260887548327446,
0.06981739401817322,
0.015531848184764385,
-0.05645519122481346,
-0.027903113514184952,
0.017121441662311554,
0.017487501725554466,
0.005672521889209747,
-0.05872611328959465,
-0.020362185314297676,
0.03654422610998154,
0.006014377810060978,
-0.025071710348129272,
0.012141664512455463,
-0.05544598773121834,
0.02719942294061184,
0.044995807111263275,
-0.06728751957416534,
0.011353494599461555,
-0.009871670044958591,
-0.0066628665663301945,
0.04781930148601532,
0.012562221847474575,
-0.012666737660765648,
-0.00499751465395093,
0.005112932994961739,
0.05324409529566765,
0.0020798395853489637,
0.01490428950637579,
0.0050830659456551075,
-0.012267016805708408,
-0.04726344347000122,
-0.013251107186079025,
0.045090194791555405,
0.005715837236493826,
0.03672715649008751,
0.0837974026799202,
-0.05746681988239288,
-0.02775578573346138,
-0.01461368054151535,
0.015289201401174068,
-0.05888272449374199,
-0.10089468955993652,
0.021346576511859894,
-0.07183848321437836,
0.04392501711845398,
0.018165383487939835,
-0.002243268769234419,
0.06103765591979027,
-0.06731250882148743,
0.023187505081295967,
0.03345672786235809,
0.0716804638504982,
-0.04301191866397858,
-0.0575593039393425,
0.005456586368381977,
0.028768029063940048,
0.01605628803372383,
-0.01357425469905138,
0.010325483046472073,
0.010501742362976074,
0.04292437434196472,
-0.019495274871587753,
0.04370983690023422,
0.043387677520513535,
-0.020741360262036324,
0.055696818977594376,
0.009925859048962593,
-0.0035422586370259523,
-0.009418969973921776,
-0.009055557660758495,
0.006083748769015074,
0.03518824279308319,
-0.005718133877962828,
0.00534273125231266,
-0.023777110502123833,
0.008999902755022049,
0.07562979310750961,
-0.03361015021800995,
0.0030613457784056664,
0.07841310650110245,
-0.016654416918754578,
-0.05236627534031868,
0.07933848351240158,
-0.02465629205107689,
0.022721299901604652,
-0.0135799003764987,
0.02406259998679161,
-0.01560902502387762,
0.023299947381019592,
-0.030897004529833794,
0.0076583316549658775,
-0.003584107384085655,
-0.01835537515580654,
0.011440932750701904,
-0.039579398930072784,
0.0001301226729992777,
0.017050813883543015,
-0.03575925529003143,
-0.03949802368879318,
0.005518963560461998,
0.028033727779984474,
0.013556213118135929,
0.005731490440666676,
0.010811913758516312,
0.0006200841744430363,
-0.022865187376737595,
0.033130109310150146,
-0.004952560644596815,
0.057519882917404175,
-0.018240228295326233,
0.043676234781742096,
0.029731236398220062,
0.025892185047268867,
0.010686751455068588,
0.07716944813728333,
0.06476529687643051,
-0.01075633056461811,
-0.007382377050817013,
-0.05781381204724312,
0.014018882997334003,
-0.0088241808116436,
0.011327561922371387,
-0.005520117934793234,
-0.006833303719758987,
0.022487273439764977,
-0.0448131337761879,
0.01652125082910061,
0.023197470232844353,
-0.06457651406526566,
0.0180178415030241,
0.04341059550642967,
0.0431152805685997,
-0.028659913688898087,
0.010861736722290516,
0.01816476322710514,
0.044978734105825424,
0.01125874649733305,
-0.030113063752651215,
-0.03378816321492195,
0.008406959474086761,
-0.006625299341976643,
-0.0031228368170559406,
-0.016392532736063004,
-0.0850917175412178,
0.00289333937689662,
0.01406831294298172,
-0.05251018702983856,
-0.021003635600209236,
-0.032435737550258636,
0.04739068076014519,
-0.009822133928537369,
-0.03650437667965889,
-0.006621770095080137,
-0.05931659787893295,
0.02409609779715538,
-0.013212358579039574,
-0.02849758416414261,
-0.02727488800883293,
-0.034897658973932266,
-0.01941165141761303,
-0.014039884321391582,
-0.038154106587171555,
0.017945611849427223,
0.020972920581698418,
-0.016337499022483826,
0.01574212685227394,
-0.0032744943164288998,
-0.00875170063227415,
-0.01327473483979702,
-0.032634031027555466,
0.03527989238500595,
-0.08811869472265244,
0.01861795410513878,
0.003354921005666256,
0.0594034418463707,
0.02046845108270645,
0.1150994524359703,
0.05504302680492401,
0.02342597022652626,
-0.009583579376339912,
-0.022945506498217583,
0.022442219778895378,
0.0303427055478096,
0.014587382785975933,
-0.08717050403356552,
-0.017856329679489136,
-0.017341280356049538,
-0.044652730226516724,
0.0015983801567927003,
-0.07338688522577286,
0.007285876199603081,
0.09113582223653793,
-0.09013856947422028,
0.026150939986109734,
-0.09362230449914932,
0.03256027027964592,
0.019183438271284103,
0.02804846130311489,
0.012762346304953098,
-0.0015222455840557814,
-0.011503759771585464,
0.057810358703136444,
-0.030984442681074142,
0.001138514606282115,
0.003920011222362518,
-0.008738426491618156,
-0.009318024851381779,
0.03459978476166725,
0.013765127398073673,
0.049535565078258514,
0.013799323700368404,
-0.03194115310907364,
-0.006366136483848095,
-0.024343764409422874,
-0.02900315448641777,
-0.011448616161942482,
-0.04045548662543297,
0.0603671558201313,
-0.01720196008682251,
0.06101532652974129,
0.061799339950084686,
-0.03447946906089783,
0.030832644551992416,
0.06568428874015808,
-0.028130892664194107,
-0.053304702043533325,
-0.0611182302236557,
0.003419659798964858,
-0.01662376895546913,
-0.029132742434740067,
-0.03749778866767883,
0.019653134047985077,
0.04124317318201065,
0.000035295026464154944,
0.009311257861554623,
-0.02672283723950386,
-0.034727126359939575,
-0.00806886050850153,
0.029386162757873535,
0.06855634599924088,
0.044730447232723236,
-0.0201023668050766,
-0.09344134479761124,
0.00847709272056818,
0.01717984303832054,
0.021305084228515625,
-0.018989255651831627,
0.017875075340270996,
-0.037287600338459015,
-0.043250683695077896,
0.014898931607604027,
0.023532461374998093,
-0.025110984221100807,
0.0003315621870569885,
-0.039994869381189346,
0.028646377846598625,
-0.033180199563503265,
0.008506914600729942,
0.027035892009735107,
0.01698109693825245,
0.023817215114831924,
0.037519123405218124,
-0.006539428606629372,
0.006456848233938217,
0.011908103711903095,
-0.03324665501713753,
-0.01783107966184616,
0.06079159304499626,
-0.02497369423508644,
-0.037996817380189896,
0.01158161275088787,
-0.008550326339900494,
-0.001400051056407392,
0.022659907117486,
0.01267253328114748,
0.05534694716334343,
0.03600016236305237,
0.02358081564307213,
0.023703932762145996,
-0.06941816210746765,
0.02701403573155403,
0.003080779453739524,
0.009411303326487541,
0.029680350795388222,
-0.03396642953157425,
0.012336360290646553,
-0.07054591923952103,
-0.003891311353072524,
0.021798603236675262,
-0.01592463254928589,
-0.023071708157658577,
0.006400975864380598,
0.056923557072877884,
0.008718173019587994,
0.025705374777317047,
0.045003775507211685,
-0.01890738308429718,
-0.026940472424030304,
-0.0009391225758008659,
-0.023163314908742905,
0.0055099488236010075,
-0.016078313812613487,
0.020237749442458153,
-0.05725397169589996,
-0.02839093655347824,
-0.04849836230278015,
0.030325381085276604,
0.03887474164366722,
0.01023173052817583,
0.03695857897400856,
-0.07756974548101425,
0.033504705876111984,
0.041124776005744934,
0.05299389362335205,
0.018602240830659866,
0.010077700018882751,
0.05277669429779053,
0.009466753341257572,
-0.03782326355576515,
0.004426517989486456,
0.002184190321713686,
0.018073543906211853,
-0.0386064350605011,
-0.03597036376595497,
0.027185678482055664,
0.045155081897974014,
-0.0690060555934906,
-0.05305957421660423,
0.05873609706759453,
0.011338459327816963,
-0.0059828306548297405,
0.007793414872139692,
-0.03863885626196861,
0.044701945036649704,
0.004982732702046633,
0.0033337518107146025,
0.024585053324699402,
-0.013007351197302341,
0.052738700062036514,
-0.023932307958602905,
-0.046083174645900726,
0.0349661260843277,
0.05452712997794151,
-0.04383107274770737,
0.05926299840211868,
0.1013118177652359,
0.019470691680908203,
-0.044616956263780594,
0.06823749840259552,
0.10298054665327072,
-0.03357839211821556,
-0.06096441298723221,
-0.00018128484953194857,
-0.0018526480998843908,
0.01071897428482771,
0.043548423796892166,
0.015138938091695309,
-0.03051017038524151,
-0.02026784047484398,
0.016564419493079185,
-0.006768952123820782,
-0.018353141844272614,
-0.08917726576328278,
0.0683136135339737,
-0.02127920836210251,
-0.07124391198158264,
0.04300917685031891,
0.06350180506706238,
-0.004508011043071747,
0.017568985000252724,
-0.01454212050884962,
-0.017212264239788055,
-0.029562415555119514,
0.052412595599889755,
-0.00657594995573163,
0.025497138500213623,
0.010218174196779728,
-0.025439277291297913,
-0.02355540730059147,
-0.027507737278938293,
-0.008155657909810543,
-0.06897319853305817,
0.014283152297139168,
0.037629686295986176,
-0.003981528803706169,
0.046734727919101715,
-0.020368169993162155,
0.022502094507217407,
0.09794251620769501,
-0.03681005910038948,
-0.02769484557211399,
0.003135459963232279,
0.013940053060650826,
-0.00821694079786539,
0.022514760494232178,
0.01803966611623764,
0.00032808081596158445,
0.015800034627318382,
-0.0023408979177474976,
0.019219331443309784,
0.02103547751903534,
0.022383779287338257,
0.01434829831123352,
0.015193174593150616,
-0.010538807138800621,
-0.0029221985023468733,
0.015348674729466438,
-0.0025360453873872757,
-0.022872166708111763,
0.01525468286126852,
0.06891466677188873,
-0.0517796128988266,
0.01324484683573246,
-0.0440189391374588,
-0.037565406411886215,
0.02265017479658127,
0.0036686735693365335,
-0.04930827394127846,
0.011617177166044712,
-0.03205110505223274,
-0.06637559086084366,
-0.022543732076883316,
-0.015397240407764912,
-0.031254250556230545,
-0.03155019134283066,
0.018212633207440376,
0.017950739711523056,
-0.025469068437814713,
-0.07576511800289154,
-0.043312571942806244,
0.01938202790915966,
0.02424183115363121,
0.006538190878927708,
0.005324739962816238,
-0.004873348865658045,
-0.027062950655817986,
-0.0022142999805510044,
0.04940169304609299,
-0.058949269354343414,
-0.02787848934531212,
0.06515224277973175,
-0.012078584171831608,
-0.0166681706905365,
0.001209973474033177,
0.0537724606692791,
0.013125885277986526,
-0.01625879853963852,
0.03241405263543129,
0.05260977894067764,
0.0030011041089892387,
-0.07319331914186478,
-0.028953373432159424,
-0.04165896400809288,
0.030955499038100243,
-0.07116274535655975,
-0.0032048197463154793,
-0.04212983325123787,
0.02954350970685482,
0.017125865444540977,
-0.04936874657869339,
0.05009617656469345,
-0.0012292807223275304,
0.006723456550389528,
-0.03622007369995117,
0.08557529002428055,
-0.01740916632115841,
0.03997360169887543,
-0.06796718388795853,
-0.03153695538640022,
-0.0335780568420887,
0.08069616556167603,
0.030599990859627724,
-0.047954559326171875,
0.01477466244250536,
-0.07809686660766602,
-0.013652320019900799,
-0.024057677015662193,
-0.010621783323585987,
-0.06944140046834946,
0.031768880784511566,
-0.029033465310931206,
0.04318173974752426,
0.0082821324467659,
-0.018616264685988426,
0.013072031550109386,
-0.04614943265914917,
0.05117280036211014,
-0.007668756879866123,
0.027665331959724426,
-0.07569149881601334,
-0.019557779654860497,
0.019594239071011543,
0.045978255569934845,
-0.018316015601158142,
-0.015650074928998947,
-0.018739409744739532,
0.053017757833004,
-0.019997727125883102,
-0.0179057028144598,
0.060094401240348816,
-0.003145904978737235,
0.07017259299755096,
0.058106739073991776,
0.011683582328259945,
-0.07107570767402649,
-0.036271195858716965,
-0.016420232132077217,
0.07449648529291153,
0.027949174866080284,
0.006431196350604296,
0.005146071780472994,
-0.05594143271446228,
-0.03480706363916397,
0.007087536156177521,
-0.07189438492059708,
-0.0066015999764204025,
0.01422619167715311,
-0.0460716150701046,
0.008703229017555714,
0.01868048496544361,
-0.00660400465130806,
0.020213132724165916,
0.018415283411741257,
-0.013138907961547375,
-0.006265445612370968,
-0.001066679717041552,
-0.017723659053444862,
-0.002106791129335761,
-0.00880664773285389,
0.016528019681572914,
0.04800165072083473,
0.006106337998062372,
0.0031269621104002,
-0.02820262312889099,
0.005160006694495678,
0.0290899146348238,
-0.05227366462349892,
-0.053791265934705734,
0.050768688321113586,
0.06721623986959457,
-0.02628648467361927,
-0.011788278818130493,
0.04000569507479668,
-0.03139100596308708,
-0.007488258183002472,
0.0004297439882066101,
-0.029547860845923424,
-0.023152818903326988,
-0.011762561276555061,
0.054703615605831146,
0.018257111310958862,
-0.05759887769818306,
0.014444580301642418,
-0.03873194381594658,
-0.06071995198726654,
-0.03715609759092331,
-0.024767370894551277,
0.01709662191569805,
0.05422991141676903,
-0.02400858886539936,
-0.03065459430217743,
-0.05155211314558983,
-0.0019094364251941442,
0.06653682887554169,
-0.03525638207793236,
0.027939168736338615,
-0.03490622714161873,
0.03490443155169487,
-0.03997351974248886,
0.02403440698981285,
0.0037394100800156593,
-0.012559332884848118,
0.007092450279742479,
0.0028822757303714752,
0.01650749333202839,
0.002895657205954194,
-0.006742025725543499,
0.011417021043598652,
0.04221455007791519,
-0.012648740783333778,
-0.03802460804581642,
0.04013765603303909,
-0.058774255216121674,
-0.016915731132030487,
0.039655670523643494,
0.015998439863324165,
0.03520691394805908,
0.001119371154345572,
-0.0256553553044796,
-0.04798414558172226,
0.024989865720272064,
0.045158788561820984,
-0.06686815619468689,
0.06051677465438843,
0.005955316126346588,
-0.04163534939289093,
-0.00505497632548213,
0.009543918073177338,
0.011450245976448059,
-0.031076516956090927,
0.00302942655980587,
-0.01042562909424305,
-0.0011171838268637657,
-0.003400663612410426,
0.031642571091651917,
-0.010578326880931854,
-0.015178781002759933,
-0.041641715914011,
0.016112325713038445,
-0.0076442197896540165,
-0.007569614797830582,
-0.02017243765294552,
-0.04534059390425682,
-0.03245972841978073,
0.06440103054046631,
-0.024578025564551353,
0.01449744962155819,
0.0012683514505624771,
0.02789750136435032,
0.09618283063173294,
0.0012209388660266995,
-0.0041308170184493065,
0.0021715592592954636,
-0.034011110663414,
-0.018865391612052917,
0.06433100253343582,
0.00322147598490119,
0.012238937430083752,
0.00506044365465641,
-0.016563791781663895,
-0.07551925629377365,
0.011784144677221775,
-0.06879730522632599,
0.026001010090112686,
-0.03738554194569588,
-0.0025664856657385826,
-0.051458436995744705,
-0.051097720861434937,
0.06465360522270203,
0.06818839907646179,
0.007934375666081905,
-0.025592364370822906,
0.001701046829111874,
0.04049406200647354,
-0.0632067546248436,
0.005587663501501083,
0.021739810705184937,
-0.06270899623632431,
-0.048385053873062134,
0.014310386031866074,
-0.041041210293769836,
-0.0569089911878109,
-0.0564083568751812,
-0.042945511639118195,
-0.020451970398426056,
0.010550168342888355,
-0.005000024568289518,
0.014330188743770123,
-0.024318739771842957,
-0.054108235985040665,
0.00769951893016696,
0.022572768852114677,
0.028137754648923874,
-0.03623587638139725,
0.011355963535606861,
-0.04588007926940918,
0.004888304974883795,
0.026010870933532715,
-0.045099932700395584,
-0.01166951097548008,
-0.02355067990720272,
0.005061278119683266,
0.04359012469649315,
-0.007600781507790089,
-0.04273846000432968,
0.08603674173355103,
-0.007744994014501572,
0.020455555990338326,
0.04949536547064781,
0.009562277235090733,
0.014669962227344513,
-0.038550492376089096,
0.002758590504527092,
-0.0582810714840889,
-0.020093658939003944,
0.018897050991654396,
0.03589111194014549,
-0.006102751474827528,
-0.002989098895341158,
-0.012804357334971428,
0.019727380946278572,
-0.022881636396050453,
0.04932720586657524,
-0.023778431117534637,
-0.023747188970446587,
0.03840041160583496
] |
<p>Is it possible to see <a href="http://en.wikipedia.org/wiki/Fraunhofer_lines" rel="nofollow">Fraunhofer lines</a> with amateur equipment?</p>
<p>Would it be possible (with reasonable effort) to identify elements or is this hard?</p> | g4786 | [
-0.03162724897265434,
-0.02154804952442646,
-0.028132198378443718,
0.015476042404770851,
0.029777085408568382,
-0.030626490712165833,
0.022838644683361053,
0.0044580004177987576,
-0.044217150658369064,
-0.025150887668132782,
-0.03590032085776329,
0.03488074243068695,
0.005764512345194817,
0.06087608262896538,
-0.012485845014452934,
-0.027058901265263557,
0.0715794712305069,
-0.030666867271065712,
0.10997835546731949,
-0.019302500411868095,
0.07169035077095032,
0.06517531722784042,
0.015847494825720787,
-0.00651450315490365,
-0.026942912489175797,
0.04724620282649994,
-0.008119280450046062,
-0.03040132112801075,
-0.09222841262817383,
-0.030477391555905342,
-0.08012934774160385,
0.010602535679936409,
0.01899981126189232,
-0.0001119796943385154,
0.02704184129834175,
0.0015424045268446207,
0.053633466362953186,
0.04526006057858467,
-0.024029284715652466,
0.07135035842657089,
-0.03652554377913475,
-0.038059428334236145,
0.016864610835909843,
-0.011295104399323463,
-0.017807986587285995,
0.008791923522949219,
-0.04656416177749634,
-0.04713340476155281,
0.0002306536480318755,
-0.009515023790299892,
0.02475878782570362,
0.03051125630736351,
0.016130467876791954,
0.020331652835011482,
0.020383533090353012,
-0.00956716388463974,
0.008715817704796791,
0.01913505792617798,
0.11549294739961624,
-0.010267013683915138,
-0.0513920933008194,
0.0357460118830204,
-0.013798562809824944,
0.002839867491275072,
0.0070731062442064285,
0.019962253049016,
0.02004450187087059,
-0.05132820084691048,
0.042654961347579956,
0.039893392473459244,
-0.044469691812992096,
0.024182774126529694,
0.0033931618090718985,
0.008378911763429642,
-0.020819155499339104,
-0.00610611354932189,
-0.052498962730169296,
-0.0009597346652299166,
0.051611125469207764,
0.04786013439297676,
0.013511762954294682,
-0.023907333612442017,
-0.03471504896879196,
0.032584693282842636,
0.06645984947681427,
-0.006178614217787981,
-0.0077994465827941895,
-0.00634490791708231,
0.03938177227973938,
0.03231091797351837,
-0.0011828404385596514,
0.06028783321380615,
0.01184369157999754,
0.003378676250576973,
0.06005615368485451,
0.04950088635087013,
-0.030138419941067696,
0.04519295319914818,
-0.021322093904018402,
-0.04682815819978714,
-0.01479051262140274,
0.02476435713469982,
-0.07935581356287003,
0.007953375577926636,
-0.014399250037968159,
0.00607687933370471,
0.08900104463100433,
-0.008875088766217232,
-0.04591171443462372,
-0.04705847054719925,
-0.01774369366466999,
-0.03165913373231888,
-0.06855900585651398,
-0.00195948570035398,
0.04216185584664345,
-0.017994215711951256,
-0.01674736477434635,
0.017153557389974594,
-0.011717110872268677,
0.04866473376750946,
0.013742366805672646,
-0.03331751748919487,
0.022462787106633186,
0.07406707853078842,
-0.009812537580728531,
0.0027902028523385525,
0.018534792587161064,
0.008281821385025978,
0.06737146526575089,
-0.08174797892570496,
-0.047563064843416214,
-0.029002683237195015,
0.10368266701698303,
-0.053087782114744186,
0.04842745512723923,
-0.014430919662117958,
-0.025225192308425903,
0.03551198169589043,
-0.020877070724964142,
0.004207126330584288,
0.03975923731923103,
0.008565256372094154,
-0.03020026534795761,
-0.047529350966215134,
0.0338396318256855,
-0.025745756924152374,
-0.04677501693367958,
0.01832001470029354,
0.013860666193068027,
0.03295468911528587,
-0.013643557205796242,
0.0403575599193573,
0.048172660171985626,
-0.012483065016567707,
-0.029346993193030357,
-0.04995020106434822,
-0.06200331822037697,
-0.04862675815820694,
-0.03626387193799019,
-0.004126667510718107,
-0.007360529620200396,
-0.006051944103091955,
-0.008754082024097443,
0.03935951739549637,
-0.011064055375754833,
0.003620157716795802,
-0.039934493601322174,
-0.03368013724684715,
0.07493700832128525,
-0.03803708404302597,
0.027660898864269257,
0.01879044994711876,
0.03325065225362778,
0.017119355499744415,
0.0038497138302773237,
0.0562303364276886,
0.033096011728048325,
-0.04546699300408363,
0.029440371319651604,
-0.000695493770763278,
-0.04085239768028259,
-0.012225503101944923,
0.013108287937939167,
-0.020611505955457687,
0.02526888996362686,
-0.002081147860735655,
-0.0016598016954958439,
0.0022032533306628466,
-0.008162761107087135,
-0.014820963144302368,
0.012677526101469994,
0.045886360108852386,
0.00043223955435678363,
0.029809294268488884,
0.011220322921872139,
0.00922821182757616,
-0.06285233050584793,
-0.002417579758912325,
0.008907526731491089,
0.0022659068927168846,
0.04429709538817406,
0.014455929398536682,
0.010066238231956959,
0.031431958079338074,
-0.015385323204100132,
-0.03719913214445114,
0.058811355382204056,
-0.020743602886795998,
-0.054193586111068726,
-0.024146130308508873,
-0.04741469398140907,
0.019711969420313835,
-0.016991455107927322,
0.005354293622076511,
-0.02015218324959278,
-0.002587672555819154,
-0.018885402008891106,
0.026256298646330833,
0.014792192727327347,
0.017753807827830315,
0.007530876901000738,
0.05227446183562279,
0.04013973847031593,
-0.040102776139974594,
0.009577966295182705,
-0.011527009308338165,
0.009697956964373589,
0.02375127747654915,
-0.040654029697179794,
-0.018493738025426865,
-0.0006723719998262823,
-0.05032787472009659,
0.00999662559479475,
-0.057309314608573914,
0.04617248475551605,
-0.0027532558888196945,
0.015672963112592697,
-0.034550607204437256,
-0.008401566185057163,
0.05492056533694267,
-0.02490764670073986,
-0.07730025798082352,
-0.004306786693632603,
-0.00957450084388256,
0.050577059388160706,
0.02756582573056221,
-0.016713902354240417,
0.047503966838121414,
-0.009668167680501938,
0.041514184325933456,
-0.02270100638270378,
0.014506782405078411,
0.0024767168797552586,
0.04717470332980156,
-0.041042495518922806,
0.01515146903693676,
-0.01695387437939644,
-0.020076366141438484,
0.02062283456325531,
0.014071149751543999,
-0.07519137859344482,
0.030791206285357475,
-0.030120179057121277,
0.05905478447675705,
-0.015576998703181744,
-0.04337181895971298,
-0.06091566011309624,
-0.030241889879107475,
-0.0015571676194667816,
-0.008341116830706596,
-0.016580112278461456,
-0.02950122579932213,
0.0260970089584589,
-0.027831319719552994,
-0.03701300919055939,
-0.0008445681887678802,
-0.005875600967556238,
0.010530850850045681,
-0.00616582902148366,
0.04213001951575279,
0.0004956591874361038,
0.0006945931818336248,
-0.02398655377328396,
0.018984004855155945,
-0.0029872525483369827,
0.06332182139158249,
0.0015606173546984792,
0.06372377276420593,
-0.050008825957775116,
0.023298971354961395,
-0.08858993649482727,
0.015088006854057312,
0.013296478427946568,
-0.0035533783957362175,
-0.06623318791389465,
-0.03532111272215843,
0.009455193765461445,
-0.020342933014035225,
0.01911965198814869,
0.03810862824320793,
0.010220342315733433,
-0.031164340674877167,
-0.005788267590105534,
-0.043255515396595,
-0.04843753203749657,
-0.050268691033124924,
0.026297733187675476,
-0.052591681480407715,
0.026314467191696167,
-0.004882398061454296,
-0.02412261813879013,
-0.011059627868235111,
0.06142934411764145,
0.030189335346221924,
0.027071498334407806,
-0.007267321925610304,
-0.01705021969974041,
-0.027311937883496284,
0.007978007197380066,
0.04399909824132919,
0.003592150751501322,
0.008615013211965561,
0.008828733116388321,
-0.06698945164680481,
0.0035373077262192965,
-0.01043380331248045,
-0.004010934382677078,
-0.008223284035921097,
-0.038356006145477295,
-0.02304442785680294,
0.013942110352218151,
-0.027754846960306168,
-0.019943473860621452,
-0.02691776491701603,
-0.0606091283261776,
-0.00987199880182743,
-0.016793077811598778,
0.009900624863803387,
0.025587912648916245,
-0.053490009158849716,
-0.0027663176879286766,
0.03908073902130127,
-0.039980996400117874,
0.007416995242238045,
-0.04915957525372505,
-0.03630073368549347,
-0.009346951730549335,
0.010025693103671074,
-0.0023034398909658194,
-0.010373024269938469,
0.03382677584886551,
0.01426492165774107,
-0.006112048402428627,
-0.05318092927336693,
0.011804555542767048,
-0.013753034174442291,
0.05072646588087082,
0.036408957093954086,
-0.020675480365753174,
-0.008746928535401821,
0.006255167070776224,
-0.01489473506808281,
0.06469282507896423,
-0.027270538732409477,
0.01647152751684189,
-0.011420932598412037,
-0.03137236088514328,
0.09161260724067688,
0.02467471919953823,
-0.012545337900519371,
0.003139120526611805,
-0.015997735783457756,
0.01922689750790596,
0.02074860781431198,
-0.07772605121135712,
0.022612297907471657,
-0.0030163703486323357,
0.006691351532936096,
0.009174544364213943,
0.09832119941711426,
-0.08391490578651428,
-0.011137256398797035,
0.008537063375115395,
-0.0241656843572855,
0.03234361112117767,
-0.03905303031206131,
0.005148790776729584,
-0.019751692190766335,
0.03660358488559723,
-0.01708054728806019,
-0.0018187499372288585,
-0.05083989351987839,
-0.0381973534822464,
0.009442123584449291,
-0.07233420759439468,
-0.006840229034423828,
-0.005153826903551817,
0.0024685945827513933,
-0.028793135657906532,
0.07728289067745209,
0.026465337723493576,
-0.0007107620476745069,
-0.02128840982913971,
0.07183706015348434,
-0.02281174808740616,
0.029556579887866974,
-0.009637054987251759,
-0.014487090520560741,
0.018527990207076073,
-0.04238438606262207,
-0.04558873921632767,
-0.04496864601969719,
0.02825716696679592,
-0.03507109358906746,
0.0053453827276825905,
-0.023780234158039093,
-0.004697016905993223,
-0.046413976699113846,
0.027829110622406006,
0.01839790865778923,
-0.004459559917449951,
0.008737750351428986,
-0.025789709761738777,
-0.05591815710067749,
-0.06990829855203629,
0.02261556312441826,
-0.01092784758657217,
-0.03218461200594902,
0.04273630678653717,
0.051718298345804214,
0.03793042525649071,
-0.047441817820072174,
-0.010054274462163448,
-0.0026874798350036144,
-0.06568055599927902,
0.008303270675241947,
-0.05318738520145416,
0.004528914112597704,
0.024989161640405655,
0.04773404076695442,
-0.016482742503285408,
0.01278559397906065,
0.013077649287879467,
0.002746827434748411,
0.012094785459339619,
0.052128661423921585,
-0.01879197545349598,
0.02170027233660221,
-0.02438901923596859,
0.014821549877524376,
-0.0338771678507328,
-0.024511907249689102,
-0.006897768471390009,
-0.0013693238142877817,
0.10021921992301941,
-0.03644354268908501,
-0.0007484200177714229,
0.0009977382142096758,
-0.02975226566195488,
0.0324038490653038,
0.028208883479237556,
-0.008556260727345943,
-0.04183068871498108,
0.031311556696891785,
0.026580577716231346,
-0.04093506559729576,
-0.0725659504532814,
-0.0012306342832744122,
0.010510013438761234,
-0.017287081107497215,
0.002753708977252245,
-0.018196644261479378,
0.05969347432255745,
0.02338561974465847,
-0.007707929704338312,
-0.03187207132577896,
-0.017427051439881325,
-0.0029189838096499443,
-0.037118569016456604,
-0.01840578392148018,
-0.05486400052905083,
0.02729441411793232,
-0.0017294607823714614,
0.02100159414112568,
0.003335765562951565,
0.014620867557823658,
-0.06595686078071594,
0.10693029314279556,
-0.0007963163661770523,
0.0019719297997653484,
0.022170361131429672,
0.04790627211332321,
-0.01970633678138256,
-0.00956396758556366,
-0.022647162899374962,
-0.07213622331619263,
0.03059602528810501,
-0.041781533509492874,
0.06253334134817123,
-0.009341621771454811,
0.043376073241233826,
-0.0008193664252758026,
0.043300870805978775,
0.0008590795332565904,
0.0197022445499897,
0.035997238010168076,
0.03261823207139969,
0.01079201977699995,
0.013774638064205647,
0.01772569678723812,
-0.05318363755941391,
-0.010067926719784737,
-0.058419231325387955,
-0.07720248401165009,
0.012031999416649342,
-0.018751593306660652,
-0.042173247784376144,
0.037361305207014084,
-0.0641879215836525,
-0.07703201472759247,
0.04180266708135605,
0.0223937276750803,
0.03334355726838112,
-0.009538727812469006,
-0.035279419273138046,
-0.04356357082724571,
-0.04302200675010681,
-0.03402953967452049,
-0.03134807571768761,
-0.016752026975154877,
0.0011434262851253152,
-0.02143222466111183,
-0.007469469681382179,
0.022532114759087563,
0.06800150871276855,
-0.013011172413825989,
0.045182473957538605,
-0.019008494913578033,
-0.006324459798634052,
0.04935701936483383,
0.017707334831357002,
0.0735744833946228,
-0.0014564506709575653,
0.03480708971619606,
0.021267836913466454,
-0.01485461462289095,
0.06710740178823471,
0.040163978934288025,
0.018435847014188766,
-0.02787483111023903,
0.035844605416059494,
-0.0034222446847707033,
0.004880070220679045,
-0.03659617155790329,
-0.01800764724612236,
0.045546434819698334,
0.02337685413658619,
-0.02355039492249489,
-0.00763269979506731,
0.016505038365721703,
0.03809303790330887,
0.02177399955689907,
-0.006547870580106974,
0.002434318885207176,
-0.034222111105918884,
0.013324087485671043,
-0.06160702556371689,
0.04740622267127037,
0.03360901400446892,
0.047009050846099854,
-0.03233342245221138,
-0.05538564920425415,
-0.03293226659297943,
0.017999591305851936,
0.03377825766801834,
-0.018262002617120743,
-0.02398120053112507,
0.06470582634210587,
-0.0039429087191820145,
0.008189619518816471,
-0.039706841111183167,
0.019433557987213135,
0.05166594684123993,
0.017354412004351616,
0.004961095750331879,
0.020527465268969536,
-0.03336401283740997,
0.035523585975170135,
-0.058340806514024734,
0.023538738489151,
0.013275780715048313,
-0.021959910169243813,
0.021072490140795708,
-0.021846193820238113,
0.02895931899547577,
-0.06247081607580185,
0.001262046629562974,
0.07846013456583023,
0.03375754877924919,
0.045925699174404144,
-0.01176486350595951,
0.0032667384948581457,
0.025874417275190353,
-0.001788730500265956,
0.0031807287596166134,
-0.008660359308123589,
0.02352183498442173,
0.020423157140612602,
-0.046191245317459106,
-0.035659030079841614,
-0.0023121994454413652,
0.0889233872294426,
-0.04740036278963089,
-0.007887528277933598,
-0.016749104484915733,
-0.006772399879992008,
0.007281437516212463,
0.019444534555077553,
-0.030445575714111328,
0.010166855528950691,
0.09818871319293976,
-0.028694426640868187,
0.004144272767007351,
-0.0076462929137051105,
-0.053279321640729904,
0.020931098610162735,
-0.059758108109235764,
0.008627085015177727,
0.020420512184500694,
-0.002567592076957226,
0.038156427443027496,
-0.007472375873476267,
-0.025809286162257195,
-0.015852948650717735,
0.019480440765619278,
0.07596085965633392,
0.010959587059915066,
-0.0038157806266099215,
0.03606140986084938,
0.05605810135602951,
0.041899874806404114,
-0.0014148529153317213,
0.03826184943318367,
0.003477888647466898,
0.028817448765039444,
-0.002283570822328329,
0.009878812357783318,
0.012553639709949493,
0.00003795395969063975,
0.01855701394379139,
-0.0055923983454704285,
0.017577221617102623,
-0.017889294773340225,
-0.001086914329789579,
0.02277984283864498,
0.07486756145954132,
-0.014176595956087112,
0.0022429772652685642,
-0.043561965227127075,
-0.09565770626068115,
-0.002315196441486478,
-0.005359632428735495,
0.014219158329069614,
-0.10900134593248367,
-0.007188725750893354,
0.031302183866500854,
-0.008242915384471416,
-0.017331833019852638,
-0.04249242693185806,
0.03942793235182762,
-0.004916040692478418,
-0.034844763576984406,
0.031209547072649002,
0.007028266787528992,
0.023421423509716988,
-0.001515558222308755,
0.009453639388084412,
0.023789724335074425,
0.003283427795395255,
-0.046249400824308395,
0.0735476091504097,
0.01542254351079464,
-0.008081008680164814,
-0.016275789588689804,
-0.017035184428095818,
-0.0518871508538723,
-0.06559053808450699,
-0.04675557464361191,
0.06537234783172607,
0.009773116558790207,
0.014611328952014446,
0.04936129227280617,
0.02100035734474659,
-0.05669901892542839,
-0.03662276640534401,
-0.07558228075504303,
0.018521428108215332,
-0.022675981745123863,
0.006875154096633196,
0.021358394995331764,
0.04429337754845619,
0.058214496821165085,
0.03678416460752487,
-0.008498914539813995,
-0.05390174314379692,
-0.024780234321951866,
-0.02187947928905487,
0.019529443234205246,
0.025745248422026634,
-0.015990640968084335,
-0.01352051179856062,
0.11683763563632965,
-0.035323914140462875,
0.016710368916392326,
-0.02400268241763115,
0.03438646346330643,
-0.020147208124399185,
0.004822391550987959,
-0.039718691259622574,
0.034385476261377335,
0.002291389275342226,
-0.03976580500602722,
-0.04948912933468819,
0.006878688931465149,
0.0012829714687541127,
0.1069076731801033,
0.001926739583723247,
0.07510848343372345,
0.04611807316541672,
-0.02147214114665985,
-0.03182980790734291,
0.022249827161431313,
0.0034440529998391867,
0.0007520239450968802,
-0.054771892726421356,
-0.054932814091444016,
0.04754944145679474,
-0.019218388944864273,
-0.04951655864715576,
-0.00005023761696065776,
0.017279740422964096,
0.0047517502680420876,
-0.026058318093419075,
-0.027237266302108765,
-0.01380640547722578,
-0.04611033946275711,
-0.06614794582128525,
0.014190588146448135,
-0.08391766250133514,
-0.008371750824153423,
0.02407812885940075,
0.04872848838567734,
0.07491686940193176,
-0.04377571865916252,
-0.01762288808822632,
0.012796847149729729,
-0.003474535420536995,
0.07640039175748825,
0.03769981488585472,
0.04076220467686653,
0.010935510508716106,
0.01744593307375908,
-0.0434076227247715,
0.05402311682701111,
-0.03849752992391586,
-0.06740309298038483,
-0.025171073153614998,
-0.01596330665051937
] |
<p>I cannot find the answer to the above question.
I know that para-positronium is created with a probability of $25\%$ and decays into 2 photons, while ortho-positronium is created with a probability of $75\%$ and decays into 3 photons.
I also know that ortho-positronium has a way longer life time than para-positronium. This, in my understanding, should not affect the number of decays per time, but just means that the ortho-positronium will decay LATER into three photons. But in the end there should be $75\%$ 3-photon-decays and $25\%$ 2-photon-decays. But in reality 2-photon-decay happens about 300 times more often than 3-photon-decay.
What information am I missing?
Thank you!</p> | g4787 | [
0.039601441472768784,
0.011328277178108692,
-0.009027503430843353,
0.022343194112181664,
0.012954432517290115,
0.03516271710395813,
0.027943337336182594,
0.0298871211707592,
0.008942225947976112,
-0.06561356037855148,
0.0015169044490903616,
0.018521353602409363,
0.041107967495918274,
-0.06800156831741333,
-0.0038372804410755634,
0.008385539054870605,
0.07588105648756027,
-0.009354222565889359,
0.011433335021138191,
0.05469780042767525,
-0.04686334356665611,
-0.06461088359355927,
-0.01112118549644947,
-0.04923604428768158,
-0.011484120972454548,
0.01543157733976841,
0.00004322600943851285,
-0.029659250751137733,
-0.024229247123003006,
-0.04276224970817566,
0.05303141474723816,
0.013914477080106735,
0.012217572890222073,
0.03429005667567253,
0.01955443248152733,
-0.07857713848352432,
0.07136061787605286,
0.03158188983798027,
-0.03734879568219185,
0.005632893182337284,
0.02632870152592659,
-0.06648582965135574,
0.06462744623422623,
-0.03162399306893349,
-0.029001716524362564,
-0.04851387068629265,
-0.04754641652107239,
0.07314608991146088,
0.00533813564106822,
-0.026252157986164093,
-0.0038202230352908373,
0.009765418246388435,
-0.002683744765818119,
0.03325168415904045,
0.056468017399311066,
0.009760145097970963,
0.04470274597406387,
-0.056351955980062485,
0.03625086694955826,
0.04136308282613754,
0.02559053525328636,
-0.04437275975942612,
-0.024234589189291,
0.001863576122559607,
0.08872933685779572,
0.005630786530673504,
0.007275926414877176,
0.015751255676150322,
0.014439071528613567,
0.043983038514852524,
0.043967682868242264,
0.042865604162216187,
-0.034481365233659744,
-0.04023851081728935,
0.05826471373438835,
0.02750597707927227,
-0.0030083858873695135,
-0.041051603853702545,
-0.0036301729269325733,
0.07795219123363495,
-0.010519145056605339,
0.004439003765583038,
0.005833504255861044,
0.0217325109988451,
0.04313518479466438,
-0.009188205003738403,
-0.014910377562046051,
-0.015331493690609932,
-0.045775339007377625,
0.0011589598143473268,
0.010976306162774563,
-0.01665116660296917,
0.04398806020617485,
-0.015378924086689949,
-0.08523281663656235,
-0.009441226720809937,
0.03146110102534294,
0.06276923418045044,
-0.028262391686439514,
0.03764950856566429,
0.024496976286172867,
-0.043447863310575485,
0.019657904282212257,
0.004184971563518047,
-0.012767376378178596,
-0.007756838575005531,
0.04195287823677063,
-0.014185010455548763,
-0.0006909525254741311,
0.0015526089118793607,
-0.03880695998668671,
0.030446432530879974,
-0.08014477044343948,
-0.017102893441915512,
0.008539922535419464,
0.05147546902298927,
0.0026481111999601126,
-0.03451501205563545,
0.016258513554930687,
0.038611941039562225,
0.07516203820705414,
-0.012691793963313103,
-0.008024906739592552,
0.042946603149175644,
-0.034980408847332,
-0.0077828532084822655,
0.010095423087477684,
0.06413517892360687,
-0.00003917888898286037,
0.06568198651075363,
-0.0008693425334058702,
0.019802656024694443,
-0.022001730278134346,
0.045401375740766525,
-0.04157290235161781,
0.07008567452430725,
0.04994076490402222,
0.017633235082030296,
0.019439201802015305,
-0.019702205434441566,
-0.03727783262729645,
-0.023089995607733727,
0.046866513788700104,
-0.014018927700817585,
-0.04107438400387764,
0.05053159222006798,
0.011898565106093884,
-0.017220858484506607,
-0.014101747423410416,
0.06252371519804001,
0.09297676384449005,
-0.04198160767555237,
0.008215490728616714,
-0.03736598789691925,
-0.037144292145967484,
-0.021076593548059464,
-0.018170494586229324,
0.018247168511152267,
-0.06005483120679855,
0.04973236098885536,
0.013796481303870678,
-0.01479156594723463,
-0.056420955806970596,
-0.025615151971578598,
0.002562562935054302,
-0.0005531440256163478,
0.007539720740169287,
-0.06388165056705475,
-0.08636287599802017,
-0.0613943487405777,
0.03365301340818405,
-0.00897944625467062,
0.02681857906281948,
0.014994326047599316,
-0.01807367242872715,
0.013660743832588196,
0.002471343381330371,
0.005078842863440514,
-0.018414178863167763,
0.027760609984397888,
0.00116746558342129,
-0.013492303900420666,
-0.056398652493953705,
-0.027858491986989975,
-0.0018210543785244226,
-0.006093642674386501,
0.01280975341796875,
-0.001996843609958887,
-0.0443163625895977,
0.04687737300992012,
-0.012347664684057236,
-0.016431275755167007,
0.017703693360090256,
0.007816433906555176,
-0.03269875422120094,
-0.002967995824292302,
-0.0064742169342935085,
-0.03356536850333214,
0.024365456774830818,
-0.023073820397257805,
-0.029853880405426025,
-0.024356486275792122,
0.025991741567850113,
-0.018611345440149307,
0.06589020043611526,
-0.057444121688604355,
-0.0026265361811965704,
0.03017192892730236,
-0.02354877069592476,
-0.025862140581011772,
0.0013385380152612925,
0.02511102892458439,
0.012751147150993347,
0.031017182394862175,
0.033785708248615265,
-0.02636103890836239,
-0.050574373453855515,
0.059451840817928314,
-0.005683511961251497,
-0.04534534364938736,
-0.012727777473628521,
0.003199475584551692,
0.022181356325745583,
-0.07217646390199661,
-0.04489840939640999,
0.02814682573080063,
-0.03877389058470726,
-0.013772561214864254,
-0.036004237830638885,
0.045628271996974945,
-0.03119727596640587,
-0.018876729533076286,
-0.02490300126373768,
-0.0005455020000226796,
0.018295209854841232,
0.02982974238693714,
0.013106628321111202,
-0.00531093729659915,
0.03196687623858452,
-0.021606383845210075,
0.0054540857672691345,
0.005913782864809036,
0.009003999643027782,
0.08963282406330109,
0.02178446389734745,
-0.11824624985456467,
-0.019765442237257957,
-0.03417643904685974,
-0.0278939139097929,
0.02468261495232582,
0.012773709371685982,
-0.030624158680438995,
-0.016433855518698692,
0.005971239414066076,
0.002740507945418358,
0.019233813509345055,
-0.02630644291639328,
0.06910201162099838,
-0.07416343688964844,
0.027529053390026093,
-0.02120172791182995,
0.01070752739906311,
-0.011311113834381104,
-0.07486703991889954,
0.03406377136707306,
0.005003472324460745,
-0.029160290956497192,
0.01571209728717804,
0.031181700527668,
0.041073255240917206,
0.001959090353921056,
0.040439337491989136,
0.024846771731972694,
-0.0018662838265299797,
0.034185003489255905,
-0.05031001195311546,
0.017862217500805855,
-0.03577802702784538,
-0.0433303602039814,
-0.057051803916692734,
-0.030278561636805534,
-0.00934553612023592,
-0.05981430038809776,
-0.010289601050317287,
0.011768873780965805,
-0.050189629197120667,
0.02996392734348774,
-0.06261184811592102,
-0.005017050541937351,
0.052635326981544495,
-0.006788540165871382,
0.056852348148822784,
0.00627500144764781,
-0.019415901973843575,
0.03818745166063309,
0.00489824777469039,
-0.003254797775298357,
-0.009308280423283577,
-0.06463133543729782,
-0.004163701087236404,
0.06585565954446793,
-0.03270374611020088,
-0.01802465133368969,
0.013022459112107754,
0.03566312417387962,
0.0008993791998364031,
-0.09292002022266388,
0.04888499528169632,
0.05113208666443825,
0.008208215236663818,
-0.037064820528030396,
0.07486025243997574,
-0.005199536215513945,
0.05049798637628555,
-0.006633775308728218,
-0.014833265915513039,
-0.029980255290865898,
0.07442569732666016,
0.003618145827203989,
0.009239635430276394,
-0.042445290833711624,
0.022151131182909012,
-0.02269744873046875,
-0.01923123002052307,
0.06186414510011673,
-0.03464560583233833,
-0.07176942378282547,
-0.0303364098072052,
0.02513870783150196,
-0.012495826929807663,
-0.018078582361340523,
-0.025912318378686905,
-0.011665083467960358,
0.02058260887861252,
-0.0412454716861248,
-0.013702143914997578,
0.04267628863453865,
-0.02638988383114338,
-0.0014751210110262036,
-0.01061917282640934,
0.04078250005841255,
0.03234795108437538,
-0.013935206457972527,
0.03187337517738342,
0.05813829228281975,
-0.061370473355054855,
0.020329490303993225,
0.024123171344399452,
0.011970692314207554,
0.03491068258881569,
0.04491830989718437,
-0.04625445976853371,
-0.022109512239694595,
0.03872363641858101,
0.017044218257069588,
0.06151873245835304,
-0.06828340888023376,
0.05259095877408981,
0.013288481160998344,
-0.05627492815256119,
0.0019662624690681696,
-0.056600574404001236,
0.020896978676319122,
-0.04726351425051689,
-0.03489145264029503,
-0.003092519473284483,
-0.025423189625144005,
0.04354183375835419,
0.04054998233914375,
0.0009041741141118109,
0.0038694175891578197,
0.027211958542466164,
0.020699717104434967,
0.001985172973945737,
0.009985920041799545,
-0.0002838223008438945,
0.03192348778247833,
0.018194569274783134,
-0.005996404681354761,
0.03363148123025894,
-0.001190775539726019,
0.002542989095672965,
0.03430655226111412,
-0.02885078825056553,
-0.008733751252293587,
-0.012404248118400574,
0.0064763533882796764,
-0.0472608283162117,
-0.0247340127825737,
-0.014610310085117817,
-0.05921783670783043,
-0.0022214343771338463,
-0.01526270154863596,
-0.03248671442270279,
0.0733867660164833,
-0.026768408715724945,
0.03243104740977287,
-0.04106320068240166,
0.040654879063367844,
0.05031886696815491,
-0.059135839343070984,
0.03789346665143967,
-0.03695739433169365,
0.02862120047211647,
0.074141725897789,
0.03544318675994873,
0.03641042485833168,
-0.01457514800131321,
-0.030715148895978928,
0.008368358947336674,
0.01441147830337286,
0.021740566939115524,
0.007322913967072964,
-0.00030576749122701585,
0.057327888906002045,
0.013471664860844612,
0.004125779494643211,
-0.029319338500499725,
0.04029017686843872,
0.01099429652094841,
0.011605163104832172,
0.030846785753965378,
0.030711373314261436,
0.00038039960782043636,
-0.011157363653182983,
0.06033042073249817,
0.020965084433555603,
-0.005876172799617052,
-0.04186108335852623,
-0.03524363785982132,
0.09427469223737717,
0.011266264133155346,
0.005757023114711046,
-0.02322930470108986,
0.01269950158894062,
-0.042067550122737885,
-0.015258952043950558,
0.020464319735765457,
0.02551843225955963,
-0.005052725784480572,
0.061962395906448364,
0.01772875152528286,
0.052252884954214096,
-0.013393191620707512,
0.014153016731142998,
-0.012597868219017982,
-0.051191385835409164,
-0.07109808921813965,
0.02615382894873619,
-0.02228066325187683,
0.012173127382993698,
0.032742224633693695,
0.022838857024908066,
-0.07795138657093048,
-0.023549886420369148,
0.029699107632040977,
0.020481683313846588,
0.04154634475708008,
0.03803006187081337,
0.09727681428194046,
-0.07867757230997086,
-0.016374630853533745,
0.02584170363843441,
-0.036106642335653305,
0.06566627323627472,
0.0003022335877176374,
-0.047772329300642014,
0.00966573879122734,
-0.024738425388932228,
-0.029807645827531815,
-0.04328560084104538,
-0.005033155903220177,
0.022966081276535988,
0.014363198541104794,
-0.04170942306518555,
0.014744441024959087,
-0.018748879432678223,
0.017260054126381874,
0.0019773519597947598,
0.024965105578303337,
0.007443928625434637,
-0.016028407961130142,
-0.005149242002516985,
-0.002913807285949588,
-0.034141138195991516,
-0.00021394471696112305,
-0.013072931207716465,
-0.015114029869437218,
-0.008879674598574638,
-0.024006962776184082,
0.025669898837804794,
0.04216970503330231,
0.04165235534310341,
0.019597386941313744,
-0.04462791234254837,
-0.05612123757600784,
-0.005279309581965208,
-0.03186481446027756,
0.029898662120103836,
0.003375329077243805,
-0.031051749363541603,
0.022239068523049355,
0.0023071966134011745,
-0.10220546275377274,
-0.04743735119700432,
-0.033628419041633606,
0.040877584367990494,
-0.027005545794963837,
-0.005945579148828983,
0.008950503543019295,
-0.023199953138828278,
-0.03151195868849754,
-0.013599885627627373,
-0.029614271596074104,
0.00016215222422033548,
0.021058231592178345,
-0.02001437358558178,
0.05820190906524658,
0.018357476219534874,
-0.01796051673591137,
0.036197684705257416,
0.005231795832514763,
0.03142716735601425,
0.014569701626896858,
0.056473519653081894,
-0.05745812878012657,
-0.07141952216625214,
-0.02387644723057747,
0.04439589008688927,
-0.024865208193659782,
0.03531069681048393,
0.0069548580795526505,
0.030054571107029915,
-0.010267223231494427,
-0.03765548765659332,
-0.03332829847931862,
0.0014908767770975828,
-0.011030678637325764,
0.0709543526172638,
-0.02415200136601925,
-0.01539484690874815,
-0.008514420129358768,
0.0020229907240718603,
0.061695490032434464,
0.03304300829768181,
-0.00547915929928422,
-0.06614390760660172,
-0.029617048799991608,
-0.006287951022386551,
0.03901024907827377,
0.0020454053301364183,
0.001809702254831791,
0.03344303369522095,
-0.03140225633978844,
0.03562307730317116,
0.047409940510988235,
0.04582930728793144,
0.03136928379535675,
0.013645230792462826,
0.00042651747935451567,
0.01641385816037655,
-0.008469803258776665,
-0.001784730702638626,
-0.011449147947132587,
0.0012644050875678658,
-0.056881267577409744,
-0.02452383004128933,
-0.031680479645729065,
-0.031159158796072006,
0.05775417387485504,
0.08521904051303864,
0.007565152831375599,
-0.06361299008131027,
-0.019900064915418625,
0.015730561688542366,
0.030872078612446785,
-0.010057594627141953,
-0.062332749366760254,
-0.04166280850768089,
-0.059646349400281906,
0.012450598180294037,
0.0028783311136066914,
-0.025750797241926193,
0.0383446179330349,
0.0029852434527128935,
0.08603425323963165,
-0.015322577208280563,
-0.019990818575024605,
0.008831565268337727,
-0.012851858511567116,
-0.012846328318119049,
0.03852386772632599,
-0.06453705579042435,
-0.052678897976875305,
0.034961894154548645,
-0.01673118583858013,
-0.0038144004065543413,
0.0052563282661139965,
-0.043122291564941406,
-0.005170498974621296,
0.0027532221283763647,
-0.034075986593961716,
0.03988128900527954,
0.032809704542160034,
0.0332016758620739,
0.03020801953971386,
0.0022829400841146708,
0.030695214867591858,
0.05086306855082512,
0.02045610174536705,
-0.028536474332213402,
0.008075196295976639,
-0.04083314538002014,
-0.019377218559384346,
0.0017324084183201194,
-0.047402821481227875,
0.03439028561115265,
0.05024244263768196,
0.021213730797171593,
0.02623746730387211,
0.004987741820514202,
-0.03029758110642433,
-0.032115351408720016,
0.0033002968411892653,
0.020218249410390854,
0.012113207019865513,
0.036345284432172775,
-0.006165007129311562,
-0.023249002173542976,
-0.009679865092039108,
0.0055336058139801025,
-0.08631569147109985,
-0.0011203597532585263,
0.05171925202012062,
-0.007273738272488117,
0.014535829424858093,
-0.048963695764541626,
-0.05893750488758087,
-0.060787469148635864,
-0.01451581995934248,
0.040822651237249374,
-0.03486539423465729,
0.09297209233045578,
-0.004739819560199976,
-0.020382272079586983,
0.03204064443707466,
0.046093471348285675,
0.0020800656639039516,
-0.026561444625258446,
0.02319290116429329,
-0.05398648604750633,
-0.045353833585977554,
0.028007104992866516,
0.006616749335080385,
0.08251121640205383,
0.026842454448342323,
0.002180566545575857,
0.0015086457133293152,
-0.017660466954112053,
-0.0644277036190033,
-0.023121677339076996,
-0.06412514299154282,
0.010400273837149143,
0.022567788138985634,
0.05732446163892746,
-0.011165782809257507,
0.010806291364133358,
-0.04606224596500397,
-0.018822884187102318,
-0.004217497538775206,
0.017043419182300568,
0.015911078080534935,
-0.050820011645555496,
0.0015882893931120634,
-0.0015104736667126417,
0.020207086578011513,
-0.009655707515776157,
0.006084233056753874,
-0.0234118290245533,
-0.03161280229687691,
-0.025366298854351044,
-0.004594812169671059,
-0.06537550687789917,
-0.03099159523844719,
0.026956982910633087,
0.07235617935657501,
-0.04704901948571205,
-0.027981018647551537,
-0.018551453948020935,
0.0036775809712707996,
-0.0024172000121325254,
-0.08768542110919952,
0.04258589446544647,
-0.007293094415217638,
-0.06715592741966248,
0.005725995171815157,
0.0179170873016119,
0.014171980321407318,
0.0283648781478405,
0.05913425609469414,
-0.032127123326063156,
-0.007329938001930714,
0.045746494084596634,
-0.04336591064929962,
0.037475813180208206,
-0.009881570935249329,
0.007100408896803856,
-0.050280045717954636,
-0.010127357207238674,
-0.009771189652383327,
-0.00248966203071177,
0.037484969943761826,
0.00919823907315731,
-0.028200069442391396,
-0.010202313773334026,
-0.05990322679281235,
-0.03999754786491394,
-0.035716015845537186,
0.013634025119245052,
-0.0230978075414896,
-0.051740117371082306,
-0.018833724781870842,
-0.05091601610183716,
0.012822065502405167,
-0.004934533033519983,
0.008441212587058544,
0.05006549507379532,
-0.0009913548128679395,
0.023105110973119736,
0.04727637395262718,
-0.039417702704668045,
-0.029052477329969406,
-0.05988601595163345,
-0.011879589408636093,
0.051655303686857224,
0.026725200936198235,
0.04645797237753868,
0.033257901668548584,
-0.018214954063296318,
-0.031187012791633606,
0.00043074938002973795,
-0.047815512865781784,
0.0025563198141753674,
0.049858007580041885,
0.02641073800623417,
0.009792412631213665,
-0.040791094303131104,
0.08126740157604218,
-0.0017092340858653188,
-0.04361913353204727,
-0.06660902500152588,
0.06190228462219238,
0.026700541377067566,
0.007988868281245232,
0.09234823286533356,
-0.05141880363225937,
0.1043563187122345,
-0.013895362615585327,
-0.011997013352811337,
-0.026485223323106766,
-0.011324488557875156,
0.00906112976372242,
-0.00465650949627161,
-0.03139864280819893,
-0.01978984661400318,
-0.020247379317879677,
-0.0218094140291214,
0.014220545068383217
] |
<p>According to classical electromagnetic theory, accelerated charges should emit radiation and lose energy. The reason given in my book why atoms don't emit radiation (say, when the atom moves along a circle) is because the atom is neutral. I can understand how this works for a neutral particle like a neutron but the atom has constituent charges within in. How can the "presence" of an opposite charge nearby stop what seems to be an intrinsic process independent of the surroundings? Do the electrons and protons emit radiation that destructively interferes or something of that sort?</p> | g4788 | [
0.024498388171195984,
0.02752572111785412,
0.011496040038764477,
0.01182573288679123,
0.058717310428619385,
0.07181323319673538,
-0.007585564162582159,
0.07290817052125931,
-0.03979494422674179,
-0.029872382059693336,
0.037023793905973434,
0.07172573357820511,
0.004655082244426012,
-0.0032513963524252176,
-0.03792582452297211,
0.010424772277474403,
0.03711630403995514,
0.00011434312182245776,
0.032670311629772186,
0.07608968019485474,
0.0060016680508852005,
0.0013551792362704873,
-0.003070851555094123,
-0.05527559667825699,
-0.04851790517568588,
0.038954511284828186,
0.01574709266424179,
-0.04552500322461128,
-0.0010967307025566697,
-0.05307920277118683,
0.05878069996833801,
-0.03184176981449127,
0.043528102338314056,
-0.02786090411245823,
0.013829649426043034,
-0.08190328627824783,
0.03174864500761032,
0.022788865491747856,
-0.0354391448199749,
0.017688460648059845,
-0.0007799226441420615,
-0.01599792204797268,
0.016809193417429924,
-0.01469875406473875,
0.03433723375201225,
0.015388144180178642,
0.024981316179037094,
-0.0024794552009552717,
-0.0021052758675068617,
-0.03819546103477478,
-0.03995861858129501,
-0.00877511315047741,
0.0007588961161673069,
-0.0047939918003976345,
0.013087530620396137,
0.01548686157912016,
-0.07813121378421783,
-0.036576442420482635,
0.06261994689702988,
-0.011761464178562164,
0.003086330136284232,
0.03689952567219734,
0.02822992578148842,
0.007061421405524015,
0.036806005984544754,
-0.03248986974358559,
-0.06370014697313309,
-0.032693132758140564,
0.021640297025442123,
0.035694271326065063,
0.05168483778834343,
-0.04142593964934349,
-0.07109736651182175,
-0.0037515293806791306,
0.05360664799809456,
0.004687006585299969,
0.05102100595831871,
-0.019703226163983345,
0.012130350805819035,
0.03774221986532211,
-0.058743804693222046,
-0.034963615238666534,
0.020935002714395523,
0.0036925978492945433,
0.06938140839338303,
-0.010777180083096027,
-0.006545789539813995,
-0.060475245118141174,
0.004185558296740055,
-0.00765131926164031,
-0.0022618738003075123,
-0.009537460282444954,
0.058418672531843185,
-0.019136758521199226,
-0.01609344407916069,
-0.016066202893853188,
-0.022541038691997528,
0.08536068350076675,
-0.014643538743257523,
-0.04250685125589371,
-0.025761447846889496,
-0.04557120054960251,
0.0372149683535099,
0.030399993062019348,
0.04677262529730797,
-0.04357681795954704,
0.01939929835498333,
-0.014499359764158726,
0.0562225766479969,
0.02183365821838379,
0.00505469786003232,
-0.055859487503767014,
-0.021867187693715096,
-0.05916902422904968,
0.008577057160437107,
0.005179083906114101,
0.06815853714942932,
-0.027253219857811928,
0.02846202254295349,
0.0891365110874176,
0.03314865007996559,
0.0920342430472374,
-0.009630550630390644,
-0.019616523757576942,
-0.034047290682792664,
-0.0040914262644946575,
0.012109420262277126,
-0.03570476919412613,
-0.004836798645555973,
0.01639256440103054,
0.0349542573094368,
0.039478134363889694,
-0.014785376377403736,
0.0361444316804409,
-0.0028970143757760525,
0.024460185319185257,
0.020347414538264275,
0.01354511920362711,
0.021654849871993065,
-0.09811560064554214,
0.031823668628931046,
0.017573658376932144,
0.016704337671399117,
-0.034309882670640945,
-0.05272844806313515,
0.02176840417087078,
-0.04346613585948944,
0.0071970801800489426,
-0.0061004627496004105,
0.005650591105222702,
0.038403335958719254,
0.0810994952917099,
0.031316496431827545,
-0.037449248135089874,
0.04288824647665024,
-0.009191522374749184,
0.03705335408449173,
0.0005120323621667922,
-0.04643093794584274,
0.05331578850746155,
0.061316415667533875,
0.029254036024212837,
-0.023675035685300827,
0.03683698549866676,
-0.05511685088276863,
-0.022344645112752914,
0.014775188639760017,
-0.05287843942642212,
0.04557397589087486,
0.0016415214631706476,
-0.0027967127971351147,
0.011029197834432125,
0.0007571937167085707,
0.02852516993880272,
-0.03617709130048752,
0.03911140188574791,
-0.019169222563505173,
-0.013166068121790886,
0.008115378208458424,
-0.04092796519398689,
-0.05386001616716385,
-0.00969825778156519,
0.03713338077068329,
-0.02600209228694439,
0.007499707862734795,
0.0314381942152977,
-0.06972059607505798,
0.04200074449181557,
-0.036886829882860184,
0.004665000829845667,
0.027991805225610733,
-0.06689702719449997,
0.02384789288043976,
0.02865538001060486,
-0.018095336854457855,
-0.09048426896333694,
-0.044420745223760605,
-0.006155228707939386,
0.055506568402051926,
-0.008364524692296982,
0.012800764292478561,
0.056637752801179886,
-0.03661125898361206,
0.005526626482605934,
0.06075039133429527,
-0.027645515277981758,
-0.015642791986465454,
-0.047727879136800766,
0.06475353240966797,
0.005594632588326931,
0.029351599514484406,
0.023874443024396896,
-0.01137258019298315,
0.0256920475512743,
-0.007799268234521151,
-0.02008407562971115,
-0.04944682866334915,
0.008116098120808601,
-0.010285701602697372,
0.01750153861939907,
-0.053096264600753784,
-0.028916332870721817,
0.02539965696632862,
-0.04933841526508331,
-0.03255338966846466,
-0.006071709096431732,
-0.07093935459852219,
-0.029321903362870216,
-0.02767583541572094,
0.0021757197100669146,
-0.08922768384218216,
0.026168227195739746,
0.023800496011972427,
-0.01997843012213707,
0.06200534850358963,
0.019413815811276436,
-0.015526368282735348,
0.029436025768518448,
0.05100806802511215,
-0.08536548912525177,
-0.047323741018772125,
0.005902578122913837,
-0.00010565331467660144,
-0.007248051930218935,
0.006395561154931784,
-0.0858282819390297,
0.06030791625380516,
-0.011756052263081074,
-0.019711341708898544,
-0.04051194712519646,
0.0641288086771965,
-0.00004365861968835816,
0.006031835917383432,
0.04471250995993614,
0.014195436611771584,
-0.023623574525117874,
-0.05840913951396942,
0.03657722473144531,
-0.05454082787036896,
-0.04004736617207527,
-0.020787792280316353,
-0.02271275967359543,
0.03907100111246109,
0.024907520040869713,
-0.057972997426986694,
0.013848119415342808,
0.002823357004672289,
0.045429378747940063,
0.002359522506594658,
-0.0022565878462046385,
-0.08243415504693985,
0.12194357067346573,
-0.021254239603877068,
0.04548213630914688,
0.01984517276287079,
0.04536391422152519,
0.02327151596546173,
-0.00975498091429472,
0.020365042611956596,
-0.01736128143966198,
-0.05376299098134041,
0.016787614673376083,
-0.011733037419617176,
-0.036861762404441833,
-0.001592282671481371,
-0.038781918585300446,
0.016714468598365784,
0.007190536707639694,
0.004107106942683458,
-0.0702994242310524,
-0.05510692298412323,
0.013701455667614937,
0.08305367082357407,
0.02885173074901104,
0.01969997212290764,
-0.0037745782174170017,
0.03786993399262428,
-0.00808517076075077,
-0.06061640754342079,
0.04283345490694046,
-0.02066880278289318,
0.008550715632736683,
-0.013217787258327007,
0.038150738924741745,
0.003651099745184183,
0.0387360118329525,
-0.07748793810606003,
-0.041058171540498734,
-0.016877779737114906,
0.037203349173069,
-0.04771075025200844,
0.009343746118247509,
-0.0492340549826622,
0.04230180010199547,
0.023375995457172394,
-0.02133871242403984,
-0.026850907132029533,
0.019169822335243225,
0.04477190971374512,
0.011242681182920933,
-0.04584544897079468,
0.0005383586976677179,
0.014214451424777508,
0.017189081758260727,
0.007746375631541014,
0.048030268400907516,
-0.012841767631471157,
-0.02634461410343647,
0.018911663442850113,
-0.010803035460412502,
0.021868295967578888,
0.011256917379796505,
-0.022801492363214493,
0.00008759713819017634,
-0.03533779829740524,
-0.060746025294065475,
0.02285926043987274,
0.061769749969244,
-0.012108494527637959,
0.0640602558851242,
0.10089793056249619,
-0.006229223683476448,
-0.03889157250523567,
-0.014961479231715202,
0.02481244131922722,
-0.018835797905921936,
-0.03404342383146286,
-0.05892796814441681,
-0.021110747009515762,
-0.00450204499065876,
0.07708380371332169,
-0.013511826284229755,
0.022194333374500275,
-0.020306328311562538,
-0.06656192243099213,
0.0031894363928586245,
-0.004476540256291628,
0.028313808143138885,
0.015115143731236458,
-0.02371322363615036,
-0.007966474629938602,
-0.008925441652536392,
0.02634562738239765,
-0.002860844135284424,
-0.052757732570171356,
0.009944738820195198,
-0.019626067951321602,
0.019080014899373055,
0.011255520395934582,
-0.03275369107723236,
0.02438236027956009,
-0.010332022793591022,
0.013861642219126225,
-0.04416103661060333,
0.010333591140806675,
-0.023906368762254715,
0.023458659648895264,
0.08908036351203918,
-0.05373544991016388,
0.0381147675216198,
0.0006435289978981018,
0.022766612470149994,
-0.032659221440553665,
0.004708497319370508,
0.018013427034020424,
0.009040544740855694,
-0.034022435545921326,
-0.00744711235165596,
-0.012418635189533234,
-0.0012878188863396645,
0.010031201876699924,
-0.043464262038469315,
-0.009387883357703686,
-0.008125056512653828,
0.013811321929097176,
-0.01106654480099678,
0.010665208101272583,
-0.037678200751543045,
0.07670214027166367,
0.013183292001485825,
0.0232116486877203,
0.06551824510097504,
-0.03858835622668266,
-0.02163171023130417,
0.03090166114270687,
0.018275484442710876,
0.029193365946412086,
0.0012535949936136603,
-0.025059528648853302,
0.00774744525551796,
-0.000003592300572563545,
0.016053112223744392,
-0.024784037843346596,
-0.03481036424636841,
-0.004384553525596857,
-0.026382481679320335,
0.013618106953799725,
-0.021754641085863113,
-0.02326117642223835,
-0.005861564073711634,
0.01716257818043232,
0.06284761428833008,
0.00015839116531424224,
-0.014842999167740345,
-0.011202259920537472,
0.1284087598323822,
0.03751751407980919,
0.00047473417362198234,
-0.013373112305998802,
0.01761726848781109,
-0.044726137071847916,
0.05061095207929611,
-0.011949185281991959,
-0.009948131628334522,
-0.010495380498468876,
0.00421615457162261,
-0.05575263872742653,
0.08111647516489029,
0.023211918771266937,
0.04056280478835106,
0.07190310955047607,
0.041732024401426315,
0.05452937260270119,
0.01583336852490902,
-0.006255538202822208,
0.09515892714262009,
-0.028787970542907715,
-0.01654529571533203,
0.02024846524000168,
-0.02546839229762554,
-0.04422187805175781,
0.005645983852446079,
-0.06923498213291168,
-0.02669023722410202,
-0.008118662983179092,
0.022895678877830505,
-0.07422894239425659,
-0.0029520713724195957,
0.0006117137963883579,
0.04665980115532875,
-0.05837481468915939,
0.00849220808595419,
0.03502499312162399,
-0.0015081196324899793,
-0.0021180978510528803,
0.015947286039590836,
-0.06744129210710526,
-0.006520203780382872,
-0.055148277431726456,
-0.01974678784608841,
0.0061726439744234085,
0.022957004606723785,
0.004905757028609514,
-0.03944925218820572,
0.02165544405579567,
-0.014433251693844795,
-0.023222677409648895,
-0.007814065553247929,
-0.012204330414533615,
0.007014283444732428,
-0.01962587982416153,
-0.046947747468948364,
-0.033598460257053375,
0.02287946827709675,
-0.015174095518887043,
-0.01816694438457489,
-0.018499815836548805,
0.06876096874475479,
0.0074111963622272015,
-0.05399738997220993,
-0.03023000992834568,
-0.004713278263807297,
-0.004523185081779957,
-0.019569186493754387,
0.036339983344078064,
0.04761398211121559,
0.022942278534173965,
0.056474123150110245,
-0.021055053919553757,
0.03219083324074745,
-0.010636289604008198,
-0.06912453472614288,
-0.06657155603170395,
-0.027315152809023857,
0.022221526131033897,
0.025146586820483208,
0.09297922998666763,
-0.02359556220471859,
-0.018885038793087006,
0.008104337379336357,
-0.048620495945215225,
0.03323514387011528,
0.04183255136013031,
0.03263689950108528,
-0.014820544980466366,
0.04787556827068329,
-0.0786772146821022,
-0.03297051042318344,
-0.06680069863796234,
-0.0020020888186991215,
-0.010548781603574753,
0.01840909942984581,
0.006964363623410463,
-0.023300688713788986,
0.09267667680978775,
0.011684603989124298,
0.015441368333995342,
0.024862850084900856,
0.012132391333580017,
0.05171852931380272,
-0.024872342124581337,
-0.0043312860652804375,
-0.062431447207927704,
0.021897755563259125,
-0.013508334755897522,
-0.01948985457420349,
0.020085422322154045,
-0.006954397074878216,
0.007471879944205284,
0.002306993119418621,
-0.03901020810008049,
-0.028425434604287148,
0.00012617780885193497,
0.035652045160532,
-0.015295062214136124,
0.02113315649330616,
-0.03346327692270279,
0.019116908311843872,
0.026792259886860847,
-0.06279914081096649,
-0.028829069808125496,
0.024397587403655052,
0.045370616018772125,
-0.010415456257760525,
0.02006419003009796,
0.017247702926397324,
0.04221908375620842,
-0.014324290677905083,
-0.046036332845687866,
-0.06946488469839096,
0.017412476241588593,
0.009658928960561752,
0.018858758732676506,
0.050051331520080566,
0.09578567743301392,
-0.03146113082766533,
0.026093611493706703,
-0.036501090973615646,
-0.00045538111589848995,
0.006669267546385527,
0.04165836423635483,
0.009096469730138779,
0.02969028241932392,
-0.035904642194509506,
0.02490546926856041,
0.0044056023471057415,
-0.01783807948231697,
-0.0022755784448236227,
-0.026229318231344223,
0.004745573736727238,
0.04658350348472595,
0.04077686741948128,
0.01965627819299698,
-0.09432043880224228,
0.02057545632123947,
0.0009499773732386529,
-0.02655918337404728,
0.013498883694410324,
0.08897651731967926,
0.008332389406859875,
-0.01210089586675167,
-0.045563362538814545,
-0.0007530187722295523,
-0.015947170555591583,
-0.014655966311693192,
-0.05116606876254082,
-0.01660921797156334,
-0.028103262186050415,
-0.02096470817923546,
-0.01221513468772173,
0.0081681152805686,
-0.022392457351088524,
0.003839869285002351,
-0.019317088648676872,
0.0881352499127388,
-0.009981225244700909,
0.006575810257345438,
-0.03316209837794304,
-0.01061144657433033,
0.019351914525032043,
-0.04612915962934494,
0.0008730828994885087,
-0.007335449103266001,
-0.02700737677514553,
-0.025943592190742493,
-0.024523213505744934,
-0.023122623562812805,
-0.03392890840768814,
-0.01872345618903637,
-0.004644201137125492,
0.004932325799018145,
0.009837653487920761,
-0.013154926709830761,
0.0577874630689621,
0.034683238714933395,
0.02284633368253708,
-0.04232621192932129,
0.07287902384996414,
0.038164906203746796,
0.016002530232071877,
-0.06088177487254143,
0.006141087971627712,
0.006624538451433182,
0.025614583864808083,
-0.00323731848038733,
-0.0022997998166829348,
0.0384279303252697,
0.00907733105123043,
0.0025335003156214952,
-0.005772748030722141,
-0.019587978720664978,
0.00111912633292377,
0.029298339039087296,
0.02120457962155342,
-0.1075882688164711,
0.01977797970175743,
0.01977371796965599,
-0.05643048882484436,
-0.020693322643637657,
0.008812295272946358,
-0.004298364743590355,
-0.05102486535906792,
0.04421509802341461,
0.02191527746617794,
0.03989577293395996,
0.022223349660634995,
-0.0028178116772323847,
0.006760488264262676,
0.01676955446600914,
-0.05705687776207924,
0.008333323523402214,
-0.04219455644488335,
0.035621918737888336,
0.029753901064395905,
0.03851332142949104,
-0.01818450540304184,
0.00628632353618741,
-0.0424286313354969,
-0.017485128715634346,
0.015492564998567104,
-0.04863794893026352,
-0.05087994784116745,
-0.03778143227100372,
-0.0038344652857631445,
0.04241156950592995,
0.01634751819074154,
-0.013212486170232296,
0.027930734679102898,
0.016397131606936455,
-0.031093139201402664,
-0.04313415288925171,
0.05380011349916458,
0.01622547022998333,
0.020926155149936676,
0.018841682001948357,
0.020800327882170677,
-0.04880029708147049,
0.026888716965913773,
-0.02485627681016922,
-0.010445467196404934,
-0.007987658493220806,
-0.031770382076501846,
0.02993708662688732,
-0.006535585969686508,
0.054627664387226105,
0.01894030161201954,
-0.004445340018719435,
0.018213726580142975,
-0.01744762621819973,
-0.03547794744372368,
0.027858980000019073,
-0.02157113514840603,
0.05737612023949623,
-0.008932054974138737,
0.02092001773416996,
0.002121215919032693,
-0.007572815753519535,
0.014547898434102535,
-0.028234681114554405,
-0.011769261211156845,
-0.0007507471018470824,
0.02000034600496292,
0.03379170969128609,
0.008435452356934547,
0.013991955667734146,
0.027411876246333122,
-0.005650883540511131,
0.04419874772429466,
0.007659484166651964,
-0.016134804114699364,
-0.041164565831422806,
0.016327593475580215,
-0.021106507629156113,
0.013342087157070637,
0.0036536557599902153,
-0.04666531831026077,
0.002261715242639184,
0.0016553228488191962,
0.06332283467054367,
0.006585454102605581,
-0.024813629686832428,
0.04703181982040405,
-0.0008527846075594425,
0.0031520023476332426,
-0.05137825757265091,
-0.036561522632837296,
0.030316460877656937,
-0.03233213350176811,
0.013917360454797745,
0.0025963669177144766,
0.026892149820923805,
-0.02224077470600605,
-0.03077109158039093,
-0.041896332055330276,
-0.08544671535491943,
-0.07208286225795746,
-0.0097566032782197,
0.04525995999574661,
0.0289958193898201,
0.047962892800569534,
-0.0257285013794899,
-0.028567271307110786,
-0.04059091955423355,
0.017440620809793472,
0.10501133650541306,
-0.02023596689105034,
-0.016408970579504967,
0.019145021215081215,
-0.013122113421559334,
-0.014607623219490051,
-0.0255560502409935,
0.001156244776211679,
-0.007837501354515553,
-0.06760770082473755,
-0.006227449513971806,
-0.06465926766395569,
-0.0412580668926239,
-0.034668296575546265
] |
<p>I have read that adiabatic process is isentropic because there is no heat exchange in an adiabatic process and thus no change in entropy.</p>
<p>But my question is - Even in adiabatic process, work can be done. Let's take an example of an adiabatic vessel with a piston attached. That vessel does not exchange heat but work can be done by pulling in or out the piston. </p>
<p>If the volume of the system changes, isn't entropy also changed, even in a reversible adiabatic process? </p>
<p>EDIT : I know that change in entropy is defined as change in heat divided by temperature. Since there is no change in heat in an adiabatic process, the entropy is zero. My question is different - What I see entropy as - It is a measure of the different microstates in which a system can be. So, even if there is no change in heat energy, can't number of thermally achievable microstates increase if we increase the volume by doing work? Why is only heat considered as a measure of entropy?</p> | g4789 | [
-0.0030476395040750504,
-0.028603097423911095,
0.01126378495246172,
-0.009966066107153893,
-0.0024832142516970634,
-0.03032085858285427,
0.007376788184046745,
0.026956629008054733,
-0.031767960637807846,
0.005764776840806007,
0.017898892983794212,
0.0567895732820034,
0.033499859273433685,
-0.0338544026017189,
0.0011371519649401307,
-0.008796739391982555,
0.0368163175880909,
0.004372109193354845,
-0.005150831304490566,
0.05766644328832626,
0.019201893359422684,
-0.012046909891068935,
0.016054697334766388,
-0.03777362033724785,
0.047362834215164185,
-0.06636501848697662,
0.01073150709271431,
-0.009709895588457584,
0.011050719767808914,
0.02622387930750847,
0.023174110800027847,
-0.0108786104246974,
0.02532321773469448,
0.01343496236950159,
-0.02079668641090393,
-0.031137127429246902,
0.05542835220694542,
0.030827637761831284,
0.05599098652601242,
-0.024071352556347847,
-0.017678294330835342,
-0.007830754853785038,
0.025392647832632065,
0.0025522280484437943,
0.016330871731042862,
0.030158136039972305,
-0.005624626763164997,
-0.00023285039060283452,
-0.002527120290324092,
0.042449720203876495,
0.024990204721689224,
-0.0038856181781738997,
0.01703495718538761,
0.013970769010484219,
0.005889024119824171,
0.032444827258586884,
-0.028281135484576225,
-0.014468638226389885,
0.051161665469408035,
0.015691235661506653,
0.03946981579065323,
-0.0002403574762865901,
0.04974878579378128,
0.024035131558775902,
0.008480789139866829,
-0.004212981555610895,
0.014110260643064976,
-0.028426237404346466,
-0.005257518962025642,
-0.0027591234538704157,
-0.03349565714597702,
-0.033304303884506226,
-0.0033912567887455225,
0.0011651443783193827,
0.03418610617518425,
-0.013948556035757065,
0.049140870571136475,
-0.05336027592420578,
0.003868474392220378,
-0.016605088487267494,
-0.036594733595848083,
-0.07661723345518112,
0.0364748015999794,
-0.032909709960222244,
0.06977896392345428,
0.02339494228363037,
0.06236705929040909,
-0.026554180309176445,
-0.029495680704712868,
0.07140172272920609,
0.009743640199303627,
-0.029084501788020134,
0.07301770150661469,
0.05238182097673416,
-0.044318944215774536,
0.04633833467960358,
-0.02871888130903244,
-0.012094364501535892,
-0.028320197016000748,
0.0001740005100145936,
-0.05119882896542549,
-0.05225006863474846,
-0.011497288011014462,
0.009528121910989285,
0.004949723836034536,
-0.027536263689398766,
0.008618490770459175,
-0.04699636250734329,
-0.036253999918699265,
0.04118644818663597,
0.009163935668766499,
-0.03943033888936043,
-0.0693439319729805,
-0.00841471366584301,
-0.00009058004798134789,
-0.00156788167078048,
0.04117467999458313,
0.016591276973485947,
-0.02231316640973091,
0.021992376074194908,
0.06898051500320435,
0.04666002839803696,
0.012193826027214527,
0.011225055903196335,
0.0007754451362416148,
0.059275973588228226,
-0.0030129363294690847,
-0.018330348655581474,
0.00155309634283185,
0.007697003427892923,
0.01935771107673645,
0.020001795142889023,
-0.020218826830387115,
-0.02427525259554386,
0.00478404201567173,
0.012033289298415184,
-0.004862275905907154,
-0.024628518149256706,
0.038757871836423874,
0.005659368354827166,
0.012138730846345425,
-0.013812110759317875,
-0.006887088529765606,
0.00818540807813406,
-0.031215127557516098,
-0.0342516265809536,
-0.03697758913040161,
-0.021881885826587677,
0.056690435856580734,
-0.02412986569106579,
0.03140607848763466,
0.04359956085681915,
0.03952443599700928,
-0.048219937831163406,
-0.0016276746755465865,
0.014016498811542988,
0.008583621121942997,
0.006982466205954552,
0.05821330472826958,
-0.004136407282203436,
0.08087117224931717,
-0.013542610220611095,
0.05043572559952736,
-0.026845330372452736,
-0.043516844511032104,
0.0473204180598259,
-0.06285470724105835,
-0.011877330020070076,
0.04203407093882561,
-0.040212176740169525,
-0.06697191298007965,
-0.035047031939029694,
-0.07475180178880692,
0.052842073142528534,
0.006631800904870033,
0.004475802183151245,
-0.012180645950138569,
0.08213575929403305,
0.008481338620185852,
-0.05200516805052757,
-0.02693307027220726,
0.024992527440190315,
0.05477195978164673,
-0.08435530215501785,
0.004420432727783918,
0.058646123856306076,
0.0010469516273587942,
0.04009699076414108,
-0.046950072050094604,
-0.009034796617925167,
0.007045128848403692,
0.024718644097447395,
0.02552022598683834,
0.02653668075799942,
0.009186094626784325,
-0.03608449921011925,
0.001428023213520646,
-0.05224606394767761,
-0.02639612928032875,
-0.012009583413600922,
0.020051205530762672,
0.020733799785375595,
0.014001608826220036,
0.0239732563495636,
0.012480674311518669,
0.021138282492756844,
-0.045397527515888214,
0.0325915552675724,
-0.010734645649790764,
-0.015488063916563988,
0.07078913599252701,
-0.0042079719714820385,
-0.029946302995085716,
-0.020510349422693253,
-0.024552486836910248,
-0.006432786583900452,
-0.004990541376173496,
-0.009496747516095638,
0.017718642950057983,
-0.03403540328145027,
-0.01168085541576147,
-0.010641849599778652,
0.01794395036995411,
0.04557750001549721,
-0.028631621971726418,
0.0029376461170613766,
-0.05418156832456589,
0.022991489619016647,
0.018550418317317963,
0.043931152671575546,
-0.08204531669616699,
0.05695924907922745,
0.01843026466667652,
-0.04535558447241783,
-0.02587217278778553,
0.020023372024297714,
0.03267819434404373,
0.07423712313175201,
0.019658207893371582,
0.013566394336521626,
