question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
|---|---|---|
<p>A molecule consists of two atoms whose centers are located at $\mathbf{r}_1$ and $\mathbf{r}_2$ respectively. The atoms are connected by a bond that can be approximated by a
harmonic spring, so that its energy as a function of the separation between the atoms $\mathbf{r}=\mathbf{r}_1-\mathbf{r}_2$
is $$U(r) = (akTr^2)/2$$</p>
<p>Assuming that the molecule lives in one dimensions, what will be the overdamped <a href="http://en.wikipedia.org/wiki/Langevin_equation" rel="nofollow">Langevin equation</a>(s) for the motion of the molecule?</p> | g4551 | [
-0.016309421509504318,
-0.003920344635844231,
-0.023572593927383423,
-0.039882250130176544,
-0.004695965442806482,
-0.04747225344181061,
0.029477840289473534,
0.005701916292309761,
-0.01461838185787201,
-0.018434986472129822,
-0.02909044176340103,
-0.012525692582130432,
-0.0388580858707428,
-0.07632242143154144,
0.021019302308559418,
-0.04376125708222389,
-0.03280464932322502,
0.01752714440226555,
0.01184193603694439,
-0.04585566744208336,
-0.019101349636912346,
-0.013092460110783577,
0.005364106502383947,
-0.04119914025068283,
-0.0025713902432471514,
-0.01673860289156437,
-0.0007564100669696927,
-0.035269465297460556,
-0.11841987073421478,
-0.01681523025035858,
-0.02850411646068096,
0.012369035743176937,
0.04932861030101776,
-0.040056876838207245,
-0.030781524255871773,
0.027394914999604225,
0.041489120572805405,
0.0033557957503944635,
0.025168390944600105,
-0.024591119959950447,
-0.014777361415326595,
-0.04952767863869667,
0.0406339131295681,
0.0016015605069696903,
0.05234324559569359,
-0.011089247651398182,
0.022941051051020622,
0.021074466407299042,
0.011636819690465927,
0.020146705210208893,
0.007870111614465714,
0.04546534642577171,
0.0025263961870223284,
0.018193230032920837,
-0.008632590994238853,
0.008415247313678265,
-0.0013223475543782115,
-0.017653224989771843,
0.06719446927309036,
-0.0023186728358268738,
0.023436609655618668,
-0.005489209201186895,
-0.05105320364236832,
-0.0032805728260427713,
0.013265776447951794,
-0.011994091793894768,
-0.05582723021507263,
-0.03821248561143875,
0.05996940657496452,
-0.11331377178430557,
-0.015529362484812737,
0.015358299016952515,
-0.04841732233762741,
0.025939442217350006,
-0.026969151571393013,
0.01845746673643589,
0.0003648226847872138,
-0.02285253256559372,
-0.03167209401726723,
-0.013001677580177784,
-0.030097810551524162,
0.05599556490778923,
0.0027853860519826412,
0.007273260969668627,
0.07392209023237228,
0.0276512298732996,
0.06226116418838501,
0.030850714072585106,
-0.0369952917098999,
0.0011064542923122644,
0.02460869774222374,
-0.027227357029914856,
0.014686960726976395,
-0.04518149793148041,
0.01606476679444313,
-0.047893330454826355,
-0.038481198251247406,
0.011403477750718594,
0.015869401395320892,
-0.03161587938666344,
-0.035719506442546844,
0.03969377651810646,
-0.012008334510028362,
-0.029749704524874687,
0.051313210278749466,
0.008639544248580933,
-0.01975901983678341,
-0.00867706909775734,
-0.07074937224388123,
0.030936433002352715,
-0.0019764185417443514,
0.01233645435422659,
0.011111853644251823,
-0.02254619263112545,
0.01870998740196228,
-0.053357452154159546,
0.043708283454179764,
-0.02210792526602745,
-0.011223851703107357,
0.02437477745115757,
-0.01343295443803072,
0.08525297790765762,
0.06445232033729553,
0.02516026981174946,
-0.03265095502138138,
0.02363843098282814,
0.010148679837584496,
0.008730931207537651,
-0.00843960139900446,
0.019493917003273964,
0.001959816552698612,
-0.05650988966226578,
0.05024105682969093,
0.005605942104011774,
0.008206646889448166,
0.055783916264772415,
-0.02781340852379799,
0.04920900985598564,
-0.06306605786085129,
0.051105670630931854,
0.032047443091869354,
-0.051661260426044464,
0.026353470981121063,
-0.03356492519378662,
-0.10039357841014862,
0.03001735545694828,
0.04323400557041168,
-0.02180749922990799,
0.030238837003707886,
-0.024898169562220573,
-0.02158546820282936,
0.01287473551928997,
-0.03358655050396919,
-0.00954637210816145,
0.030481943860650063,
-0.0024406483862549067,
-0.009834691882133484,
0.05220947414636612,
0.0011118402471765876,
-0.03393546864390373,
-0.013440691865980625,
0.02926545776426792,
0.022037550806999207,
-0.00916850846260786,
-0.04058297723531723,
-0.038552265614271164,
0.03162765130400658,
-0.0369144082069397,
-0.021718084812164307,
0.0032923235557973385,
-0.016169393435120583,
-0.06650412827730179,
-0.03931092843413353,
0.04379880055785179,
0.009546445682644844,
0.04085012897849083,
0.0006534772692248225,
-0.0058624958619475365,
-0.009791521355509758,
0.042222507297992706,
0.031110471114516258,
0.017738645896315575,
0.02706802822649479,
0.0010076953331008554,
0.024419518187642097,
0.05202553793787956,
-0.013304986990988255,
0.0319671668112278,
-0.04685256630182266,
-0.002279980108141899,
0.0028791846707463264,
0.012414154596626759,
0.022100679576396942,
0.003572101704776287,
-0.044594623148441315,
0.020764438435435295,
0.040232934057712555,
-0.028153633698821068,
0.004464772995561361,
0.03268260136246681,
0.006937515921890736,
0.0029984270222485065,
0.05398918315768242,
0.035513728857040405,
0.07728399336338043,
0.016241034492850304,
0.0006528886733576655,
-0.009700185619294643,
0.027978364378213882,
-0.003637390909716487,
0.008387177251279354,
0.04027457535266876,
-0.012376219965517521,
0.0444391705095768,
-0.013015944510698318,
-0.04921724274754524,
0.05554848536849022,
-0.021842358633875847,
-0.027645420283079147,
0.053396616131067276,
0.021104441955685616,
0.003010965185239911,
0.06723713129758835,
-0.0037669481243938208,
0.011489378288388252,
-0.024686921387910843,
-0.015574846416711807,
-0.06660788506269455,
0.01523226872086525,
0.05383908376097679,
0.031106727197766304,
-0.0008938209502957761,
-0.01067293994128704,
0.005499949213117361,
0.0017810931894928217,
0.05138728395104408,
-0.06443362683057785,
0.061999641358852386,
-0.01845400221645832,
-0.025662006810307503,