0.020232493057847023,
-0.06789018213748932,
-0.043594490736722946,
0.009500473737716675,
0.023803070187568665,
0.0004370843817014247,
-0.02043643221259117,
0.010311044752597809,
0.03683124855160713,
-0.017519095912575722,
0.02836407721042633,
-0.008387667126953602,
-0.011659652926027775,
-0.005831477232277393,
-0.009624376893043518,
-0.01562035083770752,
0.019228415563702583,
-0.004236326552927494,
-0.017223728820681572,
-0.03132607787847519,
0.02340489625930786,
0.010322934947907925,
0.020014945417642593,
0.012751677073538303,
0.016259459778666496,
0.021268421784043312,
-0.044163189828395844,
-0.024820270016789436,
-0.014317875728011131,
0.008580251596868038,
0.018520552664995193,
0.033505335450172424,
-0.05085039883852005,
0.05980439856648445,
0.03833971545100212,
-0.04613983631134033,
0.030999964103102684,
-0.039417024701833725,
0.0203300379216671,
-0.021025098860263824,
-0.009423972107470036,
-0.03430269658565521,
-0.027487846091389656,
0.024040693417191505,
0.032676082104444504,
-0.014646475203335285,
-0.029908398166298866,
-0.003616983536630869,
-0.002805555472150445,
-0.0637655258178711,
0.019623909145593643,
-0.024506796151399612,
0.02310810051858425,
0.002241067821159959,
-0.022442519664764404,
0.0052530099637806416,
0.001230162917636335,
-0.06741383671760559,
0.007836190983653069,
0.029979946091771126,
-0.02336505986750126,
-0.022914452478289604,
-0.02466500550508499,
-0.03421337530016899,
0.0728684514760971,
0.07394394278526306,
-0.08601755648851395,
-0.039835087954998016,
-0.024539457634091377,
0.01853417418897152,
-0.030345957726240158,
0.007037051022052765,
-0.03248196467757225,
-0.027292128652334213,
-0.059435516595840454,
0.010756008327007294,
0.013010386377573013,
-0.07986905425786972,
0.04602691903710365,
0.013810687698423862,
0.01859252341091633,
-0.016961276531219482,
0.022972339764237404,
0.008862165734171867,
0.03374990075826645,
0.008916482329368591,
-0.04018932953476906,
-0.04301626235246658,
-0.12266688048839569,
0.005621931049972773,
-0.019777348265051842,
-0.021687861531972885,
-0.035479262471199036,
-0.019432097673416138,
-0.05478391796350479,
-0.04593820497393608,
-0.050067055970430374,
-0.007910452783107758,
0.05559410899877548,
0.051526814699172974,
-0.01288785133510828,
0.035994432866573334,
0.02137564681470394,
0.005350381135940552,
-0.008568815886974335,
0.02294558472931385,
-0.018157154321670532,
-0.025908110663294792,
0.012925438582897186,
0.02394280582666397,
0.1167043074965477,
-0.03216354548931122,
0.03333526849746704,
0.00312615605071187,
-0.014002257958054543,
0.053747620433568954,
0.03475945442914963,
0.004839814268052578,
-0.02330813556909561,
-0.03222360834479332,
-0.03601076453924179,
-0.052517347037792206,
0.037176065146923065,
-0.01612594909965992,
0.002036512829363346,
0.02353491447865963,
0.003248967695981264,
-0.0017348836408928037,
0.029095282778143883,
-0.00976580660790205,
-0.003458247985690832,
-0.09586659073829651,
-0.03672875091433525,
0.004179573152214289,
0.08460506796836853,
0.011546645313501358,
0.04411517456173897,
0.03706882894039154,
-0.029422514140605927,
-0.01278728898614645,
0.07043466717004776,
-0.005681983195245266,
-0.004626161884516478,
-0.07640751451253891,
0.007282080128788948,
0.02552015334367752,
-0.04723028838634491,
0.022975584492087364,
-0.04295097663998604,
-0.03210560232400894,
0.00943908654153347,
-0.005235652904957533,
-0.009327067993581295,
-0.020205283537507057,
-0.025186123326420784,
0.03059520572423935,
0.03802664950489998,
-0.03163474053144455,
0.007837376557290554,
0.02422691322863102,
-0.014167004264891148,
0.011921665631234646,
-0.06213310360908508,
0.006967632565647364,
0.03347329795360565,
-0.025229794904589653,
0.03797632455825806,
-0.00043964284122921526,
-0.02392362244427204,
-0.03431985154747963,
0.036082684993743896,
-0.009418674744665623,
-0.030217453837394714,
-0.04021688178181648,
-0.03805563598871231,
-0.018984276801347733,
-0.03460226207971573,
-0.07753321528434753,
0.04076904430985451,
0.06725223362445831,
0.003202355932444334,
0.03295859694480896,
-0.01198068168014288,
0.0935010313987732,
0.006516031455248594,
0.08659699559211731,
0.035441845655441284,
-0.01638875901699066,
-0.021117284893989563,
-0.030098211020231247,
0.02577449008822441,
0.006631733383983374,
-0.02019689232110977,
0.018372833728790283,
0.023903852328658104,
0.046798884868621826,
-0.043412528932094574,
-0.003778697457164526,
0.0021820268593728542,
-0.0019660834223031998,
0.03237255662679672,
0.060096580535173416,
-0.0305649247020483,
0.023039530962705612,
-0.030363310128450394,
0.0164842139929533,
-0.007601025048643351,
-0.05370210483670235,
-0.022443443536758423,
-0.050670672208070755,
-0.059616442769765854,
0.01649339497089386,
-0.03322022035717964,
-0.024891667068004608,
0.01707957126200199,
0.029764534905552864,
-0.023106718435883522,
0.01678020879626274,
-0.0433647446334362,
0.0561334453523159,
-0.013146786019206047,
-0.06543517112731934,
0.04261952266097069,
0.038888830691576004,
-0.0196747537702322,
-0.015578106977045536,
-0.011951221153140068,
0.029502563178539276,
-0.07755141705274582,
-0.010214012116193771,
0.06942112743854523,
0.036944933235645294,
-0.01657431200146675,
0.06487701833248138,
-0.027074523270130157,
0.030073758214712143,
0.01536443829536438,
-0.03310249745845795,
0.014944922178983688,
0.006661024875938892,
0.01900610141456127,
0.015336521901190281,
0.03949357941746712,
0.04345805197954178,
0.0535612590610981,
0.006577888038009405,
-0.04395357519388199,
0.024174926802515984,
-0.014605267904698849,
-0.00588616356253624,
0.02742571011185646,
0.08252930641174316,
0.04099879041314125,
-0.0359063558280468,
-0.011100027710199356,
0.02140633948147297,
-0.013799645937979221,
-0.013790950179100037,
-0.028369780629873276,
-0.0033351026941090822,
-0.033758968114852905,
-0.017976712435483932,
-0.02229182980954647,
-0.0007028217078186572,
-0.03946368396282196,
-0.023707758635282516,
-0.0044529857113957405,
-0.03783329948782921,
-0.031002584844827652,
0.013331063091754913,
-0.020049190148711205,
0.013823670335114002,
-0.030367353931069374,
0.04475734755396843,
0.05005607381463051,
-0.05096300318837166,
-0.004384969361126423,
-0.07406911253929138,
0.033054083585739136,
-0.007959364913403988,
0.0031614615581929684,
-0.013264184817671776,
0.048413731157779694,
0.026514548808336258,
-0.024461744353175163,
0.018303019925951958,
-0.022292539477348328,
0.025338442996144295,
0.008129796013236046,
0.0909074991941452,
0.020119694992899895,
0.057149820029735565,
0.00628040311858058,
0.01921599544584751,
-0.03901151195168495,
-0.00770416809245944,
-0.025769734755158424,
0.06271445006132126,
0.07484935969114304,
0.04933323711156845,
0.05040585622191429,
-0.08377672731876373,
-0.021445469930768013,
0.0017222375608980656,
-0.04255009442567825,
-0.026963941752910614,
-0.037674736231565475,
-0.05336979776620865,
-0.009376910515129566,
-0.028273185715079308,
-0.02426222711801529,
0.04806969687342644,
0.00678948312997818,
-0.0479724183678627,
-0.022257285192608833,
0.01745058223605156,
-0.009615421295166016,
0.02851974219083786,
0.030729573220014572,
-0.05180276930332184,
0.049194011837244034,
0.06641614437103271,
-0.00193495221901685,
-0.0018213650910183787,
0.012177962809801102,
-0.09295674413442612,
0.0069873700849711895,
0.010647076182067394,
0.009671919047832489,
0.06536547094583511,
0.021733107045292854,
0.038258448243141174,
-0.00030662360950373113,
0.010294740088284016,
0.05973975360393524,
-0.006013070233166218,
-0.10172528773546219,
-0.002684013219550252,
-0.04013087972998619,
0.0013498995685949922,
-0.0959615632891655,
0.010931548662483692,
-0.023545730859041214,
0.0007054508896544576,
-0.030590908601880074,
0.023653151467442513,
-0.01137235015630722,
0.028854262083768845,
-0.001042687683366239,
0.0587000697851181,
-0.052964918315410614,
-0.03804946318268776,
-0.059508316218853,
0.043936945497989655,
-0.05166034400463104,
-0.00010253420623484999,
-0.06453357636928558,
0.015823544934391975,
0.03982236608862877,
0.0500020906329155,
-0.04802432283759117,
0.01218203455209732,
-0.0025151290465146303,
-0.06580932438373566,
-0.07119499146938324,
0.03880440816283226,
-0.031200960278511047,
0.05052277073264122,
0.01673542521893978,
-0.013682116754353046,
-0.05018679425120354,
0.04655828699469566,
0.0588439516723156,
-0.01764754205942154,
0.002920630155131221,
-0.05848776921629906,
-0.011981908231973648,
-0.007800478953868151,
0.004971510265022516,
-0.0006930372328497469,
0.02517709881067276,
-0.00776701932772994,
0.12570549547672272,
-0.019538098946213722,
-0.0018692403100430965,
0.02510909177362919,
-0.060456473380327225,
0.07158538699150085,
0.03774501010775566,
0.02516569383442402,
-0.01753956265747547,
0.046064771711826324,
-0.07271204143762589,
0.05165594071149826,
-0.003692415077239275,
-0.03474044054746628,
-0.0416288860142231,
-0.022850757464766502,
0.11500270664691925,
-0.030461110174655914,
-0.00046397559344768524,
0.006760867778211832,
-0.015324351377785206,
0.051779359579086304,
-0.011667019687592983,
-0.031072530895471573,
-0.02628360502421856,
0.0006002234295010567,
-0.048140719532966614,
-0.020443929359316826,
-0.007191897369921207,
-0.03681771084666252,
-0.021672509610652924,
0.018878614529967308,
-0.016474178060889244,
0.0361248180270195,
-0.03338797390460968,
0.003442905144765973,
-0.02087911032140255,
-0.017580075189471245,
0.0486464686691761,
0.03158058598637581,
0.02131710760295391,
0.06954096257686615,
0.01534541230648756,
0.044579874724149704,
0.04257237911224365,
-0.0003072747786063701,
-0.0076223453506827354,
-0.03228502720594406,
0.024623950943350792,
-0.020734773948788643,
-0.008493206463754177,
0.04781300574541092,
-0.000049728430894901976,
0.043286893516778946,
0.028156574815511703,
0.035031791776418686,
0.028266478329896927,
-0.007301704958081245,
-0.011429480277001858,
-0.040479470044374466,
0.022913239896297455,
0.011818776838481426,
-0.06299852579832077,
0.08491747826337814,
-0.06743263453245163,
0.02293563075363636,
0.01914653554558754,
-0.012988320551812649,
0.02400827780365944,
0.022796625271439552,
-0.007411720231175423,
-0.04344669729471207,
0.02247990295290947,
-0.0002471156476531178,
0.02150741219520569,
0.021320246160030365,
-0.044352613389492035,
-0.07199631631374359,
0.03615780174732208,
-0.007877533324062824,
-0.017971836030483246,
0.03325922042131424,
0.004469334613531828,
0.0005707700620405376,
-0.020631449297070503,
0.0467899926006794,
-0.034314803779125214,
-0.0076589747332036495,
0.010597107000648975,
0.040819913148880005,
0.01699884422123432,
-0.06037984415888786,
-0.04369448125362396,
-0.054882124066352844,
-0.05466028302907944,
-0.03174858167767525,
0.006255031563341618,
-0.03384607285261154,
-0.010191230103373528,
0.029911378398537636,
-0.06822217255830765,
-0.08607910573482513,
-0.0483858622610569,
-0.027072878554463387,
-0.003771938616409898,
-0.0358419232070446,
0.0028617200441658497,
-0.04261752590537071,
0.018780691549181938,
0.06894551217556,
0.04613688960671425,
-0.024202626198530197,
-0.04402794688940048,
0.03549664840102196,
0.04754330962896347,
0.015967123210430145,
0.04765373468399048,
-0.004355601500719786,
0.004569598939269781,
-0.007040701806545258,
0.07975649833679199,
0.01249352004379034,
0.004238684196025133,
-0.09386756271123886,
-0.02148042432963848,
0.030181096866726875,
0.02682689018547535,
-0.02678847499191761,
-0.037757325917482376,
-0.017761988565325737,
0.015974847599864006,
-0.05344053730368614,
-0.006909811403602362,
0.004504811950027943,
0.006552436854690313,
-0.006140832789242268,
-0.017101619392633438,
0.021148478612303734,
-0.020117783918976784,
0.019190022721886635,
-0.05726131424307823,
-0.008036330342292786,
-0.020213695243000984,
-0.008717980235815048,
-0.002523641334846616,
0.012613492086529732
] |
<p>Momentum measures how hard it is to stop an object. While Photons are massless they still have relativistic mass and energy. My question is can something stop photons other than being absorbed by something?</p>
<p>What does momentum mean when talking about massless particles?</p> | g4790 | [
0.030482955276966095,
-0.021304652094841003,
0.028515884652733803,
-0.0020826130639761686,
0.04730270057916641,
0.08827286958694458,
-0.011907057836651802,
0.09626877307891846,
-0.033203136175870895,
0.006373629905283451,
-0.0019776325207203627,
-0.016030559316277504,
-0.040115658193826675,
-0.014477611519396305,
-0.02653566561639309,
0.003901384538039565,
0.07334480434656143,
-0.026422759518027306,
0.006462453864514828,
0.049624353647232056,
-0.030265172943472862,
-0.010456988587975502,
-0.02228519134223461,
-0.027936292812228203,
-0.06160937622189522,
0.026176417246460915,
-0.03061099350452423,
-0.004039740189909935,
0.006683033891022205,
-0.008002935908734798,
0.0007787492941133678,
-0.0697820633649826,
0.002039066283032298,
-0.04422851651906967,
-0.00030622552731074393,
-0.021977348253130913,
0.0754561647772789,
-0.043959904462099075,
0.022467035800218582,
0.030961008742451668,
-0.022837305441498756,
0.014433112926781178,
-0.03840849548578262,
-0.019358793273568153,
-0.002709286753088236,
0.02527512051165104,
-0.00043718336382880807,
-0.04117359220981598,
0.03642961010336876,
-0.04653297737240791,
-0.01790503039956093,
0.009778735227882862,
-0.00035892167943529785,
0.039861273020505905,
-0.018500380218029022,
0.010162905789911747,
0.020281394943594933,
-0.05787331238389015,
0.03515421599149704,
0.0364641435444355,
-0.0024166726507246494,
0.0251513309776783,
0.01074538379907608,
0.013683474622666836,
0.01603327877819538,
-0.0489705391228199,
-0.04286947846412659,
-0.023798037320375443,
0.015087790787220001,
0.01360875740647316,
0.06014087796211243,
0.04247589781880379,
-0.040045659989118576,
-0.02856145240366459,
0.020971285179257393,
-0.0006303242407739162,
-0.05658426880836487,
0.034312713891267776,
-0.005205076653510332,
-0.00133028463460505,
-0.019990775734186172,
-0.018062777817249298,
0.04006297141313553,
-0.04944629222154617,
0.10372304916381836,
-0.014137093909084797,
-0.013435517437756062,
-0.03156983479857445,
-0.07382932305335999,
-0.01874075084924698,
0.07049867510795593,
-0.018593329936265945,
0.04152293503284454,
0.0034313269425183535,
-0.006630741059780121,
0.017780115827918053,
-0.01270056888461113,
0.0331425666809082,
-0.038357339799404144,
-0.032884448766708374,
-0.020635712891817093,
0.040087345987558365,
0.00866384245455265,
0.029933907091617584,
0.06348737329244614,
-0.027838999405503273,
-0.013801030814647675,
-0.023182939738035202,
0.028732139617204666,
0.0021411774214357138,
0.007209455128759146,
-0.03802969679236412,
-0.0345856249332428,
-0.04370901733636856,
-0.08341145515441895,
-0.039033614099025726,
0.12829522788524628,
-0.042415469884872437,
-0.015283954329788685,
0.06631921976804733,
0.03518904000520706,
0.05083529278635979,
-0.011188525706529617,
0.05601910501718521,
0.0011301612248644233,
-0.02058917097747326,
0.005947943311184645,
0.005374014377593994,
-0.007768729701638222,
-0.0030105675105005503,
0.046495407819747925,
-0.002009141258895397,
-0.005298150237649679,
-0.012883991934359074,
-0.059631526470184326,
0.024024998769164085,
0.018761219456791878,
-0.013025169260799885,
0.04243066906929016,
-0.03057260811328888,
0.0676688402891159,
0.05056610330939293,
0.03448211029171944,
0.022858140990138054,
-0.003796841949224472,
-0.04763519763946533,
-0.03844203054904938,
0.04880566895008087,
0.008844150230288506,
0.060352105647325516,
0.04765014350414276,
0.0491199754178524,
-0.004628604277968407,
0.016876230016350746,
0.055696528404951096,
0.001303502474911511,
-0.00010106537956744432,
0.053644757717847824,
0.0031544617377221584,
0.0595657043159008,
0.04390724003314972,
0.05046968534588814,
0.013634778559207916,
-0.03755014017224312,
-0.06064058467745781,
-0.026592997834086418,
-0.00435204803943634,
-0.06796006113290787,
-0.08242478966712952,
-0.030998652800917625,
-0.0014311405830085278,
0.03425070643424988,
-0.012758040800690651,
0.09075505286455154,
-0.012142736464738846,
-0.01708213984966278,
-0.025394272059202194,
0.04041158780455589,
0.019288791343569756,
0.004089465830475092,
-0.0047750105150043964,
0.004233000334352255,
0.050638582557439804,
0.004573846235871315,
-0.01945275254547596,
0.03867414966225624,
0.027503736317157745,
0.05950216203927994,
-0.009249498136341572,
-0.00023469144070986658,
-0.04203023388981819,
0.026657696813344955,
0.04715028777718544,
0.0003783483407460153,
0.017850330099463463,
0.017665067687630653,
0.0029933578334748745,
0.025906579568982124,
-0.0013654030626639724,
0.0008469967870041728,
-0.014538586139678955,
0.042211856693029404,
-0.06307149678468704,
-0.0021811749320477247,
0.04257834330201149,
-0.03502834588289261,
0.006105308886617422,
-0.0030208684038370848,
0.0038633537478744984,
0.02241717465221882,
0.1019824892282486,
-0.013111138716340065,
0.009273480623960495,
0.01594601385295391,
-0.010944590903818607,
-0.010663425549864769,
0.03328721597790718,
0.009779203683137894,
0.00026211870135739446,
-0.019220922142267227,
-0.04590728133916855,
-0.047643955796957016,
-0.020244846120476723,
-0.029457397758960724,
-0.03787660598754883,
0.04354463145136833,
-0.03471146523952484,
-0.03426117077469826,
0.031073803082108498,
0.0527193658053875,
-0.04643880948424339,
0.009351620450615883,
0.000616647710558027,
-0.0003304581332486123,
0.041265830397605896,
0.030566519126296043,
-0.024041445925831795,
0.009673344902694225,
0.004149679094552994,
-0.005461510736495256,
0.04795941337943077,
-0.018031001091003418,
-0.038267072290182114,
-0.07428638637065887,
0.01606415957212448,
-0.03390531614422798,
-0.006145618390291929,
0.027899211272597313,
-0.02388126403093338,
-0.013564796186983585,
0.042049866169691086,
0.0072121708653867245,
0.010742935352027416,
0.03341729938983917,
0.014711253345012665,
-0.01750798709690571,
-0.007679847069084644,
0.05435163155198097,
-0.11622631549835205,
-0.018443137407302856,
0.03912251442670822,
0.012569150887429714,
-0.027941875159740448,
0.012014896608889103,
-0.012370813637971878,
-0.004163061268627644,
-0.04350467771291733,
0.07353903353214264,
0.061531443148851395,
0.015877854079008102,
-0.029663611203432083,
0.04989224672317505,
0.0029901841189712286,
0.029156526550650597,
0.04182945191860199,
0.012381755746901035,
0.03450842946767807,
-0.030969364568591118,
0.006060800049453974,
-0.03822188451886177,
-0.021845372393727303,
0.03264342248439789,
-0.10948765277862549,
0.009713050909340382,
0.002206360222771764,
-0.05161416530609131,
-0.016079256311058998,
-0.01485470961779356,
-0.028063857927918434,
-0.04012207314372063,
-0.028535744175314903,
0.025014126673340797,
0.09480232000350952,
-0.0037720610853284597,
0.005265031475573778,
0.042782846838235855,
0.014976299367845058,
-0.020104508846998215,
-0.025832604616880417,
-0.0006896950653754175,
0.03223805129528046,
-0.0041023860685527325,
-0.009951180778443813,
-0.043086692690849304,
0.01919061318039894,
0.018541481345891953,
-0.06354627758264542,
0.04657641798257828,
-0.010276048444211483,
0.004171774256974459,
-0.035413820296525955,
0.09136589616537094,
-0.029698505997657776,
0.0473938062787056,
-0.017478499561548233,
-0.0058090281672775745,
0.00040541941416449845,
-0.002879456616938114,
-0.009409239515662193,
0.02864963188767433,
-0.03197159990668297,
-0.030658377334475517,
0.048092637211084366,
-0.019071590155363083,
0.08281415700912476,
0.018122650682926178,
-0.043488867580890656,
0.030348002910614014,
-0.043848082423210144,
-0.016791781410574913,
-0.004093097522854805,
-0.017314059659838676,
-0.018993834033608437,
-0.00017445442790631205,
0.0003212546871509403,
-0.002654230920597911,
0.02288026548922062,
0.00816830899566412,
0.09056469053030014,
0.0062876371666789055,
0.027566317468881607,
-0.016150260344147682,
-0.014384147711098194,
0.022442303597927094,
-0.0200208630412817,
0.0359339602291584,
0.011824501678347588,
-0.03191166743636131,
0.041293367743492126,
-0.01216130144894123,
0.05596241354942322,
0.05589418113231659,
0.015043732710182667,
-0.044724345207214355,
-0.0448061004281044,
0.006197003182023764,
0.01370045356452465,
0.03774125128984451,
0.03679833188652992,
-0.0276038758456707,
0.008095231838524342,
0.022521402686834335,
0.016809625551104546,
-0.021783525124192238,
-0.02517077326774597,
-0.016413023695349693,
-0.014613675884902477,
-0.0668526217341423,
0.015847908332943916,
-0.012859942391514778,
-0.01403213944286108,
-0.02913680486381054,
-0.054794490337371826,
0.06055265665054321,
-0.03534677252173424,
-0.008821274153888226,
0.015442609786987305,
-0.010902322828769684,
0.05225031450390816,
0.0001996869541471824,
-0.010130512528121471,
-0.028972618281841278,
-0.011061146855354309,
0.04266935586929321,
-0.04385194927453995,
0.03161429613828659,
-0.019125254824757576,
0.02871088869869709,
0.027509626001119614,
-0.014441326260566711,
0.0025460210163146257,
-0.05559423193335533,
-0.03615141659975052,
-0.022441834211349487,
0.04541424661874771,
-0.03289628401398659,
-0.010325959883630276,
-0.04837685823440552,
0.030464937910437584,
0.017841624096035957,
0.008725347928702831,
0.057997748255729675,
-0.01687552034854889,
-0.024913646280765533,
0.04206247627735138,
0.07637129724025726,
0.05250994861125946,
-0.011204062961041927,
-0.028284166008234024,
-0.0329761803150177,
-0.01563098467886448,
-0.009370420128107071,
-0.03314308077096939,
-0.04231072962284088,
-0.05230532959103584,
0.016879383474588394,
-0.03801369667053223,
0.00011374876339687034,
-0.014910358004271984,
0.03417429327964783,
0.022002914920449257,
0.034741632640361786,
-0.006003230810165405,
0.03566638007760048,
-0.034321870654821396,
0.03172457218170166,
0.02158057875931263,
0.028171522542834282,
-0.06181281432509422,
-0.008110756985843182,
0.0429777130484581,
-0.02077229507267475,
-0.029238885268568993,
0.012282285839319229,
-0.022145168855786324,
0.02309320867061615,
-0.013276508077979088,
0.0012527917278930545,
0.027031971141695976,
0.01527425181120634,
0.06824983656406403,
0.02795487269759178,
0.03526100143790245,
-0.04264797642827034,
-0.031046153977513313,
0.03068637289106846,
0.019948914647102356,
0.012943685054779053,
-0.01058966014534235,
0.04081588238477707,
-0.00038193646469153464,
-0.009457864798605442,
-0.062380511313676834,
-0.03253139927983284,
-0.006741809658706188,
0.04547341912984848,
-0.03758961707353592,
-0.002597726183012128,
0.018821461126208305,
0.023181570693850517,
-0.044953081756830215,
-0.008963970467448235,
0.09552788734436035,
-0.01007471326738596,
0.02615640126168728,
-0.05058547109365463,
-0.03842879459261894,
-0.0026093609631061554,
-0.050035543739795685,
-0.0017484447453171015,
-0.0007038951152935624,
-0.005199854262173176,
-0.03240948170423508,
0.043967995792627335,
0.013778343796730042,
-0.055889423936605453,
-0.0543503575026989,
-0.01587737165391445,
0.0423739030957222,
-0.03829105198383331,
-0.0004215563531033695,
0.017080659046769142,
0.0016373791731894016,
-0.023168649524450302,
0.00000884572000359185,
-0.03487671539187431,
-0.051806770265102386,
0.0782732218503952,
0.018691008910536766,
-0.040361806750297546,
0.016282789409160614,
0.03445091098546982,
-0.04283099249005318,
-0.007145536597818136,
0.032778024673461914,
0.055445555597543716,
-0.011313416063785553,
0.021899962797760963,
-0.025305522605776787,
-0.004977798089385033,
0.010869850404560566,
-0.04184070602059364,
-0.0011142235016450286,
0.0008792041917331517,
-0.01357194036245346,
-0.02226351574063301,
0.011663717217743397,
-0.036542098969221115,
-0.0021512710954993963,
0.03919173777103424,
0.0016618281370028853,
0.03178141266107559,
-0.0019456740701571107,
-0.0026684722397476435,
-0.02099151536822319,
0.003026033053174615,
-0.00476568890735507,
-0.0037057604640722275,
0.0033211878035217524,
-0.01019458007067442,
-0.051282189786434174,
-0.045578185468912125,
0.03198622539639473,
-0.007518335245549679,
0.03812694177031517,
-0.05891964212059975,
-0.020390866324305534,
-0.06013486534357071,
0.004086279310286045,
0.06730782240629196,
0.06944097578525543,
-0.02365165203809738,
0.05337468534708023,
-0.02609522081911564,
-0.031172696501016617,
-0.0582086406648159,
0.021698636934161186,
-0.006574617233127356,
0.01856321096420288,
-0.009162901900708675,
-0.02829783782362938,
-0.048088714480400085,
0.013788331300020218,
0.0846669152379036,
-0.028050879016518593,
-0.016012152656912804,
0.02419908158481121,
-0.02461349219083786,
0.011869749054312706,
-0.06352584809064865,
0.010027441196143627,
0.0049284291453659534,
-0.06370614469051361,
-0.028463130816817284,
-0.05350014939904213,
0.03595145046710968,
-0.007399263326078653,
0.014785218052566051,
-0.018886733800172806,
-0.06017657741904259,
0.04168035835027695,
-0.005449835676699877,
0.03884253650903702,
-0.025374799966812134,
0.004737445618957281,
-0.01226096786558628,
-0.006779239512979984,
-0.06613495200872421,
-0.004712850321084261,
0.007668103091418743,
0.007421886082738638,
0.034806180745363235,
0.008888502605259418,
0.02782905288040638,
-0.012763612903654575,
0.015357817523181438,
-0.011179140768945217,
0.024032453075051308,
-0.04315744340419769,
-0.008786259219050407,
0.033421531319618225,
0.0444556288421154,
0.04411005228757858,
-0.12566852569580078,
-0.007932220585644245,
0.020771993324160576,
-0.013395678251981735,
0.01477172039449215,
0.07897341996431351,
0.0430867075920105,
-0.0009711654856801033,
-0.006280713714659214,
-0.015480689704418182,
-0.017300760373473167,
-0.026409124955534935,
-0.003801779355853796,
0.01895952597260475,
-0.02896014414727688,
-0.02471509948372841,
0.039711691439151764,
-0.02384859137237072,
0.018742302432656288,
0.004570684861391783,
0.020240480080246925,
0.005580482538789511,
0.07847172021865845,
-0.008243211545050144,
-0.05798311531543732,
-0.008668068796396255,
-0.060091644525527954,
-0.027745194733142853,
0.019300401210784912,
0.02378552220761776,
-0.022109735757112503,
-0.02057947963476181,
-0.04813524708151817,
-0.06230843439698219,
0.02306133322417736,
-0.021405693143606186,
-0.020497644320130348,
0.001792083028703928,
-0.05113784223794937,
0.010258530266582966,
0.01821153424680233,
0.06397487968206406,
0.04683283343911171,
-0.00017471991304773837,
0.09100358188152313,
0.04336738586425781,
0.0156735647469759,
-0.03098021261394024,
-0.028588997200131416,
0.04509516432881355,
0.005656821187585592,
0.0020107056479901075,
0.0380205363035202,
-0.014503899961709976,
0.017386168241500854,
0.05850781500339508,
-0.013699283823370934,
0.082354836165905,
0.0023687477223575115,
0.02456820197403431,
0.0547264888882637,
-0.03550003841519356,
0.02585059590637684,
0.0028730144258588552,
-0.04333125799894333,
-0.06651477515697479,
-0.08026371151208878,
-0.0757530927658081,
0.015614645555615425,
0.03131354600191116,
0.016012271866202354,
-0.037286948412656784,
0.02277379110455513,
-0.00596027122810483,
0.008088900707662106,
0.03907850384712219,
-0.04737398773431778,
0.022346844896674156,
-0.016965331509709358,
0.018366534262895584,
0.0037183091044425964,
0.017082009464502335,
0.01578541472554207,
0.0053051128052175045,
-0.056276462972164154,
-0.014878016896545887,
-0.01024160347878933,
-0.0197924617677927,
-0.07778940349817276,
-0.051941875368356705,
-0.03686753660440445,
0.04793494939804077,
-0.024731336161494255,
-0.03654281049966812,
0.03270707279443741,
-0.038468074053525925,
-0.016252906993031502,
-0.012137768790125847,
0.10958294570446014,
-0.018564820289611816,
0.027996689081192017,
0.0015421236166730523,
0.012629309669137001,
-0.014095070771872997,
0.06451380997896194,
0.025658434256911278,
-0.0389791876077652,
-0.02660914696753025,
0.006535776425153017,
0.05945463106036186,
-0.0330507755279541,
-0.0060804844833910465,
-0.04640583693981171,
0.03417522460222244,
0.0703451856970787,
-0.02887238934636116,
-0.0011224759509786963,
-0.03965635970234871,
-0.029601871967315674,
0.0482407882809639,
0.015896178781986237,
0.003555968636646867,
-0.006056857295334339,
-0.020227601751685143,
-0.011247332207858562,
-0.012576393783092499,
0.013458718545734882,
-0.022587357088923454,
-0.00816793367266655,
0.0006067014764994383,
-0.02059437334537506,
-0.04967017471790314,
-0.02228819765150547,
-0.0355687215924263,
0.001240456709638238,
0.04181639105081558,
-0.025195637717843056,
-0.003140371758490801,
-0.017420167103409767,
-0.044136401265859604,
-0.058694858103990555,
-0.0653175413608551,
-0.052913542836904526,
0.031056787818670273,
-0.004878961946815252,
0.012912173755466938,
0.007681429851800203,
-0.02111802250146866,
0.04269877448678017,
-0.06484536826610565,
0.017633957788348198,
-0.023015083745121956,
0.017067909240722656,
-0.01528796087950468,
-0.0012351502664387226,
-0.01112343743443489,
-0.03390302509069443,
0.029912929981946945,
-0.07838667184114456,
-0.027582796290516853,
0.08209821581840515,
0.010013180784881115,
-0.037927109748125076,
-0.0014548215549439192,
0.05295925587415695,
0.07365972548723221,
0.007702345494180918,
0.004597358405590057,
0.06576750427484512,
-0.005689664278179407,
0.058441244065761566,
0.04172426834702492,
-0.07557635009288788,
-0.05855530500411987,
0.007126818411052227,
-0.06153195723891258,
-0.014450930058956146,
0.037769071757793427,
0.0416082926094532,
-0.05003195255994797,
-0.02383045293390751,
-0.001591305946931243,
-0.0786340981721878,
-0.013742874376475811,
-0.016828779131174088
] |
<h1>Question</h1>
<p>This is from my textbook:</p>
<blockquote>
<p>There are 2 balls of the same size made of rubber and iron respectively kept on the smooth surface of a moving train. Which ball will move faster when the train brakes suddenly?</p>
</blockquote>
<h1>My Answer</h1>
<p>In that start it seems simple. Let the iron ball be called $A$ and the rubber one $B$. The mass of the iron ball is greater as:</p>
<p>$$
(1)\ M = V \cdot D \\
(2)\ D_A > D_B \\
(3)\ V_A = V_B \ \ [From\ Q] \\
(4) M_A > M_B \ \ [From (1), (2), (3)] \\
$$</p>
<p>Then we have to consider what forces are acting on it. The only ones I could think of were friction with the floor and air resistance.</p>
<p>If we consider friction, then we can easily conclude that the rubber ball moved slower as rubber creates a <em>lot</em> of friction. But since they mentioned the floor was 'smooth', I thought we should ignore that.</p>
<p>So all that's left is air resistance (denoted by $F$).</p>
<p>$$
(5) F = m \cdot a \ \ \rightarrow \ \ a = \frac{F}{M} \\
(6) Surface\ Area_A = Surface\ Area_B \ \ [From (3)] \\
(7) F_{iron} = F_{rubber} \ \ [From (6)] \\
(8) a_A < a_B \ \ [From (4),(5),(7)]
$$</p>
<p>That means the rubber ball will move faster than the iron one (and therefore that the iron ball will stop before the rubber one does).</p>
<h1>Another answer</h1>
<p>But my teacher (who'd given me this problem) disagrees. Her argument is:</p>
<blockquote>
<p>Consider everything with reference to the train. Before braking, the balls are stationary (w.r.t. the train). When the train brakes, negative acceleration is provided to the train. That means the balls will move forward w.r.t. the train. But since the iron ball has a greater mass and so inertia, it will move slower.</p>
</blockquote>
<p>which give the same answer.</p>
<h3>Doubts</h3>
<p>So my questions are:</p>
<ol>
<li><p>Was my teacher's approach correct? Seems a bit unsound to me, but that just may be b'coz I don't have enough intuition for switching inertial frames of reference.</p></li>
<li><p>Are there any other forces in play over here? I could only think of 2: air resistance and friction.</p></li>
<li><p>Should air resistance be considered?</p></li>
<li><p>Should friction be considered? In that case, the rubber ball will be significantly slowed.</p></li>
</ol> | g4791 | [
0.0641808733344078,
0.012212765403091908,
0.01851215958595276,
0.034958142787218094,
0.05641748011112213,
0.037501245737075806,
0.10763871669769287,
-0.004683586768805981,
-0.056511230766773224,
-0.03448706492781639,
0.0014104311121627688,
-0.008541096933186054,
0.06039531156420708,
-0.026611188426613808,
0.00006248201680136845,
0.025553669780492783,
0.07147280126810074,
-0.029565997421741486,
-0.030430404469370842,
-0.013205969706177711,
0.04372137039899826,
0.05781072378158569,
-0.020676178857684135,
-0.023492220789194107,
0.0037945127114653587,
0.012751933187246323,
-0.02406328357756138,
-0.053695470094680786,
0.005717420019209385,
0.0038131005130708218,
0.02800299972295761,
-0.04358584061264992,
-0.004191403742879629,
-0.06899350881576538,
-0.04961998015642166,
-0.010564657859504223,
0.019176198169589043,
0.01431317999958992,
-0.02082754857838154,
0.006722266785800457,
0.07165876030921936,
-0.04724690690636635,
0.03655921667814255,
-0.03760438412427902,
0.023971091955900192,
-0.00983284693211317,
0.0011085171718150377,
-0.002442907774820924,
0.0018680966459214687,
0.0006601203349418938,
0.007569958455860615,
0.06122651696205139,
-0.006075895391404629,
-0.01641055755317211,
-0.04011555016040802,
0.10247907787561417,
0.03443752974271774,
-0.02458295039832592,
0.03413613140583038,
0.0074938624165952206,
-0.07849176228046417,
-0.013366245664656162,
-0.017384933307766914,
-0.07033374160528183,
0.04292214661836624,
-0.004719824530184269,
-0.008133959956467152,
0.007531628478318453,
0.037498101592063904,
0.00908738188445568,
0.04581451043486595,
0.012038917280733585,
0.01683402620255947,
-0.00814339891076088,
-0.051078591495752335,
0.0032135117799043655,
0.03167050704360008,
-0.009166218340396881,
0.028772013261914253,
0.02784445881843567,
-0.010898021049797535,
0.0323617123067379,
0.019000902771949768,
0.026917334645986557,
0.06407169252634048,
0.0021860806737095118,
-0.004501937888562679,
0.008802882395684719,
-0.027892816811800003,
0.007691114209592342,
0.005385325290262699,
-0.020300541073083878,
0.10562188923358917,
0.06630711257457733,
-0.024173863232135773,
0.0038856733590364456,
-0.05799064040184021,
0.07757212966680527,
0.0037292628549039364,
0.013562645763158798,
-0.019171124324202538,
-0.043815672397613525,
0.017366768792271614,
-0.025838425382971764,
0.03087736666202545,
-0.05017504096031189,
0.0174080990254879,
0.00686771422624588,
-0.027123989537358284,
-0.05927978828549385,
0.021671853959560394,
-0.03279492259025574,
-0.07398930937051773,
-0.07011615484952927,
-0.015631472691893578,
-0.02011444792151451,
0.04171137139201164,
0.002638133941218257,
-0.0006306578288786113,
0.044262997806072235,
-0.024694783613085747,
0.006436407100409269,
-0.0019788076169788837,
0.02946864627301693,
0.03064478188753128,
-0.05162039399147034,
-0.0167648084461689,
0.01479225605726242,
0.031543511897325516,
-0.0055118040181696415,
-0.022520525380969048,
0.029772529378533363,
0.028093351051211357,
-0.06155027449131012,
-0.04764658957719803,
0.023719610646367073,
0.001376652391627431,
0.03500562533736229,
0.03239523246884346,
0.005538937635719776,
0.018063697963953018,
0.034172024577856064,
0.019018320366740227,
-0.004449314903467894,
-0.05546184256672859,
0.08918897062540054,
-0.025491954758763313,
0.0009405846940353513,
0.037188559770584106,
0.004108377266675234,
0.02456335909664631,
0.04580890014767647,
-0.042609360069036484,
-0.025542620569467545,
0.06624478846788406,
0.0032082642428576946,
0.038055796176195145,
0.03515409305691719,
0.035679906606674194,
-0.018042759969830513,
0.04876311868429184,
-0.030437899753451347,
0.0017825617687776685,
0.025314893573522568,
-0.06454455852508545,
0.06438934057950974,
-0.05949272960424423,
-0.037749435752630234,
-0.008098050020635128,
-0.038088805973529816,
-0.04362452030181885,
-0.0074338242411613464,
0.011963307857513428,
0.04847462475299835,
-0.026865174993872643,
0.008383524604141712,
0.09190282970666885,
-0.09406527131795883,
-0.04859190434217453,
-0.005254278425127268,
0.05780629813671112,
-0.003991642501205206,
0.0040547545067965984,
-0.03232322633266449,
0.006654927507042885,
0.00749022513628006,
-0.026095999404788017,
0.04156756401062012,
-0.06781478971242905,
-0.028295692056417465,
-0.0700334757566452,
-0.00012945423077326268,
0.03985586762428284,
0.037849102169275284,
-0.024809671565890312,
0.012422136031091213,
0.021367693319916725,
0.018897227942943573,
0.01664150506258011,
-0.017146579921245575,
-0.02635931596159935,
0.04593365639448166,
-0.002633439376950264,
-0.0005740395281463861,
-0.03630724921822548,
-0.04806172475218773,
-0.012712866067886353,
0.024415435269474983,
0.010517663322389126,
0.010610484518110752,
0.03653770685195923,
0.005472490098327398,
0.004293001722544432,
-0.0023323697969317436,
-0.020131824538111687,
0.009875500574707985,
0.021845286712050438,
0.013057688251137733,
-0.02628866210579872,
0.023683054372668266,
0.025473617017269135,
-0.01376856118440628,
0.004436732269823551,
-0.059081148356199265,
-0.045352503657341,
-0.08869855105876923,
0.0028797907289117575,
-0.03818048909306526,
-0.05108829587697983,
0.08153627067804337,
-0.03831345960497856,
0.0038987433072179556,
-0.03247808292508125,
-0.016467362642288208,
0.028337405994534492,
0.022528158500790596,
0.013630653731524944,
0.023416277021169662,
-0.016272051259875298,
0.01233893446624279,
0.09684348106384277,
0.04183239862322807,
0.007790225092321634,
-0.03347383067011833,
0.002042878419160843,
-0.04716953635215759,
0.02715333178639412,
-0.0351291224360466,
0.01822833903133869,
0.06234893947839737,
-0.04344150051474571,
0.0025487046223133802,
0.000272822508122772,
-0.0069581372663378716,
0.029586222022771835,
-0.058880776166915894,
-0.04668712243437767,
-0.0018907254561781883,
-0.03240020573139191,
-0.034924786537885666,
0.012955348007380962,
-0.050491683185100555,
0.03240559622645378,
0.06541500240564346,
-0.08150367438793182,
0.004157272167503834,
-0.020942414179444313,
0.022882184013724327,
0.008111215196549892,
0.008542072959244251,
-0.011013721115887165,
-0.017742766067385674,
-0.013195764273405075,
0.016399754211306572,
0.008792977780103683,
-0.037692587822675705,
-0.008530220948159695,
-0.05139986053109169,
-0.001888649770990014,
-0.015572662465274334,
-0.030793126672506332,
0.02937648817896843,
-0.031003084033727646,
-0.05967859923839569,
0.05842782184481621,
-0.04596699774265289,
0.009006652981042862,
0.019546274095773697,
-0.023940706625580788,
0.02731521800160408,
-0.04515259712934494,
0.059303343296051025,
0.09795228391885757,
0.050911493599414825,
0.019045287743210793,
0.07810142636299133,
-0.01530619990080595,
-0.05049441382288933,
-0.05162433534860611,
0.053317006677389145,
0.03695027902722359,
-0.027453158050775528,
-0.025252940133213997,
0.03327617421746254,
0.06506867706775665,
-0.030914276838302612,
-0.02186080999672413,
0.017487481236457825,
-0.01499354187399149,
-0.038984328508377075,
0.033414728939533234,
0.02959190122783184,
-0.0017210975056514144,
-0.0197357926517725,
-0.04388733580708504,
-0.03848899528384209,
0.0038478635251522064,
0.020621877163648605,
0.05947888642549515,
0.022820260375738144,
-0.034013185650110245,
-0.023916427046060562,
0.01448657177388668,
-0.010577190667390823,
0.022601844742894173,
0.0426718071103096,
0.0003177280887030065,
0.01246828306466341,
-0.001967167714610696,
-0.03103792667388916,
0.006049582734704018,
0.06277503073215485,
-0.057291995733976364,
-0.00588588509708643,
-0.0359732024371624,
-0.054593343287706375,
0.022060533985495567,
0.05522105470299721,
0.03543132543563843,
-0.014078771695494652,
-0.0360630638897419,
-0.02306239865720272,
-0.018285540863871574,
-0.005953057669103146,
0.012678610160946846,
0.03910432755947113,
0.004479940049350262,
0.010621822439134121,
-0.003895309055224061,
-0.010053406469523907,
0.08976868540048599,
-0.042291752994060516,
0.0437992662191391,
-0.017827633768320084,
0.013173507526516914,
0.04440368711948395,
0.020625390112400055,
-0.01783968321979046,
-0.030073899775743484,
-0.023660937324166298,
-0.010424974374473095,
0.004740850999951363,
-0.002641176339238882,
0.04948849603533745,
-0.006504098419100046,
-0.0014396501937881112,
-0.027384433895349503,
-0.0013211446348577738,
-0.028189560398459435,
-0.009862189181149006,
0.016267064958810806,
-0.020441051572561264,
-0.05500197038054466,
0.03871515765786171,
0.04907844960689545,
-0.03567752614617348,
0.025532692670822144,
-0.017806751653552055,
-0.007643526419997215,
-0.04428957402706146,
0.020332589745521545,
0.06461148709058762,
0.011697974056005478,
0.005583661142736673,
0.05277761071920395,
0.0538971871137619,
0.003822773927822709,
-0.02969268150627613,
0.07021532952785492,
-0.06247987970709801,
-0.021201947703957558,
0.015280126594007015,
-0.02682388201355934,
-0.03540773689746857,
0.009568754583597183,
-0.0009015814866870642,
0.019968166947364807,
-0.028219792991876602,
0.019517868757247925,
0.05939485505223274,
-0.020118096843361855,
0.00962092261761427,
-0.07881146669387817,
0.051680393517017365,
-0.07769220322370529,
0.020102331414818764,
0.015946226194500923,
-0.06523595005273819,
-0.005509941838681698,
0.018111804500222206,
-0.018963929265737534,
-0.06928498297929764,
-0.08468044549226761,
-0.06426073610782623,
-0.017172105610370636,
0.008041509427130222,
-0.004600850399583578,
0.07816949486732483,
-0.017177361994981766,
-0.03737211227416992,
0.04073294252157211,
0.018894460052251816,
0.008654761128127575,
-0.053246911615133286,
0.03316628560423851,
0.012872513383626938,
0.058996111154556274,
0.022665150463581085,
-0.016957653686404228,
-0.029785679653286934,
0.0031378306448459625,
0.03104446269571781,
-0.0166629608720541,
0.010798974893987179,
0.0008790683350525796,
0.04177360236644745,
-0.011133013293147087,
0.03664640709757805,
0.06112613528966904,
0.004360413644462824,
0.009320605546236038,
0.08348044753074646,
-0.012014989741146564,
-0.013595695607364178,
-0.020853785797953606,
0.03734627738595009,
-0.05271540582180023,
-0.043061234056949615,
-0.026997171342372894,
-0.034523237496614456,
0.02002364955842495,
0.03457134962081909,
0.03378234803676605,
0.044802211225032806,
-0.007124264724552631,
-0.0017429483123123646,
-0.010157736018300056,
-0.005705664865672588,
-0.02373940870165825,
0.019544562324881554,
0.06727173179388046,
0.018805617466568947,
-0.007867828942835331,
0.03761589899659157,
-0.026185600087046623,
0.018344586715102196,
-0.026715602725744247,
-0.004316020291298628,
-0.05559806898236275,
0.015608241781592369,
0.013123982585966587,
-0.020194778218865395,
-0.017414502799510956,
0.05744800344109535,
0.07900787889957428,
0.016481464728713036,
0.047208014875650406,
0.006061385851353407,
0.06738025695085526,
-0.013977437280118465,
-0.059376321732997894,
0.007001026067882776,
0.05387391895055771,
0.003894932335242629,
-0.007206792011857033,
-0.008358809165656567,
-0.018246807157993317,
0.012200016528367996,
0.048676349222660065,
0.0015548658557236195,
0.04544371739029884,
0.03699278086423874,
-0.032670848071575165,
0.00812320876866579,
-0.07053238153457642,
0.011126863770186901,
-0.015511739067733288,
-0.014981886371970177,
-0.04728349670767784,
-0.018301429226994514,
-0.075428806245327,
-0.0019393119728192687,
0.020803039893507957,
-0.012467406690120697,
0.019498882815241814,
0.012913066893815994,
0.03640935197472572,
-0.010465899482369423,
-0.002682911464944482,
0.03500360623002052,
-0.03368515148758888,
0.07522819936275482,
0.0070119681768119335,
-0.004755537956953049,
-0.026314275339245796,
-0.03382853418588638,
0.020034383982419968,
-0.0031501862686127424,
-0.010924643836915493,
-0.022932738065719604,
0.05319052189588547,
-0.03882932290434837,
0.010701928287744522,
-0.03406846523284912,
-0.01365321222692728,
0.05277600139379501,
0.029887571930885315,
-0.06384932994842529,
-0.04726839438080788,
0.01581723988056183,
0.011165368370711803,
-0.03856080025434494,
0.007851592265069485,
0.006826288066804409,
-0.032801952213048935,
0.01923247054219246,
0.002558196196332574,
-0.04903781786561012,
0.017997784540057182,
0.01110700611025095,
-0.023799188435077667,
-0.017738288268446922,
0.04981712996959686,
0.028180355206131935,
-0.01594688557088375,
-0.03319818899035454,
-0.06128055974841118,
-0.04314999654889107,
0.030508896335959435,
-0.02443884313106537,
-0.016854628920555115,
0.01842823252081871,
-0.05055735260248184,
-0.036763980984687805,
-0.04041661322116852,
0.05542806163430214,
0.05994758754968643,
-0.0081024756655097,
0.0352654904127121,
-0.007979038171470165,
0.00020641827723011374,
-0.046856991946697235,
0.04130828380584717,
-0.03140552341938019,
0.014253329485654831,
-0.009702881798148155,
-0.01511100772768259,
0.004062260501086712,
0.033634983003139496,
-0.01309497281908989,
0.023163337260484695,
0.007996723055839539,
0.005171990022063255,
0.04028497263789177,
0.006184516008943319,
-0.020874256268143654,
-0.04639382287859917,
-0.024940144270658493,
-0.05085698887705803,
0.032082490622997284,
-0.05059264227747917,
0.0066825575195252895,
0.0052850572392344475,
-0.04224742203950882,
-0.015281272120773792,
-0.003927771933376789,
-0.05048713460564613,
-0.028175869956612587,
0.007243096828460693,
-0.054811906069517136,
-0.0405086874961853,
-0.0002143962192349136,
-0.005653472151607275,
-0.01813754253089428,
-0.038484517484903336,
0.003113166894763708,
-0.07666130363941193,
0.013739023357629776,
-0.04720751941204071,
0.03788505122065544,
-0.03416421264410019,
0.004413587041199207,
0.05900268629193306,
-0.04922955855727196,
-0.0023757743183523417,
0.022045303136110306,
0.02247648499906063,
-0.01469546277076006,
-0.013748284429311752,
0.01254698634147644,
-0.046574387699365616,
0.026466237381100655,
0.027432510629296303,
0.05522069334983826,
-0.026528386399149895,
0.02263285219669342,
0.026653634384274483,
-0.008461831137537956,
0.0713365450501442,
-0.03803236782550812,
0.011322399601340294,
-0.028572192415595055,
0.02971179410815239,
-0.031668536365032196,
0.07262273877859116,
-0.006168826948851347,
-0.05835619568824768,
0.013173039071261883,
-0.041310086846351624,
0.023791123181581497,
0.03247789666056633,
-0.04727434366941452,
-0.09929288923740387,
0.0831950306892395,
-0.017365222796797752,
0.0607418417930603,
0.010770585387945175,
0.009528880007565022,
0.015443770214915276,
0.03966143727302551,
-0.03158191964030266,
0.013574124313890934,
-0.07206011563539505,
0.07749603688716888,
0.003743140259757638,
-0.01625717617571354,
0.07386669516563416,
-0.02465607225894928,
0.00723137566819787,
0.02257756143808365,
-0.055764615535736084,
0.017304666340351105,
-0.035841796547174454,
-0.012837056070566177,
-0.06719733029603958,
-0.01958339847624302,
0.04169134423136711,
0.010083691217005253,
0.060764238238334656,
0.0032290073577314615,
-0.047172002494335175,
-0.04592457041144371,
-0.021726088598370552,
0.04383598268032074,
-0.023801695555448532,
0.08481574058532715,
-0.0455019436776638,
0.01680237054824829,
-0.01854318380355835,
-0.007994219660758972,
0.03202640637755394,
-0.03637492656707764,
0.039533548057079315,
0.04167093709111214,
0.04787072166800499,
0.0724840983748436,
-0.0007279872079379857,
-0.017301488667726517,
0.02878333255648613,
-0.01768738031387329,
-0.024943895637989044,
0.022991156205534935,
-0.02242925576865673,
-0.006307261064648628,
-0.008814842440187931,
0.030184440314769745,
-0.02901623398065567,
0.0013409560779109597,
0.01938372105360031,
-0.07374047487974167,
0.04676147177815437,
0.007405387237668037,
0.028733445331454277,
0.0702337846159935,
-0.03199246898293495,
-0.035080455243587494,
-0.021434606984257698,
0.04189259558916092,
-0.014825072139501572,
-0.014082523994147778,
-0.05551411584019661,
0.011072367429733276,
-0.009565433487296104,
0.02547569014132023,
0.015094855800271034,
-0.011072761379182339,
-0.027641547843813896,
-0.0012657517800107598,
-0.05756879597902298,
-0.025626201182603836,
0.02375093102455139,
0.0481790229678154,
0.021060839295387268,
0.011545033194124699,
-0.021387044340372086,
0.022261131554841995,
0.013816227205097675,
-0.015061991289258003,
0.0530751571059227,
-0.0209104735404253,
-0.02238466963171959,
0.012547707185149193,
-0.03509140759706497,
-0.04243248328566551,
-0.01289098709821701,
-0.01823650673031807,
-0.0007261080900207162,
-0.02357296459376812,
-0.01755358837544918,
-0.02540319785475731,
-0.043514225631952286,
-0.0388147234916687,
-0.0025317200925201178,
0.004460498224943876,
-0.026946598663926125,
-0.0024143902119249105,
0.028266537934541702,
0.028702067211270332,
-0.07495267689228058,
0.003293847432360053,
-0.024365928024053574,
-0.08977769315242767,
0.014869584701955318,
0.01729792170226574,
-0.020406095311045647,
0.0038726304192095995,
0.014563275501132011,
0.05528419464826584,
0.005646306090056896,
-0.01403070893138647,
0.00986192375421524,
0.0027593679260462523,
-0.0770534798502922,
0.023971106857061386,
0.02133304625749588,
-0.01125952135771513,
-0.013692541979253292,
0.029003474861383438,
0.02034454606473446,
-0.013460000976920128,
-0.008550604805350304,
0.030544163659214973,
-0.019761061295866966,
-0.04936101287603378,
0.006379508879035711,
-0.06029943376779556,
-0.01789672300219536,
0.04286491498351097
] |
<p>I am going through the <a href="http://www.staff.science.uu.nl/~aruty101/lecture1.pdf" rel="nofollow">lecture note</a> by Gleb Arutyunov on the derivation of critical dimension for bosonic string theory. I was able to reproduce all the results till the last step given on page 62. </p>
<p>For $[S^{i-},S^{j-}]$, the term that should vanish and give us the critical dimension is</p>
<p>\begin{equation}
\sum_{n=1}^{\infty}\left[\left(\frac{4\pi T}{(p^{+})^{2}} 2(n-1)-\frac{f(n)}{n^{2}}\right)\alpha_{n}^{[i}\alpha_{n}^{j]}\right]
\end{equation}</p>
<p>where </p>
<p>\begin{equation}
f(n)=\frac{4\pi T}{(p^{+})^{2}}\left[\frac{n(n^{2}-1)}{12}(D-2)+2an\right]
\end{equation}</p>
<p>I realize that I might be missing something obvious but at this moment I don't see how the above expression can vanish for all $n$ when $D=26$ and $a=1$. Thanks!</p> | g4792 | [
0.023311180993914604,
-0.011190149001777172,
0.023103974759578705,
-0.011622573249042034,
0.018797673285007477,
0.02205873280763626,
0.02041599527001381,
-0.030396275222301483,
-0.06310346722602844,
0.018917886540293694,
-0.04936981946229935,
0.015639975666999817,
0.0017386781983077526,
0.024859745055437088,
0.04464014992117882,
-0.02426423318684101,
0.02985864132642746,
-0.028695136308670044,
-0.030111532658338547,
-0.06355885416269302,
-0.01730816625058651,
-0.04010992869734764,
0.003841881873086095,
-0.031400538980960846,
0.0483960323035717,
0.010367645882070065,
0.007008249405771494,
0.020503930747509003,
0.013318195939064026,
0.005892191547900438,
0.0619213804602623,
0.020157482475042343,
0.043915245682001114,
-0.0016789513174444437,
0.02711779624223709,
-0.025639450177550316,
0.07125161588191986,
0.04413623362779617,
0.029001260176301003,
-0.04086083546280861,
-0.012588869780302048,
-0.018008477985858917,
-0.03062201291322708,
0.003684103721752763,
-0.015559381805360317,
0.004242919851094484,
-0.05953085049986839,
0.02464534342288971,
-0.018724601715803146,
-0.08613688498735428,
0.07663522660732269,
0.013711388222873211,
0.04192112758755684,
-0.05923421308398247,
-0.035158030688762665,
0.034192685037851334,
-0.04427202790975571,
-0.0494377501308918,
0.04089784622192383,
0.0461258590221405,
-0.00013223745918367058,
0.023183124139904976,
-0.0250563882291317,
-0.0016303010052070022,
0.02153092436492443,
-0.00735225947573781,
-0.018914051353931427,
-0.02378511056303978,
-0.0009649891871958971,
0.0019516871543601155,
0.0005285797524265945,
0.023157857358455658,
0.02869955450296402,
0.01883140206336975,
-0.027869699522852898,
0.011769376695156097,
0.00795853789895773,
0.0027445813175290823,
-0.06416023522615433,
0.017040742561221123,
-0.06105659902095795,
0.0017959855031222105,
-0.008206023834645748,
-0.059494104236364365,
0.0238126702606678,
-0.04677006974816322,
0.02892812341451645,
-0.004359295591711998,
-0.02018149197101593,
0.013729988597333431,
0.012853539548814297,
0.038081493228673935,
-0.009708725847303867,
0.0370786190032959,
0.031241493299603462,
-0.021714670583605766,
0.00525050750002265,
0.023822002112865448,
-0.031471896916627884,
-0.02964150533080101,
0.008725302293896675,
0.04152462258934975,
0.052978768944740295,
-0.04371846094727516,
0.013724989257752895,
-0.002523103728890419,
0.019805895164608955,
0.03419412672519684,
0.028007695451378822,
-0.042604949325323105,
-0.03723030164837837,
-0.02187947742640972,
-0.06590018421411514,
-0.009266551584005356,
-0.033945657312870026,
0.03805210068821907,
0.009126978926360607,
-0.022655842825770378,
0.02918611466884613,
0.005111354868859053,
0.001882326090708375,
-0.05701802670955658,
0.07095518708229065,
0.03326544165611267,
0.009828655049204826,
0.011925546452403069,
-0.027598809450864792,
0.03200307488441467,
0.0662980005145073,
0.020780878141522408,
-0.020140476524829865,
0.008318666368722916,
0.04073411226272583,
0.03628057986497879,
0.07854397594928741,
0.003301819320768118,
-0.030109597370028496,
0.020226238295435905,
0.0019974070601165295,
-0.023158427327871323,
-0.026433873921632767,
-0.008957111276686192,
0.01742137037217617,
0.028863634914159775,
-0.06589522957801819,
-0.007851367816329002,
0.02579667791724205,
-0.04642103984951973,
-0.02157660946249962,
-0.07689377665519714,
0.003580148331820965,
0.05032186582684517,
0.001186409150250256,
-0.041903503239154816,
-0.041246891021728516,
0.028349772095680237,
0.06052178516983986,
-0.008101838640868664,
-0.04454459622502327,
-0.029426712542772293,
0.0005532236536964774,
-0.004734611138701439,
0.012532053515315056,
0.042963769286870956,
-0.04783308133482933,
0.005275087431073189,
-0.03799838572740555,
-0.05134516954421997,
-0.050230398774147034,
0.005603459198027849,
-0.050158314406871796,
0.008461752906441689,
0.04313211143016815,
0.05974665656685829,
0.06566721946001053,
0.04096902534365654,
0.021225424483418465,
0.057410094887018204,
-0.02701854147017002,
0.003738750470802188,
-0.024362854659557343,
-0.04591528698801994,
0.031060516834259033,
-0.04034724086523056,
0.02655409649014473,
0.02662109024822712,
-0.026538323611021042,
0.024290859699249268,
0.015071089379489422,
-0.029561052098870277,
-0.09582290798425674,
0.027008863165974617,
0.025586657226085663,
0.032180748879909515,
0.017508750781416893,
0.03135298192501068,
0.044337864965200424,
-0.07955729961395264,
0.01193773653358221,
0.04748962074518204,
-0.08230475336313248,
0.03028922714293003,
0.08025187999010086,
-0.021608425304293633,
0.03155075013637543,
0.005318946670740843,
-0.013898505829274654,
0.04608232155442238,
-0.0521157905459404,
-0.04711570963263512,
0.003600963857024908,
-0.04014841839671135,
-0.056615885347127914,
0.03392314910888672,
-0.03445461392402649,
-0.015398538671433926,
0.008402565494179726,
0.016987953335046768,
-0.03008950874209404,
0.09172217547893524,
0.004171811975538731,
0.004275768529623747,
0.029616152867674828,
-0.007516901940107346,
-0.020646430552005768,
0.03852276876568794,
-0.007639922667294741,
-0.01547284796833992,
-0.011078479699790478,
-0.0027400858234614134,
-0.03297707810997963,
-0.031833767890930176,
-0.027108214795589447,
-0.055395953357219696,
-0.04756570979952812,
0.020482251420617104,
-0.008718757890164852,
-0.039849281311035156,
0.01763897016644478,
0.04652729630470276,
-0.04650523141026497,
0.031419381499290466,
-0.04412359371781349,
0.02987155131995678,
0.0002885206777136773,
-0.015817921608686447,
0.017994308844208717,
-0.01892464980483055,
-0.01592370867729187,
-0.028856594115495682,
-0.025017952546477318,
-0.032294392585754395,
0.000882193329744041,
0.057241521775722504,
-0.005264031235128641,
0.055585816502571106,
0.034132715314626694,
0.030614079907536507,
-0.015327041037380695,
-0.0010702562285587192,
-0.018863599747419357,
-0.02891913801431656,
0.004050802439451218,
0.03130389004945755,
-0.040469877421855927,
0.008129904046654701,
-0.011939706280827522,
0.013251385651528835,
0.005344382021576166,
0.045230451971292496,
-0.02859693206846714,
0.054877832531929016,
-0.027516912668943405,
0.0274505652487278,
0.0025033734273165464,
-0.004656536038964987,
-0.06638127565383911,
0.016548359766602516,
0.04065876454114914,
0.04795343428850174,
-0.033321913331747055,
0.04147126525640488,
0.0018272030865773559,
0.03241962566971779,
0.0005650217062793672,
-0.05301208794116974,
0.02052972838282585,
0.03951461985707283,
-0.010591736994683743,
-0.0712408721446991,
-0.00021674601885024458,
0.0010731455404311419,
-0.05117792263627052,
-0.023361600935459137,
-0.007824183441698551,
0.07239861786365509,
-0.0520043671131134,
-0.033561114221811295,
0.01777695305645466,
-0.01829887181520462,
-0.00011015486234100536,
-0.018542209640145302,
-0.0027231830172240734,
-0.026034202426671982,
0.0344180166721344,
0.02781147137284279,
-0.01299802865833044,
-0.055220987647771835,
-0.0422760508954525,
-0.0405195988714695,
-0.04486854374408722,
-0.027141757309436798,
0.09150426089763641,
-0.035344336181879044,
0.018677521497011185,
0.03277474641799927,
0.045018695294857025,
0.007837303914129734,
0.02872624807059765,
-0.0006748749292455614,
-0.011549575254321098,
-0.011700519360601902,
0.008334281854331493,
0.008498012088239193,
0.0014795566676184535,
-0.020304447039961815,
-0.013743086718022823,
0.026303589344024658,
-0.05229482054710388,
0.038661107420921326,
-0.027014287188649178,
-0.005461513996124268,
0.033083658665418625,
-0.027087515220046043,
-0.062332361936569214,
0.011873997747898102,
-0.06497105211019516,
0.0261117834597826,
0.0633874461054802,
0.01322255376726389,
-0.041997577995061874,
-0.0011429792502894998,
0.06256599724292755,
-0.008379083126783371,
0.02153172716498375,
0.02372759021818638,
-0.04817163944244385,
0.00709571223706007,
0.03699443116784096,
-0.025493759661912918,
0.008220246061682701,
0.018070533871650696,
0.021502358838915825,
-0.05057971924543381,
-0.04096241295337677,
0.06479453295469284,
0.0406743623316288,
-0.011119944043457508,
0.00987737812101841,
-0.020541107282042503,
0.011340638622641563,
-0.039175961166620255,
0.044078290462493896,
0.009188802912831306,
0.015976782888174057,
-0.008734709583222866,
0.05989557504653931,
0.030579671263694763,
-0.018313001841306686,
-0.028483420610427856,
0.07632163166999817,
0.017271697521209717,
-0.017903264611959457,
-0.03224226087331772,
-0.0028830242808908224,
-0.061819784343242645,
-0.031123662367463112,
-0.021395260468125343,
0.003582731354981661,
0.012228406965732574,
0.04719279333949089,
0.020473873242735863,
0.011457671411335468,
-0.04077092558145523,
0.004529176279902458,
0.02597278356552124,
-0.036336738616228104,
-0.04826706647872925,
-0.05262450873851776,
-0.025163568556308746,
-0.025926999747753143,
-0.010299070738255978,
0.008984305895864964,
-0.05424172431230545,
0.01781233213841915,
0.043011657893657684,
-0.029949521645903587,
0.05308801308274269,
-0.06676848232746124,
-0.036782484501600266,
-0.034935563802719116,
0.026126137003302574,
0.03635711595416069,
-0.014561044983565807,
-0.018704790621995926,
-0.03699042275547981,
0.06370885670185089,
0.058677658438682556,
0.034998681396245956,
-0.011794501915574074,
0.0018420710694044828,
-0.01963959075510502,
-0.004249165765941143,
-0.01221633329987526,
0.030529910698533058,
-0.06244822219014168,
-0.008737384341657162,
-0.008714696392416954,
-0.015572221018373966,
-0.03893011435866356,
0.08122929185628891,
-0.04210576042532921,
-0.038150712847709656,
-0.037216369062662125,
0.010685409419238567,
-0.028449492529034615,
-0.0053482335060834885,
0.03666684776544571,
-0.02595273219048977,
0.050783026963472366,
-0.032834019511938095,
0.05391519516706467,
-0.017026374116539955,
0.025739939883351326,
-0.08132922649383545,
0.05618269741535187,
-0.06206949055194855,
0.037104133516550064,
0.022601602599024773,
0.042843785136938095,
0.007245131768286228,
-0.006074657663702965,
0.04976901039481163,
-0.0188854169100523,
0.02942625992000103,
0.015078689903020859,
0.014033172279596329,
-0.10139323770999908,
0.059929125010967255,
0.017587950453162193,
-0.04083443433046341,
0.004234322812408209,
0.015881352126598358,
-0.010656528174877167,
0.06758968532085419,
-0.01867983490228653,
-0.04989737272262573,
0.05776680260896683,
0.035664450377225876,
-0.020787198096513748,
-0.009204032830893993,
0.022050056606531143,
-0.051836397498846054,
0.003526372369378805,
0.06658728420734406,
-0.034724704921245575,
0.01914733275771141,
-0.005735251121222973,
0.0012781352270394564,
-0.007843243889510632,
-0.009424091316759586,
-0.0018931915983557701,
0.001771189970895648,
-0.04559354856610298,
-0.04363984242081642,
0.008403764106333256,
-0.024521851912140846,
0.011740387417376041,
0.009813451208174229,
-0.03071475587785244,
0.029308494180440903,
-0.06245407089591026,
0.017257343977689743,
0.003485626308247447,
-0.04672785475850105,
0.039173293858766556,
-0.034737393260002136,
-0.046779241412878036,
-0.043921418488025665,
0.0691588968038559,
0.016538286581635475,
0.005725197959691286,
-0.025704342871904373,
-0.001885394798591733,
-0.06269881129264832,
0.017216548323631287,
0.030458496883511543,
-0.06439723819494247,
-0.03794786334037781,
0.021341631188988686,
-0.05723601579666138,
-0.02376585826277733,
0.012169517576694489,
-0.032735999673604965,
-0.050237901508808136,
0.045824989676475525,
0.05035143718123436,
0.01922418177127838,
0.034310195595026016,
0.027279457077383995,
0.025609347969293594,
0.02644108049571514,
0.042007576674222946,
0.05020180344581604,
0.02709612250328064,
0.026735249906778336,
-0.006943872198462486,
-0.004504408687353134,
-0.0262296125292778,
-0.02577928639948368,
0.08288468420505524,
0.030315963551402092,
0.01679057441651821,
0.022432995960116386,
0.012780917808413506,
0.08194613456726074,
-0.07264316827058792,
-0.06853049248456955,
0.03851500526070595,
-0.0005379613139666617,
-0.0356636717915535,
-0.068201944231987,
-0.015326819382607937,
0.0017498164670541883,
0.028874237090349197,
-0.02596277929842472,
-0.021173464134335518,
0.003362723160535097,
-0.009468941949307919,
-0.022324617952108383,
-0.030324727296829224,
0.029330046847462654,
-0.009292022325098515,
0.043901797384023666,
-0.007976306602358818,
0.019677525386214256,
0.020417816936969757,
-0.01013132557272911,
0.060515373945236206,
0.011583242565393448,
-0.00028281364939175546,
-0.026409408077597618,
-0.031240809708833694,
-0.026671232655644417,
0.03400397673249245,
-0.003251112997531891,
0.038129571825265884,
0.02296328730881214,
-0.015135244466364384,
-0.02539278008043766,
-0.03972132131457329,
-0.045416101813316345,
-0.05977460369467735,
0.006688685622066259,
-0.04012979567050934,
-0.0316125862300396,
-0.0008508616592735052,
0.0170352254062891,
0.07022222131490707,
0.023089004680514336,
-0.017746714875102043,
0.02978486381471157,
-0.004847027361392975,
0.0032463723327964544,
0.07671651989221573,
0.03210429474711418,
-0.038405247032642365,
-0.027026351541280746,
-0.023775089532136917,
-0.0065445187501609325,
-0.007211971562355757,
0.008593169040977955,
0.033726874738931656,
-0.04370763525366783,
-0.07263939827680588,
0.005457880906760693,
-0.03252342715859413,
-0.06794343888759613,
0.03738560900092125,
-0.007006804924458265,
-0.01845252886414528,
0.01658831350505352,
0.01568051613867283,
0.027713006362318993,
0.029970981180667877,
-0.049414534121751785,
0.020480211824178696,
0.009295777417719364,
-0.058032598346471786,
0.0020163417793810368,
0.046948086470365524,
-0.0099877854809165,
0.03512290120124817,
0.04790554195642471,
-0.010164923965930939,
0.07080930471420288,
-0.019434627145528793,
-0.023666799068450928,
0.03471958264708519,
0.07654298841953278,
0.01896343193948269,
0.05406326800584793,
0.063140869140625,
0.051321979612112045,
0.009307925589382648,
-0.06313975900411606,
0.0700511708855629,
0.0416877306997776,
0.004304878879338503,
0.00027600571047514677,
0.07559774816036224,
-0.005558645352721214,
0.0855940505862236,
0.005124587099999189,
0.03880729526281357,
0.06644997000694275,
-0.015026820823550224,
0.0011545667657628655,
0.021805474534630775,
-0.037406887859106064,
-0.05635068193078041,
0.03628702834248543,
0.034123603254556656,
0.030757537111639977,
-0.01700127311050892,
0.023786285892128944,
-0.02713354118168354,
-0.024975914508104324,
-0.05502861738204956,
0.02800583839416504,
-0.020141178742051125,
-0.009418975561857224,
0.07905949652194977,
0.0008672792464494705,
-0.046375662088394165,
0.010088867507874966,
0.023649390786886215,
-0.028162015601992607,
-0.0841141790151596,
0.026736145839095116,
0.06377483904361725,
-0.008945096284151077,
0.01013689674437046,
-0.03912334889173508,
-0.04037176072597504,
-0.05930476263165474,
0.020177004858851433,
-0.03757183253765106,
0.021638771519064903,
0.021767161786556244,
-0.012981520965695381,
-0.008211281150579453,
-0.0012244232930243015,
-0.012930258177220821,
-0.016739122569561005,
0.061768461018800735,
0.042301397770643234,
-0.04396785795688629,
0.02704618126153946,
-0.047103673219680786,
-0.010575944557785988,
0.05181453377008438,
-0.038470834493637085,
0.047531262040138245,
-0.0013449344551190734,
0.04720677435398102,
0.03245394676923752,
0.023178264498710632,
-0.007328610867261887,
0.029106255620718002,
-0.008464252576231956,
0.00008530831837560982,
-0.056995686143636703,
-0.08234217017889023,
-0.022653281688690186,
0.014211251400411129,
0.055884864181280136,
-0.013796564191579819,
0.010050403885543346,
0.009266839362680912,
-0.0381305068731308,
-0.033226922154426575,
0.0720863863825798,
-0.012494435533881187,
0.06695004552602768,
-0.035197023302316666,
-0.017114054411649704,
0.026304008439183235,
0.028044013306498528,
0.05935684219002724,
0.05867450311779976,
-0.011707058176398277,
-0.07493002712726593,
0.016292273998260498,
-0.04455232247710228,
0.016082968562841415,
-0.03021226078271866,
-0.035846222192049026,
-0.020501157268881798,
-0.04580129683017731,
0.023649293929338455,
0.06953981518745422,
-0.04001181945204735,
0.0376124382019043,
0.04279570281505585,
-0.014028310775756836,
-0.005037632770836353,
-0.022723423317074776,
-0.015491080470383167,
-0.039732012897729874,
0.00475579546764493,
-0.04406259208917618,
0.017321515828371048,
-0.062150321900844574,
-0.07970461994409561,
-0.035304367542266846,
-0.06591010838747025,
-0.020017122849822044,
0.0498066172003746,
0.011037688702344894,
-0.026484521105885506,
-0.029542000964283943,
-0.01006373018026352,
0.020481331273913383,
-0.042293112725019455,
0.03366759419441223,
0.01952548325061798,
0.004343756008893251,
0.027745310217142105,
-0.05269823595881462,
-0.023569846525788307,
-0.026867572218179703,
0.031274739652872086,
0.0033387565053999424,
-0.019919833168387413,
0.04705512523651123,
-0.05848752334713936,
0.02826349250972271,
0.016912205144762993,
-0.02336709015071392,
-0.017345674335956573,
0.008050267584621906,
0.009421291761100292,
0.08201044797897339,
-0.005730553530156612,
0.022260814905166626,
-0.0026515594217926264,
-0.01651662401854992,
0.015139440074563026,
-0.0011443323455750942,
0.004146584775298834,
-0.0125424237921834,
-0.013933507725596428,
0.04863841086626053,
-0.027090298011898994,
-0.05743969976902008,
-0.0011311800917610526,
0.027967305853962898
] |
<p>We see light as having travelled in a straight line from stars or galaxies light years away from us. However it's path is more likely of multiple curves as a result of gravity along the journey (gravitational lensing) . How can we be sure that the accelerations thus experienced have not produced braking radiation (<a href="http://en.wikipedia.org/wiki/Bremsstrahlung" rel="nofollow">bremsstrahlung</a>) thereby reducing the energy and therefore frequency of the light spectrum leading to an apparent red shift?</p> | g4793 | [
-0.0007209887262433767,
0.06678803265094757,
0.0072653829120099545,
0.03093184530735016,
0.05006337910890579,
0.03459588810801506,
0.005144990514963865,
-0.008699728175997734,
-0.0289929136633873,
-0.03245365992188454,
0.04328274726867676,
0.0031648147851228714,
0.08377605676651001,
0.052986059337854385,
-0.0007805582717992365,
-0.046563372015953064,
0.06887146085500717,
-0.036345865577459335,
0.048815954476594925,
-0.02448027953505516,
-0.01943669468164444,
0.025225836783647537,
-0.046907681971788406,
-0.06257578730583191,
-0.053829651325941086,
0.03961728513240814,
-0.0013205392751842737,
-0.021535973995923996,
-0.04097302630543709,
-0.018679559230804443,
0.058521319180727005,
-0.047901611775159836,
0.03365683928132057,
-0.015088352374732494,
0.0035595661029219627,
-0.035341184586286545,
0.05541323497891426,
0.03446916118264198,
0.017820125445723534,
0.036536768078804016,
-0.0035006804391741753,
-0.0594354011118412,
0.014484012499451637,
0.031484030187129974,
0.06377005577087402,
0.02460034377872944,
0.02121472731232643,
-0.02207772433757782,
0.035886846482753754,
0.009840099141001701,
-0.03980781510472298,
0.06097356230020523,
-0.0007757608545944095,
0.041749369353055954,
-0.01219693012535572,
-0.0025776708498597145,
-0.005501312669366598,
-0.01647183671593666,
0.037402428686618805,
-0.007077732123434544,
-0.036402057856321335,
-0.0073098186403512955,
0.020229140296578407,
-0.022875774651765823,
0.018270811066031456,
-0.048430345952510834,
-0.043783556669950485,
-0.028744056820869446,
0.02982456050813198,
-0.0029248674400150776,
0.038020651787519455,
0.0039716013707220554,
-0.05970323458313942,
-0.007489333860576153,
-0.009837999939918518,
-0.025878487154841423,
-0.03300775587558746,
0.03052079863846302,
-0.046179745346307755,
0.043904341757297516,
-0.03263877332210541,
0.01384950615465641,
-0.062169648706912994,
0.020975079387426376,
0.09598734974861145,
-0.027257924899458885,
0.012569284997880459,
0.02136852778494358,
0.0024100022856146097,
0.0017541948473080993,
0.06788786500692368,
-0.020076194778084755,
0.053843408823013306,
-0.02951001189649105,
5.472936095429759e-7,
0.004910496063530445,
0.013789253309369087,
0.07140026241540909,
-0.017176451161503792,
-0.019816391170024872,
-0.07521284371614456,
0.017252614721655846,
-0.03783392533659935,
0.002550461096689105,
0.029406892135739326,
-0.06699853390455246,
-0.011703389696776867,
-0.013097552582621574,
0.05322117730975151,
-0.06785379350185394,
0.01250272337347269,
-0.06308818608522415,
0.0023016934283077717,
-0.03168976306915283,
-0.03890922665596008,
-0.039196308702230453,
0.07404444366693497,
0.01043800450861454,
-0.012797747738659382,
0.04942764341831207,
0.007905012927949429,
-0.02611255645751953,
-0.03768756613135338,
0.06976188719272614,
-0.0161292664706707,
0.004871309734880924,
-0.04402853175997734,
-0.0575740784406662,
0.04542706906795502,
0.0025853326078504324,
-0.06058700755238533,
0.02751062996685505,
0.0037259713280946016,
0.02805454656481743,
0.007583577651530504,
-0.01240875106304884,
0.06136779859662056,
0.030580876395106316,
-0.013206417672336102,
0.007065996993333101,
0.029205376282334328,
-0.027297278866171837,
0.028229432180523872,
-0.04086718335747719,
-0.03644797205924988,
0.010213500820100307,
-0.0764993205666542,
-0.0052561527118086815,
0.0544750951230526,
0.032202158123254776,
0.0075943488627672195,
0.05673087388277054,
-0.01247815415263176,
-0.03295572102069855,
0.005664163734763861,
-0.0634642243385315,
-0.02164197526872158,
-0.016594622284173965,
-0.04203728213906288,
0.048764944076538086,
0.06662685424089432,
-0.07247267663478851,
0.009082109667360783,
0.0370420441031456,
-0.05369194597005844,
0.012763908132910728,
-0.013344629667699337,
-0.04245973378419876,
0.020694751292467117,
-0.06500879675149918,
-0.07251851260662079,
-0.0013060609344393015,
0.04147695004940033,
-0.0007236878736875951,
0.011017401702702045,
0.04401927813887596,
0.06582697480916977,
-0.042803969234228134,
-0.02964777685701847,
0.04916268214583397,
-0.019913790747523308,
-0.0011931916233152151,
-0.02176285721361637,
-0.001779752317816019,
0.04454810917377472,
-0.0305536687374115,
-0.03618757054209709,
-0.06525933742523193,
-0.009424116462469101,
0.03815809264779091,
0.024991994723677635,
-0.044708333909511566,
0.02720790170133114,
-0.00331311859190464,
-0.021675733849406242,
-0.06604190170764923,
-0.04255406931042671,
-0.005462970118969679,
-0.003563785692676902,
0.05741891264915466,
-0.0031059475149959326,
0.05191706120967865,
-0.05416049435734749,
-0.0036470750346779823,
0.05106303095817566,
0.0185877475887537,
0.03694211691617966,
-0.00734790600836277,
-0.012102639302611351,
-0.007985872216522694,
0.020252995193004608,
0.03309138864278793,
0.03665909543633461,
-0.02379528619349003,
-0.04502357542514801,
0.0039701759815216064,
-0.0025338318664580584,
0.003082324517890811,
0.06077178195118904,
0.01414635218679905,
-0.026122454553842545,
0.034124016761779785,
0.01338998693972826,
-0.016239110380411148,
-0.006816343404352665,
-0.05941883847117424,
-0.034792132675647736,
-0.005399521440267563,
0.027706259861588478,
-0.02732723020017147,
-0.0014687558868899941,
-0.018755264580249786,
-0.018349457532167435,
-0.05019497126340866,
0.0778777077794075,
-0.04967207461595535,
-0.02142217569053173,
-0.0005963451112620533,
0.06450191140174866,
0.0050417701713740826,
0.021962298080325127,
-0.042929332703351974,
-0.04774540290236473,
-0.01092520635575056,
0.02231592684984207,
0.024528276175260544,
0.06165006384253502,
-0.01715666800737381,
-0.00713095348328352,
-0.011737427674233913,
0.030093125998973846,
-0.0020125715527683496,
-0.004784708376973867,
0.017820177599787712,
-0.02533910982310772,
0.043457865715026855,
-0.049761779606342316,
0.08374479413032532,
-0.07063951343297958,
0.04458773881196976,
-0.0228275116533041,
-0.014789204113185406,
0.016690727323293686,
-0.022074822336435318,
-0.05985020101070404,
0.02874012105166912,
-0.009519718587398529,
-0.011728904210031033,
-0.04410246014595032,
-0.014197955839335918,
0.0012376636732369661,
0.033713191747665405,
0.03565359115600586,
0.019925933331251144,
0.032949384301900864,
0.0057398416101932526,
-0.01739872246980667,
-0.029853040352463722,
0.004761502146720886,
-0.004092492163181305,
-0.013553222641348839,
-0.007141986396163702,
-0.05407705530524254,
0.019751332700252533,
-0.006095344666391611,
-0.016813239082694054,
0.046089716255664825,
0.052972860634326935,
-0.006958015728741884,
0.02184785157442093,
-0.04157788306474686,
-0.007536463439464569,
0.08254654705524445,
0.026791129261255264,
-0.04001685604453087,
0.020738063380122185,
0.03161955624818802,
0.02682548761367798,
-0.006635680794715881,
-0.001351298182271421,
0.014203636907041073,
-0.04537796229124069,
-0.023383518680930138,
0.017538346350193024,
0.002224493306130171,
-0.020158538594841957,
-0.05492660775780678,
-0.05448121577501297,
-0.009039073251187801,
-0.001370054204016924,
-0.0005588518688455224,
0.012742401100695133,
0.022469419986009598,
0.06850439310073853,
-0.03194957599043846,
-0.05850169435143471,
-0.03174662962555885,
-0.01385909877717495,
0.05885034799575806,
0.04178054630756378,
-0.027412278577685356,
-0.03265981748700142,
-0.053513091057538986,
-0.0417388491332531,
0.005614129360765219,
-0.0012707831338047981,
-0.0010006548836827278,
-0.023730548098683357,
-0.015904640778899193,
-0.012946892529726028,
0.005305889528244734,
0.0194686409085989,
-0.07657720148563385,
-0.02112387865781784,
-0.029892966151237488,
0.011169595643877983,
-0.012729795649647713,
0.04046662896871567,
0.07081501930952072,
0.03410734981298447,
-0.019654422998428345,
-0.018933840095996857,
-0.05642330273985863,
0.015233621001243591,
0.008122921921312809,
0.000021043268134235404,
-0.005284839775413275,
0.004524235147982836,
0.0016275367233902216,
-0.08362690359354019,
0.0681791827082634,
-0.020625358447432518,
0.01123124547302723,
-0.05773022025823593,
-0.025474589318037033,
0.0207218024879694,
-0.012917227111756802,
0.04579038918018341,
0.052905745804309845,
-0.040213312953710556,
0.012105125002563,
0.006738240364938974,
-0.06414536386728287,
0.0005267953965812922,
0.006724984850734472,
-0.025530856102705002,
-0.001669383025728166,
0.04150950536131859,
0.013422884047031403,
-0.02105685882270336,
-0.052812542766332626,
-0.058334220200777054,
-0.05605744943022728,
0.0077775754034519196,
0.035654813051223755,
0.020144077017903328,
0.04212426766753197,
0.038025494664907455,
-0.04135967046022415,
0.09327612072229385,
0.027088560163974762,
-0.0058611612766981125,
0.09184485673904419,
-0.01072229165583849,
-0.007374875713139772,
-0.010313903912901878,
-0.034015920013189316,
-0.07947677373886108,
0.01121133379638195,
0.01480272226035595,
-0.00857997965067625,
-0.0674644187092781,
0.0379866398870945,
-0.033637337386608124,
0.03208532556891441,
-0.058034881949424744,
0.012849261984229088,
0.0051166098564863205,
0.01690245419740677,
0.0242366474121809,
0.012231425382196903,
0.019645022228360176,
0.0004917301703244448,
0.003189425216987729,
-0.03244495391845703,
0.000814939325209707,
0.04808438941836357,
-0.001195275690406561,
0.017428556457161903,
0.011513620615005493,
0.016876475885510445,
-0.03840511664748192,
0.008327935822308064,
-0.059551432728767395,
0.06787697970867157,
0.005127994809299707,
0.03952644392848015,
-0.03687174245715141,
0.01828068681061268,
0.014984184876084328,
0.02833496406674385,
0.05570108816027641,
0.031568292528390884,
-0.019096560776233673,
-0.050801537930965424,
0.10384047031402588,
0.04456288740038872,
-0.023218534886837006,
-0.03283749148249626,
0.040470533072948456,
0.008422606624662876,
-0.006500596646219492,
-0.006611148361116648,
0.029593221843242645,
-0.025030657649040222,
0.04645233973860741,
0.0005461325054056942,
0.04256521537899971,
0.0300695039331913,
0.029858537018299103,
0.05203918367624283,
-0.03200238570570946,
0.017074985429644585,
0.002358329249545932,
0.013042569160461426,
0.06577526777982712,
-0.014904641546308994,
0.009814715944230556,
0.0314939022064209,
-0.02068830281496048,
-0.015175729990005493,
0.012356989085674286,
-0.02897872030735016,
0.04469030350446701,
0.031458087265491486,
-0.013511262834072113,
-0.0469663180410862,
0.03592466935515404,
0.032375652343034744,
0.01549031026661396,
0.02247362583875656,
0.009765283204615116,
0.027362262830138206,
0.0028698944952338934,
0.013484456576406956,
-0.028867870569229126,
-0.05368007346987724,
-0.020076822489500046,
0.00947020947933197,
-0.006283059250563383,
-0.04421631246805191,
0.0025716659147292376,
-0.0035004771780222654,
-0.020264483988285065,
0.01655801758170128,
-0.030240120366215706,
-0.045485809445381165,
0.0018497719429433346,
-0.0179771538823843,
-0.029065579175949097,
-0.0014772459398955107,
0.005525507498532534,
0.054457180202007294,
-0.0750473290681839,
-0.050709765404462814,
0.0696628987789154,
-0.06251964718103409,
0.04466764256358147,
-0.009767021052539349,
-0.021008223295211792,
0.046679072082042694,
-0.020563123747706413,
-0.016179775819182396,
-0.07511710375547409,
-0.021335769444704056,
0.024120334535837173,
0.008756360970437527,
0.0255507193505764,
-0.010355781763792038,
0.015808383002877235,
-0.06114436313509941,
0.004078886471688747,
0.041445065289735794,
-0.03448085859417915,
-0.00025012539117597044,
0.037532541900873184,
0.07108679413795471,
-0.025697650387883186,
-0.03130645677447319,
0.05554276704788208,
-0.062046755105257034,
-0.005950387567281723,
0.04218931868672371,
0.04280322790145874,
0.04460114613175392,
-0.04834657534956932,
-0.04655790328979492,
0.04438180848956108,
0.0654713585972786,
-0.06066880747675896,
-0.05174272507429123,
0.0002459509123582393,
0.0019724685698747635,
-0.01263550203293562,
0.0866575688123703,
0.042270250618457794,
0.008917112834751606,
0.0011578871635720134,
0.011586659587919712,
-0.014643755741417408,
0.015928661450743675,
-0.02692108042538166,
0.04238869249820709,
-0.028479522094130516,
0.03835738077759743,
-0.021801665425300598,
0.08458668738603592,
0.005946459714323282,
0.0006391193601302803,
-0.0301867313683033,
-0.07469715923070908,
0.003380606649443507,
0.014227915555238724,
0.04575709253549576,
-0.012060094624757767,
0.019138174131512642,
-0.05187130346894264,
0.006211654748767614,
-0.03176334127783775,
-0.08679120987653732,
0.01743701472878456,
0.021974895149469376,
0.029250726103782654,
0.027427345514297485,
-0.046418629586696625,
0.011594824492931366,
0.06527577340602875,
-0.05927273631095886,
-0.05400584638118744,
-0.035279322415590286,
0.010509505867958069,
-0.012999061495065689,
0.01587289571762085,
0.0051621063612401485,
0.07579005509614944,
-0.025143112987279892,
0.037788599729537964,
-0.0701906830072403,
0.04660364240407944,
0.0021050081122666597,
-0.0036947608459740877,
0.001083550974726677,
-0.0015126564539968967,
0.01902448572218418,
0.010556885972619057,
-0.012635725550353527,
-0.02650749497115612,
0.0020086944568902254,
-0.045175742357969284,
-0.003250355599448085,
0.02599233202636242,
0.009891219437122345,
0.07547395676374435,
-0.0371813029050827,
-0.06537716835737228,
0.0028285218868404627,
-0.012383431196212769,
0.049782175570726395,
0.056646764278411865,
-0.04713134095072746,
0.004393111914396286,
-0.043481290340423584,
-0.006430269218981266,
-0.019140461459755898,
-0.0883621796965599,
-0.05485812574625015,
-0.04022762551903725,
0.04459277167916298,
-0.0341167226433754,
0.003718877909705043,
-0.037488121539354324,
0.04717912897467613,
0.038537658751010895,
-0.031223513185977936,
0.0704529657959938,
-0.06492452323436737,
-0.018225666135549545,
0.022905508056282997,
0.07010532170534134,
0.018159668892621994,
0.021085133776068687,
0.03484894707798958,
-0.006186074111610651,
0.035674747079610825,
-0.058640483766794205,
0.007938867434859276,
-0.04084508493542671,
0.028483863919973373,
0.013340498320758343,
-0.02330847829580307,
0.05358013138175011,
-0.02446999028325081,
0.028875265270471573,
-0.0006700012017972767,
0.016980864107608795,
0.03645341843366623,
-0.028299642726778984,
0.007577971555292606,
-0.006492437794804573,
0.03608674556016922,
-0.003467065282166004,
0.004297551233321428,
-0.05097339302301407,
0.05081513151526451,
0.026207104325294495,
0.0539957620203495,
-0.05301533639431,
0.05916848033666611,
0.0010851069819182158,
-0.0069188084453344345,
0.004699435085058212,
0.0006324144778773189,
0.03186880052089691,
0.0018015644745901227,
-0.0659041628241539,
0.01535942405462265,
-0.05345144495368004,
-0.045280784368515015,
0.00404244614765048,
-0.049631696194410324,
-0.04225775972008705,
-0.04076646268367767,
0.014769689179956913,
-0.01076561026275158,
-0.0017334003932774067,
0.04467251896858215,
-0.026664890348911285,
0.0702037438750267,
0.005206268280744553,
-0.11980327218770981,
-0.008140158839523792,
-0.031315915286540985,
-0.030147632583975792,
-0.001923228963278234,
0.006186412647366524,
0.015496078878641129,
-0.016034575179219246,
-0.0682770386338234,
-0.004413508344441652,
0.04368376359343529,
-0.011746997013688087,
0.006390763446688652,
0.00044445201638154685,
0.028429372236132622,
-0.02760952338576317,
0.006625094451010227,
-0.056381989270448685,
0.03667141869664192,
0.036496762186288834,
0.029576949775218964,
0.016090014949440956,
0.03949699550867081,
0.03789576143026352,
0.03887399286031723,
-0.008606013841927052,
0.01274849008768797,
-0.024547116830945015,
0.03621383383870125,
-0.02840575762093067,
-0.03298530355095863,
-0.04139422997832298,
0.048901405185461044,
0.009997406043112278,
-0.040006786584854126,
0.013335758820176125,
-0.03715949133038521,
-0.009052273817360401,
0.007346059661358595,
0.04508693888783455,
0.006808409933000803,
-0.011673733592033386,
0.04898599907755852,
0.025751370936632156,
0.005322418175637722,
-0.02312300354242325,
0.019428694620728493,
-0.042726676911115646,
-0.005174856632947922,
0.006354217883199453,
0.04212002456188202,
0.012812657281756401,
0.01705448143184185,
0.008852067403495312,
0.03557351976633072,
-0.012902631424367428,
0.00675926823168993,
0.010929449461400509,
0.06838072091341019,
0.011615847237408161,
0.02239435724914074,
-0.03509359434247017,
-0.019257165491580963,
-0.030132081359624863,
-0.007775207050144672,
0.02202627994120121,
-0.014980806969106197,
0.018894048407673836,
-0.043670881539583206,
-0.008076071739196777,
-0.04623012617230415,
-0.023536987602710724,
0.04618432745337486,
0.014765491709113121,
-0.04159795120358467,
-0.07257264852523804,
0.012004531919956207,
0.024349013343453407,
-0.006521186325699091,
-0.047528594732284546,
0.007030403707176447,
-0.023547738790512085,
-0.007212300784885883,
0.003870142623782158,
0.042087167501449585,
0.020291032269597054,
-0.0098454300314188,
0.017766829580068588,
0.02212042175233364,
0.045391686260700226,
-0.01819731667637825,
0.01721416972577572,
0.009589200839400291,
-0.013595212250947952,
0.016260122880339622,
0.005472609307616949,
-0.03916749358177185,
-0.011150912381708622,
-0.030817560851573944,
-0.05383816361427307,
-0.03153290972113609,
-0.035544365644454956,
-0.0345701240003109,
0.013885739259421825,
0.00746585987508297,
-0.024044634774327278,
-0.053384698927402496,
0.025832070037722588,
0.026452817022800446
] |
<p>I'm a high school senior and I have to write a paper about <a href="http://en.wikipedia.org/wiki/Resonance" rel="nofollow">resonance</a> and differential equations. I've been searching the Internet for a long time, but I haven't found an equation that is properly explained. Could anyone explain whether there is an equation to describe the amplitude and if so, whether you could explain to me how you can obtain this formula? </p> | g4794 | [
0.014105628244578838,
0.040704891085624695,
-0.023686930537223816,
-0.04839864373207092,
0.028431983664631844,
-0.02037750743329525,
0.04984447360038757,
0.04788816347718239,
-0.01818498969078064,
-0.0332443006336689,
-0.04250558093190193,
0.01709676720201969,
0.05275748297572136,
0.017174070701003075,
0.025485415011644363,
-0.0193055160343647,
-0.010337380692362785,
0.043104078620672226,
-0.01827179826796055,
-0.029189731925725937,
-0.025794336572289467,
0.02648172155022621,
-0.018283626064658165,
-0.039033256471157074,
-0.002332782605662942,
0.002730088774114847,
-0.0021732309833168983,
-0.044642165303230286,
-0.053312066942453384,
-0.056989651173353195,
-0.01013499591499567,
-0.009345428086817265,
0.07349440455436707,
0.06550795584917068,
-0.004087874665856361,
-0.006590147037059069,
-0.02323230914771557,
0.07905356585979462,
0.01584969088435173,
0.016778461635112762,
0.0698067918419838,
0.005720940884202719,
0.0011687817750498652,
-0.04585753753781319,
0.00836097914725542,
-0.011540258303284645,
-0.04632038623094559,
-0.031116895377635956,
-0.00918599497526884,
-0.02559554949402809,
-0.010482929646968842,
0.012455891817808151,
0.03807580843567848,
-0.016296060755848885,
-0.05840648338198662,
-0.00414312956854701,
0.0076979054138064384,
0.00951817911118269,
0.019984278827905655,
0.0033257261384278536,
-0.012003980576992035,
0.013548893854022026,
-0.03514450415968895,
0.026423819363117218,
0.07572796195745468,
-0.01942252181470394,
0.01622188463807106,
-0.07265889644622803,
0.00037782973959110677,
-0.033343348652124405,
-0.005294606555253267,
-0.029665792360901833,
-0.07239574939012527,
-0.01817118562757969,
0.02383456379175186,
-0.0039403242990374565,
0.041400693356990814,
-0.018743667751550674,
0.00974541250616312,
0.0074841538444161415,
-0.013540413230657578,
0.04790908470749855,
0.06154939532279968,
0.0468207523226738,
0.06056886538863182,
-0.0277181975543499,
0.04661031439900398,
-0.004006209317594767,
0.05886407569050789,
-0.02552684023976326,
0.010162962600588799,
0.015518310479819775,
0.04109305143356323,
-0.06924817711114883,
0.03323754295706749,
0.00021194358123466372,
-0.04256471246480942,
0.059617143124341965,
-0.06198795884847641,
-0.045043278485536575,
-0.027006642892956734,
0.016442878171801567,
-0.011235276237130165,
-0.019487017765641212,
0.030980408191680908,
0.037376996129751205,
0.038601260632276535,
-0.0537075437605381,
-0.03992205485701561,
-0.016504306346178055,
-0.05110633000731468,
-0.015559790655970573,
-0.0205736942589283,
0.0018060001311823726,
0.023561552166938782,
-0.06118996813893318,
0.02617623843252659,
-0.056590259075164795,
-0.012817978858947754,
0.03636068105697632,
0.021797064691781998,
0.028046870604157448,
-0.011020456440746784,
0.025895986706018448,
-0.03397068381309509,
0.06532182544469833,
0.04132356867194176,
0.040809426456689835,
0.04071972891688347,
0.06804532557725906,
0.04779898747801781,
0.002341556129977107,
0.021669095382094383,
0.01144751813262701,
0.018443208187818527,
0.054223913699388504,
-0.00734446058049798,
-0.002483941148966551,
0.01851223036646843,
0.030885735526680946,
0.05712202563881874,
-0.0174209326505661,
0.010531384497880936,
-0.07241342216730118,
-0.0449768602848053,
0.033100828528404236,
-0.0023413493763655424,
-0.02242189645767212,
0.04540558159351349,
0.02413981407880783,
0.01550837978720665,
0.030117586255073547,
0.04271862655878067,
-0.048348866403102875,
-0.04115505516529083,
0.02177530527114868,
0.01132633350789547,
-0.023412903770804405,
-0.039353568106889725,
-0.005978995002806187,
0.06813038885593414,
-0.009381654672324657,
-0.03656865656375885,
0.010173575021326542,
-0.0936630442738533,
0.0024670218117535114,
0.03462384268641472,
-0.03292549401521683,
-0.030706854537129402,
-0.028552953153848648,
-0.030247097834944725,
0.01313856989145279,
0.03001033328473568,
0.0278833769261837,
-0.00001129960310208844,
0.0764489620923996,
0.04435121640563011,
-0.007388802245259285,
0.013181351125240326,
0.0169934444129467,
0.005222473293542862,
0.030361225828528404,
0.03638596087694168,
-0.08405751734972,
0.03708703815937042,
0.005714628379791975,
0.01856229454278946,
0.007571169640868902,
-0.027602503076195717,
0.00882565975189209,
-0.003183708293363452,
-0.015899453312158585,
0.005609454121440649,
0.005261248908936977,
0.005705821327865124,
0.019248025491833687,
0.0151171013712883,
-0.01870669424533844,
-0.013904090039432049,
0.0620230957865715,
0.04246992617845535,
0.02939535491168499,
0.03180690482258797,
-0.05873424559831619,
0.017842723056674004,
-0.018369033932685852,
-0.022838138043880463,
-0.0016986584523692727,
0.020875288173556328,
-0.019446827471256256,
-0.027329182252287865,
-0.06264911592006683,
0.045186832547187805,
0.038445308804512024,
-0.05017737299203873,
-0.0008165054605342448,
0.01270386017858982,
-0.011568755842745304,
-0.004622936248779297,
0.035010021179914474,
0.003659800859168172,
-0.026250578463077545,
-0.03692403435707092,
0.0022925827652215958,
-0.020971650257706642,
0.03659592196345329,
-0.0030310801230371,
-0.052744265645742416,
-0.029338866472244263,
0.022467108443379402,
-0.04791250079870224,
-0.029383022338151932,
-0.04519741237163544,
-0.006795232649892569,
0.005798844154924154,
0.058398641645908356,
-0.0036781919188797474,
-0.012822545133531094,
-0.03910622000694275,
0.04038305953145027,
-0.02529197558760643,
0.004093930125236511,
-0.022670792415738106,
0.05395975336432457,
-0.03130500391125679,
-0.025103166699409485,
0.05533051863312721,
0.0017483190167695284,
0.015503584407269955,
0.014418761245906353,
0.016584645956754684,
-0.027614153921604156,
0.03132488951086998,
-0.022461576387286186,
0.00305629288777709,
0.0038891276344656944,
-0.01328311488032341,
0.05725517496466637,
-0.056090980768203735,
-0.04275527969002724,
0.01730385050177574,
0.03232026845216751,
-0.002540167421102524,
-0.003916786517947912,
-0.13180862367153168,
-0.05745415389537811,
0.015549495816230774,
-0.011503469198942184,
-0.027618972584605217,
-0.0052883196622133255,
-0.006424400955438614,
0.02357248216867447,
0.0025352267548441887,
-0.007561871316283941,
-0.040100812911987305,
-0.02962319366633892,
-0.011792952194809914,
-0.03915143385529518,
0.015603380277752876,
-0.05160877853631973,
0.009559952653944492,
-0.0011445379350334406,
0.028164653107523918,
0.009339146316051483,
0.001832087873481214,
-0.014956994913518429,
0.027303170412778854,
0.07229597121477127,
-0.04353688284754753,
0.02329072542488575,
-0.042458437383174896,
-0.012964094989001751,
-0.06110021099448204,
0.026663819327950478,
-0.0866900086402893,
0.0643569678068161,
0.03859041631221771,
-0.03576390817761421,
0.00046153520816005766,
0.07534265518188477,
-0.022101392969489098,
-0.03046245686709881,
0.02417297102510929,
-0.05255155265331268,
0.00744718499481678,
0.019736941903829575,
-0.01775786280632019,
-0.03728253021836281,
0.0005993631202727556,
0.06613487750291824,
-0.07397522032260895,
-0.030665531754493713,
0.02379017509520054,
0.0001372194819850847,
0.009669573046267033,
0.03829888254404068,
-0.013551430776715279,
-0.018112484365701675,
0.09324010461568832,
-0.01280455943197012,
-0.017982594668865204,
-0.07510551065206528,
0.03660639002919197,
0.0003277320647612214,
-0.017815908417105675,
-0.04250499606132507,
-0.037040792405605316,
0.03932280093431473,
-0.08123663067817688,
-0.06062717363238335,
0.023747248575091362,
0.0005970660713501275,
-0.014376526698470116,
-0.04854252561926842,
0.02084881253540516,
-0.028460541740059853,
0.02752353623509407,
0.017428258433938026,
0.008453870192170143,
0.04140102490782738,
-0.03127831220626831,
-0.036260467022657394,
-0.061372242867946625,
-0.05717938765883446,
-0.022014038637280464,
0.04080427810549736,
0.017298297956585884,
0.00008782814256846905,
0.001182451262138784,
-0.03918261080980301,
-0.012280557304620743,
-0.024343617260456085,
0.004278184846043587,
-0.07918604463338852,
-0.0007882638019509614,
-0.03552403301000595,
0.06194920092821121,
0.02871835045516491,
0.030113795772194862,
0.0035410167183727026,
0.014817547984421253,
-0.037671007215976715,
-0.010645953007042408,
0.008159905672073364,
0.008640293031930923,
-0.0329352505505085,
0.0119126932695508,
0.031588248908519745,
-0.07302569597959518,
0.008246649987995625,
-0.012385116890072823,
-0.017499759793281555,
-0.008733115158975124,
0.03591230884194374,
-0.0049302647821605206,
-0.1095295399427414,
-0.029979925602674484,
-0.0156402550637722,
-0.06703963130712509,
0.020915795117616653,
-0.055171575397253036,
0.03700743615627289,
0.0012799358228221536,
-0.037151437252759933,
0.04502931237220764,
-0.03176594153046608,
-0.04942499101161957,
0.016051433980464935,
0.02581973932683468,
-0.04020784795284271,
0.0015526080969721079,
-0.04768100753426552,
-0.012507746927440166,
0.03692599758505821,
0.005825946573168039,
-0.002836062805727124,
0.0040182690136134624,
-0.013246114365756512,
-0.03596671670675278,
0.03865177929401398,
-0.002780808135867119,
0.030669977888464928,
0.01239820197224617,
0.07133305072784424,
0.02298799902200699,
0.06763900816440582,
0.0394669808447361,
-0.017870135605335236,
-0.08255419880151749,
0.021354293450713158,
-0.05138640105724335,
0.010601741261780262,
-0.01580384373664856,
-0.040770258754491806,
-0.013144036754965782,
0.08745638281106949,
0.08840213716030121,
-0.08714111894369125,
0.04291791468858719,
0.029856767505407333,
0.01570441573858261,
0.03740209341049194,
0.034051455557346344,
-0.038159314543008804,
0.015480771660804749,
0.02243891917169094,
0.026033876463770866,
0.02000914141535759,
0.014793292619287968,
0.03685929253697395,
0.014500230550765991,
-0.0368971973657608,
-0.03235667571425438,
0.04446415603160858,
-0.057967934757471085,
0.02101830393075943,
-0.06209713593125343,
0.02143050916492939,
0.07341492176055908,
-0.0247856006026268,
0.04647945612668991,
-0.01264126691967249,
0.014148060232400894,
0.014762581326067448,
-0.040923964232206345,
0.07646206766366959,
-0.012486780062317848,
-0.04997321590781212,
-0.02867230400443077,
-0.035990044474601746,
-0.0341724269092083,
0.04842023923993111,
-0.01503463089466095,
-0.033678315579891205,
-0.012383378110826015,
0.0067395856603980064,
-0.03117562271654606,
0.03471202775835991,
0.014845733530819416,
-0.003303601173684001,
0.02755502052605152,
-0.04931552708148956,
0.041225723922252655,
-0.0037674629129469395,
0.056651771068573,
-0.07787513732910156,
0.047756586223840714,
-0.010145922191441059,
-0.04912889003753662,
-0.05722886323928833,
0.015038270503282547,
-0.023159349337220192,
0.014865678735077381,
0.010421447455883026,
0.05025181174278259,
-0.0024541739840060472,
0.019753852859139442,
-0.034296564757823944,
-0.023629458621144295,
-0.04338362067937851,
-0.004698274191468954,
0.0234989020973444,
0.035409267991781235,
-0.02970043756067753,
0.022592268884181976,
0.05341792479157448,
-0.019303765147924423,
0.021253250539302826,
-0.0029952393379062414,
-0.004426097963005304,
-0.030619487166404724,
0.05032308027148247,
-0.031611762940883636,
-0.04853023588657379,
0.03155339136719704,
-0.03632292523980141,
-0.023080551996827126,
-0.02017267234623432,
-0.021840950474143028,
-0.05431704595685005,
-0.030269838869571686,
0.009463704191148281,
-0.04160986468195915,
0.013714823871850967,
-0.020967045798897743,
0.01377311535179615,
0.002336903940886259,
-0.044263508170843124,
0.007716963067650795,
0.07041628658771515,
-0.013346806168556213,
-0.05179939791560173,
0.06746786832809448,
0.04280097782611847,
0.015134601853787899,
-0.01670408435165882,
-0.06498303264379501,
0.009478352032601833,
-0.010271367616951466,
0.08416281640529633,
0.043909233063459396,
0.0021855218801647425,
-0.004364973399788141,
-0.032345034182071686,
0.021305404603481293,
-0.011308732442557812,
-0.03345770388841629,
0.025793099775910378,
0.05070513114333153,
0.016308048740029335,
-0.032842643558979034,
0.033836621791124344,
-0.010333290323615074,
0.015674863010644913,
0.056603800505399704,
-0.05746328830718994,
0.029126334935426712,
-0.022218313068151474,
-0.036613643169403076,
0.001017105532810092,
-0.007536530960351229,
0.061143968254327774,
0.023545075207948685,
0.05494994297623634,
0.00043340501724742353,
-0.03545553609728813,
0.01943221129477024,
-0.01937045156955719,
0.029636532068252563,
0.02688036859035492,
-0.07072079926729202,
-0.007418493740260601,
-0.005930980667471886,
0.029195545241236687,
-0.02175888605415821,
0.03741466999053955,
0.03369065374135971,
-0.01874515414237976,
-0.04703577235341072,
-0.03692646697163582,
0.056991104036569595,
0.026293188333511353,
-0.0004224204458296299,
0.01858016662299633,
-0.05385447293519974,
-0.035244569182395935,
-0.005903943441808224,
0.022467156872153282,
0.05927266925573349,
-0.019115135073661804,
0.019689397886395454,
0.0072614108212292194,
-0.032922644168138504,
0.026868147775530815,
0.011239217594265938,
0.06527581065893173,
-0.023341476917266846,
-0.036668021231889725,
-0.05570372939109802,
-0.029524337500333786,
-0.03813309222459793,
0.0374884307384491,
0.03573988750576973,
0.002279458800330758,
-0.0029357606545090675,
-0.009771527722477913,
-0.03323739022016525,
0.007380317896604538,
0.03815203532576561,
0.036843616515398026,
-0.008940481580793858,
0.0033791365567594767,
-0.06171403080224991,
-0.018430490046739578,
-0.012496736831963062,
-0.02789735049009323,
0.019087472930550575,
0.03171928599476814,
0.035345349460840225,
-0.021177168935537338,
0.00797664001584053,
0.0317392535507679,
0.023867595940828323,
0.027833444997668266,
0.044608935713768005,
-0.020284993574023247,
0.044367965310811996,
-0.029307544231414795,
-0.07185862958431244,
0.028311772271990776,
-0.010890057310461998,
0.06971782445907593,
0.03641214594244957,
-0.027956070378422737,
-0.006714212708175182,
-0.002518450142815709,
-0.015738699585199356,
0.05030867084860802,
0.03770449757575989,
-0.0010851211845874786,
0.011557555757462978,
-0.07017020881175995,
0.016934463754296303,
-0.018215708434581757,
0.029542630538344383,
0.042974188923835754,
-0.06286755949258804,
-0.02384655363857746,
0.017536204308271408,
-0.03417327255010605,
0.020659124478697777,
-0.017337193712592125,
0.022183166816830635,
0.061389051377773285,
-0.0034732616040855646,
0.027446789667010307,
-0.02591078355908394,
0.017504634335637093,
0.034461572766304016,
0.014018523506820202,
-0.03382426127791405,
0.047159332782030106,
0.034127168357372284,
0.007838524878025055,
-0.04058146849274635,
-0.01788610778748989,
0.032727763056755066,
-0.01323719508945942,
-0.07761222869157791,
0.007069890853017569,
0.020645711570978165,
-0.048349883407354355,
-0.0037617329508066177,
0.07060931622982025,
-0.011073032394051552,
-0.004626728128641844,
0.03184282407164574,
0.01376215647906065,
0.03624361753463745,
-0.010893972590565681,
-0.017143651843070984,
-0.007598625496029854,
0.016328809782862663,
0.0009510110830888152,
-0.028321202844381332,
0.035470373928546906,
0.024135772138834,
-0.03769085928797722,
0.0025439676828682423,
0.03330286592245102,
0.05243779346346855,
-0.05229178071022034,
0.027359910309314728,
-0.029330333694815636,
-0.03273366019129753,
0.056174859404563904,
0.0017070639878511429,
-0.02093380317091942,
0.0028523197397589684,
0.011606025509536266,
0.03750714287161827,
-0.0546533577144146,
-0.0006822760333307087,
-0.04596887156367302,
-0.052933745086193085,
0.05694003403186798,
-0.014971408993005753,
0.05880451202392578,
0.03549984470009804,
0.044405654072761536,
-0.046067554503679276,
-0.04321557283401489,
-0.058494552969932556,
-0.05461021140217781,
-0.0068164002150297165,
-0.00770050473511219,
-0.016983622685074806,
0.03870845213532448,
0.0014634947292506695,
-0.004872151184827089,
0.03586864098906517,
-0.06733259558677673,
-0.011586829088628292,
0.019335197284817696,
-0.005506570916622877,
-0.006790835876017809,
0.01620296947658062,
-0.06448248028755188,
-0.005964675452560186,
-0.00907952431589365,
0.004613122902810574,
0.02612633816897869,
0.0188659206032753,
-0.00901829730719328,
-0.04050546512007713,
0.03818265348672867,
-0.01847117207944393,
0.06168089807033539,
-0.06681231409311295,
-0.010400298051536083,
-0.0008828708669170737,
-0.001778837526217103,
0.03151218593120575,
-0.06142592430114746,
0.017456267029047012,
0.011057448573410511,
-0.031050540506839752,
-0.009420464746654034,
0.030945707112550735,
0.008204460144042969,
0.012197201140224934,
0.061150144785642624,
0.021804125979542732,
0.051158830523490906,
-0.009623100981116295,
0.0295738335698843,
-0.014146066270768642,
0.05150792747735977,
-0.007543615996837616,
0.010917562060058117,
0.06931579113006592,
-0.045374635607004166,
-0.01219139713793993,
-0.04047532379627228,
0.011152050457894802,
0.005338032729923725,
0.0026607438921928406,
0.010989084839820862,
0.056455910205841064,
-0.053155723959207535,
-0.020324721932411194,
0.00433423463255167,
-0.0063339476473629475,
0.06180497258901596,
0.09863534569740295,
-0.08500736206769943,
0.03024083562195301,
0.04916337504982948,
-0.0025687506422400475,
-0.0328250378370285,
0.003090108744800091,
0.06742292642593384,
0.048956044018268585,
0.008280528709292412,
-0.04331079497933388,
-0.05039430409669876,
-0.042757369577884674,
0.0069892266765236855
] |
<p>I am looking for some more information about how to obtain electricity from heat directly. This e.g. involves the Seebeck effect, as I have found it is called, where a material produces a voltage across when heated in one end and having the other end slightly cooler. This should be the princip in measuring instruments etc., since just a small voltage is created.</p>
<p><a href="https://en.wikipedia.org/wiki/Thermoelectric_effect" rel="nofollow">This Wikipedia link</a> explains what the phenomenon is about. But it is not well explained in an understandable language (for me at least). And it doesn't dive deep enough into the reason.</p>
<p>Are there someone who can in a down-to-earth way explain how and why a voltage can be measured between the ends of a bar of a certain material, when it is heated in one end? My question regards what happens on the atomic scale - can heat push electrons or what?</p>
<p>Thanks.</p> | g163 | [
0.05649855360388756,
0.053584493696689606,
-0.021411603316664696,
-0.011242551729083061,
0.06041935086250305,
-0.00362830376252532,
-0.023065052926540375,
0.03460650518536568,
-0.060376349836587906,
0.03345613554120064,
-0.02802262455224991,
0.03497922793030739,
-0.03320421278476715,
0.019447864964604378,
0.04366118833422661,
-0.03258329629898071,
0.035073768347501755,
0.001246205996721983,
0.053459495306015015,
0.08338624238967896,
-0.03661710396409035,
-0.02337140403687954,
0.019603967666625977,
-0.076810322701931,
-0.03837475925683975,
-0.022881174460053444,
-0.01774274930357933,
0.024529332295060158,
-0.0146105345338583,
-0.05970991402864456,
-0.010187468491494656,
0.00043237899080850184,
0.08676222711801529,
-0.010998113080859184,
-0.05973924696445465,
-0.044419076293706894,
0.045896440744400024,
-0.017596270889043808,
-0.021460765972733498,
0.01310546975582838,
-0.048569392412900925,
-0.00009332939225714654,
0.009240688756108284,
-0.010394616052508354,
0.044294726103544235,
-0.019570304080843925,
-0.060452625155448914,
0.00499256607145071,
-0.009322574362158775,
-0.011610740795731544,
-0.002587634604424238,
-0.004056231118738651,
0.0725654661655426,
0.007540084421634674,
0.0005191460368223488,
-0.060313716530799866,
-0.02735213004052639,
0.014753175899386406,
0.13145416975021362,
0.005357629153877497,
0.06325158476829529,
0.06763686239719391,
-0.037806522101163864,
-0.004063961561769247,
0.057398490607738495,
0.010310479439795017,
-0.05815275013446808,
0.026168808341026306,
0.0017053515184670687,
0.031630873680114746,
-0.011442236602306366,
-0.03839722275733948,
-0.027388371527194977,
-0.05937425047159195,
0.04541001096367836,
-0.026246344670653343,
0.010347194038331509,
-0.018545323982834816,
0.042597703635692596,
0.01829051785171032,
-0.004536401014775038,
-0.06419844180345535,
0.01750212535262108,
0.008074132725596428,
0.011056370101869106,
-0.01193118654191494,
-0.0024379245005548,
0.022858794778585434,
-0.05034918710589409,
-0.04724425822496414,
0.0044273254461586475,
-0.005847746506333351,
0.07338390499353409,
-0.014554981142282486,
-0.014798876829445362,
-0.019184863194823265,
-0.011516586877405643,
0.05315050110220909,
0.021442055702209473,
0.01906086504459381,
-0.023096369579434395,
0.008747261948883533,
-0.011881905607879162,
0.032073959708213806,
-0.03818260505795479,
-0.003556413808837533,
0.02166949212551117,
0.016467193141579628,
-0.006544029340147972,
0.01357755996286869,
-0.04188268259167671,
-0.04285632446408272,
-0.042732398957014084,
0.0564078725874424,
0.002703003352507949,
0.027842490002512932,
0.04897298663854599,
0.01053099986165762,
-0.0400635227560997,
0.0478767454624176,
0.04501991346478462,
0.04909265413880348,
0.027591871097683907,
0.014634928666055202,
-0.040292564779520035,
0.05640759319067001,
0.04844074696302414,
-0.0021194785367697477,
-0.024738488718867302,
-0.006500201765447855,
0.000017919401216204278,
-0.0064462339505553246,
-0.031817566603422165,
0.00965973362326622,
0.039642125368118286,
0.033319853246212006,
0.014689430594444275,
0.012495798990130424,
0.0015895721735432744,
0.012006103061139584,
0.03499825298786163,
-0.05914809927344322,
-0.07242722064256668,
-0.06944314390420914,
-0.028010113164782524,
0.028077097609639168,
-0.04868476092815399,
-0.003461251500993967,
0.06829101592302322,
0.017179878428578377,
0.026356633752584457,
0.02200634963810444,
-0.007205480709671974,
-0.041926220059394836,
-0.004555015359073877,
-0.057440899312496185,
0.04361312836408615,
-0.008599236607551575,
0.03913755342364311,
0.011308598332107067,
-0.008067998103797436,
-0.006007677875459194,
0.014119411818683147,
0.0031828859355300665,
-0.011804231442511082,
-0.007080709096044302,
0.01834763213992119,
-0.041638631373643875,
0.03236757963895798,
-0.03760962933301926,
-0.056364547461271286,
-0.00841276254504919,
-0.011593326926231384,
0.0512758307158947,
0.013772214762866497,
0.06949780881404877,
0.06101231276988983,
0.03458482399582863,
0.042304255068302155,
-0.05391211062669754,
-0.08865561336278915,
-0.02806009165942669,
0.06662924587726593,
-0.04355638846755028,
0.0017985198646783829,
0.0006822271971032023,
0.010656139813363552,
0.033760856837034225,
0.025708086788654327,
-0.008210680447518826,
-0.05512047931551933,
-0.06262054294347763,
-0.0206651259213686,
-0.007753008045256138,
-0.0243969839066267,
-0.043798286467790604,
0.024799976497888565,
-0.00828291941434145,
-0.029181459918618202,
-0.07029516994953156,
-0.019555356353521347,
0.01186319813132286,
0.02524079941213131,
0.02752833627164364,
0.02111736312508583,
0.05552085116505623,
-0.0064262510277330875,
-0.044446911662817,
0.04235561937093735,
-0.007176203653216362,
0.00351596693508327,
0.01478047389537096,
0.06508000940084457,
-0.029561219736933708,
-0.011157877743244171,
0.03295808658003807,
-0.04141996055841446,
-0.042729008942842484,
-0.0026073618791997433,
0.011482015252113342,
0.02204935997724533,
-0.005324917379766703,
-0.013354530557990074,
0.01473307702690363,
-0.056986045092344284,
-0.02196407876908779,
-0.020527904853224754,
-0.0330079011619091,
-0.07305100560188293,
-0.00012870626233052462,
-0.05515996366739273,
0.014502163976430893,
0.04246955364942551,
-0.04861650615930557,
0.015099668875336647,
0.03178999945521355,
-0.013874244876205921,
-0.0020073549821972847,
-0.03517432138323784,
-0.010184026323258877,
-0.030871784314513206,
-0.0634940043091774,
-0.036665406078100204,
0.036299485713243484,
0.012206122279167175,
-0.027245335280895233,
0.06025436520576477,
0.02648714743554592,
0.018452977761626244,
-0.022319970652461052,
0.06309450417757034,
-0.021438922733068466,
-0.02961329184472561,
0.025126809254288673,
-0.029769884422421455,
-0.03378776088356972,
-0.006903190165758133,
0.06275162100791931,
-0.03363919258117676,
-0.05930252745747566,
-0.007677955087274313,
0.024751601740717888,
0.020745795220136642,
0.0307399220764637,
-0.021326618269085884,
-0.06333471089601517,
-0.020038478076457977,
-0.01713615655899048,
0.001768601592630148,
-0.02513384260237217,
-0.0022524113301187754,
0.0784996971487999,
-0.0051166885532438755,
-0.022220546379685402,
0.03809145838022232,
-0.03618958964943886,
0.045810502022504807,
-0.06616608053445816,
0.07741524279117584,
-0.08026377111673355,
0.005552258808165789,
-0.004550824407488108,
-0.01020872499793768,
0.01649225503206253,
-0.028317904099822044,
0.006040148437023163,
-0.03707199543714523,
-0.025799408555030823,
-0.003717196173965931,
0.037366319447755814,
0.05491407588124275,
-0.04074830561876297,
0.0488772913813591,
-0.00343822012655437,
-0.02768540568649769,
-0.02444915473461151,
0.04628502205014229,
-0.007662435527890921,
-0.026859579607844353,
-0.024142544716596603,
-0.010672001168131828,
-0.06000380963087082,
-0.05847589671611786,
-0.022492380812764168,
0.0019624531269073486,
0.0000633811141597107,
-0.05704379081726074,
-0.045842353254556656,
0.027619974687695503,
0.0037552895955741405,
-0.016210926696658134,
-0.04370816424489021,
0.04112658649682999,
0.011298537254333496,
-0.05969568341970444,
0.004936511162668467,
-0.055949218571186066,
0.015899041667580605,
0.022836988791823387,
0.00784064270555973,
0.025423642247915268,
-0.025040939450263977,
0.01280608307570219,
-0.014656073413789272,
0.016443679109215736,
0.014324254356324673,
0.042864080518484116,
-0.0464266873896122,
-0.006204071454703808,
-0.04134047403931618,
-0.0028604271356016397,
0.0018206223612651229,
-0.058046672493219376,
-0.0506834015250206,
-0.05196200683712959,
-0.04200190305709839,
-0.04877127334475517,
0.03421447426080704,
0.011515019461512566,
0.08041336387395859,
0.006028411909937859,
-0.02987300045788288,
-0.05694761499762535,
0.03378240019083023,
-0.012632696889340878,
0.01165345124900341,
-0.033407341688871384,
0.016713449731469154,
-0.04750179871916771,
-0.0274161659181118,
0.01708006113767624,
-0.014898516237735748,
0.0011458229273557663,
-0.0038319765590131283,
-0.05332876369357109,
0.013866228982806206,
0.02689274027943611,
0.027691202238202095,
-0.008818214759230614,
-0.00014076587103772908,
0.014503851532936096,
0.002778872847557068,
0.04149339720606804,
-0.0602983795106411,
-0.020920444279909134,
0.008371498435735703,
0.018650105223059654,
0.04456070810556412,
0.022214718163013458,
-0.05683162063360214,
-0.038985513150691986,
-0.03189418464899063,
-0.05532879754900932,
0.006421747151762247,
0.031000468879938126,
-0.013690195977687836,
0.04176201671361923,
0.04559846222400665,
-0.05997847393155098,
0.05077061802148819,
-0.03548780083656311,
0.05226229131221771,
0.06766500324010849,
0.04258304089307785,
0.02124921791255474,
-0.01651834324002266,
-0.07874850183725357,
0.03441131114959717,
-0.013598252087831497,
-0.07836859673261642,
-0.004160590935498476,
-0.01033263560384512,
-0.025638870894908905,
0.06489522755146027,
-0.023541847243905067,
-0.06889206171035767,
0.01590421050786972,
-0.03620690852403641,
0.03318050876259804,
0.0522402785718441,
0.025748634710907936,
-0.020742977038025856,
0.006160486023873091,
0.012520830146968365,
-0.048611003905534744,
-0.04840881749987602,
0.06793783605098724,
-0.0643811821937561,
-0.03783782199025154,
-0.044449202716350555,
-0.03139026090502739,
-0.017855016514658928,
0.011586686596274376,
-0.04062836617231369,
0.02534591406583786,
-0.030636174604296684,
0.06966596841812134,
-0.005689647514373064,
0.0776061937212944,
0.019154531881213188,
0.003854071954265237,
0.02032928727567196,
-0.006288950797170401,
0.01640515774488449,
-0.019134927541017532,
0.11102943122386932,
-0.030599795281887054,
-0.02676275186240673,
0.01362895779311657,
-0.016793889924883842,
-0.005683629773557186,
0.008102412335574627,
-0.04899691045284271,
0.02645619958639145,
-0.05500010401010513,
0.03269999101758003,
-0.05417807027697563,
0.10054076462984085,
-0.030986053869128227,
0.0417509563267231,
0.06872685253620148,
0.009490828961133957,
-0.023518342524766922,
-0.00889728032052517,
0.01053120382130146,
0.03527863696217537,
-0.02460590936243534,
-0.04262236878275871,
-0.050730641931295395,
-0.06855684518814087,
-0.07635535299777985,
-0.01648145541548729,
-0.06349212676286697,
-0.021015625447034836,
0.027229029685258865,
-0.014329494908452034,
0.01445469819009304,
0.003829680848866701,
0.012087377719581127,
-0.019116653129458427,
0.0014288974925875664,
-0.05610301345586777,
0.002768532373011112,
0.03385331854224205,
-0.00041936460183933377,
-0.0343920923769474,
-0.011102678254246712,
-0.007802821230143309,
-0.03200200945138931,
0.018486736342310905,
-0.008944782428443432,
0.04806045815348625,
0.010302004404366016,
0.02736729383468628,
0.046060845255851746,
-0.02067086286842823,
0.0174496378749609,
-0.047520801424980164,
-0.04303550347685814,
-0.07304927706718445,
-0.0023248104844242334,
0.03799717128276825,
0.03945378214120865,
0.03290807455778122,
-0.04205511137843132,
-0.023964591324329376,
-0.06748038530349731,
0.08709803968667984,
0.030532794073224068,
0.0039892857894301414,
0.005502678919583559,
0.04225851967930794,
-0.020024709403514862,
-0.028689691796898842,
-0.07856066524982452,
0.02055688574910164,
0.04119865596294403,
0.0027779857628047466,
-0.011478613130748272,
-0.006082199048250914,
0.030686454847455025,
0.046673163771629333,
0.0066192615777254105,
0.051071301102638245,
0.02065904438495636,
-0.0034801780711859465,
0.04927508905529976,
-0.0225849412381649,
0.024608762934803963,
-0.05198952183127403,
-0.045319925993680954,
0.03311340883374214,
-0.009935767389833927,
0.01332795899361372,
0.025613537058234215,
-0.004346989560872316,
-0.008468205109238625,
-0.027253201231360435,
-0.010288874618709087,
0.011685076169669628,
0.022801212966442108,
-0.03290871903300285,
-0.0032114540226757526,
0.0035900529474020004,
0.004739484749734402,
0.012919517233967781,
-0.05947007238864899,
0.04514145851135254,
0.03848438709974289,
0.04842332750558853,
0.026548534631729126,
0.04009215161204338,
0.03400161489844322,
0.03712724521756172,
-0.013641005381941795,
-0.010670891962945461,
0.004690706264227629,
0.012263053096830845,
-0.010116257704794407,
-0.006300870329141617,
0.04184103384613991,
-0.00856463797390461,
-0.021894866600632668,
0.05650633946061134,
0.056160103529691696,
-0.014439008198678493,
-0.00785363931208849,
-0.03150153160095215,
0.0593983456492424,
0.015379936434328556,
0.049246225506067276,
0.038160644471645355,
0.049138784408569336,
-0.004737416282296181,
0.01361616887152195,
-0.0022553594317287207,
0.04039620980620384,
-0.06288158893585205,
0.001146238762885332,
-0.021266095340251923,
0.07067830860614777,
0.045618847012519836,
0.06711280345916748,
0.016132676973938942,
-0.0014106997987255454,
-0.029640790075063705,
-0.018115030601620674,
0.0016522612422704697,
0.03372645005583763,
0.06958632916212082,
0.06464853882789612,
-0.024180637672543526,
-0.0012701906962320209,
-0.056584469974040985,
0.00891687348484993,
0.037707868963479996,
0.004831064958125353,
-0.02540651150047779,
0.00802959781140089,
0.011606293730437756,
0.010373189114034176,
0.021652111783623695,
0.00012592988787218928,
0.04181220009922981,
0.04062061384320259,
0.017944756895303726,
-0.044354166835546494,
-0.0011596021940931678,
0.03489142656326294,
-0.05087001249194145,
-0.031665753573179245,
-0.05843329802155495,
-0.006463884375989437,
0.021949829533696175,
-0.007688275538384914,
0.013492216356098652,
0.022879133000969887,
-0.014145249500870705,
0.009392492473125458,
0.07933588325977325,
-0.03278428316116333,
-0.07386933267116547,
0.0060856095515191555,
-0.04102106764912605,
0.007288726512342691,
-0.00895018596202135,
0.01276347041130066,
-0.0028180109802633524,
0.0061569311656057835,
-0.016087695956230164,
-0.03546008840203285,
0.012200462631881237,
-0.002035262295976281,
-0.05337289720773697,
-0.0338248610496521,
-0.028256189078092575,
-0.05649964138865471,
-0.03989594057202339,
0.05452679842710495,
0.007680274546146393,
-0.0358465202152729,
-0.04779449477791786,
0.01536360289901495,
0.018353203311562538,
0.033938344568014145,
0.01360391080379486,
-0.044104475528001785,
0.055092256516218185,
0.0706234946846962,
0.0498189851641655,
-0.02821776084601879,
0.03229066729545593,
0.017372747883200645,
0.03504418209195137,
0.005262239836156368,
0.0387367308139801,
0.030486540868878365,
-0.011642138473689556,
0.059078723192214966,
0.02951936051249504,
-0.020725904032588005,
-0.01861574314534664,
0.02012745290994644,
0.08098601549863815,
-0.02372300624847412,
-0.004794812761247158,
-0.02487334795296192,
0.028048204258084297,
-0.026269234716892242,
0.00762574328109622,
-0.019382599741220474,
-0.04739626869559288,
-0.06650050729513168,
0.03682653233408928,
-0.006697574630379677,
0.007031774148344994,
0.025270510464906693,
-0.025033608078956604,
-0.00020949289319105446,
-0.015603771433234215,
0.012523257173597813,
-0.008281437680125237,
0.04407743364572525,
0.052005358040332794,
0.026809658855199814,
0.061027806252241135,
-0.028156807646155357,
-0.033516112715005875,
0.006046465132385492,
-0.013711697421967983,
-0.008436297066509724,
-0.07903435826301575,
0.022872885689139366,
-0.003859793534502387,
-0.0020845907274633646,
0.0063352142460644245,
0.01480493601411581,
0.04042010009288788,
-0.02865259163081646,
-0.07607179135084152,
-0.03717890754342079,
-0.0013810782693326473,
0.009111016057431698,
-0.06211236119270325,
-0.015196348540484905,
-0.01907036080956459,
-0.03789910674095154,
0.04481525719165802,
0.003641166491433978,
0.044584985822439194,
-0.0006792892818339169,
0.02134421095252037,
-0.022439392283558846,
0.026508670300245285,
0.04285333305597305,
0.015878845006227493,
0.017172440886497498,
-0.013271876610815525,
-0.021136634051799774,
0.03142890706658363,
0.039725225418806076,
-0.008972815237939358,
0.004509154241532087,
0.0014886934077367187,
0.0016752569936215878,
0.017169028520584106,
0.00042140024015679955,
-0.02238844893872738,
0.0017539672553539276,
-0.0007380309398286045,
0.039708029478788376,
0.00860892329365015,
0.08253753930330276,
0.04606926068663597,
0.009026901796460152,
0.0018256009789183736,
-0.02811235748231411,
-0.0030163610354065895,
0.04666725918650627,
-0.00024886796018108726,
-0.01292862556874752,
0.021030215546488762,
-0.0006721843383274972,
-0.02268378809094429,
-0.026963770389556885,
0.03271864354610443,
-0.024289431050419807,
-0.0171221774071455,
0.03052457422018051,
0.01809075102210045,
0.09219343960285187,
0.03086281567811966,
0.012252534739673138,
-0.018833203241229057,
-0.03124580904841423,
0.015418088994920254,
0.05125240236520767,
-0.019387783482670784,
0.07036590576171875,
-0.012741301208734512,
0.04644704610109329,
0.004532749764621258,
-0.0056459843181073666,
-0.05855078250169754,
-0.019611112773418427,
-0.022613095119595528,
-0.08176027238368988,
0.06092848256230354,
-0.00708282645791769,
0.00034931505797430873,
-0.04689028859138489,
0.0016743572195991874,
-0.031988129019737244,
0.0017586768371984363,
0.014382525347173214,
-0.02930048294365406,
-0.0337495282292366,
0.010257739573717117,
0.0009268201538361609,
0.010421954095363617,
-0.07347873598337173,
-0.0016362721798941493,
0.021109605208039284,
0.04612800106406212,
-0.02120343968272209,
0.010554066859185696,
-0.01967190019786358,
-0.027898568660020828
] |
<p>As I was reading about the experimental arrangement for photoelectric effect, I saw a diagram that puzzled my knowledge of electrodes. I found that in the experimental setup the cathode of the photoelectric plate or emitter was connected to the positive terminal of the cell. Why is it so? How can a negative electrode be connected to positive terminal of a cell?</p>
<p>I read Wikipedia article on cathode and it said " In a device which consumes power, the cathode is negative, and in a device which provides power, the cathode is positive". What does this mean?</p> | g164 | [
0.012920553795993328,
0.0006969515816308558,
-0.02792271040380001,
0.06842780858278275,
0.03735500946640968,
0.01208264660090208,
0.001631704973988235,
-0.003507012501358986,
-0.04678269848227501,
0.0157969631254673,
-0.006417927797883749,
0.02391096018254757,
0.035370610654354095,
0.0380331315100193,
0.04253911226987839,
-0.023855989798903465,
0.04972156137228012,
0.03935530036687851,
0.08067119866609573,
0.03723927214741707,
-0.055512040853500366,
0.05234923213720322,
-0.090090811252594,
-0.00884274858981371,
-0.06977614760398865,
-0.008792087435722351,
-0.022628895938396454,
0.008672390133142471,
-0.010179626755416393,
-0.06586350500583649,
0.009448346681892872,
-0.06340526044368744,
0.04664035141468048,
0.059628259390592575,
-0.029512932524085045,
-0.0132727837190032,
0.05372157320380211,
0.05209200084209442,
-0.020267769694328308,
0.03536481782793999,
-0.0026546150911599398,
0.051663000136613846,
0.012732014060020447,
-0.008729570545256138,
-0.019166015088558197,
0.0014161830767989159,
-0.015119162388145924,
0.021022360771894455,
0.030973102897405624,
-0.04451413452625275,
-0.009112408384680748,
0.009963812306523323,
-0.003117429092526436,
-0.02546694502234459,
0.08574993908405304,
0.05686544254422188,
0.02371327206492424,
-0.04165050387382507,
0.029042566195130348,
0.006016729865223169,
-0.02587873302400112,
0.013610211201012135,
0.0038858919870108366,
0.01233996544033289,
0.0674322247505188,
-0.00941488053649664,
-0.018960455432534218,
-0.006678819190710783,
-0.01118001900613308,
0.043634332716464996,
-0.003815250238403678,
-0.026284243911504745,
-0.035075489431619644,
-0.03251441568136215,
0.051264673471450806,
-0.004831686615943909,
0.07173209637403488,
-0.07791925966739655,
0.047472383826971054,
0.04822363331913948,
0.021375903859734535,
-0.050552695989608765,
0.05260641127824783,
0.021480081602931023,
0.01315323170274496,
0.014368091709911823,
0.01422084216028452,
-0.009711317718029022,
-0.07776430249214172,
-0.004657668061554432,
-0.0036031745839864016,
-0.03646606579422951,
0.06421773880720139,
-0.0012230018619447947,
-0.038070064038038254,
0.036066439002752304,
0.06075651943683624,
0.03839481249451637,
-0.033053841441869736,
0.02011881396174431,
0.00030470965430140495,
-0.012088936753571033,
-0.0029418570920825005,
0.03331151604652405,
-0.027481861412525177,
-0.006322841159999371,
0.019418207928538322,
0.005357932765036821,
0.045707203447818756,
0.017661549150943756,
-0.05677736550569534,
-0.02639157511293888,
-0.0412476547062397,
-0.027076002210378647,
0.01455613598227501,
0.013858654536306858,
0.06209547445178032,
-0.051795609295368195,
-0.012351719662547112,
-0.01563407853245735,
0.015297701582312584,
0.06328392773866653,
-0.022541774436831474,
0.011860155500471592,
-0.011142365634441376,
-0.01447728555649519,
-0.010132993571460247,
-0.04127033054828644,
-0.009053802117705345,
0.07375089079141617,
0.04856328293681145,
0.0012269439175724983,
-0.05513753741979599,
0.008575533516705036,
0.07205121219158173,
0.03258763998746872,
0.04784652218222618,
-0.06219979375600815,
0.049390777945518494,
-0.011071261949837208,
0.00519780907779932,
0.02719653956592083,
-0.049940161406993866,
-0.01635303720831871,
-0.0034992974251508713,
-0.00866918545216322,
0.05082187429070473,
-0.0072890110313892365,
0.02891623228788376,
0.07145480811595917,
0.0475863479077816,
-0.0621572770178318,
-0.023203492164611816,
-0.043266430497169495,
0.03750009089708328,
-0.033042214810848236,
0.019895615056157112,
0.00023634864191990346,
0.02765798009932041,
0.021362964063882828,
0.03907529264688492,
0.01336249802261591,
-0.012474079616367817,
-0.0029629606287926435,
-0.038580335676670074,
-0.08785856515169144,
0.033987004309892654,
-0.01403490174561739,
-0.0026413416489958763,
-0.006520724389702082,
-0.004477806389331818,
0.01678539626300335,
0.0029362356290221214,
-0.009454185143113136,
0.06743435561656952,
0.0299348384141922,
0.000812395999673754,
0.023912709206342697,
0.024704713374376297,
0.037345632910728455,
-0.07490359991788864,
-0.0019976324401795864,
-0.024791158735752106,
-0.09168408066034317,
-0.02759791724383831,
-0.003882716642692685,
-0.048796646296978,
-0.04604068025946617,
-0.027581823989748955,
0.014958040788769722,
0.03628561645746231,
-0.03402198478579521,
0.008481265045702457,
0.021720165386795998,
-0.0603158138692379,
-0.04014446213841438,
-0.02951860800385475,
-0.010345958173274994,
0.026036886498332024,
-0.0790611132979393,
0.003138955682516098,
0.023842807859182358,
-0.004674925934523344,
0.05998437479138374,
0.01204772014170885,
-0.0621354803442955,
-0.04687870666384697,
-0.05932918190956116,
0.030091945081949234,
-0.02598380669951439,
-0.012014184147119522,
0.010006336495280266,
0.004444286692887545,
0.0009329537278972566,
-0.04964185878634453,
-0.03391873463988304,
-0.016180017963051796,
-0.01737896353006363,
-0.014858643524348736,
-0.05208325386047363,
-0.04529770091176033,
-0.021893443539738655,
0.015343288891017437,
-0.024116594344377518,
0.011402745731174946,
0.053464166820049286,
0.02603859081864357,
-0.013082858175039291,
-0.03924833610653877,
-0.009206699207425117,
-0.10457993298768997,
0.002679280936717987,
-0.003630120540037751,
-0.06812869757413864,
-0.004441179800778627,
0.028298629447817802,
-0.03249061480164528,
0.001679563894867897,
-0.05540027841925621,
-0.02602398581802845,
-0.025871263816952705,
-0.06772652268409729,
-0.01933511160314083,
0.019586985930800438,
-0.0527360737323761,
-0.024091951549053192,
0.028853952884674072,
0.0021723415702581406,
-0.022102702409029007,
0.06176154315471649,
0.047136686742305756,
-0.012633726932108402,
0.030370958149433136,
0.04908474534749985,
0.02185637317597866,
-0.08338157832622528,
-0.06160712242126465,
0.04944552481174469,
-0.05659592151641846,
-0.020923519507050514,
-0.017114441841840744,
-0.04380452260375023,
-0.06539718806743622,
0.02274787239730358,
-0.07871130108833313,
-0.007269822992384434,
-0.06626970320940018,
-0.007330006454139948,
0.07294564694166183,
-0.04465928673744202,
-0.03439818695187569,
0.0360947847366333,
0.04018706455826759,
-0.011017017997801304,
0.02688663825392723,
-0.019017674028873444,
-0.00669980188831687,
-0.031778398901224136,
0.039492856711149216,
-0.027514832094311714,
0.05696822330355644,
0.006571290548890829,
-0.07101157307624817,
0.027499012649059296,
-0.003526329528540373,
0.010749675333499908,
0.05640186369419098,
-0.031044363975524902,
-0.05977974086999893,
-0.002622866304591298,
0.0001017461545416154,
-0.04131503030657768,
0.00441207829862833,
-0.011290766298770905,
0.03320164233446121,
-0.01196139957755804,
0.05350430682301521,
-0.02184661477804184,
-0.06433698534965515,
-0.020497934892773628,
-0.023396164178848267,
0.006224960554391146,
-0.07386058568954468,
-0.01543300598859787,
0.06161779910326004,
0.05262766405940056,
-0.02895178087055683,
-0.015852943062782288,
-0.03688136488199234,
0.058160342276096344,
-0.05005815625190735,
-0.03948312625288963,
-0.04401694983243942,
-0.018787402659654617,
-0.022640354931354523,
0.04320145025849342,
-0.029905017465353012,
-0.002243499271571636,
0.01044145505875349,
-0.0028914897702634335,
0.0253896564245224,
0.03228713944554329,
-0.005393222905695438,
0.026203662157058716,
0.013420500792562962,
0.0011377668706700206,
0.022274170070886612,
-0.02693171799182892,
0.027898143976926804,
0.004148250445723534,
0.00977283250540495,
0.07486718893051147,
-0.05815121531486511,
-0.01616189442574978,
0.020404493436217308,
-0.02080906741321087,
-0.041910916566848755,
0.04547784477472305,
-0.031502220779657364,
-0.013365333899855614,
0.051748380064964294,
0.02663401886820793,
-0.06885244697332382,
-0.04206473007798195,
-0.010979893617331982,
-0.026080740615725517,
0.01703599840402603,
0.04292362183332443,
0.03750867396593094,
-0.012380462139844894,
0.024928273633122444,
0.05228988826274872,
-0.00694175623357296,
0.03756449744105339,
-0.07528450340032578,
0.01962018758058548,
-0.06094317138195038,
0.027527187019586563,
-0.08470762521028519,
0.04116981104016304,
-0.009868195280432701,
0.017145711928606033,
0.030086200684309006,
-0.001243854290805757,
0.007648814935237169,
0.01215269137173891,
-0.022807441651821136,
-0.008002838119864464,
-0.027515331283211708,
-0.015493949875235558,
0.011581779457628727,
-0.006645882502198219,
-0.02871575765311718,
-0.0004723372985608876,
0.04245791956782341,
-0.028327366337180138,
-0.015375467017292976,
0.007045380771160126,
-0.05384562164545059,
0.07446303218603134,
-0.013721656985580921,
0.000451805186457932,
0.060246121138334274,
0.0005197404534555972,
0.049401186406612396,
0.002492595696821809,
-0.03251609578728676,
0.0478728711605072,
-0.03365657478570938,
-0.011357619427144527,
-0.031918734312057495,
0.01191482599824667,
-0.03930306062102318,
-0.033356476575136185,
-0.012228524312376976,
-0.0019020549952983856,
-0.020818298682570457,
-0.004285454284399748,
0.048523496836423874,
-0.03352956473827362,
0.048427414149045944,
0.029069656506180763,
0.019591353833675385,
-0.03415834531188011,
-0.026963120326399803,
-0.008720495738089085,
0.03830894082784653,
-0.013869034126400948,
0.05176911503076553,
-0.0007315836846828461,
-0.020286161452531815,
-0.011647593230009079,
-0.043261680752038956,
-0.04462913051247597,
0.03513279929757118,
-0.029347237199544907,
0.024114467203617096,
0.012698352336883545,
0.08202224969863892,
0.05172411724925041,
0.05979039892554283,
0.04733065143227577,
0.007692006882280111,
-0.08534015715122223,
0.009736296720802784,
0.08108548074960709,
-0.02153913863003254,
-0.05800105631351471,
0.02684343419969082,
-0.03114159218966961,
0.012194416485726833,
0.014142489992082119,
0.01634305901825428,
0.03624403849244118,
-0.04292847961187363,
0.02079286053776741,
-0.01981966197490692,
0.11191550642251968,
0.017412282526493073,
0.03849900886416435,
0.08914674818515778,
-0.03957635164260864,
-0.029509656131267548,
-0.02836928889155388,
0.05813545361161232,
0.004360256250947714,
-0.06209727004170418,
0.01532734651118517,
0.001362356822937727,
-0.02715001255273819,
-0.005718734581023455,
0.024659888818860054,
-0.03129955753684044,
-0.030144749209284782,
0.016492092981934547,
-0.015801534056663513,
-0.014935123734176159,
-0.03758348897099495,
-0.006700377911329269,
0.05410146713256836,
-0.014086881652474403,
-0.02824990265071392,
0.03535694256424904,
0.05346227064728737,
0.060435809195041656,
-0.004132410511374474,
-0.039787422865629196,
-0.05583902448415756,
-0.059234268963336945,
-0.002251859987154603,
-0.024658529087901115,
0.024080313742160797,
0.028599439188838005,
0.06909000873565674,
0.005551532842218876,
-0.06966923922300339,
-0.009208663366734982,
0.012219511903822422,
-0.03723818063735962,
0.0029572886414825916,
0.025531141087412834,
0.03060377947986126,
-0.007352524437010288,
-0.04370518773794174,
0.038814131170511246,
-0.019224973395466805,
-0.05350116640329361,
0.020498519763350487,
-0.02537037990987301,
-0.03666716068983078,
-0.0015577934682369232,
-0.014367490075528622,
0.020867006853222847,
-0.02139453776180744,
-0.05057400465011597,
-0.007610621862113476,
-0.0029514103662222624,
0.03665034472942352,
-0.027183933183550835,
0.005371402483433485,
0.05003899335861206,
-0.02613137848675251,
-0.039427194744348526,
0.011503850109875202,
0.04241374880075455,
0.008114967495203018,
-0.004827272612601519,
-0.019703544676303864,
0.04811227694153786,
0.0031779552809894085,
-0.015005461871623993,
0.006060638464987278,
-0.05050987750291824,
0.019651353359222412,
0.004248255398124456,
0.0472472682595253,
-0.06102918088436127,
-0.018478307873010635,
-0.0038172199856489897,
0.04846156761050224,
0.016774069517850876,
0.008579359389841557,
-0.023908406496047974,
-0.03669106960296631,
0.00006074839984648861,
-0.003913681022822857,
0.0006673497846350074,
0.06769340485334396,
0.09963802248239517,
0.014815982431173325,
0.008262120187282562,
0.052092377096414566,
0.004310816526412964,
0.06938709318637848,
-0.06377420574426651,
-0.08503688126802444,
-0.003055495908483863,
-0.011387819424271584,
0.07766024023294449,
0.00583089841529727,
0.028608916327357292,
-0.03737761825323105,
0.03021364100277424,
-0.005695854779332876,
0.08290333300828934,
0.026781195774674416,
-0.019135233014822006,
0.03822379931807518,
-0.04179782792925835,
0.016944553703069687,
-0.02059067226946354,
0.013349032029509544,
0.046691831201314926,
0.013550665229558945,
-0.004979151766747236,
-0.008250545710325241,
0.007585740648210049,
-0.013843431137502193,
0.02348092943429947,
-0.1261407434940338,
0.017050765454769135,
0.04630446434020996,
-0.004538046661764383,
0.02101406641304493,
0.015339935198426247,
-0.01088088471442461,
-0.0020375545136630535,
0.03318807855248451,
0.005815071519464254,
-0.019704114645719528,
0.09206992387771606,
-0.0019989493303000927,
0.0077904765494167805,
-0.008334603160619736,
0.041465435177087784,
0.03508096933364868,
0.04217807203531265,
0.0595565028488636,
0.0027615816798061132,
0.03384196013212204,
0.01923643983900547,
0.026259275153279305,
-0.030240315943956375,
-0.0368354395031929,
0.02042984403669834,
0.026949932798743248,
-0.006282178685069084,
-0.009491241537034512,
0.004650237038731575,
-0.051911089569330215,
-0.0013760154834017158,
0.004053157288581133,
-0.023720258846879005,
0.02185572125017643,
0.02123463898897171,
-0.0009281769162043929,
-0.00905703380703926,
0.03882770985364914,
-0.007561104372143745,
0.007731696590781212,
0.020617585629224777,
0.0007682103896513581,
0.008449568413197994,
-0.027245745062828064,
0.0222255140542984,
0.0001320158044109121,
0.07021768391132355,
0.009597365744411945,
0.04761696979403496,
0.045661237090826035,
-0.009545650333166122,
0.03990998864173889,
-0.023005718365311623,
-0.05348977819085121,
0.058340366929769516,
-0.01781746745109558,
-0.024218516424298286,
-0.006534643936902285,
-0.018591349944472313,
0.07500843703746796,
0.00561757106333971,
-0.05743497610092163,
-0.008653547614812851,
0.006887171417474747,
0.02615996263921261,
0.05581824854016304,
0.0035175331868231297,
-0.003678401466459036,
0.0042600929737091064,
-0.0356278158724308,
-0.0341416597366333,
-0.016759736463427544,
-0.06514380127191544,
0.030988801270723343,
0.00886385515332222,
-0.023481054231524467,
0.0001118356449296698,
0.009999130852520466,
0.07443662732839584,
-0.011872478760778904,
-0.06030739098787308,
0.03620360419154167,
-0.005327384918928146,
0.03944384679198265,
0.016339102759957314,
0.011038430966436863,
0.0060616908594965935,
-0.006391475908458233,
-0.0017112171044573188,
0.019290169700980186,
-0.016037913039326668,
-0.014293608255684376,
-0.03445182368159294,
-0.010813373140990734,
0.025949621573090553,
0.018584119156003,
-0.023825569078326225,
-0.004435211885720491,
-0.022762341424822807,
-0.01996542327105999,
-0.01594139263033867,
-0.023934409022331238,
-0.06709595769643784,
0.02733793668448925,
-0.02359504997730255,
0.02922002226114273,
0.013272974640130997,
-0.0007722923764958978,
-0.04259175434708595,
0.0028490161057561636,
-0.03898165002465248,
-0.02510281279683113,
-0.0017998790135607123,
-0.012928912416100502,
-0.05891183391213417,
0.007588065695017576,
0.04836118966341019,
0.008591949008405209,
-0.006562747061252594,
-0.05255679041147232,
-0.01227712631225586,
-0.03690376132726669,
-0.020968012511730194,
-0.04159944877028465,
-0.014956967905163765,
-0.06231167912483215,
-0.030830174684524536,
-0.024173272773623466,
-0.00189198215957731,
-0.047836292535066605,
0.027920527383685112,
-0.05438700690865517,
0.004558825399726629,
-0.011008956469595432,
0.06403008103370667,
-0.0076254261657595634,
0.02879059687256813,
0.024451633915305138,
-0.009934278205037117,
0.04733491316437721,
0.0403171144425869,
-0.09262645244598389,
-0.028856761753559113,
0.04223053902387619,
0.04723266139626503,
-0.027918130159378052,
0.017690135166049004,
0.04126011207699776,
-0.04103365167975426,
-0.03070966899394989,
-0.01375377643853426,
0.01220529992133379,
0.028866952285170555,
-0.004465775098651648,
0.010915884748101234,
0.02884715422987938,
-0.006404475308954716,
0.024242857471108437,
-0.013797745108604431,
0.047406941652297974,
-0.0453939326107502,
0.01909136027097702,
-0.006703266873955727,
-0.02534514106810093,
-0.017677035182714462,
0.055076684802770615,
0.03054937534034252,
-0.011971191503107548,
0.022761603817343712,
0.019676296040415764,
-0.04129974916577339,
0.047967392951250076,
0.02332758903503418,
0.020038191229104996,
-0.023653943091630936,
0.0018981057219207287,
-0.004741813987493515,
0.015073884278535843,
0.02687300741672516,
0.011692479252815247,
0.036170609295368195,
-0.04741089046001434,
-0.018630055710673332,
-0.03435565531253815,
-0.00561003852635622,
-0.017216522246599197,
-0.005753034725785255,
0.021824905648827553,
0.027390025556087494,
0.0071471622213721275,
-0.01759720966219902,
0.012255842797458172,
-0.011786660179495811,
0.028008876368403435,
0.053555697202682495,
-0.038403745740652084,
-0.013097690418362617,
-0.021112417802214622,
0.028578082099556923,
0.007060709409415722,
-0.014037653803825378,
-0.010884691961109638,
0.02284912019968033,
-0.047227248549461365,
-0.05174839496612549,
0.012882145121693611,
-0.041308820247650146,
-0.047652460634708405
] |
<p>Regarding conservation of mass-energy <a href="http://en.wikipedia.org/wiki/Conservation_law" rel="nofollow">Wikipedia</a> says: <strong>"this is an exact law, or more precisely, has never been shown to be violated."</strong></p>
<p>However, regarding quantum fluctuations, Wikipedia says <a href="http://en.wikipedia.org/wiki/Quantum_fluctuation" rel="nofollow">here</a>: "<strong>That means that conservation of energy can appear to be violated, but only for small times</strong>".</p>
<p>I thought to resolve the two conflicting statements by proposing that the virtual particles from quantum fluctuations are created/destroyed from the "noise energy" of the uncertainty principle. Hence, the energy is already there. Is this correct?</p>
<p>If this is incorrect, how can we resolve the two?</p> | g4795 | [
0.05931144580245018,
-0.020279571413993835,
0.007473823148757219,
0.03793776035308838,
0.07154843211174011,
0.005289504304528236,
-0.007095102686434984,
0.024016140028834343,
-0.036346107721328735,
0.02853456698358059,
-0.006255007348954678,
-0.03852929174900055,
-0.018727337941527367,
0.029907040297985077,
-0.05984115228056908,
0.038897804915905,
0.09230860322713852,
0.012390360236167908,
-0.011218090541660786,
0.09368892759084702,
-0.054033972322940826,
-0.0464383102953434,
-0.04591044411063194,
-0.0016833029221743345,
-0.024044660851359367,
-0.009424664080142975,
-0.0045575411058962345,
-0.0100173344835639,
-0.03926894813776016,
-0.009274020791053772,
0.04615442082285881,
0.020674971863627434,
0.07911838591098785,
-0.05021843686699867,
0.003660611342638731,
-0.0017528889002278447,
0.04052716866135597,
-0.04687896743416786,
0.025813288986682892,
0.017969710752367973,
0.018138159066438675,
0.011035915464162827,
0.015157726593315601,
-0.021852366626262665,
0.012977941893041134,
0.012765701860189438,
-0.03447414189577103,
-0.012126841582357883,
-0.05135078728199005,
-0.004016314633190632,
0.04256555065512657,
0.03142574802041054,
0.048627134412527084,
0.0456530787050724,
0.039757538586854935,
0.038191769272089005,
0.03616606444120407,
-0.029087040573358536,
0.041042741388082504,
0.017511604353785515,
0.05781794711947441,
-0.008691205643117428,
0.017877725884318352,
0.04479507356882095,
0.04003438726067543,
-0.041967958211898804,
-0.07803390920162201,
-0.023397091776132584,
0.009205063804984093,
-0.0016133206663653255,
0.047554031014442444,
0.009162215515971184,
-0.04942980408668518,
0.0024355172645300627,
-0.00806459877640009,
0.037861183285713196,
0.025372490286827087,
0.026042306795716286,
-0.030602803453803062,
-0.014254494570195675,
-0.09374700486660004,
-0.019428132101893425,
0.02710149809718132,
0.01360323466360569,
0.047781169414520264,
-0.01994098536670208,
-0.03691748529672623,
0.02328798733651638,
0.024398747831583023,
-0.0045908186584711075,
-0.015081692487001419,
-0.02114878222346306,
0.0706619918346405,
-0.01390895340591669,
0.007445002906024456,
0.009713584557175636,
-0.039435405284166336,
0.06970707327127457,
-0.06799245625734329,
0.0034657760988920927,
-0.02886607125401497,
-0.04417513310909271,
0.014508158899843693,
0.003182879649102688,
-0.003447212977334857,
-0.007896593771874905,
-0.008565529249608517,
0.012846975587308407,
-0.0011182812741026282,
0.00179742940235883,
0.0011926757870242,
-0.06394796818494797,
0.023788029327988625,
-0.009049741551280022,
-0.034269608557224274,
-0.011831353418529034,
0.06419908255338669,
0.021780434995889664,
0.006040435750037432,
0.052125588059425354,
-0.017891818657517433,
0.004277417901903391,
0.043981071561574936,
0.04849071800708771,
-0.011865953914821148,
-0.011859274469316006,
0.020961390808224678,
0.02848094142973423,
0.07074970006942749,
-0.05724521726369858,
0.008000423200428486,
0.0010047039249911904,
-0.0036604725755751133,
0.030869880691170692,
0.028421923518180847,
-0.03280037268996239,
0.05585229769349098,
0.023678503930568695,
0.027890700846910477,
-0.03263567015528679,
-0.002886746544390917,
0.01400114968419075,
0.01702752895653248,
-0.02028602547943592,
-0.00539594329893589,
-0.012694107368588448,
-0.011853230185806751,
-0.03592003881931305,
0.038104601204395294,
0.0142836794257164,
0.026746660470962524,
0.08685380965471268,
-0.05876179784536362,
-0.03577068820595741,
-0.023574868217110634,
-0.013706337660551071,
-0.004313287790864706,
0.01187676377594471,
-0.051473792642354965,
0.019725188612937927,
0.011279796250164509,
-0.037383269518613815,
0.10616546869277954,
0.017541270703077316,
0.004728075582534075,
0.047687578946352005,
0.003833661787211895,
-0.07126406580209732,
-0.019140318036079407,
-0.028425278142094612,
-0.036027684807777405,
-0.008405608125030994,
-0.0016580005176365376,
-0.016339845955371857,
-0.009266508743166924,
0.05336969345808029,
-0.02374875545501709,
-0.07247141748666763,
-0.008252553641796112,
-0.0471016950905323,
-0.03582921251654625,
-0.01560008805245161,
0.025188259780406952,
-0.015915466472506523,
-0.0013993759639561176,
0.027905050665140152,
0.01955752819776535,
-0.0250408872961998,
-0.040566809475421906,
-0.015681028366088867,
-0.0469762422144413,
-0.012814829126000404,
-0.015468885190784931,
-0.004292068537324667,
0.0034832411911338568,
0.028689058497548103,
-0.0032520508393645287,
-0.04167977347970009,
-0.047400251030921936,
-0.0020560501143336296,
0.0163163710385561,
0.014088360592722893,
-0.010087995789945126,
-0.03043794073164463,
0.0007143573020584881,
0.03180857002735138,
-0.006722452584654093,
0.007723779883235693,
-0.06857877224683762,
-0.027764247730374336,
0.05422127619385719,
-0.017454097047448158,
-0.030927078798413277,
0.025987764820456505,
-0.013727398589253426,
-0.03632417693734169,
-0.0034996720496565104,
0.024674147367477417,
-0.008969737216830254,
-0.04001139849424362,
-0.02402617782354355,
0.043692849576473236,
0.06026436388492584,
-0.011984307318925858,
-0.006987252272665501,
0.021974626928567886,
-0.061742525547742844,
-0.06886520981788635,
-0.09603748470544815,
0.055253468453884125,
-0.012629386968910694,
-0.014442873187363148,
-0.03707478940486908,
0.026207532733678818,
0.03153157979249954,
0.075233094394207,
0.006077607627958059,
0.0071901604533195496,
0.0239393450319767,
0.03448314964771271,
0.02934224158525467,
0.010779319331049919,
-0.026844676584005356,
-0.01842401921749115,
0.016435861587524414,
-0.01993115246295929,
-0.014855138957500458,
-0.011058478616178036,
0.032290730625391006,
0.00787657592445612,
0.012956246733665466,
-0.0028331568464636803,
0.011203553527593613,
-0.02453509159386158,
0.04883769527077675,
-0.016766371205449104,
0.03512376919388771,
0.0009172791615128517,
-0.026268264278769493,
0.010943506844341755,
0.03912661597132683,
-0.055758215487003326,
0.022221742197871208,
0.017411572858691216,
0.03023604303598404,
-0.028676709160208702,
0.03378155082464218,
0.029026687145233154,
-0.06944403052330017,
-0.03906622529029846,
-0.03932386264204979,
0.053302690386772156,
-0.02491196244955063,
0.0640406683087349,
0.01775464601814747,
0.0005049137980677187,
-0.0052283466793596745,
0.0070595215074718,
0.027344301342964172,
0.01303218211978674,
-0.06517600268125534,
0.08164184540510178,
-0.060397014021873474,
-0.01128147542476654,
0.04992084950208664,
-0.055155977606773376,
-0.05144284665584564,
-0.0504656583070755,
0.01200229860842228,
0.00012005442113149911,
-0.01866687647998333,
0.017614388838410378,
0.03605463355779648,
0.012734177522361279,
-0.06183448061347008,
0.02939521335065365,
0.006555871106684208,
-0.03335263207554817,
-0.014011325314640999,
0.06108711287379265,
0.022279858589172363,
0.028630904853343964,
-0.025700196623802185,
0.05940010026097298,
0.058691758662462234,
0.06543708592653275,
-0.037085868418216705,
-0.005296237301081419,
0.03144894912838936,
-0.012390628457069397,
-0.03697622939944267,
0.0587877556681633,
0.0023298305459320545,
0.0026946496218442917,
-0.0032975836656987667,
0.011320957913994789,
-0.006801420822739601,
0.02718428336083889,
0.018088767305016518,
-0.021090256050229073,
-0.051546622067689896,
0.014825188554823399,
0.01206151396036148,
-0.007167445961385965,
0.01926695927977562,
0.01854522153735161,
-0.06767594814300537,
-0.0053895507007837296,
0.022367434576153755,
0.011506156995892525,
0.004888531286269426,
-0.0172859076410532,
-0.02526223286986351,
-0.07271266728639603,
-0.04535236209630966,
-0.061611030250787735,
0.017527049407362938,
-0.03328315168619156,
0.0391361229121685,
0.007555237039923668,
0.0038120090030133724,
0.04295659437775612,
0.0026275021955370903,
0.012976572848856449,
-0.008352626115083694,
0.053481828421354294,
-0.02683825045824051,
-0.03172921761870384,
-0.007784256245940924,
-0.031111251562833786,
0.09329909831285477,
0.01581205241382122,
0.01962597481906414,
0.024071257561445236,
-0.014850514009594917,
0.022482508793473244,
-0.04664738476276398,
0.03190625458955765,
0.016495930030941963,
-0.027228249236941338,
-0.007834645919501781,
-0.009685182012617588,
0.09300787001848221,
0.0018151061376556754,
-0.043180424720048904,
0.014890278689563274,
-0.033831361681222916,
0.03802932798862457,
0.04527631402015686,
-0.0025822818279266357,
-0.006183350924402475,
-0.014541232027113438,
-0.024879595264792442,
0.006671377457678318,
0.052265334874391556,
-0.007093376480042934,
0.09914562106132507,
0.00934024527668953,
-0.0482623428106308,
0.007297000382095575,
0.02893681637942791,
0.021358003839850426,
0.01044208463281393,
-0.003423599759116769,
0.013464996591210365,
0.016396883875131607,
-0.05713317170739174,
0.009701242670416832,
0.007681873627007008,
-0.012071913108229637,
-0.013175290077924728,
-0.031080326065421104,
-0.002632905263453722,
0.021408358588814735,
0.0041072433814406395,
0.0273490771651268,
0.025550588965415955,
-0.04155754670500755,
-0.014216860756278038,
0.027310125529766083,
0.021658360958099365,
0.059409547597169876,
-0.016586055979132652,
-0.010529246181249619,
0.007208627182990313,
0.012289839796721935,
0.01241474598646164,
-0.036907702684402466,
-0.04935809224843979,
-0.01708894409239292,
-0.04165569320321083,
-0.004471910186111927,
-0.016955504193902016,
-0.030506335198879242,
-0.014102555811405182,
-0.0014546200400218368,
-0.02069021202623844,
-0.05463544279336929,
0.060129277408123016,
0.007998977787792683,
0.027958407998085022,
0.014558481052517891,
-0.01718401536345482,
-0.02648426964879036,
-0.03765696659684181,
0.045515112578868866,
0.011576573364436626,
-0.020828034728765488,
-0.0024409221950918436,
-0.04575629532337189,
0.03322991356253624,
0.017635619267821312,
-0.010214601643383503,
0.038250017911195755,
-0.04192211106419563,
0.004675315227359533,
-0.046014804393053055,
0.006851095240563154,
0.03154465928673744,
0.04650118947029114,
0.08140598982572556,
-0.02150905132293701,
0.04774680733680725,
0.04099869355559349,
0.005295871291309595,
0.07063291221857071,
-0.025441819801926613,
0.0015392772620543838,
0.048873867839574814,
-0.02963172271847725,
-0.025695431977510452,
0.013577882200479507,
0.026940850540995598,
-0.015802400186657906,
0.02237999066710472,
-0.04707404226064682,
-0.06450235098600388,
0.02439062111079693,
0.020645584911108017,
0.03185900300741196,
-0.05709869787096977,
0.019832968711853027,
0.07163224369287491,
0.03656255453824997,
-0.0027843969874083996,
-0.0033591899555176497,
-0.06882023066282272,
-0.00938857439905405,
-0.07843253761529922,
-0.04000161960721016,
0.0277700237929821,
0.008314442820847034,
0.014379924163222313,
-0.00027736148331314325,
0.01804768480360508,
-0.039244644343853,
-0.0038849369157105684,
-0.020715858787298203,
0.022028714418411255,
-0.05871092900633812,
-0.05283549800515175,
-0.03551911190152168,
0.04452557489275932,
0.061871401965618134,
0.010725983418524265,
0.013651859015226364,
-0.004433549474924803,
-0.007220958825200796,
0.020870935171842575,
-0.011000181548297405,
0.009915410540997982,
0.04745713248848915,
0.003123941831290722,
-0.0030484171584248543,
0.09840118139982224,
-0.03595956414937973,
0.010222501121461391,
-0.020006723701953888,
-0.05348347872495651,
-0.04605550691485405,
-0.029052462428808212,
-0.04060892015695572,