-0.009880189783871174,
0.03162332624197006,
-0.0043848357163369656,
-0.05178969353437424,
0.02584856189787388,
-0.007246959023177624,
0.0889795795083046,
-0.006793824024498463,
-0.048260316252708435,
0.04384583607316017,
-0.003981728572398424,
0.0035687147174030542,
0.03597380965948105,
-0.009961800649762154,
0.005567100830376148,
0.0075455475598573685,
-0.01337601151317358,
0.009358071722090244,
-0.033794600516557693,
-0.06356137990951538,
-0.0024203998036682606,
0.0005226942012086511,
0.03690674155950546,
-0.011947635561227798,
-0.05527729168534279,
-0.03141098469495773,
-0.01809641160070896,
0.04340800270438194,
-0.005183337721973658,
0.009686592034995556,
0.011145083233714104,
0.07699314504861832,
-0.04311693087220192,
0.05102555453777313,
-0.03590336814522743,
0.002272261306643486,
0.006169618107378483,
-0.03841019049286842,
0.01665865071117878,
0.023945041000843048,
0.01602930761873722,
-0.008779799565672874,
-0.01383456401526928,
0.02466961182653904,
0.033686313778162,
-0.02688685990869999,
-0.04253420606255531,
0.0752047672867775,
0.021205924451351166,
-0.08292039483785629,
-0.024932220578193665,
0.06785966455936432,
0.004986818879842758,
0.0354977622628212,
0.004725820850580931,
0.01440275739878416,
0.011337422765791416,
-0.039439521729946136,
-0.010572697035968304,
0.05721601843833923,
-0.04840109869837761,
0.01200664322823286,
0.004807149060070515,
0.028776338323950768,
0.018162839114665985,
0.034441299736499786,
-0.016930347308516502,
-0.035819221287965775,
-0.0029986980371177197,
0.0013969417195767164,
0.025759609416127205,
0.02213870733976364,
0.06135788932442665,
-0.008139170706272125,
-0.03365090489387512,
-0.008194591850042343,
-0.05164365842938423,
-0.07513584941625595,
0.03661598637700081,
-0.04941466823220253,
0.019793877378106117,
-0.0459277369081974,
-0.011940420605242252,
-0.026237092912197113,
0.04912669211626053,
-0.0029268318321555853,
-0.07543451339006424,
-0.00936428364366293,
-0.03073710761964321,
-0.05898764729499817,
0.04476258158683777,
0.06516311317682266,
0.045442987233400345,
-0.006928927265107632,
-0.005260244477540255,
-0.023400304839015007,
-0.03498075157403946,
0.017375856637954712,
0.007947697304189205,
-0.0008415772463195026,
-0.07220622152090073,
-0.033088814467191696,
0.02415548264980316,
-0.010761838406324387,
0.020272191613912582,
0.0258732158690691,
-0.06320261210203171,
0.03827857971191406,
0.002674219897016883,
-0.06403002142906189,
-0.011299011297523975,
-0.018598591908812523,
0.0031245513819158077,
-0.002635293174535036,
-0.006909777410328388,
-0.02296772412955761,
0.01730361022055149,
0.017934229224920273,
-0.021952416747808456,
0.005930901505053043,
0.033098965883255005,
-0.034557778388261795,
0.006529961712658405,
0.03212963789701462,
0.01514529064297676,
-0.06644504517316818,
-0.02945738285779953,
0.05127309262752533,
-0.026671307161450386,
-0.05530658736824989,
-0.06076524406671524,
-0.03820722550153732,
0.0075674159452319145,
-0.06036046892404556,
0.03920880705118179,
-0.023787200450897217,
0.005122035276144743,
0.0028121857903897762,
-0.0006699530640617013,
0.05001423507928848,
0.06150900572538376,
0.011042156256735325,
0.009003642946481705,
0.010380163788795471,
-0.022649362683296204,
-0.0038768101949244738,
-0.040311627089977264,
-0.032092370092868805,
0.01666548289358616,
0.01681329496204853,
0.03507419675588608,
-0.07317337393760681,
0.029320010915398598,
0.057970065623521805,
0.03905152156949043,
-0.0026135609950870275,
0.030825380235910416,
0.03377225995063782,
-0.03287961333990097,
0.03349120169878006,
-0.02780444361269474,
0.04688138887286186,
-0.003306163242086768,
-0.032966796308755875,
0.0000398954980482813,
0.057367775589227676,
0.05087748169898987,
-0.014178642071783543,
-0.009655015543103218,
0.02224566601216793,
0.03888774663209915,
0.07461553066968918,
0.06459455192089081,
-0.05163629353046417,
0.03389575332403183,
0.006345891859382391,
0.002289772965013981,
-0.011603130958974361,
-0.06617554277181625,
0.007601347751915455,
-0.027893060818314552,
0.06554943323135376,
0.03229610621929169,
0.00472661666572094,
-0.023746846243739128,
0.004466851241886616,
0.07913631200790405,
-0.02981301210820675,
-0.029676711186766624,
-0.04313253238797188,
-0.03286666423082352,
0.024972757324576378,
-0.002371738897636533,
0.028751369565725327,
-0.023061128333210945,
0.014064684510231018,
-0.0031657873187214136,
0.01472700759768486,
0.02147175744175911,
0.03602949529886246,
0.01843763142824173,
0.02570599503815174,
0.01892085000872612,
0.037152405828237534,
0.03701697662472725,
0.0026729702949523926,
0.012783173471689224,
-0.07772626727819443,
0.04155992716550827,
-0.08322993665933609,
-0.01713845692574978,
0.044313833117485046,
-0.025714658200740814,
-0.0019850805401802063,
0.022162986919283867,
-0.011903081089258194,
-0.08221518248319626,
0.01912325993180275,
0.005764079745858908,
0.03290526196360588,
-0.0012751412577927113,
-0.025662651285529137,
-0.02222536876797676,
0.005188813433051109,
0.007087804842740297,
-0.060973186045885086,
0.022343670949339867,
-0.030365008860826492,
-0.059607937932014465,
0.052035994827747345,
0.03398977220058441,
0.02785845287144184,
-0.007633681874722242,
0.040417563170194626,
-0.01740795560181141,
-0.05191970616579056,
0.006532727740705013,
0.02322760969400406,
-0.002875491278246045,
-0.017478371039032936,
-0.02392636612057686,
0.021606585010886192,
0.03850718215107918,
-0.010704242624342442,
0.019428668543696404,
0.02523045800626278,
-0.032545581459999084,
-0.05759590491652489,
0.01718274876475334,
0.026996301487088203,
0.023165017366409302,
0.041554249823093414,
-0.02987784519791603,
-0.008291474543511868,
-0.0005025843856856227,
-0.03431852534413338,
-0.05274612084031105,
-0.05135029926896095,
0.000014222394383978099,
0.0016902321949601173,
-0.06622327119112015,
0.06032101809978485,
-0.0016710967756807804,
-0.015570602379739285,
0.0019219830865040421,
0.06836920231580734,
0.03734789416193962,
0.01192420069128275,
-0.07373525947332382,
0.017374059185385704,