0.0035923984833061695,
-0.03215203061699867,
-0.020524149760603905,
0.06550714373588562,
0.014714398421347141,
0.003670841921120882,
-0.004789417609572411,
-0.04161133989691734,
-0.025648275390267372,
-0.023174075409770012,
-0.0022297250106930733,
0.023197460919618607,
0.016308175399899483,
0.007204715628176928,
0.04647274687886238,
0.030786897987127304,
-0.040509384125471115,
-0.030114736407995224,
0.03660399466753006,
0.03330450505018234,
0.039990805089473724,
-0.00569671206176281,
0.006564687006175518,
-0.010106299072504044,
0.018234560266137123,
-0.06747011095285416,
0.017053434625267982,
0.07081757485866547,
-0.004764467943459749,
0.003652924671769142,
-0.027585206553339958,
0.03305291384458542,
-0.019405588507652283,
0.009068080224096775,
-0.04175880551338196,
-0.02201918326318264,
-0.0014640968292951584,
0.05220811814069748,
0.013377804309129715,
0.012583459727466106,
0.04947410523891449,
0.03640655055642128,
-0.019129756838083267,
0.0138217993080616,
-0.042146336287260056,
-0.039884284138679504,
0.013775776140391827,
-0.041396163403987885,
-0.018406715244054794,
-0.00014485804422292858,
-0.040350575000047684,
-0.012752917595207691,
0.005997684318572283,
0.028380611911416054,
0.018831418827176094,
-0.0019384912448003888,
-0.045568373054265976,
-0.009374264627695084,
0.01229365635663271,
0.008765043690800667,
0.04195479303598404,
-0.03644523769617081,
0.06734208017587662,
0.02368197962641716,
-0.017450222745537758,
-0.058702003210783005,
-0.0704946517944336,
0.07595500349998474,
-0.020256588235497475,
0.10644648224115372,
0.023768413811922073,
0.008951225318014622,
0.022414494305849075,
-0.0051087792962789536,
-0.010381177999079227,
-0.044615987688302994,
-0.06732820719480515,
-0.08253323286771774,
-0.011384163051843643,
0.01980540156364441,
0.009611748158931732,
-0.05469709634780884,
0.005484241992235184,
0.008225908502936363,
0.007905692793428898,
-0.001141510671004653,
0.06519865989685059,
0.053239479660987854,
0.03332525119185448,
-0.0225239098072052,
-0.04445143789052963,
0.014622468501329422,
-0.06379956752061844,
-0.025809580460190773,
0.020187389105558395,
-0.055915288627147675,
-0.059313416481018066,
0.01705412194132805,
0.0018523092148825526,
-0.046949148178100586,
-0.029209256172180176,
-0.0262316782027483,
0.044853173196315765,
-0.016230981796979904,
-0.07854694128036499,
0.07746391743421555,
-0.08213069289922714,
0.02405189722776413,
-0.05514548718929291,
0.03891279548406601,
0.007693479303270578,
-0.0005347935948520899,
-0.03379996493458748,
-0.013910045847296715,
-0.033544063568115234,
0.05501088872551918,
-0.008039245381951332,
0.009270201437175274,
0.006544121075421572,
0.01973058469593525,
0.016161199659109116,
0.03242103010416031,
0.06608249247074127,
0.012621227651834488,
0.0094554852694273,
-0.012085391208529472,
0.06457328051328659,
0.008638999424874783,
-0.011998921632766724,
0.005986138712614775,
0.043026018887758255,
0.05844203755259514,
-0.050468817353248596,
0.02908707596361637,
-0.04529997706413269,
-0.003980540670454502,
-0.011038005352020264,
-0.001059392699971795,
-0.045571811497211456,
0.029361380264163017,
0.11098998785018921,
0.014701991342008114,
-0.04835358262062073,
0.026021357625722885,
0.09568345546722412,
-0.008544761687517166,
-0.05409356206655502,
-0.004219383466988802,
0.009926341474056244,
-0.01535277534276247,
-0.018346795812249184,
-0.03445299342274666,
-0.00044061950757168233,
0.0641612783074379,
-0.02883797325193882,
-0.04564981162548065,
0.02991333231329918,
-0.0708477646112442,
0.009710549376904964,
-0.08713098615407944,
0.02853347547352314,
-0.06820064038038254,
0.030250826850533485,
0.014290962368249893,
-0.01523779146373272,
-0.04127508029341698,
-0.015357021242380142,
-0.04101390019059181,
0.038592081516981125,
-0.07674551010131836,
-0.04354466497898102,
-0.034837011247873306,
0.04385862499475479,
-0.04459232836961746,
-0.04965867102146149,
0.0574629008769989,
0.007897350005805492,
0.037833284586668015,
0.025899339467287064,
-0.04597870260477066,
-0.035222481936216354,
-0.023055855184793472,
0.011248605325818062,
0.016288066282868385,
-0.05692952871322632,
0.03992476686835289,
-0.031199069693684578,
0.008797935210168362,
-0.020754072815179825,
-0.01245131529867649,
0.005299846176058054,
-0.02988695167005062,
-0.03638404607772827,
-0.015994785353541374,
0.06230195611715317,
0.016259176656603813,
0.011925595812499523,
0.006570932921022177,
-0.017159640789031982,
0.025289492681622505,
-0.0012124759377911687,
0.0146593376994133,
0.01290140487253666,
0.038201406598091125,
0.050665564835071564,
-0.03349126875400543,
-0.031123138964176178,
-0.029888389632105827,
0.044871699064970016,
-0.06569746136665344,
-0.0060953558422625065,
0.005021536722779274,
0.047835271805524826,
-0.08443047106266022,
-0.01562388427555561,
-0.014899566769599915,
0.055059242993593216,
-0.021280702203512192,
0.011707015335559845,
-0.034626610577106476,
-0.09460841864347458,
-0.017088783904910088,
0.006308454554527998,
-0.009928235784173012,
-0.02519313059747219,
0.0451141819357872,
0.005183435510843992,
0.0018349685706198215,
-0.04579411447048187,
-0.021301286295056343,
-0.01923532225191593,
0.005122933071106672,
-0.00440928153693676,
0.07548267394304276,
0.033352095633745193,
0.020792042836546898,
-0.035631678998470306,
-0.010048099793493748,
0.03535877540707588,
-0.016650337725877762,
0.05203266441822052,
-0.03480970859527588,
-0.05307164415717125,
-0.043216295540332794,
-0.03025457076728344,
-0.01982228457927704,
-0.0056017558090388775,
-0.06023387610912323,
0.027139494195580482,
-0.006738065276294947,
-0.03166332095861435,
0.0741875097155571,
0.038189422339200974,
-0.06588561087846756,
0.06586424261331558,
-0.003502843203023076,
0.008531248196959496,
0.01857224851846695,
-0.005345504265278578,
-0.027563225477933884,
0.0014633846003562212,
0.00010088685667142272,
-0.04716873914003372,
-0.002889754716306925,
0.027023641392588615,
0.013757224194705486
] |
<p>My elementary school playground was made of asphalt and had a track painted on with white lines. While walking on the track, I noticed that cracks in the asphalt often followed the paint.</p>
<p>The conclusion I came to and that I still hold is that the white tape on the black asphalt causes a temperature difference due to the different amounts of sunlight absorbed and that this difference accounts for the cracking.</p>
<p>Is this correct? Is there more to the story?</p> | g4796 | [
0.06133860722184181,
-0.011177015490829945,
-0.008392196148633957,
-0.05553532764315605,
0.0334131196141243,
0.057421304285526276,
0.03776291012763977,
0.08348796516656876,
-0.017511360347270966,
-0.02424055151641369,
0.021505285054445267,
-0.043577007949352264,
0.005231604911386967,
0.0058253793977200985,
0.011799341067671776,
-0.024635639041662216,
-0.01052416954189539,
-0.05895266309380531,
0.04011410474777222,
-0.007961507886648178,
0.028196413069963455,
-0.022340264171361923,
0.006155745126307011,
-0.05662993714213371,
0.003961643669754267,
-0.0013908998807892203,
-0.01654919423162937,
-0.016936443746089935,
0.013369272463023663,
-0.03280838206410408,
0.05170772597193718,
-0.026137575507164,
0.008870590478181839,
-0.0443982370197773,
-0.046977099031209946,
-0.005877201445400715,
0.037630412727594376,
0.03309283033013344,
0.03256971761584282,
-0.04329977184534073,
0.05210822448134422,
-0.02260286919772625,
0.04804418981075287,
0.031542811542749405,
-0.014003204181790352,
-0.04588377848267555,
-0.10485398024320602,
0.01901107281446457,
0.021349867805838585,
0.011755718849599361,
0.009686357341706753,
0.006287028081715107,
-0.011456629261374474,
-0.025138959288597107,
0.008920187130570412,
-0.041012439876794815,
0.014417587779462337,
0.020086167380213737,
-0.008268959820270538,
0.05252722278237343,
0.0010901184286922216,
-0.012785905972123146,
-0.044871389865875244,
-0.037444815039634705,
0.0076759266667068005,
0.017003394663333893,
0.026541493833065033,
-0.03293921798467636,
0.06053467467427254,
0.026020629331469536,
0.0034924582578241825,
0.0013670893386006355,
0.01572084054350853,
0.025697868317365646,
0.024507705122232437,
0.011942217126488686,
-0.010695370845496655,
-0.027580667287111282,
0.01373522449284792,
0.09074549376964569,
-0.014968774281442165,
0.06542250514030457,
-0.0748273953795433,
0.10435879975557327,
0.04254027083516121,
-0.03561180457472801,
0.010473333299160004,
0.01645750179886818,
-0.10433273017406464,
0.028566185384988785,
0.037805650383234024,
-0.03267966955900192,
0.02867499738931656,
0.01921510510146618,
0.009204727597534657,
-0.0709085464477539,
0.027056150138378143,
0.07416879385709763,
-0.002707144943997264,
0.036589547991752625,
-0.0668700560927391,
-0.06526051461696625,
-0.00787847675383091,
-0.033056363463401794,
0.06324540078639984,
0.016669170930981636,
-0.027389045804739,
0.02614068239927292,
-0.041347358375787735,
-0.009374809451401234,
0.008659626357257366,
-0.019290242344141006,
-0.07141495496034622,
-0.03879927098751068,
0.0628853589296341,
0.03263585641980171,
0.014330624602735043,
-0.0525607205927372,
0.011559054255485535,
-0.05201418325304985,
-0.025872481986880302,
-0.028293551877141,
0.0019729938358068466,
0.059391945600509644,
0.054743390530347824,
0.0001820534816943109,
0.05574517697095871,
-0.004687915090471506,
-0.0003811579954344779,
0.023907875642180443,
-0.037176087498664856,
0.018372047692537308,
0.03737917169928551,
0.03711909055709839,
-0.0038256552070379257,
0.05780830979347229,
0.026664741337299347,
0.0876464918255806,
-0.024014834314584732,
0.029124796390533447,
0.006700271274894476,
0.024061433970928192,
0.0025321957655251026,
0.025529948994517326,
0.005408287514001131,
0.06168246641755104,
-0.031261831521987915,
0.02711273729801178,
0.05623498186469078,
0.004373534582555294,
-0.025753125548362732,
-0.011463163420557976,
-0.01611829549074173,
0.006574380677193403,
-0.020843505859375,
0.0322052538394928,
-0.05579906329512596,
-0.026128727942705154,
0.05578114837408066,
0.025345582515001297,
0.05610303208231926,
-0.038618359714746475,
0.004345509689301252,
0.024759573861956596,
-0.01874048262834549,
0.0012999282917007804,
0.003576122922822833,
0.03846204653382301,
0.0004605850554071367,
0.0023591690696775913,
-0.023289544507861137,
-0.02714286558330059,
-0.01481571327894926,
0.048112571239471436,
-0.03216705471277237,
0.004010985139757395,
0.04255511611700058,
-0.0527355782687664,
0.051328517496585846,
-0.0010620398679748178,
0.017446190118789673,
0.005090193822979927,
-0.0036336774937808514,
-0.0658041387796402,
0.05819106847047806,
0.03947281464934349,
-0.007200099527835846,
-0.09295973181724548,
-0.0978691577911377,
0.029966270551085472,
-0.06787020713090897,
-0.03944149613380432,
0.0008426515851169825,
0.020513232797384262,
-0.02648717164993286,
-0.0550483800470829,
-0.018465345725417137,
0.028131239116191864,
-0.05189371854066849,
0.05116169899702072,
0.02617909573018551,
0.027614576742053032,
-0.040633056312799454,
-0.03601185977458954,
-0.04877816140651703,
0.017222166061401367,
-0.05629519000649452,
0.002917747013270855,
0.026404492557048798,
-0.026076320558786392,
0.006485168356448412,
0.04864540696144104,
0.014142025262117386,
-0.027458414435386658,
-0.021899620071053505,
0.032825712114572525,
0.024811217561364174,
-0.022693093866109848,
0.005023130215704441,
0.03100227564573288,
0.034991759806871414,
0.039058852940797806,
0.04810994490981102,
-0.041021060198545456,
-0.01585996150970459,
0.02014206536114216,
-0.07664427161216736,
-0.02787802740931511,
-0.013264723122119904,
0.03764999285340309,
-0.056036800146102905,
-0.07203582674264908,
-0.00448291702196002,
0.07671036571264267,
-0.026230892166495323,
0.005973816383630037,
-0.026392772793769836,
-0.06061028689146042,
0.04282565042376518,
0.02771524339914322,
0.00189215037971735,
-0.019641315564513206,
-0.022578200325369835,
0.021943945437669754,
0.07377537339925766,
-0.014855174347758293,
0.013101408258080482,
-0.007428754586726427,
0.02221917174756527,
0.09693561494350433,
0.04083350673317909,
0.04036707431077957,
-0.0767502635717392,
-0.03444943204522133,
0.0328860804438591,
0.009593857452273369,
0.005968585144728422,
-0.005488080438226461,
-0.03526778146624565,
-0.049988262355327606,
-0.05549346283078194,
-0.06888776272535324,
0.0010194790083914995,
-0.017510944977402687,
0.003959876950830221,
0.019385632127523422,
-0.03853819891810417,
0.012961333617568016,
-0.04218275099992752,
-0.008092401549220085,
0.006468334700912237,
0.02741747535765171,
-0.01229534950107336,
0.01471719890832901,
-0.024477772414684296,
-0.012134592048823833,
0.012109564617276192,
0.03563113883137703,
0.010454186238348484,
-0.03392893448472023,
0.007957912050187588,
0.03904252126812935,
-0.0423138253390789,
-0.05262303724884987,
0.08980578184127808,
-0.0360494889318943,
-0.01286679320037365,
0.028280146420001984,
-0.002474906388670206,
0.05664103105664253,
0.015757398679852486,
0.0315740741789341,
0.03169916197657585,
-0.01331556960940361,
0.0007634439971297979,
0.02590450458228588,
-0.058845214545726776,
-0.03237481787800789,
0.009050313383340836,
0.023895876482129097,
-0.02211783453822136,
0.013919585384428501,
-0.04244343936443329,
-0.029336581006646156,
0.029663346707820892,
0.011059167794883251,
-0.02900032140314579,
-0.0002514459192752838,
0.03480023890733719,
-0.04632338881492615,
-0.02038625441491604,
-0.024540085345506668,
0.031966838985681534,
-0.010139668360352516,
-0.0552738718688488,
0.009281368926167488,
-0.04355299100279808,
-0.006585592869669199,
0.06688322126865387,
-0.04993174970149994,
0.012544631958007812,
0.027042068541049957,
-0.052124202251434326,
0.030126720666885376,
0.0036140100564807653,
0.013010513968765736,
0.057007744908332825,
-0.06908156722784042,
0.026653550565242767,
0.03056049905717373,
-0.004462825134396553,
0.01575746014714241,
-0.06869082897901535,
-0.020263202488422394,
0.031072232872247696,
-0.0000987075618468225,
-0.039387576282024384,
-0.020237548276782036,
-0.004083581734448671,
-0.023755993694067,
0.0053158910013735294,
0.01245947740972042,
-0.038408443331718445,
-0.02636142261326313,
-0.02623455785214901,
-0.004043702967464924,
0.04254620149731636,
0.002876624930649996,
-0.0344284251332283,
0.06880144774913788,
0.09817611426115036,
-0.00004467250982997939,
-0.062139008194208145,
-0.0768107920885086,
0.014069587923586369,
0.027185646817088127,
0.013819366693496704,
0.08089114725589752,
-0.008741769008338451,
0.01271146908402443,
0.059375569224357605,
-0.05692816525697708,
0.016085239127278328,
-0.04888634383678436,
0.04990328475832939,
0.0033072528894990683,
0.009831318631768227,
0.0017694055568426847,
0.012833149172365665,
0.01040965598076582,
-0.08211692422628403,
0.0713753029704094,
-0.025093069300055504,
0.032448284327983856,
0.002521912567317486,
0.03125012665987015,
0.05855612829327583,
0.005179612431675196,
0.012866758741438389,
0.029689138755202293,
0.010487349703907967,
0.008204438723623753,
-0.02838749811053276,
0.04301859065890312,
0.005098892841488123,
0.010051990859210491,
-0.04941919073462486,
0.004390585236251354,
-0.00970910768955946,
-0.01716824807226658,
-0.015784412622451782,
-0.009200532920658588,
-0.02045084536075592,
-0.03546367585659027,
0.030637461692094803,
-0.020431557670235634,
0.013288022950291634,
0.006845529656857252,
-0.00018334011838305742,
-0.023761194199323654,
-0.013544781133532524,
0.03910483792424202,
0.03151758387684822,
-0.005489396397024393,
-0.05151619762182236,
-0.051100291311740875,
0.031891871243715286,
-0.01961204595863819,
0.023479683324694633,
0.016400666907429695,
0.047068629413843155,
-0.01605260744690895,
-0.021251920610666275,
-0.0682762935757637,
0.028944816440343857,
-0.021249597892165184,
0.016209160909056664,
0.04259370639920235,
-0.01297767274081707,
0.014374954625964165,
0.008235241286456585,
-0.016893301159143448,
0.0024955759290605783,
-0.0064300899393856525,
0.06512856483459473,
0.031094316393136978,
-0.003719017608091235,
0.010633059777319431,
-0.020215224474668503,
-0.0373794287443161,
0.006774054374545813,
-0.0025866020005196333,
-0.1018824502825737,
-0.054658737033605576,
-0.023685486987233162,
0.010812755674123764,
0.004277313128113747,
0.013789053075015545,
0.03229345753788948,
-0.003933751955628395,
0.02803901396691799,
-0.0019462991040199995,
0.0008051063632592559,
-0.03814174234867096,
0.018497833982110023,
0.024648917838931084,
-0.04557153582572937,
-0.039808355271816254,
-0.01367660891264677,
0.05363733321428299,
-0.0512726791203022,
-0.009764999151229858,
0.05474979057908058,
0.014216561801731586,
-0.00021481295698322356,
-0.05396977439522743,
-0.0287559125572443,
-0.03442095220088959,
-0.005979070905596018,
0.05511585995554924,
-0.03844713419675827,
0.02199670858681202,
0.0596587248146534,
0.004992191214114428,
-0.0027701084036380053,
-0.013066486455500126,
0.028017574921250343,
0.013826827518641949,
-0.0076913912780582905,
0.04998273402452469,
-0.027378616854548454,
0.014176329597830772,
-0.01527020987123251,
-0.06080768629908562,
0.008931862190365791,
-0.03973052278161049,
-0.042972858995199203,
0.0051973736844956875,
0.027470365166664124,
-0.06249135360121727,
0.005312958266586065,
0.06428015977144241,
0.04343096539378166,
-0.040774453431367874,
-0.06537178158760071,
0.013224822469055653,
-0.03849419206380844,
0.028125783428549767,
0.0368756428360939,
-0.04186629876494408,
0.08972547203302383,
-0.005989988800138235,
0.004473401233553886,
0.09930887073278427,
-0.09185149520635605,
-0.08718769252300262,
0.007546590641140938,
0.03244828060269356,
0.037790581583976746,
-0.009628286585211754,
-0.00048071847413666546,
0.010582534596323967,
0.044338855892419815,
0.0381164625287056,
0.08680618554353714,
0.0218385998159647,
-0.04964226484298706,
-0.03348473086953163,
0.022717243060469627,
0.09302689880132675,
0.02325073815882206,
0.046102821826934814,
-0.015635807067155838,
0.023149169981479645,
0.0028684663120657206,
-0.007121220231056213,
-0.017757276073098183,
0.019005311653017998,
-0.0028903100173920393,
-0.05285049229860306,
-0.02418813481926918,
-0.019631285220384598,
-0.0225425623357296,
0.013318241573870182,
-0.01799972914159298,
-0.014911883510649204,
0.008812393061816692,
-0.025268832221627235,
-0.003996455576270819,
-0.006364200729876757,
0.039418596774339676,
-0.013259239494800568,
0.023222338408231735,
0.049316734075546265,
-0.008177606388926506,
-0.02690083719789982,
0.023032162338495255,
-0.02845040336251259,
-0.003176606958732009,
0.025454780086874962,
0.04181528836488724,
-0.06024029105901718,
0.06410661339759827,
0.028955550864338875,
-0.01053277775645256,
-0.043196383863687515,
-0.022561147809028625,
-0.03575354814529419,
0.03476347774267197,
-0.07191228121519089,
0.025474466383457184,
0.07771985977888107,
0.03965860605239868,
0.0023994850926101208,
0.01952473632991314,
0.008238248527050018,
-0.07497167587280273,
-0.03606073185801506,
-0.007406167685985565,
-0.02045891247689724,
0.06245167553424835,
-0.043338872492313385,
-0.047238465398550034,
0.05116719380021095,
0.03351416811347008,
0.001631526043638587,
-0.03642942011356354,
-0.0028334830421954393,
0.034627050161361694,
0.02709990367293358,
0.009409517981112003,
-0.0024624259676784277,
0.05936455354094505,
0.016376109793782234,
-0.04280208423733711,
0.010224558413028717,
-0.02147570624947548,
0.03103105165064335,
-0.017145996913313866,
-0.033379629254341125,
-0.013224427588284016,
0.012050767429172993,
-0.011824220418930054,
-0.05860535055398941,
0.007796927820891142,
-0.03814369812607765,
-0.015764066949486732,
-0.012168392539024353,
-0.012517822906374931,
0.0170156080275774,
-0.01316329650580883,
-0.008018266409635544,
-0.006265403237193823,
0.012888441793620586,
0.004418327938765287,
0.029505932703614235,
-0.031870950013399124,
0.023748096078634262,
0.017474180087447166,
-0.03474774211645126,
-0.0160343237221241,
-0.021529169753193855,
0.03058789297938347,
-0.05676247924566269,
0.01859234645962715,
-0.017790012061595917,
0.013293223455548286,
-0.01897081732749939,
0.025291549041867256,
-0.007903164252638817,
0.021534336730837822,
0.041182637214660645,
0.031238174065947533,
0.05178651213645935,
-0.02697340026497841,
0.047600939869880676,
0.05464606732130051,
0.027359211817383766,
0.015419685281813145,
-0.09337730705738068,
-0.0070955450646579266,
0.028910618275403976,
0.013291975483298302,
-0.0004419009783305228,
0.03494444116950035,
-0.0016746019246056676,
-0.04499887302517891,
-0.012951583601534367,
-0.014084961265325546,
0.03423577919602394,
-0.0309609342366457,
0.02028384990990162,
-0.03663792088627815,
0.03152093663811684,
0.003025974379852414,
0.02013345994055271,
0.022097701206803322,
-0.0154185201972723,
-0.05940498411655426,
0.013113786466419697,
-0.02177993394434452,
0.018579958006739616,
-0.012655477039515972,
0.06307463347911835,
-0.03324323147535324,
0.04990396276116371,
0.007714077364653349,
0.047967664897441864,
-0.03643044829368591,
0.009197356179356575,
0.029358457773923874,
-0.037714678794145584,
-0.03575670346617699,
0.0018917903071269393,
0.0047480203211307526,
0.022472066804766655,
-0.06043074652552605,
-0.01360287331044674,
0.06611895561218262,
-0.005991150625050068,
-0.07178617268800735,
-0.05334968492388725,
-0.0626954659819603,
0.007258008234202862,
-0.014593287371098995,
0.017979804426431656,
0.007444628514349461,
0.05860140547156334,
-0.03646362945437431,
-0.017524000257253647,
0.044464245438575745,
0.006397448945790529,
0.048358116298913956,
-0.002378089353442192,
0.03672423213720322,
0.008257943205535412,
-0.02701551280915737,
0.037648845463991165,
0.04056107997894287,
0.01572994515299797,
0.03157944977283478,
-0.021534498780965805,
-0.026698853820562363,
0.005451146513223648,
0.005688966251909733,
-0.015254458412528038,
-0.037997882813215256,
-0.008775101974606514,
-0.01479440089315176,
-0.02658724971115589,
-0.010306007228791714,
0.040791105479002,
-0.044452451169490814,
-0.0030754271429032087,
0.020764749497175217,
-0.022389071062207222,
-0.011512426659464836,
0.015137435868382454,
-0.019527848809957504,
-0.019617492333054543,
-0.06077326461672783,
-0.011061066761612892,
-0.016091477125883102,
0.0729784369468689,
0.0070503028109669685,
0.013011201284825802,
-0.017922166734933853,
-0.03503521904349327,
-0.054029352962970734,
-0.01181604154407978,
0.016794130206108093,
0.002687341533601284,
0.044370874762535095,
0.068094402551651,
-0.08010657131671906,
-0.030324943363666534,
-0.011639231815934181,
-0.06463325023651123,
-0.016954364255070686,
0.002088809385895729,
0.00981326773762703,
0.00561943044885993,
-0.01880662515759468,
0.01845335215330124,
-0.025282856076955795,
-0.00871253851801157,
0.05505568906664848,
-0.07961658388376236,
0.023428374901413918,
0.01612120307981968,
-0.030888652428984642,
0.02055756375193596,
0.003843862097710371,
-0.049307163804769516,
-0.018846509978175163,
0.06032562628388405,
0.060521263629198074,
-0.0027816174551844597,
-0.024647695943713188,
0.018944919109344482,
-0.0013236862141638994,
0.017906147986650467,
-0.003742521395906806,
-0.01724419742822647,
-0.031153185293078423,
-0.007896256633102894,
0.0151217607781291,
0.0604662261903286,
0.0008475412614643574,
-0.021149666979908943,
-0.03519931435585022,
-0.015362771227955818,
-0.059282511472702026,
-0.00025324715534225106,
-0.000025301886125816964,
-0.004518278408795595,
-0.02497308887541294,
0.002910998649895191,
0.03122233971953392,
-0.032909564673900604,
-0.05073908716440201,
-0.020948639139533043,
-0.01808927394449711,
-0.05591556429862976,
-0.017761534079909325,
0.00896536000072956,
0.04175770655274391,
-0.011403003707528114
] |
<p>The <a href="http://en.wikipedia.org/wiki/Gibbons%E2%80%93Hawking%E2%80%93York_boundary_term" rel="nofollow">Gibbons-Hawking-York term</a> which supplements the Einstein-Hilbert action is,</p>
<p>$$S_{GH} = \frac{1}{8\pi G} \int_{\partial M} d^3 x\sqrt{-h} \, K$$</p>
<p>where $\partial M$ is the boundary of the manifold $M$, $K$ is the trace of the extrinsic curvature, and $h_{\mu \nu}$ is the induced metric on the boundary of the manifold. My questions are:</p>
<ol>
<li><p>Is there a general formula for the metric $h_{\mu \nu}$ in terms of the metric $g_{\mu \nu}$ of the manifold M?</p></li>
<li><p>Is there a general formula for the inward/outward normal?</p></li>
</ol> | g4797 | [
0.015532133169472218,
0.027839986607432365,
-0.034698765724897385,
-0.00021600247418973595,
-0.01941796764731407,
0.02140119858086109,
0.032144322991371155,
0.010984363965690136,
-0.03844885155558586,
0.0068318904377520084,
0.01670277677476406,
0.028963854536414146,
0.009088181890547276,
0.016357891261577606,
-0.01063468400388956,
-0.030478252097964287,
0.017123619094491005,
-0.04585282504558563,
-0.013111798092722893,
0.026346618309617043,
-0.059329643845558167,
0.016934895887970924,
-0.02443505823612213,
0.017966415733098984,
0.08046375215053558,
-0.03984791785478592,
0.07242725044488907,
-0.022414829581975937,
-0.04743792861700058,
-0.014167035929858685,
0.03126539662480354,
0.02693539299070835,
0.019652461633086205,
-0.0323924794793129,
0.0007191809709183872,
0.07675877213478088,
0.012636319734156132,
0.04074918106198311,
0.009760958142578602,
-0.0018792577320709825,
0.05223323404788971,
-0.08595255017280579,
0.018986040726304054,
0.045173414051532745,
0.008385339751839638,
0.04451005905866623,
-0.02464289218187332,
0.007045608013868332,
0.0518098808825016,
-0.022906219586730003,
-0.06846072524785995,
0.08946865051984787,
0.0060132527723908424,
-0.04743633419275284,
-0.0037253384944051504,
-0.0004124599799979478,
-0.017110487446188927,
-0.02384456992149353,
0.028181802481412888,
0.01012769527733326,
-0.03004385158419609,
-0.041239067912101746,
0.0014893091283738613,
0.021843545138835907,
0.02333051711320877,
-0.058859311044216156,
-0.0431719534099102,
-0.0679139494895935,
-0.007391680497676134,
0.03594430163502693,
0.04009920731186867,
-0.0175680723041296,
0.06459999084472656,
0.030397793278098106,
-0.03165704011917114,
0.0017496910877525806,
0.030437853187322617,
0.03109346702694893,
0.05217761918902397,
0.005756238009780645,
-0.028925782069563866,
-0.0466199591755867,
0.034352656453847885,
-0.06822387129068375,
0.08582314848899841,
0.05325085669755936,
0.008394947275519371,
0.03614524379372597,
-0.03845059871673584,
-0.008495938032865524,
-0.002924080938100815,
-0.022939598187804222,
-0.02424664795398712,
0.0036839547101408243,
0.014603570103645325,
0.016663286834955215,
-0.027730846777558327,
-0.006567300297319889,
-0.048359766602516174,
-0.00027001925627700984,
-0.027857284992933273,
-0.0015569613315165043,
0.04799269884824753,
-0.018007410690188408,
0.00808676891028881,
0.005710597150027752,
0.0840831845998764,
-0.01413270365446806,
0.006758886389434338,
0.017846569418907166,
-0.03702115640044212,
-0.004734134767204523,
-0.020570063963532448,
-0.03522831201553345,
0.007678071036934853,
-0.0386698953807354,
0.003341442672535777,
-0.06655990332365036,
-0.016628853976726532,
0.03850777447223663,
0.0407821349799633,
0.006824215408414602,
-0.02280152030289173,
-0.03763488680124283,
-0.01679658517241478,
0.0350956916809082,
0.020787348970770836,
-0.005694144871085882,
0.04050176963210106,
0.011081273667514324,
0.051952168345451355,
0.015734508633613586,
0.028323328122496605,
0.01593136042356491,
-0.040795695036649704,
0.03416293486952782,
0.03232719004154205,
0.05277969315648079,
-0.012032292783260345,
-0.032227303832769394,
-0.03741908445954323,
-0.0845789760351181,
0.0272133219987154,
-0.01806376688182354,
-0.059029243886470795,
0.07169659435749054,
-0.0017011426389217377,
-0.07316963374614716,
0.04405735060572624,
-0.01686687394976616,
0.027953045442700386,
0.08999369293451309,
-0.004352561663836241,
-0.005363491829484701,
-0.00473300414159894,
0.0016820664750412107,
-0.029804859310388565,
-0.024211082607507706,
-0.004330267198383808,
0.008691608905792236,
0.08415040373802185,
-0.017287351191043854,
0.02961234375834465,
0.07125348597764969,
-0.06810015439987183,
-0.004254298284649849,
-0.03396766632795334,
-0.022939831018447876,
0.00053928152192384,
-0.08615528792142868,
0.0071637495420873165,
-0.004127290099859238,
0.012783212587237358,
0.028307391330599785,
-0.005371966399252415,
0.05030829459428787,
0.006765051279217005,
-0.01893427036702633,
0.025485508143901825,
-0.004016104619950056,
-0.0250267144292593,
-0.007276287768036127,
0.05122145637869835,
-0.06070534139871597,
-0.004401577636599541,
-0.055348582565784454,
-0.028884997591376305,
-0.012823806144297123,
-0.00603635236620903,
0.05506821349263191,
-0.018114350736141205,
0.015720680356025696,
0.04829902946949005,
0.013041974976658821,
-0.009208738803863525,
0.017216039821505547,
0.07540566474199295,
-0.004588989540934563,
-0.004128364846110344,
0.024540307000279427,
-0.017340010032057762,
0.021040484309196472,
-0.006201523821800947,
-0.04705161973834038,
0.03240426257252693,
-0.006928083952516317,
0.038286417722702026,
0.0088652940467,
0.015862762928009033,
-0.017519129440188408,
0.015260263346135616,
-0.07926575839519501,
-0.0056236060336232185,
0.03043300099670887,
0.005544724874198437,
0.004927811678498983,
-0.02067667432129383,
-0.009726381860673428,
-0.012308877892792225,
0.03347639739513397,
-0.0027804793789982796,
0.040805503726005554,
0.00646934425458312,
0.011773157864809036,
-0.002706692321226001,
0.009656371548771858,
0.011530570685863495,
-0.017488282173871994,
-0.012668201699852943,
0.049002159386873245,
-0.04370245710015297,
-0.07151208072900772,
-0.004317073617130518,
-0.03330203518271446,
0.025163892656564713,
-0.02649773471057415,
-0.004010278731584549,
-0.030853748321533203,
0.006990359164774418,
0.04437173157930374,
0.018703505396842957,
0.019895056262612343,
-0.047491833567619324,
-0.0038607302121818066,
-0.022269513458013535,
-0.0029556569643318653,
0.04827228561043739,
-0.02777070738375187,
-0.03887038677930832,
-0.0026524332351982594,
0.005141064524650574,
0.0174137894064188,
-0.004606676287949085,
-0.005748341325670481,
0.029933761805295944,
-0.002328466158360243,
-0.07896551489830017,
-0.04014571011066437,
-0.1005023792386055,
-0.06502694636583328,
0.013033696450293064,
-0.07961109280586243,
0.024907058104872704,
-0.0014948309399187565,
-0.08767487853765488,
-0.04508526250720024,
-0.01309621799737215,
-0.0020979600958526134,
-0.010498307645320892,
0.035164427012205124,
0.015567791648209095,
0.05457590892910957,
0.01349599752575159,
0.04209931939840317,
-0.03850240632891655,
-0.027785765007138252,
-0.04946422949433327,
-0.032595448195934296,
0.03721008449792862,
-0.02816152013838291,
-0.04633551090955734,
-0.01205777283757925,
-0.027672791853547096,
-0.03885878995060921,
0.04773387685418129,
-0.09138628095388412,
-0.0198261309415102,
0.05167101323604584,
-0.016156891360878944,
0.03386232629418373,
0.00470372661948204,
-0.004125626757740974,
-0.020780546590685844,
0.045016661286354065,
-0.0003214206371922046,
-0.00802183710038662,
0.005035498645156622,
0.04016105830669403,
-0.006339538376778364,
0.035185281187295914,
0.010827218182384968,
-0.08832576870918274,
-0.05616148188710213,
-0.018977100029587746,
-0.036320820450782776,
0.005713303107768297,
0.027953898534178734,
-0.09593366086483002,
0.016530590131878853,
-0.02463548816740513,
0.0411437563598156,
0.050332196056842804,
0.011279990896582603,
-0.019435646012425423,
-0.0038508931174874306,
0.03870997577905655,
0.0006512464606203139,
-0.02447029948234558,
-0.013246390037238598,
0.01808469370007515,
-0.040689315646886826,
0.008878299035131931,
-0.04855414107441902,
0.0010341714369133115,
0.015291270799934864,
0.041924312710762024,
-0.020955421030521393,
0.01147645153105259,
-0.042630553245544434,
-0.018952658399939537,
-0.02054624632000923,
-0.06138794869184494,
0.010726405307650566,
0.024046849459409714,
-0.041611090302467346,
-0.014676211401820183,
-0.0076056597754359245,
0.019984684884548187,
0.0456550270318985,
-0.003397128777578473,
0.03165043890476227,
-0.03903811424970627,
-0.04066557437181473,
0.058953918516635895,
-0.01633588597178459,
-0.07440938800573349,
0.017490282654762268,
0.06251310557126999,
-0.049386266618967056,
0.006203001830726862,
-0.03315926715731621,
-0.03492511436343193,
0.019506080076098442,
-0.011477376334369183,
0.026814153417944908,
-0.03462874889373779,
-0.0016234340146183968,
0.06960052996873856,
0.053328774869441986,
-0.015496749430894852,
0.001831746194511652,
-0.053550343960523605,
-0.033412590622901917,
0.09963909536600113,
0.008913028985261917,
-0.04221807047724724,
0.03614042326807976,
-0.015635160729289055,
-0.03176585212349892,
0.009721726179122925,
0.06129390373826027,
0.014329832047224045,
0.03294139355421066,
0.01374125201255083,
-0.0314481295645237,
-0.015072787180542946,
-0.004895337857306004,
0.0002847115683835,
-0.03037644363939762,
0.003808647859841585,
-0.020488081499934196,
0.0647759884595871,
0.04689592868089676,
0.039081357419490814,
0.041181571781635284,
-0.01792076602578163,
-0.003512779949232936,
-0.039828576147556305,
0.03058801405131817,
-0.025709452107548714,
-0.051959823817014694,
-0.019516626372933388,
0.031597983092069626,
-0.03429217264056206,
0.021079350262880325,
0.0011300717014819384,
0.0009436021209694445,
0.014910366386175156,
-0.06572170555591583,
0.05026330426335335,
0.029500311240553856,
-0.010564608499407768,
-0.007310916669666767,
0.025947926566004753,
-0.019404124468564987,
-0.05159127712249756,
0.038291268050670624,
-0.016848286613821983,
-0.004247873555868864,
0.021759290248155594,
-0.005992240272462368,
-0.06251207739114761,
0.005098526831716299,
-0.01760404370725155,
0.0383870005607605,
-0.04301060736179352,
0.05935550481081009,
-0.021130522713065147,
-0.08034790307283401,
-0.031011782586574554,
0.01193477027118206,
-0.00705448305234313,
0.06341283768415451,
0.0432078093290329,
-0.01862104795873165,
0.0207572840154171,
0.025897132232785225,
-0.00036022262065671384,
-0.006997661665081978,
0.015256972052156925,
0.004894089885056019,
-0.009517739526927471,
-0.04633353650569916,
0.06556075811386108,
-0.06297513097524643,
0.0538845993578434,
-0.026616739109158516,
0.04596026986837387,
0.0022476613521575928,
-0.0486874133348465,
0.013088749721646309,
0.02267836593091488,
0.009615792892873287,
-0.023761821910738945,
0.020296629518270493,
0.005361889023333788,
0.006483934819698334,
-0.03146333619952202,
-0.007298585493117571,
-0.04552021250128746,
-0.01695358194410801,
-0.0065774256363511086,
-0.008031711913645267,
-0.005881895311176777,
0.005366732366383076,
0.040171604603528976,
0.0034748355392366648,
0.027901573106646538,
-0.013793403282761574,
-0.016245655715465546,
0.005643890704959631,
-0.012861307710409164,
-0.009024075232446194,
0.03270963206887245,
0.03353727236390114,
0.0015129215316846967,
-0.06513924151659012,
0.055333543568849564,
0.030802035704255104,
0.012689411640167236,
0.04333316907286644,
0.04770375043153763,
0.011486589908599854,
-0.03275945410132408,
0.03522901609539986,
0.046901438385248184,
-0.038072433322668076,
-0.01180415228009224,
-0.055569179356098175,
-0.017067495733499527,
-0.004648484289646149,
0.013920442201197147,
0.034925565123558044,
0.05808037519454956,
-0.018617527559399605,
0.002624956890940666,
0.011423869989812374,
-0.049247998744249344,
-0.004959780257195234,
-0.02343502640724182,
-0.01586705446243286,
-0.06467112898826599,
0.007342370692640543,
0.012996533885598183,
-0.017069775611162186,
-0.009568720124661922,
0.003567195264622569,
-0.010218385607004166,
-0.028906751424074173,
-0.053931307047605515,
-0.004616188816726208,
0.032284215092659,
-0.01499500684440136,
0.008485366590321064,
0.03026939183473587,
0.0555000938475132,
0.05379108712077141,
-0.026522232219576836,
0.019327428191900253,
0.04110788553953171,
0.015141424722969532,
-0.04570476710796356,
-0.04110141471028328,
0.011097108945250511,
0.04331859573721886,
0.040856409817934036,
0.0009528675000183284,
0.0433482825756073,
0.00890081375837326,
-0.007524085696786642,
0.028713636100292206,
-0.02085277810692787,
0.02133181132376194,
-0.002034517703577876,
0.04738299548625946,
-0.01323650125414133,
0.038243841379880905,
-0.06933190673589706,
0.08649246394634247,
-0.006486615166068077,
-0.01119269523769617,
-0.0025142314843833447,
0.0348597876727581,
0.03513573482632637,
0.06021125614643097,
-0.018807752057909966,
-0.012736866250634193,
0.02643515355885029,
0.03304611146450043,
-0.07190380990505219,
-0.05696801841259003,
-0.008067158050835133,
-0.02108437940478325,
0.04921034350991249,
-0.04199937731027603,
0.02190377563238144,
-0.05335824564099312,
-0.0009751027100719512,
0.04449736699461937,
-0.05578853189945221,
0.017277998849749565,
-0.028332741931080818,
-0.014096537604928017,
-0.010004078969359398,
-0.02644404210150242,
0.0614737942814827,
0.05564924329519272,
-0.024668797850608826,
-0.02765355259180069,
-0.058893680572509766,
0.01803428679704666,
-0.015339146368205547,
-0.019621780142188072,
0.05766836926341057,
-0.004799149464815855,
-0.0023686725180596113,
-0.022200284525752068,
-0.04675982892513275,
0.08178701251745224,
-0.06872668117284775,
0.01581074856221676,
0.03448504954576492,
0.010353976860642433,
0.033524539321660995,
0.040997061878442764,
0.036925800144672394,
0.006375559605658054,
-0.022716108709573746,
-0.047190941870212555,
0.06648565828800201,
-0.057316042482852936,
0.03092137537896633,
0.034220971167087555,
-0.06659970432519913,
-0.050935663282871246,
-0.029532289132475853,
-0.029683582484722137,
-0.013740606606006622,
0.05370738357305527,
0.03361230343580246,
0.041061945259571075,
0.018316952511668205,
-0.04923868924379349,
-0.05392046645283699,
0.01914926990866661,
-0.04894986003637314,
0.04078134894371033,
0.005346131511032581,
0.012152942828834057,
-0.021637238562107086,
-0.023149695247411728,
0.012191294692456722,
0.06601741909980774,
-0.019721174612641335,
0.06409849971532822,
0.01416005752980709,
-0.02684355154633522,
-0.049910541623830795,
-0.012440701946616173,
0.013858366757631302,
0.015298036858439445,
0.006148187443614006,
0.015162583440542221,
0.018720371648669243,
-0.03470054641366005,
-0.05622726306319237,
0.02481735497713089,
-0.011799233965575695,
-0.027954047545790672,
-0.056367743760347366,
-0.003799023572355509,
0.01562147680670023,
0.01060772966593504,
0.04381152242422104,
0.058502234518527985,
-0.00887235626578331,
-0.006286711432039738,
-0.018744846805930138,
-0.04702300578355789,
0.05138680711388588,
0.0634651631116867,
0.01163111999630928,
-0.06468866020441055,
-0.049309372901916504,
-0.030580399557948112,
0.05136542767286301,
0.011526195332407951,
0.053406715393066406,
0.012709720060229301,
0.04622402787208557,
-0.011650238186120987,
0.02044418267905712,
-0.02650902047753334,
-0.026759693399071693,
-0.06403306871652603,
-0.012897788546979427,
0.0031596082262694836,
0.03537658229470253,
-0.0806158035993576,
0.07186576724052429,
0.029325369745492935,
-0.011364834383130074,
-0.023066028952598572,
0.041965972632169724,
-0.062246520072221756,
0.025281129404902458,
-0.042367685586214066,
-0.021914906799793243,
-0.012237696908414364,
-0.0877288356423378,
0.009284134022891521,
0.03046906739473343,
0.020533790811896324,
0.025563247501850128,
-0.01610368676483631,
0.04136519506573677,
0.0225453432649374,
0.03955698385834694,
0.01116312574595213,
-0.0324067547917366,
0.01232865359634161,
-0.045623816549777985,
-0.06932476162910461,
0.04106252267956734,
-0.015871021896600723,
0.02599782682955265,
0.008213242515921593,
0.04485582187771797,
-0.023036204278469086,
-0.0268892552703619,
0.0047182971611619,
0.01162246335297823,
0.007662101183086634,
-0.021702280268073082,
-0.09097050130367279,
0.01587439887225628,
0.07032519578933716,
-0.054228704422712326,
-0.009189286269247532,
0.04613349586725235,
-0.028955303132534027,
0.01290721446275711,
-0.02997455559670925,
-0.005823513492941856,
-0.0025488745886832476,
0.011075632646679878,
0.014756125397980213,
0.13590018451213837,
0.0071686552837491035,
0.0013153146719560027,
0.017112918198108673,
0.018741877749562263,
-0.014090527780354023,
0.02302916720509529,
-0.015502937138080597,
-0.005587498191744089,
-0.04239755496382713,
-0.0063280630856752396,
-0.00078824523370713,
-0.03272346034646034,
0.015421747229993343,
0.019093889743089676,
-0.0036168494261801243,
-0.02489669993519783,
0.0351252406835556,
0.010826168581843376,
0.04477154463529587,
-0.04285995662212372,
0.06203668192028999,
-0.06986770778894424,
-0.02719312533736229,
0.02445300854742527,
-0.06836257874965668,
-0.034627657383680344,
-0.04301432520151138,
-0.006014645099639893,
0.009484712965786457,
-0.05694996938109398,
-0.013979408890008926,
0.020875923335552216,
-0.025713125243782997,
-0.02980528585612774,
0.004000903107225895,
0.007911616005003452,
0.02472245879471302,
0.004371552728116512,
0.012949671596288681,
-0.08007185906171799,
0.047472499310970306,
0.03292841464281082,
0.027478819712996483,
-0.03693113103508949,
0.0209807101637125,
-0.053555529564619064,
0.003603246994316578,
0.024464420974254608,
0.043389249593019485,
0.04291645064949989,
0.05239987373352051,
-0.030128540471196175,
0.07539315521717072,
0.046154242008924484,
0.008320889435708523,
0.04616684094071388,
0.027385322377085686,
-0.07045355439186096,
-0.023266926407814026,
0.03232625871896744,
0.0028633123729377985,
-0.02087634801864624,
0.01981382817029953,
-0.03273108974099159,
-0.013126088306307793,
0.03307188302278519,
-0.0008463806589134037,
-0.01686970889568329,
0.012018217705190182,
0.02422041818499565
] |
<p>In 2006 the radius for a possible internal structure of the electron has been pinned down to $10^{-18} m$. This validates the approximation of electrons as point particles at long distances, e.g. in an atom. The upper bound on the internal electron radius has been derived from a very precise measurement of the $g$-factor, see</p>
<p><a href="http://gabrielse.physics.harvard.edu/gabrielse/papers/2006/HarvardElectronMagneticMoment2006.pdf" rel="nofollow">New Measurement of the Electron Magnetic Moment Using a One-Electron Quantum Cyclotron</a></p>
<p>What I don't understand is how did they determine the relation between the $g$-facor and the radius of the internal structure?</p>
<p>As far as I understand they compare the $g$ factor of a point particle to the $g$ factor of an extend particle. But how do you calculate the $g$ factor of a point particle or an extend particle?</p> | g4798 | [
0.009171425364911556,
0.0016321645816788077,
-0.007420891430228949,
-0.06242719292640686,
0.046589989215135574,
0.0034148325212299824,
0.0276804156601429,
0.024312924593687057,
-0.06636644899845123,
0.018198182806372643,
-0.015913598239421844,
0.07383127510547638,
-0.007017380557954311,
-0.05874670296907425,
0.0658169537782669,
-0.01045642513781786,
0.03189627081155777,
0.012130466289818287,
-0.0032171655911952257,
0.03701653704047203,
0.026380490511655807,
-0.05329205468297005,
0.02248424105346203,
-0.014421607367694378,
-0.023953935131430626,
0.023015035316348076,
0.021788761019706726,
0.00850293692201376,
-0.03700445219874382,
0.022803641855716705,
-0.02665689028799534,
-0.016189169138669968,
0.020293379202485085,
-0.048643458634614944,
0.06983305513858795,
-0.023651795461773872,
0.02282184548676014,
0.06623097509145737,
0.011756147257983685,
-0.044437263160943985,
0.007974613457918167,
-0.056046728044748306,
-0.018936457112431526,
0.01795079931616783,
0.03652656823396683,
0.014934290200471878,
-0.0355578251183033,
-0.012119387276470661,
0.04527800530195236,
-0.0189206600189209,
-0.07840008288621902,
0.05407920107245445,
-0.00007730675133643672,
0.009945616126060486,
0.02679389901459217,
0.005752882920205593,
-0.041635531932115555,
0.025583378970623016,
0.05709955096244812,
0.020398156717419624,
0.024957625195384026,
-0.030026407912373543,
-0.020631374791264534,
0.01080787368118763,
-0.03844638913869858,
0.0018103126203641295,
-0.07755055278539658,
0.021368296816945076,
-0.10746512562036514,
-0.04360698163509369,
0.005327665247023106,
-0.12914671003818512,
0.005819288548082113,
-0.044340830296278,
-0.07544619590044022,
-0.0038814423605799675,
-0.03322656825184822,
0.060385171324014664,
0.062185999006032944,
0.041377000510692596,
-0.023184970021247864,
-0.02600007876753807,
0.04479386284947395,
-0.035225361585617065,
-0.0033605871722102165,
0.019437642768025398,
-0.010504952631890774,
0.03404776751995087,
0.0387435145676136,
0.0017788875848054886,
0.009350363165140152,
-0.038478802889585495,
0.012565573677420616,
0.008691909722983837,
-0.004229550249874592,
0.020945217460393906,
-0.00461888313293457,
0.048386868089437485,
0.005457856692373753,
0.006485088728368282,
-0.0006611960125155747,
-0.004869085270911455,
0.023560119792819023,
0.041932299733161926,
0.0019427912775427103,
0.01670992746949196,
0.019579101353883743,
-0.024094432592391968,
0.02110607735812664,
0.018292250111699104,
-0.09679743647575378,
-0.0017820099601522088,
-0.016012534499168396,
-0.024541260674595833,
-0.049203529953956604,
-0.041622381657361984,
0.09205708652734756,
-0.004776214715093374,
0.04948042333126068,
0.03526792675256729,
-0.0018811444751918316,
0.02209244668483734,
0.028182003647089005,
0.05245679244399071,
-0.0679926946759224,
0.004477812442928553,
0.008161678910255432,
0.004285725299268961,
0.019327640533447266,
-0.020053593441843987,
0.029571838676929474,
0.029700035229325294,
0.04442507028579712,
0.0104435496032238,
-0.005723646841943264,
0.033640723675489426,
0.00826186966150999,
-0.010416891425848007,
-0.037693049758672714,
0.05266616865992546,
-0.048914067447185516,
-0.002048840979114175,
0.024421462789177895,
-0.026477482169866562,
-0.0183316171169281,
0.02142352983355522,
-0.030141759663820267,
-0.04140901193022728,
-0.001424623653292656,
0.03175961598753929,
0.032674577087163925,
0.022740105167031288,
0.01078541949391365,
0.02545960247516632,
-0.009310992434620857,
-0.011484578251838684,
0.012803985737264156,
-0.00008732084825169295,
0.005739938002079725,
0.07312466949224472,
0.007837359793484211,
-0.016662778332829475,
-0.00257139652967453,
0.05354107543826103,
-0.04043852165341377,
0.005587472114712,
0.03617849946022034,
-0.01020563580095768,
-0.053222671151161194,
-0.09410088509321213,
-0.037817809730768204,
0.02024894766509533,
0.030957438051700592,
-0.04379851371049881,
0.008841551840305328,
0.03680497407913208,
0.02172457054257393,
-0.018085364252328873,
0.019449623301625252,
0.002476163674145937,
-0.010708827525377274,
-0.018723005428910255,
0.08074820786714554,
0.02650502137839794,
-0.05311765894293785,
0.031041555106639862,
0.0010135722113773227,
0.02630617469549179,
0.04082122817635536,
-0.0015935248229652643,
-0.004067561589181423,
-0.010283084586262703,
-0.03183009847998619,
-0.006175826769322157,
-0.028923790901899338,
-0.04015764221549034,
0.04336216673254967,
-0.055066075176000595,
-0.021005528047680855,
0.0037996764294803143,
-0.040962692350149155,
0.0032624469604343176,
-0.03548272326588631,
0.051398348063230515,
0.11166056245565414,
-0.06678153574466705,
-0.020945796743035316,
0.0026349748950451612,
0.059447962790727615,
0.014583651907742023,
0.011116217821836472,
-0.011454492807388306,
-0.05488961562514305,
0.02946615032851696,
0.031678736209869385,
-0.07875914871692657,
-0.022023407742381096,
0.007830917835235596,
0.004224168136715889,
0.002245544223114848,
-0.025149989873170853,
-0.008858160115778446,
0.1018177941441536,
-0.019793981686234474,
0.0004210188635624945,
0.007925719022750854,
0.008170343935489655,
0.01891459710896015,
0.003547165310010314,
-0.009319775737822056,
-0.07527432590723038,
0.045291706919670105,
-0.047672808170318604,
-0.023697629570961,
0.01011674851179123,
-0.01003242190927267,
-0.08480243384838104,
-0.08714883774518967,
-0.02173447236418724,
-0.012249896302819252,
0.02374301850795746,
-0.010408966802060604,
-0.06415616720914841,
-0.011762777343392372,
-0.004223393276333809,
-0.020128993317484856,
0.014423128217458725,
-0.03247850015759468,
-0.03548741713166237,
-0.0074857198633253574,
0.014956636354327202,
0.034080974757671356,
0.018435265868902206,
0.02616184391081333,
-0.022726496681571007,
-0.012603476643562317,
0.022381460294127464,
-0.003079456277191639,
-0.10063537210226059,
-0.09306754916906357,
0.0071615478955209255,
-0.0011407398851588368,
-0.003933383151888847,
-0.017796162515878677,
-0.03280296549201012,
-0.022027436643838882,
-0.010141800157725811,
0.007661342620849609,
-0.007372742053121328,
-0.019497420638799667,
-0.028148189187049866,
0.06963519006967545,
0.00012603153300005943,
-0.005734241101890802,
-0.0015665744431316853,
-0.09411709010601044,
-0.015711385756731033,
0.0071795484982430935,
0.07203449308872223,
-0.036718450486660004,
-0.020474867895245552,
0.010741122998297215,
-0.03177785128355026,
0.01060805656015873,
-0.04152132570743561,
-0.015503358095884323,
0.026086824014782906,
0.022711338475346565,
-0.05886923521757126,
-0.03830336779356003,
-0.021979505196213722,
0.03784944489598274,
0.023725885897874832,
0.01098848506808281,
-0.0012159532634541392,
0.07548690587282181,
0.0747753232717514,
0.026060882955789566,
0.02169262059032917,
0.01661692000925541,
0.039574433118104935,
0.006223561242222786,
-0.08940504491329193,
0.00811954215168953,
0.005867114756256342,
-0.024081196635961533,
-0.0003655938489828259,
-0.030874699354171753,
-0.053981341421604156,
-0.04235711321234703,
0.0024249807465821505,
0.008847384713590145,
-0.013999629765748978,
-0.06488168239593506,
0.013469917699694633,
-0.05098731815814972,
0.035310227423906326,
0.08451281487941742,
-0.011280099861323833,
0.035425834357738495,
0.026437604799866676,
-0.0674598291516304,
0.024160295724868774,
-0.025873128324747086,
0.030053576454520226,
0.02317512221634388,
-0.037233706563711166,
0.02039387822151184,
-0.0038215480744838715,
-0.017835421487689018,
-0.024966198951005936,
0.0040181539952754974,
-0.003707933472469449,
-0.006234894506633282,
-0.018260233104228973,
-0.06807219982147217,
0.03769015893340111,
0.051310934126377106,
0.034899141639471054,
-0.035255368798971176,
-0.05162578076124191,
-0.038389503955841064,
-0.04319381341338158,
0.009761928580701351,
0.04882385954260826,
0.022646384313702583,
-0.03969978541135788,
0.02797907218337059,
0.006777120754122734,
-0.017577722668647766,
-0.050467245280742645,
-0.004909206181764603,
-0.030938228592276573,
0.019735360518097878,
0.022895682603120804,
0.0032416062895208597,
-0.01755736954510212,
-0.003089624922722578,
-0.03696662187576294,
-0.03129892796278,
0.05454619601368904,
-0.039631620049476624,
0.1173509806394577,
-0.006700755562633276,
-0.021380195394158363,
-0.014470892027020454,
0.011062545701861382,
0.021397557109594345,
0.02430352009832859,
-0.0077852001413702965,
-0.016969753429293633,
-0.028767555952072144,
0.05394776165485382,
0.05286961421370506,
0.010578485205769539,
-0.05300457403063774,
0.04029504209756851,
-0.006197665818035603,
-0.015357968397438526,
-0.025220561772584915,
0.05452669784426689,
0.08477753400802612,
-0.013436357490718365,
-0.05096321925520897,
-0.002761469455435872,
-0.031519435346126556,
-0.04737309738993645,
-0.014195309951901436,
-0.008585394360125065,
-0.03220239654183388,
-0.005734927486628294,
-0.048683106899261475,
-0.020539546385407448,
-0.004428089130669832,
0.030580174177885056,
0.014832133427262306,
0.028865046799182892,
-0.009581148624420166,
0.03003011830151081,
0.035425473004579544,
0.0006096573197282851,
0.01565214991569519,
0.007094946689903736,
0.0018906272016465664,
-0.002674760529771447,
0.003796467324718833,
0.011169559322297573,
-0.007190300617367029,
-0.012272397987544537,
-0.06480564177036285,
-0.04734937101602554,
0.10240329056978226,
0.01374771073460579,
-0.046330589801073074,
0.014084835536777973,
-0.058551326394081116,
-0.007668911479413509,
-0.03396590054035187,
0.020447345450520515,
-0.024497566744685173,
0.007438801694661379,
0.027354950085282326,
0.03041963465511799,
-0.01626908779144287,
-0.031028827652335167,
0.005141386762261391,
-0.030570389702916145,
0.06003624200820923,
0.0058728428557515144,
0.0034191724844276905,
0.03511866182088852,
-0.03279053792357445,
-0.0031826160848140717,
-0.006719158496707678,
-0.0127580426633358,
0.05666065588593483,
-0.05387130007147789,
0.0050787292420864105,
-0.004151209723204374,
-0.033160775899887085,
0.040440354496240616,
-0.012858724221587181,
0.05528188869357109,
0.038606055080890656,
0.006545247044414282,
-0.013526475057005882,
-0.07706873118877411,
0.02920832484960556,
0.0028844019398093224,
-0.02098679728806019,
0.027717463672161102,
-0.06369511783123016,
0.011273879557847977,
0.01902085170149803,
0.006707349326461554,
-0.031500302255153656,
-0.013815484941005707,
-0.0318804532289505,
0.014058737084269524,
-0.03296276181936264,
-0.046108443289995193,
0.004476996138691902,
-0.017746340483427048,
0.041895754635334015,
0.029476569965481758,
0.017164846882224083,
0.006930055562406778,
-0.012347348034381866,
-0.02943444438278675,
0.018722129985690117,
-0.0004047681868541986,
0.008921820670366287,
-0.017576690763235092,
-0.031682129949331284,
0.055523984134197235,
0.012458980083465576,
-0.0235234797000885,
-0.035352252423763275,
-0.013058392331004143,
-0.04512374848127365,
-0.03494904562830925,
0.019112903624773026,
0.020385291427373886,
-0.04826006665825844,
0.01748811826109886,
0.0035536657087504864,
-0.007354218978434801,
0.018694283440709114,
0.0016490976558998227,
-0.011009394191205502,
-0.015364841558039188,
0.028744708746671677,
-0.0058462233282625675,
-0.0270614605396986,
0.013520577922463417,
0.010729926638305187,
0.015042468905448914,
-0.0038589900359511375,
-0.003712123492732644,
-0.03347409889101982,
-0.047358185052871704,
0.01705893687903881,
-0.028352010995149612,
0.025925492867827415,
-0.004753484856337309,
0.08109424263238907,
0.03994297236204147,
-0.0375666581094265,
0.004609074909240007,
-0.01601184718310833,
-0.009917930699884892,
0.0010366924107074738,
0.050862494856119156,
-0.010703980922698975,
0.07196509838104248,
-0.00625248160213232,
0.0051878890953958035,
0.05287374556064606,
0.025626277551054955,
-0.02930615097284317,
0.08557575941085815,
-0.0019316710531711578,
0.05467202886939049,
-0.03026358038187027,
-0.013704695738852024,
0.04722725227475166,
0.005427125375717878,
-0.04646304249763489,
0.04983483999967575,
0.009849149733781815,
0.01526676770299673,
-0.027402738109230995,
-0.013909592293202877,
0.03749199956655502,
-0.03533735126256943,
-0.027317745611071587,
-0.030956454575061798,
-0.007807547692209482,
0.024754585698246956,
-0.04013051465153694,
0.015758223831653595,
-0.028019562363624573,
-0.04853806644678116,
0.00508987158536911,
-0.05964745581150055,
0.008767363615334034,
-0.015542491339147091,
0.015917740762233734,
0.026354683563113213,
0.007117831148207188,
-0.035190947353839874,
-0.002872709184885025,
-0.02061733789741993,
-0.009637383744120598,
0.06336381286382675,
-0.010200552642345428,
0.07708719372749329,
0.028830967843532562,
0.011210083961486816,
-0.0012859487906098366,
0.06315487623214722,
-0.06427373737096786,
0.010987632907927036,
0.023445840924978256,
0.008804325014352798,
-0.00764442328363657,
0.010484485886991024,
-0.04304022341966629,
0.010927674360573292,
0.018612587824463844,
0.015154832042753696,
-0.030623776838183403,
-0.014542479999363422,
-0.02501869574189186,
0.043335262686014175,
0.052910901606082916,
0.030696546658873558,
-0.01906568557024002,
0.007269507739692926,
-0.012298047542572021,
0.044392913579940796,
0.0738620012998581,
-0.012483006343245506,
-0.03498183190822601,
0.029096702113747597,
0.08007147163152695,
-0.07914411276578903,
-0.016379214823246002,
0.08389479666948318,
0.012239763513207436,
0.00005954284279141575,
0.005631155334413052,
-0.018206527456641197,
0.01197703368961811,
-0.028786979615688324,
0.021626463159918785,
-0.016697291284799576,
-0.04263736307621002,
0.014074981212615967,
0.043711524456739426,
0.051939450204372406,
0.058551300317049026,
0.02605670504271984,
-0.011431862600147724,
0.018965642899274826,
0.021552076563239098,
0.026192449033260345,
-0.020468106493353844,
-0.03039447031915188,
-0.008460678160190582,
-0.023928800597786903,
0.06326036900281906,
0.058504097163677216,
0.030742349103093147,
0.051148634403944016,
-0.0033804168924689293,
0.026574838906526566,
-0.0295619685202837,
-0.016498733311891556,
-0.007578948512673378,
-0.018816661089658737,
0.005015446804463863,
-0.06447100639343262,
-0.021587423980236053,
-0.03362267464399338,
0.049154531210660934,
0.017574205994606018,
-0.0056468890979886055,
0.069126658141613,
-0.027275003492832184,
-0.01571526564657688,
0.030795713886618614,
-0.007021642290055752,
0.011129513382911682,
-0.002075615804642439,
0.051686447113752365,
0.034400831907987595,
0.006396921817213297,
0.0377851240336895,
0.051190175116062164,
-0.012378170154988766,
-0.09881940484046936,
-0.059663113206624985,
-0.016402874141931534,
-0.04663640633225441,
-0.044031769037246704,
-0.012489186599850655,
0.06820688396692276,
-0.026727864518761635,
0.015968715772032738,
0.042870134115219116,
-0.03009488619863987,
0.00250384327955544,
0.03803310543298721,
0.01068864669650793,
-0.021436292678117752,
0.018596678972244263,
-0.0012753016781061888,
-0.03963853791356087,
-0.02083260752260685,
-0.021008973941206932,
-0.019783252850174904,
0.09947584569454193,
-0.02800726145505905,
-0.014153940603137016,
0.010203147307038307,
-0.011734829284250736,
-0.07082361727952957,
-0.023671863600611687,
-0.05850537121295929,
0.005749277770519257,
0.012786882929503918,
-0.022112587466835976,
-0.06461252272129059,
0.030282026156783104,
0.032907500863075256,
-0.0354352667927742,
-0.024101871997117996,
-0.0430205836892128,
-0.00272009358741343,
-0.0045593599788844585,
0.048982832580804825,
0.04345234856009483,
0.029015490785241127,
-0.06403832137584686,
-0.012994923628866673,
-0.05846581608057022,
-0.05582496151328087,
0.06960682570934296,
0.03137078881263733,
-0.005152761470526457,
-0.010734009556472301,
0.017104296013712883,
-0.09059160947799683,
0.06005829945206642,
0.0038955186028033495,
-0.009548185393214226,
0.04792439565062523,
-0.0018378611421212554,
-0.025362998247146606,
0.012290001846849918,
-0.04883643612265587,
0.014697589911520481,
-0.020541025325655937,
0.08862810581922531,
0.039317935705184937,
-0.03573594242334366,
0.02995976060628891,
-0.019142592325806618,
0.005055685993283987,
-0.0071550821885466576,
-0.0081862173974514,
0.07184579968452454,
0.011223828420042992,
0.07871118187904358,
0.02895018644630909,
0.0049543376080691814,
0.02331867441534996,
0.04989380016922951,
-0.028669293969869614,
-0.013980226591229439,
-0.04516573250293732,
0.022773489356040955,
0.009867286309599876,
-0.058435335755348206,
-0.02148314006626606,
0.04702576994895935,
-0.022460518404841423,
0.036896783858537674,
-0.0008044525166042149,
-0.03205642104148865,
-0.00024943429161794484,
-0.03470926731824875,
-0.04100166633725166,
-0.06656407564878464,
0.015863358974456787,
0.02109365165233612,
-0.048622410744428635,
0.045092251151800156,
0.00562607916072011,
0.013376470655202866,
0.01836857572197914,
0.03765758126974106,
-0.012769706547260284,
0.007067611441016197,
-0.01829184591770172,
0.00410805270075798,
0.06510207802057266,
0.027461543679237366,
0.014039764180779457,
-0.05410332977771759,
0.006296574603766203,
-0.003715676022693515,
-0.000040934774006018415,
0.041871946305036545,
-0.06142303720116615,
-0.04439936578273773,
0.0251039769500494,
0.018951382488012314,
0.01527403388172388,
0.014225436374545097,
0.04710804298520088,
0.04130201041698456,
0.044382330030202866,
0.02217930555343628,
-0.007933189161121845,
-0.04724179953336716,
0.0309597197920084
] |
<p>I have a tube with a length "L" and diameter "d" that is open on 1 side .
At a certain point ( say "x" ) from the closed end of the tube, I have a gas with a high pressure.</p>
<p>At this point, "x", there is also a weight of mass "m".
It is also known what the velocity of the weight is at point "L".</p>
<p>Initially :</p>
<p><img src="http://i.imgur.com/DPXFndD.png" alt="initial"></p>
<p>Finally :</p>
<p><img src="http://i.imgur.com/xu5Qmmr.png" alt="final"></p>
<p>Assuming that the tube is held stationary, what force is imparted on the closed section of tubing ( left side )?</p>
<p>Basically, think of it as a rifle barrel with a bullet inside. I wish to find a expression for the force on the closed end of the tube as it varies with time.</p>
<p>What I propose :
Determine the Work by the gas. And since work is defined as $W = Fx $ and then $ \frac{dW}{dt} = \frac{d(Fx)}{dt}$ perhaps this could lead to an expression for force?</p> | g4799 | [
0.018474627286195755,
-0.03361969441175461,
-0.021471170708537102,
-0.031109843403100967,
0.021580148488283157,
-0.013069038279354572,
0.03524226322770119,
0.007251081056892872,
-0.12162356823682785,
-0.04101330041885376,
-0.029781490564346313,
0.026076434180140495,
-0.00974410679191351,
0.02428060956299305,
0.024337345734238625,
0.055688269436359406,
0.08767315000295639,
-0.036261703819036484,
0.00803985632956028,
0.039530858397483826,
0.0004083187668584287,
0.02276569791138172,
0.007383106742054224,
-0.06174755096435547,
0.06762097030878067,
-0.026552211493253708,
0.07171866297721863,
0.023974603042006493,
-0.022027146071195602,
-0.004988796543329954,
-0.009735059924423695,
0.01547322329133749,
0.03423142805695534,
-0.011086080223321915,
-0.007660987786948681,
-0.050949301570653915,
0.049514856189489365,
-0.013007374480366707,
0.05815485864877701,
-0.05004896596074104,
0.00630703940987587,
-0.02430664375424385,
0.011672502383589745,
0.07626687735319138,
-0.0002453428751323372,
-0.03024164028465748,
-0.04194033145904541,
0.0196344256401062,
-0.028552720323204994,
0.00028605025727301836,
0.01751818135380745,
0.07160542905330658,
-0.06160758435726166,
-0.055545009672641754,
0.03280270844697952,
0.02225530706346035,
0.004345966503024101,
0.01760786771774292,
0.02610592171549797,
-0.0084066828712821,
-0.023425981402397156,
-0.002849317854270339,
-0.02440151758491993,
-0.0029393620789051056,
0.06853599846363068,
-0.03684728592634201,
-0.006097365636378527,
-0.020965734496712685,
0.04474397376179695,
-0.009040674194693565,
-0.03364647924900055,
-0.04628479480743408,
0.004722291138023138,
-0.007605122867971659,
-0.07081671059131622,
-0.0017486969009041786,
-0.027029728516936302,
0.014925510622560978,
-0.02878527157008648,
-0.028039412572979927,
-0.021670248359441757,
-0.02332136780023575,
0.04531093314290047,
-0.004940330050885677,
0.006585181225091219,
-0.05909590423107147,
-0.013423402793705463,
-0.007115382235497236,
-0.027600370347499847,
0.01702459715306759,
-0.0037900893948972225,
0.0002701041812542826,
0.08884856104850769,
0.0028397399000823498,
0.008400458842515945,
-0.04566052183508873,
-0.02487064152956009,
0.08223985880613327,
-0.01688525080680847,
0.012571784667670727,
-0.008982494473457336,
-0.04151527211070061,
-0.043635234236717224,
0.0029649517964571714,
0.015986261889338493,
-0.034001246094703674,
-0.01645280048251152,
0.03528166562318802,
-0.021305518224835396,
-0.04859890043735504,
0.00951257161796093,
-0.00028695634682662785,
-0.04729824885725975,
-0.02164352871477604,
0.008399605751037598,
-0.06565118581056595,
0.007866638712584972,
0.0075111398473382,
-0.0518835075199604,
0.039205729961395264,
-0.024556828662753105,
-0.02869912050664425,
-0.02722857892513275,
0.03012264147400856,
-0.03843209147453308,
0.012712124735116959,
0.0006499033770523965,
0.005564370658248663,
-0.005140252877026796,
-0.006127238739281893,
0.03554781153798103,
0.009087948128581047,
0.016725940629839897,
0.05109528452157974,
-0.0037198748905211687,
0.03503930941224098,
-0.07098256051540375,
0.03351253643631935,
0.020821452140808105,
0.01697164960205555,
0.015347195789217949,
0.0006412262446247041,
-0.042429812252521515,
0.044655486941337585,
-0.03328118473291397,
0.025307906791567802,
-0.09568864107131958,
-0.05782632902264595,
0.0725208967924118,
-0.05530716851353645,
0.00043360816198401153,
0.09751348197460175,
-0.030860891565680504,
-0.04571741446852684,
0.0556977279484272,
-0.016916409134864807,
0.037296194583177567,
0.04957730323076248,
-0.009848104789853096,
-0.007597404532134533,
0.04355229437351227,
-0.03507998585700989,
0.062152642756700516,
-0.00516613619402051,
-0.05228762701153755,
0.05052395537495613,
-0.04356567934155464,
0.0024930026847869158,
0.02076519839465618,
-0.06401175260543823,
-0.09251157194375992,
-0.02799379453063011,
-0.017671821638941765,
-0.003763345070183277,
0.017409322783350945,
0.029776083305478096,
0.017303405329585075,
-0.009223487228155136,
0.028273658826947212,
0.053567901253700256,
0.057078003883361816,
-0.08227290213108063,
0.03892521932721138,
-0.046905726194381714,
-0.01860620267689228,
0.04115716740489006,
0.01624699868261814,
-0.03372405096888542,
-0.08779758960008621,
-0.023072784766554832,
-0.0021933652460575104,
0.009045860730111599,
0.016764845699071884,
0.024606745690107346,
-0.07192178815603256,
0.04031260311603546,
0.016728835180401802,
-0.0910184308886528,
0.013044951483607292,
-0.012780026532709599,
-0.057891227304935455,
0.048018451780080795,
0.02747265063226223,
0.06356964260339737,
0.0194019116461277,
0.018256977200508118,
0.016534510999917984,
0.06085111200809479,
-0.049666352570056915,
0.04572783038020134,
-0.004781554453074932,
0.021992985159158707,
0.0041287620551884174,
0.023372093215584755,
-0.020521676167845726,
-0.02621513046324253,
0.009186317212879658,
0.08504177629947662,
-0.014158811420202255,
0.04106450825929642,
0.007490500342100859,
0.02656734175980091,
-0.009071830660104752,
0.005861713085323572,
-0.08026114851236343,
-0.05776617303490639,
0.04762649908661842,
-0.01785973645746708,
-0.03414585068821907,
0.028305644169449806,
-0.0031580093782395124,
0.05289054289460182,
0.024046897888183594,
-0.02314179576933384,
0.06066501885652542,
-0.02549763210117817,
0.020458698272705078,
-0.026039907708764076,
0.0009105453500524163,
0.019810788333415985,
0.02482576109468937,
-0.06986800581216812,
-0.047112319618463516,
-0.03710557520389557,
-0.035639647394418716,
0.03259263560175896,
0.027832068502902985,
0.03693601116538048,
0.0505315326154232,
-0.006166481412947178,
-0.022111479192972183,
-0.006346705835312605,
-0.024053288623690605,
0.00750036770477891,
0.0004969178116880357,
-0.015845434740185738,
-0.042860064655542374,
0.015560062602162361,
-0.0485212467610836,
-0.042599327862262726,
-0.0159140732139349,
-0.005022107157856226,
0.028611276298761368,
0.1145876869559288,
-0.03833485022187233,
0.03774276748299599,
-0.009936326183378696,
0.005569586995989084,
0.026567794382572174,
0.048369575291872025,
-0.03318236768245697,
-0.014238178730010986,
0.030233783647418022,
-0.01767386682331562,
0.00967645738273859,
-0.04932211712002754,
0.007711246144026518,
-0.0657707005739212,
-0.01704634167253971,
0.04007016122341156,
0.02820143848657608,
0.03148984909057617,
-0.038183048367500305,
0.08828417956829071,
-0.008419709280133247,
-0.02491670660674572,
0.06782127171754837,
-0.025709684938192368,
0.02494424767792225,
-0.048097193241119385,
0.039024654775857925,
0.05399294197559357,
-0.01916295848786831,
0.0262666754424572,
0.010344615206122398,
0.053592052310705185,
0.039887573570013046,
0.021466659381985664,
0.005255162250250578,
0.011772792786359787,
-0.025850709527730942,
-0.048102475702762604,
-0.015428926795721054,
0.030329663306474686,
0.008266733959317207,
-0.02453780360519886,
-0.012027016840875149,
-0.04207776114344597,
-0.01911069266498089,
-0.02865927293896675,
-0.02935335598886013,
0.028314221650362015,
0.05405597388744354,
-0.057337693870067596,
-0.0891026109457016,
-0.013661699369549751,
-0.001721523585729301,
-0.044579386711120605,
0.004290061537176371,
-0.0039918203838169575,
-0.025167929008603096,
-0.03437706083059311,
0.03644063323736191,
-0.005769688170403242,
-0.03085765801370144,
0.011633683927357197,
-0.04975707456469536,
0.008586027659475803,
-0.07071748375892639,
0.00044513173634186387,
-0.011285221204161644,
0.01886330544948578,
-0.013090708293020725,
-0.029843097552657127,
0.012845303863286972,
-0.023189686238765717,
0.0056763216853141785,
0.03179442137479782,
0.010833252221345901,
0.02162497118115425,
-0.03764265775680542,
-0.029449431225657463,
-0.04687667638063431,
0.02388327196240425,
0.01969715766608715,
0.00031268942984752357,
-0.00904118176549673,
0.04596259072422981,
0.0582575798034668,
-0.015935132279992104,
0.014211534522473812,
-0.029590923339128494,
0.04552464932203293,
-0.004633414559066296,
0.04213052615523338,
0.015697380527853966,
0.06885161995887756,
-0.0012686080299317837,
-0.032674580812454224,
0.009738286957144737,
-0.006139816250652075,
-0.06004690006375313,
-0.06522715091705322,
0.04152076691389084,
-0.0206492580473423,
-0.04828338325023651,
0.038512036204338074,
0.08746186643838882,
-0.007532762363553047,
-0.015308460220694542,
0.028911959379911423,
-0.047794222831726074,
0.024570133537054062,
0.04462551325559616,
-0.02122017741203308,
-0.016713809221982956,
-0.01780472695827484,
-0.010062161833047867,
0.03352358937263489,
0.023243913426995277,
0.022900395095348358,
0.04403918236494064,
-0.08057765662670135,
-0.005792083218693733,
-0.016346700489521027,
-0.010694372467696667,
-0.029268333688378334,
0.039381444454193115,
0.0663641020655632,
-0.03651709854602814,
0.01728755049407482,
-0.04045537859201431,
-0.02522774413228035,
0.05868007242679596,
-0.0038296361453831196,
0.003959247376769781,
0.07274997234344482,
-0.016334306448698044,
-0.04457845166325569,
-0.05877840891480446,
0.028666222468018532,
0.02320381999015808,
-0.0014075973303988576,
0.028522858396172523,
-0.061991337686777115,
0.0093005346134305,
0.060956936329603195,
-0.02086932398378849,
0.041141558438539505,
0.01673167385160923,
-0.03865697234869003,
-0.04300474375486374,
-0.0031447140499949455,
0.0036014029756188393,
-0.007909296080470085,
-0.05858166888356209,
0.0424971766769886,
0.00573302898555994,
0.004260252229869366,
-0.015136327594518661,
0.04041437432169914,
0.05477623641490936,
0.022597532719373703,
-0.03382706642150879,
-0.017261767759919167,
0.0295554231852293,
0.02789156138896942,
0.040075842291116714,
0.03871695324778557,
-0.04291554540395737,
-0.022565161809325218,
-0.0038628780748695135,
-0.033549416810274124,
0.026967773213982582,
-0.05920844152569771,
0.024936720728874207,
0.0008540030103176832,
-0.03444785252213478,
0.013717489317059517,
0.06381358206272125,
0.032761137932538986,
0.046893760561943054,
-0.016417715698480606,
-0.006360155530273914,
0.02603558637201786,
0.05029081553220749,
-0.01138670276850462,
-0.04104272648692131,
0.05307254567742348,
-0.019222017377614975,
-0.07702530920505524,
-0.006616712082177401,
-0.040402550250291824,
-0.06466636061668396,
0.04988063871860504,
0.02827591262757778,
0.02678842656314373,
-0.01665087603032589,
-0.012998211197555065,
-0.007552298717200756,
-0.023115476593375206,
0.007806086912751198,
-0.019893888384103775,
0.019524982199072838,
-0.026412438601255417,
-0.015141955576837063,
-0.04347163438796997,
0.0012030829675495625,
0.010505268350243568,
0.004239617846906185,
-0.010015925392508507,
0.018127860501408577,
0.03817365691065788,
0.03254874050617218,
0.005771008785814047,
-0.029498755931854248,
0.007654701825231314,
-0.003951997961848974,
0.05985051020979881,
-0.03588160127401352,
-0.012339703738689423,
0.009335733018815517,
0.06272205710411072,
0.008680541068315506,
0.03535670414566994,
-0.05919196829199791,
-0.03372390940785408,
-0.009582438506186008,
-0.035797301679849625,
-0.017344357445836067,
0.04994523897767067,
0.041606057435274124,
0.027884533628821373,
-0.023205365985631943,
-0.007126884534955025,
-0.0007805295754224062,
0.05212366580963135,
0.03066244162619114,
0.046378038823604584,
0.011670541949570179,
-0.0270013939589262,
0.015415788628160954,
0.007634010165929794,
-0.0005827650893479586,
-0.011295751668512821,
0.10164029151201248,
0.002676380332559347,
-0.005126099102199078,
-0.0049195559695363045,
0.021072102710604668,
0.0016916923923417926,
0.08171796053647995,
0.027996420860290527,
0.01599174365401268,
0.009377149865031242,
0.005296135321259499,
0.012238136492669582,
-0.02482730709016323,
-0.012730074115097523,
0.007881944999098778,
0.04913296550512314,
-0.02123849093914032,
0.038280192762613297,
0.02092413790524006,
0.002230132697150111,
-0.004983951337635517,
-0.026702426373958588,
-0.014146189205348492,
-0.013630816712975502,
-0.004241927061229944,
0.011179463937878609,
-0.032579466700553894,
0.02699633315205574,
-0.047624703496694565,
-0.04840807989239693,
-0.00879682321101427,
0.0605940967798233,
0.038261547684669495,
0.021647660061717033,
-0.042340293526649475,
0.006147992797195911,
0.011079521849751472,
0.044631168246269226,
0.02855876460671425,
0.015314612537622452,
-0.004270974546670914,
-0.03778403252363205,
0.0012015003012493253,
0.037159789353609085,
-0.006625742185860872,
-0.049301836639642715,
0.029718007892370224,
-0.03544935584068298,
-0.03878852725028992,
0.042198434472084045,
-0.016173621639609337,
0.00106827262789011,
-0.03294464200735092,
-0.004139075055718422,
-0.002335348865017295,
0.016484154388308525,
-0.0073243845254182816,
0.021528415381908417,
0.05059434100985527,
-0.0012186625972390175,
-0.04225420579314232,
-0.043648380786180496,
0.007007177919149399,
0.050309889018535614,
0.05715546756982803,
0.0012077006977051497,
0.025083309039473534,
-0.044814493507146835,
-0.04583996906876564,
0.03965020179748535,
0.03537437692284584,
-0.04362621530890465,
-0.028357407078146935,
-0.010472360998392105,
0.06230892241001129,
-0.007067975588142872,
-0.010814796201884747,
0.005384949967265129,
0.008179571479558945,
-0.055897414684295654,
0.04363234341144562,
0.0312894731760025,
-0.0021919677965343,
-0.013752981089055538,
0.004967871122062206,
-0.0009163343347609043,
-0.023345965892076492,
-0.0023746115621179342,
-0.00919360388070345,
-0.0614764541387558,
-0.03676334023475647,
0.002956487936899066,
-0.014965321868658066,
0.026417888700962067,
0.04995664209127426,
0.006789070554077625,
0.03426562249660492,
-0.007806381676346064,
-0.02779368869960308,
0.02281137928366661,
0.04462941363453865,
-0.021566618233919144,
0.01939539983868599,
-0.030767150223255157,
-0.04555913060903549,
0.03331340476870537,
0.05543704703450203,
0.045905712991952896,
0.026980170980095863,
-0.0076302774250507355,
-0.013600832782685757,
0.03074076771736145,
0.04235048592090607,
0.023295961320400238,
0.001129926647990942,
0.021197590976953506,
0.033084478229284286,
0.009676698595285416,
-0.03550081327557564,
0.03234534338116646,
0.019118962809443474,
-0.075186587870121,
-0.008981173858046532,
0.021134141832590103,
-0.029061665758490562,
0.030782736837863922,
0.034502554684877396,
-0.028309205546975136,
-0.0018641124479472637,
-0.04235564544796944,
0.05518011748790741,
-0.019448060542345047,
0.05066371709108353,
0.027369504794478416,
0.06582143157720566,
0.009287777356803417,
-0.022893348708748817,
-0.018166277557611465,
0.05089844390749931,
-0.04061543196439743,
-0.04036286845803261,
0.07157579809427261,
0.04284471645951271,
-0.046894319355487823,
-0.015062320046126842,
0.019764354452490807,
-0.030798345804214478,
-0.032937370240688324,
0.06350241601467133,
-0.06457158178091049,
-0.005995832849293947,
-0.005299328360706568,
-0.049068450927734375,
0.01489193458110094,
-0.06445125490427017,
-0.020143700763583183,
-0.04193493723869324,
0.02552419900894165,
0.0046984427608549595,
-0.032952435314655304,
0.06298790127038956,
0.016990341246128082,
-0.03047036938369274,
-0.002931369701400399,
-0.024460526183247566,
-0.007160921581089497,
-0.027085943147540092,
-0.008799102157354355,
0.011725420132279396,
-0.022727839648723602,
-0.008765194565057755,
-0.05334162712097168,
0.0239484291523695,
-0.03377601131796837,
0.0029067464638501406,
-0.07816726714372635,
-0.001270268578082323,
-0.023691557347774506,
-0.017464585602283478,
-0.037385232746601105,
-0.0033174578566104174,
0.003019107971340418,
0.004587584175169468,
-0.023770902305841446,
0.012131639756262302,
0.02165408618748188,
0.06384148448705673,
0.0779334232211113,
0.016088292002677917,
-0.03424888104200363,
-0.011204252019524574,
0.0318196564912796,
0.016665611416101456,
0.013425708748400211,
0.009468541480600834,
0.035786282271146774,
-0.012669812887907028,
-0.0017645523184910417,
-0.022894050925970078,
-0.06359835714101791,
-0.0344683937728405,
-0.031035637483000755,
0.020340660586953163,
-0.027677852660417557,
-0.04339229315519333,
0.016620229929685593,
-0.0034180842339992523,
-0.004106629174202681,
-0.042118318378925323,
-0.033011872321367264,
-0.0003573409921955317,
-0.033976465463638306,
-0.0037191181909292936,
0.0411464087665081,
-0.016191964969038963,
0.003475741483271122,
-0.008882220834493637,
-0.027606062591075897,
-0.0583435595035553,
-0.01901997998356819,
-0.025994593277573586,
-0.09331052750349045,
0.04135439917445183,
-0.020653527230024338,
-0.011948645114898682,
0.025848999619483948,
0.016576897352933884,
0.01127141248434782,
0.09215167164802551,
0.021235430613160133,
0.021942216902971268,
0.05286543443799019,
-0.036243367940187454,
-0.06265884637832642,
0.043153874576091766,
-0.038118865340948105,
-0.05981152504682541,
-0.015436029992997646,
-0.01973128132522106,
0.03404301404953003,
-0.014830192551016808,
0.015771638602018356,
0.04043412208557129,
0.03960448130965233,
0.020052161067724228,
0.05603838339447975,
-0.015564183704555035,
0.018976781517267227,
-0.056805141270160675,
-0.04658636450767517,
-0.07269637286663055,
-0.05554172769188881,
0.0559508353471756,
0.008223224431276321,
-0.015675561502575874,
-0.024007052183151245,
0.09207791835069656,
-0.04098851606249809,
0.005810190457850695,
0.025761116296052933,
-0.051376812160015106,
0.034121863543987274,
-0.0228158887475729
] |
<p>The electron contains finite negative charge.The same charges repel each other.What makes electron stable and why does it not burst? Is it a law of nature that the electron charge is the smallest possible charge that can exist independently? What is a charge after all? Is it like space and time or we can explain it in terms of some other physical quantities? </p> | g329 | [
0.04935776814818382,
0.062089815735816956,
-0.009633841924369335,
0.024256667122244835,
0.07462623715400696,
0.05688507854938507,
-0.052140697836875916,
0.012261842377483845,
-0.05326414108276367,
-0.030992532148957253,
-0.02117295190691948,
0.01164177991449833,
0.010388902388513088,
0.0075143794529139996,
-0.012987911701202393,
0.009175868704915047,
0.06909296661615372,
0.016945911571383476,
0.056187089532613754,
0.05064785107970238,
-0.017356188967823982,
-0.02856101095676422,
0.06274519115686417,
-0.04565635323524475,
-0.03310981020331383,
0.03494349122047424,
0.0378103144466877,
0.0380810908973217,
0.036511197686195374,
-0.05394013598561287,
0.051572468131780624,
-0.007950340397655964,
0.04343148320913315,
-0.04646197706460953,
-0.01716115139424801,
-0.038881316781044006,
-0.020395485684275627,
-0.009328518062829971,
0.038101620972156525,
0.028872307389974594,
0.00914384052157402,
-0.018318697810173035,
0.013523392379283905,
-0.060726989060640335,
0.011716579087078571,
0.0016920852940529585,
0.0265412125736475,
-0.01602671854197979,
0.004849093034863472,
-0.08004247397184372,
-0.027553889900445938,
0.03889825567603111,
0.023242492228746414,
-0.03153127431869507,
0.03717250004410744,
-0.034834664314985275,
0.01474845688790083,
0.02995043620467186,
0.039902690798044205,
0.007455687969923019,
-0.02231622114777565,
0.04004625976085663,
0.006319340784102678,
0.09553606063127518,
0.030297599732875824,
-0.052963174879550934,
-0.09213889390230179,
-0.021621720865368843,
0.04809839278459549,
0.03461839631199837,
-0.0071410732343792915,
-0.13191697001457214,
-0.06060324236750603,
-0.016464989632368088,
0.020410936325788498,
0.018062729388475418,
0.02748483046889305,
-0.01836668886244297,
0.015129591338336468,
-0.035802289843559265,
-0.015514697879552841,
-0.015477352775633335,
0.021459059789776802,
-0.0017157759284600616,
0.0581270307302475,
-0.04080279916524887,
0.0013847628142684698,
-0.05606643483042717,
-0.030341384932398796,
0.008273246698081493,
0.010320439003407955,
0.005217426456511021,
0.02723083086311817,
-0.017390422523021698,
-0.007887439802289009,
-0.013948085717856884,
-0.02345709502696991,
0.017972614616155624,
-0.009498109109699726,
-0.04234154894948006,
-0.014600260183215141,
-0.013816909864544868,
0.012904815375804901,
0.019149968400597572,
0.01004214771091938,
0.020655186846852303,
-0.04495381936430931,
0.008610901422798634,
0.029767753556370735,
-0.002994357142597437,
0.044154711067676544,
-0.03492332249879837,
-0.024390900507569313,
-0.023007884621620178,
-0.00777857331559062,
0.042413659393787384,
0.057743560522794724,
-0.05926026776432991,
0.03487822413444519,
-0.00021965819178149104,
0.05506954714655876,
-0.0019306393805891275,
0.03226407989859581,
-0.0005986645701341331,
-0.06437105685472488,
-0.02484390325844288,
0.012400219216942787,
-0.006311184726655483,
0.039327219128608704,
-0.056175317615270615,
-0.025640901178121567,
0.024154359474778175,
-0.0821281149983406,
-0.03757192939519882,
0.010332670994102955,
0.020881127566099167,
-0.037954650819301605,
0.04191996157169342,
-0.0175673495978117,
-0.01661451905965805,
-0.00976734422147274,
0.014561868272721767,
0.029847612604498863,
-0.0062372395768761635,
-0.01321563869714737,
-0.0008858072105795145,
-0.03883245587348938,
0.011590918526053429,
0.0015989497769623995,
0.04652465879917145,
0.002562754787504673,
0.05551541596651077,
0.008009062148630619,
-0.031159065663814545,
-0.007035521324723959,
-0.06460389494895935,
0.1101326122879982,
-0.002865911927074194,
-0.03436765447258949,
-0.04593797028064728,
0.05469295755028725,
-0.011873452924191952,
-0.003751609241589904,
0.018234027549624443,
-0.048827048391103745,
-0.003350270679220557,
-0.005759932566434145,
-0.05316746234893799,
0.017357349395751953,
0.01440167985856533,
0.004665387328714132,
-0.08230345696210861,
0.019341658800840378,
0.050404902547597885,
0.044664863497018814,
0.012625599279999733,
-0.06981930881738663,
-0.05061594769358635,
0.029806407168507576,
-0.04780213162302971,
-0.03812530264258385,
0.011239121668040752,
0.0470295213162899,
0.02545252814888954,
0.03214692696928978,
0.0516967736184597,
-0.007896458730101585,
0.020936306565999985,
0.018104448914527893,
-0.05296711623668671,
-0.03870374336838722,
-0.04419698193669319,
-0.008182822726666927,
0.031237564980983734,
0.034723419696092606,
-0.07042478024959564,
-0.016334321349859238,
-0.022694280371069908,
0.007276296149939299,
-0.054771967232227325,
-0.002937738783657551,
0.033825501799583435,
0.02857043780386448,
0.0031126937828958035,
0.02104819566011429,
-0.021947845816612244,
-0.057054303586483,
-0.05015754699707031,
0.025186320766806602,
0.015191913582384586,
0.05615398660302162,
-0.04164403676986694,
0.03498378396034241,
0.06155858933925629,
-0.04224088788032532,
-0.0873507484793663,
-0.0028616345953196287,
0.027807731181383133,
-0.05189605802297592,
0.003720382694154978,
-0.02138807438313961,
0.013072559610009193,
0.009535904973745346,
0.004362822975963354,
0.020973917096853256,
0.029570449143648148,
0.014617614448070526,
-0.012342987582087517,
-0.00658000074326992,
-0.019763095304369926,
-0.08199390023946762,
0.00464691873639822,
-0.061889976263046265,
-0.020840579643845558,
0.015903834253549576,
0.05866357311606407,
0.01576581411063671,
0.008412633091211319,
-0.03605407103896141,
-0.004655873402953148,
-0.05099179223179817,
0.01073612179607153,
0.03275197744369507,
0.043508123606443405,
-0.0011518234387040138,
-0.03423804044723511,
0.0033313571475446224,
0.009608966298401356,
0.01976650208234787,
-0.02071860060095787,
0.010721003636717796,
-0.02926124818623066,
-0.03910881653428078,
0.014895958825945854,
-0.0771113708615303,
-0.03723197057843208,
-0.02904408425092697,
0.029328275471925735,
-0.030283665284514427,
-0.04014032334089279,
0.017332831397652626,
0.05962839350104332,
-0.009578688070178032,
-0.004620273597538471,
-0.09009835124015808,
-0.04431350156664848,
-0.025395290926098824,
0.03283711522817612,
0.014521953649818897,
0.014937950298190117,
-0.0003318691742606461,
0.08003254979848862,
-0.021419957280158997,
-0.024640846997499466,
0.016526537016034126,
-0.0008081523119471967,
-0.030931074172258377,
0.008167107589542866,
0.021017123013734818,
-0.06992509216070175,
0.030546076595783234,
0.03886380419135094,
-0.029550377279520035,
-0.0074596400372684,
0.00318579631857574,
-0.007111686281859875,
0.034051813185214996,
-0.003179343184456229,
0.004779508337378502,
0.025437558069825172,
-0.06182513386011124,
-0.02060181275010109,
0.05774496868252754,
-0.024296050891280174,
-0.026847010478377342,
0.05543801933526993,
0.017542146146297455,
-0.02732939086854458,
-0.03376507759094238,
0.015844305977225304,
-0.010356015525758266,
0.006411225534975529,
-0.022466639056801796,
0.014962481334805489,
0.05967295914888382,
0.03198821470141411,
-0.0451679602265358,
-0.01022407878190279,
-0.06640496850013733,
0.007535328157246113,
-0.023479700088500977,
0.03720903396606445,
-0.003489301074296236,
0.018701734021306038,
-0.017701679840683937,
0.024887338280677795,
-0.06414882838726044,
0.04449464753270149,
0.03685811534523964,
-0.0401231124997139,
-0.0337991900742054,
-0.06654104590415955,
-0.023627085611224174,
-0.02968418411910534,
0.03912322223186493,
0.031118763610720634,
-0.06612137705087662,
-0.007247201632708311,
0.0024541313759982586,
0.030344316735863686,
0.01667313650250435,
0.03024902753531933,
0.012940225191414356,
0.006017595995217562,
0.03732806444168091,
-0.06272763758897781,
-0.03163404017686844,
0.018546629697084427,
0.038725968450307846,
0.02438025362789631,
0.04535885900259018,
-0.012250684201717377,
-0.05953025072813034,
-0.02604592777788639,
0.007892193272709846,
0.003931321669369936,
-0.014569963328540325,
-0.034927692264318466,
0.05226835981011391,
-0.023383600637316704,
0.04291209578514099,
-0.02255587838590145,
-0.006426422856748104,
-0.04329466447234154,
-0.009557054378092289,
-0.031008845195174217,
-0.006104317028075457,
-0.002273665275424719,
-0.030691122636198997,
0.020125597715377808,
0.011416888795793056,
-0.04588383063673973,
0.07852665334939957,
-0.019459543749690056,
-0.0017208043718710542,
0.02287842519581318,
-0.03671080619096756,
0.015754053369164467,
0.027355100959539413,
-0.04450278356671333,
-0.04236447438597679,
-0.032801903784275055,
-0.03095221146941185,
0.012453128583729267,
0.02222372405230999,
-0.03574328497052193,
0.006751107983291149,
0.038113877177238464,
-0.022708093747496605,
-0.026458770036697388,
0.013266515918076038,
-0.04031454771757126,
0.040352851152420044,
-0.0029337946325540543,
0.014692084863781929,
0.017020368948578835,
-0.025013523176312447,
-0.013878638856112957,
-0.05681440606713295,
-0.0077080135233700275,
0.003193225711584091,
-0.048341136425733566,
-0.023505179211497307,
0.007465290371328592,
0.05503115803003311,
0.01024380512535572,
0.03247008100152016,
-0.06662429869174957,
0.038575951009988785,
-0.02413478121161461,
0.05502926558256149,
0.023132117465138435,
-0.026713529601693153,
-0.06761159747838974,
0.05492759868502617,
0.044345807284116745,
0.04457506909966469,
0.016791971400380135,
-0.021695025265216827,
-0.033144835382699966,
-0.008116506971418858,
0.08537707477807999,
0.006742010824382305,
-0.02506846748292446,
-0.01934712380170822,
-0.0006688812281936407,
0.02513548731803894,
-0.02271934412419796,
0.046079132705926895,
0.027666624635457993,
0.07073012739419937,
0.03605867177248001,
-0.02986753359436989,
-0.03828929364681244,
-0.02915019355714321,
0.05038654804229736,
0.027014531195163727,
-0.008669133298099041,
-0.04795514792203903,
0.037898339331150055,
-0.013550985604524612,
0.021815208718180656,
0.023723118007183075,
0.008356902748346329,
-0.007232350297272205,
-0.017407920211553574,
-0.02297157235443592,
0.042955126613378525,
-0.05063878744840622,
0.05577918514609337,
0.07790088653564453,
-0.006728544365614653,
0.07589258998632431,
0.05320464074611664,
-0.03715462610125542,
0.04478851333260536,
-0.019032305106520653,
0.01768915355205536,
-0.04138575866818428,
0.008068572729825974,
0.016102734953165054,
0.03219464421272278,
-0.01038371305912733,
-0.01629515364766121,
0.016671687364578247,
0.013936981558799744,
-0.05020185932517052,
-0.028292054310441017,
0.041705455631017685,
0.0209524966776371,
-0.020975319668650627,
0.0010333555983379483,
0.04476850852370262,
0.03544876351952553,
0.03083333931863308,
-0.05811280384659767,
-0.01680559292435646,
0.017754502594470978,
0.0026561697013676167,
0.0034174825996160507,
0.009966611862182617,
0.05543985962867737,
0.007281241938471794,
-0.04153692349791527,
0.05649409070611,
-0.04778332635760307,
-0.0020941095426678658,
-0.03169112280011177,
-0.024325283244252205,
0.012511305510997772,
0.03151267394423485,
-0.004182229749858379,
-0.035712506622076035,
0.052233949303627014,
-0.050331465899944305,
0.0005006795399822295,
-0.02972927689552307,
0.04374894127249718,
-0.051682304590940475,
-0.06163187325000763,
-0.018066244199872017,
0.03801575303077698,
0.04662798345088959,
0.04252570867538452,
-0.013847450725734234,
-0.024711938574910164,
-0.014701444655656815,
0.06495008617639542,
0.033580996096134186,
0.01785818673670292,
-0.042909957468509674,
-0.008755200542509556,
-0.03440938517451286,
0.012789541855454445,
0.015428470447659492,
-0.013895167969167233,
0.054850175976753235,
-0.05836141109466553,
-0.03928183764219284,
-0.039995644241571426,
-0.04206017404794693,
-0.0037315820809453726,
0.021758541464805603,
0.015134846791625023,
0.014696983620524406,
0.007194245234131813,
-0.0301851574331522,
-0.013844986446201801,
-0.03787862882018089,
0.027882417663931847,
0.02372899278998375,
-0.023044848814606667,
0.05564826354384422,
-0.012759216129779816,
0.038996580988168716,
0.006305891554802656,
-0.03437380865216255,
-0.07812044769525528,
0.028546784073114395,
0.01741468906402588,
0.011096881702542305,
-0.02504701353609562,
-0.008453182876110077,
-0.01635614037513733,
-0.0298408642411232,
0.008498826064169407,
0.0006623316439799964,
0.030659427866339684,
0.020796384662389755,
-0.00072832265868783,
0.013406410813331604,
-0.027056556195020676,
0.026473719626665115,
0.060995426028966904,
0.026171473786234856,
-0.019242510199546814,
-0.04045170918107033,
0.04904691129922867,
0.01703486032783985,
-0.01955294795334339,
-0.03246275335550308,
0.0776866152882576,
-0.02194797806441784,
-0.01643490232527256,
0.04655588045716286,
0.01683763787150383,
0.02215563878417015,
0.011892291717231274,
-0.04065855219960213,
-0.02384309098124504,
-0.004653621464967728,
0.03921139985322952,
-0.025032944977283478,
0.06660368293523788,
0.0038007234688848257,
0.04115138575434685,
0.02067497745156288,
-0.016193892806768417,
-0.018368622288107872,
0.00716814398765564,
0.00835686456412077,
0.005263571627438068,
0.03493054211139679,
0.0007051307475194335,
0.04299098625779152,
-0.04001016169786453,
-0.005478654522448778,
0.0184065792709589,
-0.06848764419555664,
-0.05720167234539986,
0.07173699885606766,
0.03354405611753464,
0.01562464889138937,
-0.0424295999109745,
0.0011778685729950666,
0.05570447817444801,
-0.0014739768812432885,
-0.017314165830612183,
0.05022873729467392,
-0.02776419371366501,
0.04883484169840813,
0.008836479857563972,
0.030324993655085564,
-0.022295234724879265,
0.03791598230600357,
-0.033305369317531586,
0.013712561689317226,
-0.053628481924533844,
-0.011622441932559013,
-0.009969132021069527,
-0.009385514073073864,
0.08540371805429459,
-0.005162406247109175,
0.014113751240074635,
0.06498681753873825,
0.05618320778012276,
0.021300775930285454,
0.03141728788614273,
-0.07423938065767288,
0.04745238646864891,
-0.046132590621709824,
0.04233386740088463,
0.01185812521725893,
-0.06770223379135132,
0.002738284645602107,
-0.0340404286980629,
-0.043695688247680664,
0.018326200544834137,
-0.049696993082761765,
0.04035407304763794,
-0.007506355177611113,
-0.05787070840597153,
-0.030632898211479187,
0.051373109221458435,
0.025730397552251816,
0.04977924004197121,
0.022680021822452545,
0.06017882749438286,
0.0466902032494545,
-0.025744181126356125,
-0.05380229651927948,
0.033493343740701675,
0.01735646277666092,
0.08411271125078201,
0.011796684935688972,
0.025277502834796906,
-0.022491436451673508,
0.021667003631591797,
0.020176922902464867,
0.01285862922668457,
-0.02712296135723591,
-0.046182483434677124,
0.05550007149577141,
0.03363335505127907,
-0.016628630459308624,
0.03007999062538147,
0.04467209056019783,
-0.08658083528280258,
0.024143878370523453,
-0.02880375273525715,
0.012879110872745514,
-0.007313495967537165,
-0.008015411905944347,
-0.0018406531307846308,
-0.04786926135420799,
-0.01497696153819561,
-0.02158375456929207,
-0.01073048822581768,
-0.0078980578109622,
-0.07272930443286896,
-0.00729213235899806,
0.02259124629199505,
0.04374127462506294,
0.022362040355801582,
0.04628314450383186,
0.013304428197443485,
-0.05269628018140793,
-0.036744531244039536,
-0.01576853357255459,
-0.029309106990695,
-0.00008851676830090582,
-0.02733500301837921,
0.02956143207848072,
0.010472363792359829,
-0.026939906179904938,
0.023537645116448402,
0.019704023376107216,
0.07786158472299576,
0.05098988115787506,
-0.001354391104541719,
-0.0010969603899866343,
0.014785606414079666,
0.05608228221535683,
0.013357487507164478,
-0.012821671552956104,
-0.025544898584485054,
-0.016173703595995903,
0.03181234747171402,
0.027653368189930916,
-0.016732648015022278,
0.021076170727610588,
-0.045037176460027695,
0.06978490203619003,
-0.009029540233314037,
-0.02021455205976963,
-0.01211625151336193,
-0.011558844707906246,
-0.05038780719041824,
-0.0018579316092655063,
-0.019388537853956223,
0.025703517720103264,
-0.060990385711193085,
0.028436237946152687,
0.026717226952314377,
0.03033492900431156,
-0.022274736315011978,
-0.0343904048204422,
-0.026719817891716957,
-0.07747452706098557,
-0.07261785119771957,
0.0009294697665609419,
-0.028831491246819496,
0.019767940044403076,
-0.037392668426036835,
0.05954918637871742,
-0.026719696819782257,
0.004850213415920734,
0.05758945271372795,
-0.05651431903243065,
0.04218306764960289,
0.06200789660215378,
-0.028443971648812294,
0.02236209250986576,
-0.03205366060137749,
-0.02039681375026703,
-0.03362365812063217,
0.0209237951785326,
0.010960254818201065,
0.012871713377535343,
-0.013391198590397835,
-0.05299956351518631,
0.013455239124596119,
-0.021301740780472755,
0.03801361843943596,
-0.020587390288710594,
0.054933302104473114,
0.04177841916680336,
-0.005022629164159298,
-0.013643110170960426,
0.01691739447414875,
0.025852637365460396,
-0.0037896577268838882,
-0.06233356148004532,
-0.07899925857782364,
-0.06530284136533737,
-0.02909979782998562,
-0.035734958946704865,
0.01171765848994255,
0.07492760568857193,
-0.035804569721221924,
0.0004076901823282242,
-0.048866014927625656,
-0.023162417113780975,
0.020186634734272957,
0.07439524680376053,
0.012035123072564602,
0.009455143474042416,
0.011178660206496716,
0.006842380855232477,
0.04095233231782913,
0.06143585592508316,
-0.0031495667062699795,
0.020640403032302856,
-0.0013329540379345417,
-0.0246558990329504,
-0.05493924021720886,
-0.008797811344265938,
-0.04374949634075165
] |
<p>In Chiral representation, a Majorana spinor looks like:</p>
<p>$$\psi=\begin{pmatrix}
\psi_L\\
-i\sigma^2\psi_L^*\end{pmatrix}$$ </p>
<p>In this representation the Right handed field is the charge-conjugate of the left handed field. i.e., $(\psi_R)^c=\psi_L$, where $$\psi_R=\begin{pmatrix}
0\\
-i\sigma^2\psi_L^*\end{pmatrix}$$</p>
<p>and also $\psi^c=e^{i\phi}\psi$</p>
<ol>
<li><p>How does it look like in Majorana Representation, explicitly in the form of a column vector? What is the usefulness of Majorana representation?</p></li>
<li><p>Can I use the condition $\psi^c=e^{i\phi}\psi$ to be the definition of a Majorana fermion?</p></li>
</ol> | g4800 | [
0.0486723817884922,
-0.006399708334356546,
0.004282078240066767,
-0.09559676796197891,
0.07070264220237732,
-0.034308698028326035,
0.030812762677669525,
0.007114456966519356,
-0.004707420710474253,
0.002126724226400256,
-0.013404273428022861,
-0.02485593408346176,
-0.023581473156809807,
0.01034123171120882,
0.0673157349228859,
0.014596185646951199,
0.04966828227043152,
0.017790742218494415,
0.0027558349538594484,
-0.04149042069911957,
-0.028822047635912895,
0.03303121030330658,
-0.005976029671728611,
0.03654806688427925,
0.05348842963576317,
-0.028075650334358215,
0.027118252590298653,
-0.0031077128369361162,
0.0038341840263456106,
-0.03637944534420967,
0.01342338602989912,
0.016309799626469612,
0.06946633756160736,
-0.017817150801420212,
-0.012958243489265442,
0.024306083098053932,
0.05447966605424881,
0.03795289620757103,
0.042859263718128204,
-0.042243022471666336,
0.016750657930970192,
-0.01441396214067936,
0.00023478960792999715,
-0.01561861764639616,
-0.04882434383034706,
0.035947535187006,
-0.029783042147755623,
0.03359195217490196,
-0.06513108313083649,
0.041911207139492035,
0.0023978971876204014,
-0.026299959048628807,
0.007976371794939041,
0.07865923643112183,
0.04894164949655533,
0.012223588302731514,
0.013459601439535618,
-0.02167646400630474,
0.030879080295562744,
0.07608620077371597,
-0.010562890209257603,
-0.057881150394678116,
-0.01568162627518177,
0.027215799316763878,
0.05330837890505791,
-0.03143175318837166,
-0.0418517105281353,
0.04641137272119522,
-0.033215492963790894,
0.030156953260302544,
-0.020844288170337677,
-0.05594509840011597,
0.09064130485057831,
-0.015077922493219376,
-0.02100757695734501,
0.008732086047530174,
-0.017576459795236588,
-0.03968445211648941,
0.045113783329725266,
0.0004668984329327941,
-0.006284818518906832,
-0.06675995141267776,
0.005433626938611269,
-0.016055764630436897,
0.03547097370028496,
-0.003117057727649808,
-0.02053845487535,
-0.020845135673880577,
-0.008979862555861473,
0.005974851083010435,
-0.0003301372635178268,
-0.010678006336092949,
-0.007873201742768288,
-0.01103612594306469,
-0.012203256599605083,
-0.06806151568889618,
-0.07879871129989624,
0.017032895237207413,
-0.015052735805511475,
-0.010718999430537224,
0.004865116439759731,
0.08486318588256836,
0.07343947142362595,
0.04074745252728462,
-0.019036022946238518,
0.0656716525554657,
0.06212178245186806,
-0.01989046297967434,
-0.010325245559215546,
0.005477706901729107,
-0.031364452093839645,
0.05625361576676369,
-0.034081898629665375,
0.04955480247735977,
-0.05632908642292023,
-0.008581198751926422,
0.07936044782400131,
-0.06311142444610596,
0.027371030300855637,
0.044813212007284164,
0.01058361679315567,
-0.018093431368470192,
0.0773933082818985,
0.04270457103848457,
0.04682546108961105,
-0.012621152214705944,
-0.017243344336748123,
0.03609216958284378,
0.06554204970598221,
-0.06576139479875565,
0.016820957884192467,
-0.04050922766327858,
0.011938582174479961,
0.008990994654595852,
0.04390419274568558,
0.03661871701478958,
-0.05488485470414162,
0.011889428831636906,
-0.0023348722606897354,
-0.02984321117401123,
0.031049618497490883,
-0.02007901296019554,
-0.008754472248256207,
-0.013957849703729153,
0.0037078927271068096,
-0.0412122942507267,
0.028233690187335014,
-0.05546533316373825,
0.06560412794351578,
0.05059249326586723,
-0.016456933692097664,
0.0514763668179512,
-0.015061525627970695,
-0.017803005874156952,
-0.005282477010041475,
0.001794752199202776,
0.07075595110654831,
-0.030745750293135643,
-0.03888123854994774,
-0.0470312163233757,
0.02890104241669178,
0.002563406713306904,
0.01350742019712925,
-0.012335607782006264,
0.014897986315190792,
-0.020148104056715965,
0.011453376151621342,
-0.06750455498695374,
-0.01143576204776764,
-0.053367458283901215,
0.014285373501479626,
0.026085369288921356,
-0.02167496643960476,
-0.038737937808036804,
0.04935020953416824,
0.005789345595985651,
-0.07666214555501938,
0.017070814967155457,
0.06726997345685959,
0.025906996801495552,
-0.0471622534096241,
0.031940821558237076,
-0.03054879978299141,
0.008848492056131363,
-0.06157856434583664,
-0.046267956495285034,
-0.007744334638118744,
0.08815076947212219,
0.01608913205564022,
-0.01914058066904545,
0.02459428273141384,
0.03101135417819023,
0.013727284036576748,
0.09451733529567719,
-0.00042520955321379006,
-0.017463134601712227,
0.002049986971542239,
-0.04102867841720581,
-0.09986107796430588,
-0.023028023540973663,
-0.011789161711931229,
-0.029561061412096024,
-0.0037484278436750174,
0.012995433062314987,
0.004451055079698563,
-0.004015278536826372,
-0.033727239817380905,
-0.010262871161103249,
0.006501116789877415,
0.00209848303347826,
0.006108288653194904,
-0.022375725209712982,
0.004572571255266666,
0.038447484374046326,
-0.028167059645056725,
-0.030495094135403633,
0.01627175323665142,
-0.010855860076844692,
-0.05645733326673508,
0.07813622802495956,
0.026807861402630806,
-0.08923404663801193,
0.043970659375190735,
0.007663497235625982,
0.011107363738119602,
0.08255641907453537,
-0.010686608962714672,
0.02719719149172306,
0.011449044570326805,
0.01126665249466896,
-0.055409450083971024,
0.04657251760363579,
0.007190035656094551,
0.019586820155382156,
-0.02136245183646679,
-0.049601227045059204,
-0.06713788211345673,
0.030910540372133255,
0.021417589858174324,
0.008031257428228855,
-0.0026000544894486666,
-0.02833542227745056,
-0.025224629789590836,
0.06311994791030884,
-0.01569899171590805,
-0.003726632334291935,
0.03190847486257553,
0.024826176464557648,
-0.04449225962162018,
0.038854748010635376,
-0.005171749275177717,
-0.000777148175984621,
-0.05568333715200424,
0.07539860159158707,
-0.0018171813571825624,
-0.030652755871415138,
0.002119318349286914,
-0.047363027930259705,
-0.02041010744869709,
0.013459006324410439,
0.015929244458675385,
0.02125716581940651,
-0.004036839120090008,
0.02621004730463028,
-0.010658732615411282,
-0.026183802634477615,
0.061625249683856964,
0.06595020741224289,
0.02499285154044628,
0.020993413403630257,
-0.055774420499801636,
0.08622262626886368,
0.010297748260200024,
0.00005193372635403648,
0.004013862926512957,
-0.030784668400883675,
-0.04467007890343666,
-0.01129960548132658,
0.005675967782735825,
-0.07534274458885193,
0.02005751244723797,
-0.0035566941369324923,
0.005837075412273407,
0.004310971591621637,
0.008299645036458969,
-0.035738877952098846,
0.035223595798015594,
-0.003596784546971321,
0.07134775817394257,
0.01815277338027954,
-0.06477785110473633,
0.038371454924345016,
0.009811296127736568,
-0.07164686918258667,
0.021891381591558456,
-0.04739600047469139,
0.03399888426065445,
-0.041698187589645386,
-0.008135069161653519,
0.07926520705223083,
0.06374141573905945,
-0.030482154339551926,
-0.018112311139702797,
-0.023372512310743332,
0.043014392256736755,
0.022208968177437782,
-0.07580116391181946,
0.007190260570496321,
-0.02253696322441101,
-0.033149268478155136,
-0.015354613773524761,
0.028761092573404312,
0.04351372644305229,
0.004737613257020712,
-0.07157035171985626,
-0.0099740419536829,
-0.013081155717372894,
0.035873059183359146,
0.0036344535183161497,
0.010950444266200066,
0.0016033173305913806,
-0.03129374980926514,
0.04017346724867821,
0.05640416219830513,
-0.0014419014332816005,
0.0005167501512914896,
0.00019160605734214187,
0.01989271491765976,
-0.019215412437915802,
-0.033711716532707214,
-0.005336305126547813,
0.043179456144571304,
0.036095015704631805,
0.05530436709523201,
-0.07643674314022064,
0.05142959952354431,
-0.0956106185913086,
0.0035434227902442217,
-0.023625966161489487,
-0.029465580359101295,
-0.02009459212422371,
-0.008304756134748459,
-0.039028510451316833,
-0.044273968786001205,
0.013639244250953197,
-0.02408725768327713,
-0.03160211816430092,
-0.02935125306248665,
0.016881758347153664,
-0.011458903551101685,
-0.05560749024152756,
-0.04084847494959831,
0.017776651307940483,
0.04064856097102165,
-0.001378019223921001,
-0.010358143597841263,
0.013167150318622589,
0.025223499163985252,
0.007012642920017242,
0.029679784551262856,
0.0448836050927639,
-0.005093859974294901,
0.03570378199219704,
-0.027727307751774788,
-0.0059388731606304646,
-0.0016523824306204915,
-0.0068110134452581406,
0.03001978062093258,
0.019827039912343025,
0.018084781244397163,
0.03290603309869766,
-0.0188234094530344,
-0.0029801633208990097,
-0.02318056859076023,
-0.028373433277010918,
-0.0510706901550293,
-0.043856970965862274,
-0.045499805361032486,
-0.04535558447241783,
-0.0018353924388065934,
-0.06572332978248596,
0.008468122221529484,
0.032437514513731,
0.01633923500776291,
-0.006438411772251129,
0.01618998497724533,
0.0005528576439246535,
0.03677767515182495,
-0.019182614982128143,
0.009978012181818485,
-0.052609361708164215,
-0.02593079023063183,
-0.012765333987772465,
-0.010600772686302662,
0.03262278065085411,
0.015615370124578476,
0.007970068603754044,
-0.023467354476451874,
-0.07442428916692734,
0.009399295784533024,
-0.04953185096383095,
0.03625797480344772,
0.09987549483776093,
-0.029285449534654617,
0.011238925158977509,
-0.015295103192329407,
-0.035134509205818176,
-0.03851785883307457,
0.023309223353862762,
-0.06790019571781158,
0.01288001798093319,
-0.010144115425646305,
-0.03232507035136223,
-0.035397034138441086,
0.039253950119018555,
0.004510696977376938,
-0.02654559724032879,
-0.003127369564026594,
-0.01451354194432497,
-0.008692137897014618,
0.07102498412132263,
0.01857251487672329,
0.013666254468262196,
0.012303534895181656,
0.03200201690196991,
0.03708226606249809,
0.10342247784137726,
0.015730172395706177,
-0.019418440759181976,
-0.013136257417500019,
0.06860946863889694,
0.0859091728925705,
0.02192280814051628,
0.04281531274318695,
-0.022376492619514465,
0.0043966700322926044,
-0.08565230667591095,
-0.03649256005883217,
0.047068819403648376,
0.022258687764406204,
-0.019697194918990135,
-0.016686521470546722,
0.01989089511334896,
-0.005665763281285763,
-0.06760842353105545,
0.0008913136553019285,
-0.03180571645498276,
-0.0010971282608807087,
0.006451652850955725,
-0.025501366704702377,
-0.0364428348839283,
0.025790270417928696,
0.0007094288012012839,
0.000723145145457238,
0.04554840177297592,
-0.03975934162735939,
-0.0095458272844553,
-0.04317406192421913,
0.005311735440045595,
0.003865976817905903,
-0.013796127401292324,
-0.04726921021938324,
-0.035047419369220734,
-0.004471944645047188,
0.0073968456126749516,
0.006992419715970755,
-0.05109510198235512,
-0.020792193710803986,
0.050923630595207214,
-0.0477142259478569,
0.0008730651461519301,
-0.038493234664201736,
-0.0015353034250438213,
-0.07311086356639862,
-0.020867526531219482,
0.020647777244448662,
-0.006120928563177586,
-0.0317784920334816,
-0.02145821787416935,
-0.024758169427514076,
-0.028061768040060997,
-0.05358702316880226,
0.0033869678154587746,
0.024020906537771225,
-0.0004918910562992096,
-0.025854825973510742,
-0.000679401564411819,
-0.038429006934165955,
-0.0025427236687391996,
0.016929177567362785,
0.009092195890843868,
0.05532894283533096,
-0.04089795798063278,
0.028444450348615646,
0.021977657452225685,
0.044634170830249786,
0.0049567753449082375,
-0.000013555889381677844,
0.027600623667240143,
0.0013279318809509277,
0.00030105901532806456,
-0.005695793777704239,
-0.002561952918767929,
0.031487490981817245,
-0.005947133060544729,
0.019698677584528923,
0.031332969665527344,
0.026819787919521332,
-0.03018513135612011,
0.027125610038638115,
0.008667616173624992,
0.016822993755340576,
-0.010824109427630901,
0.017406199127435684,
-0.014599167741835117,
0.0014157643308863044,
-0.023670058697462082,
0.015191176906228065,
-0.004103296902030706,
-0.03943055495619774,
0.003831581911072135,
-0.02031003311276436,
0.02817239798605442,
-0.06916172057390213,
-0.012261362746357918,
0.02331847883760929,
0.02646365575492382,
-0.06327120959758759,
0.04122638329863548,
0.05243511497974396,
-0.051022473722696304,
-0.05693158134818077,
0.009715261869132519,
0.031156543642282486,
0.0022585317492485046,
-0.08112891018390656,
0.013623857870697975,
0.04449453577399254,
0.02793947234749794,
0.02758033201098442,
-0.03071143664419651,
-0.03348315879702568,
-0.008239706046879292,
0.017451362684369087,
0.0012305865529924631,
0.04093233495950699,
0.03566499054431915,
0.01683099754154682,
-0.012433279305696487,
0.015194186009466648,
-0.018196625635027885,
0.007599049713462591,
-0.021582160145044327,
-0.05003569647669792,
0.0379117988049984,
0.00020587965263985097,
-0.04903990775346756,
-0.0140775665640831,
0.004563495516777039,
0.02765297330915928,
-0.004700132180005312,
0.025523079559206963,
0.017516177147626877,
-0.029213296249508858,
-0.022950395941734314,
-0.010408077389001846,
-0.01857079565525055,
-0.047437895089387894,
0.03574560955166817,
0.007633406203240156,
-0.04288017749786377,
-0.005661798641085625,
0.05541761964559555,
0.042706385254859924,
0.0035105454735457897,
0.00531748728826642,
0.05447668209671974,
0.004419066943228245,
-0.0012551631079986691,
0.00479044858366251,
0.06267404556274414,
-0.01372883003205061,
-0.034026481211185455,
0.013588914647698402,
0.007705938536673784,
-0.00013185507850721478,
-0.04867853596806526,
0.015538685955107212,
0.011696700006723404,
0.0005564742023125291,
-0.023618118837475777,
0.026311099529266357,
-0.0008496323134750128,
0.013822538778185844,
-0.021755069494247437,
0.0016124657122418284,
-0.0547465942800045,
0.038917575031518936,
-0.01798989437520504,
-0.020722320303320885,
0.06912399083375931,
0.04811717942357063,
0.02215849794447422,
0.012067909352481365,
0.043963633477687836,
0.04018561169505119,
-0.06692668795585632,
-0.005616653244942427,
-0.019361363723874092,
0.03548125922679901,
0.03743003308773041,
-0.014061766676604748,
-0.02967364713549614,
0.010705639608204365,
-0.00421365350484848,
-0.0534161739051342,
0.026530276983976364,
0.06611388921737671,
-0.03350411728024483,
0.02045683190226555,
-0.03569195047020912,
0.04363369196653366,
0.034778352826833725,
0.01218128576874733,
-0.0010057786712422967,
0.09247329086065292,
-0.018269259482622147,
0.05814487859606743,
0.03885785862803459,
0.018721066415309906,
0.03983252868056297,
-0.020848877727985382,
0.0646539181470871,
0.0165975671261549,
0.016633793711662292,
-0.02118910849094391,
-0.09923200309276581,
0.006802041083574295,
0.023885495960712433,
0.05319871008396149,
-0.03142099827528,
0.03459547460079193,
0.008843627758324146,
-0.021778050810098648,
-0.040005430579185486,
0.015921620652079582,
0.00010536287300055847,
0.011684983968734741,
-0.06628353893756866,
-0.04923310503363609,
0.02723175287246704,
0.002202287781983614,
0.02071157470345497,
-0.01758357137441635,
-0.09442850947380066,
-0.020427554845809937,
0.06824935227632523,
0.015399893745779991,
-0.021899856626987457,
-0.08676809817552567,
0.008420332334935665,
-0.04838864877820015,
-0.052722424268722534,
-0.054876718670129776,
-0.006965243723243475,
0.0479588508605957,
0.009444254450500011,
-0.02128368243575096,
0.046096768230199814,
-0.019409121945500374,
-0.07269078493118286,
-0.05169100686907768,
-0.05312369763851166,
0.04449375718832016,
-0.01947821117937565,
-0.052257899194955826,
-0.012620138004422188,
-0.03445841372013092,
-0.00901444349437952,
-0.013941309414803982,
-0.03734095022082329,
0.022070327773690224,
0.008839936926960945,
-0.012223533354699612,
-0.00603710301220417,
-0.025894703343510628,
0.015619903802871704,
0.01232745498418808,
-0.003293961752206087,
0.039504315704107285,
0.047259531915187836,
-0.017757466062903404,
-0.002012288197875023,
0.000929497939068824,
-0.04394891485571861,
0.009673221036791801,
-0.005371480248868465,
0.024850906804203987,
0.024076245725154877,
0.05719481036067009,
0.06041640788316727,
-0.01813974417746067,
-0.011636451818048954,
0.01005603838711977,
0.07517500221729279,
-0.020831219851970673,
0.003979496657848358,
0.0008581838337704539,
-0.04836011305451393,
0.037468161433935165,
-0.016346778720617294,
0.05490012839436531,
0.02365981414914131,
0.028615523129701614,
0.012472249567508698,
0.05953368917107582,
-0.01243309210985899,
0.014134829863905907,
0.026760602369904518,
-0.025282343849539757,
-0.01926761120557785,
-0.0024532086681574583,
-0.013573174364864826,
0.015486284159123898,
-0.022158706560730934,
-0.03297366946935654,
-0.022468652576208115,
0.04756946116685867,
0.043528228998184204,
0.058859169483184814,
0.005699777510017157,
-0.03416573628783226,
-0.04735374078154564,
0.0953911691904068,
-0.04931490868330002,
0.009779785759747028,
0.006332870572805405,
-0.05828607827425003,
-0.006583649665117264,
-0.04866156354546547,
-0.025317924097180367,
-0.008265441283583641,
-0.022255266085267067,
-0.04458894953131676,
-0.03929204121232033,
-0.009452542290091515,
-0.03654753044247627,
-0.00835125707089901,
0.028925219550728798,
-0.04440569505095482,
-0.0003743119304999709,
-0.001599303912371397,
0.005882890895009041,
0.07191014289855957,
0.028554845601320267,
0.05411240831017494,
0.04420125484466553,
0.014102563261985779,
0.0174497589468956,
0.0119633749127388,
0.035054463893175125,
-0.059401411563158035,
-0.02712394669651985,
-0.014672334305942059,
-0.029518520459532738,
-0.0641581118106842,
-0.034488875418901443,
-0.007472295314073563
] |
<p>In the context of asymptotic symmetry groups, what is a boundary current? Why is it called a "current"? </p>
<p>Context: I'm reading Strominger's recent paper on Asymptotic symmetry group of Yang-Mills (link <a href="http://arxiv.org/abs/1308.0589">here</a>) and he has a section on the boundary current (section 2.3). I can follow the math completely fine, but some of the words are confusing to me. </p> | g4801 | [
0.043124761432409286,
0.001451669493690133,
-0.001626489800401032,
-0.01977035216987133,
0.048783522099256516,
0.008806944824755192,
0.0734882652759552,
0.00787351280450821,
-0.02443613111972809,
0.02695385366678238,
0.025807064026594162,
0.039274901151657104,
-0.012641558423638344,
0.020857850089669228,
-0.029927076771855354,
-0.04895920678973198,
0.016529500484466553,
-0.0009263096726499498,
0.025282887741923332,
-0.010214291512966156,
-0.0477682389318943,
0.01853703148663044,
0.0036826336290687323,
-0.022645315155386925,
0.03857989236712456,
0.019228879362344742,
0.027384037151932716,
-0.05864030867815018,
-0.016536548733711243,
-0.05952522158622742,
-0.005887478124350309,
0.056519243866205215,
0.07413565367460251,
-0.04985622689127922,
-0.04647035896778107,
-0.03451581671833992,
0.05083140358328819,
0.016905615106225014,
0.016447272151708603,
-0.01855820044875145,
0.08917205780744553,
-0.0008383286185562611,
-0.018579676747322083,
0.0013838077429682016,
-0.004631044343113899,
0.01920049637556076,
-0.046863749623298645,
-0.04382795840501785,
0.01992012746632099,
-0.013883339241147041,
0.012288238853216171,
0.06368058174848557,
0.06028301641345024,
0.009150657802820206,
0.0301055908203125,
-0.04909916967153549,
0.05902290344238281,
0.007251921109855175,
0.03878351300954819,
0.014589897356927395,
-0.041502345353364944,
0.04167044907808304,
0.007200968451797962,
0.016243169084191322,
0.0499514564871788,
-0.023079875856637955,
-0.05521403253078461,
-0.004887736402451992,
0.0035109608434140682,
0.04227205365896225,
0.022802315652370453,
-0.016527941450476646,
0.007984927855432034,
0.016706598922610283,
-0.05182928591966629,
0.02641693502664566,
0.009612513706088066,
-0.00161334581207484,
0.05175265669822693,
-0.006849042139947414,
-0.030301479622721672,
-0.05332831293344498,
-0.020224012434482574,
0.014875354245305061,
0.09533429145812988,
0.0014961096458137035,
-0.06423521786928177,
0.017131488770246506,
-0.033853039145469666,
-0.012132210657000542,
-0.016290292143821716,
-0.024675771594047546,
0.009055839851498604,
-0.06927259266376495,
0.04225970059633255,
0.022390803322196007,
0.026976313441991806,
0.03450120612978935,
-0.028712205588817596,
0.08509160578250885,
-0.07981429249048233,
-0.026614418253302574,
0.018250910565257072,
0.01197477150708437,
-0.03588331863284111,
0.009360297583043575,
0.04015646129846573,
-0.05450515076518059,
-0.007466419599950314,
-0.015063825063407421,
-0.005169332027435303,
-0.012193032540380955,
-0.047900158911943436,
0.015608767047524452,
-0.021276865154504776,
0.02454952709376812,
0.014650164172053337,
0.0013691518688574433,
0.021390289068222046,
0.026164719834923744,
0.007196719292551279,
-0.011333839036524296,
-0.06394938379526138,
-0.011803742498159409,
-0.018464220687747,
0.01369726937264204,
-0.017941169440746307,
-0.027847718447446823,
0.07069791853427887,
-0.02314133755862713,
0.010183632373809814,
0.008804237470030785,
-0.018281854689121246,
-0.016308357939124107,
-0.007519155275076628,
0.053078509867191315,
-0.0039357393980026245,
-0.0037009622901678085,
0.0675792247056961,
0.02799185924232006,
-0.024147026240825653,
-0.043914686888456345,
0.0031326315365731716,
-0.0067398627288639545,
-0.032927386462688446,
0.021043982356786728,
-0.011043272912502289,
-0.058053746819496155,
0.03771097585558891,
0.014091508463025093,
0.026839565485715866,
0.09123364090919495,
-0.012115058489143848,
-0.030019916594028473,
0.019618868827819824,
0.00023774951114319265,
0.032233983278274536,
-0.03199329599738121,
0.04058679938316345,
0.022526010870933533,
0.04139082878828049,
0.014719496481120586,
-0.04205623269081116,
0.02281421422958374,
-0.07418645918369293,
-0.0560385026037693,
0.0084824925288558,
-0.015452777966856956,
-0.028475956991314888,
-0.04004025086760521,
-0.011790182441473007,
0.047617945820093155,
0.03914061188697815,
0.04087318480014801,
0.06641735136508942,
0.03646952658891678,
-0.010235113091766834,
-0.0549609400331974,
0.04195453226566315,
0.02126152440905571,
-0.06243535503745079,
-0.0026828942354768515,
0.05940793454647064,
0.020786190405488014,
-0.063821941614151,
0.03752338886260986,
-0.0410638153553009,
0.00908481702208519,
0.02106221579015255,
-0.006522209849208593,
0.005607078783214092,
0.043272003531455994,
0.0022433551494032145,
0.08014790713787079,
-0.032465219497680664,
0.003711442928761244,
0.02211333066225052,
-0.0786522626876831,
-0.0027357705403119326,
-0.05578584223985672,
0.00528325792402029,
0.05157112330198288,
-0.02837233804166317,
-0.013383455574512482,
0.05032394453883171,
0.04116169735789299,
-0.005203003529459238,
0.01130523718893528,
0.03474021330475807,
0.01249707117676735,
0.05596719682216644,
-0.02392725460231304,
0.06784040480852127,
0.035202205181121826,
-0.025257987901568413,
-0.023874670267105103,
-0.03027280978858471,
0.03297455236315727,
-0.02816075272858143,
0.00616502808406949,
0.01871810294687748,
-0.07982473820447922,
0.028864441439509392,
0.02608661539852619,
-0.04211890697479248,
0.007761065848171711,
-0.03904866427183151,
-0.01408802717924118,
-0.040208566933870316,
0.002292086835950613,
-0.0867268517613411,
-0.015431281179189682,
-0.051166459918022156,
-0.02923930250108242,
-0.011045265942811966,
0.03762076422572136,
-0.009062269702553749,
0.024675946682691574,
0.016748549416661263,
-0.02145359106361866,
-0.02118411473929882,
0.006952200550585985,
0.04645564407110214,
0.024624032899737358,
0.014295686967670918,
0.04596565663814545,
0.027940183877944946,
0.005502020474523306,
-0.03341022506356239,
0.024422289803624153,
0.04729345068335533,
-0.039248645305633545,
-0.0024187294766306877,
0.0023496574722230434,
-0.008915882557630539,
-0.06650928407907486,
0.010766027495265007,
0.07973407208919525,
-0.013959183357656002,
-0.04919162020087242,
0.021993139758706093,
-0.046056490391492844,
0.07204257696866989,
-0.007532280404120684,
0.0007869344553910196,
-0.056218475103378296,
-0.0029152443166822195,
0.022703347727656364,
0.04631767049431801,
0.03767676278948784,
-0.022139638662338257,
0.027464037761092186,
0.024307729676365852,
-0.022813929244875908,
-0.03924558684229851,
-0.025183502584695816,
0.017419911921024323,
-0.09331869333982468,
0.0639723390340805,
-0.04362603649497032,
0.052031319588422775,
-0.00037527107633650303,
0.012968527153134346,
-0.015334678813815117,
-0.006690913811326027,
-0.02927338145673275,
-0.0442361906170845,
-0.019842015579342842,
-0.008363202214241028,
-0.022770147770643234,
-0.03462773934006691,
-0.022266438230872154,
0.02567307837307453,
0.015293062664568424,
0.05421464517712593,
-0.009930435568094254,
0.03637651354074478,
0.007655882742255926,
-0.025681667029857635,
0.021950995549559593,
-0.03133806958794594,
0.01594095304608345,
0.005368134938180447,
0.0101902075111866,
0.05224354937672615,
0.04157658666372299,
-0.02389892004430294,
-0.02655201032757759,
-0.025546392425894737,
0.015834713354706764,
-0.010686575435101986,
0.032510433346033096,
0.006364557426422834,
0.019030243158340454,
-0.04531817510724068,
0.030362918972969055,
-0.033613547682762146,
0.017342722043395042,
-0.06277621537446976,
-0.021552205085754395,
-0.01568075828254223,
0.049075059592723846,
0.07125439494848251,
0.01843719556927681,
-0.014961982145905495,
0.029401134699583054,
-0.03114437311887741,
-0.03260611742734909,
-0.007246451452374458,
-0.04977687448263168,
-0.006781463045626879,
-0.05701737850904465,
0.03816688060760498,
-0.00922122597694397,
-0.0257020965218544,
-0.048609815537929535,
-0.028062865138053894,
0.029425425454974174,
-0.0000838522391859442,
-0.024401504546403885,
0.09206745028495789,
-0.013741516508162022,
-0.007082656491547823,
0.049240242689847946,
0.055083516985177994,
-0.023417115211486816,
-0.0783763974905014,
-0.008710083551704884,
-0.056699492037296295,
0.010512836277484894,
-0.008080997504293919,
0.028562480583786964,
-0.002858866471797228,
-0.024681737646460533,
-0.02819804474711418,
-0.02120136469602585,
-0.03901836276054382,
-0.0008684288477525115,
-0.02603629045188427,
0.027246976271271706,
-0.010594191029667854,
0.022393422201275826,
0.026731716468930244,
0.062733955681324,
0.010854927822947502,
-0.013580026105046272,
-0.01584445871412754,
-0.016175342723727226,
-0.024644095450639725,
-0.07585126161575317,
0.09367102384567261,
-0.025879334658384323,
-0.037895701825618744,
0.06011718511581421,
0.015080654993653297,
-0.03276563435792923,
-0.03135266900062561,
0.03366602212190628,
-0.0360933393239975,
0.03567870333790779,
0.017513878643512726,
-0.0018445078749209642,
0.05649818480014801,
-0.002420247532427311,
0.004086412955075502,
0.011754220351576805,
-0.039377421140670776,
0.016040202230215073,
-0.009577201679348946,
-0.027795080095529556,
0.04084979370236397,
0.005580517929047346,
0.0005823617684654891,
-0.04847928136587143,
-0.021629001945257187,
-0.045866724103689194,
0.007072874810546637,
0.015808437019586563,
0.058062776923179626,
-0.010825714096426964,
0.022075669839978218,
0.026561656966805458,
-0.023217493668198586,
0.031852610409259796,
0.07412254065275192,
-0.013245094567537308,
0.02905658259987831,
-0.03316149488091469,
0.04442782700061798,
-0.019520925357937813,
-0.06913171708583832,
0.04488538205623627,
0.011091754771769047,
-0.0016295467503368855,
0.01277351938188076,
-0.012271581217646599,
0.04302547127008438,
-0.03339841961860657,
0.014392890967428684,
0.006080553401261568,
0.011583641171455383,
-0.00023780761694069952,
-0.013815920799970627,
0.033811070024967194,
-0.01579655148088932,
0.05454515665769577,
0.02110104076564312,
0.03548244386911392,
-0.0463363379240036,
-0.06422753632068634,
0.003964560106396675,
0.044162869453430176,
-0.05780217796564102,
0.0017903120024129748,
-0.06001508980989456,
0.030733240768313408,
0.02245902083814144,
0.009087463840842247,
-0.0313573032617569,
0.030207104980945587,
0.10645969957113266,
0.006952724419534206,
0.015598272904753685,
0.04440214857459068,
0.018860898911952972,
0.009547370485961437,
-0.0344284325838089,
-0.039072271436452866,
0.026127036660909653,
-0.004812212195247412,
-0.057230137288570404,
0.03000364825129509,
-0.020526636391878128,
-0.043754566460847855,
-0.00623824167996645,
-0.08163386583328247,
0.024152439087629318,
0.03927244246006012,
-0.044155899435281754,
0.02999752014875412,
-0.07001885026693344,
-0.03038984164595604,
0.025461221113801003,
-0.024188270792365074,
0.03319934010505676,
-0.03258828818798065,
0.027376562356948853,
-0.044339295476675034,
-0.04187893867492676,
-0.08006709069013596,
0.022684777155518532,
0.039964497089385986,
-0.02224930375814438,
0.0459248311817646,
0.014362912625074387,
-0.00041888171108439565,
0.011645182967185974,
-0.000532658479642123,
-0.035854846239089966,
0.008020328357815742,
0.008660612627863884,
0.0020918326918035746,
0.03143501654267311,
0.030486518517136574,
-0.009751270525157452,
-0.021628487855196,
0.017642591148614883,
0.03374067693948746,
-0.009885757230222225,
-0.011277156881988049,
-0.009424722753465176,
0.0196439977735281,
0.010997217148542404,
0.0032668637577444315,
-0.019812796264886856,
0.014099497348070145,
0.04281510040163994,
0.02858508750796318,
-0.03570070117712021,
-0.026372790336608887,
0.017786480486392975,
0.007101623807102442,
-0.021850086748600006,
-0.01674260012805462,
0.03669808432459831,
0.12859022617340088,
0.01609170250594616,
-0.0031642711255699396,
0.05856161564588547,
-0.008954856544733047,
0.007911245338618755,
-0.03562348708510399,
-0.004595466423779726,
-0.005420828238129616,
0.07801323384046555,
0.038019537925720215,
-0.043350376188755035,
-0.008284558542072773,
0.0051740133203566074,
0.011115208268165588,
-0.0041289301589131355,
0.018560318276286125,
0.0031312466599047184,
-0.04930444061756134,
0.017827583476901054,
-0.021526644006371498,
-0.07965204864740372,
0.02511165663599968,
0.014736022800207138,
0.07085400819778442,
0.05593397468328476,
-0.03826998919248581,
0.05465191975235939,
-0.06598924845457077,
0.04799411818385124,
-0.06157725676894188,
0.019915420562028885,
-0.0310236643999815,
-0.0033483856823295355,
0.006347911432385445,
-0.035539355129003525,
0.01918683759868145,
-0.04454008489847183,
0.029769403859972954,
-0.03038214147090912,
0.011426718905568123,
-0.012200579978525639,
-0.03753971308469772,
-0.01441185548901558,
-0.015765806660056114,
0.018673155456781387,
-0.043372202664613724,
0.017771899700164795,
-0.045184992253780365,
-0.029572680592536926,
0.011088326573371887,
-0.013064414262771606,
-0.01705384999513626,
-0.020483586937189102,
-0.03396670147776604,
0.06277772784233093,
-0.02279939316213131,
-0.010445824824273586,
-0.062282685190439224,
0.04592166841030121,
-0.049655646085739136,
-0.049941495060920715,
-0.03764461353421211,
0.0040808022022247314,
0.0242801234126091,
0.0434691421687603,
0.013051966205239296,
0.049737945199012756,
-0.007867311127483845,
-0.033949412405490875,
-0.01143327634781599,
-0.0438215509057045,
-0.02702476643025875,
-0.04238879680633545,
0.006770727690309286,
-0.015469098463654518,
-0.03891538083553314,
0.07433111220598221,
-0.06995730102062225,
0.009656408801674843,
0.022519169375300407,
-0.024359839037060738,
-0.02762269228696823,
0.056907180696725845,
-0.02969558723270893,
-0.019635571166872978,
0.04787880554795265,
0.007825433276593685,
0.017349734902381897,
0.0293858852237463,
-0.028157822787761688,
0.0075998748652637005,
0.06299213320016861,
0.020112546160817146,
-0.0451195053756237,
0.04503069818019867,
-0.005470686592161655,
0.018167464062571526,
0.0038384604267776012,
0.05421890318393707,
0.0669737160205841,
0.026239467784762383,
-0.01228452567011118,
-0.028737006708979607,
0.04021903872489929,
0.01232635322958231,
-0.020976413041353226,
-0.009402938187122345,
0.06466464698314667,
0.04635259881615639,
-0.05058584734797478,
-0.042961303144693375,
-0.013655918650329113,
0.006840677000582218,
0.01791430078446865,
0.017823481932282448,
-0.009166588075459003,
0.07103463262319565,
-0.007416303735226393,
0.064066082239151,
0.01619548350572586,
0.030039316043257713,
0.016649633646011353,
0.02264498360455036,
0.02826905995607376,
-0.025290964171290398,
0.016142917796969414,
0.001174596487544477,
-0.03383242338895798,
-0.040107473731040955,
0.03438770771026611,
-0.008222074247896671,
-0.034580618143081665,
0.0658736526966095,
0.02762274630367756,
-0.017671043053269386,
0.0233813114464283,
-0.02344324439764023,
-0.005216567777097225,
-0.014067213051021099,
-0.04399490728974342,
-0.008683913387358189,
0.0506720170378685,
-0.011638689786195755,
-0.00017476090579293668,
-0.01658502407371998,
0.006273095961660147,
-0.07776311784982681,
0.05273798108100891,
-0.0850755125284195,
-0.01783459261059761,
0.008754612877964973,
0.0081131337210536,
-0.027187993749976158,
-0.05142315849661827,
-0.035994961857795715,
-0.003457956947386265,
-0.023435141891241074,
-0.0701272264122963,
0.05121583864092827,
0.02322791889309883,
-0.003545207204297185,
-0.015108016319572926,
0.01771399937570095,
-0.003326324513182044,
-0.03219595551490784,
-0.03438261151313782,
0.002523883478716016,
-0.017327260226011276,
-0.03020836040377617,
-0.03573517128825188,
0.05594410002231598,
0.0590922012925148,
-0.009369432926177979,
-0.049047086387872696,
0.05906865373253822,
-0.01786099001765251,
0.008674471639096737,
0.01602102257311344,
-0.05823834612965584,
0.018403010442852974,
-0.03171397000551224,
-0.017605401575565338,
-0.0035663549788296223,
0.0300456453114748,
0.030124403536319733,
-0.02365901879966259,
-0.021916355937719345,
-0.04040275514125824,
-0.04163072630763054,
0.05768728628754616,
0.000984423328191042,
0.03954099491238594,
0.026156842708587646,
0.021844591945409775,
-0.01758231781423092,
-0.041772305965423584,
0.04773714020848274,
0.015109819360077381,
0.053605686873197556,
-0.012252327986061573,
0.010828551836311817,
-0.024429963901638985,
-0.030300116166472435,
-0.03601864352822304,
-0.06599512696266174,
0.009643313474953175,
0.07087589800357819,
-0.02029717154800892,
0.009111246094107628,
0.05875718221068382,
0.024754345417022705,
-0.053969576954841614,
0.00017193658277392387,
0.0194874107837677,
0.024885671213269234,
0.0307276900857687,
-0.07764707505702972,
-0.025152193382382393,
-0.09725844860076904,
-0.018630284816026688,
0.00998464971780777,
0.022579383105039597,
-0.04033752158284187,
-0.02472817897796631,
-0.041833583265542984,
0.051182087510824203,
-0.019782422110438347,
-0.01735648885369301,
-0.06467515975236893,
0.020962029695510864,
0.01829601265490055,
-0.07440035790205002,
0.0666712075471878,
-0.0029362330678850412,
0.05766914039850235,
-0.07451636344194412,
0.019666071981191635,
-0.024183010682463646,
-0.003336520865559578,
-0.016551267355680466,
-0.0006215350003913045,
0.004271410871297121,
0.05140446871519089,
0.0008294372237287462,
-0.006155576091259718,
0.02021264098584652,
0.008168862201273441,
0.00951489619910717,
-0.008789475075900555,
-0.025940656661987305,
-0.012179723009467125,
-0.0015153679996728897,
-0.045023296028375626,
0.04176020249724388,
-0.03614240884780884,
0.009305998682975769,
0.013823851943016052,
0.050305187702178955,
-0.01683109626173973,
-0.00535631412640214,
-0.09719762206077576,
-0.04877639561891556
] |
<p>The Higgs is not detected in the asymptotic data, so it is possible that there is no particle interpretation for the Higgs quantum field. Indeed, the Higgs potential is only positive definite if the quartic term is included --- the quadratic term corresponds to a negative mass term. It would seem, therefore, that the Higgs field does not have an on-shell mass spectrum, so that there is no straightforward particle interpretation.</p>
<p>One can say that there is an effective field theory in which there is a resonance near a given mass that we will call the Higgs <em>resonance</em>, but in the absence of a pure mass shell spectrum (that is, if there is a continuous mass spectrum), it is generally taken in QFT that there is no particle interpretation. The resonance is clearly not a $\delta$-function, so is there some other precise way in which we can call the Higgs a particle?</p>
<p>Of course this doesn't call into question the empirical effectiveness of the Standard Model of Particle Physics, it only asks about its interpretation and about how we put the Mathematics into words.</p>
<p>I was somewhat struck by Rolf Heuer's observation (this morning) that this is the first observation of a scalar particle. Indeed, according to the SM, there are no quantum fields that have non-zero mass terms in the absence of interactions. In the absence of interactions, the Higgs field is a massless scalar field. Should we say that it is the Higgs <em>interaction</em> that gives mass to the standard model? (EDIT: Is it better to say that every term that is not quadratic in the fields <em>contributes</em> towards the effective masses of each of the asymptotically observed fields? Or what alternative phrasing is closer to the Mathematics of the interacting fields?)</p>
<p>EDIT(2, $\scriptstyle\mathsf{see\ below\ for\ the\ comment\ that\ prompted\ this\ possible\ rephrasing}$): Is there any part of the definition of "particle" that is not a matter of convention? Does the Higgs cross that bar?</p> | g4802 | [
0.05726585164666176,
0.007621366064995527,
0.023040395230054855,
-0.05662867799401283,
0.04550054296851158,
0.03431399166584015,
-0.017412466928362846,
0.015619833953678608,
-0.016249733045697212,
-0.02730119787156582,
0.030573252588510513,
-0.03108837828040123,
0.04818156361579895,
0.02207406610250473,
-0.036230482161045074,
0.008478826843202114,
0.05838586017489433,
-0.014045932330191135,
0.024607742205262184,
0.055068954825401306,
-0.019570475444197655,
-0.0035459864884614944,
-0.04971093311905861,
0.0455298088490963,
-0.04712241142988205,
0.009862938895821571,
0.0017488183220848441,
-0.0046014972031116486,
0.04832431674003601,
-0.05400974303483963,
0.05474824458360672,
0.003399750217795372,
0.06870550662279129,
-0.021888261660933495,
0.017273742705583572,
-0.056164003908634186,
0.057218242436647415,
0.06596669554710388,
-0.04175371676683426,
-0.03158782422542572,
-0.0017214723629876971,
-0.04485023394227028,
0.0038258240092545748,
0.020800592377781868,
0.016582725569605827,
0.057598404586315155,
0.005678238347172737,
0.015406827442348003,
0.028497420251369476,
-0.037739794701337814,
0.020972665399312973,
-0.030984267592430115,
0.045464519411325455,
0.0434894822537899,
0.018235579133033752,
0.031126298010349274,
0.038889553397893906,
0.03211582452058792,
0.04259985312819481,
-0.017109617590904236,
-0.0077575803734362125,
0.0343322828412056,
0.004914043005555868,
0.015466623939573765,
0.07030593603849411,
0.02367473393678665,
-0.09883511066436768,
-0.01593690551817417,
-0.029935793951153755,
-0.027745310217142105,
0.054498765617609024,
-0.03625032678246498,
-0.05183509364724159,
0.030285906046628952,
-0.025957699865102768,
0.0378650538623333,
-0.04581650719046593,
-0.030003443360328674,
0.021281462162733078,
-0.047185804694890976,
-0.009708736091852188,
-0.06915439665317535,
-0.009566148743033409,
-0.0013932379661127925,
0.11056385189294815,
-0.06960225850343704,
0.00016762918676249683,
-0.03448997065424919,
0.004094432108104229,
-0.005050248932093382,
-0.011815366335213184,
-0.02223021909594536,
0.031442608684301376,
0.005314394365996122,
0.01317334733903408,
0.001409750198945403,
0.018925292417407036,
0.023747967556118965,
-0.009256280958652496,
0.023064134642481804,
-0.009649956598877907,
0.02956237457692623,
0.008457934483885765,
-0.02603018470108509,
0.0006279360968619585,
0.01966889388859272,
0.03638586029410362,
0.01346268318593502,
0.032109420746564865,
0.0021871004719287157,
-0.02958505041897297,
0.05040592700242996,
0.03517618775367737,
-0.060651376843452454,
-0.030339771881699562,
-0.04769780486822128,
0.1104806587100029,
-0.022021612152457237,
-0.011303325183689594,
0.05831468477845192,
-0.003692759433761239,
0.02615971304476261,
0.05143383890390396,
0.04225161671638489,
-0.040910717099905014,
-0.05167108774185181,
-0.00367876049131155,
0.04566410928964615,
-0.005250884220004082,
-0.035080764442682266,
-0.007663885597139597,
0.018202034756541252,
0.025774499401450157,
0.04589179903268814,
-0.024796679615974426,
0.027025561779737473,
0.06807547062635422,
-0.05170918628573418,
0.05067356303334236,
-0.01680595986545086,
-0.038922734558582306,
-0.01956586167216301,
-0.015398559160530567,
-0.012025381438434124,
0.00869185570627451,
0.033715441823005676,
0.029185999184846878,
0.007634277921169996,
-0.0010580241214483976,
0.08427419513463974,
0.05076466128230095,
0.06691116839647293,
-0.0012036687694489956,
0.03232627734541893,
0.0016897215973585844,
-0.010708877816796303,
0.049773771315813065,
0.009136640466749668,
-0.03214191272854805,
-0.004691617097705603,
0.029017578810453415,
-0.037192102521657944,
0.0019221617840230465,
-0.043172817677259445,
-0.042361244559288025,
-0.0035988432355225086,
0.0017973040230572224,
-0.0630442351102829,
-0.015383797697722912,
-0.005173667799681425,
-0.03965264558792114,
0.03178013116121292,
-0.01640772633254528,
0.0356442965567112,
-0.0031894012354314327,
0.00870449561625719,
0.009842104278504848,
0.0072989510372281075,
0.014321797527372837,
0.03552678972482681,
-0.048230674117803574,
-0.010969569906592369,
0.025445885956287384,
-0.013485190458595753,
-0.044852059334516525,
0.02311786636710167,
-0.00026989768957719207,
0.03663550317287445,
0.040585268288850784,
0.01530330441892147,
-0.06802504509687424,
-0.006142867729067802,
0.0013458775356411934,
0.06002597138285637,
0.016708603128790855,
0.06431734561920166,
0.03569706901907921,
-0.023313693702220917,
0.020477132871747017,
-0.04442392662167549,
0.016396207734942436,
0.05709018558263779,
-0.03750722110271454,
-0.003959536552429199,
0.05772750824689865,
-0.054909564554691315,
0.006503772456198931,
-0.020519321784377098,
0.009848134592175484,
-0.039334602653980255,
-0.00784830842167139,
-0.055928055197000504,
-0.018840620294213295,
0.007097119931131601,
-0.019848376512527466,
-0.039852336049079895,
-0.07435836642980576,
0.042873725295066833,
0.03797304257750511,
-0.011838612146675587,
-0.07393765449523926,
-0.06469094753265381,
0.005525515880435705,
-0.03346249833703041,
-0.043533045798540115,
0.040362365543842316,
-0.007994528859853745,
0.019903086125850677,
-0.03681281581521034,
0.033876918256282806,
-0.031802698969841,
-0.05031239613890648,
-0.010439546778798103,
-0.0038993526250123978,
-0.013022564351558685,
-0.005737959407269955,
0.0003330559120513499,
-0.01570269651710987,
0.05162518844008446,
0.11168505996465683,
0.06105829030275345,
-0.011121856048703194,
-0.10133447498083115,
-0.004797648638486862,
0.05585380271077156,
0.006610253360122442,
0.05831994116306305,
0.04785562679171562,
-0.03939389809966087,
-0.017524398863315582,
0.007935070432722569,
0.02495560795068741,
0.018894962966442108,
-0.046314965933561325,
0.03525437042117119,
-0.024583762511610985,
0.00014824372192379087,
-0.013234373182058334,
-0.03265635296702385,
-0.02977086417376995,
0.031858041882514954,
-0.0526067279279232,
-0.011127427220344543,
0.04131056368350983,
-0.0020019456278532743,
-0.0494229830801487,
-0.03786364570260048,
0.01619904860854149,
-0.019683972001075745,
-0.03799787536263466,
-0.05161220580339432,
-0.043901652097702026,
0.0472298301756382,
0.017273418605327606,
-0.02651120536029339,
-0.05191168189048767,
-0.030508143827319145,
0.0500779002904892,
0.0876258835196495,
-0.031911175698041916,
0.038967955857515335,
0.021809950470924377,
0.01932400092482567,
0.015351202338933945,
0.028216155245900154,
-0.023049943149089813,
-0.028279723599553108,
-0.05115297809243202,
0.02692096121609211,
0.036468952894210815,
0.0539504736661911,
-0.0630718246102333,
0.0037932684645056725,
0.023076195269823074,
-0.06764661520719528,
0.04799354821443558,
0.016879163682460785,
0.012408604845404625,
0.04441525414586067,
0.037807267159223557,
-0.027415387332439423,
0.05177203565835953,
-0.05500293895602226,
-0.011611980386078358,
0.012403772212564945,
-0.040475428104400635,
-0.02160836011171341,
-0.03485262021422386,
-0.0028340169228613377,
-0.025332748889923096,
0.009396282024681568,
0.07021204382181168,
0.016904201358556747,
0.02998236007988453,
-0.05308382213115692,
0.04109496995806694,
-0.04847347363829613,
0.03634195029735565,
-0.05392276495695114,
0.004667376168072224,
-0.027994055300951004,
-0.030579863116145134,
0.06943090260028839,
-0.01032381970435381,
-0.00860214326530695,
0.033792685717344284,
-0.017135586589574814,
0.010433701798319817,
-0.04673556983470917,
-0.07404864579439163,
0.005783967208117247,
-0.006918434053659439,
-0.005864685866981745,
-0.011181609705090523,
-0.030428607016801834,
-0.02846863865852356,
0.0020864123944193125,
-0.03061056323349476,
0.06757304817438126,
0.04662008583545685,
0.04134776070713997,
0.02701522223651409,
-0.085518479347229,
0.010717484168708324,
-0.047133151441812515,
0.0360213965177536,
-0.033424828201532364,
-0.03596334531903267,
0.008068379014730453,
-0.024156169965863228,
0.005344246979802847,
0.08300501853227615,
-0.01136115100234747,
0.015435053035616875,
-0.025306137278676033,
0.010782789438962936,
-0.0007700285059399903,
0.04116380214691162,
0.017810935154557228,
-0.053955405950546265,
-0.025926951318979263,
-0.0057430691085755825,
-0.004751309286803007,
0.06027880311012268,
-0.0018195363227277994,
-0.009059070609509945,
-0.028376832604408264,
-0.03197944909334183,
0.01116134598851204,
-0.005167054943740368,
-0.004791697952896357,
-0.03848258778452873,
0.01667395606637001,
0.004252071026712656,
-0.03583435341715813,
-0.05840475112199783,
0.06113380193710327,
-0.051849234849214554,
-0.0001961633242899552,
0.0009204167872667313,
-0.043106064200401306,
0.038986846804618835,
-0.006931097712367773,
-0.009067031554877758,
0.04428550601005554,
0.015482514165341854,
-0.07740762829780579,
0.004639080259948969,
-0.042301684617996216,
0.019986966624855995,
0.010277945548295975,
0.02381891757249832,
-0.005710503552109003,
0.0342039093375206,
0.008261711336672306,
-0.06485345959663391,
0.02143370546400547,
-0.04769521579146385,
-0.0002591616939753294,
0.0032572783529758453,
0.0033485237509012222,
-0.004721669480204582,
0.038115378469228745,
-0.0178803950548172,
0.020175160840153694,
0.016323929652571678,
0.04619845002889633,
-0.04806402698159218,
0.01673448458313942,
-0.04221809282898903,
-0.022837568074464798,
-0.003947627265006304,
-0.012588566169142723,
-0.00221602083183825,
0.0378015860915184,
0.02020171657204628,
0.03161069005727768,
-0.05179921165108681,
-0.009661028161644936,
0.02952178195118904,
0.005918430630117655,
-0.02347703091800213,
0.002815829124301672,
0.0032088779844343662,
-0.035752493888139725,
0.05305545777082443,
0.007336741778999567,
0.04302932694554329,
-0.06538019329309464,
-0.016889043152332306,
0.04911905527114868,
0.02660249173641205,
0.00881282053887844,
0.0020826212130486965,
-0.03137727081775665,
0.01537331286817789,
-0.07880473881959915,
-0.02451448142528534,
0.06040406972169876,
0.03773222118616104,
0.012894948944449425,
-0.008664194494485855,
0.005076983943581581,
0.014436058700084686,
-0.027400575578212738,
0.02983057126402855,
-0.007495630532503128,
0.011517807841300964,
-0.015894215553998947,
-0.019724363461136818,
-0.026185134425759315,
0.051815733313560486,
-0.06529932469129562,
-0.019708694890141487,
0.052254896610975266,
-0.023176943883299828,
-0.05018024146556854,
0.043675489723682404,
-0.011893858201801777,
-0.046909257769584656,
-0.06636007130146027,
-0.015054121613502502,
0.031003784388303757,
0.045991215854883194,
0.02131626568734646,
-0.04365749657154083,
-0.08327675610780716,
-0.02206282690167427,
-0.015372976660728455,
-0.040985483676195145,
0.00312807341106236,
0.01829039864242077,
0.06263110041618347,
-0.10251826792955399,
0.019018065184354782,
-0.025940196588635445,
0.009505539201200008,
-0.029227567836642265,
-0.03191942349076271,
-0.06350928544998169,
0.022655634209513664,
0.0017721375916153193,
0.018964512273669243,
0.03342040628194809,
-0.008243036456406116,
0.049982212483882904,
-0.00012014540698146448,
0.014685667119920254,
-0.013719380833208561,
-0.02818145975470543,
0.0041102459654212,
0.011548779904842377,
-0.0066858697682619095,
-0.029037201777100563,
0.055581286549568176,
-0.03264184668660164,
0.006631442811340094,
-0.04169067367911339,
0.008292930200695992,
0.028967026621103287,
-0.031966838985681534,
-0.03450459986925125,
-0.01337952259927988,
0.06160592660307884,
-0.023160601034760475,
0.08637973666191101,
0.017927374690771103,
-0.04042532667517662,
0.002559359883889556,
-0.018603384494781494,
0.038695819675922394,
-0.015920206904411316,
-0.0037084578070789576,
-0.005571803078055382,
-0.01759696938097477,
-0.004343471024185419,
-0.031373005360364914,
0.016366686671972275,
-0.0037077690940350294,
0.030975710600614548,
-0.0010378629667684436,
0.005856938660144806,
-0.053638141602277756,
-0.024032393470406532,
0.0556144155561924,
-0.03914783522486687,
0.015502719208598137,
-0.022937124595046043,
0.02351369708776474,
0.052535682916641235,
0.0560804158449173,
0.007148242089897394,
0.04323158785700798,
0.0334327407181263,
0.024708876386284828,
-0.06487397849559784,
-0.027806909754872322,
-0.000943287624977529,
0.03438052535057068,
0.03472999483346939,
-0.05241573229432106,
0.017200961709022522,
0.05321734771132469,
0.016063502058386803,
0.012834190391004086,
0.044105127453804016,
0.015647752210497856,
-0.0067670829594135284,
0.05676112323999405,
-0.017441123723983765,
-0.06606204807758331,
0.011240513995289803,
-0.010738919489085674,
0.00972880981862545,
-0.0021308884024620056,
0.061675556004047394,
0.025322670117020607,
0.013771330937743187,
-0.004013185389339924,
-0.0403311550617218,
-0.010815082117915154,
0.0043062204495072365,
-0.004619597923010588,
-0.022885674610733986,
-0.012440800666809082,
0.033544622361660004,
0.012079750187695026,
-0.08238311856985092,
0.006413981318473816,
-0.04015457630157471,
0.007549079600721598,
0.02227056212723255,
-0.011755399405956268,
0.03195832669734955,
-0.010333342477679253,
0.02411825954914093,
0.000786872988101095,
0.03140982612967491,
-0.06329421699047089,
0.019750302657485008,
0.0021065808832645416,
0.026956068351864815,
0.02848503366112709,
-0.07972250133752823,
-0.03350718319416046,
0.001735981903038919,
-0.0017838870408013463,
-0.02282887138426304,
0.019159682095050812,
0.06205127015709877,
-0.028646470978856087,
-0.030779583379626274,
-0.07170484960079193,
0.04124351963400841,
-0.007958541624248028,
0.02771662175655365,
-0.006104991305619478,
-0.04715779423713684,
-0.032803237438201904,
-0.0020675247069448233,
-0.007345888763666153,
0.01344056986272335,
0.0021754116751253605,
-0.056151486933231354,
0.0043784561567008495,
0.01689564809203148,
-0.013554872944951057,
0.04638248309493065,
-0.0682472214102745,
0.007245185319334269,
-0.04291427135467529,
0.02526448853313923,
-0.024375570937991142,
-0.008243969641625881,
-0.009396945126354694,
-0.0563705712556839,
-0.011570014990866184,
0.03606586158275604,
-0.03781438618898392,
-0.04620179533958435,
-0.01551941316574812,
0.0411481112241745,
0.023827893659472466,
-0.0785413384437561,
0.027811460196971893,
-0.0812029018998146,
-0.02674831636250019,
0.021736176684498787,
0.041546206921339035,
-0.06708362698554993,
0.04314827919006348,
0.016180196776986122,
0.028339656069874763,
0.038674868643283844,
-0.016345931217074394,
0.03288491442799568,
-0.023600785061717033,
0.01315075159072876,
0.03688553720712662,
-0.0017217134591192007,
-0.048157621175050735,
0.054944876581430435,
0.043247442692518234,
-0.04027095064520836,
-0.0547637864947319,
-0.020517125725746155,
0.023620234802365303,
0.012420016340911388,
-0.07551064342260361,
-0.008209415711462498,
-0.017932359129190445,
-0.0015624407678842545,
-0.009751586243510246,
-0.018313804641366005,
0.008627100847661495,
0.01111249253153801,
0.03861340507864952,
0.04121043160557747,
0.040902215987443924,
-0.016751080751419067,
-0.04026869311928749,
-0.007552916184067726,
0.0007446627714671195,
-0.031228581443428993,
0.0011692719999700785,
0.026112638413906097,
0.0014923053095117211,
-0.01653234474360943,
-0.03435191139578819,
0.004514451138675213,
0.04092944785952568,
-0.08168971538543701,
-0.04755524545907974,
-0.015565881505608559,
0.012425591237843037,
-0.04079427942633629,
-0.0095057999715209,
0.037221573293209076,
-0.04793216288089752,
0.004938115365803242,
0.0005681260954588652,
0.017493922263383865,
0.023066846653819084,
0.03975917026400566,
-0.01740330271422863,
-0.000325748638715595,
-0.028712747618556023,
0.015819869935512543,
-0.044321514666080475,
0.046275317668914795,
0.016800960525870323,
0.01724090613424778,
0.022642964497208595,
-0.06599565595388412,
-0.02050139382481575,
-0.02587364800274372,
0.022045396268367767,
0.039975158870220184,
0.015250680036842823,
-0.003312554908916354,
0.005814789794385433,
-0.020298058167099953,
-0.0036563430912792683,
-0.03565683960914612,
0.061516739428043365,
0.017745256423950195,
0.02912740409374237,
-0.009628649801015854,
-0.056080568581819534,
0.030849920585751534,
0.007879017852246761,
0.0830460861325264,
0.033360403031110764,
0.020649682730436325,
0.011477272026240826,
0.025059165433049202,
-0.008447263389825821,
0.026325896382331848,
0.01681249774992466,
-0.052124567329883575,
0.005808686837553978,
0.06435505300760269,
-0.022354301065206528,
-0.04217814281582832,
-0.03085349313914776,
0.015296326950192451,
-0.019698310643434525,
0.039106398820877075,
0.03695331886410713,
0.0006248824065551162,
-0.02242024801671505,
0.0541096031665802,
0.008256169967353344,
-0.001150954165495932,
-0.12053007632493973,
0.005166440736502409,
-0.01124604232609272,
0.07538598775863647,
0.0359329991042614,
0.003214891068637371,
0.0005635466077364981,
-0.022580934688448906,
0.019387053325772285,
-0.008862807415425777,
-0.008575107902288437,
-0.03141770139336586,
0.021641433238983154,
-0.04206642508506775,
0.034972041845321655,
0.001029787352308631,
-0.029695721343159676,
-0.012421971186995506,
-0.02679676003754139,
0.11679765582084656,
0.03149306774139404,
-0.07215652614831924,
0.0036957755219191313,
0.030216744169592857,
-0.018537549301981926,
-0.030383780598640442,
0.014816309325397015,
-0.05102112889289856,
0.028007598593831062,
0.03923025727272034,
-0.052472058683633804,
-0.015961064025759697,
0.04802071303129196,
0.0074751186184585094
] |
<p>What is the principle behind <a href="http://en.wikipedia.org/wiki/Centrifugation" rel="nofollow">centrifugation</a>?</p>
<p>I understand the idea that you spin something around the centripetal force will cause an apparent force on the spinning system.