-0.005654076114296913,
0.01770087704062462,
0.05453815683722496,
0.06697282195091248,
-0.03063269704580307,
0.01858549751341343,
-0.0073628914542496204,
0.06005144491791725,
-0.07647979259490967,
-0.034809764474630356,
0.03152785822749138,
0.00015825674927327782,
0.03427859768271446,
-0.039217546582221985,
0.026262497529387474,
-0.033418796956539154,
-0.00875814724713564,
-0.025962280109524727,
-0.029068443924188614,
0.006971731781959534,
-0.008588938973844051,
-0.09334239363670349,
0.008748800493776798,
-0.02344512566924095,
0.07098785787820816,
0.006899337284266949,
0.0015308562433347106,
-0.008907419629395008,
-0.04435822367668152,
0.05674240365624428,
-0.0028244382701814175,
-0.04354178160429001,
0.029668912291526794,
0.05607736110687256,
-0.08056338131427765,
-0.048091571778059006,
-0.004042159300297499,
0.06021392345428467,
0.030684558674693108,
-0.0016948156990110874,
-0.019149092957377434,
0.007838128134608269,
-0.018029773607850075,
-0.0024234233424067497,
0.026514019817113876,
0.013375353999435902,
0.01032609399408102,
-0.03717702627182007,
-0.03255562484264374,
0.027538366615772247,
-0.010724259540438652,
0.048839740455150604,
0.04699351638555527,
0.042252350598573685,
0.05383426696062088,
-0.055200494825839996,
-0.02620469219982624,
-0.04858109727501869,
0.06558573246002197,
-0.035014331340789795,
-0.047054681926965714,
-0.03390143811702728,
0.02481982111930847,
0.0033806010615080595,
0.011860747821629047,
0.04101233184337616,
0.002022054512053728,
-0.031091663986444473,
-0.027308212593197823,
0.02749507874250412,
-0.014131449162960052,
0.02093874290585518,
0.045473042875528336,
-0.020446021109819412,
0.025163860991597176,
0.03642095625400543,
-0.025245683267712593,
-0.01904136687517166,
0.09076914191246033,
-0.0032090756576508284,
0.039393194019794464,
-0.01982121914625168,
-0.022537019103765488,
-0.07230910658836365,
-0.03595361113548279,
-0.044987551867961884,
-0.006988685578107834,
-0.06300605833530426,
-0.021998684853315353,
0.04719824716448784,
0.04249362647533417,
0.0017077912343665957,
0.01023491844534874,
-0.033707693219184875,
0.005614316090941429,
0.0415818952023983,
-0.033373914659023285,
-0.004611905664205551,
-0.012424422428011894,
0.00021953260875307024,
0.0037945813965052366,
0.029354486614465714,
0.01776745915412903,
0.008425794541835785,
-0.0030094326939433813,
-0.01502467691898346,
0.052642904222011566,
0.06880490481853485,
0.015747403725981712,
-0.03561675548553467,
0.031204361468553543,
0.009794758632779121,
0.04399247094988823,
0.0610564686357975,
0.04110081493854523,
0.028340758755803108,
-0.043659135699272156,
0.05901618301868439,
0.036297757178545,
0.013537412509322166,
0.07165469229221344,
0.011362945660948753,
0.02371339127421379,
0.019244248047471046,
0.027128029614686966,
-0.0068467166274785995,
-0.08192417770624161,
0.02707555517554283,
0.03519964963197708,
0.11916827410459518,
-0.04730062186717987,
0.04672522470355034,
0.04131921008229256,
-0.015682220458984375,
-0.07140551507472992,
-0.02287304773926735,
0.05884459987282753,
-0.03612206503748894,
-0.09322667866945267,
-0.04767994210124016,
-0.025442158803343773,
-0.0029572471976280212,
-0.020242633298039436,
0.00834718532860279,
-0.015329279936850071,
0.012379939667880535,
-0.002689934801310301,
0.011403549462556839,
0.020374692976474762,
-0.007412669714540243,
-0.028066378086805344,
-0.03393271192908287,
0.01282759103924036,
-0.031079018488526344,
-0.007377796806395054,
0.08346661180257797,
0.0355616919696331,
-0.01091750618070364,
-0.0494169220328331,
-0.007421927060931921,
-0.03062816895544529,
-0.01819208450615406,
0.02468210831284523,
0.005067470017820597,
-0.05937987193465233,
-0.0034587562549859285,
0.027904586866497993,
0.04693864285945892,
-0.0018404454458504915,
-0.08485674113035202,
0.013764106668531895,
-0.0065383994951844215,
0.00507162744179368,
-0.06383108347654343,
-0.04525590315461159,
0.0734110176563263,
0.03882165625691414,
-0.03624335676431656,
-0.03686665743589401,
-0.038375452160835266,
0.0002207651559729129,
0.05324932187795639,
-0.01077143382281065,
-0.014028504490852356,
-0.00922966655343771,
0.04079674184322357,
-0.011843022890388966,
0.027618413791060448,
0.013940810225903988,
-0.004066139459609985,
0.008765642531216145,
-0.04609028995037079,
-0.0013779641594737768,
0.06401243060827255,
-0.004431167151778936,
-0.053600285202264786,
-0.014428605325520039,
-0.044614262878894806,
0.0011307087261229753,
0.02206711657345295,
0.01767812669277191,
0.06502775847911835,
0.006290176883339882,
0.04266127571463585,
0.052590567618608475,
-0.018944263458251953,
-0.0036507765762507915,
0.04247181490063667,
0.03755957633256912,
-0.06005382910370827,
-0.023664379492402077,
0.04236602783203125,
0.02148733101785183,
-0.06294425576925278,
-0.04607998579740524,
-0.05153055116534233,
-0.05787885561585426,
-0.009853964671492577,
0.02150457724928856,
-0.03839516267180443,
-0.026001425459980965,
-0.024215389043092728,
-0.0044208974577486515,
0.04118742793798447,
-0.056075721979141235,
-0.018085777759552002,
0.019489867612719536,
0.000017467440557084046,
-0.03674260899424553,
0.020052069798111916,
-0.07441160082817078,
-0.06236758083105087,
0.022921031340956688,
-0.022968459874391556,
0.0008266797522082925,
-0.03483787551522255,
-0.03937743604183197,
0.003985494375228882,
0.09968169778585434,
-0.0027703926898539066,
0.037255749106407166,
-0.007842331193387508,
-0.007868326269090176,
0.0002824232797138393,
0.0578930489718914,
-0.06603754311800003,
-0.0133998803794384,
0.01175704412162304,
-0.017660755664110184,
-0.009845660999417305,
-0.05941576510667801,
0.02399449236690998,
0.010922979563474655,
0.02459302917122841,
-0.008279310539364815,
-0.026425380259752274,
-0.02211119420826435,
0.006870614364743233
] |
<p>I'm having some trouble with successfully working out a rotation about the $z$-axis on the <a href="http://en.wikipedia.org/wiki/Bloch_sphere" rel="nofollow">Bloch sphere</a>.
Now, I know how this is performed, in principle.