However I don't quite grasp how particles (in the non subatomic sense) with different density should be affected differently.</p>
<p>Quite coarsely, I would expect to write down Newton's second law, but then the mass would simplify and the acceleration of every particle would be the same, regardless of mass.</p>
<p>Is friction the answer? Or am I missing something silly?</p> | g4803 | [
0.06571784615516663,
0.03838037699460983,
-0.0031876296270638704,
0.036895010620355606,
0.06380706280469894,
0.029210152104496956,
0.05946606025099754,
0.06812293827533722,
-0.031034130603075027,
-0.03141629695892334,
-0.0002546822652220726,
-0.06892181187868118,
0.005481054075062275,
0.005110400728881359,
0.019998367875814438,
0.05200325697660446,
0.053261373192071915,
0.019063295796513557,
0.030824147164821625,
0.04820755496621132,
-0.016084594652056694,
0.0018219599733129144,
-0.05467291921377182,
-0.060888782143592834,
-0.034316565841436386,
0.015570646151900291,
-0.05637245997786522,
-0.014532906003296375,
-0.012840931303799152,
0.024726230651140213,
0.0008233790867961943,
0.009250383824110031,
-0.020447297021746635,
-0.0671963319182396,
0.01646435633301735,
-0.07851938158273697,
0.026598049327731133,
-0.029674259945750237,
-0.024616925045847893,
-0.0022638950031250715,
0.03411056101322174,
0.029289178550243378,
0.02429811656475067,
-0.05469224601984024,
-0.027466019615530968,
0.03244064375758171,
-0.02216278947889805,
-0.01289528701454401,
-0.08376214653253555,
0.04346585273742676,
-0.051891885697841644,
0.004693481605499983,
0.007259389851242304,
0.06360656768083572,
-0.00719691626727581,
0.049112096428871155,
0.05678834766149521,
0.001749457442201674,
0.017052926123142242,
0.006419353187084198,
-0.047990504652261734,
0.0018370288889855146,
0.008035499602556229,
-0.015926731750369072,
-0.00208431133069098,
-0.08076498657464981,
0.008792026899755001,
0.044396888464689255,
0.01177715603262186,
0.04938457906246185,
-0.007601233199238777,
-0.02327795699238777,
-0.019486716017127037,
-0.049584079533815384,
-0.020661944523453712,
-0.0002636989520397037,
0.0005474931676872075,
0.018594713881611824,
0.008162446320056915,
-0.04059729725122452,
-0.03302557393908501,
0.0421883799135685,
0.009599294513463974,
-0.002410419285297394,
0.045394569635391235,
-0.03756339102983475,
-0.04564046487212181,
-0.05348845198750496,
-0.00020408038108143955,
-0.019121816381812096,
0.05121432989835739,
-0.017074288800358772,
0.06841025501489639,
0.01550321001559496,
-0.04001450166106224,
-0.042645759880542755,
0.0043092090636491776,
0.05522872135043144,
-0.015367986634373665,
0.0072256880812346935,
-0.026035724207758904,
0.02647252194583416,
0.06053760275244713,
-0.05409911647439003,
0.06269089132547379,
-0.008239983581006527,
0.07289944589138031,
0.044605765491724014,
0.013485753908753395,
-0.0163697712123394,
-0.018030164763331413,
-0.031971339136362076,
-0.03610857203602791,
0.01091298833489418,
0.017721140757203102,
-0.037067659199237823,
0.06248306855559349,
0.04397844895720482,
0.006009887903928757,
0.06590037047863007,
0.006593077909201384,
0.030054893344640732,
-0.014504160732030869,
0.06087435409426689,
-0.07281474024057388,
0.0059136864729225636,
0.05448198318481445,
0.009470488876104355,
0.020842384546995163,
-0.015435859560966492,
0.038148459047079086,
-0.016902850940823555,
-0.0024949463550001383,
-0.018749287351965904,
-0.009545867331326008,
0.04454350844025612,
-0.10056960582733154,
-0.021518293768167496,
0.009462685324251652,
-0.03855527564883232,
0.019474798813462257,
-0.0503922738134861,
0.024239767342805862,
-0.0039505683816969395,
-0.00573768699541688,
-0.012470224872231483,
-0.04110985994338989,
-0.008011742495000362,
0.03128448501229286,
0.005835348274558783,
0.023322051391005516,
0.02766747958958149,
0.08233847469091415,
-0.04625236243009567,
0.10017875581979752,
0.04271882399916649,
0.06797610223293304,
0.03733230009675026,
0.00865133572369814,
0.020745759829878807,
0.07538675516843796,
-0.05534597858786583,
0.010470765642821789,
0.0029109888710081577,
-0.05759177729487419,
0.029604436829686165,
-0.01966387964785099,
-0.07279235124588013,
0.0019695672672241926,
-0.03397240862250328,
-0.05620585009455681,
-0.011205191724002361,
-0.03234143927693367,
0.07364807277917862,
-0.034764744341373444,
0.04416818916797638,
-0.0001428443065378815,
0.014787315391004086,
0.02264309674501419,
0.00976657122373581,
-0.003628198755905032,
0.01821538805961609,
0.0009549304959364235,
0.027943463996052742,
0.046983689069747925,
0.05301610380411148,
0.02531401440501213,
0.033014968037605286,
-0.02463763952255249,
0.02073754370212555,
0.019271383062005043,
-0.037778276950120926,
0.008247235789895058,
0.026508640497922897,
-0.024567585438489914,
0.02686360850930214,
-0.02637198008596897,
-0.036616019904613495,
-0.04530215263366699,
0.03138162940740585,
-0.016835758462548256,
0.006960326340049505,
0.02703704498708248,
-0.04244779795408249,
0.02043023519217968,
-0.010880423709750175,
-0.026309393346309662,
-0.019904859364032745,
0.02246391400694847,
-0.004920675419270992,
0.046944841742515564,
0.010484498925507069,
0.01295214518904686,
0.006740762386471033,
-0.06908588111400604,
-0.004251563455909491,
0.03754778578877449,
0.037399254739284515,
0.028048956766724586,
0.0259445421397686,
-0.04102398455142975,
-0.05983972176909447,
0.02053084224462509,
0.027427485212683678,
-0.0352545902132988,
0.000014925257346476428,
-0.01054429728537798,
-0.03501763194799423,
-0.05477462708950043,
0.07263394445180893,
-0.02783736027777195,
0.024743368849158287,
-0.023773744702339172,
0.012600289657711983,
0.04278417304158211,
0.05123911798000336,
-0.015944112092256546,
-0.032690782099962234,
0.047719165682792664,
0.03684573620557785,
0.014162072911858559,
-0.03693331778049469,
0.007521570194512606,
-0.04295937716960907,
0.03825610131025314,
-0.08384131640195847,
0.024879764765501022,
-0.015026398934423923,
-0.026976149529218674,
-0.018546700477600098,
0.03178197517991066,
-0.025035642087459564,
-0.00797986425459385,
-0.03680569306015968,
0.07138614356517792,
-0.011322615668177605,
-0.06952126324176788,
0.0320424847304821,
-0.024876810610294342,
-0.013969514518976212,
0.024063611403107643,
0.025250021368265152,
-0.012124045751988888,
0.07139423489570618,
-0.01597212255001068,
-0.01797473058104515,
-0.006568018812686205,
0.011733166873455048,
-0.0007831352413631976,
0.0543162040412426,
-0.018131118267774582,
0.06652127951383591,
-0.06278634816408157,
0.04010270908474922,
0.0003046034253202379,
-0.005188428331166506,
0.041107866913080215,
-0.0022999641951173544,
-0.02071484550833702,
-0.0027068108320236206,
0.01341995783150196,
0.041255805641412735,
-0.005402255803346634,
-0.005216702818870544,
0.06897211819887161,
-0.05102100595831871,
-0.0028503432404249907,
-0.05045726150274277,
-0.03942172974348068,
0.018452590331435204,
0.010298114269971848,
0.01025410182774067,
0.043528396636247635,
-0.011049595661461353,
0.05646057054400444,
0.015913505107164383,
0.07068367302417755,
-0.02040867507457733,
-0.012894337996840477,
0.03002701885998249,
0.012921666726469994,
-0.023693470284342766,
-0.012857994996011257,
0.048836272209882736,
-0.005250008776783943,
0.08579278737306595,
-0.029931778088212013,
-0.06965351849794388,
-0.06677613407373428,
0.011329853907227516,
-0.03882088139653206,
0.08369981497526169,
0.01710859127342701,
-0.027402665466070175,
-0.057660061866045,
-0.09000504016876221,
0.011600716970860958,
0.030632296577095985,
0.06609008461236954,
-0.0038255471736192703,
-0.06384807825088501,
-0.03761443495750427,
0.0360945500433445,
-0.08391618728637695,
0.05007808655500412,
0.04083755612373352,
-0.058958057314157486,
-0.029170870780944824,
0.015032932162284851,
-0.07294308394193649,
0.0216350220143795,
0.007099770475178957,
-0.07776233553886414,
-0.012393670156598091,
-0.10566580295562744,
-0.010624067857861519,
0.005161741748452187,
-0.05332239717245102,
-0.017184454947710037,
0.039416298270225525,
-0.017689881846308708,
-0.07264111191034317,
-0.06555631011724472,
-0.023366441950201988,
-0.04492868483066559,
0.05601470172405243,
0.027306227013468742,
0.034413620829582214,
0.03730546683073044,
0.010255000554025173,
0.06897673010826111,
-0.0323001928627491,
0.0548899844288826,
-0.01152664702385664,
0.016880447044968605,
0.04116665944457054,
0.036164283752441406,
0.03770449012517929,
-0.006266195327043533,
0.022119538858532906,
0.023071985691785812,
-0.049610260874032974,
-0.008988984860479832,
0.011991717852652073,
-0.018548570573329926,
0.04900383576750755,
0.0028894769493490458,
-0.02706395648419857,
-0.012942948378622532,
-0.04374157637357712,
-0.033223312348127365,
-0.044893644750118256,
-0.0016632896149531007,
-0.0020333502907305956,
0.029848255217075348,
0.01271103136241436,
0.03539871424436569,
0.02476286143064499,
-0.04047277942299843,
-0.0045169382356107235,
0.006034863647073507,
0.0563032440841198,
-0.0017611348303034902,
0.009852726943790913,
-0.03988546133041382,
0.04995445907115936,
-0.1047215610742569,
0.02570437453687191,
0.007785913534462452,
-0.04750370234251022,
0.011431151069700718,
-0.010450450703501701,
0.03335168957710266,
-0.040013398975133896,
0.05523272976279259,
-0.005938016809523106,
-0.030481504276394844,
-0.087034210562706,
0.022971713915467262,
-0.009730513207614422,
-0.022125201299786568,
0.04319343343377113,
-0.0335296131670475,
-0.018027594313025475,
0.027068201452493668,
-0.027227818965911865,
-0.03066924400627613,
-0.021101586520671844,
0.003849468193948269,
0.018944842740893364,
0.046177588403224945,
0.03414228558540344,
-0.015694502741098404,
0.011427706107497215,
-0.013952072709798813,
-0.02710154838860035,
-0.017765067517757416,
0.01564236544072628,
-0.029769739136099815,
-0.012094401754438877,
-0.004275800660252571,
0.017920851707458496,
0.00859595276415348,
0.039753079414367676,
-0.09477073699235916,
0.0663318857550621,
0.028994088992476463,
-0.02304942160844803,
-0.026439307257533073,
-0.03830235078930855,
-0.02148774079978466,
0.020117931067943573,
0.01060111541301012,
0.02361680567264557,
-0.07252416759729385,
-0.0480056069791317,
-0.03137703612446785,
0.02335304208099842,
0.0339198037981987,
0.028756922110915184,
-0.009724758565425873,
0.07084988802671432,
0.011690634302794933,
-0.016390163451433182,
0.035064540803432465,
0.10652364790439606,
-0.013101707212626934,
-0.033676132559776306,
-0.03205008804798126,
-0.02948782965540886,
-0.016504326835274696,
-0.03121785633265972,
-0.031173255294561386,
-0.02143237739801407,
-0.009300840087234974,
0.044076915830373764,
-0.006675561890006065,
-0.01272811833769083,
-0.005745129659771919,
0.015084302984178066,
-0.069487065076828,
-0.007286186330020428,
-0.048749301582574844,
-0.0407162606716156,
-0.009810729883611202,
0.027931366115808487,
-0.016650227829813957,
-0.029002230614423752,
-0.030316157266497612,
-0.0025443704798817635,
-0.029657719656825066,
-0.04592614620923996,
-0.022797029465436935,
0.01099125575274229,
0.0644255056977272,
0.02498430386185646,
0.03326300531625748,
-0.00756504200398922,
0.03575718030333519,
-0.011058025993406773,
-0.02417862042784691,
-0.005466025322675705,
0.06120100989937782,
-0.03699048236012459,
0.0015106447972357273,
0.02437269687652588,
-0.011483913287520409,
0.050604503601789474,
0.041981179267168045,
-0.004059833008795977,
-0.017992857843637466,
-0.012285261414945126,
-0.027332168072462082,
-0.023340541869401932,
0.009005322121083736,
0.002205959288403392,
0.03610120713710785,
-0.057493261992931366,
-0.02449512854218483,
0.005922113079577684,
-0.024386215955018997,
-0.01615329459309578,
-0.028199603781104088,
0.03016079030930996,
0.01716858334839344,
0.037537071853876114,
0.04849058389663696,
-0.040348026901483536,
0.025169232860207558,
0.05588240176439285,
-0.04244593530893326,
0.053467974066734314,
-0.006078542210161686,
0.005290631204843521,
-0.006599167361855507,
0.033457137644290924,
-0.0059918505139648914,
0.021055275574326515,
0.031180717051029205,
-0.004884873516857624,
0.005538589786738157,
0.021504046395421028,
-0.01653371751308441,
-0.056439872831106186,
-0.05480976402759552,
-0.012365274131298065,
-0.019260674715042114,
0.03222183883190155,
0.026268644258379936,
0.08774073421955109,
0.01734490692615509,
-0.005800254642963409,
0.06560248136520386,
0.01523901429027319,
-0.05649208277463913,
-0.05982276052236557,
0.01866980269551277,
0.024540090933442116,
0.038831572979688644,
0.006768690887838602,
-0.008259008638560772,
0.001719196094200015,
-0.00836431048810482,
0.04373575747013092,
-0.01757887192070484,
0.01715533807873726,
-0.009611500427126884,
-0.01866242289543152,
0.05360244959592819,
-0.053184229880571365,
-0.05360029637813568,
0.07665697485208511,
0.029990877956151962,
0.009640831500291824,
-0.04510697349905968,
0.04123607650399208,
-0.0056652189232409,
-0.006410536821931601,
-0.00564188975840807,
-0.00680186040699482,
0.027520323172211647,
-0.048010531812906265,
0.04940800741314888,
0.0011018613586202264,
-0.009936606511473656,
-0.025661485269665718,
-0.012819159775972366,
-0.016352230682969093,
0.051682669669389725,
0.027226131409406662,
-0.01935499534010887,
0.027939582243561745,
0.003924528602510691,
0.004720783792436123,
0.01790151372551918,
0.05285809189081192,
-0.012702022679150105,
-0.009562255814671516,
-0.06820432841777802,
0.01693272404372692,
0.037347156554460526,
-0.0009346642764285207,
0.005698200780898333,
-0.010439988225698471,
-0.008625779300928116,
-0.00610744021832943,
-0.02729679085314274,
0.0119106350466609,
0.06791197508573532,
-0.02515273354947567,
-0.01562856137752533,
-0.026596007868647575,
-0.019747814163565636,
0.03922508656978607,
-0.012744207866489887,
0.015701450407505035,
-0.00315620144829154,
-0.01429043710231781,
0.03580067679286003,
-0.04111308977007866,
0.030924076214432716,
0.010579063557088375,
0.03275560215115547,
0.022923259064555168,
0.00565167935565114,
-0.02170402556657791,
-0.005195919889956713,
-0.037056777626276016,
0.025789011269807816,
0.005558876786381006,
-0.05818919464945793,
0.0019062166102230549,
-0.009052217938005924,
-0.0019418023293837905,
0.04788754880428314,
0.006639961618930101,
-0.04273359850049019,
-0.0018729881849139929,
0.013524985872209072,
-0.04460739716887474,
-0.02660536579787731,
-0.022256653755903244,
0.0407259538769722,
-0.05000612884759903,
0.03155195713043213,
-0.009246110916137695,
-0.0181971937417984,
0.045613691210746765,
0.08277449011802673,
-0.035182155668735504,
0.05321510136127472,
0.00003524848216329701,
0.05403285473585129,
0.04593800753355026,
-0.049212951213121414,
0.04170161113142967,
-0.037725403904914856,
0.025979861617088318,
0.05623338371515274,
0.0257255919277668,
0.016348564997315407,
0.03072645701467991,
0.04667012766003609,
-0.010508229024708271,
-0.08948586881160736,
-0.004869774449616671,
-0.0019209316233173013,
0.011529134586453438,
-0.00829781498759985,
0.0061770230531692505,
-0.021478086709976196,
-0.035521768033504486,
-0.06524470448493958,
0.017674973234534264,
0.02083326317369938,
0.020421521738171577,
0.008537407964468002,
0.009579421952366829,
0.04800375923514366,
-0.0017218425637111068,
-0.11306513100862503,
-0.03650408610701561,
0.007830522023141384,
-0.009992335923016071,
-0.0073760030791163445,
0.05067206546664238,
-0.025598356500267982,
0.009655875153839588,
0.03599226847290993,
-0.007410123012959957,
-0.019080692902207375,
-0.0698641687631607,
-0.04110244661569595,
0.015467747114598751,
0.009375907480716705,
-0.03285546228289604,
0.0014097081730142236,
-0.06818712502717972,
0.01793961599469185,
0.018378889188170433,
0.014878406189382076,
-0.04116091877222061,
0.0400492288172245,
0.0007926241378299892,
-0.0022887049708515406,
0.014675176702439785,
-0.049344468861818314,
0.050420474261045456,
-0.014121931046247482,
-0.04376338794827461,
0.01227250974625349,
-0.004494968336075544,
-0.0263371579349041,
-0.0038503047544509172,
0.01897341012954712,
0.02743685618042946,
0.09178172796964645,
0.011890887282788754,
0.003374999389052391,
-0.01431797631084919,
0.013388169929385185,
-0.039406999945640564,
-0.03809916973114014,
-0.026735907420516014,
-0.0062814755365252495,
-0.012417570687830448,
0.0019535846076905727,
0.013647583313286304,
-0.05572863295674324,
-0.006263055372983217,
0.06504780054092407,
-0.0067236945033073425,
0.01033073104918003,
0.016016937792301178,
-0.009022305719554424,
0.02744933031499386,
-0.00979770440608263,
-0.026074441149830818,
-0.026302538812160492,
-0.02755754254758358,
0.028144488111138344,
0.05630228668451309,
0.0036360493395477533,
-0.04559838026762009,
-0.01139324065297842,
-0.010261614806950092,
0.0010829466627910733,
-0.029447071254253387,
-0.0206321869045496,
0.05085267499089241,
-0.04930847883224487,
0.010546778328716755,
0.020803814753890038,
0.017774319276213646,
-0.028559885919094086,
0.020031316205859184,
0.019292155280709267,
-0.024340953677892685,
-0.06542917340993881,
-0.05378153920173645,
0.0152894863858819,
-0.03168310225009918,
0.011339851655066013,
-0.008019531145691872,
-0.021423669531941414,
0.0006839935667812824,
0.007946020923554897,
0.021154915913939476,
0.028055759146809578,
0.012849252671003342,
-0.00034712839988060296,
-0.00839653518050909,
-0.05510176718235016,
-0.025799274444580078,
-0.0020102623384445906,
-0.07918424159288406,
-0.018991481512784958,
0.03151163458824158,
0.01008274033665657,
-0.054691363126039505,
-0.03914850950241089,
-0.011000385507941246,
-0.02362675964832306,
0.009896492585539818,
-0.01230632048100233,
-0.006756666116416454,
-0.014840586110949516,
-0.016759471967816353
] |
<blockquote>
<p>Could life on earth survive a large pole shift caused by an asteroid collision?</p>
</blockquote>
<p>I became aware that there are people who believe that the earth's pole suddenly shifts. That is, its rotational axis changes rather than its magnetic axis. This is listed in wikipedia as follows:</p>
<p><strong>Cataclysmic pole shift hypothesis</strong>
The cataclysmic pole shift hypothesis is the conjecture that there have been rapid shifts in the relative positions of the modern-day geographic locations of the poles and the axis of rotation of a planet. For the Earth, such a dynamic change could create calamities such as floods and tectonic events.<br>
...<br>
The field has attracted pseudoscientific authors offering a variety of evidence, including psychic readings.<br>
...<br>
<a href="http://en.wikipedia.org/wiki/Cataclysmic_pole_shift_hypothesis">http://en.wikipedia.org/wiki/Cataclysmic_pole_shift_hypothesis</a></p>
<p>While watching a chess game at the local club a fellow member told me that he'd found the solution for where oil came from. It was long and involved. One of its features required that the earth's axis be changed by 90 degrees due to the collision of an asteroid a few million years ago. The idea was that the earth's axis used to be in the plane of the earth's orbit, but then it was knocked into its current rotation axis tilt of around 23 degrees. This changed the climate and buried a lot of stuff.</p>
<p>The axis shift seemed to be an obvious weak link with the theory in that it involves the simplest physics. I told him that any asteroid large enough to change the earth's axis an appreciable amount (i.e. 70 degrees!) would cause so much damage as to destroy all life on the surface of the planet including its oceans. I'd have forgotten about it, but the other night, while listening to the radio, a guest appeared who had an idea that was similar. So this seems like a common target for pseudoscience.</p>
<p>And so my question is this: Would an asteroid collision sufficient to immediately change the earth's rotation axis wipe out all life on the planet?</p> | g4804 | [
0.04273994266986847,
0.020218828693032265,
0.00860159657895565,
-0.010859698988497257,
0.012630164623260498,
0.030363867059350014,
-0.007529000751674175,
0.011258113197982311,
0.018870864063501358,
0.0002090865164063871,
0.016456443816423416,
-0.03110251948237419,
0.08502542227506638,
-0.07355623692274094,
0.018123438581824303,
-0.029481511563062668,
0.019216271117329597,
-0.004355074372142553,
0.03802362084388733,
0.002144478727132082,
0.017883868888020515,
-0.036250144243240356,
0.03391792252659798,
-0.018410392105579376,
-0.04056709632277489,
-0.03593681380152702,
-0.010431278496980667,
-0.013886622153222561,
0.016511069610714912,
0.019277697429060936,
-0.01962471753358841,
-0.016603810712695122,
-0.009144471026957035,
-0.029069170355796814,
-0.050636935979127884,
-0.04006683826446533,
-0.027834424749016762,
0.015126344747841358,
0.05709289014339447,
0.02181963063776493,
-0.05362531542778015,
-0.019001752138137817,
0.11387255042791367,
-0.008470738306641579,
0.03636959195137024,
-0.04829755797982216,
-0.027678560465574265,
-0.02623656764626503,
0.02181338705122471,
-0.015655549243092537,
-0.05492342263460159,
-0.025747476145625114,
0.06589094549417496,
0.032475538551807404,
0.014330215752124786,
0.05879272148013115,
0.05187312886118889,
0.026222143322229385,
0.03476830944418907,
-0.03712216764688492,
-0.034004971385002136,
-0.0006350040785036981,
-0.02875700034201145,
-0.012670810334384441,
0.01114490907639265,
-0.06773333996534348,
-0.053040988743305206,
0.0332346111536026,
0.04924270138144493,
-0.035168908536434174,
0.06098930537700653,
-0.03479902818799019,
-0.03066752851009369,
-0.050820671021938324,
-0.00040065153734758496,
0.0615144781768322,
0.011655761860311031,
-0.010181382298469543,
0.006698411423712969,
0.025483932346105576,
-0.013604061678051949,
0.004579583648592234,
0.0010379897430539131,
0.03222642093896866,
0.027398372069001198,
-0.03865519538521767,
0.010797878727316856,
-0.006335042882710695,
0.00996787566691637,
-0.012420017272233963,
0.052747827023267746,
-0.044201090931892395,
-0.030965594574809074,
0.007886172272264957,
-0.04632982611656189,
-0.002947897417470813,
-0.02609359100461006,
0.0671365037560463,
-0.023251300677657127,
0.06759514659643173,
-0.03436572104692459,
-0.05874121934175491,
-0.011863349005579948,
0.012099000625312328,
0.019196217879652977,
0.0037321546114981174,
0.009138419292867184,
-0.020114123821258545,
0.008483970537781715,
-0.0067347874864935875,
0.049481190741062164,
-0.018772384151816368,
0.0009671506704762578,
-0.027566080912947655,
-0.0009989223908632994,
-0.06565762311220169,
0.07527624070644379,
0.0015432212967425585,
0.040121618658304214,
0.10360560566186905,
-0.00426422618329525,
0.02100767381489277,
0.02188936620950699,
0.06746257841587067,
-0.01732059009373188,
-0.07541052997112274,
-0.01933327503502369,
-0.0032718051224946976,
0.0899106040596962,
-0.024467362090945244,
-0.03818487375974655,
0.031126169487833977,
-0.028795599937438965,
0.03420984745025635,
0.009782635606825352,
0.03403206542134285,
0.021113382652401924,
-0.0071470411494374275,
0.002550625940784812,
0.012837115675210953,
0.04443483427166939,
0.0462036058306694,
0.036361608654260635,
0.003520568832755089,
-0.024976124987006187,
0.03870439901947975,
0.03727291151881218,
-0.05027952417731285,
0.08863053470849991,
-0.008334153331816196,
0.009770479053258896,
0.03108280897140503,
-0.008783218450844288,
-0.03960445523262024,
0.04126115143299103,
0.04475921019911766,
-0.028880305588245392,
0.003773741889744997,
0.019107313826680183,
-0.013316402211785316,
0.023890968412160873,
-0.039816055446863174,
-0.03220796212553978,
0.011824262328445911,
-0.032583288848400116,
0.05359489098191261,
0.0022247894667088985,
0.02042817696928978,
-0.0489848293364048,
0.023402424529194832,
-0.05284278467297554,
-0.026791412383317947,
0.082778200507164,
0.02054225467145443,
-0.009458093903958797,
0.01794877089560032,
-0.016502130776643753,
-0.04830183833837509,
-0.057853806763887405,
-0.013508632779121399,
0.016939349472522736,
-0.006045124027878046,
0.005619251634925604,
0.019825536757707596,
0.06071413308382034,
-0.01706603355705738,
-0.009553561918437481,
0.03331120312213898,
-0.01678067445755005,
0.03811560571193695,
-0.008753043599426746,
-0.09687338769435883,
-0.0321655310690403,
0.006871635094285011,
0.05026009678840637,
-0.029985859990119934,
0.019376153126358986,
0.02561921998858452,
-0.07853808999061584,
-0.0014542542630806565,
0.016518566757440567,
0.024699771776795387,
0.04391896724700928,
0.02057494968175888,
-0.026950258761644363,
-0.013636617921292782,
-0.004759234841912985,
-0.0018481481820344925,
0.014156377874314785,
-0.04444504156708717,
0.09500481188297272,
0.01888662576675415,
-0.031160438433289528,
0.02502020262181759,
-0.06757515668869019,
0.04479021579027176,
-0.0451640859246254,
0.048239193856716156,
-0.0368557870388031,
-0.024698613211512566,
0.04405399039387703,
-0.011134556494653225,
0.027494389563798904,
-0.0010186063591390848,
0.030210761353373528,
0.0472622886300087,
-0.02806476131081581,
-0.024989793077111244,
0.031067533418536186,
-0.03372598811984062,
-0.012193446047604084,
0.04071357473731041,
0.015562588348984718,
-0.037477824836969376,
-0.0015668267151340842,
0.0489463172852993,
0.027500711381435394,
-0.043322641402482986,
0.037417951971292496,
0.0005102712893858552,
0.02330305613577366,
-0.0494435615837574,
-0.01982460357248783,
-0.01639375276863575,
0.028763635084033012,
-0.011996390298008919,
0.05855199694633484,
0.005257320590317249,
0.01875920407474041,
0.007392108906060457,
0.0473799966275692,
-0.07287411391735077,
-0.06659121066331863,
0.07538338750600815,
0.01075772475451231,
-0.038530200719833374,
-0.021836187690496445,
0.11638975143432617,
0.021408746019005775,
0.0055399141274392605,
-0.03888974338769913,
-0.011099482886493206,
0.03618425503373146,
0.0348769873380661,
-0.043369460850954056,
0.023226354271173477,
-0.0730692446231842,
0.0223773792386055,
0.001110970857553184,
0.006142693571746349,
-0.018624523654580116,
-0.038944490253925323,
0.0019232076592743397,
0.08542460948228836,
-0.021509449928998947,
0.017269713804125786,
-0.03631538897752762,
-0.0162357147783041,
-0.017613090574741364,
0.018848586827516556,
0.008790943771600723,
0.023714333772659302,
-0.02640480175614357,
-0.018050337210297585,
0.04076186940073967,
0.02743357978761196,
-0.05396419018507004,
0.0444621779024601,
-0.0589565671980381,
0.02248871698975563,
-0.018806003034114838,
-0.0025670838076621294,
0.072358638048172,
0.00917909201234579,
0.013180316425859928,
0.07059358060359955,
0.008508199825882912,
-0.019769886508584023,
-0.059503618627786636,
0.023120444267988205,
0.0369325615465641,
-0.017137495800852776,
-0.01248991210013628,
0.040256209671497345,
0.05015306919813156,
0.03498496860265732,
-0.04747186601161957,
-0.05721729248762131,
-0.040739454329013824,
-0.00825861282646656,
-0.0335751473903656,
0.020547546446323395,
-0.01968129724264145,
0.017232684418559074,
-0.041783545166254044,
0.001676390995271504,
-0.04829682409763336,
0.03886451572179794,
0.06147558242082596,
0.004481069277971983,
0.008053313940763474,
-0.05424114316701889,
-0.07471700757741928,
0.058901097625494,
0.01423241663724184,
0.018393749371170998,
-0.05689307302236557,
-0.028483446687459946,
-0.03631208464503288,
-0.018415318801999092,
0.009643390774726868,
0.03722749277949333,
-0.026701997965574265,
-0.008881437592208385,
-0.0859588086605072,
-0.008128457702696323,
0.043065913021564484,
0.022768443450331688,
0.016106946393847466,
0.007200579158961773,
-0.049366991966962814,
-0.029327470809221268,
-0.010008552111685276,
-0.08638084679841995,
0.04011751338839531,
0.059141505509614944,
0.04592663794755936,
-0.06187833845615387,
0.004918145481497049,
0.00524180568754673,
0.07791352272033691,
-0.04509267956018448,
-0.020854929462075233,
0.022638743743300438,
0.0670095682144165,
0.01791020855307579,
0.0224270261824131,
0.016972916200757027,
-0.009245846420526505,
0.038788605481386185,
0.021805860102176666,
-0.016615789383649826,
0.04141094535589218,
-0.03981108218431473,
0.00240974104963243,
0.07769845426082611,
-0.032702744007110596,
0.016195541247725487,
0.009489523246884346,
0.0327635258436203,
0.032419152557849884,
0.01288050226867199,
-0.020974136888980865,
0.01837780699133873,
0.012829368934035301,
0.03524215519428253,
0.03695651888847351,
0.030787495896220207,
-0.06993814557790756,
0.025948116555809975,
0.03499913215637207,
-0.024039320647716522,
0.021080920472741127,
0.03171541169285774,
0.002814243081957102,
-0.03149234130978584,
-0.006114794407039881,
-0.019093677401542664,
-0.016836965456604958,
-0.012532691471278667,
0.021800901740789413,
-0.07371850311756134,
0.008707830682396889,
-0.047969382256269455,
0.025113537907600403,
0.0036603775806725025,
-0.07726423442363739,
-0.03154047578573227,
0.011300768703222275,
0.004407207481563091,
0.010106507688760757,
0.014336993917822838,
0.021328050643205643,
0.00896823313087225,
0.005273685324937105,
0.01257694698870182,
0.0268779918551445,
0.01692807860672474,
-0.007679576985538006,
-0.05707666650414467,
0.0039568496868014336,
0.032900359481573105,
-0.12211982160806656,
-0.03837236016988754,
0.007573347073048353,
0.03283485397696495,
0.010474157519638538,
0.03035486675798893,
0.05218307301402092,
-0.018361637368798256,
-0.04203621670603752,
0.01783750206232071,
-0.05415574833750725,
-0.010527754202485085,
-0.005783404223620892,
0.04384354129433632,
0.03818082436919212,
-0.034761250019073486,
-0.010086989030241966,
0.00465388922020793,
0.02067180536687374,
-0.0007186765433289111,
-0.011244161985814571,
0.03489753603935242,
0.00247150263749063,
-0.0015947887441143394,
-0.021934503689408302,
-0.0019562069792300463,
-0.007952634245157242,
-0.029178297147154808,
-0.01634693332016468,
-0.024517517536878586,
0.024860985577106476,
0.014326666481792927,
-0.00240400992333889,
0.029917381703853607,
-0.024246079847216606,
0.018233751878142357,
0.05748810991644859,
-0.01282585971057415,
-0.012028995901346207,
-0.02184894308447838,
0.07785410434007645,
0.05845722183585167,
-0.019556134939193726,
-0.04080412909388542,
-0.022527778521180153,
0.02383570559322834,
-0.030237292870879173,
0.03927283361554146,
0.004849907476454973,
0.02123909629881382,
0.05010353401303291,
0.048680368810892105,
0.055322352796792984,
-0.02013935148715973,
-0.006596151739358902,
-0.0732726976275444,
0.0006357143865898252,
-0.060374047607183456,
-0.07233835756778717,
-0.011352606117725372,
0.003851141780614853,
0.06614567339420319,
-0.10059703886508942,
0.020112525671720505,
-0.01824941113591194,
-0.029183069244027138,
0.005597332492470741,
-0.06439197063446045,
-0.011090789921581745,
-0.05979505926370621,
-0.00869021937251091,
-0.013300983235239983,
-0.003724117297679186,
-0.05449271947145462,
-0.07052545249462128,
0.0005417929496616125,
0.013147005811333656,
-0.007359991781413555,
0.02874591201543808,
-0.00983278825879097,
-0.022261610254645348,
0.006931675132364035,
-0.04131918400526047,
-0.022464893758296967,
-0.010783184319734573,
-0.0894700437784195,
-0.04656572639942169,
0.03987535461783409,
-0.0052359942346811295,
0.012350206263363361,
0.032496169209480286,
-0.027891580015420914,
-0.002882575849071145,
-0.024232199415564537,
0.01948208548128605,
0.010645083151757717,
0.015530796721577644,
0.03254985809326172,
-0.0039333440363407135,
0.026774568483233452,
0.01252296008169651,
0.056358277797698975,
0.002806656761094928,
-0.028517629951238632,
-0.01678997091948986,
0.010602258145809174,
-0.013182109221816063,
-0.020914914086461067,
-0.02331114374101162,
-0.046555597335100174,
-0.021387673914432526,
-0.005517630837857723,
0.006877501495182514,
-0.015710536390542984,
-0.029783297330141068,
-0.01221025362610817,
-0.06337297707796097,
0.034430451691150665,
-0.02405070886015892,
-0.03440232574939728,
-0.05263868719339371,
-0.041464757174253464,
-0.036046985536813736,
-0.04422999918460846,
-0.027848364785313606,
-0.023021714761853218,
0.03907567262649536,
-0.037394873797893524,
-0.0509825125336647,
0.002260833978652954,
0.09787152707576752,
0.013458373956382275,
-0.041354164481163025,
-0.02073659375309944,
-0.015096282586455345,
0.021345164626836777,
0.023887874558568,
-0.010539937764406204,
-0.015429598279297352,
0.06849556416273117,
0.02556120790541172,
-0.0412040576338768,
-0.019651196897029877,
0.01182511541992426,
-0.027225125581026077,
-0.005907139275223017,
0.036650400608778,
-0.05522947013378143,
-0.034394215792417526,
0.013916880823671818,
-0.01409823913127184,
-0.018089067190885544,
0.0013801369350403547,
-0.00680162850767374,
0.018037881702184677,
-0.02966734580695629,
0.0637722909450531,
0.03404261916875839,
-0.011670836247503757,
-0.01403348334133625,
-0.03441648930311203,
-0.0011062450939789414,
0.0522950179874897,
-0.011141053400933743,
-0.022262858226895332,
0.046559564769268036,
-0.03956932947039604,
0.04748421162366867,
-0.011724240146577358,
-0.06287112832069397,
-0.005508820991963148,
-0.024251114577054977,
0.044328413903713226,
0.023824986070394516,
-0.0394592247903347,
0.023757735267281532,
0.026813628152012825,
-0.0579281710088253,
0.013109255582094193,
0.015084310434758663,
-0.022341137751936913,
0.005926296580582857,
-0.04521748796105385,
-0.06171918660402298,
-0.057593684643507004,
0.0365719310939312,
-0.040651071816682816,
0.007722831331193447,
0.015895970165729523,
0.005372967105358839,
0.06952448934316635,
0.033559300005435944,
0.02190822921693325,
-0.0012995062861591578,
-0.007566150743514299,
0.013654915615916252,
0.02022712491452694,
-0.019533811137080193,
0.047155432403087616,
0.042925912886857986,
-0.002935157623142004,
-0.0020880200900137424,
-0.045980460941791534,
-0.02363177016377449,
-0.00609084777534008,
0.02537662722170353,
-0.04092128202319145,
0.011465726420283318,
0.011410304345190525,
0.008497797884047031,
-0.026638470590114594,
-0.029300617054104805,
-0.029519297182559967,
-0.004349907860159874,
0.011531596072018147,
-0.020006826147437096,
0.0340246744453907,
0.039468683302402496,
-0.02001664973795414,
-0.02438005805015564,
0.0147127415984869,
0.008411101065576077,
0.020007086917757988,
0.032310180366039276,
-0.02071635238826275,
-0.008819697424769402,
-0.006772791501134634,
0.026191798970103264,
-0.006948459427803755,
-0.030097471550107002,
0.003898623865097761,
-0.024762174114584923,
-0.011662827804684639,
0.023939363658428192,
-0.04556993767619133,
-0.017817474901676178,
-0.012552397325634956,
-0.021588431671261787,
0.027544168755412102,
0.004532996565103531,
-0.037794411182403564,
0.01935926266014576,
0.016690434888005257,
0.03572424128651619,
0.0006014969549141824,
-0.0031638590153306723,
0.029204275459051132,
-0.03530498966574669,
-0.013729408383369446,
-0.02595723420381546,
0.006232708226889372,
-0.06276724487543106,
-0.05283514782786369,
-0.018488233909010887,
0.02175605297088623,
-0.06501113623380661,
0.008453684858977795,
0.03273368999361992,
-0.051511239260435104,
0.027903180569410324,
-0.009934637695550919,
0.012143870815634727,
0.02571788802742958,
-0.006226914003491402,
0.037754546850919724,
-0.09531404078006744,
0.02954168990254402,
0.036077748984098434,
0.05181669816374779,
0.022589368745684624,
0.02382127195596695,
0.00271140830591321,
-0.03896808624267578,
-0.014335939660668373,
0.035431157797575,
0.0688682571053505,
0.010124939493834972,
-0.03994760289788246,
-0.011241072788834572,
0.06842275708913803,
-0.02601988986134529,
0.017924750223755836,
-0.013010585680603981,
-0.02670198306441307,
-0.04874469339847565,
0.05312608182430267,
0.0273593682795763,
-0.012850390747189522,
-0.00724245049059391,
0.03137189894914627,
-0.012541785836219788,
-0.018527714535593987,
0.10453520715236664,
0.043851353228092194,
0.007371541578322649,
0.005460785236209631,
-0.0496419332921505,
0.07066845148801804,
0.066195048391819,
0.010141154751181602,
0.04091425612568855,
-0.0029021408408880234,
0.010272008366882801,
0.005131380166858435,
0.06356234103441238,
0.016558995470404625,
0.014158183708786964,
0.03729899600148201,
-0.09829070419073105,
-0.00842446368187666,
0.0209303367882967,
-0.022987771779298782,
-0.013348807580769062,
0.03556418791413307,
0.02684595435857773,
-0.02789471484720707,
0.011057285591959953,
-0.0580127090215683,
0.027021655812859535,
0.038814883679151535,
-0.027456946671009064,
-0.03932776302099228,
0.014740168116986752,
-0.0035197874531149864,
-0.09554340690374374,
-0.0031488994136452675,
-0.06795772910118103,
-0.00625751493498683,
0.00812055915594101,
-0.007656914182007313,
-0.002172211417928338,
0.010799912735819817,
0.00012118593440391123,
0.0010137376375496387,
0.007355123292654753,
0.050822410732507706,
-0.01489573810249567,
0.0015598922036588192,
0.00351342442445457,
-0.012048667296767235,
-0.10273121297359467,
-0.015536654740571976,
-0.002442434197291732,
0.04635626822710037,
-0.01626543700695038,
0.01599986106157303,
0.007237238343805075,
-0.0632452741265297,
-0.031066803261637688,
-0.0007921148790046573,
0.09567824751138687,
-0.009476295672357082,
0.0035193366929888725,
-0.029909005388617516,
-0.02006249502301216,
0.05130279064178467
] |
<p>For example, when we meassure Higgs boson mass to be 125 GeV, do we think about renormalized or pole mass? Should the mass of the Higgs change if it is produced at higher energies?</p> | g4805 | [
0.021743452176451683,
-0.00898081623017788,
0.01183511782437563,
-0.03496823087334633,
0.04486915096640587,
0.03667794167995453,
-0.03059396892786026,
0.06064118817448616,
-0.013160644099116325,
-0.03109174594283104,
-0.06184544414281845,
0.005468499846756458,
0.006030856631696224,
0.050108253955841064,
0.006734040100127459,
-0.009899911470711231,
0.06184706836938858,
-0.046827055513858795,
0.019292594864964485,
0.04577197879552841,
0.00032829074189066887,
-0.03298249468207359,
-0.008663367480039597,
0.01245214231312275,
-0.03556356206536293,
0.05491644889116287,
0.016032395884394646,
-0.021461796015501022,
0.010571207851171494,
0.010752882808446884,
-0.01131278183311224,
0.014091304503381252,
0.04151787981390953,
-0.011525306850671768,
-0.044465743005275726,
-0.0905878096818924,
0.058263614773750305,
0.019073553383350372,
0.03221273049712181,
-0.06858734786510468,
0.03498189523816109,
-0.03272602707147598,
0.0317542627453804,
-0.03695604205131531,
-0.054146863520145416,
0.059707462787628174,
0.04438143968582153,
-0.01452628429979086,
0.05373512953519821,
0.039657872170209885,
0.009366714395582676,
0.0498928427696228,
0.04378119111061096,
0.06930842995643616,
0.04270688816905022,
0.07220577448606491,
0.0007030782871879637,
-0.006336035672575235,
0.03713071346282959,
0.016674082726240158,
0.020081575959920883,
0.0030370084568858147,
-0.03348002955317497,
-0.02524823136627674,
0.03247123211622238,
-0.0002473424538038671,
-0.09805327653884888,
0.033860497176647186,
-0.006056605838239193,
-0.022355884313583374,
0.017464596778154373,
-0.05163417384028435,
-0.03571413829922676,
0.021118715405464172,
0.02105260267853737,
-0.028722714632749557,
-0.024387570098042488,
-0.02364277094602585,
-0.05335189774632454,
0.001989297801628709,
-0.026084579527378082,
-0.034088268876075745,
0.061550360172986984,
-0.04763715714216232,
0.048072632402181625,
-0.046202290803194046,
-0.0038368143141269684,
0.004116283729672432,
-0.0027768071740865707,
0.05571220442652702,
0.02155354432761669,
-0.07417784631252289,
0.03407856822013855,
0.0246437881141901,
-0.03786015138030052,
-0.033125992864370346,
0.006857419386506081,
0.02148684300482273,
0.031564582139253616,
0.03393924981355667,
-0.053397540003061295,
0.03671915829181671,
-0.05075480416417122,
-0.03214319050312042,
-0.028637899085879326,
-0.011480506509542465,
0.06814975291490555,
-0.029768696054816246,
0.03688989207148552,
-0.029266877099871635,
-0.038956448435783386,
-0.04596809670329094,
-0.07487013190984726,
0.04811801388859749,
-0.08581015467643738,
-0.027744276449084282,
0.10322239995002747,
0.005917426198720932,
-0.010429640300571918,
0.07040718197822571,
0.040508635342121124,
-0.013628754764795303,
0.01434379443526268,
-0.0019308412447571754,
0.011372818611562252,
-0.035168882459402084,
-0.04251367598772049,
-0.003403078531846404,
0.03766022250056267,
-0.018072575330734253,
-0.028039271011948586,
-0.003505225060507655,
-0.020929673686623573,
0.02087734453380108,
0.026622774079442024,
0.008394340984523296,
0.03206357732415199,
0.029188157990574837,
0.03953545540571213,
0.0073743537068367004,
0.05012508109211922,
0.00780471321195364,
0.015189094468951225,
-0.01157226599752903,
0.034965187311172485,
-0.010811270214617252,
0.010499273426830769,
-0.015491706319153309,
0.005069943610578775,
0.1020316630601883,
0.018924487754702568,
0.05547593906521797,
0.027037488296628,
-0.01607922650873661,
0.025038916617631912,
-0.016727492213249207,
-0.012798437848687172,
0.005192408338189125,
-0.015076695010066032,
-0.025514403358101845,
0.029183661565184593,
-0.0696152076125145,
0.012418784201145172,
0.015483968891203403,
-0.00382598745636642,
0.03563876077532768,
0.05708204582333565,
0.01100911758840084,
-0.035180944949388504,
-0.04731457680463791,
-0.03963931277394295,
0.05565587058663368,
-0.02253473736345768,
0.005682734772562981,
0.054889678955078125,
0.05930448696017265,
-0.02219204790890217,
-0.031398579478263855,
0.013482150621712208,
0.07409206032752991,
0.02092432975769043,
-0.01803525723516941,
0.011846628971397877,
-0.04961934685707092,
-0.02750442549586296,
0.005557290744036436,
-0.02489303983747959,
0.034008994698524475,
0.08204668015241623,
0.06095333397388458,
-0.02692597173154354,
0.01790141686797142,
-0.04875637963414192,
0.01934615708887577,
-0.004473665729165077,
0.0003374548687133938,
0.0009139403118751943,
-0.03753663972020149,
-0.012743644416332245,
0.01130484975874424,
-0.034195996820926666,
-0.017772767692804337,
-0.006836296990513802,
-0.0026248744688928127,
-0.01089453510940075,
-0.03705092519521713,
0.030587734654545784,
0.04083113372325897,
0.00912471767514944,
-0.05067761242389679,
0.08750464022159576,
-0.059420641511678696,
-0.006939683575183153,
0.049652811139822006,
-0.07264494895935059,
0.04386564716696739,
0.02361266128718853,
0.032986439764499664,
0.05139872804284096,
0.03143312409520149,
-0.0848471000790596,
-0.05370311066508293,
0.026926597580313683,
0.05138486623764038,
-0.02475537545979023,
-0.02763347141444683,
-0.03069564327597618,
-0.027176570147275925,
-0.015999997034668922,
0.02617182955145836,
0.007595456205308437,
-0.001556932576932013,
0.02396770380437374,
0.004835203289985657,
0.013931785710155964,
-0.015955112874507904,
-0.034189656376838684,
-0.02133641205728054,
0.0709715411067009,
0.010149865411221981,
0.04478070139884949,
-0.021550623700022697,
-0.030417462810873985,
0.013970471918582916,
0.0217782873660326,
-0.0004882887587882578,
0.07121945172548294,
0.04733272269368172,
-0.025161614641547203,
0.038614630699157715,
0.004512713756412268,
-0.003273995826020837,
0.016820166260004044,
-0.0031750898342579603,
-0.009930441156029701,
-0.0032170566264539957,
0.016312506049871445,
0.05966649949550629,
-0.04156237095594406,
-0.019810279831290245,
0.0393979549407959,
-0.0716288611292839,
-0.026045607402920723,
0.0350116491317749,
-0.0524275004863739,
-0.0017287625232711434,
-0.00809739250689745,
-0.012648465111851692,
-0.03217324987053871,
0.00589725049212575,
0.0011101975105702877,
0.05712677910923958,
0.02824767865240574,
0.06149646267294884,
-0.022938130423426628,
-0.035904593765735626,
-0.023469073697924614,
0.008851868100464344,
0.0406763069331646,
-0.054686080664396286,
0.0068947989493608475,
-0.02010248973965645,
-0.013773548416793346,
-0.004483354277908802,
-0.0005664727068506181,
-0.030626820400357246,
-0.04873203858733177,
-0.09645217657089233,
-0.020045815035700798,
0.021697403863072395,
-0.01838349737226963,
-0.028436560183763504,
0.05045883730053902,
-0.03425633907318115,
-0.021507157012820244,
0.025301773101091385,
0.05120231956243515,
0.0420641154050827,
0.0021183823700994253,
0.0020831141155213118,
0.004590913653373718,
0.013953467831015587,
-0.0828581377863884,
-0.009638608433306217,
0.012157739140093327,
0.019353892654180527,
-0.0007470975397154689,
0.043154023587703705,
0.01269109919667244,
-0.0673755630850792,
-0.012809552252292633,
0.042586904019117355,
-0.0065657636150717735,
0.005092386621981859,
-0.051769647747278214,
0.008842121809720993,
-0.010627826675772667,
0.037383630871772766,
-0.019533630460500717,
-0.07570076733827591,
-0.06906995177268982,
-0.0037069169338792562,
0.0032290066592395306,
-0.0070117139257490635,
-0.025927789509296417,
0.044136349111795425,
0.02776804380118847,
0.020006529986858368,
-0.07548245787620544,
-0.05722610279917717,
0.029745817184448242,
0.031787969172000885,
-0.05742134153842926,
0.035279273986816406,
-0.002916606841608882,
0.025003336369991302,
0.040744081139564514,
-0.009290015324950218,
0.0847994014620781,
0.05213363841176033,
0.01734915003180504,
-0.0006622858927585185,
-0.024056166410446167,
0.018765509128570557,
0.027490301057696342,
0.030674360692501068,
-0.03126072883605957,
-0.08291619271039963,
0.036463767290115356,
-0.022481543943285942,
0.027763042598962784,
0.06099656969308853,
-0.010618505999445915,
0.028451839461922646,
-0.010470246896147728,
0.03156067430973053,
-0.04598895087838173,
0.01398097537457943,
-0.026407748460769653,
-0.03019596077501774,
0.04677075892686844,
0.027555113658308983,
-0.021919844672083855,
-0.04206983372569084,
-0.0658227875828743,
0.019381295889616013,
-0.01948700286448002,
-0.014418801292777061,
-0.0038399717304855585,
-0.0001327019272139296,
-0.009542329236865044,
-0.016658928245306015,
-0.0008323054644279182,
0.038999274373054504,
-0.035077761858701706,
-0.014418094418942928,
0.0618419274687767,
0.03513135388493538,
-0.010259303264319897,
-0.007577353157103062,
0.018932200968265533,
-0.036153607070446014,
-0.017689311876893044,
-0.06686786562204361,
-0.07291250675916672,
-0.006470364052802324,
-0.005695825908333063,
-0.013995636254549026,
0.003522592829540372,
-0.03478114679455757,
-0.021316492930054665,
-0.01536930538713932,
0.03794809430837631,
-0.024350468069314957,
0.08594096451997757,
-0.02734822779893875,
0.027578892186284065,
-0.025996625423431396,
0.034839026629924774,
0.016788288950920105,
-0.03709312900900841,
0.029816526919603348,
0.005504045635461807,
-0.018839869648218155,
-0.0008669000817462802,
0.004391102585941553,
0.04886321350932121,
-0.03026503138244152,
0.006339283660054207,
-0.05778045207262039,
0.03324062377214432,
0.02472759783267975,
0.016646303236484528,
-0.011921015568077564,
-0.006467906292527914,
-0.054581139236688614,
-0.015075808390974998,
-0.022929055616259575,
0.007926546037197113,
0.01631099544465542,
0.027458474040031433,
0.013692236505448818,
0.01995088905096054,
-0.00023237933055497706,
0.008177380077540874,
0.05843169614672661,
0.06380576640367508,
0.009416288696229458,
-0.056759655475616455,
-0.042534761130809784,
0.05497697368264198,
-0.01696099154651165,
-0.009451483376324177,
-0.08683475852012634,
-0.008483011275529861,
0.06807234138250351,
-0.0025021920446306467,
-0.0032506061252206564,
0.005047488491982222,
0.0075332242995500565,
0.044232383370399475,
-0.04507257416844368,
-0.037106432020664215,
0.010719791986048222,
0.00796410720795393,
0.026640763506293297,
-0.04537409916520119,
0.01834384724497795,
0.007161015644669533,
-0.004481854848563671,
-0.08066426217556,
0.02292528748512268,
-0.01599843241274357,
-0.030311452224850655,
0.04652351886034012,
0.013061572797596455,
-0.022664399817585945,
0.03865090385079384,
-0.029605671763420105,
-0.021106526255607605,
-0.06832142919301987,
-0.021020278334617615,
0.035247184336185455,
0.014920013956725597,
-0.011825070716440678,
0.0017368418630212545,
-0.03708764538168907,
-0.029201773926615715,
-0.02432645671069622,
-0.031939420849084854,
-0.017493117600679398,
-0.03612353280186653,
0.04257442057132721,
-0.003584928810596466,
0.03514361381530762,
0.04465405270457268,
-0.020774124190211296,
-0.08226784318685532,
-0.044409945607185364,
-0.06486209481954575,
-0.036362044513225555,
0.013099901378154755,
-0.02607247605919838,
-0.031405895948410034,
-0.0030269199050962925,
0.005518055055290461,
-0.06782478094100952,
-0.0331188403069973,
0.06441362202167511,
-0.012582075782120228,
-0.0075337826274335384,
0.056947845965623856,
0.06873701512813568,
-0.0021884061861783266,
0.05559999868273735,
0.002776355016976595,
-0.05660578981041908,
-0.04855688288807869,
-0.010877380147576332,
0.028842583298683167,
-0.020113611593842506,
-0.00498488312587142,
0.002333020092919469,
0.01913583278656006,
0.004625326953828335,
0.0687708854675293,
0.03978195786476135,
-0.06866534054279327,
0.042837370187044144,
-0.008846273645758629,
-0.01929200254380703,
0.02375844120979309,
0.013408783823251724,
0.002516247797757387,
0.0327204205095768,
-0.03769327327609062,
-0.014210901223123074,
0.07613503932952881,
0.018966272473335266,
-0.031187664717435837,
0.02403343841433525,
-0.03797087445855141,
0.05255775898694992,
-0.01284610852599144,
-0.004822717048227787,
-0.005822803359478712,
-0.019546929746866226,
-0.03614955395460129,
0.060456015169620514,
0.01818680763244629,
0.033259324729442596,
-0.013799421489238739,
0.06177792698144913,
0.04994632303714752,
0.006955238990485668,
0.011257356032729149,
-0.02774999849498272,
0.024582277983427048,
0.032561253756284714,
-0.004432085435837507,
-0.011790894903242588,
-0.007596218958497047,
0.032130174338817596,
0.04345483332872391,
0.04375999793410301,
0.0019036013400182128,
-0.02152182161808014,
-0.01591702550649643,
0.05942155420780182,
-0.06667351722717285,
-0.06390929967164993,
0.01636485569179058,
0.007208820432424545,
0.008295916020870209,
-0.0044563403353095055,
0.017627909779548645,
0.016799787059426308,
-0.015842141583561897,
-0.015396338887512684,
0.0068006874062120914,
-0.008547377772629261,
0.01678771898150444,
0.026243772357702255,
0.02182462438941002,
0.045387670397758484,
-0.09209955483675003,
0.05036163702607155,
-0.020725049078464508,
0.0148274851962924,
-0.028209926560521126,
0.012725136242806911,
0.016984356567263603,
-0.020944371819496155,
0.0020312918350100517,
0.020134735852479935,
0.03064005635678768,
-0.028049707412719727,
0.010964695364236832,
0.027336793020367622,
-0.033008456230163574,
0.008546890690922737,
-0.010278579778969288,
-0.0051805851981043816,
-0.01999262534081936,
0.025382261723279953,
-0.008800815790891647,
-0.001143053756095469,
0.028061890974640846,
0.004930536262691021,
0.11245840787887573,
0.0031770658679306507,
0.017409630119800568,
0.014972318895161152,
0.03634489327669144,
-0.02571866847574711,
0.033420078456401825,
-0.033819906413555145,
-0.03904170170426369,
-0.02696414478123188,
0.012768502347171307,
0.07638541609048843,
-0.0020752677228301764,
-0.012180603109300137,
-0.030710643157362938,
0.012366363778710365,
-0.001823834259994328,
0.021631108596920967,
0.0774126946926117,
-0.02049536257982254,
-0.0004488508275244385,
0.05385030433535576,
-0.06121727079153061,
0.05039351433515549,
-0.03839676082134247,
-0.028705934062600136,
-0.028823889791965485,
-0.004713886883109808,
0.08810018748044968,
-0.04166311398148537,
0.012441346421837807,
0.048288702964782715,
0.0007220420520752668,
0.07692523300647736,
-0.02106313407421112,
0.0324888601899147,
-0.013493981212377548,
0.057065561413764954,
-0.007258233148604631,
0.049615442752838135,
-0.006313520483672619,
-0.013243667781352997,
0.03444072604179382,
-0.00000624082258582348,
0.02859259396791458,
-0.026934487745165825,
0.04749087989330292,
-0.023674024268984795,
0.029863866046071053,
-0.06882160156965256,
-0.01799779012799263,
-0.022616660222411156,
0.003953103441745043,
-0.00846138596534729,
0.019006062299013138,
-0.07364316284656525,
0.0016855119029060006,
0.0022100985515862703,
-0.000005524607786355773,
0.0057312119752168655,
-0.019531650468707085,
-0.04209219664335251,
-0.004777319263666868,
-0.040139347314834595,
-0.033370837569236755,
-0.00015334447380155325,
0.014483464881777763,
-0.03325890749692917,
0.021195104345679283,
0.05956820771098137,
-0.019291656091809273,
-0.07335598766803741,
0.026600098237395287,
0.004545123316347599,
-0.005810444243252277,
-0.012483075261116028,
0.03537193313241005,
0.019521411508321762,
-0.022773250937461853,
0.019771412014961243,
0.0230306014418602,
-0.003090251935645938,
-0.047539107501506805,
-0.03568405658006668,
-0.009469662792980671,
-0.012706627137959003,
-0.06584642082452774,
-0.04324999824166298,
-0.011438225395977497,
-0.05982914939522743,
0.057496048510074615,
-0.016745571047067642,
0.051532115787267685,
-0.004762429744005203,
0.008571376092731953,
-0.034582607448101044,
0.035968322306871414,
-0.0029305247589945793,
0.021622486412525177,
-0.02240840531885624,
-0.009710634127259254,
-0.001067264238372445,
0.00606216536834836,
0.04293336719274521,
0.042789630591869354,
-0.05849505960941315,
-0.031277790665626526,
0.017936130985617638,
0.023642392829060555,
0.01265234686434269,
-0.039018914103507996,
0.006453327834606171,
0.04039613530039787,
0.029939990490674973,
-0.01902461051940918,
0.028055448085069656,
-0.01419647317379713,
0.016472654417157173,
0.04533764347434044,
-0.052941933274269104,
0.018997952342033386,
0.014786021783947945,
-0.017587751150131226,
0.046212922781705856,
0.08875502645969391,
-0.04500456899404526,
-0.03674188628792763,
-0.07143524289131165,
-0.038610056042671204,
-0.02421201951801777,
-0.02117159590125084,
-0.0350157767534256,
0.05546816065907478,
-0.06661952286958694,
-0.022871164605021477,
0.021906323730945587,
-0.013276258483529091,
-0.009613591246306896,
0.032251399010419846,
-0.02317195013165474,
0.029513340443372726,
-0.023512713611125946,
0.03278088942170143,
-0.03136342018842697,
-0.024542149156332016,
-0.0254360344260931,
-0.004657486919313669,
0.04109735041856766,
-0.009601540863513947,
-0.004864638205617666,
-0.03356526792049408,
0.009049291722476482,
-0.045641664415597916,
0.01993800699710846,
0.04392172023653984,
-0.02495594136416912,
-0.01761513575911522,
0.0025754086673259735,
-0.03390849754214287,
0.0006203213124535978,
-0.040198419243097305,
-0.06952507793903351,
-0.005221894942224026,
-0.07266849279403687,
0.05742823705077171,
-0.06023051589727402,
-0.04389936849474907,
0.023708293214440346,
0.010490300133824348,
-0.02037358470261097,
-0.041583649814128876,
0.02191092260181904,
-0.060215406119823456,
0.026676969602704048,
-0.05589579418301582,
-0.03482164815068245,
0.010546390898525715,
-0.005823397543281317,
-0.023982832208275795
] |
<p>I couldn't find one but assumed it must exist. Tried to find it on the back of an envelope, but got to an ugly differential equation I can't solve.</p>
<p>I'm assuming a square duct of infinite length, incompressible fluid, constant pressure gradient. The flow is steady. I'm also assuming there's only flow down the duct (z direction).</p>
<p>I get to here (seemed trivial, might still be wrong), then I'm stuck.</p>
<p>$$
\frac{\partial^2 v_z(x,y)}{\partial x^2} +
\frac{\partial^2 v_z(x,y)}{\partial y^2} =
\frac{\Delta P}{\mu \Delta X}
$$</p> | g4806 | [
0.04645182192325592,
-0.003725457238033414,
-0.023520253598690033,
-0.005931810010224581,
0.02935141883790493,
-0.01743263006210327,
0.024783750995993614,
0.025066550821065903,
-0.042916469275951385,
-0.09189388155937195,
-0.02300083637237549,
0.047712091356515884,
0.04669652506709099,
0.006301225163042545,
0.00022908208484295756,
-0.007601604796946049,
0.03164328262209892,
-0.015900464728474617,
0.0031289937905967236,
-0.03569408506155014,
-0.02800837717950344,
-0.00004926961628370918,
0.07352906465530396,
-0.060434963554143906,
0.05164164677262306,
0.0043063391931355,
0.05343625694513321,
-0.004012796562165022,
-0.08088640868663788,
0.015872051939368248,
-0.0205283984541893,
0.028239311650395393,
0.050847381353378296,
0.036150913685560226,
-0.012212906964123249,
-0.00019984872778877616,
-0.007686743978410959,
-0.02875223569571972,
0.08234953880310059,
-0.0036276187747716904,
0.011181455105543137,
-0.03643740341067314,
-0.01601698063313961,
0.0021931391675025225,
-0.021697722375392914,
-0.006817485671490431,
-0.07074926048517227,
0.0074315969832241535,
-0.009291430935263634,
-0.0024361114483326674,
0.08788313716650009,
0.05941202864050865,
0.04366036504507065,
-0.03498511388897896,
-0.04032018780708313,
0.03524577617645264,
0.021021785214543343,
-0.04353934898972511,
0.023311706259846687,
0.02806055173277855,
-0.04781650751829147,
0.010621326975524426,
0.01447792537510395,
-0.03067759796977043,
0.012334543280303478,
-0.010788078419864178,
-0.01215157750993967,
-0.08610869199037552,
0.007096004206687212,
0.024604981765151024,
0.04093654081225395,
-0.00002481340925442055,
0.04979655146598816,
0.030815845355391502,
-0.015551860444247723,
0.03723588213324547,
0.010159640572965145,
-0.049007292836904526,
0.03448443487286568,
-0.05332218110561371,
-0.04023750126361847,
0.03805560991168022,
0.006018887739628553,
0.01215794961899519,
0.03942735493183136,
0.006299939006567001,
0.015016114339232445,
0.0003299417730886489,
-0.07144397497177124,
-0.051756009459495544,
-0.10730210691690445,
0.044474028050899506,
-0.050653498619794846,
-0.03533782809972763,
0.05680181458592415,
-0.050980765372514725,
-0.00598171865567565,
0.04529177397489548,
-0.04273441433906555,
-0.031809721142053604,
0.024724049493670464,
-0.012499749660491943,
0.014903138391673565,
0.05392707511782646,
-0.029858319088816643,
-0.02430623769760132,
0.020193275064229965,
0.015663176774978638,
0.025655874982476234,
-0.06984034925699234,
0.02858784794807434,
0.004052143078297377,
-0.06738368421792984,
-0.013255026191473007,
0.04182612895965576,
0.011910207569599152,
-0.015590706840157509,
-0.004580012988299131,
-0.0813412144780159,
0.012388891540467739,
0.0023565359879285097,
-0.0024690746795386076,
-0.002190161030739546,
0.060679543763399124,
0.00033309185528196394,
0.06767116487026215,
-0.008334251120686531,
0.053249914199113846,
0.03757258877158165,
0.010554280132055283,
0.013506917282938957,
-0.0020332003477960825,
-0.0012916182167828083,
-0.031093759462237358,
-0.010853524319827557,
0.0330478735268116,
-0.05537974461913109,
-0.004818921908736229,
-0.03260180726647377,
0.03197754919528961,
0.0227814931422472,
-0.08763166517019272,
-0.004354078788310289,
0.028567610308527946,
0.007898956537246704,
0.009888431057333946,
-0.026487551629543304,
0.01832636632025242,
-0.033941783010959625,
-0.041466910392045975,
-0.027840226888656616,
0.06888967752456665,
-0.0008801538497209549,
0.019955391064286232,
-0.0421159490942955,
-0.011680100113153458,
0.028429895639419556,
0.04800954461097717,
0.01693464256823063,
-0.03146994113922119,
0.014937382191419601,
0.06557127833366394,
0.027952181175351143,
-0.02574327029287815,
-0.052289750427007675,
0.03486208990216255,
-0.028822988271713257,
-0.021736958995461464,
-0.021309956908226013,
0.049790870398283005,
-0.006391898263245821,
0.0005918474635109305,
0.0582246370613575,
0.044306956231594086,
0.010149323381483555,
0.02079617790877819,
-0.003984229639172554,
-0.018489038571715355,
0.03204502910375595,
-0.018931707367300987,
0.04540465772151947,
-0.027153773233294487,
0.039945222437381744,
-0.03836550936102867,
-0.002541542984545231,
0.0022721784189343452,
-0.03954086825251579,
0.005086011718958616,
-0.0465775802731514,
-0.06810085475444794,
0.025074342265725136,
0.02187887392938137,
0.030945206061005592,
0.05501236394047737,
0.0032811451237648726,
0.014593953266739845,
0.02095429040491581,
-0.12416574358940125,
-0.05259300768375397,
0.039805326610803604,
0.04992404207587242,
0.03449537605047226,
0.09822926670312881,
0.02806517295539379,
-0.03679184243083,
0.016644686460494995,
-0.017810022458434105,
-0.0078904302790761,
0.018192578107118607,
0.029690075665712357,
-0.020565159618854523,
-0.07551484555006027,
0.01843481883406639,
0.027777839452028275,
0.0063181063160300255,
-0.0921654999256134,
0.03508855774998665,
0.017467739060521126,
-0.006564978044480085,
0.0019080382771790028,
0.01727858930826187,
0.03860483691096306,
-0.0132152633741498,
-0.04024584963917732,
-0.03728625550866127,
0.0046702842228114605,
-0.017418382689356804,
-0.031689632683992386,
0.011710750870406628,
0.005233766045421362,
-0.01921573095023632,
-0.02453909069299698,
0.014319886453449726,
-0.02730588987469673,
0.005842684302479029,
-0.016812222078442574,
-0.002789564896374941,
0.024363914504647255,
-0.027458101511001587,
-0.0008846087148413062,
-0.007402858231216669,
-0.02562001161277294,
-0.021867908537387848,
0.04441816732287407,
0.06523655354976654,
0.03147595748305321,
0.023272482678294182,
0.025697952136397362,
0.06264050304889679,
-0.010401752777397633,
0.023084238171577454,
-0.03473677486181259,
0.00017925878637470305,
0.011122561059892178,
0.013443083502352238,
0.005355579312890768,
-0.035478197038173676,
-0.009731411933898926,
-0.002787361852824688,
-0.07801172137260437,
-0.07839439809322357,
0.0021475821267813444,
0.048605699092149734,
0.0406266413629055,
-0.08329331129789352,
0.022201886400580406,
-0.018699951469898224,
-0.0002910191542468965,
0.052313197404146194,
0.03413774073123932,
0.01862882450222969,
0.011843615211546421,
0.002154821064323187,
-0.015949873253703117,
-0.007625996135175228,
0.008190447464585304,
0.02700415998697281,
-0.016161832958459854,
-0.044822875410318375,
0.04723891615867615,
0.09756287932395935,
-0.01054443046450615,
0.01097123883664608,
0.026578636839985847,
0.039950113743543625,
-0.037377625703811646,
0.047540437430143356,
0.03377963975071907,
0.004322182387113571,
-0.004710034467279911,
-0.021522480994462967,
-0.022041447460651398,
-0.031158003956079483,
0.0038495168555527925,
0.026788195595145226,
0.001211061142385006,
0.03342064470052719,
-0.01272925827652216,
-0.010722502134740353,
-0.04891226068139076,
0.005711293779313564,
-0.007392920088022947,
0.02865510992705822,
-0.013908881694078445,
-0.015475255437195301,
-0.061041928827762604,
-0.0010103201493620872,
-0.014346413314342499,
0.0444052591919899,
-0.023915506899356842,
0.06283571571111679,
0.004156789276748896,
0.02126143127679825,
0.005374619737267494,
0.01124800555408001,
0.015678683295845985,
0.0234934501349926,
-0.04485514760017395,
0.011790999211370945,
0.06331043690443039,
0.05936218425631523,
-0.01080322265625,
0.03744901344180107,
0.007561216596513987,
-0.017902247607707977,
-0.014181538484990597,
-0.058051034808158875,
0.045212071388959885,
-0.04139016941189766,
-0.005237532313913107,
0.009282510727643967,
-0.0015615748707205057,
0.016965065151453018,
0.007669492624700069,
0.039979998022317886,
-0.007291396148502827,
-0.03461970016360283,
0.05502844974398613,
0.07324330508708954,
0.007179131265729666,
-0.008998691104352474,
-0.014205172657966614,
-0.03950905054807663,
-0.008306840434670448,
-0.0029295547865331173,
-0.053504083305597305,
0.001403093570843339,
0.09036000818014145,
0.04997801408171654,
0.012144786305725574,
0.035344380885362625,
-0.05489325895905495,
-0.014998359605669975,
-0.021387513726949692,
-0.018641864880919456,
-0.025178570300340652,
0.07442046701908112,
-0.060368385165929794,
-0.009895119816064835,
0.020563656464219093,
0.03504899889230728,
-0.036716461181640625,
0.008373891934752464,
-0.013074771501123905,
0.044185757637023926,
-0.03325478360056877,
0.0409935861825943,
-0.007928445003926754,
-0.07700707763433456,
-0.022415976971387863,
-0.0017338679172098637,
-0.026731684803962708,
-0.022662898525595665,
0.036012157797813416,
-0.034562889486551285,
-0.09090374410152435,
-0.054675519466400146,
0.01418731827288866,
0.01083208154886961,
0.05373146012425423,
0.03138743340969086,
-0.015203235670924187,
0.004796728491783142,
0.03966226428747177,
-0.04574316740036011,
-0.037709299474954605,
-0.04433031007647514,
-0.01664300262928009,
0.048111677169799805,
-0.01042614970356226,
0.024435529485344887,
-0.02119237743318081,
-0.04412892833352089,
0.01284174993634224,
-0.045529961585998535,
-0.006637930870056152,
0.033486172556877136,
0.019855376332998276,
-0.07226766645908356,
-0.060706689953804016,
0.025551510974764824,
0.013067183084785938,
0.03370732441544533,
0.029763847589492798,
-0.052639298141002655,
-0.019130883738398552,
-0.015288159251213074,
-0.04922672361135483,
-0.0033090338110923767,
-0.033440280705690384,
0.018223952502012253,
-0.05739641189575195,
0.022324560210108757,
-0.0053743962198495865,
0.03129321336746216,
-0.021092548966407776,
0.017613429576158524,
-0.013144774362444878,
0.05409305542707443,
-0.03254899010062218,
0.059864696115255356,
0.001155931269749999,
-0.022030185908079147,
-0.0432693175971508,
0.03839539736509323,
0.052152153104543686,
0.05142931267619133,
0.005321531556546688,
-0.018550198525190353,
-0.06142335385084152,
-0.011805130168795586,
0.021074680611491203,
-0.04449575021862984,
0.025498120114207268,
0.005748601630330086,
0.051640789955854416,
-0.018230494111776352,
-0.07539321482181549,
-0.0264863520860672,
0.10631422698497772,
0.040933478623628616,
-0.05334921553730965,
0.010164097882807255,
-0.00872915517538786,
0.02497284486889839,
0.026191068813204765,
0.032463438808918,
-0.04566441848874092,
-0.0048477365635335445,
0.020460249856114388,
-0.04330964758992195,
-0.0014915280044078827,
-0.014817078597843647,
0.0008892764453776181,
0.04223509505391121,
-0.0094990199431777,
-0.0037448236253112555,
-0.03578605502843857,
0.006874357350170612,
0.043655332177877426,
0.002016106154769659,
-0.0059623378328979015,
-0.0007473197183571756,
0.04971401020884514,
0.044325124472379684,
-0.06685991585254669,
0.00231303833425045,
0.027740489691495895,
-0.015830863267183304,
-0.07921753823757172,
-0.008300336077809334,
0.05632494390010834,
0.0019795799162238836,
0.04910615086555481,
-0.0062753125093877316,
0.013756372965872288,
-0.00978331733494997,
0.026299746707081795,
0.03183351084589958,
-0.03279602900147438,
-0.03712104260921478,
0.019352208822965622,
0.008020474575459957,
-0.0005593210808001459,
0.027383049950003624,
-0.0019125534454360604,
-0.10247723013162613,
0.018995294347405434,
0.0206883754581213,
-0.06121765077114105,
0.022947046905755997,
0.009173569269478321,
-0.014292046427726746,
-0.01548065710812807,
-0.07536482810974121,
-0.037940435111522675,
0.024153372272849083,
-0.067191943526268,
0.05488820746541023,
0.03469137102365494,
-0.06641341000795364,
0.006274465471506119,
0.0057939146645367146,
-0.029173193499445915,
0.06639713793992996,
0.04738258570432663,
-0.05784262716770172,
0.017255714163184166,
-0.00013496767496690154,
0.07255750894546509,
-0.014483529143035412,
-0.03976387903094292,
0.03636413812637329,
-0.0024931496009230614,
-0.0035586112644523382,
-0.0028265900909900665,
-0.0594925694167614,
-0.027177751064300537,
-0.013600502163171768,
-0.049887847155332565,
0.07851964980363846,
0.031011179089546204,
-0.0607287660241127,
0.02855651080608368,
-0.013103256933391094,
0.007468693424016237,
-0.11855004727840424,
-0.03489801660180092,
-0.021976720541715622,
-0.0323595255613327,
0.00483394879847765,
-0.056237246841192245,
-0.022967034950852394,
-0.024326644837856293,
-0.03741449490189552,
0.012374748475849628,
0.016156332567334175,
0.028284039348363876,
-0.02100241929292679,
-0.015303832478821278,
0.06181585416197777,
0.018172737210989,
0.010947350412607193,
0.04925800487399101,
-0.0178163293749094,
0.02076822705566883,
0.040567073971033096,
0.04536147788167,
0.0031831986270844936,
-0.0021215977612882853,
0.021709250286221504,
-0.012190954759716988,
-0.031969208270311356,
0.05511705204844475,
0.014162079431116581,
-0.06652506440877914,
0.048222616314888,
-0.019791219383478165,
-0.03227178752422333,
-0.04916107654571533,
-0.0017764520598575473,
-0.04778417944908142,
-0.01635289192199707,
0.014548146165907383,
-0.05833492800593376,
-0.04409782588481903,
-0.028607232496142387,
0.046341750770807266,
0.03146341070532799,
0.055856816470623016,
0.005858705844730139,
0.010288667865097523,
-0.00015101216558832675,
0.040639203041791916,
0.03547821566462517,
0.002299446379765868,
-0.06269688904285431,
-0.006839246954768896,
0.03658287599682808,
-0.00275305169634521,
-0.022803572937846184,
0.03054833598434925,
0.03279074653983116,
-0.02481069415807724,
0.005279208533465862,
0.027424486353993416,
-0.013770464807748795,
-0.01820930279791355,
-0.008500512689352036,
0.0749974474310875,
-0.014416261576116085,
-0.019404446706175804,
-0.016335926949977875,
-0.0002235975698567927,
0.015560278668999672,
-0.02614845335483551,
0.020631594583392143,
0.04848407581448555,
0.00860552303493023,
0.04648313671350479,
-0.01667255163192749,
0.05183592438697815,
-0.0024624215438961983,
0.02340049296617508,
-0.002455378184095025,
0.021217158064246178,
-0.013211512006819248,
0.03346855193376541,
0.0012057936983183026,
0.00694353599101305,
0.02361242100596428,
0.025126729160547256,
0.035385970026254654,
-0.008411657996475697,
0.02129349857568741,
-0.05171157419681549,
-0.03507687896490097,
0.07387891411781311,
0.036117762327194214,
-0.06437015533447266,
0.04431619495153427,
-0.0014915537321940064,
-0.05193907767534256,
-0.07215157151222229,
0.05228598788380623,
-0.005799584556370974,
-0.019711410626769066,
-0.005158843472599983,
0.0481908954679966,
0.002137020230293274,
0.056455325335264206,
-0.02959870919585228,
-0.014061720110476017,
-0.03105253539979458,
-0.054048120975494385,
0.005818525329232216,
-0.008215378038585186,
0.005784725304692984,
0.043820153921842575,
0.033387910574674606,
0.0385359525680542,
0.037841398268938065,
0.059103675186634064,
0.04462645575404167,
0.03669903799891472,
-0.004253168124705553,
0.005725512281060219,
0.0072843958623707294,
-0.06485823541879654,
-0.013699552975594997,
0.021087756380438805,
0.020303284749388695,
-0.00041682663140818477,
-0.01104965340346098,
-0.028852086514234543,
0.02414291724562645,
-0.010032735764980316,
-0.01687164232134819,
0.02452615089714527,
-0.01599620282649994,
0.00981155689805746,
-0.013268835842609406,
0.028539206832647324,
0.04574498534202576,
0.014728963375091553,
0.005312695167958736,
0.008180266246199608,
-0.053370796144008636,
0.016033180058002472,
-0.03180811554193497,
0.013230519369244576,
-0.041998960077762604,
-0.005780176259577274,
0.018587101250886917,
-0.02915060892701149,
0.013974985107779503,
0.04078219458460808,
0.01659107580780983,
0.02298186533153057,
-0.015811387449502945,
0.05011783912777901,
-0.0006305358838289976,
0.004255286417901516,
-0.04669944569468498,
-0.05141036957502365,
-0.028981707990169525,
0.01792268641293049,
-0.07138803601264954,
0.022082818672060966,
0.06475814431905746,
-0.014330321922898293,
0.03919617831707001,
0.05155174806714058,
-0.019779212772846222,
-0.020018169656395912,
-0.0029424710664898157,
-0.024001173675060272,
0.025510495528578758,
0.002366074360907078,
0.007385747507214546,
0.06561584770679474,
0.03972100093960762,
-0.03280358016490936,
0.0032147460151463747,
-0.02375241555273533,
-0.042007461190223694,
-0.011529219336807728,
-0.0020610997453331947,
0.024722862988710403,
-0.02030622959136963,
0.01715862564742565,
-0.002921356586739421,
-0.06023932993412018,
-0.01183345727622509,
-0.0039187464863061905,
0.0028625200502574444,
-0.08494795858860016,
0.003538003657013178,
0.0011002513347193599,
-0.027938272804021835,
-0.019079657271504402,
-0.00152546726167202,
-0.019767163321375847,
-0.08196203410625458,
-0.00256459042429924,
0.00843182485550642,
-0.050092220306396484,
-0.06126862391829491,
-0.020923135802149773,
0.009636087343096733,
-0.01133290957659483,
0.00256448145955801,
0.007150087505578995,
0.04304438829421997,
-0.013624471612274647,
-0.06725215911865234,
-0.020226938650012016,
0.020515076816082,
0.009447629563510418,
-0.009543306194245815,
0.0016341477166861296,
-0.07730571180582047,
-0.026159146800637245,
-0.01259901188313961,
0.09293053299188614,
0.007344841957092285,
-0.03903186321258545,
0.009254115633666515,
0.026981543749570847,
-0.02039964310824871,
0.06348925828933716,
0.02949783392250538,
-0.0030408636666834354,
-0.011340504512190819,
0.04959622770547867,
-0.0401516854763031,
0.0307553019374609,
0.02185424044728279,
-0.05549408495426178,
0.006818797904998064,
-0.04865777865052223,
-0.04272102192044258,
-0.017760535702109337,
0.02796238847076893,
-0.01240493357181549,
-0.022229693830013275,
-0.011514252051711082,
-0.005877441726624966
] |
<p>If the S-Matrix is the only observable, that rules out both generalized free fields and Wick-ordered polynomials of generalized free fields as interesting Physical models, because both result in a unit S-matrix. Neither possibility has been developed since the 1960s when these results were proved, and when the S-Matrix was ascendant as the only observable in Particle Physics.</p>
<p>If the S-matrix is not the only quantum field observable, which it certainly seems not to be in Condensed Matter Physics and in Quantum Optics, to name just two fields in which Wightman or correlation functions play a large part in modeling, does that encourage us to construct Wick-ordered polynomials of generalized free fields as algebraic, non-dynamical deformations of free fields? In such a construction, the point is to avoid deforming a Hamiltonian or Lagrangian evolution, instead working with deformations of the observables, requiring for example that all observables and all states will be constructed as Wick-ordered polynomials in a Wick-ordered operator-valued distribution such as $\hat\Phi(x)=:\!\!\hat\phi(x)+\lambda\hat\phi^\dagger\hat\phi(x)^2\!\!:$. The Hamiltonian is taken to be a derived quantity in this approach.</p>
<p>The S-Matrix seems remarkable, in that it requires us to set up a hyperplane at an initial time $t_I$ and another at a final time $t_F$, and another two hyperplanes between which the interaction will be nontrivial, at times $t_I<t_A<t_B<t_F$, all of which is not Lorentz-invariant, then take the limits $t_I\rightarrow-\infty,t_A\rightarrow-\infty,t_B\rightarrow+\infty,t_F\rightarrow+\infty$. It seems that in no other branch of Physics would we construct such an idealization and say it's the only possible way to report the experimental data. In other words, I wonder, going further, whether the S-matrix even is an observable? Particle Physics seems to be the only field in Physics that seems to think it is.</p>
<p><strong>post-Answer addition.</strong> It's Greenberg who proves in JMathPhys 3, 31(1962) that Wick-ordered finite polynomials in the field have a trivial S-matrix, and I think, without looking it up, that it's also Greenberg who introduced and ruled out generalized free fields. I've resisted doing something else because Wick-ordered polynomials in a generalized free field seem to give such a lot of freedom to create models that surely they can be useful, which I know is not a good reason, but I had to feel how bad it is before I could move on. I suppose I was almost ready to give up this way of doing things before I asked this question. While Tim van Beeks' response is definitely of interest, and Matt's Answer is clearly the "right" answer, but doesn't go into the periphery of the question in the right way to help me, it was Marcel's response that particularly pushed me.</p>
<p>My comment to Marcel indicates the way I'm now going to take this, to functions of the field such as $\hat\Phi(x)=\tanh{(\hat\phi(x))}$. Insofar as we can say that the measured value of $\hat\phi(x)$ is almost always $\pm\infty$ in the vacuum state, because the expected value $\left<0\right|\hat\phi(x)\left|0\right>$ is zero and we can say, loosely, that the variance is $\infty$ in the vacuum state, presumably $\left<0\right|\delta(\hat\Phi(x)-\lambda)\left|0\right>$ is non-zero only for $\lambda=\pm 1$ (though with some worries about this construction). It's not clear that we even have to introduce normal-ordering. $\tanh{(\hat\phi(x))}$ is of course a bounded operator of the unbounded Wightman free field, whereas no nontrivial polynomial in the field $\hat\phi(x)$ can be a bounded operator. The particular choice of $\hat\Phi(x)=\tanh{(\hat\phi(x))}$ is clearly a particular coordinatization; if we change the coordinatization by taking a function of $\hat\Phi(x)$, we in general get a measurement operator that results in two discrete values of the field, mapping $\pm 1$ to $a,b$ respectively. If we take something different from the real Klein-Gordon field, my aim as I envisage it four hours after first imagining it is to map something like an $SU(3)$ invariant Wightman field, say, to a finite number of discrete values. If such an $SU(3)$ symmetry is unbroken, the relationships between each of the discrete values will all be the same, but if the $SU(3)$ symmetry is broken, there presumably has to be a coordinate-free way in which the relationships between the different discrete values are different. There will, I now suppose, have to be enough distinction between raising and lowering operators between different sectors of the theory and measurement operators to allow there to be a concept of an S-matrix.</p>
<p>This may look crazy, but I'll also put on the table here why the structures of the Feynman graphs formalism encourage me. We introduce connected Feynman graphs at different orders to calculate $n$-point connected Wightman functions. Although we typically expand the series in terms of the number of loops, we can alternatively expand the series in terms of the number of points we have introduced between the $n$ points at which we measure; the extra points ensure that there are infinite numbers of different paths between the $n$ points. With something like $\hat\Phi(x)$, we introduce an infinite number of paths directly between the $n$ points, without introducing any extra points, so we need, in effect, a transformation of the superposition of an infinite number of Feynman path integrals into a superposition of an infinite number of weighted <em>direct</em> paths between the $n$ points. Getting the weights on the direct paths right is of course rather important, and I also imagine the analytic structure has to be rather carefully done, particularly if I don't use normal-ordering. I'll do any amount of work to avoid renormalization, even in its modern gussied up form.</p>
<p>It seems to me significant that the quantum field $\hat\Phi(x)=\tanh{(\hat\phi(x))}$ is not reducible. A number of proofs concerning Wightman fields rely on this property.</p>
<p>If anyone else understands this (or reads this far) I'll be surprised. In any case I expect it will look very different a few years down the road if I ever manage to get it into a journal. Although I've worked in and around the Wightman axioms for the last few years, I find it interesting that I can now feel some pull towards something like the Haag-Kastler axioms. <em>Lots</em> of work to do! Thank you all! Good luck with your own crazy schemes!</p>
<p><strong>That's the question (and the to me unexpected state of play a day later). Completely separately, as an example</strong>, <em>to show the way I'm going with this, hopefully</em> (which, a day later, looks as if it will be only a background concern for the next little while, but I think not likely to be completely forgotten by me), the real-space commutator of the creation and annihilation operator-valued distributions of the free field of mass $m$ is, in terms of Bessel functions, $$C_m(x)=\frac{m\theta(x^2)}{8\pi\sqrt{x^2}}\left[Y_1(m\sqrt{x^2})+i\varepsilon(x_0)J_1(m\sqrt{x^2})\right]$$
$$\qquad\qquad+\frac{m\theta(-x^2)}{4\pi^2\sqrt{-x^2}}K_1(m\sqrt{-x^2})-\frac{i}{4\pi}\varepsilon(x_0)\delta(x^2).$$
If we take a weighted average of this object with the normalized weight function
$w_{\alpha,R}(m)=\theta(m)\frac{R(Rm)^{\alpha-1} {\rm e}^{-Rm}}{\Gamma(\alpha)}, 0<\alpha\in \mathbb{R},\ 0<R$, $\int w_{\alpha,R}(m)C_m(x)dm$, we obtain the commutator of a particular generalized free field, which can be computed exactly in terms of Hypergeometric functions and which at space-like separation $\mathsf{r}=\sqrt{-x^\mu x_\mu}$ is asymptotically
$\frac{\Gamma(\alpha+1)R^{\alpha}}{\pi\Gamma(\frac{\alpha+1}{2})^2\bigl(2\mathsf{r})^{\alpha+2}}$, and at time-like separation $\mathsf{t}=\sqrt{x^\mu x_\mu}$ is asymptotically
$$\frac{\cos{(\frac{\pi\alpha}{2})}\Gamma(\frac{\alpha}{2}+1)R^\alpha}
{4\sqrt{\pi^3}\Gamma(\frac{\alpha+1}{2})\mathsf{t}^{\alpha+2}}
-i\frac{R^\alpha}{4\Gamma\left(-\frac{\alpha}{2}\right)\Gamma\left(\frac{\alpha+1}{2}\right)\mathsf{t}^{\alpha+2}},$$
except for $\alpha$ an even integer. At small space-like or time-like separation, the real part of this generalized free field is $-\frac{1}{4\pi^2x^\mu x_\mu}$, identical to that of the massless or massive free particle, independent of mass, but we can tune the 2-point function at large distances to be any power of the separation smaller than an inverse square law. On the light-cone itself, the delta-function component is again identical to that of the massless or massive free particle, independent of mass.</p>
<p>There is of course an infinity of possible normalized weight functions, a half-dozen of which I have worked out exactly and asymptotically, and somewhat obsessively, by use of MAPLE and Gradshteyn & Ryzhik, though I've managed to stop myself at the moment.
In a subsequent edit, I can't resist adding what we obtain if we use the weight function $w_{\mathsf{sm}[R]}(m)=\frac{\theta(m)R\exp{\left(-\frac{1}{mR}\right)}}{2(mR)^4},\ 0<R$ [using 6.591.1-3 from Gradshteyn & Ryzhik]. This function is smooth at $m=0$, and results at time-like separation in
$$\left\{Y_2\!\left(\sqrt{\frac{2\mathsf{t}}{R}}\right)+iJ_2\!\left(\sqrt{\frac{2\mathsf{t}}{R}}\right)\right\}
\frac{K_2\!\left(\sqrt{\frac{2\mathsf{t}}{R}}\right)}{8\pi R^2}
\asymp \frac{\exp{\left(-i\sqrt{\frac{2\mathsf{t}}{R}}+\frac{\pi}{4}\right)}
\exp{\left(-\sqrt{\frac{2\mathsf{t}}{R}}\right)}}
{16\pi\sqrt{R^3\mathsf{t}}}$$
and at space-like separation in
$$\frac{K_2\!\left((1+i)\sqrt{\frac{\mathsf{r}}{R}}\right)
K_2\!\left((1-i)\sqrt{\frac{\mathsf{r}}{R}}\right)}{4\pi^2R^2}
\asymp \frac{\exp{\left(-2\sqrt{\frac{\mathsf{r}}{R}}\right)}}
{16\pi\sqrt{R^3\mathsf{r}}}.$$
I wish I could do this integral for more general parameters, but hey! This weight function has observable effects only at space-like and time-like separation $\mathsf{r}<R$ and $\mathsf{t}<R$, so this is essentially unobservable if $R$ is small enough. The kicker is that this decreases faster than polynomially in both space-like <em>and</em> time-like directions.</p>
<p>The generalized free field construction always results in a trivial $n$-point function for $n>2$, however by introducing also Wick-ordered polynomials of these generalized free fields, we can also tune the $n$-point connected correlation functions, which are generally non-trivial and to my knowledge finite for all $n$. All this is far too constructive, of course, to prove much. I think I propose this more as a way to report the $n$-point correlation functions in a manner comparable to the Kallen-Lehmann representation of the 2-point correlation function than as something truly fundamental, because I think it does not generalize well to curved space-time.</p> | g4807 | [
0.01096934825181961,
0.012031053192913532,
0.0010965103283524513,
-0.0645689144730568,
0.03136834502220154,
-0.01757093518972397,
0.02854977920651436,
0.009013248607516289,
0.027674924582242966,
-0.027287399396300316,
-0.03233619034290314,
0.025829950347542763,
0.010498455725610256,
-0.017980031669139862,
-0.018920574337244034,
0.032918937504291534,
0.035109929740428925,
-0.002728170482441783,
-0.01811201497912407,
-0.042410992085933685,
-0.021436970680952072,
0.023079512640833855,
0.025000272318720818,
0.009518890641629696,
-0.08024964481592178,
-0.02172352746129036,
0.03068884089589119,
-0.0713639035820961,
-0.03316829726099968,
0.01713026501238346,
0.04304507002234459,
0.011265716515481472,
0.006787722464650869,
-0.03549541160464287,
-0.04955596104264259,
0.03170308843255043,
0.03576434776186943,
0.025386998429894447,
0.03454958647489548,
0.05088639631867409,
-0.02087908424437046,
-0.028556274250149727,
0.0019394006812945008,
-0.024189064279198647,
0.04360159486532211,
0.03370656073093414,
-0.02093641273677349,
0.04245783016085625,
-0.02852192148566246,
0.0022307324688881636,
0.023503661155700684,
0.05203525722026825,
0.04330602288246155,
-0.029155561700463295,
0.009625601582229137,
0.061763595789670944,
0.050060905516147614,
0.01236573327332735,
0.043903108686208725,
0.07006880640983582,
-0.008924477733671665,
-0.0547352209687233,
0.029905732721090317,
-0.007952178828418255,
0.011746929958462715,
0.006792163942009211,
-0.05122460424900055,
0.027226924896240234,
-0.04526326805353165,
-0.011636028066277504,
-0.028419703245162964,
-0.08269350230693817,
0.020250022411346436,
0.022508325055241585,
0.019103974103927612,
0.052884239703416824,
-0.010075997561216354,
-0.031913209706544876,
0.04264475405216217,
-0.03253374248743057,
-0.042733993381261826,
0.018438715487718582,
-0.00940899457782507,
0.009816369973123074,
0.021038096398115158,
-0.06136569380760193,
0.013021528720855713,
-0.036965712904930115,
0.04447776451706886,
0.04527932405471802,
0.04416688159108162,
0.009975292719900608,
0.03499772772192955,
0.06187751144170761,
-0.023661848157644272,
0.008653577417135239,
0.03333999589085579,
0.010611211881041527,
-0.022863024845719337,
-0.03445745259523392,
-0.02634662576019764,
0.030420949682593346,
-0.0004184382560197264,
0.0025029205717146397,
0.026496725156903267,
-0.04297591745853424,
0.007918576709926128,
0.02311471663415432,
0.039204686880111694,
0.06083438917994499,
-0.03567545488476753,
0.04791366681456566,
-0.031393904238939285,
-0.020302318036556244,
-0.042918797582387924,
-0.02122332900762558,
-0.014788936823606491,
-0.03261491283774376,
0.02536834217607975,
0.059405166655778885,
-0.0031512463465332985,
-0.04336906224489212,
0.025104016065597534,
0.06699011474847794,
-0.036881089210510254,
0.001022607902996242,
-0.01447130087763071,
0.038919489830732346,
-0.05895473435521126,
-0.03407878801226616,
0.0273468978703022,
-0.044766493141651154,
0.004354514181613922,
0.07284943014383316,
-0.01701965369284153,
-0.03888107091188431,
-0.06603356450796127,
0.04403834417462349,
0.04601654037833214,
-0.036091648042201996,
-0.032648880034685135,
-0.042646922171115875,
-0.04774678125977516,
-0.06354855746030807,
-0.019753122702240944,
0.040308382362127304,
0.07096473127603531,
-0.03143109008669853,
0.02754104696214199,
0.03667693957686424,
0.034171342849731445,
0.06559114158153534,
-0.10236340761184692,
0.03395562246441841,
0.00683917012065649,
0.016611989587545395,
0.023333856835961342,
-0.06436730176210403,
0.005873572081327438,
-0.01814272627234459,
0.0207440797239542,
0.021052854135632515,
0.07902217656373978,
0.03029203787446022,
-0.019694333896040916,
-0.0164414681494236,
0.012930759228765965,
-0.09357161819934845,
-0.021491896361112595,
-0.09219919145107269,
-0.07329759746789932,
0.015403236262500286,
-0.029961328953504562,
0.025467339903116226,
0.017992261797189713,
0.01292091142386198,
-0.037932753562927246,
0.0013219924876466393,
0.055783338844776154,
0.0205440241843462,
-0.021358387544751167,
0.02004869095981121,
-0.03792707249522209,
-0.0724511370062828,
0.003795820055529475,
0.019679509103298187,
-0.0374501571059227,
0.03868325799703598,
-0.024814851582050323,
-0.013163509778678417,
0.023660877719521523,
-0.026433421298861504,
-0.010535436682403088,
0.03638669103384018,
-0.022946655750274658,
0.04474323242902756,
0.005564157851040363,
-0.04417050629854202,
0.055072955787181854,
0.016087859869003296,
0.014272861182689667,
0.010153382085263729,
-0.02721434459090233,
0.012697936967015266,
-0.005365961231291294,
-0.00836334191262722,
0.00489923357963562,
0.01748773641884327,
0.016219763085246086,
0.001198098063468933,
0.06120624020695686,
-0.07910657674074173,
0.05023457854986191,
0.011206111870706081,
0.04077423736453056,
-0.0872051864862442,
-0.021014109253883362,
-0.010454757139086723,
0.019716909155249596,
0.009939523413777351,
-0.012264903634786606,
-0.03668422996997833,
0.05456621199846268,
-0.022414039820432663,
0.008902110159397125,
-0.016884619370102882,
0.048743631690740585,
0.003457604441791773,
-0.004991765134036541,
0.01557039376348257,
-0.1320362538099289,
-0.005961783230304718,
-0.050835832953453064,
-0.04896494373679161,
0.048585910350084305,
0.002715481212362647,
-0.005831355229020119,
0.031067008152604103,
0.038939688354730606,
0.02051784284412861,
-0.008991146460175514,
0.0197305791079998,
-0.043701816350221634,
0.033409543335437775,
0.002395557938143611,
-0.05210164561867714,
0.004400395788252354,
0.04091921076178551,
0.013128208927810192,
-0.01727985590696335,
0.007817331701517105,
0.004071107599884272,
-0.018058111891150475,
-0.01252671703696251,
-0.0369732603430748,
-0.025570739060640335,
0.010309644974768162,
0.005065750330686569,
-0.03331778943538666,
-0.025202568620443344,
-0.02201795019209385,
-0.017559168860316277,
-0.041420355439186096,
-0.0396210215985775,
-0.015311206690967083,
0.04595167189836502,
-0.019896961748600006,
0.012131287716329098,
0.01490328274667263,
-0.012240526266396046,
-0.026272589340806007,
0.06347889453172684,
0.037060223519802094,
0.017563121393322945,
-0.00797092542052269,
0.05147654190659523,
-0.06991632282733917,
0.0106736421585083,
0.015156797133386135,
-0.02251492626965046,
-0.038302261382341385,
0.01757790334522724,
-0.041807420551776886,
0.05392363667488098,
0.06767885386943817,
-0.03968490660190582,
0.009935436770319939,
-0.0000465665762021672,
-0.011557155288755894,
0.026169802993535995,
0.010246685706079006,
0.05274781212210655,
-0.014469144865870476,
0.019146667793393135,
-0.0762990266084671,
-0.019778629764914513,
-0.0033308479469269514,
-0.04387454316020012,
0.030997853726148605,
0.0665232390165329,
0.005034677218645811,
-0.0030087195336818695,
0.027306674048304558,
0.059498582035303116,
0.03169459477066994,
-0.027303772047162056,
-0.031873222440481186,
-0.04894682765007019,
0.014619537629187107,
-0.020602740347385406,
0.0509108230471611,
0.0033820040989667177,
-0.04705488681793213,
-0.02409403584897518,
-0.011335889808833599,
-0.00830250233411789,
-0.024238990619778633,
0.061174046248197556,
0.017653724178671837,
-0.014675979502499104,
-0.041664525866508484,
-0.016045285388827324,
0.031157517805695534,
-0.05481720343232155,
0.09219549596309662,
0.02657925710082054,
-0.019686004146933556,
0.006624066270887852,
-0.04018031805753708,
-0.051813192665576935,
0.004263906739652157,
-0.028222639113664627,
0.031063739210367203,
-0.032598983496427536,
-0.06759173423051834,
-0.059612080454826355,
-0.02984963357448578,
-0.031075071543455124,
0.03421851247549057,
-0.05992463231086731,
-0.024540800601243973,
-0.05018594488501549,
-0.05008817836642265,
-0.02049204893410206,
-0.07061409950256348,
-0.03576382249593735,
-0.08033857494592667,
0.012898671440780163,
0.017817450687289238,
0.011721407994627953,
0.049089860171079636,
-0.01070511806756258,
0.04736766591668129,
0.03699694946408272,
-0.01361317839473486,
0.03859439492225647,
0.03271239250898361,
0.013294892385601997,
0.0517553985118866,
-0.036014579236507416,
-0.06687895208597183,
0.012673141434788704,
0.04186548665165901,
-0.040077924728393555,
-0.026542071253061295,
0.03327587619423866,
0.005328349303454161,
-0.0008658966398797929,
0.026970768347382545,
-0.02695588581264019,
-0.0062216720543801785,
-0.0484393835067749,
0.013045942410826683,
0.015272804535925388,
-0.006645886693149805,
0.05221686139702797,
0.023670034483075142,
-0.0221475288271904,
-0.018349463120102882,
-0.008626443333923817,
-0.014540527947247028,
0.004030061420053244,
0.063969686627388,
0.001804585219360888,
0.019186077639460564,
0.051750313490629196,
-0.03540096804499626,
-0.03220302239060402,
-0.06205403432250023,
0.007031925953924656,
0.034744225442409515,
0.04895900934934616,
0.014771392568945885,
-0.00547515694051981,
0.0496811643242836,
0.03287024796009064,
-0.014771431684494019,
0.026562048122286797,
-0.01716792955994606,
0.016567321494221687,
0.07178177684545517,
-0.06315112859010696,
0.021649828180670738,
-0.0556553453207016,
-0.0004049173148814589,
-0.03451727703213692,
0.03268600255250931,
0.0004235987435095012,
0.024116266518831253,
-0.0661710798740387,
-0.01698792353272438,
0.0014806973049417138,
0.017109829932451248,
-0.019950687885284424,
0.017329886555671692,
-0.015280250459909439,
-0.028251290321350098,
-0.03968528285622597,
-0.02390398271381855,
-0.0250789076089859,
0.016562188044190407,
0.028454342857003212,
0.05760494992136955,
0.009950210340321064,
-0.0038052513264119625,
0.006720860954374075,
0.025432085618376732,
-0.007849403657019138,
-0.04253978654742241,
-0.03000752627849579,
0.048048291355371475,
0.03882757946848869,
0.0252551082521677,
-0.011501552537083626,
0.03766733035445213,
0.025583511218428612,
-0.029855400323867798,
-0.010915831662714481,
0.0017394270980730653,
0.001963070360943675,
0.01843012310564518,
-0.02042972669005394,
-0.002256372943520546,
-0.007894939742982388,
0.000467342440970242,
-0.057969145476818085,
-0.017507165670394897,
0.02822282910346985,
-0.030148649588227272,
0.021962322294712067,
0.013792508281767368,
0.06714130192995071,
0.03247008100152016,
0.0048947823233902454,
0.001548040541820228,
-0.06001829728484154,
-0.01545988954603672,
0.026408808305859566,
0.005626094993203878,
-0.01271183229982853,
-0.13694952428340912,
-0.06337101012468338,
0.010209506377577782,
0.0022460781037807465,
0.05875089764595032,
0.022915905341506004,
-0.0889543890953064,
0.025136055424809456,
-0.12098690867424011,
-0.011804248206317425,
0.02614785172045231,
-0.012854276224970818,
0.02804170362651348,
-0.0092937545850873,
-0.03688473254442215,
-0.011499928310513496,
-0.055640678852796555,
-0.04460911825299263,
-0.017745109274983406,
-0.0323040634393692,
-0.0011396489571779966,
0.017694631591439247,
0.05586959049105644,
-0.003772143507376313,
0.06970620900392532,
0.03662838414311409,
-0.0335109643638134,
0.014424042776226997,
-0.03760681673884392,
-0.02184644341468811,
0.06199898198246956,
-0.0037515326403081417,
0.014790025539696217,
0.0045543694868683815,
0.0038009253330528736,
0.004433644004166126,
0.0003711111203301698,
-0.019053706899285316,
-0.027701904997229576,
-0.0217195525765419,
-0.05922282859683037,
0.04324303939938545,
-0.01382777001708746,
-0.005607335828244686,
-0.01070354226976633,
0.024604273959994316,
0.032093700021505356,
0.023135371506214142,
-0.028498385101556778,
0.020655345171689987,
0.03670940920710564,
-0.02628503367304802,
0.08092401176691055,
-0.012525634840130806,
-0.0255894735455513,
0.0019266105955466628,
0.009716040454804897,
-0.0256175734102726,
-0.000594048120547086,
-0.1053156703710556,
0.030293995514512062,
-0.012379026971757412,
0.06999208778142929,
-0.007114967331290245,
0.005959768313914537,
0.0831020325422287,
-0.022809140384197235,
-0.0403364822268486,
0.023420944809913635,
-0.026563124731183052,
0.03534557297825813,
-0.01700877584517002,
0.03129839524626732,
0.006978202611207962,
-0.013315875083208084,
-0.03338851407170296,
-0.007506785448640585,
0.020030783489346504,
0.06147851049900055,
0.0015629709232598543,
-0.0024931656662374735,
-0.010706032626330853,
0.031838200986385345,
0.01165453065186739,
-0.030874740332365036,
0.001609999337233603,
-0.027964016422629356,
0.00024554799892939627,
0.025263719260692596,
-0.04704637825489044,
-0.05369700491428375,
-0.028574176132678986,
-0.04481205716729164,
-0.018120603635907173,
0.018802044913172722,
0.03076143004000187,
-0.04425375536084175,
-0.07439538091421127,
-0.008114416152238846,
0.024748779833316803,
0.006074350792914629,
0.01646365597844124,
0.05195104703307152,
0.0545349195599556,
-0.005549473222345114,
0.04100215807557106,
0.058494359254837036,
0.001379285822622478,
-0.015683338046073914,
0.05406198650598526,
-0.023682808503508568,
0.06221887096762657,
0.01617780141532421,
0.05269436165690422,
0.03906974568963051,
-0.035781584680080414,
0.04267645254731178,
-0.027653558179736137,
-0.03302508220076561,
-0.017563970759510994,
-0.013245691545307636,
0.048597078770399094,
0.050633903592824936,
-0.020237896591424942,
-0.01339726522564888,
0.034827765077352524,
-0.02086777426302433,
0.0058582196943461895,
0.05477871745824814,
0.05442517250776291,
-0.020387649536132812,
-0.0302167646586895,
0.002171136671677232,
0.02440781146287918,
-0.035002756863832474,
0.020727921277284622,
0.04680350795388222,
-0.030295589938759804,
-0.005296372342854738,
0.06460565328598022,
-0.021547431126236916,
-0.005110159050673246,
0.033435724675655365,
-0.0762060135602951,
-0.006814533844590187,
0.04743730276823044,
-0.03303316608071327,
-0.01104268990457058,
-0.0077188750728964806,
0.006848324090242386,
-0.00978169497102499,
0.0032204475719481707,
0.014074890874326229,
-0.04535871371626854,
-0.018142884597182274,
-0.03760374337434769,
0.05037340894341469,
0.04099231958389282,
-0.07958006113767624,
-0.008171042427420616,
0.009252524934709072,
0.047509390860795975,
-0.014184804633259773,
0.015453842468559742,
-0.016149185597896576,
0.02219477854669094,
0.023537512868642807,
-0.035784780979156494,
0.034265775233507156,
0.034766100347042084,
0.0012903895694762468,
-0.016381151974201202,
0.011415477842092514,
0.025287926197052002,
-0.0018520393641665578,
0.03173423185944557,
-0.062351636588573456,
0.06123184785246849,
0.03543293848633766,
0.02835817076265812,
-0.017162898555397987,
0.04000729322433472,
0.020590733736753464,
-0.03852662816643715,
-0.01056168507784605,
0.0780036672949791,
0.0031923309434205294,
-0.0021806550212204456,
-0.051281947642564774,
0.04502284154295921,
0.037036627531051636,
0.021072881296277046,
-0.014842294156551361,
0.002879335079342127,
-0.024345997720956802,
0.002271089004352689,
0.04379895329475403,
-0.03276717662811279,
0.003953860606998205,
-0.002500201342627406,
-0.04425143450498581,
-0.03757156804203987,
0.022198043763637543,
-0.04267161712050438,
-0.034997034817934036,
0.00158644316252321,
-0.06545718014240265,
0.004294374957680702,
0.033208753913640976,
-0.008522982709109783,
0.009396681562066078,
-0.028484711423516273,
-0.02010992541909218,
-0.020371610298752785,
0.05272778868675232,
-0.04505215957760811,
0.033480189740657806,
0.08519339561462402,
-0.006033551413565874,
0.0027461822610348463,
-0.02403680793941021,
0.05078655481338501,
0.0024346685968339443,
0.03901452198624611,
-0.019113117828965187,
0.03360934555530548,
-0.001309956656768918,
0.030953800305724144,
-0.010171611793339252,
-0.020719042047858238,
0.009392703883349895,
-0.03453903645277023,
-0.01567625254392624,
-0.023766854777932167,
0.003194404998794198,
-0.006874375510960817,
0.08479529619216919,
0.005875816103070974,
0.007118969224393368,
0.059068869799375534,
0.00480172922834754,
-0.020299741998314857,
-0.06003483012318611,
-0.02829887717962265,
0.032752856612205505,
0.02051648683845997,
0.009716632775962353,
-0.015588012523949146,
-0.04955322667956352,
-0.00691301329061389,
-0.03250197693705559,
-0.0016087285475805402,
-0.018964868038892746,
0.03906934708356857,
0.052241601049900055,
0.04449304938316345,
-0.012848789803683758,
0.002197266323491931,
0.014583169482648373,
-0.02537127211689949,
-0.025996388867497444,
0.01630321703851223,
-0.0665777251124382,
-0.011296897195279598,
-0.006495328154414892,
0.04180680215358734,
-0.020211011171340942,
-0.008213737048208714,
0.019084015861153603,
-0.024221530184149742,
-0.031921662390232086,
-0.09374210983514786,
-0.022174149751663208,
0.04657909646630287,
-0.011701404117047787,
-0.020265288650989532,
-0.01852167584002018,
0.02266019396483898,
-0.001514626550488174,
-0.022293588146567345,
-0.02502414584159851,
-0.04437209293246269,
0.0037891175597906113,
0.022771213203668594,
0.03789597749710083,
-0.027699515223503113,
-0.040529701858758926,
0.03189734369516373,
0.020780831575393677,
-0.00733595946803689,
-0.0010768906213343143,
0.02631310001015663,
0.017422040924429893,
0.03942563757300377,
0.030870599672198296,
-0.08862673491239548,
0.05251361057162285,
-0.024853378534317017,
0.07184256613254547,
0.0665973350405693,
0.0019214304629713297,
0.02004965767264366,
-0.018546106293797493,
0.039340049028396606,
-0.0770031288266182,
-0.009504664689302444,
-0.004846467170864344,
0.04805415868759155
] |
<p>Let's say there is two tubes(cylinders with no tops or bottoms) with charges $q_1$ and $q_2$, radii $b_1$ and $b_2$, lengths $l_1$ and $l_2$. These tubes are located along the axis of each other's surfaces like in this figure:
<img src="http://i.stack.imgur.com/stO7E.png" alt="two cylinders along the same axis, separated by a gap"></p>
<p>If the electric field that the first tube creates on a point is;
$$
E = \frac{q}{4\pi\varepsilon_0}\left(\frac{1}{\sqrt{b^2 + (c-a)^2}} - \frac{1}{\sqrt{b^2 + (c+a)^2}}\right)
$$
where $b$ is the radius of the tube, $c-a$ is the distance between the centre of the furthest part of the tube and the point, $c+a$ is the distance between the centre of the closest part of the tube and the point, $q$ is the total cahrge on the tube and
$\epsilon_0$ is the electric constant. Here is the figure of the tube and the point for those who didn't understand from my description:
<img src="http://i.stack.imgur.com/ZqnNg.png" alt="variable definitions for one tube"></p>
<p>The question is how can I calculate the force between these two tubes? If I have to integrate something please show me how to do it since I have never taken a course on calculus.</p>
<p>Update:The electric field formula I found is not true since it is valid for a point on axis of the cylinder. Thus I would be pleased if you could show me how to solve the problem from the beginning.</p> | g4808 | [
0.0457504503428936,
-0.02984566055238247,
-0.018611235544085503,
-0.020706918090581894,
0.047413166612386703,
0.034576695412397385,
0.03826206177473068,
-0.020658152177929878,
-0.07854369282722473,
0.006692040245980024,
-0.036360908299684525,
0.06065300852060318,
-0.034737203270196915,
-0.030067307874560356,
0.024202460423111916,
0.06213202327489853,
0.0634300485253334,
-0.04298115521669388,
0.007346877362579107,
-0.011147437617182732,
-0.011011630296707153,
-0.033644821494817734,
0.014573649503290653,
-0.03461063280701637,
-0.052715785801410675,
-0.03371941298246384,
0.005955324973911047,
0.053738854825496674,
-0.024644311517477036,
-0.050667811185121536,
-0.02621839940547943,
0.0541340671479702,
0.07733237743377686,
-0.008466498926281929,
-0.008472076617181301,
0.0016006042715162039,
-0.010321051813662052,
0.00838577188551426,
-0.0051790219731628895,
-0.04009716212749481,
0.033469971269369125,
0.02165331318974495,
0.04536188021302223,
0.006515477318316698,
-0.006565100979059935,
-0.07157879322767258,
-0.041309550404548645,
-0.014442604966461658,
0.0027743312530219555,
0.009023094549775124,
0.006608293391764164,
0.016868123784661293,
-0.022185493260622025,
-0.0513448566198349,
0.0050912946462631226,
0.029415763914585114,
0.07166094332933426,
-0.0162830650806427,
0.018993251025676727,
0.02620292268693447,
-0.00554960360750556,
-0.003389844438061118,
0.0071699186228215694,
0.05580828711390495,
0.02890433743596077,
0.005022276192903519,
-0.018533380702137947,
0.02075316198170185,
-0.0649435892701149,
-0.0025630630552768707,
-0.0808449536561966,
-0.04811312258243561,
0.02073419839143753,
-0.010232564993202686,
-0.09466441720724106,
0.000518744345754385,
0.03212544694542885,
0.004641578067094088,
0.012790831737220287,
-0.0779191181063652,
0.027195097878575325,
0.00602019764482975,
0.03703681379556656,
0.026793908327817917,
0.06212553009390831,
-0.05488963797688484,
-0.008047984912991524,
-0.012121454812586308,
-0.04287673905491829,
0.008080647327005863,
-0.022364458069205284,
0.005261414684355259,
0.08301576226949692,
0.012010568752884865,
0.030692551285028458,
-0.09663312137126923,
-0.0000855994294397533,
0.07598138600587845,
0.03252839669585228,
-0.01455514132976532,
-0.06414713710546494,
0.016584090888500214,
0.03636176139116287,
0.02413281239569187,
-0.022292712703347206,
-0.029350342229008675,
-0.00029260810697451234,
0.03682412952184677,
0.008021325804293156,
-0.024206344038248062,
-0.012354923412203789,
-0.06985935568809509,
-0.025994418188929558,
-0.036551542580127716,
0.011952283792197704,
-0.054284170269966125,
0.04471518471837044,
-0.03516874089837074,
-0.00818165298551321,
0.008199869655072689,
-0.02849108912050724,
0.045390043407678604,
0.058745235204696655,
-0.015415404923260212,
-0.044232700020074844,
-0.01902136579155922,
-0.04813192039728165,
-0.017217548564076424,
0.04105069115757942,
0.025640401989221573,
0.05143381655216217,
-0.02393214963376522,
0.02947596274316311,
-0.00405728118494153,
-0.04084979370236397,
0.08605136722326279,
-0.05232115462422371,
-0.03969394788146019,
0.025659482926130295,
0.01498587429523468,
-0.025335213169455528,
-0.04725470393896103,
-0.005051394924521446,
-0.0012596515007317066,
-0.007108261808753014,
0.01757054775953293,
-0.03929053619503975,
-0.08262112736701965,
0.026321575045585632,
-0.012236005626618862,
0.04265490546822548,
0.07496977597475052,
0.0002478744718246162,
-0.024034302681684494,
0.02881968393921852,
-0.0099937180057168,
0.037700094282627106,
0.06630639731884003,
0.028530653566122055,
-0.023389531299471855,
0.03841519355773926,
0.012794890441000462,
0.0702395960688591,
-0.027934569865465164,
-0.016214190050959587,
0.01836448535323143,
0.0006739994278177619,
-0.06120239198207855,
-0.0029230944346636534,
-0.040489450097084045,
-0.044629864394664764,
-0.006955672986805439,
0.03249480947852135,
0.008365985006093979,
0.05885523185133934,
0.0388469435274601,
-0.03625893220305443,
0.006145221181213856,
0.025991816073656082,
-0.013503617607057095,
0.014242507517337799,
0.014928633347153664,
0.002337988466024399,
0.03243952989578247,
-0.05447784811258316,
0.015108712017536163,
0.013135997578501701,
0.013929670676589012,
-0.02049901895225048,
0.0042590429075062275,
-0.032117944210767746,
-0.0014011281309649348,
-0.001016208785586059,
0.012599905952811241,
-0.08394361287355423,
0.060008205473423004,
0.04873242601752281,
-0.04750834405422211,
0.018397634848952293,
0.020633159205317497,
0.009097698144614697,
0.03506989777088165,
0.03358905389904976,
0.030546149238944054,
0.023807521909475327,
0.017868269234895706,
-0.026075227186083794,
-0.053900498896837234,
0.03232815861701965,
0.00363665958866477,
-0.0016684785950928926,
0.010419478639960289,
-0.006660098675638437,
0.036483876407146454,
-0.05605171248316765,
-0.08042408525943756,
-0.023473301902413368,
-0.011538366787135601,
-0.10324534773826599,
0.030139489099383354,
0.012992401607334614,
-0.019909027963876724,
0.0749577209353447,
-0.041775841265916824,
-0.07324522733688354,
-0.02496749721467495,
0.059254348278045654,
0.0255295243114233,
-0.04433963820338249,
-0.006472161039710045,
-0.05692998692393303,
0.0018471111543476582,
0.012141705490648746,
-0.04887530580163002,
0.03261717036366463,
0.04994509741663933,
-0.037934523075819016,
-0.010789003223180771,
0.00041991681791841984,
-0.002080600243061781,
0.040116652846336365,
-0.05102568492293358,
-0.0069013722240924835,
-0.011002941057085991,
0.016584059223532677,
0.013714848086237907,
0.048666372895240784,
0.02840917557477951,
-0.023224715143442154,
0.03844480961561203,
0.019266881048679352,
-0.006470298394560814,
-0.024254024028778076,
0.06147493049502373,
-0.0029088177252560854,
-0.012907151132822037,
-0.04090415686368942,
-0.003415991785004735,
0.02236092835664749,
-0.07713346928358078,
0.011637462303042412,
0.010338823311030865,
0.022496987134218216,
0.09233210980892181,
-0.06863240897655487,
0.011051518842577934,
-0.044640254229307175,
0.024956054985523224,
0.039379458874464035,
-0.009054511785507202,
-0.0634109303355217,
0.07760631293058395,
0.02262681908905506,
-0.035616859793663025,
0.03817152976989746,
-0.03799625486135483,
0.005261257290840149,
-0.024505607783794403,
0.006483520846813917,
0.017460549250245094,
0.05439711734652519,
-0.018841823562979698,
0.006948244757950306,
0.03205227851867676,
0.024887189269065857,
-0.04388181492686272,
0.04732644557952881,
0.004150571301579475,
0.02462085895240307,
-0.010263392701745033,
-0.02865953929722309,
0.017861364409327507,
0.04754794389009476,
-0.021750614047050476,
0.052865806967020035,
0.01994902640581131,
0.02054152823984623,
-0.0180834773927927,
-0.010320322588086128,
-0.03314266726374626,
-0.03322996944189072,
-0.03246072307229042,
0.0013159944210201502,
0.017805254086852074,
0.016568409278988838,
-0.033433299511671066,
-0.0003257703210692853,
-0.07101557403802872,
0.0011195166734978557,
0.001749906805343926,
-0.025839820504188538,
-0.001583950244821608,
0.05833815410733223,
-0.06750411540269852,
-0.03291855752468109,
-0.007407310418784618,
0.023791169747710228,
-0.051284246146678925,
0.017059076577425003,
0.05141881853342056,
-0.028718266636133194,
-0.08095045387744904,
0.012123201973736286,
0.029253298416733742,
0.021957088261842728,
0.04147237166762352,
-0.037877827882766724,
0.014361146837472916,
-0.011110888794064522,
-0.016877219080924988,
-0.026253528892993927,
0.03329458832740784,
0.0047395252622663975,
-0.05578180029988289,
0.003250845242291689,
-0.021621596068143845,
0.01993940770626068,
0.05472523719072342,
0.020264362916350365,
0.01061184797435999,
-0.05424507334828377,
0.006541449110955,
-0.030074436217546463,
-0.009535793215036392,
-0.008602685295045376,
0.017165616154670715,
-0.00020809924171771854,
0.07017561793327332,
0.05709058418869972,
-0.012164643034338951,
0.00881893653422594,
-0.05232541263103485,
0.0814194604754448,
-0.010014834813773632,
0.009801182895898819,
-0.007600330747663975,
-0.0026348147075623274,
-0.004072233103215694,
-0.04931126534938812,
0.04929366335272789,
0.04767985641956329,
-0.05353272706270218,
-0.04155276343226433,
0.009484401904046535,
-0.045230183750391006,
-0.08868619799613953,
0.027000321075320244,
0.07430111616849899,
-0.02431846782565117,
-0.04699362441897392,
-0.002473212545737624,
-0.016477763652801514,
-0.009107925929129124,
0.04388107731938362,
0.013292768970131874,
-0.05008476972579956,
0.027753444388508797,
0.00247568660415709,
-0.022731006145477295,
0.04244716838002205,
0.0412447489798069,
0.05298999324440956,
-0.0254207756370306,
0.006619206164032221,
-0.022689616307616234,
-0.024452215060591698,
0.0009423220762982965,
0.026640456169843674,
0.06494751572608948,
-0.06841155141592026,
0.018864639103412628,
-0.0013358071446418762,
-0.08222711831331253,
0.025482991710305214,
0.006095307879149914,
-0.020957257598638535,
0.03959805145859718,
-0.004212347790598869,
-0.024476399645209312,
-0.027680056169629097,
0.05875292047858238,
0.016978556290268898,
0.015807513147592545,
0.0033266721293330193,
-0.0345396064221859,
-0.05763283744454384,
0.03623388707637787,
0.036265138536691666,
0.077131487429142,
0.006213890854269266,
0.008035490289330482,
0.009396011009812355,
0.007377650588750839,
-0.060054928064346313,
0.04696407541632652,
0.021230299025774002,
-0.03744875267148018,
0.040853872895240784,
0.009521552361547947,
-0.007846411317586899,
0.021080881357192993,
0.03421185538172722,
0.01867920719087124,
-0.05395793542265892,
-0.045422837138175964,
0.010589854791760445,
0.08002788573503494,
0.00034961377969011664,
0.04787926748394966,
-0.001676970161497593,
-0.04594090208411217,
0.04624470695853233,
-0.04528176784515381,
-0.037338949739933014,
-0.03535164147615433,
0.00431651808321476,
0.0003632500593084842,
-0.03402567654848099,
-0.00790244247764349,
0.016434386372566223,
0.043422967195510864,
-0.005377040710300207,
0.00426072534173727,
-0.029018327593803406,
0.003589281812310219,
0.021825117990374565,
-0.02970181778073311,
-0.05109923705458641,
0.03249946981668472,
-0.02429857850074768,
-0.010364742018282413,
-0.014045322313904762,
-0.003668400226160884,
-0.01619693636894226,
0.00950145348906517,
-0.010963684879243374,
0.008233622647821903,
0.010171596892178059,
0.0056209685280919075,
-0.037778761237859726,
0.00014860105875413865,
0.033258888870477676,
-0.014721730723977089,
0.004851538222283125,
0.06142512336373329,
-0.048752930015325546,
-0.063125841319561,
-0.023695487529039383,
-0.006822903174906969,
0.010790984146296978,
-0.012533966451883316,
0.04959738999605179,
0.023689499124884605,
-0.000830064935144037,
-0.021648384630680084,
-0.024830352514982224,
-0.02857450395822525,
0.04156440496444702,
-0.01150711253285408,
-0.05171052739024162,
-0.04942058399319649,
-0.0028743622824549675,
0.01499877031892538,
0.027953531593084335,
0.026065057143568993,
-0.022036174312233925,
0.012180314399302006,
0.03723563253879547,
-0.00013117166236042976,
-0.0015038345009088516,
-0.016549671068787575,
0.02099030278623104,
0.04889286309480667,
0.002968515967950225,
-0.006178106181323528,
-0.02703172154724598,
0.028797505423426628,
0.0016183702973648906,
-0.004083595704287291,
0.06294823437929153,
-0.027438955381512642,
0.020498570054769516,
-0.026263685896992683,
0.019436167553067207,
0.010298681445419788,
0.043813660740852356,
0.02881612442433834,
-0.02322293072938919,
0.011096294037997723,
0.03493012860417366,
0.025680096819996834,
0.004561904352158308,
0.03253250941634178,
-0.003881089622154832,
-0.02326802723109722,
0.042865876108407974,
-0.03908650949597359,
0.0042771450243890285,
-0.0012843020958825946,
0.02860836498439312,
0.05939262732863426,
-0.0035027035046368837,
0.0024149075616151094,
-0.01659543253481388,
-0.01606205478310585,
-0.004700681194663048,
-0.0382663756608963,
-0.049590401351451874,
0.03034902922809124,
0.011481751687824726,
-0.012219930067658424,
-0.013405036181211472,
-0.026760131120681763,
-0.02344057708978653,
-0.04014702886343002,
-0.03700593113899231,
0.016060983762145042,
-0.05052689090371132,
0.052345629781484604,
-0.05601523444056511,
0.030594205483794212,
0.004009070340543985,
0.0014284878270700574,
0.06837619096040726,
-0.03682669252157211,
0.0024057317059487104,
-0.06366634368896484,
0.04101652279496193,
0.061273541301488876,
0.007793222554028034,
-0.016602668911218643,
0.024402547627687454,
0.01091159787029028,
-0.012490618973970413,
0.020501751452684402,
0.02981552481651306,
0.013595056720077991,
-0.026973603293299675,
-0.0022812257520854473,
-0.029730169102549553,
0.06153425946831703,
-0.056078583002090454,
0.018579384312033653,
0.03436034545302391,
-0.031303521245718,
0.007774867583066225,
0.0030474213417619467,
0.030804110690951347,
0.07370717078447342,
0.04290718212723732,
0.06837320327758789,
-0.01925426535308361,
-0.041183918714523315,
-0.06497606635093689,
0.049591176211833954,
0.01104293018579483,
-0.030743679031729698,
0.020222797989845276,
-0.010863695293664932,
0.049117524176836014,
0.0013482957147061825,
0.024270085617899895,
-0.0071304128505289555,
-0.01589607447385788,
-0.02195785567164421,
0.07398074865341187,
0.005281476303935051,
-0.07094551622867584,
0.050696782767772675,
-0.08433859795331955,
0.0025672398041933775,
-0.037335772067308426,
0.02545982412993908,
-0.08226697891950607,
-0.017754195258021355,
-0.04494243115186691,
0.01910211332142353,
0.0371222048997879,
0.01972772926092148,
0.08455117791891098,
0.024990445002913475,
0.032866016030311584,
0.03191175311803818,
0.013479433953762054,
0.05502792447805405,
0.009213687852025032,
-0.00032875360921025276,
-0.04179694503545761,
-0.041067492216825485,
-0.07761049270629883,
0.02115473710000515,
0.05968674272298813,
-0.0243985652923584,
0.02045498602092266,
-0.01541085634380579,
0.018687808886170387,
-0.015458966605365276,
0.01830284856259823,
-0.028058286756277084,
0.0038238391280174255,
0.01850026473402977,
0.004388145636767149,
-0.031127404421567917,
-0.008056262508034706,
0.01564853824675083,
0.032218851149082184,
-0.056717708706855774,
-0.00007844036008464172,
0.0726514384150505,
-0.06657446920871735,
0.031204218044877052,
-0.014547956176102161,
0.026731358841061592,
0.02812928892672062,
0.016066044569015503,
0.03424995765089989,
0.051151812076568604,
-0.008515952154994011,
-0.008562698028981686,
0.07505041360855103,
-0.0029482529498636723,
0.04206874221563339,
0.030054042115807533,
0.052839890122413635,
0.021919336169958115,
-0.04183740168809891,
0.027322940528392792,
-0.0022645664867013693,
-0.013768156059086323,
0.06197865307331085,
0.01426530722528696,
0.004289986100047827,
-0.018067145720124245,
0.022368384525179863,
-0.06510062515735626,
-0.03844156488776207,
-0.0029834590386599302,
-0.014715678058564663,
-0.018990324810147285,
-0.02397678606212139,
-0.0149677200242877,
-0.040114182978868484,
-0.01326833013445139,
-0.028002602979540825,
0.0008614192483946681,
0.013106882572174072,
-0.0171787329018116,
-0.041128888726234436,
-0.022407913580536842,
-0.05087872967123985,
-0.0012202680809423327,
-0.04134684428572655,
-0.014696978963911533,
0.021255269646644592,
-0.024062426760792732,
-0.05349666625261307,
0.023363705724477768,
0.03841134160757065,
-0.0182874146848917,
-0.04097983241081238,
-0.04266148433089256,
-0.005569677799940109,
-0.04426692798733711,
-0.0009489586809650064,
-0.031869132071733475,
-0.02393157407641411,
0.06280188262462616,
-0.010514019057154655,
0.00031739912810735404,
0.022381283342838287,
0.0088515505194664,
0.0019346812041476369,
-0.01715240441262722,
-0.02045368403196335,
0.02357511594891548,
-0.011812946759164333,
0.007474970538169146,
0.06934665888547897,
0.042743124067783356,
-0.036805685609579086,
0.02889767661690712,
-0.047804590314626694,
0.023082109168171883,
0.009407689794898033,
0.003083307994529605,
0.004947278648614883,
0.012339804321527481,
0.059075530618429184,
-0.0362168624997139,
0.010459568351507187,
0.04666941612958908,
0.040373291820287704,
0.015495052561163902,
0.020027050748467445,
0.03926197066903114,
0.013582143932580948,
-0.07309065014123917,
0.08603671193122864,
0.024131417274475098,
-0.01581089198589325,
-0.048472948372364044,
-0.01861581951379776,
0.027157112956047058,
-0.08622106164693832,
-0.017833512276411057,
-0.012533423490822315,
-0.03080332837998867,
-0.018756680190563202,
-0.021771064028143883,
-0.046104103326797485,
-0.0069508738815784454,
-0.002403469290584326,
-0.045323796570301056,
0.08567561209201813,
-0.016892166808247566,
-0.0012144031934440136,
0.0015546026406809688,
0.005150573793798685,
0.02798331528902054,
-0.01759611815214157,
-0.015305835753679276,
-0.05327831208705902,
-0.02216087281703949,
-0.005079682916402817,
-0.024933479726314545,
0.006831918843090534,
-0.01888980343937874,
0.09585493803024292,
0.04684149846434593,
0.007222152780741453,
-0.0019558044150471687,
-0.03152019903063774,
0.012295414693653584,
-0.03173522278666496,
0.06579941511154175,
-0.1083947941660881,
-0.06496194750070572,
0.022936174646019936,
-0.01074615865945816,
-0.0038049567956477404,
-0.04056428372859955,
0.036861833184957504,
-0.0429769866168499,
0.034990906715393066,
0.024467255920171738,
-0.03013468347489834,
-0.024850742891430855,
-0.010481927543878555
] |
<p>As I have understood it, the Standard Model includes particles that carry the different forces, e.g. the electromagnetic (EM) force, the gravitational (G) force. When talking about EM fields such as visible light or microwaves, the associated particle is said to be the photon. But what about a static EM field without any electricity, like a common household magnet? How does that magnet communicate its force? Via photons?</p> | g4809 | [
0.02656210958957672,
0.03313743695616722,
-0.019324742257595062,
0.002377802738919854,
0.07308242470026016,
0.045997269451618195,
-0.0035264710895717144,
0.006915183272212744,
-0.009914404712617397,
-0.03456838056445122,
0.004288210067898035,
-0.027288300916552544,
0.035322513431310654,
-0.03416784852743149,
-0.04198671132326126,
0.05667384713888168,
0.055482082068920135,
0.015456678345799446,
0.02528875321149826,
0.05037536472082138,
0.02514485828578472,
0.011409583501517773,
0.042171865701675415,
-0.05158723145723343,
-0.0608602873980999,
0.027730179950594902,
0.036689650267362595,
-0.05384733900427818,
0.012081596069037914,
-0.0630820244550705,
0.009568320587277412,
0.0018238348420709372,
0.04701901227235794,
-0.04594549164175987,
-0.019788889214396477,
-0.037593528628349304,
0.016878707334399223,
0.03609783202409744,
-0.0016421184409409761,
0.037378717213869095,
0.02036583237349987,
-0.003103414783254266,
-0.021425588056445122,
0.005922866519540548,
0.046748604625463486,
0.029221201315522194,
-0.030594799667596817,
-0.019184472039341927,
-0.06602887809276581,
-0.05300143361091614,
-0.016346348449587822,
-0.011672955006361008,
0.032534290105104446,
0.05239701271057129,
0.07775573432445526,
-0.02319565787911415,
0.05605721101164818,
-0.007023205514997244,
0.0758872702717781,
0.025055447593331337,
-0.009081445634365082,
0.005831773858517408,
0.003728626063093543,
0.014377794228494167,
0.028967637568712234,
0.0014356316532939672,
-0.05033113807439804,
-0.02368531934916973,
-0.006326125003397465,
0.019892334938049316,
-0.022269519045948982,
-0.0032124300487339497,
-0.021956300362944603,
-0.030555028468370438,
0.01209015492349863,
0.01721968501806259,
0.02271066978573799,
-0.032874446362257004,
0.02261756733059883,
0.01450598705559969,
-0.006068831775337458,
-0.0007699733250774443,
0.042679160833358765,
-0.058031994849443436,
0.08927129954099655,
-0.02915954403579235,
-0.07178743928670883,
-0.04072697088122368,
0.023633336648344994,
-0.06360762566328049,
0.04201390594244003,
0.02370058186352253,
0.0438179187476635,
0.0013521276414394379,
0.020159833133220673,
-0.021001089364290237,
0.008977075107395649,
0.09215745329856873,
0.034271810203790665,
-0.07066073268651962,
-0.022356180474162102,
-0.034773342311382294,
-0.006434581242501736,
0.013496693223714828,
0.00938654225319624,
0.0036639885511249304,
0.008083873428404331,
0.07343696057796478,
0.02243863232433796,
0.013798963278532028,
-0.05147750675678253,
0.010242676362395287,
-0.045308563858270645,
0.007107594981789589,
-0.009271721355617046,
-0.053680069744586945,
0.08323636651039124,
-0.031205691397190094,
0.03384097293019295,
0.03220893070101738,
-0.015196443535387516,
0.04083798825740814,
0.009521134197711945,
0.032442398369312286,
-0.07511242479085922,
-0.035520754754543304,
0.05254597216844559,
0.04847974330186844,
-0.0413091778755188,
-0.06490474939346313,
0.03262219578027725,
0.008724537678062916,
-0.04638666287064552,
-0.0019249669276177883,
-0.006508676800876856,
0.0022976952604949474,
0.02983839064836502,
-0.026716070249676704,
0.026226164773106575,
0.009823814034461975,
-0.015208665281534195,
-0.032119717448949814,
0.02179679088294506,
-0.06852393597364426,
-0.02012486383318901,
0.01631423458456993,
0.021130705252289772,
-0.015256986953318119,
0.019932908937335014,
0.04412255808711052,
0.01872902363538742,
0.04770052060484886,
-0.0012858257396146655,
-0.02219683676958084,
0.046288151293992996,
-0.05487357825040817,
0.06347834318876266,
-0.0025459760800004005,
-0.022300880402326584,
-0.010977973230183125,
0.08229052275419235,
-0.018517183139920235,
0.02718646079301834,
-0.03809891641139984,
-0.036354806274175644,
-0.0016182407271116972,
0.03559153527021408,
-0.04685322940349579,
0.048498526215553284,
-0.03341018408536911,
-0.016029290854930878,
-0.010289940983057022,
-0.026578757911920547,
0.09392733126878738,
-0.021310750395059586,
-0.00606163777410984,
-0.01736161671578884,
-0.03872981667518616,
-0.02486497536301613,
-0.017147405073046684,
-0.01460046786814928,
-0.03383069857954979,
0.03142892196774483,
-0.020445864647626877,
-0.022733362391591072,
0.04098361358046532,
-0.06239376962184906,
0.013239536434412003,
0.020193200558423996,
0.02503914199769497,
-0.0720747858285904,
-0.003656744724139571,
0.007643513381481171,
0.03712579235434532,
0.005782146006822586,
-0.023955857381224632,
-0.014875166118144989,
-0.02041170746088028,
0.026523185893893242,
0.02703278139233589,
-0.021759988740086555,
0.03958533704280853,
-0.007296617608517408,
0.036564942449331284,
0.0588870495557785,
-0.007095063105225563,
0.026116900146007538,
-0.015341246500611305,
0.08736732602119446,
-0.03058132715523243,
0.043109018355607986,
-0.011004270054399967,
0.008798296563327312,
-0.05840060114860535,
-0.013412369415163994,
-0.05840800702571869,
-0.05697273090481758,
0.01108127273619175,
-0.04113621637225151,
-0.007784924935549498,
-0.05123857036232948,
-0.03026534430682659,
0.027867350727319717,
-0.026014866307377815,
-0.03936025872826576,
-0.022037310525774956,
0.01012620609253645,
0.03110990859568119,
-0.0034400993026793003,
0.02233974263072014,
-0.02085082232952118,
-0.01842529885470867,
0.0030401607509702444,
0.03897246718406677,
0.046140942722558975,
0.031149279326200485,
-0.039207302033901215,
0.01168165635317564,
-0.011909284628927708,
-0.013377436436712742,
-0.01131714042276144,
-0.017642492428421974,
0.02874489687383175,
-0.020367318764328957,
-0.013165399432182312,
-0.03195944055914879,
0.06876716762781143,
0.010836103931069374,
0.010097719728946686,
0.0019480269402265549,
0.04485534131526947,
-0.06450735777616501,
-0.019134432077407837,
-0.04312450438737869,
0.013663937337696552,
-0.0397539883852005,
-0.032973695546388626,
0.0031904582865536213,
-0.08327177166938782,
-0.05187683179974556,
-0.04330991208553314,
-0.050931163132190704,
0.01267289835959673,
0.06815580278635025,
0.013274172320961952,
-0.04299267381429672,
0.014406400732696056,
0.03020218200981617,
0.022723713889718056,
0.00019495858578011394,
-0.018744859844446182,
0.01787569560110569,
0.0007036520983092487,
-0.04344066604971886,
0.003913986962288618,
-0.054677050560712814,
-0.011846999637782574,
0.005109678953886032,
0.03647838905453682,
-0.0002942396095022559,
-0.00035358488094061613,
0.006477867718786001,
0.01756138913333416,
-0.04251306504011154,
-0.016581282019615173,
-0.055320724844932556,
-0.027413111180067062,
-0.029657546430826187,
-0.0596310980618,
-0.05284596234560013,
-0.016884950920939445,
0.028827860951423645,
0.05085711553692818,
-0.0009003216400742531,
-0.04734071344137192,
0.038907185196876526,
0.059295035898685455,
0.01943092979490757,
-0.042459700256586075,
0.045620374381542206,
0.010363159701228142,
0.044548191130161285,
-0.008707309141755104,
0.02428678795695305,
-0.010574028827250004,
-0.0030564195476472378,
-0.07541340589523315,
-0.028120137751102448,
0.026535123586654663,
-0.0003811225469689816,
-0.02051720581948757,
0.08945620059967041,
0.03978964686393738,
0.0566985160112381,
-0.0807221457362175,
-0.03485690429806709,
0.0215670894831419,
0.016831444576382637,
-0.02337217703461647,
0.009237492457032204,
-0.03192506358027458,
-0.06575516611337662,
0.007343281991779804,
-0.05992122367024422,
0.042854562401771545,
0.06211351603269577,
-0.03216611593961716,
0.02782530151307583,
-0.05244622752070427,
-0.01844523288309574,
0.02141585201025009,
-0.009601268917322159,
-0.01557640265673399,
0.02028687298297882,
-0.11021800339221954,
0.01647563837468624,
-0.018116099759936333,
0.003487281035631895,
0.03294306993484497,
-0.010438939556479454,
0.03591844439506531,
-0.03603372722864151,
-0.0830751359462738,
-0.0011171955848112702,
-0.05164414271712303,
0.012445601634681225,
-0.01660587266087532,
-0.07857341319322586,
0.05707279592752457,
-0.03572889417409897,
0.02207575924694538,
0.00423240615054965,
0.025362521409988403,
0.01742374151945114,
-0.05121445655822754,
0.010726885870099068,
-0.007916375994682312,
-0.02809140644967556,
0.026712678372859955,
-0.0017078424571081996,
0.04633213207125664,
0.01541928667575121,
0.02472049556672573,
0.04023057222366333,
-0.018337862566113472,
0.01588512770831585,
-0.014402095228433609,
0.01784001663327217,
0.03727540001273155,
-0.00806442741304636,
-0.007494634483009577,
-0.002742958487942815,
-0.04748193174600601,
0.028819231316447258,
0.004995405208319426,
-0.049225546419620514,
0.06533557176589966,
-0.053608909249305725,
-0.05600404739379883,
0.01911555975675583,
-0.017436623573303223,
0.05241614207625389,
-0.021211137995123863,
0.029601193964481354,
0.06361856311559677,
0.03391840308904648,
-0.03724636137485504,
0.052452486008405685,
-0.023388804867863655,
0.012313543818891048,
-0.0014120495179668069,
-0.03575051948428154,
-0.00025225093122571707,
0.05505434423685074,
0.04275069385766983,
-0.03131921961903572,
0.02548757568001747,
0.0012332123005762696,
0.08561583608388901,
0.007144348230212927,
0.06866350024938583,
0.08508080244064331,
0.006644763983786106,
-0.009546655230224133,
0.03440486267209053,
0.05173209309577942,
0.0038304671179503202,
-0.06350795179605484,
0.03387311473488808,
-0.02034231834113598,
0.015525171533226967,
0.006507257465273142,
0.014071585610508919,
-0.0201314277946949,
0.11496356129646301,
0.02232072502374649,
0.012282049283385277,
-0.0017392816953361034,
0.009196172468364239,
-0.027350828051567078,
-0.00870123878121376,
0.019599702209234238,
0.0028204245027154684,
-0.012523935176432133,
-0.049659885466098785,
0.07161390036344528,
0.03369683772325516,
0.00598584720864892,
-0.037709176540374756,
0.00040569479460828006,
0.013460543937981129,
0.022287769243121147,
0.03038419783115387,
0.004375495482236147,
-0.01103744562715292,
0.010804708115756512,
-0.020565221086144447,
-0.0008311776327900589,
0.027674449607729912,
0.007148273754864931,
0.09627196937799454,
0.013957388699054718,
0.06675215065479279,
-0.08640498667955399,
-0.029916349798440933,
0.045607682317495346,
-0.03435921296477318,
-0.004869484342634678,
-0.07791686803102493,
0.022781167179346085,
0.028282195329666138,
0.029607607051730156,
-0.08417769521474838,
-0.024964412674307823,
-0.017080603167414665,
0.012110738083720207,
0.016405651345849037,
-0.03862461820244789,
0.04084462672472,
-0.01938651129603386,
-0.07805207371711731,
-0.0161589328199625,
0.011818751692771912,
0.028558989986777306,
0.048085231333971024,
0.014775019139051437,
-0.02647867426276207,
-0.010323318652808666,
-0.058802857995033264,
-0.022384611889719963,
-0.007040363270789385,
0.030494263395667076,
0.03302288427948952,
-0.0033614542335271835,
-0.019728409126400948,
0.0029902560636401176,
-0.021298397332429886,
-0.050501711666584015,
0.019419195130467415,
-0.048232898116111755,
0.03682684898376465,
0.03793032094836235,
0.021105404943227768,
0.033810295164585114,
-0.042180586606264114,
0.007685122080147266,
-0.0020676245912909508,
0.051856521517038345,
0.012914489954710007,
-0.027532128617167473,
0.03261058032512665,
-0.02468034438788891,
-0.04078872501850128,
-0.0545479841530323,
-0.09632830321788788,
-0.0011185421608388424,
-0.015847599133849144,
-0.03199095278978348,
-0.0018325676210224628,
0.015651019290089607,
-0.018206294625997543,
-0.014951829798519611,
-0.017770007252693176,
0.01978493109345436,
0.01148830447345972,
0.06801038235425949,
0.03727157786488533,
0.004460789263248444,
0.007460348773747683,
0.0379214845597744,
-0.010237915441393852,
-0.05029181391000748,
-0.028697289526462555,
0.023007307201623917,
0.0016262345016002655,
0.04380225017666817,
-0.01372499205172062,
-0.005995811428874731,
-0.0025503423530608416,
0.045741915702819824,
-0.041005752980709076,
-0.009251217357814312,
0.032218046486377716,
-0.021452154964208603,
0.007208588067442179,
0.0007182802073657513,
-0.04888828843832016,
0.03776881471276283,
0.04825437813997269,
0.020182864740490913,
-0.026286864653229713,
0.03917953372001648,
0.042525630444288254,
-0.006483912467956543,
0.03529375046491623,
-0.05438241735100746,
0.06430202722549438,
0.0030588279478251934,
-0.023173319175839424,
0.048297662287950516,
-0.002451919252052903,
0.0017112488858401775,
0.06141303852200508,
-0.004700051620602608,
0.0159738939255476,
0.026661721989512444,
0.040702562779188156,
0.008440461941063404,
0.04468603804707527,
-0.020584939047694206,
-0.01872849091887474,
0.019751446321606636,
0.01145939901471138,
0.022586364299058914,
0.009866917505860329,
-0.014927181415259838,
0.028957845643162727,
-0.02580917254090309,
0.007121590431779623,
-0.027288097888231277,
0.0009713270119391382,
0.00873437151312828,
-0.004816216882318258,
-0.04751896858215332,
0.014959742315113544,
-0.01321213599294424,
0.0024250363931059837,
-0.06384824961423874,
-0.006159378215670586,
0.039328303188085556,
0.008540813811123371,
0.05951247364282608,
-0.0019494793377816677,
0.004619977902621031,
-0.0132423285394907,
0.0033962999004870653,
-0.007144392002373934,
-0.02255803346633911,
-0.112062007188797,
0.007214659824967384,
0.0468432679772377,
0.044798582792282104,
0.04561519995331764,
-0.03384668752551079,
0.005136578343808651,
0.07578533887863159,
-0.06345400959253311,
-0.014862514100968838,
0.03871634975075722,
0.04443071782588959,
-0.008419466204941273,
-0.03140237554907799,
0.0185884777456522,
-0.022852463647723198,
-0.04620830714702606,
0.0025895468425005674,
0.02475040778517723,
-0.008540961891412735,
0.0580793172121048,
0.06878270208835602,
0.00847158208489418,
0.016559313982725143,
-0.007175958715379238,
0.006603161338716745,
0.08280033618211746,
-0.004500003065913916,
-0.016943417489528656,
-0.034886304289102554,
0.01115263532847166,
-0.002977551892399788,
-0.021860413253307343,
-0.029935481026768684,
-0.013383114710450172,
-0.03758945316076279,
0.02440798655152321,
-0.0629989430308342,
-0.028485149145126343,
-0.014600340276956558,
-0.051496993750333786,
0.0006422870792448521,
-0.10205449908971786,
-0.0958312600851059,
0.050698742270469666,
-0.02925448678433895,
-0.01506754569709301,
-0.024585768580436707,
-0.010462039150297642,
0.032138384878635406,
0.04003164544701576,
-0.03197663277387619,
-0.04326628893613815,
0.029742714017629623,
0.0295279361307621,
0.04640042781829834,
-0.014570525847375393,
0.043740950524806976,
-0.03850070759654045,
-0.038947079330682755,
0.014952954836189747,
0.017233898863196373,
-0.001551983063109219,
0.05436549335718155,
0.06456030905246735,
0.013380344957113266,
-0.055026233196258545,
-0.0013894214062020183,
0.0041510434821248055,
0.010533376596868038,
-0.02616945467889309,
0.06312939524650574,
-0.04799574986100197,
-0.03467842936515808,
-0.025220125913619995,
0.0023041823878884315,
-0.025717878714203835,
0.04986446723341942,
0.01832050085067749,
0.0075463843531906605,
0.022160815075039864,
-0.03369952365756035,
-0.026665939018130302,
0.01976473070681095,
0.004635415505617857,
0.022005131468176842,
0.03470185771584511,
0.034209053963422775,
0.007697118911892176,
-0.05953299254179001,
0.05561625212430954,
0.005236292723566294,
-0.005016266833990812,
-0.05268304795026779,
-0.009199012070894241,
0.0073656002059578896,
-0.006691146641969681,
-0.06301034241914749,
-0.04418475925922394,
0.01709846965968609,
0.028710894286632538,
-0.05763434246182442,
-0.004957098513841629,
0.062213748693466187,
0.022757675498723984,
0.04874945804476738,
-0.012654900550842285,
0.04335465654730797,
0.008065768517553806,
0.021355466917157173,
0.023901144042611122,
-0.004360628314316273,
0.017722321674227715,
-0.07017982751131058,
-0.001256014802493155,
-0.0072832065634429455,
0.004585058428347111,
-0.06427004933357239,
0.005178140476346016,
0.020354527980089188,
0.02962498553097248,
0.0411849319934845,
-0.021979020908474922,
-0.04255089908838272,
-0.025708727538585663,
-0.017949294298887253,
0.01736036129295826,
-0.005038631148636341,
-0.04505901038646698,
-0.03730347380042076,
-0.030582094565033913,
-0.015722136944532394,
-0.0017355121672153473,
0.052174102514982224,
0.008992694318294525,
0.025606581941246986,
0.010418493300676346,
0.07156413793563843,
-0.021756630390882492,
0.05308475345373154,
0.0225420780479908,
-0.025169141590595245,
0.008828924968838692,
-0.01272688340395689,
-0.02730119228363037,
-0.010493671521544456,
-0.04570856690406799,
0.031203031539916992,
-0.0007838093442842364,
-0.05128965899348259,
0.016654105857014656,
-0.03198003023862839,
-0.018069379031658173,
-0.025031359866261482,
0.005423777271062136,
0.010108033195137978,
-0.007784954737871885,
-0.0002512063947506249,
-0.004860196728259325,
-0.005972728598862886,
0.0032988889142870903,
0.011514503508806229,
0.00033394270576536655,
-0.06513997912406921,
-0.0519854761660099,
0.018958942964673042,
0.02447635680437088,
-0.003585346508771181,
-0.07006967812776566,
-0.018155165016651154,
-0.0399804525077343,
0.017230721190571785,
-0.0026717877481132746,
0.005233407486230135,
-0.015962228178977966,
0.020131221041083336,
0.05534395948052406,
-0.11492791026830673,
0.007002946920692921,
0.022890180349349976,
-0.00011589978385018185,
-0.029593581333756447,
-0.04108940437436104,
0.010719556361436844,
-0.02576308324933052,
0.0021755939815193415,
-0.027048802003264427,
-0.01055329479277134,
-0.024134229868650436,
0.03491180017590523
] |
<p>Referring particularly to </p>
<p><a href="http://arxiv.org/abs/hep-th/9909056" rel="nofollow">http://arxiv.org/abs/hep-th/9909056</a></p>
<p>in regard to the wave equation for Schwarzschild-AdS black holes (p.4), I'm trying to understand tortoise coordinates. </p>
<p>So starting with the 4-dimensionalSchwarzschild-AdS metric in the general form</p>
<p>$$ds^2=-f(r )dt^2+\frac{dr^2}{f(r )}+r^2(d\theta^2+sin^2 \theta d\phi^2),$$</p>
<p>if I want to find the wave equation $\Box \phi=0$ in the Schrodinger-like form. This is done by introducing the separation of variables </p>
<p>$$\phi=\frac{\psi(r ) Y(\theta,\phi)e^{-i\omega t}}{r}$$</p>
<p>and then using the <a href="http://en.wikipedia.org/wiki/Eddington%E2%80%93Finkelstein_coordinates#Tortoise_coordinate" rel="nofollow">tortoise coordinate</a> $dr_*=\frac{dr}{f(r )}$ to get </p>
<p>$$(\partial_{r_*}^2+\omega^2-V(r_*))\psi=0.$$</p>
<p>But I don't fully understand what this tortoise coordinate really does. In fact when I go through these calculations myself, I use the transformation</p>
<p>$$\psi'(r ) \to \frac{\psi'(r )}{f(r )}$$</p>
<p>and (fortunately) get the Schrodinger like form as in the paper above. However, they never explicitly state the potential and what I find is</p>
<p>$$V(r_*)=\frac{-\ell(\ell+1) f(r )+rf'(r )}{r^2}.$$</p>
<p>where $\ell$ is the angular momentum mode. <strong>But note</strong>, in my transformation, I never mentioned $r_*$ and hence why my $V(r_*)$ doesn't actually mention an $r_*$. This is where my confusion lies. </p>
<p>Is my potential right if I just replace the $r$ by $r_*$? i.e</p>
<p>$$V(r_*)=\frac{-\ell(\ell+1) f(r_* )+r_*f'(r_* )}{r_*^2}?$$</p>
<p>(I highly doubt it.) And if not, how do I recover $V(r )$ from here?</p>
<p>P.s. It would actually also be extremely helpful if someone knew $V(r )$, i.e. potential in original coordinates, for the Schwarzschild-AdS black hole. </p> | g4810 | [
0.022100171074271202,
-0.02643366903066635,
-0.01146326120942831,
-0.00042715121526271105,
0.048944223672151566,
0.02885650284588337,
0.05447961390018463,
0.02381892502307892,
-0.02583775296807289,
0.002686987863853574,
0.007696919608861208,
0.028121063485741615,
0.021247731521725655,
-0.02038360945880413,
0.014882289804518223,
0.004609681200236082,
0.03866152837872505,
0.022348837926983833,
0.04874342679977417,
-0.05724690109491348,
0.03503107652068138,
-0.022320911288261414,
0.07362542301416397,
-0.04061952605843544,
-0.008367498405277729,
-0.019237389788031578,
-0.025973988696932793,
0.009384630247950554,
-0.024559177458286285,
0.009520194493234158,
0.02826898917555809,
0.07961032539606094,
0.07688456773757935,
0.025039605796337128,
-0.027156643569469452,
0.02240264229476452,
0.07616624236106873,
0.05446583032608032,
-0.01892024837434292,
0.01085522398352623,
-0.03108353726565838,
-0.025016730651259422,
0.024957308545708656,
0.01738479919731617,
-0.02245907299220562,
-0.05639790743589401,
0.01024826429784298,
0.0032782370690256357,
-0.007423518691211939,
0.0016957505140453577,
0.0072411284781992435,
0.057202938944101334,
0.06496545672416687,
0.02287088893353939,
0.009154370985925198,
0.07602450251579285,
0.03267763927578926,
-0.029256222769618034,
0.046609796583652496,
0.09703550487756729,
-0.04842246696352959,
0.0025479968171566725,
0.003948443569242954,
0.023209858685731888,
0.04271380230784416,
-0.012119811959564686,
-0.030933432281017303,
-0.029347898438572884,
-0.06646359711885452,
-0.07530197501182556,
-0.022318407893180847,
-0.05163756012916565,
0.03567224368453026,
0.02864142507314682,
-0.06045672670006752,
0.01954786106944084,
0.0008323862566612661,
-0.019821416586637497,
0.02829139307141304,
-0.018507802858948708,
0.027929019182920456,
-0.04465029016137123,
0.029164183884859085,
0.010258941911160946,
0.06749578565359116,
0.02107664756476879,
0.03412982076406479,
0.03377032279968262,
0.03179197013378143,
0.018579846248030663,
0.035517215728759766,
-0.04779466986656189,
0.009862185455858707,
-0.01799013838171959,
-0.015456322580575943,
-0.005524341017007828,
-0.02611474320292473,
0.025336654856801033,
-0.012245075777173042,
-0.02019740454852581,
-0.0359305702149868,
0.023792719468474388,
0.010443758219480515,
-0.03104425221681595,
-0.00965536292642355,
-0.047930099070072174,
0.052603334188461304,
0.009914935566484928,
0.026611341163516045,
0.002855767263099551,
-0.03234276920557022,
-0.035832203924655914,
-0.026108384132385254,
-0.03406508266925812,
-0.08327740430831909,
-0.04088282585144043,
0.013633552938699722,
0.0016918089240789413,
-0.05508898198604584,
0.0525224506855011,
0.024585245177149773,
-0.0024725014809519053,
0.10967236757278442,
0.03736988455057144,
0.031116057187318802,
-0.021062249317765236,
-0.014860328286886215,
-0.03191808983683586,
0.07450447231531143,
-0.0006916483398526907,
-0.012461126782000065,
-0.011789578944444656,
0.05873691663146019,
-0.016288407146930695,
-0.01566970907151699,
0.012047061696648598,
-0.04219711571931839,
-0.01945892535150051,
-0.005394800566136837,
0.02741273120045662,
-0.04771071672439575,
-0.0662601888179779,
0.004258562345057726,
0.007344704121351242,
-0.011637537740170956,
-0.009184534661471844,
0.0019600370433181524,
-0.038239553570747375,
0.06729160249233246,
-0.03668626770377159,
0.01838444173336029,
0.06943559646606445,
-0.034678272902965546,
0.010938135907053947,
-0.04042121022939682,
-0.02719651348888874,
0.04467951878905296,
-0.01218150369822979,
0.025101054459810257,
0.001246725907549262,
0.062409233301877975,
-0.014861375093460083,
0.02559305727481842,
0.0421750433743,
-0.02019289880990982,
0.03335138037800789,
0.042125266045331955,
-0.0545949786901474,
0.006523876916617155,
-0.0666164979338646,
-0.05501197278499603,
-0.005234525538980961,
0.03731095790863037,
-0.018904834985733032,
0.01854759268462658,
0.03468240797519684,
-0.0776548981666565,
-0.01797662489116192,
0.045585326850414276,
0.10310076922178268,
0.0050747995264828205,
-0.0032050330191850662,
0.027356743812561035,
-0.027691425755620003,
0.017335431650280952,
-0.018638975918293,
0.08688981086015701,
0.010978548787534237,
0.017566926777362823,
0.056468378752470016,
-0.05179823935031891,
-0.0013241987908259034,
0.03212122991681099,
0.03839151933789253,
0.02436225488781929,
0.07885879278182983,
0.023170173168182373,
-0.03193570300936699,
-0.013237947598099709,
0.08291463553905487,
-0.0021205332595854998,
0.03860408812761307,
0.03427411988377571,
0.009327337145805359,
0.03336784616112709,
-0.002789405407384038,
-0.024597473442554474,
-0.028212381526827812,
0.007686443626880646,
0.00726472120732069,
-0.004125154577195644,
-0.01818077452480793,
-0.0047323680482804775,
-0.021292679011821747,
-0.05618030205368996,
0.03480231761932373,
-0.007035386748611927,
0.06549200415611267,
-0.043689318001270294,
0.029708685353398323,
-0.055710699409246445,
-0.0391116589307785,
-0.018584594130516052,
-0.00820646621286869,
-0.0344557985663414,
0.015588349662721157,
-0.008626425638794899,
0.017587734386324883,
0.016001051291823387,
0.0036562951281666756,
-0.0411670058965683,
-0.032471079379320145,
0.009876985102891922,
0.0014489839086309075,
0.046985652297735214,
0.011252984404563904,
-0.016798879951238632,
-0.018586551770567894,
0.002415265189483762,
-0.007051772903650999,
0.05843459069728851,
-0.02347548119723797,
-0.043864656239748,
-0.006908129435032606,
0.07100886106491089,
0.06255616247653961,
0.071037158370018,
0.05064649134874344,
-0.027909450232982635,
-0.026938999071717262,
0.010670318268239498,
-0.013771248050034046,
0.01925322227180004,
-0.04456507787108421,
0.005625686142593622,
-0.0024208028335124254,
0.018595188856124878,
0.017093664035201073,
-0.029264558106660843,
0.005358947440981865,
-0.04147617146372795,
0.01242081355303526,
0.00010018259490607306,
0.04442105069756508,
-0.06551184505224228,
-0.005576032213866711,
0.01440323144197464,
0.026650022715330124,
0.05759495124220848,
-0.027010269463062286,
-0.03598914295434952,
0.04588115215301514,
0.03474346548318863,
0.0160834901034832,
-0.04713011533021927,
-0.06446665525436401,
-0.04654715210199356,
0.008377970196306705,
0.01943122036755085,
0.056987278163433075,
-0.010891538113355637,
-0.000453643238870427,
-0.04252295941114426,
-0.008751219138503075,
-0.020240310579538345,
-0.049143075942993164,
-0.006633146200329065,
0.07469695806503296,
-0.0018132674740627408,
-0.033670660108327866,
-0.029935795813798904,
0.018441909924149513,
0.006322304252535105,
0.006129049696028233,
0.006009550299495459,
0.022630849853157997,
-0.008858843706548214,
-0.01808456890285015,
0.009975693188607693,
0.049040742218494415,
0.01523955725133419,
-0.019781671464443207,
-0.027562608942389488,
0.0008137722034007311,
-0.008002476766705513,
0.00865897350013256,
-0.0379004143178463,
-0.005689456593245268,
-0.015141993761062622,
0.021482858806848526,
0.020426686853170395,
0.009587900713086128,
-0.0019420325988903642,
-0.014736585319042206,
-0.06092679128050804,
0.004072105512022972,
-0.003740259213373065,
-0.03270363435149193,
-0.0055012269876897335,
0.016781721264123917,
-0.04889065772294998,
-0.020816534757614136,
0.0009981489274650812,
0.021403411403298378,
0.0675436481833458,
0.081179179251194,
-0.0197520162910223,
-0.03030702844262123,
-0.0589623786509037,
-0.02502605691552162,
0.01865529641509056,
0.014315749518573284,
0.0621129609644413,
-0.0009244938846677542,
-0.06838345527648926,
-0.014554379507899284,
-0.060630105435848236,
0.06006648764014244,
0.04356132820248604,
-0.031429510563611984,
0.041627656668424606,
-0.0420505627989769,
0.013983992859721184,
0.07547593861818314,
-0.024206766858696938,
-0.022001266479492188,
0.009623322635889053,
0.03341124951839447,
0.03013133816421032,
-0.053262859582901,
-0.08470617234706879,
0.023289352655410767,
0.03064557909965515,
0.008071040734648705,
0.03208392113447189,
0.03584675490856171,
0.0044954316690564156,
0.02241661585867405,
0.03004864975810051,
0.02446100115776062,
0.010527974925935268,
-0.05442085489630699,
-0.038306426256895065,
-0.003828134387731552,
-0.02532903291285038,
-0.023990441113710403,
0.023201603442430496,
-0.020622210577130318,
-0.052979882806539536,
-0.028026331216096878,
0.04992940276861191,
-0.0020641018636524677,
0.04296448081731796,
0.012413166463375092,
0.000330116949044168,
-0.04371834918856621,
-0.004282393958419561,
0.013507393188774586,
-0.011967944912612438,
0.026512421667575836,
-0.020655950531363487,
-0.028487006202340126,
0.010297685861587524,
-0.026538299396634102,
-0.031756725162267685,
-0.02744227461516857,
-0.011647043749690056,
0.016970040276646614,
-0.01885366439819336,
-0.007174653001129627,
-0.009060442447662354,
-0.01577502116560936,
-0.006364881061017513,
-0.04313376173377037,
-0.008502285927534103,
-0.02057688683271408,
0.007860526442527771,
0.00029333666316233575,
-0.06405647099018097,
0.04742143675684929,
-0.0190134234726429,
0.005914423149079084,
0.03443457931280136,
-0.006519682705402374,
-0.018298665061593056,
0.02774769999086857,
0.015973854809999466,
0.0030887098982930183,
0.03764966502785683,
-0.020649658516049385,
-0.028557879850268364,
-0.0429140068590641,
0.06123395264148712,
-0.05073543265461922,
0.03496067598462105,
-0.0033438662067055702,
0.0020310659892857075,
-0.05321183428168297,
-0.042989689856767654,
0.017192916944622993,
0.017302703112363815,
-0.026191677898168564,
0.03341609239578247,
0.033738989382982254,
-0.015648286789655685,
-0.015186226926743984,
0.01944965496659279,
0.03087271936237812,
-0.010217253118753433,
0.021157056093215942,
-0.004516660235822201,
0.0013306548353284597,
-0.0012962468899786472,
0.04311911761760712,
-0.10087914764881134,
0.05944368988275528,
-0.034550007432699203,
-0.02924409881234169,
-0.058033302426338196,
0.07251569628715515,
0.00010987225687131286,
0.018508408218622208,
0.025343459099531174,
-0.06159080192446709,
-0.019983835518360138,
0.029917223379015923,
0.028932906687259674,
0.022616557776927948,
0.00711310189217329,
0.013333365321159363,
-0.041303955018520355,
0.04400213062763214,
0.04233594983816147,
-0.0717683881521225,
0.06557128578424454,
0.003427863819524646,
-0.010384135879576206,
0.01976470649242401,
-0.013662823475897312,
0.0074584828689694405,
-0.06940627098083496,
-0.023373618721961975,
-0.020931102335453033,
-0.015329542569816113,
0.021477222442626953,
-0.009156391955912113,
-0.053293097764253616,
-0.003792469622567296,
-0.027360111474990845,
-0.034779440611600876,
-0.018649065867066383,
-0.023566966876387596,
0.015308207832276821,
-0.013013172894716263,
0.00509622972458601,
0.06625843048095703,
-0.020922956988215446,
-0.06393667310476303,
-0.038499053567647934,
-0.06238409876823425,
-0.032248761504888535,
0.06255003064870834,
0.038418352603912354,
0.016348280012607574,
-0.028145521879196167,
0.02767099440097809,
-0.05431554093956947,
0.018232690170407295,
-0.02447926625609398,
0.06475640833377838,
0.03141012415289879,
0.0513891838490963,
-0.01988934352993965,
-0.039174534380435944,
0.001636881148442626,
0.03384828194975853,
0.044803641736507416,
-0.014983687549829483,
-0.013653984293341637,
0.027718273922801018,
-0.03756406158208847,
-0.03486571088433266,
-0.01196083053946495,
-0.024676086381077766,
-0.002231026766821742,
0.05037568137049675,
0.08103819936513901,
0.02410765178501606,
0.01771177351474762,
0.04962655156850815,
0.026974689215421677,
-0.041437190026044846,
-0.029663776978850365,
0.031537652015686035,
0.0018229042179882526,
-0.046416789293289185,
0.002856202656403184,
0.01869865506887436,
-0.02515546604990959,
-0.07945724576711655,
0.0031746781896799803,
0.03180558234453201,
0.032107770442962646,
-0.04240737110376358,
0.03240391984581947,
0.01739192195236683,
-0.022342534735798836,
-0.014104938134551048,
0.029566045850515366,
-0.018114794045686722,
-0.01829580031335354,
-0.04636421799659729,
-0.023344725370407104,
0.01998104341328144,
0.0474538691341877,
-0.0019227380398660898,
0.00908047053962946,
-0.05292874574661255,
0.03668558597564697,
-0.04519214853644371,
0.005243299063295126,
-0.016664491966366768,
-0.0037690058816224337,
0.048159461468458176,
-0.09243080765008926,
0.019343221560120583,
-0.019239258021116257,
-0.01158759742975235,
-0.04910750687122345,
0.005833188537508249,
-0.055569589138031006,
-0.031315166503190994,
-0.0027191194240003824,
-0.011351256631314754,
0.03347017988562584,
0.039933886379003525,
0.012980380095541477,
-0.07610220462083817,
-0.058203279972076416,
-0.07884499430656433,
0.044877633452415466,
0.026199813932180405,
-0.017411451786756516,
0.025418097153306007,
0.017312899231910706,
-0.022588679566979408,
0.029295941814780235,
-0.0132928267121315,
0.06101645901799202,
0.04395178332924843,
-0.04747723788022995,
0.04786764457821846,
-0.012803352437913418,
-0.012979981489479542,
0.023182084783911705,
-0.015120468102395535,
0.0002646929060574621,
-0.019100472331047058,
0.02610958181321621,
0.005340323783457279,
-0.03610149770975113,
-0.02223335951566696,
0.0442093200981617,
-0.01880023628473282,
-0.019472533836960793,
0.04249105602502823,
-0.016771286725997925,
-0.042350031435489655,
0.0011045732535421848,
-0.027088677510619164,
0.009394640102982521,
0.049157433211803436,
-0.04404103010892868,
-0.020327094942331314,
0.023371150717139244,
-0.019505150616168976,
0.06428290158510208,
0.02258358895778656,
-0.028108300641179085,
-0.017142316326498985,
0.03197869285941124,
0.028196150436997414,
0.023357383906841278,
0.03471001237630844,
-0.013098560273647308,
-0.0037880109157413244,
-0.040708981454372406,
-0.0393633097410202,
-0.009807255119085312,
-0.0051298318430781364,
-0.016637014225125313,
0.05200463533401489,
-0.04606098681688309,
0.030060365796089172,
0.0630224421620369,
0.021641656756401062,
-0.011914395727217197,
0.04187823832035065,
-0.012134277261793613,
-0.040897488594055176,
0.07553688436746597,
0.005039388779550791,
0.004746699705719948,
0.01445975061506033,
0.06805131584405899,
0.04636227339506149,
-0.031019141897559166,
-0.027486516162753105,
-0.0017590787028893828,
-0.013379696756601334,
0.013990046456456184,
-0.011922553181648254,
0.02668515034019947,
-0.007461709436029196,
-0.013825740665197372,
0.05000245198607445,
-0.04849153384566307,
0.010804974474012852,
0.015032008290290833,
0.05847366526722908,
0.014554103836417198,
-0.015877388417720795,
0.02655159868299961,
0.0029156734235584736,
-0.08038749545812607,
-0.0015955868875607848,
-0.031019223853945732,
0.018622232601046562,
-0.0785241425037384,
0.037333495914936066,
0.03511246666312218,
-0.0396612323820591,
-0.06688211858272552,
0.038249507546424866,
-0.003233684226870537,
-0.07529844343662262,
-0.04816697910428047,
0.0545952133834362,
-0.034096311777830124,
-0.07750397175550461,
0.004488267004489899,
-0.0177590511739254,
-0.05319448187947273,
0.012574225664138794,
-0.050638459622859955,
0.03285529464483261,
-0.02252085506916046,
-0.02460743673145771,
0.04551388695836067,
-0.004880007356405258,
0.025855936110019684,
0.04387449473142624,
-0.06300870329141617,
-0.053483083844184875,
-0.029599765315651894,
0.01689894311130047,
0.03566272184252739,
0.030196404084563255,
-0.04571479186415672,
0.021745465695858,
0.009372862987220287,
0.024845780804753304,
-0.07971907407045364,
0.017824960872530937,
-0.05530594289302826,
0.005986684001982212,
-0.04518898203969002,
0.009429050609469414,
-0.02953016571700573,
0.050780996680259705,
-0.06960497796535492,
0.09059740602970123,
-0.022326283156871796,
0.06347145140171051,
-0.029393842443823814,
-0.006869967561215162,
0.019564025104045868,
0.04613498970866203,
-0.03004101850092411,
0.01997712068259716,
0.06693531572818756,
-0.03892533481121063,
-0.005710819270461798,
0.04490170255303383,
0.05200275406241417,
0.010297300294041634,
-0.012712346389889717,
-0.021755611523985863,
-0.03625480830669403,
0.048495594412088394,
0.06277965754270554,
-0.01780545525252819,
-0.011945933103561401,
-0.05015033110976219,
0.04894647374749184,
0.016702426597476006,
0.019387945532798767,
0.042056601494550705,
-0.04118646681308746,
-0.07497280836105347,
0.019877608865499496,
-0.02283269725739956,
-0.029963763430714607,
-0.06407210975885391,
-0.018465951085090637,
0.014599727466702461,
-0.04274630546569824,
-0.025257395580410957,
0.03253628686070442,
-0.021591661497950554,
-0.04629674553871155,
-0.01702279783785343,
-0.032020751386880875,
0.021614892408251762,
0.013435608707368374,
0.003964517265558243,
-0.04146232083439827,
-0.00888284295797348,
0.03667720407247543,
-0.01780625618994236,
0.033024221658706665,
-0.009883319959044456,
-0.009906926192343235,
-0.0063749756664037704,
-0.04863454028964043,
0.007892080582678318,
0.005092653911560774,
0.013153155334293842,
0.015287728980183601,
-0.014593597501516342,
0.0287828017026186,
0.05639238655567169,
0.02046990394592285,
-0.0017877286300063133,
-0.02617359161376953,
-0.07462862879037857,
-0.01342002209275961,
0.015753282234072685,
0.015170961618423462,
-0.0508204847574234,
-0.012054921127855778,
0.0005920174880884588,
-0.06741641461849213,
0.020337484776973724,
-0.010993915610015392,
-0.08624611049890518,
-0.007643044460564852,
0.059944119304418564
] |
<p>Two friends, $A$ and $B$ are part of an experiment. $A$ is placed in a closed box and made to accelerate in free space at an acceleration $g$. $B$ is also placed in a closed box, but is made to rotate in a circle at uniform speed, such that the radial acceleration is also $g$. Can $A$ and $B$ perform some experiment from their boxes to tell who is moving radially and who is moving linearly?</p> | g4811 | [
0.007301126141101122,
0.011191046796739101,
-0.00035644700983539224,
-0.024880673736333847,
0.06632671505212784,
-0.032953448593616486,
0.04845164343714714,
-0.04157650098204613,
-0.06153591722249985,
-0.014647716656327248,
0.009437537752091885,
0.04429326951503754,
-0.00891109835356474,
-0.02087576501071453,
0.017176030203700066,
-0.008426260203123093,
0.06763873249292374,
-0.0455588772892952,
0.029155081138014793,
-0.007715742569416761,
0.05288079008460045,
0.05945003777742386,
-0.010643200017511845,
0.020955145359039307,
0.07428349554538727,
-0.02084728702902794,
-0.02430703118443489,
-0.03401879966259003,
-0.0656556785106659,
-0.031206635758280754,
-0.005754056852310896,
-0.03536680340766907,
0.03914254903793335,
-0.020251939073204994,
0.006820651236921549,
-0.02682272344827652,
0.04650692269206047,
-0.01612052135169506,
-0.02042936533689499,
0.011510881595313549,
0.0061445995233953,
-0.006728172767907381,
0.016116296872496605,
-0.018199743703007698,
0.02953069843351841,
0.02717108279466629,
0.055523693561553955,
-0.011823195032775402,
0.1025080755352974,
0.03176457807421684,
-0.06795146316289902,
0.010141415521502495,
-0.027228156104683876,
-0.011616820469498634,
-0.017105424776673317,
0.043423499912023544,
-0.037352584302425385,
-0.01764153502881527,
0.08930927515029907,
-0.014803620055317879,
-0.0177699513733387,
-0.002960984129458666,
0.0095957200974226,
-0.049071721732616425,
0.051804907619953156,
0.007883024401962757,
0.03295943886041641,
0.014600812457501888,
-0.034123171120882034,
-0.046083517372608185,
0.015496989712119102,
-0.04569658264517784,
0.03357125446200371,
0.013046850450336933,
-0.039547085762023926,
0.03863336890935898,
0.017168596386909485,
-0.006927381735295057,
-0.011012244038283825,
0.006340292282402515,
0.0015599563485011458,
-0.007402263581752777,
-0.001855470472946763,
0.02918241359293461,
0.02153262309730053,
0.00911322608590126,
0.026700440794229507,
-0.019535306841135025,
-0.01212919782847166,
0.019816400483250618,
0.05747109279036522,
-0.057413533329963684,
0.10250595957040787,
0.06141756474971771,
-0.01040932908654213,
0.06754989176988602,
-0.03941633179783821,
0.02077961340546608,
0.03374750539660454,
0.0009245218243449926,
0.0046525984071195126,
0.018659032881259918,
-0.0563603937625885,
0.004502216354012489,
0.03593927249312401,
-0.05806433781981468,
0.04287669435143471,
0.008203469216823578,
-0.061443183571100235,
-0.057945940643548965,
-0.0164529737085104,
-0.08177990466356277,
-0.05437735840678215,
-0.024777382612228394,
-0.0011807535775005817,
-0.038618505001068115,
0.040741562843322754,
-0.003917391877621412,
-0.002076527802273631,
0.04048345983028412,
0.031294919550418854,
0.05182322859764099,
-0.05144772306084633,
0.044742804020643234,
-0.0009643759112805128,
0.05245168134570122,
-0.006627942901104689,
-0.033249326050281525,
0.007218277081847191,
0.008688228204846382,
-0.024773726239800453,
0.011618295684456825,
0.046157076954841614,
0.0016279672272503376,
-0.036039937287569046,
0.016612304374575615,
-0.039425209164619446,
0.011491455137729645,
0.023844463750720024,
-0.028494108468294144,
-0.00608617439866066,
-0.008449866436421871,
-0.016595598310232162,
0.00923025794327259,
0.040887340903282166,
0.0320725217461586,
0.03733617812395096,
0.007688644342124462,
0.04676306992769241,
0.08981724828481674,
0.014047124423086643,
0.08443548530340195,
0.0014556326204910874,
0.01713668927550316,
0.011489401571452618,
-0.00855223461985588,
-0.05350193753838539,
-0.052930012345314026,
0.04543871805071831,
0.020352093502879143,
0.027038415893912315,
-0.008966854773461819,
-0.004382419865578413,
-0.0024360953830182552,
-0.05364634841680527,
0.016120698302984238,
-0.016202371567487717,
-0.014878204092383385,
0.07444369047880173,
-0.01161884143948555,
-0.038514796644449234,
-0.05114464834332466,
0.0023138702381402254,
0.031289830803871155,
-0.018708737567067146,
0.030021069571375847,
-0.003451249096542597,
-0.04955962300300598,
0.006256102118641138,
0.014430485665798187,
-0.03298486769199371,
-0.012030934914946556,
0.02254762127995491,
-0.03709511458873749,
-0.013928350992500782,
0.006496725603938103,
-0.031167780980467796,
0.02333095669746399,
-0.08454542607069016,
-0.02042338252067566,
0.03988797217607498,
-0.06250689178705215,
-0.02496003359556198,
-0.010476999916136265,
-0.02642807923257351,
0.0056985835544764996,
0.00382985663600266,
-0.018157679587602615,
0.001331668347120285,
0.03738544136285782,
-0.018715806305408478,
-0.0069746822118759155,
0.04601655900478363,
0.025161385536193848,
-0.012845009565353394,
-0.04419996589422226,
-0.006945620756596327,
-0.029496893286705017,
0.030994892120361328,
0.00017068235320039093,
0.0297945998609066,
0.0202226173132658,
-0.005410226993262768,
0.02203134447336197,
0.06682178378105164,
-0.013982600532472134,
0.05152544379234314,
0.03670943155884743,
0.010454431176185608,
0.003230087459087372,
-0.039113227277994156,
-0.029298974201083183,
0.026243770495057106,
-0.0465066097676754,
0.008683358319103718,
-0.042990196496248245,
-0.008870059624314308,
0.002992132445797324,
-0.06512309610843658,
0.04078324884176254,
-0.054215963929891586,
0.008244656026363373,
0.05067868530750275,
0.0019659041427075863,
0.020324507728219032,
-0.00690523162484169,
-0.018740816041827202,
0.018158376216888428,
0.025438055396080017,
0.03022836521267891,
0.021906211972236633,
0.03725467622280121,
-0.06454534083604813,
-0.0028863882180303335,
0.015211699530482292,
-0.04516330361366272,
0.0675647109746933,
0.013746768236160278,
0.030767006799578667,
0.02217218279838562,
-0.04902736097574234,
0.050196144729852676,
-0.01497983280569315,
0.03302251175045967,
-0.01913098245859146,
0.04181898012757301,
-0.014081721194088459,
0.0019341245060786605,
-0.04080278426408768,
-0.05321909859776497,
0.04636494070291519,
-0.029076380655169487,
-0.010649635456502438,
0.06112213432788849,
0.0014407301787286997,
-0.05556371435523033,
0.018562152981758118,
0.031297434121370316,
-0.026909181848168373,
0.03527487814426422,
-0.09340494126081467,
0.027541227638721466,
0.030177831649780273,
0.07117250561714172,
-0.0184846892952919,
-0.03050801157951355,
0.043732307851314545,
-0.0017810419667512178,
-0.024930207058787346,
0.020848272368311882,
-0.03209594264626503,
-0.0614846907556057,
-0.0429406575858593,
0.0476803183555603,
0.012507508508861065,
-0.01590924896299839,
0.030973482877016068,
0.021841656416654587,
-0.038048870861530304,
0.02434343472123146,
-0.04847107455134392,
0.050585247576236725,
0.061827611178159714,
0.001406066701747477,
0.007806695997714996,
0.055505651980638504,
0.025699863210320473,
-0.009723988361656666,
0.05727314576506615,
0.0033262018114328384,
-0.017163684591650963,
-0.07188857346773148,
0.00285037187859416,
0.03971311077475548,
0.017441097646951675,
-0.019538795575499535,
-0.0602186918258667,
-0.05910101160407066,
-0.01260954700410366,
0.018925953656435013,
-0.008376026526093483,
-0.007452530320733786,
-0.025265613570809364,
0.0035034928005188704,
0.019530171528458595,
-0.056062813848257065,
-0.01999497041106224,
0.03800145909190178,
0.05766979977488518,
0.052630845457315445,
-0.006599305663257837,
-0.043164849281311035,
-0.03060290776193142,
0.006557683926075697,
0.05460629612207413,
-0.0035466193221509457,
-0.003142764326184988,
-0.004354030825197697,
-0.045865610241889954,
-0.08375299721956253,