A rotation of the Bloch-sphere around an axis $\boldsymbol n$ by an angle $\theta$ is given by
$$ R_{\boldsymbol n}(\theta)=e^{-i\theta \boldsymbol \sigma\cdot \boldsymbol n/2} $$
where $\boldsymbol \sigma$ is the vector of Pauli-matrices.</p>
<p>So for example if I start in \begin{pmatrix}
1 \\
0 \\
\end{pmatrix}</p>
<p>And I want to rotate by pi/2 around the x-axis, I simply compute the product with </p>
<p>\begin{pmatrix}
\frac{1}{\sqrt{2}} & \frac{-i}{\sqrt{2}} \\
\frac{-i}{\sqrt{2}} & \frac{1}{\sqrt{2}} \\
\end{pmatrix}</p>
<p>And I end up with
\begin{pmatrix}
\frac{1}{\sqrt{2}} \\
\frac{-i}{\sqrt{2}} \\
\end{pmatrix}</p>
<p>However, now I want to rotate this around the z-axis, by an angle theta. Now from what I can tell this simply corresponds to the matrix multiplication with
\begin{pmatrix}
e^{\frac{-i\theta}{2}} & 0 \\
0 & e^{\frac{i\theta}{2}} \\
\end{pmatrix}</p>
<p>so that I end up with the vector</p>
<p>\begin{pmatrix}
\frac{e^{\frac{-i\theta}{2}}}{\sqrt{2}} \\
\frac{-ie^{\frac{i\theta}{2}}}{\sqrt{2}} \\
\end{pmatrix}</p>
<p>However, here things go wrong. For example, I know that if I rotate by $2\pi$, I should end up back at the same spot, but instead I end up at
\begin{pmatrix}
\frac{-1}{\sqrt{2}} \\
\frac{i}{\sqrt{2}} \\
\end{pmatrix}</p>
<p>which is not correct. Could someone point out the obvious error?</p> | g4552 | [
0.02497856505215168,
-0.023963358253240585,
0.00178770802449435,
-0.0044845761731266975,
0.03851904720067978,
-0.0930095687508583,
0.11256830394268036,
-0.023757876828312874,
-0.048417508602142334,
0.03754020109772682,
0.002992857014760375,
0.10134435445070267,
0.038625240325927734,
-0.019500242546200752,
0.02764807641506195,
-0.03520987555384636,
0.008364572189748287,
0.04101601988077164,
0.009101251140236855,
0.020441725850105286,
0.001484014093875885,
0.019030869007110596,
0.014830132946372032,
-0.010030869394540787,
0.010186731815338135,
-0.03667162358760834,
0.021731192246079445,
0.039074428379535675,
-0.023616133257746696,
0.03077387996017933,
0.014176447875797749,
0.025753473863005638,
0.03484690561890602,
-0.012378718703985214,
0.004676151089370251,
-0.018914829939603806,
0.026313358917832375,
-0.001433609169907868,
0.07199858874082565,
0.007824147120118141,
-0.010264784097671509,
-0.035659316927194595,
0.015067407861351967,
0.0011298737954348326,
0.017248395830392838,
-0.043223705142736435,
-0.03460415452718735,
0.04778696224093437,
-0.02765633538365364,
0.05945981293916702,
0.0673232227563858,
0.0172440018504858,
0.08004617691040039,
-0.007235368248075247,
-0.02349056303501129,
-0.0029031308367848396,
0.053102120757102966,
-0.0006252567400224507,
0.04657404124736786,
0.043110840022563934,
0.009646336548030376,
-0.046278055757284164,
-0.03515021502971649,
0.030178265646100044,
0.02120094746351242,
-0.016723880544304848,
-0.004915945697575808,
0.03148871287703514,
-0.0565255805850029,
0.025449149310588837,
-0.03719811141490936,
-0.032614950090646744,
0.05540521442890167,
-0.029407264664769173,
-0.050316449254751205,
0.011593850329518318,
0.03149161860346794,
-0.02533111162483692,
0.04771972820162773,
0.0014348513213917613,
0.0013730089413002133,
-0.002606113674119115,
0.016085464507341385,
0.019529590383172035,
0.043845612555742264,
0.035159867256879807,
0.012730756774544716,
-0.018131591379642487,
0.032735880464315414,
-0.010364863090217113,
0.057964298874139786,
0.0010899602202698588,
-0.012821371667087078,
0.01744241639971733,
-0.05062315613031387,
-0.000999109703116119,
-0.04849991574883461,
0.015101243741810322,
-0.03123447857797146,
0.02495424635708332,
0.0023264081683009863,
0.027742203325033188,
0.024274330586194992,
-0.027927085757255554,
-0.002397069474682212,
0.0431048609316349,
0.010640264488756657,
-0.006548886653035879,
0.013701332733035088,
0.017857693135738373,
-0.030502934008836746,
-0.030397411435842514,
-0.019671745598316193,
-0.016546282917261124,
-0.049223996698856354,
0.014008047059178352,
0.04861411824822426,
0.043031949549913406,
0.040877483785152435,
0.03298591822385788,
-0.0034094350412487984,
-0.000008132716175168753,
0.05923149734735489,
0.020305974408984184,
-0.043226320296525955,
-0.004365552682429552,
-0.006849511526525021,
0.0026070706080645323,
0.04220369830727577,
-0.056053295731544495,
-0.05442804470658302,
-0.03509527072310448,
0.026081332936882973,
0.008856920525431633,
-0.021490318700671196,
0.014758460223674774,
-0.04843704029917717,
-0.0012224081438034773,
0.009809487499296665,
0.0504145585000515,
-0.03887178748846054,
-0.04370893910527229,
0.010439641773700714,
-0.06720287352800369,
-0.02011880837380886,
0.01056559570133686,
-0.024065088480710983,
-0.06716828793287277,
0.06310263276100159,
0.03715288266539574,
-0.043478477746248245,
0.08424554765224457,
0.004149009473621845,
-0.013987085781991482,
0.0003887569182552397,
0.029642971232533455,
0.0005233106203377247,
-0.05259602144360542,
0.024382345378398895,
0.0225504320114851,
0.03956117480993271,
-0.03523920476436615,
0.010623550042510033,
-0.026750903576612473,
-0.031233420595526695,
0.004170290660113096,
-0.0428021177649498,
0.007824033498764038,
-0.026774965226650238,
-0.08952518552541733,
-0.029201796278357506,
-0.027207596227526665,
0.045639265328645706,
0.020958395674824715,
-0.015917720273137093,
0.03381131589412689,
-0.013817332684993744,
0.020088693127036095,
0.0645199716091156,
0.07033514976501465,
0.020188840106129646,
-0.019293347373604774,
-0.009782882407307625,
0.03297971189022064,
0.01986113004386425,
-0.012882119044661522,
-0.012837464921176434,
0.009406008757650852,
-0.09746754169464111,
0.010318882763385773,
-0.0045097265392541885,
0.015541628003120422,
-0.0010655567748472095,
0.022022226825356483,
0.003680889494717121,
0.02697342075407505,
0.035176146775484085,
-0.0618266761302948,
-0.039456434547901154,
0.05459016188979149,
-0.009097674861550331,
0.01650221459567547,
0.09477698802947998,
-0.015269387513399124,
0.008578558452427387,
-0.01100847963243723,
0.02790083922445774,
-0.0659560114145279,
-0.006011251360177994,
0.09582681208848953,
0.00903119146823883,
0.0019509091507643461,
-0.01075572706758976,
-0.01647656410932541,
-0.0313408300280571,
-0.0015223247464746237,
0.017337879166007042,
0.019458388909697533,
-0.032854847609996796,
0.02101755328476429,
0.02145574428141117,
0.025970814749598503,
-0.07770989835262299,
-0.046370334923267365,
-0.003845621133223176,
0.01553377602249384,
0.0418696328997612,
-0.006046974565833807,
0.024907764047384262,
0.07274676114320755,
-0.0303791631013155,
0.003592701628804207,
-0.005369913298636675,
0.016706380993127823,
0.013947690837085247,
-0.06494468450546265,
-0.00502103241160512,
0.04392068833112717,
0.021365173161029816,
0.04927261173725128,
-0.03517785668373108,
0.015775278210639954,
-0.010489214211702347,
-0.029765255749225616,
0.061274196952581406,
-0.04565860703587532,
0.04261438921093941,
-0.03745565935969353,
-0.017675526440143585,
-0.0055565740913152695,
0.016830096021294594,
-0.03745788335800171,
-0.03149355202913284,
0.016647936776280403,
0.05207689106464386,
-0.026509076356887817,
-0.02795233391225338,
0.046185851097106934,
0.019285108894109726,
0.011871757917106152,
-0.02742692269384861,
-0.015098530799150467,
-0.01902301236987114,
0.05702413618564606,
-0.013148820027709007,
0.003637633053585887,
-0.07624299079179764,
0.028852956369519234,
0.04615335911512375,
-0.003955300897359848,
-0.04240693897008896,
0.03717563673853874,
0.055974967777729034,
0.061344441026449203,
-0.043601468205451965,
-0.04721684753894806,
0.005736774764955044,
0.0214371494948864,
-0.04083297401666641,
0.032726727426052094,
-0.0071295578964054585,
0.0027446672320365906,
-0.021897591650485992,
0.023998605087399483,
0.024451131001114845,
-0.03355021774768829,
-0.030571866780519485,
0.042570386081933975,
-0.05481559410691261,
0.0019147255225107074,
-0.052606672048568726,
0.007293415255844593,
0.03796957805752754,
-0.03601030632853508,
0.002797035500407219,
0.034036338329315186,
0.043415240943431854,
-0.041803501546382904,
0.029128849506378174,
0.04752142354846001,
0.07152635604143143,
-0.041999511420726776,
0.014634504914283752,
-0.016500506550073624,
0.052281517535448074,
-0.016231361776590347,
-0.019123174250125885,
-0.0960037037730217,
0.010164249688386917,
0.09262349456548691,
-0.00521340174600482,
-0.01507888175547123,
0.02145027182996273,
-0.04984887316823006,
-0.07047196477651596,
-0.0071275862865149975,
-0.050086863338947296,
-0.05247241631150246,
0.017295507714152336,
0.026466794312000275,
-0.06982330977916718,
0.04399700090289116,
0.0069082812406122684,
0.0459950715303421,
0.01277161855250597,
0.010494653135538101,
-0.04389479011297226,
0.015523207373917103,
-0.014030274003744125,
-0.06180279329419136,
0.03856944292783737,
0.036524008959531784,
0.0013594042975455523,
-0.008994256146252155,
-0.02208598330616951,
-0.03436511754989624,
-0.004451949615031481,
0.029566733166575432,
-0.02232520282268524,
-0.028718801215291023,
-0.03067765012383461,
-0.002515734639018774,
0.022644249722361565,
-0.037893205881118774,
-0.04491454362869263,
-0.007243932690471411,
-0.03285735473036766,
0.0009348159073852003,
0.019704420119524002,
0.010973624885082245,
0.009507800452411175,
-0.02795334905385971,
0.0003315969661343843,
0.010566182434558868,
0.04951377958059311,
0.07079071551561356,
0.04417208209633827,
0.04821750149130821,
0.021524500101804733,
0.006813031621277332,
0.006424000486731529,
-0.062442805618047714,
-0.02607627585530281,
0.016577662900090218,
0.005295492708683014,
-0.03227977082133293,
0.021966084837913513,
0.08383092284202576,
-0.0004637211677618325,
-0.020307831466197968,
-0.000835652812384069,
-0.03832254186272621,
0.0266825370490551,
0.012656415812671185,
-0.057505376636981964,
-0.025653960183262825,
-0.0381721556186676,
-0.009624548256397247,
-0.017969045788049698,
-0.005647923797369003,
-0.03468095511198044,
-0.01916033960878849,
-0.06665528565645218,
0.009667987003922462,
0.015899481251835823,
0.03262697160243988,
0.019282879307866096,
0.023653682321310043,
0.01638515293598175,
-0.012612525373697281,
-0.010876396670937538,
-0.004666936118155718,
0.03985055163502693,
-0.01664315164089203,
0.00979781337082386,
0.00208851951174438,
-0.01610170677304268,
0.04072542488574982,
-0.0643577054142952,
0.06068640574812889,
0.017298536375164986,
0.0021489558275789022,
0.02714274637401104,
-0.019617710262537003,
0.0345846489071846,
0.0176839716732502,
-0.059330202639102936,
0.014171185903251171,
0.024756284430623055,
-0.013091335073113441,
-0.02520245686173439,
0.026597823947668076,
0.018201226368546486,
-0.05555345490574837,
0.07799812406301498,
0.03913233056664467,
0.012045462615787983,
-0.010542490519583225,
-0.001756124896928668,
-0.04510350152850151,
-0.0518769733607769,
-0.01021893322467804,
0.010140299797058105,
-0.0217193141579628,
0.013847677037119865,
0.02525912970304489,
0.023164549842476845,
-0.06212831661105156,
0.061159487813711166,
-0.020713800564408302,
-0.02066572941839695,
0.02193356491625309,
-0.031685344874858856,
-0.01625666581094265,
-0.04804740846157074,
-0.0571567565202713,
-0.015076116658747196,
0.027736879885196686,
0.03708145394921303,
-0.0063008530996739864,
0.028928391635417938,
0.01969148963689804,
-0.019695868715643883,
-0.03809486702084541,
0.009405410848557949,
-0.016491573303937912,
-0.012762220576405525,
-0.0439022034406662,
0.021438028663396835,
-0.020806415006518364,
-0.000603107619099319,
-0.009928982704877853,
0.06453892588615417,
-0.0434199795126915,
0.017268793657422066,
-0.00030979508301243186,
-0.02531706541776657,
0.05921775475144386,
-0.034028127789497375,
-0.01612820103764534,
0.03246789798140526,
-0.014950195327401161,
-0.05341778323054314,
0.012511711567640305,
0.026154816150665283,
0.05417927727103233,
-0.009571961127221584,
-0.001080094836652279,
0.0034031879622489214,
0.007343986537307501,
-0.053377702832221985,
0.05942332744598389,
0.038685526698827744,
-0.0030363118276000023,
-0.009747705422341824,
0.054784104228019714,
-0.017349012196063995,
0.04507749155163765,
-0.03657430782914162,
-0.03575372323393822,
-0.0398133248090744,
0.0007936928886920214,
0.038767009973526,
0.017803320661187172,
0.028993673622608185,
0.013356231153011322,
-0.05770514905452728,
-0.04447872191667557,
0.005870737135410309,
-0.02431110292673111,
0.028177278116345406,
0.046466439962387085,
-0.02672063745558262,
-0.05241226777434349,
0.005722029134631157,
-0.04908375442028046,
0.0012125765206292272,
-0.04281999170780182,
-0.00458733132109046,
0.015950752422213554,
-0.0057274289429187775,
0.042113397270441055,
-0.005227759014815092,
-0.02467966265976429,
-0.04194929823279381,
-0.000485335651319474,
0.041365377604961395,
0.010934348218142986,
-0.031250059604644775,
0.029333170503377914,
-0.005709296092391014,
0.004411614965647459,
0.011930268257856369,
-0.03925936669111252,
0.005738449282944202,
-0.011774798855185509,
-0.0068160612136125565,
-0.022216303274035454,
-0.012780147604644299,
-0.018806805834174156,