0.019294731318950653,
0.05616161599755287,
0.03245479241013527,
-0.011232271790504456,
0.018630778416991234,
0.005556630901992321,
-0.029579173773527145,
0.03881502524018288,
-0.026006700471043587,
0.022729646414518356,
-0.02396618388593197,
-0.004198999609798193,
-0.05514103174209595,
-0.001049232087098062,
0.00830085389316082,
0.04588285833597183,
0.020707078278064728,
-0.033929526805877686,
0.024044636636972427,
0.008354080840945244,
0.007750802207738161,
-0.038643233478069305,
0.020011840388178825,
-0.052838366478681564,
-0.02257835678756237,
-0.00020511630282271653,
0.043947238475084305,
-0.029240073636174202,
-0.04298165440559387,
-0.014854535460472107,
-0.049018774181604385,
0.01197013072669506,
0.0035079584922641516,
0.023652510717511177,
0.008892799727618694,
0.009179692715406418,
0.00737146707251668,
0.06405308842658997,
-0.0030244565568864346,
-0.03931420296430588,
-0.018993018195033073,
-0.017566272988915443,
0.022288326174020767,
-0.018749143928289413,
0.06626377999782562,
-0.05488782003521919,
0.016986817121505737,
-0.016007158905267715,
-0.03557822108268738,
0.06113671883940697,
-0.010052986443042755,
0.031417351216077805,
-0.01255730725824833,
-0.03346601873636246,
0.02096720226109028,
0.046226877719163895,
0.015166017226874828,
0.0008363508968614042,
0.0554557666182518,
-0.009524247609078884,
0.01165910717099905,
-0.022684261202812195,
-0.04009860008955002,
-0.015288906171917915,
-0.005238644313067198,
-0.017136244103312492,
0.017365621402859688,
-0.03607770428061485,
-0.007102951407432556,
-0.005705488380044699,
-0.005455274134874344,
0.05874373018741608,
-0.03071640618145466,
-0.026752928271889687,
-0.024259110912680626,
-0.014941598288714886,
-0.04031571373343468,
0.02579784393310547,
0.0035192547366023064,
0.019835958257317543,
-0.051814936101436615,
-0.01481503527611494,
-0.028965182602405548,
-0.04960501194000244,
0.026568109169602394,
0.015731720253825188,
-0.0182462427765131,
0.007302999962121248,
-0.014006786979734898,
-0.0054109105840325356,
0.019450252875685692,
0.03319622576236725,
0.03384103626012802,
-0.052157312631607056,
-0.025322183966636658,
0.07303846627473831,
0.027490487322211266,
0.04122921824455261,
-0.023132750764489174,
-0.06780561804771423,
0.04240162670612335,
-0.0047628870233893394,
-0.024012193083763123,
0.01891145668923855,
-0.01516437716782093,
0.0009678626665845513,
-0.0380173996090889,
-0.006322644650936127,
0.020770780742168427,
0.061648447066545486,
-0.015883147716522217,
0.03008388541638851,
-0.0060616773553192616,
-0.0362808033823967,
-0.0054839057847857475,
0.10229284316301346,
-0.02837243303656578,
-0.01920687034726143,
-0.002147095277905464,
-0.02468806877732277,
-0.012035033665597439,
-0.0029854346066713333,
0.02462833933532238,
0.031030669808387756,
0.0040233442559838295,
-0.026792451739311218,
0.007224247790873051,
-0.016391171142458916,
0.012392380274832249,
0.011408726684749126,
-0.06696242839097977,
-0.03464723378419876,
0.025359293445944786,
0.011890225112438202,
-0.008649143390357494,
0.01148142945021391,
-0.04194442555308342,
-0.05648566409945488,
0.013340159319341183,
-0.01177876628935337,
-0.015750771388411522,
-0.00131507427431643,
0.022032732143998146,
0.0260815117508173,
-0.07223261892795563,
-0.028516823425889015,
0.015611794777214527,
0.03688100725412369,
-0.02512734942138195,
-0.03885500133037567,
-0.05414978042244911,
0.04349708557128906,
0.022698158398270607,
-0.06132053956389427,
0.056059129536151886,
0.013995811343193054,
-0.019264066591858864,
0.030085720121860504,
0.04516518488526344,
0.005434975028038025,
0.015597336925566196,
0.027111545205116272,
0.02588564157485962,
0.012800347059965134,
-0.015026865527033806,
0.016824867576360703,
0.01958511956036091,
-0.0676812008023262,
-0.023819459602236748,
0.013332471251487732,
-0.06343678385019302,
0.041507139801979065,
0.07286185026168823,
0.010987463407218456,
-0.07218970358371735,
0.09431692212820053,
-0.0008912549237720668,
-0.03148442134261131,
-0.008810616098344326,
0.08217526227235794,
-0.07411956787109375,
-0.008686080574989319,
0.038980916142463684,
0.04444621875882149,
-0.06689313054084778,
0.03151705488562584,
0.011461819522082806,
0.00041397465975023806,
-0.04272313788533211,
-0.047136761248111725,
0.07923292368650436,
0.008980901911854744,
-0.009968794882297516,
0.020194392651319504,
0.011892018839716911,
0.04327908158302307,
0.0031673740595579147,
0.04456685110926628,
0.013181786984205246,
0.07582694292068481,
0.049311645328998566,
0.01470130868256092,
0.046397700905799866,
-0.02725052647292614,
0.001920729991979897,
-0.07322414964437485,
0.04915459826588631,
-0.041544653475284576,
0.025251418352127075,
0.011757703498005867,
-0.0391656756401062,
-0.054329827427864075,
0.04540878161787987,
0.010720711201429367,
-0.03380599990487099,
0.005686691030859947,
-0.04948435723781586,
0.005951945669949055,
0.022977860644459724,
0.006562761031091213,
-0.062320344150066376,
0.005415478255599737,
0.03243350610136986,
0.0014463146217167377,
-0.028170866891741753,
0.019139349460601807,
-0.04409250617027283,
-0.030347915366292,
-0.022731516510248184,
-0.002217425499111414,
0.06774163246154785,
0.029355177655816078,
0.08235152065753937,
-0.016304707154631615,
0.008791375905275345,
-0.043934766203165054,
0.01909423992037773,
-0.043755799531936646,
0.025025395676493645,
-0.005888649728149176,
-0.02034848742187023,
-0.02525637485086918,
-0.0472305528819561,
0.02042817324399948,
0.038969818502664566,
-0.014969372190535069,
0.011830870993435383,
0.017922110855579376,
-0.004495334345847368,
0.026199283078312874,
0.018847409635782242,
-0.0013323926832526922,
-0.009500793181359768,
-0.06655296683311462,
0.01972510851919651,
0.05946735292673111,
-0.017001988366246223,
0.0405108705163002,
0.010717494413256645,
-0.029727822169661522,
-0.03189116716384888,
-0.08369358628988266,
-0.04855027794837952,
0.05097488313913345,
-0.08773405104875565,
-0.023545194417238235,
-0.02710258588194847,
0.020745858550071716,
-0.008875549770891666,
0.053897444158792496,
0.006691138260066509,
-0.016616864129900932,
0.06609863042831421,
-0.011633513495326042,
-0.009194815531373024,
-0.030504945665597916,
-0.03860383480787277,
0.01874850131571293,
0.026209957897663116,
-0.02783249318599701,
-0.031526122242212296,
0.009923962876200676,
0.0172441303730011,
0.06493169069290161,
0.012499745935201645,
0.009522635489702225,
0.058417946100234985,
-0.022227050736546516,
-0.003146616742014885,
-0.012181547470390797,
0.062439605593681335,
-0.05967281013727188,
-0.059439174830913544,
-0.016468830406665802,
-0.011013450101017952,
-0.0048270318657159805,
-0.08415832370519638,
-0.020719455555081367,
0.01877368800342083,
0.05224129930138588,
0.015397575683891773,
0.011387493461370468,
-0.013749747537076473,
0.010868570767343044,
0.054661136120557785,
0.0013027869863435626,
-0.027862505987286568,
0.08242303878068924,
0.011818480677902699,
-0.007956700399518013,
0.05680141597986221,
0.06122661381959915,
-0.047069065272808075,
0.006665071938186884,
-0.04250383749604225,
-0.037235599011182785,
0.031566787511110306,
-0.01982899196445942,
-0.007469449192285538,
-0.02414572983980179,
-0.01937123015522957,
-0.017730774357914925,
-0.014561962336301804,
0.02895965799689293,
-0.042410578578710556,
0.005162184126675129,
0.04399184137582779,
0.043204981833696365,
0.003462695050984621,
-0.06139547377824783,
-0.060316301882267,
-0.012853890657424927,
-0.03375891596078873,
-0.035732585936784744,
-0.04628689959645271,
-0.06092444062232971,
-0.08261125534772873,
0.040509555488824844,
-0.016093693673610687,
-0.03612719848752022,
0.02367301657795906,
0.0011613467941060662,
0.007670482154935598,
0.07621723413467407,
0.01891481876373291,
0.0008131709764711559,
0.013368003070354462,
-0.044400934129953384,
-0.00526971323415637,
-0.07453352957963943,
-0.00045320275239646435,
-0.007000142242759466,
-0.01821640133857727,
0.08463432639837265,
-0.00981865357607603,
0.06571555882692337,
-0.004965655039995909,
-0.030653370544314384,
-0.0205205287784338,
-0.06048434227705002,
-0.041668206453323364,
0.03301170840859413,
0.043973926454782486,
-0.009934145957231522,
0.006830602418631315,
0.010026280768215656,
-0.055288221687078476,
0.029969751834869385,
-0.035334616899490356,
0.024021049961447716,
-0.029639676213264465,
0.03279181942343712,
-0.002950473688542843,
0.0255629550665617,
0.023358508944511414,
-0.011181443929672241,
-0.037520162761211395,
0.016311168670654297,
-0.03802839666604996,
-0.0343453623354435,
0.014241435565054417,
0.10075727105140686,
0.03018934652209282,
0.013529119081795216,
0.009804397821426392,
-0.01512750145047903,
-0.07851580530405045,
0.03744400665163994,
0.0509604848921299,
-0.009718462824821472,
-0.021973859518766403,
0.018859531730413437,
0.01605238951742649,
-0.06941820681095123,
-0.027412040159106255,
-0.05251143127679825,
-0.06025233492255211,
0.0075525036081671715,
0.010054461658000946,
-0.04357323795557022,
-0.02612369880080223,
0.007881385274231434,
-0.03907760977745056,
0.0605863481760025,
0.01702175848186016,
0.02494497410953045,
-0.011454529128968716,
-0.01538425125181675,
-0.03605945035815239,
0.04856415465474129,
-0.0375976599752903,
-0.024836182594299316,
0.027085749432444572,
0.00963221862912178,
0.012594664469361305,
-0.003199266269803047,
-0.010415478609502316,
0.060319699347019196,
0.02347051352262497,
-0.021513806656003,
-0.002606889931485057,
-0.008586982265114784,
-0.08016714453697205,
0.01719987392425537,
0.030566029250621796,
-0.0076373848132789135,
0.006429291795939207,
-0.006450787652283907,
0.030871190130710602,
-0.025408875197172165,
-0.09696470946073532,
-0.008674535900354385,
-0.036269765347242355,
0.018257521092891693,
-0.02537146583199501,
-0.02283521741628647,
0.015527763403952122,
0.06272362172603607
] |
<p>When water freezes in a pipe it can crack the pipe open. I assume this takes quite a lot of energy as when I try to crack a pipe it can be hard work!</p>
<p>I think water freezing is a result of energy (heat) being lost from the water and out of the pipe into the freezing environment around it. </p>
<p>So what energy is cracking the pipe and how? When warm and not frozen there is more energy in the pipe than when frozen?</p>
<p>My secondary question might be - is this a particular phenomenon of water or would other matter crack open a pipe when it freezes solid from liquid?</p>
<p>Andrew</p> | g4812 | [
0.025301119312644005,
0.024385787546634674,
0.005764308851212263,
-0.03893745318055153,
-0.033043451607227325,
0.018412530422210693,
0.036871179938316345,
0.07821699976921082,
-0.058433257043361664,
-0.00549980066716671,
0.002390959532931447,
0.021027369424700737,
-0.021388685330748558,
-0.016401804983615875,
0.009097125381231308,
0.026520710438489914,
-0.005594264250248671,
-0.0364578552544117,
0.0059169381856918335,
0.07572712749242783,
-0.024603812023997307,
-0.021780895069241524,
0.027110543102025986,
-0.015217351727187634,
-0.04067065566778183,
0.010641041211783886,
0.037542201578617096,
-0.044032350182533264,
-0.014795641414821148,
-0.03559165447950363,
0.04793943837285042,
0.02372000738978386,
-0.001707284594886005,
-0.0685969889163971,
-0.06422200798988342,
0.05206369608640671,
0.059833839535713196,
0.036459781229496,
0.07484541833400726,
0.010528595186769962,
0.0320940725505352,
0.011914626695215702,
-0.025297388434410095,
-0.002783513627946377,
0.05438704043626785,
0.04233163967728615,
-0.05104955658316612,
-0.049780916422605515,
-0.02757761813700199,
-0.03618958964943886,
0.05239637941122055,
0.005111562088131905,
-0.017865357920527458,
0.008490962907671928,
-0.051256630569696426,
0.00013119095820002258,
0.0009824290173128247,
0.038824133574962616,
0.049684811383485794,
-0.012457190081477165,
0.03147976100444794,
0.03270934894680977,
0.027071170508861542,
-0.04673144966363907,
0.0039600711315870285,
-0.01668713428080082,
0.006057205144315958,
-0.03656589239835739,
0.14151139557361603,
0.026345882564783096,
0.043885666877031326,
-0.06906051188707352,
-0.04613295942544937,
-0.0671742707490921,
-0.001831506029702723,
-0.06344959884881973,
-0.007894467562437057,
-0.01650717481970787,
0.00465443916618824,
-0.0020462775137275457,
0.05309485271573067,
-0.014013371430337429,
-0.021577533334493637,
0.06570857018232346,
0.03435754030942917,
-0.007036913186311722,
-0.0599670484662056,
-0.021154558286070824,
-0.027235670015215874,
0.02484901249408722,
-0.047152966260910034,
-0.014123862609267235,
0.05830584093928337,
0.027792219072580338,
0.014132058247923851,
0.01602461002767086,
-0.031125109642744064,
0.05635746940970421,
-0.04074711352586746,
0.03090718388557434,
-0.008998140692710876,
-0.10164295881986618,
0.03903234750032425,
-0.021980490535497665,
0.044371820986270905,
-0.02000211365520954,
0.002145071281120181,
0.0028369994834065437,
-0.058378517627716064,
0.06639736890792847,
0.010069931857287884,
-0.02455904334783554,
-0.022896932438015938,
-0.015722407028079033,
-0.017674781382083893,
0.023627957329154015,
0.10974754393100739,
-0.054804861545562744,
0.023450570181012154,
0.041960470378398895,
0.04551281780004501,
0.019474679604172707,
-0.016758009791374207,
0.04469240456819534,
-0.013020789250731468,
0.00534933852031827,
0.05648608133196831,
-0.029316280037164688,
-0.03562997281551361,
0.015488512814044952,
0.004438532050698996,
0.006294798105955124,
-0.022365055978298187,
-0.006603172980248928,
-0.0030708517879247665,
0.058602701872587204,
-0.05666528269648552,
0.0374581478536129,
0.002881115535274148,
0.03890091925859451,
0.03026086837053299,
0.05170387029647827,
0.011309192515909672,
0.04324575513601303,
-0.007324628997594118,
-0.015121115371584892,
-0.06336282938718796,
-0.036970485001802444,
-0.018616503104567528,
0.03313101828098297,
-0.0030769561417400837,
0.013463742099702358,
0.024579327553510666,
-0.0788048580288887,
0.04514581710100174,
-0.016134552657604218,
-0.04093996062874794,
-0.010245426557958126,
0.01545368880033493,
0.06769653409719467,
0.02380513586103916,
-0.057521793991327286,
0.05116794630885124,
0.058762047439813614,
-0.014914783649146557,
-0.01142172608524561,
0.008813631720840931,
0.010063858702778816,
0.06156351789832115,
0.03127655014395714,
-0.033960022032260895,
0.018345005810260773,
-0.030201388522982597,
0.01824493333697319,
0.020077597349882126,
0.05560218170285225,
0.024667492136359215,
-0.0180401299148798,
-0.01705273799598217,
-0.0006383913569152355,
-0.015007004141807556,
-0.015109632164239883,
-0.033812664449214935,
-0.05151606351137161,
-0.020643441006541252,
0.004190446808934212,
0.033634744584560394,
-0.00020817502809222788,
0.04183637350797653,
0.006190217565745115,
-0.03367142751812935,
-0.01761700212955475,
0.06326909363269806,
0.0200725719332695,
0.02828780561685562,
-0.01718899980187416,
-0.0212602186948061,
-0.005621705204248428,
-0.06320184469223022,
0.00776713527739048,
0.03716577589511871,
-0.04152015596628189,
-0.019470160827040672,
-0.011862707324326038,
-0.02614617720246315,
0.04506983235478401,
-0.04806399345397949,
0.014739099889993668,
-0.05304936692118645,
0.0062922886572778225,
0.01013191882520914,
-0.008456312119960785,
0.04037275165319443,
-0.007162405643612146,
-0.039551105350255966,
0.08439233899116516,
-0.00014877812645863742,
-0.06696047633886337,
-0.023785332217812538,
0.014259262941777706,
0.07959587872028351,
0.023741919547319412,
-0.007300030905753374,
-0.012996810488402843,
-0.06684490293264389,
0.018954917788505554,
-0.029409924522042274,
-0.030054312199354172,
0.002817311091348529,
0.030874043703079224,
-0.07692176848649979,
0.04378259554505348,
0.02091621421277523,
0.026049308478832245,
0.020317746326327324,
-0.0038323577027767897,
-0.046167273074388504,
0.02478455938398838,
0.037319306284189224,
-0.029449893161654472,
-0.026666540652513504,
0.050632353872060776,
-0.04384595528244972,
0.024777831509709358,
0.024611003696918488,
-0.005803827662020922,
0.0288003608584404,
-0.06486785411834717,
-0.01303513441234827,
0.04764103516936302,
0.02777252346277237,
0.030283544212579727,
-0.007174653001129627,
0.0016729943454265594,
0.009317531250417233,
-0.042858682572841644,
0.02250482328236103,
0.04436066746711731,
-0.03014148212969303,
-0.050382908433675766,
-0.013793804682791233,
0.02346689999103546,
0.02338608354330063,
0.024123234674334526,
-0.03884221240878105,
0.0035537390504032373,
-0.011188778094947338,
-0.010777030140161514,
-0.026235854253172874,
-0.013552120886743069,
-0.05665745586156845,
0.05832858011126518,
-0.038775090128183365,
0.01730714738368988,
0.007806778885424137,
-0.04360499978065491,
-0.0484163798391819,
0.023619873449206352,
0.0010535700712352991,
-0.0916837528347969,
0.025821290910243988,
0.014686767011880875,
-0.06357893347740173,
0.015333354473114014,
0.015233431942760944,
-0.06786979734897614,
-0.025393644347786903,
0.007612084038555622,
0.024698931723833084,
-0.03171507269144058,
0.033222880214452744,
0.003320584539324045,
-0.028494257479906082,
-0.02025770954787731,
0.020850714296102524,
0.044583726674318314,
-0.047624703496694565,
-0.006019541062414646,
0.006450166925787926,
-0.013466387055814266,
-0.02724243700504303,
-0.00891634076833725,
-0.05027860403060913,
-0.011552384123206139,
-0.033826302736997604,
0.05548745393753052,
-0.013018560595810413,
-0.021226488053798676,
0.0010218294337391853,
-0.00623032683506608,
0.00722428597509861,
0.0331866592168808,
-0.011071923188865185,
0.016820775344967842,
-0.03285648301243782,
0.006141236051917076,
-0.07576889544725418,
0.025346098467707634,
0.017180196940898895,
-0.056441135704517365,
-0.07851138710975647,
0.00613625580444932,
0.020451122894883156,
0.007423707749694586,
-0.034324515610933304,
-0.01172835286706686,
0.0039048725739121437,
-0.032936178147792816,
-0.03957393020391464,
0.012714184820652008,
0.004281926434487104,
0.024582156911492348,
-0.06405693292617798,
-0.014932842925190926,
-0.024355629459023476,
-0.023148711770772934,
-0.0016149276634678245,
0.006406974513083696,
0.06455489248037338,
0.050806012004613876,
0.04340828210115433,
0.026264578104019165,
-0.06687254458665848,
-0.013707895763218403,
0.017856651917099953,
-0.011737159453332424,
0.015135286375880241,
0.004865131340920925,
0.014059704728424549,
-0.01929616555571556,
0.03558355197310448,
0.00364444637671113,
-0.04981677606701851,
-0.012623691000044346,
-0.01724673993885517,
-0.011910079047083855,
-0.01101381704211235,
0.058455176651477814,
-0.003782179905101657,
0.023343918845057487,
0.024489380419254303,
-0.058683283627033234,
0.08634557574987411,
0.007276608143001795,
-0.08685218542814255,
-0.039950575679540634,
0.06349769234657288,
-0.08298313617706299,
-0.07343296706676483,
-0.03488190099596977,
0.03649640455842018,
0.031767163425683975,
-0.04773746058344841,
0.02083280123770237,
0.03664311766624451,
-0.021627338603138924,
0.006949140690267086,
-0.00448607187718153,
-0.006088127847760916,
0.021394528448581696,
0.0037224125117063522,
-0.04457184299826622,
0.017538897693157196,
0.011712008155882359,
0.01139085367321968,
-0.03913892060518265,
0.020715925842523575,
-0.008020995184779167,
0.03307964652776718,
-0.03728858754038811,
0.023806968703866005,
0.006660489831119776,
-0.0007932805456221104,
0.06502778828144073,
0.01995604671537876,
0.025673240423202515,
0.017895467579364777,
0.026597997173666954,
-0.01813286356627941,
-0.006920178420841694,
-0.006476156879216433,
0.009841752238571644,
0.004895567428320646,
0.02028828114271164,
0.05746660754084587,
-0.0016172740142792463,
0.03914967551827431,
-0.021916920319199562,
-0.03395753726363182,
-0.029349422082304955,
0.06614310294389725,
-0.032356902956962585,
-0.02059497870504856,
-0.06902875751256943,
-0.023588286712765694,
-0.023810064420104027,
0.03417687118053436,
-0.0447106659412384,
0.03425931558012962,
-0.018097322434186935,
0.012039401568472385,
-0.046430639922618866,
-0.04495292156934738,
-0.006418297532945871,
-0.07292744517326355,
0.09141163527965546,
0.0018626591190695763,
-0.03703422471880913,
-0.026648903265595436,
-0.019583942368626595,
0.03854633495211601,
0.026638539507985115,
-0.019938310608267784,
-0.02830415591597557,
0.044686898589134216,
0.048515740782022476,
0.031598277390003204,
-0.04269292578101158,
-0.04145305976271629,
0.0035174491349607706,
0.05441466346383095,
0.04264100641012192,
-0.0014508188469335437,
0.01660321094095707,
0.0415603406727314,
0.005936538800597191,
0.02301691100001335,
-0.013722645118832588,
-0.0032511516474187374,
-0.034847572445869446,
-0.028439654037356377,
0.01674763113260269,
0.036632440984249115,
-0.07217493653297424,
0.04764937609434128,
-0.025424810126423836,
-0.04236245155334473,
-0.0014014891348779202,
-0.054349347949028015,
0.06960619240999222,
-0.041497811675071716,
-0.04598693922162056,
0.02712247520685196,
-0.014495553448796272,
-0.007781648077070713,
-0.02285207062959671,
0.03809462860226631,
-0.04572969675064087,
0.006051794625818729,
0.03715319186449051,
0.019200917333364487,
0.03481312468647957,
0.0191955603659153,
0.07028820365667343,
0.035766180604696274,
0.045244768261909485,
-0.03029816225171089,
-0.016403280198574066,
0.04776788130402565,
-0.019355408847332,
0.01994890347123146,
0.03306671604514122,
-0.013808946125209332,
0.02328355982899666,
0.004145512823015451,
0.008381388150155544,
-0.07529222965240479,
0.05709510296583176,
0.023110253736376762,
-0.007754031103104353,
0.041071292012929916,
0.0764208510518074,
0.029293200001120567,
0.03330472484230995,
-0.014402623288333416,
0.006678469479084015,
0.015691984444856644,
0.010005111806094646,
0.009824574925005436,
0.022538432851433754,
0.05403325706720352,
-0.008881375193595886,
-0.021101098507642746,
-0.020459214225411415,
0.06112808361649513,
0.04274811968207359,
0.019208548590540886,
-0.045565031468868256,
0.03683562949299812,
-0.0175685565918684,
0.004119487479329109,
0.011514237150549889,
-0.07889468967914581,
0.04138774052262306,
0.08688032627105713,
-0.04719110205769539,
-0.04941793903708458,
-0.0037742655258625746,
-0.015070569701492786,
-0.03360017389059067,
-0.028611108660697937,
-0.013442772440612316,
-0.0089934216812253,
0.027617381885647774,
-0.02055683173239231,
-0.042680609971284866,
-0.007572661153972149,
0.01933448389172554,
0.011495049111545086,
0.01349618099629879,
0.06839833408594131,
-0.01430591382086277,
0.030109446495771408,
-0.01567705161869526,
-0.04898259788751602,
-0.019763300195336342,
-0.005646135658025742,
-0.028340982273221016,
0.002310575917363167,
0.05768126994371414,
0.03326518461108208,
0.00924153346568346,
0.08621787279844284,
0.04714082553982735,
0.022828007116913795,
-0.04574096202850342,
-0.024353761225938797,
0.01235460676252842,
0.02427365444600582,
-0.040729083120822906,
-0.006974107585847378,
0.0528072789311409,
0.012327549047768116,
-0.0034256414510309696,
0.0024386148434132338,
-0.013027441687881947,
0.009961705654859543,
-0.043747637420892715,
-0.03176049515604973,
-0.05562903732061386,
-0.014881565235555172,
-0.011764423921704292,
-0.01210438460111618,
-0.02264893241226673,
0.08513285219669342,
-0.044633861631155014,
-0.09610894322395325,
-0.043204810470342636,
0.09081567823886871,
0.005086839664727449,
0.04583818465471268,
0.05281499773263931,
0.0174566637724638,
-0.03383082523941994,
-0.04923059791326523,
0.04531487077474594,
-0.06495608389377594,
0.021673258394002914,
-0.008153105154633522,
-0.07593120634555817,
0.03712119534611702,
0.024412615224719048,
0.011592944152653217,
0.007737672887742519,
0.0008045061840675771,
0.04216306656599045,
-0.008673842065036297,
0.016387606039643288,
-0.021628553047776222,
0.0023803384974598885,
0.004801553208380938,
-0.043506208807229996,
0.008906081318855286,
-0.06315042823553085,
-0.0073724729008972645,
-0.022231854498386383,
0.015687989071011543,
-0.02412068285048008,
-0.06247517839074135,
0.030215764418244362,
-0.06026940420269966,
0.04181012138724327,
0.02716953307390213,
-0.024288920685648918,
-0.07297160476446152,
0.01511157862842083,
0.05679876729846001,
0.04577299952507019,
-0.02209191769361496,
0.029968788847327232,
0.006612610537558794,
0.01868549734354019,
0.06257739663124084,
0.0010569053702056408,
-0.021716969087719917,
-0.03578264266252518,
0.00812972616404295,
-0.025474946945905685,
0.022213777527213097,
-0.03224572911858559,
0.016315996646881104,
-0.028691302984952927,
0.02860892377793789,
-0.018709076568484306,
0.03931354731321335,
0.011475509963929653,
-0.06185345724225044,
0.037688057869672775,
0.016200074926018715,
-0.05285574868321419,
-0.00485855620354414,
0.02655426412820816,
-0.03936077654361725,
0.10058735311031342,
0.01696047931909561,
-0.002688666572794318,
-0.0034195808693766594,
0.02758503518998623,
0.028305815532803535,
0.02269933745265007,
0.046226318925619125,
0.001696320017799735,
0.04145176708698273,
0.02175043523311615,
-0.0546266995370388,
0.047516774386167526,
0.005022284109145403,
-0.009886851534247398,
-0.008366196416318417,
-0.046578776091337204,
-0.009089192375540733,
-0.0707574337720871,
-0.019133364781737328,
-0.06449322402477264,
-0.011065690778195858,
0.055070146918296814,
-0.0469956137239933,
-0.027773592621088028,
0.016502054408192635,
0.006521754898130894,
-0.025883888825774193,
0.06870979815721512,
0.029195798560976982,
-0.010359941981732845,
-0.0028675938956439495,
0.08111155778169632,
-0.00006826758908573538,
-0.004010648000985384,
0.011413086205720901,
0.003343135118484497,
0.00665285112336278,
0.01006102841347456,
-0.02833194099366665,
-0.0010053688893094659,
-0.014298365451395512,
-0.013904377818107605,
-0.020185958594083786,
0.025224866345524788,
-0.002869411138817668,
-0.014879077672958374,
-0.009966272860765457,
0.029855381697416306,
-0.013744981028139591,
0.00822394248098135,
-0.005120688118040562,
-0.01448074821382761,
-0.03426327556371689,
0.026258599013090134,
0.06436239182949066,
0.0035814528819173574,
-0.014537708833813667,
-0.015295957215130329,
-0.006729811895638704,
-0.009974603541195393,
-0.028284644708037376,
-0.019052118062973022,
0.03057699277997017,
0.004697178024798632,
0.015054941177368164,
-0.0018937268760055304,
-0.044779788702726364,
-0.0041890633292496204,
0.004460248164832592,
0.021053100004792213,
0.0164895411580801,
-0.017499368637800217,
-0.0012145849177613854,
-0.014189123176038265,
-0.05071224644780159,
-0.01187228225171566,
-0.028017135336995125,
0.03307345137000084,
0.006430134177207947,
-0.024641692638397217,
-0.002633115742355585,
-0.019305961206555367,
-0.05253985524177551,
0.049381036311388016,
-0.021491169929504395,
-0.030172133818268776,
0.011805163696408272,
-0.022180100902915,
0.0008345782407559454,
-0.03584882244467735,
0.0019183222902938724,
0.017883434891700745,
0.0506681427359581,
-0.01984463445842266,
-0.05277835577726364,
0.05060110241174698,
-0.02687692828476429,
-0.02221691608428955,
0.01729517988860607,
0.017884131520986557,
-0.017937978729605675,
0.007416454143822193,
0.04046579822897911,
-0.027669576928019524,
0.006790423300117254,
0.03839310631155968,
0.05083980783820152,
0.07186504453420639,
-0.05830325558781624,
-0.07326066493988037,
0.00813915953040123,
-0.04313274100422859,
0.010393097996711731,
0.07738524675369263,
0.028664710000157356,
-0.021612994372844696,
-0.025190679356455803,
-0.04562513902783394,
-0.01425584964454174,
0.008125797845423222,
0.02698507159948349,
-0.03330942988395691,
-0.03668034449219704,
0.028863657265901566,
-0.0779251754283905,
-0.010231643915176392,
-0.004459918476641178,
0.035802703350782394,
-0.020145364105701447,
-0.0072837211191654205,
-0.044503968209028244,
0.006579041481018066,
0.026754431426525116,
-0.02222643606364727
] |
<p>I'm reading <a href="http://arxiv.org/abs/gr-qc/9804087" rel="nofollow">an article</a> which includes the following equation involving a perturbed metric:</p>
<p>$$G_{AB} = \eta_{AB} + \overset{1}{\gamma}_{AB} + 2\overset{1}{\chi}_{(A,B)}\tag{4.1}$$</p>
<p>I don't understand how this equation was obtained; in particular, I don't understand how was obtained the third summand. Is there some literature explaining how this was obtained, or can you explain where it came from?</p> | g4813 | [
0.06385478377342224,
0.009875322692096233,
-0.04342157393693924,
-0.03662576153874397,
0.060525767505168915,
0.016414150595664978,
0.06779403239488602,
-0.0008437366923317313,
-0.0686836987733841,
-0.015334094874560833,
-0.007663769647479057,
0.03074272908270359,
0.03612281009554863,
-0.07977958768606186,
0.039323557168245316,
-0.03680117055773735,
0.05801529064774513,
0.06495033204555511,
-0.013116943649947643,
0.011179397813975811,
-0.03523268923163414,
-0.036204636096954346,
0.046861302107572556,
-0.044285643845796585,
0.09826619178056717,
-0.0915435403585434,
0.04460811987519264,
-0.003104454604908824,
-0.07474104315042496,
-0.03228574991226196,
-0.05008421093225479,
0.04215311259031296,
0.034693729132413864,
-0.018736280500888824,
-0.017163623124361038,
0.015537031926214695,
0.06153657287359238,
0.024764658883213997,
-0.008867770433425903,
-0.011878053657710552,
-0.014150666072964668,
-0.00021772427135147154,
0.01406842190772295,
0.017553851008415222,
0.006028592586517334,
0.011855575256049633,
0.00687113031744957,
0.015288733877241611,
0.0005837755161337554,
0.012066185474395752,
-0.04075540229678154,
0.03285011649131775,
0.009003548882901669,
-0.03267596662044525,
-0.020903076976537704,
0.07400896400213242,
0.07842519134283066,
-0.08057010918855667,
0.050686564296483994,
0.056913480162620544,
-0.039513297379016876,
-0.08296884596347809,
-0.00012695501209236681,
-0.0024909304920583963,
0.07133055478334427,
-0.08686207234859467,
-0.028957268223166466,
-0.03481727093458176,
0.022392379119992256,
-0.02106456831097603,
0.015630541369318962,
-0.015769898891448975,
0.04948785528540611,
-0.0550779365003109,
0.01206580176949501,
0.017489604651927948,
0.007161759305745363,
-0.028715087100863457,
-0.034887831658124924,
0.020934512838721275,
0.014310715720057487,
0.032200925052165985,
0.028416790068149567,
0.0058320690877735615,
0.004394362680613995,
0.021473200991749763,
0.027417922392487526,
0.008994098752737045,
-0.037633731961250305,
-0.030256103724241257,
0.04562179371714592,
-0.036468107253313065,
0.021424675360322,
-0.047291263937950134,
-0.02175327017903328,
-0.04744930937886238,
-0.018676718696951866,
0.02525830827653408,
-0.0198165625333786,
0.023043369874358177,
-0.024791892617940903,
0.00938845332711935,
0.0041640568524599075,
0.005685868207365274,
0.011173849925398827,
0.04178377240896225,
0.03294903412461281,
0.03283953294157982,
-0.029271632432937622,
-0.011733993887901306,
-0.04301917552947998,
-0.020315172150731087,
0.0018308483995497227,
-0.04760564863681793,
-0.04298067465424538,
-0.027355968952178955,
-0.04870814457535744,
0.026372769847512245,
0.02263588272035122,
0.006121957208961248,
-0.03471434488892555,
0.021672183647751808,
-0.015215586870908737,
0.031102025881409645,
0.008337658829987049,
0.04689405858516693,
0.043983735144138336,
0.03443020209670067,
0.07310575991868973,
-0.01573084481060505,
0.024502383545041084,
-0.057830408215522766,
0.055602118372917175,
0.01221291534602642,
-0.005575433373451233,
0.06559958308935165,
-0.01216138992458582,
0.05746791511774063,
-0.05470043048262596,
0.0572807714343071,
-0.01993236318230629,
-0.07321563363075256,
0.04538055509328842,
-0.041557881981134415,
-0.019556760787963867,
0.055910203605890274,
-0.00524461455643177,
-0.03646426275372505,
0.00886294525116682,
-0.0588376447558403,
-0.01091319601982832,
0.03393598273396492,
0.0023529583122581244,
-0.029373610392212868,
0.02355850860476494,
-0.000667007640004158,
0.03948809579014778,
-0.010246713645756245,
-0.022703031077980995,
0.012422377243638039,
0.004094087053090334,
-0.03302671015262604,
-0.007959574460983276,
0.024350887164473534,
-0.03683578222990036,
0.05107961222529411,
0.060788631439208984,
-0.03808838129043579,
-0.030325280502438545,
-0.05428273603320122,
0.025403449311852455,
0.0026923026889562607,
-0.011905577965080738,
0.028356358408927917,
0.04624296724796295,
0.09066835045814514,
0.014597970992326736,
-0.019404560327529907,
0.001785573549568653,
-0.04669628664851189,
-0.022194840013980865,
-0.04901649430394173,
0.0413224957883358,
-0.02879457175731659,
0.016061946749687195,
0.017369307577610016,
-0.021486476063728333,
0.011384280398488045,
0.010460328310728073,
0.05448724702000618,
-0.05283668264746666,
0.025089969858527184,
0.06377457827329636,
0.04302733391523361,
0.017041148617863655,
0.05905555188655853,
0.04742378741502762,
-0.07586576044559479,
0.024432137608528137,
0.0628114715218544,
-0.016738416627049446,
-0.002575031714513898,
0.02551867999136448,
-0.012217666022479534,
0.027569977566599846,
-0.0008591681253165007,
-0.03246261551976204,
0.022778095677495003,
0.07483918964862823,
-0.025833284482359886,
-0.07608552277088165,
-0.003230567555874586,
0.04658157005906105,
-0.004010780714452267,
-0.04522344470024109,
-0.016478359699249268,
0.012958881445229053,
0.012437094934284687,
0.009860743768513203,
0.027198640629649162,
-0.023530153557658195,
-0.000373062735889107,
0.03425683453679085,
0.02254105731844902,
-0.02062097005546093,
0.04361448064446449,
-0.03541716933250427,
-0.009914486669003963,
-0.014256936497986317,
0.010797832161188126,
-0.01489903312176466,
-0.0795687884092331,
-0.03317350149154663,
-0.03404323384165764,
0.0266998503357172,
0.030905315652489662,
0.005600775592029095,
0.017097216099500656,
0.009275092743337154,
0.01606071926653385,
-0.011202278546988964,
-0.03069685772061348,
0.0048949941992759705,
0.007397832348942757,
0.00732902018353343,
0.0399286262691021,
0.042040370404720306,
0.0028508249670267105,
-0.03761948645114899,
0.01583140715956688,
0.010300957597792149,
-0.01753191277384758,
0.027469325810670853,
-0.04494805261492729,
-0.00622343085706234,
-0.01296753715723753,
0.021082133054733276,
-0.044447604566812515,
-0.026354685425758362,
0.01632501929998398,
-0.024516383185982704,
-0.04393799975514412,
0.035658858716487885,
-0.025221455842256546,
-0.004670204594731331,
-0.04530244693160057,
-0.023226479068398476,
-0.01941722445189953,
-0.006010829005390406,
0.018559152260422707,
-0.035289276391267776,
0.03211410716176033,
0.003379025962203741,
-0.0045410627499222755,
-0.03888891264796257,
-0.046400509774684906,
0.021161992102861404,
-0.026374157518148422,
0.02509920485317707,
-0.0027588591910898685,
-0.007699030451476574,
-0.0016846981598064303,
-0.05154063180088997,
0.00434359535574913,
0.03404240310192108,
-0.058970220386981964,
-0.02113443799316883,
0.04464747756719589,
0.037248801440000534,
-0.024284305050969124,
-0.03424118459224701,
0.03369990363717079,
0.020058248192071915,
-0.0269129890948534,
0.012391406111419201,
0.0023534127976745367,
-0.04344949871301651,
-0.028667563572525978,
0.003629429964348674,
-0.040006373077631,
-0.01606862246990204,
0.028463883325457573,
-0.040571268647909164,
-0.05229146033525467,
0.07672453671693802,
-0.039735097438097,
-0.02668743021786213,
-0.06486363708972931,
-0.0007871661800891161,
0.07323157787322998,
-0.026202727109193802,
-0.07201524823904037,
0.041483670473098755,
0.004334540572017431,
-0.021222220733761787,
0.005056988913565874,
-0.046103183180093765,
-0.047697510570287704,
0.0198336411267519,
-0.020321110263466835,
-0.014569735154509544,
-0.0718236193060875,
-0.04829927533864975,
0.039201583713293076,
-0.013903077691793442,
-0.054268330335617065,
-0.022453583776950836,
0.03673803433775902,
-0.012925342656672001,
0.01067142654210329,
0.044564973562955856,
-0.052251726388931274,
0.019560184329748154,
-0.027380147948861122,
0.03519485890865326,
-0.014168743044137955,
0.0015415697125717998,
0.0655631497502327,
0.024474764242768288,
-0.04820980131626129,
0.005928826984018087,
-0.06874986737966537,
-0.017044877633452415,
-0.0786643847823143,
-0.02359464392066002,
0.006775352638214827,
0.033181555569171906,
0.03619351238012314,
0.003892365610226989,
-0.0005251157563179731,
0.021461347118020058,
0.01916634663939476,
-0.004951755981892347,
-0.01397036761045456,
0.0217108316719532,
0.03445272892713547,
0.0008938268292695284,
0.028116727247834206,
0.020114250481128693,
-0.03037475235760212,
0.000474647298688069,
-0.053776815533638,
-0.02623412199318409,
0.025468701496720314,
0.06610749661922455,
-0.010126013308763504,
-0.0024171224795281887,
0.017506321892142296,
-0.03578516095876694,
-0.04665090888738632,
0.011927781626582146,
-0.025706086307764053,
0.01785215176641941,
0.017486967146396637,
0.01943826861679554,
-0.06631826609373093,
-0.02721186727285385,
0.00883572455495596,
-0.014015225693583488,
0.010947780683636665,
0.015213881619274616,
-0.015222451649606228,
0.021220296621322632,
-0.0008633514516986907,
-0.01066507026553154,
0.008402747102081776,
-0.006638239603489637,
-0.03004785254597664,
-0.011715413071215153,
-0.07663396745920181,
-0.01675892248749733,
-0.013183174654841423,
-0.011400504969060421,
0.035987161099910736,
-0.006701643578708172,
-0.004014885518699884,
-0.026080012321472168,
0.034121785312891006,
-0.04303710162639618,
0.048180751502513885,
-0.03197959065437317,
0.05154387280344963,
0.019394315779209137,
-0.008370106108486652,
-0.10286245495080948,
-0.023968154564499855,
0.04852718114852905,
0.02714836411178112,
0.057061150670051575,
0.0008741060737520456,
-0.014192949049174786,
0.023739315569400787,
-0.0032362411729991436,
-0.09804926067590714,
0.028733057901263237,
-0.009875318966805935,
0.07141641527414322,
0.02893572486937046,
-0.042441658675670624,
-0.027179405093193054,
-0.028836434707045555,
-0.05065631493926048,
0.025200214236974716,
0.009868979454040527,
0.038864217698574066,
0.06659179925918579,
-0.000670558016281575,
0.008031100034713745,
-0.0199343953281641,
0.04278639703989029,
0.013670511543750763,
-0.0014563273871317506,
-0.040830325335264206,
0.0643935427069664,
-0.043082643300294876,
0.010537231341004372,
-0.06395464390516281,
0.06096836179494858,
-0.005082597024738789,
-0.018100544810295105,
0.06689774990081787,
-0.003963531460613012,
-0.00774823734536767,
-0.08257326483726501,
0.056184012442827225,
-0.009535894729197025,
-0.002058829180896282,
-0.04853416979312897,
0.03251513093709946,
-0.02009757235646248,
0.01963505521416664,
-0.04869720712304115,
0.04269643500447273,
-0.01451305951923132,
-0.006866106763482094,
0.0022119286004453897,
0.017214206978678703,
0.016946159303188324,
-0.0010666893795132637,
0.010586857795715332,
-0.03358384966850281,
-0.056771889328956604,
-0.004075472708791494,
0.03850262612104416,
0.09103669226169586,
-0.0626513883471489,
0.03980298712849617,
0.057334054261446,
-0.06943918764591217,
-0.02009008824825287,
-0.0005770133575424552,
0.02480621635913849,
-0.024366626515984535,
-0.024548659101128578,
-0.053913578391075134,
0.027910379692912102,
-0.05380687117576599,
0.0071509829722344875,
-0.035097602754831314,
0.016523879021406174,
-0.0027437228709459305,
-0.005440516397356987,
0.004155335947871208,
-0.034892305731773376,
-0.017969610169529915,
0.012794348411262035,
0.023378048092126846,
-0.05720153823494911,
-0.01830662228167057,
0.03454301878809929,
0.007376621477305889,
-0.0013257371028885245,
0.026980437338352203,
-0.012497597374022007,
-0.04474826529622078,
-0.02112683095037937,
-0.007002378813922405,
-0.0006612717406824231,
0.04916346073150635,
0.028096796944737434,
-0.06809566169977188,
0.046889789402484894,
-0.036395058035850525,
0.007105004042387009,
0.007404134143143892,
0.055562764406204224,
0.05178593844175339,
-0.018766066059470177,
0.03098718822002411,
0.0280747190117836,
0.02672874927520752,
-0.03944683447480202,
0.046093277633190155,
0.0436251275241375,
-0.002426075516268611,
0.014230016618967056,
0.006273415870964527,
-0.003120824694633484,
-0.009692171588540077,
-0.035098496824502945,
0.030317503958940506,
0.007626206614077091,
0.0025397122371941805,
0.00377816054970026,
0.028395099565386772,
-0.011944115161895752,
-0.05368201062083244,
0.0034397414419800043,
0.016405697911977768,
0.005969136022031307,
-0.021470893174409866,
-0.010988308116793633,
0.011710373684763908,
0.01612475886940956,
0.10751340538263321,
-0.010367030277848244,
-0.024778591468930244,
0.05728466808795929,
0.03884182497859001,
-0.01477053016424179,
-0.00034972321009263396,
-0.09428653866052628,
0.011126005090773106,
0.07615534216165543,
0.03280363976955414,
-0.035346124321222305,
-0.028345132246613503,
0.02673150785267353,
0.02376694604754448,
-0.006628777831792831,
0.06057048961520195,
-0.03630870580673218,
0.05184953287243843,
0.0075374203734099865,
0.036140769720077515,
0.0006794609944336116,
0.012884063646197319,
0.005087392870336771,
-0.024187250062823296,
-0.04250749945640564,
-0.044015541672706604,
-0.030479254201054573,
0.026742422953248024,
0.05602053552865982,
0.0023844472598284483,
-0.10871237516403198,
-0.03657468035817146,
0.02435275726020336,
0.01992127299308777,
0.0897904485464096,
0.005349380429834127,
0.012336703017354012,
0.025605402886867523,
0.06189116835594177,
0.05810823664069176,
0.04203963652253151,
-0.014482191763818264,
-0.005875061731785536,
-0.009926948696374893,
0.04007085785269737,
-0.001682157744653523,
0.014091363176703453,
0.024746762588620186,
-0.08021192252635956,
-0.019840478897094727,
0.0368385836482048,
0.004836549051105976,
0.019384538754820824,
0.047310736030340195,
0.007614581845700741,
0.014323009178042412,
-0.011511128395795822,
-0.07887081056833267,
-0.03276301547884941,
-0.006885158363729715,
-0.012022522278130054,
0.009413596242666245,
-0.009795795194804668,
-0.00988373439759016,
-0.027667934074997902,
0.018936585634946823,
0.01544574648141861,
-0.014436011202633381,
0.03472360223531723,
0.04419456049799919,
-0.0239458866417408,
0.006443152204155922,
-0.03768058493733406,
-0.014085243456065655,
-0.02048000507056713,
0.027318747714161873,
0.01347208023071289,
-0.042881034314632416,
0.019551515579223633,
-0.006095597054809332,
-0.04552100598812103,
0.025743622332811356,
0.03278697282075882,
-0.016261694952845573,
-0.014663043431937695,
0.032622020691633224,
-0.027246510609984398,
0.057045236229896545,
-0.022624049335718155,
0.022449035197496414,
0.02398740127682686,
0.0726984366774559,
0.01205452624708414,
0.020633874461054802,
0.021702617406845093,
0.0034443873446434736,
0.0421065054833889,
-0.03899545222520828,
-0.0286432895809412,
-0.01356660295277834,
0.008268548175692558,
-0.037496745586395264,
0.04004421830177307,
0.0176075529307127,
0.054777953773736954,
-0.04587635397911072,
0.044775620102882385,
0.0019500779453665018,
-0.05331772193312645,
-0.06354328989982605,
0.029147759079933167,
0.05715117231011391,
0.04853519797325134,
-0.03344713896512985,
-0.03855843096971512,
0.030639799311757088,
-0.016460929065942764,
0.002538088709115982,
0.04829391464591026,
-0.020930681377649307,
0.0005982281873002648,
-0.013431340456008911,
0.02019289880990982,
0.06648171693086624,
-0.030671538785099983,
-0.06553343683481216,
0.028227360919117928,
0.04961078613996506,
0.08600930124521255,
0.011343950405716896,
0.03472571074962616,
0.005560221616178751,
-0.006896833889186382,
0.04698038101196289,
0.03118317201733589,
-0.009612718597054482,
-0.019230248406529427,
-0.014987720176577568,
0.0077742221765220165,
0.010476669296622276,
0.004454500507563353,
0.04647166654467583,
0.047472599893808365,
-0.003574573202058673,
-0.019962115213274956,
-0.003590765642002225,
0.03149031847715378,
-0.03720908612012863,
-0.0332624576985836,
-0.04490484669804573,
0.040486305952072144,
0.014259764924645424,
0.015918541699647903,
0.001597519381903112,
0.006640532519668341,
-0.054612431675195694,
0.06627479195594788,
-0.00640752911567688,
0.023641906678676605,
0.029829571023583412,
0.00786565151065588,
-0.035836558789014816,
0.03907952830195427,
-0.038909800350666046,
0.005072694271802902,
0.038774508982896805,
-0.04713893309235573,
-0.03307618573307991,
-0.04354911297559738,
-0.03998984023928642,
-0.027603402733802795,
0.03257107362151146,
-0.10388480126857758,
0.019275788217782974,
0.017229855060577393,
-0.03626735135912895,
-0.061094190925359726,
0.00022696384985465556,
0.013441173359751701,
0.013035711832344532,
0.021420182660222054,
-0.018069474026560783,
-0.012911995872855186,
-0.020412608981132507,
-0.006735300645232201,
-0.017316343262791634,
0.03150426223874092,
-0.022236406803131104,
-0.0911070927977562,
-0.0638868436217308,
-0.04172674939036369,
0.0033292165026068687,
-0.0076620914041996,
0.009830248542129993,
-0.0007161718676798046,
-0.020615801215171814,
-0.0613819845020771,
-0.036398209631443024,
0.0366145558655262,
-0.03385129198431969,
0.04030798375606537,
0.029524967074394226,
-0.0716521292924881,
0.032516952604055405,
0.009807898662984371,
0.01230552326887846,
-0.05589267984032631,
0.0079148905351758,
-0.027722012251615524,
0.030928513035178185,
0.02104584127664566,
-0.024625932797789574,
0.018446017056703568,
0.029966816306114197,
-0.05741189420223236,
0.05222805589437485,
0.059227097779512405,
0.045883625745773315,
0.0018717787461355329,
0.02571844309568405,
-0.011404323391616344,
0.0247152429074049,
0.01480878796428442,
0.02302786521613598,
-0.00815722718834877,
-0.04948538541793823,
-0.00954765547066927,
-0.04115327075123787,
-0.03403131663799286,
-0.025233712047338486,
-0.027538299560546875,
-0.02495753951370716,
-0.019478581845760345
] |
<blockquote>
<p>Given a delta function $\alpha\delta(x+a)$ and an infinite energy potential barrier at $[0,\infty)$, calculate the scattered state, calculate the probability of reflection as a function of $\alpha$, momentum of the packet and energy. Also calculate the probability of finding the particle between the two barriers.</p>
</blockquote>
<p>I start by setting up the standard equations for the wave function:</p>
<p>$$\begin{align}\psi_I &= Ae^{ikx}+Be^{-ikx} &&\text{when } x<-a, \\
\psi_{II} &= Ce^{ikx}+De^{-ikx} &&\text{when } -a<x<0\end{align}$$</p>
<p>The requirement for continuity at $x=-a$ means</p>
<p>$$Ae^{-ika}+Be^{ika}=Ce^{-ika}+De^{ika}$$</p>
<p>Then the requirement for specific discontinuity of the derivative at $x=-a$ gives</p>
<p>$$ik(-Ce^{-ika}+De^{ika}+Ae^{-ika}-Be^{ika}) = -\frac{2m\alpha}{\hbar^2}(Ae^{-ika}+Be^{ika})$$</p>
<p>At this point I set $A = 1$ (for a single wave packet) and set $D=0$ to calculate reflection and transmission probabilities. After a great deal of algebra I arrive at</p>
<p>$$\begin{align}B &= \frac{\gamma e^{-ika}}{-\gamma e^{ika} - 2ike^{ika}} & C &= \frac{2e^{-ika}}{\gamma e^{-ika} - 2ike^{-ika}}\end{align}$$</p>
<p>(where $\gamma = -\frac{2m\alpha}{\hbar^2}$) and so reflection prob. $R=\frac{\gamma^2}{\gamma^2+4}$ and transmission prob. $T=\frac{4}{\gamma^2+4}$.</p>
<p>Here's where I run into the trouble of figuring out the probability of finding the particle between the 2 barriers. Since the barrier at $0$ is infinite the only leak could be over the delta function barrier at $-a$. Would I want to use the previous conditions but this time set $A=1$ and $C=D$ due to the total reflection of the barrier at $0$ and then calculate $D^*D$?</p> | g4814 | [
-0.02684328332543373,
0.046253859996795654,
-0.0021065527107566595,
-0.035753458738327026,
0.028118452057242393,
0.018723631277680397,
0.07236108928918839,
0.05979714170098305,
-0.04667001962661743,
-0.027053356170654297,
0.005175916012376547,
0.05235204100608826,
-0.012738280929625034,
-0.007049511652439833,
0.023742061108350754,
-0.024841897189617157,
0.0881626233458519,
-0.01696852222084999,
0.007881173864006996,
0.024393126368522644,
-0.013563205488026142,
0.020241567865014076,
-0.05026637762784958,
-0.07045800983905792,
0.009026801213622093,
-0.021585075184702873,
0.01027944590896368,
-0.06803744286298752,
-0.07968416810035706,
0.01530924066901207,
0.00017656837007962167,
-0.029566949233412743,
0.05508184805512428,
-0.023316722363233566,
-0.023443913087248802,
-0.007931123487651348,
0.00916094146668911,
0.025068385526537895,
-0.008896656334400177,
0.012993416748940945,
0.010177130810916424,
0.012896356172859669,
-0.007940736599266529,
-0.026323655620217323,
0.019523367285728455,
0.05027853697538376,
0.0164136104285717,
0.010509014129638672,
-0.00984594039618969,
-0.022419551387429237,
-0.005192872602492571,
0.04963769391179085,
0.024609828367829323,
0.011363095603883266,
-0.05038263276219368,
0.07445573061704636,
0.04513981565833092,
-0.03649173676967621,
0.01649361290037632,
-0.005607223603874445,
0.029517056420445442,
-0.017969435080885887,
-0.0464647151529789,
-0.033177491277456284,
0.04963776841759682,
-0.06177143752574921,
-0.041669052094221115,
0.032891251146793365,
-0.006528428290039301,
-0.009658072143793106,
0.05146332457661629,
-0.061224307864904404,
0.033523786813020706,
-0.055207207798957825,
0.008192173205316067,
-0.0347287692129612,
0.0157461054623127,
-0.020192010328173637,
0.005423481576144695,
0.026582563295960426,
-0.0547451414167881,
-0.00012110557145206258,
0.01665855012834072,
0.029332799836993217,
0.015399621799588203,
0.03450915589928627,
-0.01853908784687519,
0.012991475872695446,
-0.04041288420557976,
-0.015759799629449844,
-0.025327567011117935,
-0.06440429389476776,
0.001247391221113503,
-0.020157940685749054,
0.06705428659915924,
0.007774290628731251,
-0.040388770401477814,
0.011168508790433407,
-0.012374557554721832,
-0.00465358467772603,
0.03382411226630211,
0.03239661827683449,
0.03848351538181305,
0.027296284213662148,
-0.0511653870344162,
-0.01224198192358017,
0.005369352642446756,
0.02830452285706997,
-0.022931566461920738,
-0.00158159458078444,
-0.028437647968530655,
-0.0336497463285923,
-0.04277898743748665,
-0.054462138563394547,
-0.00147237500641495,
0.012246095575392246,
0.007551298476755619,
0.0008259684545919299,
-0.04102813079953194,
0.0004721662844531238,
-0.019359668716788292,
0.008907007053494453,
-0.0014662212925031781,
0.08893086016178131,
0.020112687721848488,
0.007117787376046181,
-0.042603135108947754,
0.03144814074039459,
0.09292621165513992,
-0.0014794194139540195,
0.01602819934487343,
0.006570874713361263,
0.025821885094046593,
0.03159800171852112,
-0.014185648411512375,
-0.009063441306352615,
0.03928699344396591,
0.03239212557673454,
0.0012157175224274397,
0.020373979583382607,
-0.010066676884889603,
-0.005704519338905811,
-0.007567184511572123,
-0.003657758701592684,
-0.07632637023925781,
0.013913950882852077,
0.019560115411877632,
-0.05026062950491905,
-0.06838880479335785,
-0.026931924745440483,
-0.04138142243027687,
0.02615087665617466,
-0.041688840836286545,
0.03828669711947441,
0.021996594965457916,
-0.008027157746255398,
0.06511850655078888,
0.0009628310217522085,
-0.030652277171611786,
0.027776138857007027,
0.06603071093559265,
0.009197848848998547,
0.03289250284433365,
-0.04493164271116257,
-0.06059521064162254,
0.021622508764266968,
0.021815473213791847,
-0.0242922306060791,
0.003167420858517289,
-0.025028657168149948,
-0.011338239535689354,
0.0027111677918583155,
0.04020509496331215,
-0.003782003652304411,
0.003490590024739504,
0.07700397819280624,
-0.04897255077958107,
-0.0629192590713501,
0.015759551897644997,
0.01771053671836853,
-0.0005746057140640914,
-0.025906795635819435,
0.037913788110017776,
0.015114953741431236,
-0.02157801017165184,
-0.054676346480846405,
0.01900792121887207,
-0.01622338593006134,
-0.04163697361946106,
0.011794375255703926,
-0.04887004941701889,
0.000720387208275497,
0.026787538081407547,
0.007107392884790897,
-0.010551868937909603,
0.072514109313488,
0.10537800937891006,
-0.06313806027173996,
-0.0188234131783247,
-0.015414933674037457,
-0.038287755101919174,
0.06849130243062973,
0.06544129550457001,
0.02652551792562008,
0.0663084164261818,
0.011683115735650063,
0.03518354892730713,
0.02275058813393116,
-0.05585309490561485,
-0.01970575377345085,
-0.0030826556030660868,
-0.02058502845466137,
-0.047365475445985794,
-0.0034209878649562597,
0.06269863992929459,
-0.05959533154964447,
0.027237292379140854,
-0.018902016803622246,
-0.03733602911233902,
-0.001740546664223075,
-0.01828189194202423,
-0.008423397317528725,
0.03677145019173622,
-0.0005337775219231844,
-0.0443171001970768,
0.08668047189712524,
-0.03169528394937515,
-0.01801137998700142,
-0.047809429466724396,
0.06022213026881218,
-0.030535876750946045,
-0.04249051213264465,
-0.02621876448392868,
0.02066575363278389,
0.023943187668919563,
0.04041474312543869,
-0.02991626411676407,
0.019629033282399178,
-0.011055488139390945,
-0.031102782115340233,
0.03957580402493477,
-0.06128925457596779,
-0.07160061597824097,
0.010225558653473854,
0.022721322253346443,
-0.014790689572691917,
0.014790883287787437,
0.009822136722505093,
0.01884930394589901,
0.014126475900411606,
-0.009098739363253117,
-0.025531187653541565,
-0.040232349187135696,
0.020169846713542938,
-0.006519921123981476,
-0.07581072300672531,
-0.0054213982075452805,
0.0068172886967659,
0.007133507169783115,
-0.041662998497486115,
-0.012945950962603092,
-0.005056660622358322,
0.0011912987101823092,
-0.006052521988749504,
-0.07144305855035782,
0.02541298232972622,
-0.048647936433553696,
0.0563972182571888,
0.004734237212687731,
0.03370525315403938,
0.0013105649268254638,
0.0635177493095398,
0.07685135304927826,
0.016724027693271637,
0.005741678178310394,
-0.016850678250193596,
-0.040371786803007126,
-0.09386339783668518,
0.009909724816679955,
0.007765642832964659,
-0.05818929895758629,
0.0030235389713197947,
0.02221708372235298,
0.03919461742043495,
0.03820794075727463,
-0.05686196684837341,
0.02352050691843033,
0.07527187466621399,
0.05331103503704071,
0.04153458774089813,
-0.02828994020819664,
0.028166987001895905,
-0.01723482459783554,
-0.011314344592392445,
-0.025919385254383087,
0.03902173042297363,
0.009381243027746677,
-0.029916860163211823,
-0.04157676920294762,
-0.025405459105968475,
-0.03469747304916382,
0.06457410752773285,
-0.047822073101997375,
-0.01662791147828102,
0.060455214232206345,
-0.012386308051645756,
-0.004114573821425438,
0.037910908460617065,
0.033657461404800415,
0.044893790036439896,
0.022220252081751823,
0.03316931426525116,
0.05072612315416336,
-0.017831144854426384,
0.03794243186712265,
-0.001961939036846161,
0.006122607737779617,
0.019060447812080383,
0.0014280485920608044,
0.015631213784217834,
0.01810278929769993,
-0.02175029367208481,
0.030459294095635414,
-0.012338963337242603,
0.010175061412155628,
-0.007697350345551968,
-0.08439474552869797,
0.03869348764419556,
-0.048733681440353394,
0.03345876559615135,
0.04925625026226044,
0.016860293224453926,
0.044652409851551056,
-0.01923362724483013,
-0.03943643346428871,
-0.03169138729572296,
-0.037141114473342896,
0.02404201775789261,
0.02041858248412609,
0.0331757627427578,
0.0073712668381631374,
-0.014113161712884903,
-0.023543763905763626,
0.015616200864315033,
0.04962945729494095,
-0.05042581632733345,
0.04860911890864372,
0.06722746044397354,
0.007759445812553167,
0.0016528647392988205,
-0.0034411291126161814,
0.003083297051489353,
-0.01182597503066063,
0.05618114396929741,
0.016901500523090363,
0.02353256195783615,
-0.012671597301959991,
-0.0019344572210684419,
0.01584647409617901,
0.013142135925590992,
0.0004794544365722686,
-0.0348002128303051,
0.03311695531010628,
-0.02837299555540085,
0.034511271864175797,
-0.012916558422148228,
-0.006973476614803076,
0.0004848938842769712,
-0.0020505376160144806,
0.009570509195327759,
0.03845250606536865,
-0.029050564393401146,
-0.0011881687678396702,
0.0036631322000175714,
-0.03680329769849777,
-0.06108800694346428,
-0.037357836961746216,
-0.017623942345380783,
-0.025678284466266632,
0.035831402987241745,
-0.009475788101553917,
-0.013128806836903095,
0.015309476293623447,
0.04853992909193039,
0.07160213589668274,
0.026038991287350655,
0.013480648398399353,
-0.027759669348597527,
0.0039416709914803505,
-0.047289978712797165,
0.037954553961753845,
0.01605822704732418,
-0.040753621608018875,
0.04688573256134987,
-0.045760393142700195,
0.018012335523962975,
-0.0031801380682736635,
0.005035703536123037,
-0.08272784948348999,
0.022314883768558502,
-0.026602236554026604,
-0.002956974320113659,
-0.03860858827829361,
-0.026043236255645752,
0.011247682385146618,
-0.030413933098316193,
0.0350230373442173,
0.03072322905063629,
-0.006758515723049641,
-0.044351715594530106,
0.015034494921565056,
-0.021821435540914536,
-0.012517120689153671,
-0.0448024682700634,
-0.03582574054598808,
-0.020605584606528282,
0.0399186797440052,
-0.002126958454027772,
-0.026384683325886726,
-0.01634078286588192,
-0.03730037063360214,
-0.01418453361839056,
0.015412951819598675,
-0.025638030841946602,
0.03924589231610298,
0.02436814270913601,
0.07103465497493744,
0.010317090898752213,
0.010425835847854614,
-0.018860895186662674,
0.009682219475507736,
0.04455560818314552,
-0.05576948821544647,
0.026978248730301857,
-0.04544797167181969,
0.046723995357751846,
0.0009705443517304957,
-0.03307231515645981,
0.015592641197144985,
0.003984543960541487,
0.06962900608778,
-0.02422509342432022,
0.02198169007897377,
-0.01777670904994011,
0.024540241807699203,
0.11274973303079605,
-0.03842690587043762,
-0.09875516593456268,
0.03984912112355232,
0.002615314209833741,
-0.01323662605136633,
0.0011959392577409744,
0.0004623483691830188,
-0.045370448380708694,
-0.026297686621546745,
-0.06728719919919968,
-0.049440015107393265,
0.05864978954195976,
0.03692886233329773,
0.034149281680583954,
0.009889510460197926,
0.027263453230261803,
0.03257628530263901,
-0.048586681485176086,
0.011457225307822227,
-0.0014808067353442311,
0.008150601759552956,
0.043560225516557693,
-0.06310462951660156,
-0.032753683626651764,
0.013947290368378162,
0.07811982929706573,
0.02351248450577259,
-0.002752062864601612,
-0.028390023857355118,
0.011857675388455391,
-0.0640173926949501,
0.03503328189253807,
0.028280219063162804,
-0.00413428945466876,
-0.0031233213376253843,
0.005348353646695614,
-0.045739222317934036,
0.036715950816869736,
-0.009892059490084648,
0.007985180243849754,
-0.0459221787750721,
0.0030681295320391655,
-0.0005421007517725229,
-0.0037956254091113806,
0.06094706431031227,
-0.027448466047644615,
-0.0063058738596737385,
-0.025454891845583916,
0.04191678762435913,
-0.01984189823269844,
0.02110794559121132,
0.012067072093486786,
0.03150114789605141,
0.07780782878398895,
-0.02866150066256523,
-0.03694280982017517,
-0.018835345283150673,
-0.04699653759598732,
0.013669578358530998,
0.059357862919569016,
0.03444337472319603,
0.04251830652356148,
-0.0160817950963974,
-0.0024998821318149567,
-0.03286462649703026,
-0.040684595704078674,
-0.008581388741731644,
0.010484389029443264,
0.018490152433514595,
0.0441330224275589,
-0.08451596647500992,
-0.020059719681739807,
-0.0969349816441536,
-0.039814647287130356,
0.054655663669109344,
0.03689049184322357,
-0.015536767430603504,
0.034261323511600494,
0.024469949305057526,
-0.028094995766878128,
-0.045554835349321365,
-0.06630100309848785,
-0.05559816583991051,
-0.014142066240310669,
0.014368665404617786,
0.018269222229719162,
-0.035032037645578384,
-0.008230322040617466,
0.005957921966910362,
-0.07227050513029099,
-0.023960500955581665,
0.00017930007015820593,
0.01973613351583481,
-0.01173058245331049,
0.013807049952447414,
-0.007918153889477253,
0.0256875678896904,
0.05598900839686394,
-0.04176966845989227,
0.0010855443542823195,
-0.03263615071773529,
-0.0071744248270988464,
-0.006243125069886446,
-0.012732810340821743,
0.0450805127620697,
-0.029843628406524658,
-0.019698942080140114,
-0.026436129584908485,
0.0451061986386776,
0.007632511667907238,
0.025976723060011864,
-0.020920226350426674,
-0.028072426095604897,
0.026836443692445755,
0.015539096668362617,
-0.012417140416800976,
-0.010682289488613605,
0.004207788035273552,
0.005069774109870195,
-0.05255971476435661,
-0.02087644673883915,
0.01287059672176838,
0.00007225690933410078,
0.01694454811513424,
-0.005253038834780455,
0.018044553697109222,
-0.030504919588565826,
0.02666069194674492,
0.029257001355290413,
0.07043106853961945,
-0.056831736117601395,
-0.06882643699645996,
-0.06274192035198212,
0.003145489376038313,
-0.04873578995466232,
0.03753088414669037,
0.02655605599284172,
-0.01142000313848257,
-0.014829500578343868,
0.02338535338640213,
-0.030056187883019447,
-0.09823393821716309,
0.029966088011860847,
-0.036994460970163345,
-0.023684827610850334,
-0.058041419833898544,
0.0587209016084671,
-0.004554688464850187,
-0.026757191866636276,
-0.0444805733859539,
0.0565524622797966,
-0.029478607699275017,
-0.015414383262395859,
0.036214180290699005,
-0.006838786415755749,
-0.034870076924562454,
0.01732935570180416,
-0.009952593594789505,
-0.033791977912187576,
0.024509986862540245,
-0.012409904040396214,
0.001060888753272593,
-0.003952675964683294,
0.03041110746562481,
0.02694625034928322,
0.0026631217915564775,
0.040245477110147476,
0.006014117505401373,
-0.014319396577775478,
-0.026359334588050842,
-0.05281282588839531,
0.041541919112205505,
-0.0027558435685932636,
0.01788121834397316,
0.06578241288661957,
0.03470812737941742,
0.012172076851129532,
-0.040341008454561234,
0.04154618829488754,
0.01578512042760849,
-0.04508153721690178,
-0.044369980692863464,
0.04150989651679993,
0.029044950380921364,
0.08048795163631439,
-0.0527888648211956,
0.014920101501047611,
0.0396186001598835,
-0.04532073810696602,
0.016743959859013557,
-0.0090895164757967,
0.07513256371021271,
-0.0048530614003539085,
0.06697670370340347,
-0.008935357443988323,
0.08325963467359543,
0.04682660847902298,
0.04252583160996437,
-0.03952469304203987,
-0.00371112790890038,
0.042928390204906464,
-0.013259755447506905,
-0.11481673270463943,
-0.011030404828488827,
0.013930203393101692,
0.013996565714478493,
-0.006515024695545435,
-0.008636068552732468,
-0.05179531127214432,
0.025960203260183334,
0.046942781656980515,
-0.005347373429685831,
0.01847185753285885,
-0.026072712615132332,
-0.009475667029619217,
-0.07968855649232864,
-0.04196397215127945,
-0.011043657548725605,
-0.003968631383031607,
0.021304603666067123,
0.04590264707803726,
-0.02005145512521267,
0.004287805873900652,
-0.05733136832714081,
0.013059026561677456,
-0.057960595935583115,
-0.08947215229272842,
0.005052690859884024,
-0.01736242137849331,
0.013107764534652233,
0.07180006802082062,
0.012173360213637352,
-0.044832419604063034,
-0.008055304177105427,
0.006963180378079414,
0.026998715475201607,
-0.03966039791703224,
0.01276610791683197,
0.00872737355530262,
0.030834684148430824,
0.010959704406559467,
-0.03197864443063736,
-0.012209258042275906,
0.02496642991900444,
-0.02300582453608513,
0.019473155960440636,
0.0418681837618351,
-0.061825431883335114,
-0.034166302531957626,
0.027172928676009178,
0.038964323699474335,
0.0459272600710392,
0.06560282409191132,
-0.023987220600247383,
-0.0319448783993721,
0.0036727776750922203,
0.04448968544602394,
-0.020888492465019226,
-0.03440197557210922,
-0.0015097380382940173,
-0.012811286374926567,
-0.026601517572999,
0.03066142089664936,
-0.017815906554460526,
0.07292531430721283,
0.006511186249554157,
-0.03524033725261688,
-0.016982829198241234,
-0.0037084491923451424,
0.030120715498924255,
-0.060904596000909805,
0.08359331637620926,
0.030993692576885223,
-0.018670188263058662,
0.07484743744134903,
-0.011608698405325413,
-0.017296623438596725,
-0.05220489948987961,
0.01958724856376648,
-0.029199417680501938,
-0.005374656058847904,
-0.032910868525505066,
0.016975848004221916,
0.010480952449142933,
-0.008674965240061283,
-0.012725607492029667,
-0.07874366641044617,
-0.04836701229214668,
-0.033064063638448715,
-0.03955340012907982,
0.030623087659478188,
-0.005208868999034166,
-0.02284558117389679,
0.024116897955536842,
0.01836778037250042,
0.0016332799568772316,
-0.032320886850357056,
0.009119272232055664,
0.016117263585329056,
0.004514429718255997,
-0.029911378398537636,
-0.005443464033305645,
-0.0019802087917923927,
0.008482669480144978,
0.03810393437743187,
0.02426818199455738,
-0.04272277280688286,
0.07901027798652649,
0.06209471821784973,
-0.08449743688106537,
0.026440374553203583,
0.02026587352156639,
0.02041340433061123,
-0.009386846795678139,
0.014573928900063038,
-0.02892393246293068,
-0.027486026287078857,
0.02404434233903885,
-0.012956571765244007,
-0.04280480369925499,
0.053750183433294296,
0.013896449469029903
] |
<p>I am looking at a spin 1/2 particle in a magnetic field. This has Hamiltonian
$$H=-\mu s\cdot B_0$$
For simplicity, assume $B_0=B_0\hat z$ so $H=-\mu B_0$. I then apply a perturbative magnetic field such that
$$V'=-\mu B_1 s_x$$
First I wanted to compute $E^{(1)}$
$$E^{(1)}_n=\langle\psi_n^{(0)}|-\mu B_1s_x|\psi_n^{(0)}\rangle=\mp \mu B_1 \hbar/2$$
Now I am looking to find the first order correction to the ground state wavefunction. I know that this is given as
$$\psi^{(1)}_n=\sum_{n\neq n'} \psi^{(0)}_{n'}\frac{\langle\psi_{n'}^{(0)}|-\mu B_1s_x|\psi_{n}^{(0)}\rangle}{E_n^{(0)}-E_{n'}^{(0)}}$$
I am confused as to how to treat the summation. The only term I would get is if $n=n'$, but that would be degerate. So I am thinking that this first order correction is 0. Is this correct?</p> | g4815 | [
0.020050466060638428,
-0.06033315137028694,
-0.01589316688477993,
-0.05728056654334068,
0.054837021976709366,
-0.030052175745368004,
0.05983634665608406,
0.08172786980867386,
-0.03311730548739433,
0.020208880305290222,
-0.01684434711933136,
0.026774335652589798,
-0.010264163836836815,
0.08364643901586533,
0.008715026080608368,
0.02944812923669815,
0.04509958252310753,
0.05729677528142929,
-0.04558481648564339,
-0.07863066345453262,
0.006334016099572182,
-0.0005234388518147171,
-0.02762681432068348,
-0.016703762114048004,
0.03428160771727562,
-0.05737306550145149,
0.018651440739631653,
-0.010178702883422375,
-0.02019866555929184,
0.02745492197573185,
-0.023025086149573326,
0.05072162672877312,
0.026119334623217583,
-0.027480093762278557,
-0.018918368965387344,
0.060274962335824966,
0.05042906478047371,
0.04873112961649895,
0.04262935742735863,
-0.011514184065163136,
0.03284575790166855,
-0.05149406939744949,
0.06638731807470322,
-0.020416539162397385,
0.04360174760222435,
-0.010018913075327873,
-0.026761233806610107,
-0.005895140580832958,
-0.04252229630947113,
0.04905485734343529,
-0.03817475214600563,
-0.0036865929141640663,
0.10663377493619919,
0.013002760708332062,
-0.026187442243099213,
0.026123046875,
-0.0006369647453539073,
-0.0453919917345047,
0.06656289100646973,
0.09178195893764496,
0.050718773156404495,
-0.033668290823698044,
-0.018466517329216003,
-0.022151244804263115,
-0.04107459634542465,
0.0013619371457025409,
-0.07359658926725388,
-0.004795224405825138,
0.007988103665411472,
0.016906147822737694,
0.004394244868308306,
-0.07302992790937424,
-0.021665358915925026,
-0.013397878035902977,
-0.01258780900388956,
0.005835056770592928,
-0.0002576973638497293,
-0.019671868532896042,
0.01728983409702778,
-0.008293301798403263,
-0.046496450901031494,
-0.06419182568788528,
0.06919009983539581,
0.0022213140036910772,
-0.00845146644860506,
-0.03839786350727081,
-0.0195662509649992,
0.04142512008547783,
-0.0063735744915902615,
0.03274569660425186,
0.01073832344263792,
0.007720992900431156,
0.016649220138788223,
0.008089705370366573,
0.03216848149895668,
-0.0413600318133831,
-0.02516944892704487,
-0.02429116703569889,
0.013868101872503757,
-0.00018540369637776166,
-0.054909832775592804,
0.011624841019511223,
0.005572103895246983,
-0.012059036642313004,
0.032776206731796265,
0.04214240238070488,
0.019302694126963615,
0.019711317494511604,
-0.0391698032617569,
0.0005505197332240641,
-0.014463364146649837,
-0.022784952074289322,
0.022913295775651932,
-0.047055117785930634,
-0.09838277846574783,
-0.013540972955524921,
0.027521071955561638,
-0.023520108312368393,
-0.019337529316544533,
0.050844185054302216,
0.029605073854327202,
-0.0007654405198991299,
0.004716502968221903,
0.07285013794898987,
-0.003801122307777405,
-0.022995224222540855,
-0.08297989517450333,
0.01575670950114727,
0.0428033284842968,
0.002999458461999893,
-0.009048265404999256,
-0.004444646183401346,
0.048980582505464554,
0.04402938857674599,
-0.02369917742908001,
0.007388426456600428,
0.02368967980146408,
0.020625388249754906,
-0.03150475397706032,
0.007292985450476408,
-0.005204280838370323,
-0.07265429198741913,
0.07511764019727707,
-0.022754542529582977,
-0.0011429646983742714,
0.002250943798571825,
0.06293628364801407,
-0.0665653645992279,
0.02836187183856964,
0.03308277204632759,
0.008579757064580917,
0.046805668622255325,
0.006178094539791346,
0.043807245790958405,
0.024109112098813057,
0.0016914475709199905,
0.05669856816530228,
-0.008438743650913239,
0.007081207353621721,
0.04633020609617233,
-0.00041446759132668376,
0.03257879614830017,
-0.008912772871553898,
0.05241319164633751,
-0.016310490667819977,
0.011083852499723434,
0.06841709464788437,
-0.05651290714740753,
-0.0281171016395092,
-0.05013173073530197,
-0.006432283669710159,
0.005582052748650312,
0.01257182378321886,
0.05776553973555565,
0.0442325584590435,
0.05713135749101639,
-0.04647962376475334,
-0.014322399161756039,
-0.004233950283378363,
0.017815377563238144,
0.02456810511648655,
-0.007302694488316774,
0.007990901358425617,
0.030299682170152664,
-0.0006356616504490376,
0.011886557564139366,
-0.015015876851975918,
0.01559231337159872,
-0.04074554145336151,
0.007761965971440077,
-0.04535818472504616,
0.04730058088898659,
-0.014512610621750355,
0.07189779728651047,
0.00181191589217633,
0.04231223836541176,
-0.014382971450686455,
-0.06019352003931999,
-0.018788238987326622,
0.05088505148887634,
-0.02989177219569683,
0.05065149441361427,
0.04727168008685112,
-0.012861656956374645,
0.022348016500473022,
-0.01708058826625347,
0.03850054740905762,
0.026663940399885178,
0.03736703842878342,
-0.03522517904639244,
0.047842271625995636,
-0.010768613778054714,
0.009711465798318386,
0.02584230899810791,
-0.02028888277709484,
-0.008850871585309505,
-0.0031058944296091795,
0.007844815962016582,
-0.027043381705880165,
0.008410302922129631,
-0.04135996475815773,
-0.017737718299031258,
0.10513749718666077,
-0.023446012288331985,
-0.027092093601822853,
0.053395844995975494,
0.010730411857366562,
0.03630116209387779,
-0.03733135387301445,
-0.015054112300276756,
-0.06249871850013733,
0.01916804164648056,
-0.02716701105237007,
-0.05428171157836914,
-0.00775080407038331,
0.0037184006068855524,
-0.004699422512203455,
-0.02140916883945465,
0.03589906170964241,
0.027657056227326393,
-0.03730142489075661,
0.047346461564302444,
-0.015575908124446869,
-0.01191648468375206,
0.02182774432003498,
0.02889515645802021,
0.005368247628211975,
0.0039035999216139317,
-0.07369603961706161,
-0.019114628434181213,
0.015567006543278694,
-0.01827666163444519,
-0.016760949045419693,
0.030832409858703613,
0.010774134658277035,
-0.020891744643449783,
-0.018200838938355446,
0.0018758857622742653,
-0.008090753108263016,
-0.0616580955684185,
0.00855272263288498,
-0.007294309791177511,
0.019827578216791153,
0.021458739414811134,
-0.06892073899507523,
0.01354560349136591,
-0.03935157135128975,
0.03615882247686386,
0.04198465496301651,
-0.027275806292891502,
0.011713995598256588,
0.039147913455963135,
0.01603514887392521,
0.03838261589407921,
-0.03644491732120514,
-0.052378442138433456,
0.016292866319417953,
0.025233952328562737,
0.010101871564984322,
-0.02833268791437149,
-0.06030244752764702,
-0.03828722611069679,
-0.016306640580296516,
0.006218669470399618,
0.054472047835588455,
-0.10709076374769211,
0.001495681470260024,
-0.042373914271593094,
-0.017046287655830383,
-0.008085454814136028,
-0.012015879154205322,
0.06692114472389221,
0.019468260928988457,
0.049081869423389435,
0.0010165293933823705,
0.04246124252676964,
0.020176013931632042,
0.001659537199884653,
0.031711213290691376,
0.10220833867788315,
0.023348407819867134,
-0.024707358330488205,
-0.01954987458884716,
0.0017804851522669196,
0.0038431701250374317,
-0.0018888746853917837,
-0.010509012266993523,
-0.0391627699136734,
0.016948290169239044,
0.018261060118675232,
-0.0654887706041336,
0.054807379841804504,
-0.0030566914938390255,
-0.079290010035038,
-0.024775903671979904,
0.024569734930992126,
0.046263594180345535,
-0.0724179744720459,
0.02270697057247162,
-0.005561642348766327,
-0.035157211124897,
-0.025613918900489807,
0.013663213700056076,
-0.03261977806687355,
0.025552498176693916,
0.03381681814789772,
-0.04221082478761673,
0.008937717415392399,
-0.0627930611371994,
0.01513183955103159,
0.01959356851875782,
0.005441867280751467,
-0.006279291119426489,
-0.026035871356725693,
-0.03275492414832115,
0.007647164631634951,
-0.026072897017002106,
0.0014657833380624652,
-0.006555675063282251,
-0.04837533459067345,
-0.06267666816711426,
0.004465160891413689,
-0.021766401827335358,
0.02048713155090809,
0.01782453991472721,
-0.005153876729309559,
-0.047703344374895096,
0.020174043253064156,
-0.056759774684906006,
0.044439226388931274,
-0.049244798719882965,
0.01938570663332939,
0.015429794788360596,
0.05134472995996475,
0.022888652980327606,
0.0009433425730094314,
0.08359761536121368,
0.02647147886455059,
0.01006899494677782,
0.0027398504316806793,
-0.02720692567527294,
-0.04214442893862724,
-0.027766043320298195,
0.06686107814311981,
-0.04188466817140579,
0.00706188939511776,
0.006292338017374277,
0.01721353828907013,
-0.004902129527181387,
-0.04284835234284401,
-0.029636429622769356,
0.02300427109003067,
0.017743786796927452,
-0.017691364511847496,
-0.029394466429948807,
-0.043329209089279175,
0.01679137721657753,
-0.018993230536580086,
-0.033217187970876694,
0.009888711385428905,
-0.006435959134250879,
0.03938179463148117,
0.0004598229133989662,
0.002346586436033249,
0.028893012553453445,
0.041986215859651566,
-0.007612910587340593,
0.0037032081745564938,
0.008698935620486736,
0.025532010942697525,
-0.004989879205822945,
-0.04727557674050331,
-0.015748994424939156,
0.09055281430482864,
0.054845672100782394,
0.015355445444583893,
0.003569897497072816,
-0.03901532292366028,
-0.093106210231781,
0.040248267352581024,
0.026938006281852722,
-0.04699378460645676,
0.02332105115056038,
-0.00221212743781507,
-0.020796136930584908,
-0.0016614404739812016,
0.05886518955230713,
0.003339021233841777,
0.00810778047889471,
0.008274780586361885,
0.0005038094241172075,
0.019411975517868996,
-0.014575991779565811,
-0.0502021498978138,
-0.017479021102190018,
0.01566246896982193,
0.050819847732782364,
-0.0353269949555397,
-0.0015406145248562098,
-0.027617571875452995,
0.023069852963089943,
-0.0003050376835744828,
0.059797193855047226,
-0.04100906476378441,
-0.006247133947908878,
0.010873124934732914,
-0.011685231700539589,
-0.01106558833271265,
-0.01587512716650963,
-0.0046036080457270145,
-0.03172400966286659,
0.04168395325541496,
-0.0066576688550412655,
0.06408838927745819,
-0.12058454751968384,
0.021965457126498222,
-0.02133038453757763,
0.010363378562033176,
0.004938745405524969,
0.02065122127532959,
0.04275031387805939,
0.003231261856853962,
-0.05643516778945923,
-0.022264786064624786,
-0.008822808042168617,
-0.005936938803642988,
-0.08658188581466675,
-0.08390486240386963,
0.009899311698973179,
-0.027170130982995033,
0.03918983042240143,
0.01753712072968483,
0.00023982093262020499,
0.008520637638866901,
0.004417139571160078,
-0.04305221512913704,
-0.02294502593576908,
0.019511941820383072,
-0.020543184131383896,
0.03164946660399437,
-0.03290818631649017,
0.02100156433880329,
-0.028789587318897247,
-0.009487963281571865,
0.00551571324467659,
0.022970713675022125,
-0.028813840821385384,
-0.04457785189151764,
-0.092183418571949,
0.04072156921029091,
0.041122205555438995,
-0.05904597416520119,
0.018471945077180862,
-0.0820016860961914,
0.026938628405332565,
0.05690746009349823,
-0.01988515816628933,
-0.038689564913511276,
0.00024656904861330986,
-0.02508648671209812,
-0.026218421757221222,
-0.08527234196662903,
0.02575261890888214,
0.041116662323474884,
-0.029399484395980835,
0.006111522670835257,
0.027634987607598305,
-0.026156356558203697,
-0.013999707996845245,
-0.014539680443704128,
0.005750995595008135,
0.042058296501636505,
0.04479076340794563,
-0.012648065574467182,
0.01119773369282484,
-0.00710348691791296,
-0.03480713441967964,
-0.04916950315237045,
-0.02759508043527603,
0.03663136065006256,
-0.08608219772577286,
0.03519468009471893,
-0.019801367074251175,
0.04174674674868584,
-0.05865348502993584,
0.05017821863293648,
0.02248310297727585,
-0.0060589308850467205,
-0.00034518641768954694,
-0.005153153091669083,
-0.015624072402715683,
-0.03550983592867851,
0.04896862059831619,
0.011855856515467167,
-0.010175268165767193,
0.00835440307855606,
0.056323450058698654,
0.015737857669591904,
-0.022352546453475952,
-0.027422918006777763,
0.047876182943582535,
-0.010036783292889595,
0.011119459755718708,
-0.04256834834814072,
-0.04177037999033928,
0.02887962944805622,
-0.014588683843612671,
-0.041804466396570206,
-0.03249038755893707,
0.07542328536510468,
0.002926418324932456,
0.013175366446375847,
0.04088325798511505,
0.007813053205609322,
0.01957932487130165,
-0.00033687203540466726,
-0.056697990745306015,
-0.016230802983045578,
0.00841662660241127,
0.034542012959718704,
-0.01626100204885006,
0.0092125553637743,
0.03220332786440849,
-0.02966815046966076,
-0.044820114970207214,
0.02340235561132431,
-0.018957490101456642,
0.0011625922052189708,
0.004911764059215784,
-0.046170614659786224,
-0.04383248835802078,
-0.03111775405704975,
-0.01854574866592884,
-0.042354028671979904,
0.0008647183421999216,
0.028041262179613113,
0.011602295562624931,
-0.053816381841897964,
0.02589225210249424,
0.01768426224589348,
-0.006942111998796463,
-0.03915659338235855,
0.008177408948540688,
-0.026964064687490463,
0.012948956340551376,
-0.01941402442753315,
-0.0019010963151231408,
0.00905141793191433,
-0.008355901576578617,
-0.03493611514568329,
-0.06474822759628296,
0.003927556332200766,
0.011679986491799355,
-0.005342540796846151,
0.03715052083134651,
0.05412348359823227,
-0.00032921391539275646,
-0.03959493711590767,
-0.033502258360385895,
-0.01672310009598732,
-0.006981074810028076,
0.046478234231472015,
-0.01477194856852293,
0.008310861885547638,
-0.01146601140499115,
0.008585111238062382,
-0.04776271805167198,
-0.03658422455191612,
0.0954149067401886,
0.05256498232483864,
-0.0338670052587986,
-0.023939959704875946,
-0.0244420375674963,
-0.011295374482870102,
-0.003947042394429445,
-0.0024033118970692158,
-0.004414200782775879,
-0.03563065454363823,
-0.044457197189331055,
0.04582289606332779,
0.04225288704037666,
-0.059061162173748016,
-0.007463944144546986,
-0.030815618112683296,
0.04341613128781319,
0.04092385992407799,
-0.057379987090826035,
0.05121856927871704,
-0.0752711370587349,
0.02344139665365219,
0.035003259778022766,
-0.04806852340698242,
-0.023050541058182716,
-0.005536539014428854,
-0.04067390412092209,
-0.0354326106607914,
0.013301615603268147,
0.09836961328983307,
0.0006126214866526425,
-0.009982411749660969,
0.01573224924504757,
-0.005289123859256506,
-0.0026101062539964914,
-0.05687199532985687,
0.04312090948224068,
0.023490814492106438,
0.03168874979019165,
-0.06291785836219788,
0.031104832887649536,
-0.017224395647644997,
-0.007051706779748201,
-0.0035998986568301916,
-0.03574245423078537,
-0.031366556882858276,
-0.014013794250786304,
0.017029792070388794,
0.041991282254457474,
0.011423778720200062,
0.009924276731908321,
0.08189287036657333,
-0.04726757854223251,
0.02990814484655857,
0.04458995535969734,
-0.016980240121483803,
-0.07346595078706741,
-0.003789290552958846,
0.033792633563280106,
0.06257106363773346,
-0.08187175542116165,
0.019638950005173683,
0.01888199895620346,
0.02463521435856819,
0.016429852694272995,
0.023983938619494438,
-0.016599219292402267,
-0.01993272453546524,
0.051543839275836945,
0.08050622045993805,
0.08275321871042252,
-0.03380029276013374,
-0.027033384889364243,
-0.00991217140108347,
-0.0485524982213974,
-0.021796252578496933,
0.04612353444099426,
0.01984807476401329,
-0.003581366268917918,
-0.01464204303920269,
0.07094547152519226,
-0.0812496617436409,
-0.01332757156342268,
-0.06598368287086487,
-0.03980376571416855,
0.052892014384269714,
-0.035833586007356644,
0.020763570442795753,
0.0005984798772260547,
0.02878580056130886,
-0.01126929372549057,
-0.039943937212228775,
-0.014598347246646881,
-0.00486717326566577,
-0.021672554314136505,
0.0009007626795209944,
-0.017363986000418663,
0.03633160889148712,
-0.003834252245724201,
0.029925411567091942,
-0.008506080135703087,
0.019513394683599472,
0.0020093629136681557,
-0.002961674239486456,
0.0005475286743603647,
-0.012242279015481472,
0.010397051461040974,
-0.020412033423781395,
0.0345052145421505,
0.012597127817571163,
0.04984041675925255,
-0.021395711228251457,
0.04276478290557861,
-0.05888151749968529,
0.00029684125911444426,
-0.005387035198509693,
0.003758227452635765,
-0.014597334899008274,
0.0289311520755291,
-0.04598458483815193,
-0.03036140836775303,
0.04425784945487976,
0.015760080888867378,
-0.01499701477587223,
0.004361196421086788,
0.06914712488651276,
0.04436325654387474,
0.01253656204789877,
-0.056740909814834595,
0.020538970828056335,
0.08622854202985764,
-0.00613847840577364,
0.01158619113266468,
0.05082745850086212,
-0.018196869641542435,
-0.02716868743300438,
0.006590914912521839,
-0.014672921970486641,
-0.05128507688641548,
0.05502278730273247,
0.02358654886484146,
0.00832886341959238,
0.009620711207389832,
-0.033490825444459915,
-0.06599855422973633,
0.04845805838704109,
-0.02249913290143013,
0.036427948623895645,
-0.03575444966554642,
-0.08468896150588989,
0.04075724631547928,
0.002858125139027834,
-0.04631752893328667,
-0.036144550889730453,
0.008514028042554855,
-0.008647402748465538,
-0.016268201172351837,
0.04788321629166603,
-0.026450447738170624,
0.029599884524941444,
0.02777688577771187,
-0.04097294807434082,
0.009812532924115658,
0.06833121925592422,
0.008475229144096375,
0.044881802052259445,
0.030574452131986618,
-0.010968594811856747,
0.022555775940418243,
0.02223183959722519,
0.026674523949623108,
-0.011714940890669823,
-0.013933013193309307,
-0.0495317168533802,
-0.013507355935871601,
0.040330804884433746,
0.0016667117597535253,
0.016272319480776787,
-0.012448241002857685,
0.044319137930870056
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.