-0.03196115046739578,
0.018904808908700943,
-0.021262995898723602,
-0.057293348014354706,
0.060022640973329544,
-0.01975482702255249,
-0.008690223097801208,
-0.01819101721048355,
-0.03694579377770424,
0.04568220302462578,
-0.06297480314970016,
-0.05215084180235863,
-0.050970084965229034,
0.012693795375525951,
0.013578291051089764,
0.0011045291321352124,
-0.031237397342920303,
-0.05025598034262657,
0.10278341919183731,
-0.012531223706901073,
0.00671132979914546,
-0.05341239646077156,
0.03208230063319206,
0.019599325954914093,
-0.06368553638458252,
0.006906062364578247,
0.0018543640617281199,
0.03131483495235443,
-0.020611710846424103,
0.028686990961432457,
-0.04304123297333717,
0.020046895369887352,
-0.056839700788259506,
-0.080439992249012,
-0.0289916954934597,
0.06263938546180725,
-0.03318328410387039,
-0.010459293611347675,
0.014993288554251194,
0.007079025264829397,
0.04002264514565468,
-0.06605018675327301,
-0.016564413905143738,
-0.011392280459403992,
-0.007375738583505154,
-0.02085329033434391,
0.02996421791613102,
0.0785084143280983,
0.022777963429689407,
0.07021962851285934,
-0.020680556073784828,
-0.012549465522170067,
-0.051807429641485214,
0.04475710913538933,
0.04546758532524109,
0.03870052099227905,
-0.03254023194313049,
-0.027311336249113083,
-0.020351886749267578,
0.03210051730275154,
0.011874460615217686,
0.0361056923866272,
0.015488598495721817,
0.00818066019564867,
0.0002641504106577486,
0.01689772494137287,
-0.019752005115151405,
-0.024960674345493317,
-0.014925367198884487,
-0.012857647612690926,
-0.014360655099153519,
0.030139263719320297,
-0.09781153500080109,
0.0022078051697462797,
-0.03524859994649887,
-0.027424974367022514,
0.0050752474926412106,
0.03829459846019745,
0.01384774036705494,
-0.015049707144498825,
0.006603189744055271,
-0.06162206083536148,
0.034844424575567245,
0.06591589003801346,
0.013991276733577251,
-0.000018063812603941187,
-0.06083091348409653,
0.028393004089593887,
0.03297713026404381,
0.0384252704679966,
0.014421922154724598,
0.03833357244729996,
0.02617725171148777,
0.07222652435302734,
0.013998644426465034,
-0.026285171508789062,
-0.005787890870124102,
0.041646454483270645,
0.006367943249642849,
0.02392941154539585,
0.012761016376316547,
0.020317476242780685,
-0.09849997609853745,
-0.04348689690232277,
-0.015633191913366318,
0.014333772473037243,
0.038800667971372604,
0.017102209851145744,
0.029554355889558792,
-0.012550772167742252,
0.028855537995696068,
-0.027338752523064613,
-0.05177880823612213,
0.03848312050104141,
0.02126283384859562,
0.009824339300394058,
-0.06959355622529984,
0.08681483566761017,
0.0060034566558897495,
0.06759805232286453,
-0.011274912394583225,
0.04709026962518692,
0.012875426560640335,
0.023307498544454575,
-0.07527904212474823,
0.01573767326772213,
-0.026453537866473198,
0.061084575951099396,
-0.08398128300905228,
0.08220928907394409,
0.08561267703771591,
0.024111321195960045,
0.005226454697549343,
0.0015742952236905694,
-0.03590255230665207,
-0.011538645252585411,
0.04889438673853874,
-0.007215494755655527,
0.05702020227909088,
-0.0583813451230526,
-0.016272900626063347,
-0.0274241603910923,
0.023570742458105087,
0.04161645844578743,
-0.03972390294075012,
0.03197377920150757,
-0.011910872533917427,
0.03553127869963646,
0.06719320267438889,
-0.047170840203762054,
-0.05094226822257042,
0.049144793301820755,
-0.074375219643116,
0.001357192755676806,
-0.029039092361927032,
0.027069997042417526,
0.012038031592965126,
0.02319084294140339,
-0.08486472815275192,
-0.011528603732585907,
-0.017013469710946083,
-0.03089670091867447,
-0.10027466714382172,
-0.014469552785158157,
-0.014539994299411774,
-0.008378162980079651,
-0.044377733021974564,
0.008488408289849758,
0.009790207259356976,
0.06336880475282669,
-0.023942209780216217,
0.007590151857584715,
0.00840767566114664,
0.026203662157058716,
-0.03604278713464737,
0.010592760518193245,
0.021415112540125847,
0.01037208829075098,
-0.01444630604237318,
0.011210267432034016,
0.021417099982500076,
-0.04143469035625458,
-0.00664087850600481,
-0.03241918981075287,
0.040910083800554276,
0.05709441378712654,
-0.03740372881293297,
0.031852759420871735,
0.0044243596494197845,
-0.0013167354045435786,
-0.026040783151984215,
-0.0009427997283637524,
-0.050999365746974945,
-0.049051206558942795,
0.00418145302683115,
-0.017325744032859802,
-0.02192249521613121,
0.011639834381639957,
-0.005089328624308109,
-0.023173853754997253,
-0.07862602919340134,
0.010562318377196789,
-0.012708229944109917,
-0.03462453559041023,
-0.0068894242867827415,
-0.02081810124218464,
-0.07238104194402695,
0.010483269579708576,
0.021574556827545166,
-0.032647449523210526,
-0.03470495343208313,
0.025391094386577606,
-0.03672102093696594,
0.03458164632320404,
0.02343561127781868,
-0.02021121233701706,
0.02435978315770626,
-0.06643664836883545,
-0.0037544514052569866,
0.005278273485600948,
0.0518031120300293,
-0.050029952079057693,
-0.010837825946509838,
-0.006258607842028141,
-0.01318089384585619,
0.049026310443878174,
0.019580209627747536,
0.03636808693408966,
0.04944021627306938,
-0.033597659319639206,
0.014639812521636486,
0.028409387916326523,
-0.03788776695728302,
0.00709945522248745,
0.02340484969317913,
-0.002284696791321039,
-0.011967385187745094,
0.0530492402613163,
0.0304856114089489,
-0.052110765129327774,
-0.03634599223732948,
-0.059719402343034744,
-0.05854836478829384,
0.02595599927008152,
-0.009414752945303917,
-0.09178853780031204,
-0.043564677238464355,
0.024029193446040154
] |
<p>I am considering the cathode ray tube of the set up, when the cathode rays were discovered</p>
<p>Voltage = Very High<br />
Gas = any<br />
Atmospheric Pressure = We change</p>
<p>(In the following example i am just changing the atmospheric pressure everything else is kept same)</p>
<p>At <br />
1 atmospheric pressure (atm) -> Tube Does not glow<br />
0.1 atm -> The whole tube lightens<br />
0.01 atm -> The tube glows at the anode end (Glowing is shown as there is a detector coating of ZnS)</p>
<p>[Note: I don't have this set-up this is just taken by me from theory]</p>
<p>My Question: why when i am just reducing the atm from 1 to 0.01 first it is not glowing then it glows completely and after that it glow just at one end. Why so?</p>
<p>[I am asking this question here because on chemistry forum i was suggested by someone to post it here too as it was related to plasma and people over here could help me better. <a href="http://chemistry.stackexchange.com/questions/8632/cathode-ray-tube">Link</a> to my question on chemistry forum]</p> | g4553 | [
0.0633007362484932,
-0.007539091166108847,
0.0013254048535600305,
0.0669623389840126,
0.03272716701030731,
0.029070287942886353,
0.011183228343725204,
0.03900811821222305,
-0.055574558675289154,
-0.022641552612185478,
0.018273012712597847,
0.10159514099359512,
-0.009420421905815601,
0.0521261990070343,
-0.0026287506334483624,
-0.01452384889125824,
0.08698675036430359,
-0.007305261213332415,
0.03500714153051376,
-0.011947549879550934,
-0.06955983489751816,
-0.008029807358980179,
-0.040871452540159225,
-0.08758591115474701,
-0.036846600472927094,
0.02147754468023777,
0.016347235068678856,
0.051347069442272186,
0.025240041315555573,
-0.07873046398162842,
0.014484538696706295,
-0.017841702327132225,
0.013171052560210228,
0.050409093499183655,
0.029265237972140312,
-0.06744325906038284,
0.0444975309073925,
0.016233865171670914,
-0.029689185321331024,
0.020635798573493958,
-0.009942092932760715,
0.008488227613270283,
0.058902956545352936,
0.004515528678894043,
-0.012952379882335663,
0.013257431797683239,
-0.02145077846944332,
-0.046963416039943695,
0.005183505360037088,
-0.04944085329771042,
0.017507776618003845,
0.020391220226883888,
-0.07463380694389343,
-0.0525776743888855,
0.022157486528158188,
0.022478202357888222,
-0.05244944617152214,
-0.020313937216997147,
0.044126663357019424,
-0.025443267077207565,
0.0013512922450900078,
0.020678693428635597,
0.019199008122086525,
0.0008798864437267184,
-0.0025897445157170296,
-0.017233897000551224,
-0.028534797951579094,
-0.0197640061378479,
0.045699648559093475,
0.015035940334200859,
-0.030959779396653175,
-0.010561442002654076,
-0.04096939414739609,
0.001882305950857699,
0.016836920753121376,
0.009678604081273079,
-0.023374704644083977,
-0.005573015194386244,
-0.018010351806879044,
0.05528966709971428,
-0.035795293748378754,
0.0075146909803152084,
0.022094234824180603,
-0.008318041451275349,
-0.019111812114715576,
-0.010673324577510357,
-0.021616537123918533,
-0.029022986069321632,
-0.07188329845666885,
-0.02161371149122715,
-0.007900324650108814,
-0.07382116466760635,
0.08240485191345215,
-0.056449044495821,
0.03702491521835327,
0.040782343596220016,
0.02494179457426071,
0.08997237682342529,
0.03646856173872948,
0.01304918434470892,
-0.03461895138025284,
-0.0432480089366436,
0.007004460785537958,
0.029640795662999153,
-0.04313843697309494,
-0.0023479717783629894,
-0.021962705999612808,
0.00025352786178700626,
-0.059256553649902344,
-0.021232806146144867,
-0.01574835740029812,
-0.08007422834634781,
-0.06654644012451172,
-0.011493230238556862,
-0.0030676748137921095,
-0.023860694840550423,
0.04795073717832565,
0.014147487469017506,
-0.02325441502034664,
-0.03229966759681702,
0.045886747539043427,
0.033137332648038864,
0.030463045462965965,
-0.054026395082473755,
0.006904707755893469,
-0.03066699393093586,
0.022669441998004913,
0.017470326274633408,
0.005662619601935148,
0.015116655267775059,
-0.00980837456882,
0.017203832045197487,
-0.030259747058153152,
0.07768434286117554,
0.02984391711652279,
0.012765010818839073,
0.012737222015857697,
-0.0038394026923924685,
0.03877992555499077,
0.034006517380476,
0.0030869210604578257,
0.023196937516331673,
0.020124401897192,
0.005811949260532856,
-0.0332953967154026,
0.004825967364013195,
-0.019037935882806778,
0.015960752964019775,
0.05104374885559082,
-0.01668381318449974,
0.0006287379655987024,
0.0033219337929040194,
-0.0034034813288599253,
-0.050248920917510986,
-0.03628851845860481,
-0.03594543784856796,
0.020055552944540977,
-0.034731943160295486,
-0.004179471638053656,
0.024392828345298767,
0.0458037294447422,
-0.011148880235850811,
-0.003028874984011054,
-0.043211374431848526,
-0.05806970223784447,
0.023617645725607872,
0.018650958314538002,
-0.01638702303171158,
-0.041331641376018524,
-0.0049026040360331535,
-0.05369432270526886,
-0.03495939075946808,
-0.003348816419020295,
0.027868598699569702,
0.018975557759404182,
0.07497137039899826,
0.08983711898326874,
0.025811560451984406,
-0.013841978274285793,
0.00017206327174790204,
-0.023525236174464226,
-0.03500958904623985,
-0.009605553932487965,
-0.08927645534276962,
0.039807092398405075,
0.0075417920015752316,
-0.03547435998916626,
-0.019510678946971893,
-0.10057118535041809,
-0.0006250437581911683,
0.047522563487291336,
-0.04639414697885513,
-0.004387290682643652,
-0.0026393767911940813,
-0.0001290432846872136,
-0.04058477282524109,
-0.02632717601954937,
-0.0003630083811003715,
-0.05439772829413414,
0.039232607930898666,
-0.03989618271589279,
0.022950053215026855,
0.02703479491174221,
0.038067225366830826,
0.04293306916952133,
-0.014848786406219006,
-0.0435645692050457,
-0.007563235703855753,
-0.019411057233810425,
0.024431467056274414,
-0.004694337025284767,
0.032742563635110855,
-0.005913222208619118,
-0.00036626230576075613,
-0.05906641110777855,
0.004232686012983322,
0.00942698959261179,
0.044747743755578995,
-0.0001228380569955334,
-0.01029488630592823,
-0.0018693219171836972,
0.03543071076273918,
0.05966132506728172,
0.011878975667059422,
-0.0376950241625309,
-0.018005207180976868,
0.012778758071362972,
-0.038277920335531235,
0.045280393213033676,
0.022399835288524628,
-0.02003180794417858,
0.056313201785087585,
-0.027827763929963112,
0.012291411869227886,
0.027760185301303864,
-0.031771253794431686,
0.002896268852055073,
-0.006320987828075886,
-0.015413949266076088,
-0.020689716562628746,
-0.049204617738723755,
-0.06432650238275528,
-0.003190307877957821,
0.02952689118683338,
0.010385661385953426,
-0.009164095856249332,
0.009413646534085274,
0.012242453172802925,
-0.01639775186777115,
-0.01383443083614111,
-0.019119586795568466,
0.03551001101732254,
0.03581773862242699,
0.0588262565433979,
0.04052550345659256,
-0.053759098052978516,
-0.0791681781411171,
0.08086280524730682,
0.010518333874642849,
-0.06177666410803795,
0.002345910994336009,
-0.02713901549577713,
-0.015265888534486294,
-0.0046776821836829185,
-0.045353956520557404,
0.03656790778040886,
-0.04002945125102997,
0.026264632120728493,
0.042459629476070404,
-0.020582852885127068,
0.03602612391114235,
0.015649564564228058,
-0.029818715527653694,
0.008240197785198689,
-0.021560776978731155,
0.05025900900363922,
0.009007754735648632,
-0.026934701949357986,
0.0738142803311348,
-0.03405500203371048,
0.025400804355740547,
0.01362256333231926,
-0.12236471474170685,
-0.025073230266571045,
-0.0270497128367424,
0.004363400861620903,
0.07316888123750687,
-0.03115992061793804,
-0.03394126519560814,
0.03845199570059776,
-0.04272734001278877,
-0.03431154787540436,
0.020258376374840736,
0.021670231595635414,
0.02897857129573822,
-0.04430378973484039,
0.04351428896188736,
-0.012218019925057888,
-0.048180822283029556,
0.014320939779281616,
0.01134764589369297,
-0.02963870018720627,
-0.020515117794275284,
0.05590058118104935,
0.029631128534674644,
0.026990395039319992,
-0.03714283928275108,
0.008840998634696007,
-0.06077965348958969,
0.03247478976845741,
0.0041007986292243,
-0.015291281044483185,
0.06528524309396744,
-0.01295735128223896,
0.02965805120766163,
0.004721161909401417,
-0.015547038055956364,
-0.007838454097509384,
0.01948251761496067,
0.05820174887776375,
-0.04264429584145546,
0.0229604821652174,
-0.03543620556592941,
-0.012912832200527191,
0.008182106539607048,
-0.002675874624401331,
0.02352546714246273,
0.01160640362650156,
0.03211931139230728,
0.03487510606646538,
0.009261615574359894,
0.03600189462304115,
-0.03231343254446983,
-0.0496748611330986,
-0.004488009959459305,
-0.031109454110264778,
-0.0278006624430418,
0.07160347700119019,
-0.04011679068207741,
0.020506134256720543,
-0.009345097467303276,
-0.015280981548130512,
-0.03776963800191879,
0.024279730394482613,
0.043978821486234665,
0.007357351947575808,
-0.03449346870183945,
-0.05681004747748375,
-0.033468686044216156,
-0.008745575323700905,
0.0489470437169075,
0.030292894691228867,
-0.016691777855157852,
0.017823347821831703,
-0.08006332814693451,
-0.026140831410884857,
0.018554246053099632,
0.07895033061504364,
0.0034234027843922377,
-0.03026476874947548,
0.00945949275046587,
-0.06482771784067154,
-0.02614002302289009,
0.019484639167785645,
-0.0056941574439406395,
0.010139002464711666,
0.02712361142039299,
0.04204991087317467,
0.001568860956467688,
-0.040375661104917526,
0.008632372133433819,
-0.01563103124499321,
-0.016072163358330727,
0.0012014417443424463,
-0.020603695884346962,
-0.010500612668693066,
-0.04387129470705986,
0.03826754912734032,
0.00034400253207422793,
0.09930282086133957,
0.01478277612477541,
-0.00283183460123837,
0.01214640773832798,
-0.009469365701079369,
-0.007021821103990078,
0.06369226425886154,
-0.010428342968225479,
0.018179867416620255,
-0.04275568202137947,
-0.09529683738946915,
0.012868606485426426,
0.02204643189907074,
-0.023008903488516808,
0.02836092747747898,
0.0045781913213431835,
-0.03882945701479912,
0.04416384920477867,
0.006920052692294121,
0.004225057549774647,
-0.0247824564576149,
-0.03662038967013359,
0.01796364039182663,
0.042115841060876846,
-0.06166817620396614,
-0.007972377352416515,
-0.03646646440029144,
0.037539537996053696,
-0.005085699260234833,
0.061543360352516174,
0.03743647038936615,
-0.01831478625535965,
-0.0016300530405715108,
-0.01131153292953968,
-0.029293924570083618,
0.024812117218971252,
-0.018883127719163895,
-0.022451350465416908,
0.022599391639232635,
0.02315373905003071,
-0.009653191082179546,
0.0014043509727343917,
0.04478733614087105,
-0.03402210399508476,
-0.053011614829301834,
-0.012111141346395016,
0.08331145346164703,
0.03468191996216774,
0.01709648221731186,
0.03371806442737579,
-0.029407931491732597,
0.005130973178893328,
-0.01933605782687664,
-0.05964482203125954,
-0.010866126045584679,
-0.04455083981156349,
0.061723023653030396,
0.03215831145644188,
0.017642725259065628,
-0.007701103575527668,
0.04211638867855072,
0.10380043089389801,
-0.013345691375434399,
-0.022843752056360245,
-0.013770801946520805,
0.03926840052008629,
-0.007606214843690395,
-0.025474760681390762,
-0.03829772397875786,
0.01419103518128395,
-0.04169441759586334,
-0.06785950809717178,
0.010741563513875008,
-0.052553750574588776,
-0.04683830961585045,
0.018785029649734497,
-0.033751148730516434,
-0.03912993147969246,
0.03797554224729538,
-0.03454430773854256,
0.062054891139268875,
-0.08278284221887589,
0.04375079646706581,
-0.008694391697645187,
0.03515191003680229,
0.062316931784152985,
-0.051222193986177444,
-0.01293791551142931,
-0.08128289878368378,
-0.025052333250641823,
-0.0018412520876154304,
-0.02569877728819847,
-0.033055566251277924,
-0.0026469503063708544,
-0.0019341477891430259,
0.019587814807891846,
-0.032406993210315704,
0.00972244143486023,
-0.028942029923200607,
0.006425065919756889,
-0.05001593008637428,
-0.00499668950214982,
0.060433529317379,
0.06185011938214302,
0.03500431403517723,
0.020592905580997467,
-0.0013981153024360538,
-0.05745716020464897,
0.007996735163033009,
0.04881913959980011,
-0.014838360249996185,
0.07151187211275101,
0.0577063262462616,
0.03322553634643555,
-0.0550110787153244,
0.0538247674703598,
-0.055740438401699066,
0.046452462673187256,
-0.047944214195013046,
-0.020156793296337128,
0.08830705285072327,
-0.033947743475437164,
-0.051503896713256836,
-0.02752102166414261,
0.025079848244786263,
-0.023130597546696663,
0.02180020697414875,
0.0006212181760929525,
-0.023634739220142365,
0.044949792325496674,
0.010146870277822018,
-0.02515251934528351,
0.009634827263653278,
0.010483638383448124,
0.0021488075144588947,
-0.010249928571283817,
-0.1017250195145607,
-0.07543759047985077,
0.031588856130838394,
-0.009638425894081593,
-0.0011872918112203479,
-0.022250857204198837,
-0.00372351985424757,
0.0024463466834276915,
-0.010628774762153625,
0.030696090310811996,
0.04218029975891113,
-0.020776836201548576,
0.011030678637325764,
0.05495719984173775,
0.00953659787774086,
0.005960557144135237,
-0.017901763319969177,
0.06421361118555069,
0.0002513617801014334,
0.023666882887482643,
0.0034145235549658537,
0.008470661006867886,
-0.012543532997369766,
0.03915486857295036,
-0.001625241944566369,
-0.005027557723224163,
0.022287307307124138,
0.026720445603132248,
0.022621048614382744,
0.018320463597774506,
-0.008747276850044727,
-0.010490477085113525,
0.014193011447787285,
0.01104272436350584,
-0.03875020891427994,
0.022579699754714966,
0.048234157264232635,
-0.011994383297860622,
0.03418391942977905,
-0.010149763897061348,
0.038615379482507706,
0.006082755979150534,
0.019747352227568626,
0.05961108207702637,
-0.05899616703391075,
0.025421015918254852,
-0.009304379113018513,
-0.011753734201192856,
0.021084312349557877,
0.10475849360227585,
-0.044208500534296036,
-0.025834959000349045,
0.03546439856290817,
0.03357549384236336,
-0.0003577987081371248,
0.010112525895237923,
-0.019266782328486443,
-0.001584632322192192,
-0.09747292101383209,
0.0022173570469021797,
0.044811833649873734,
-0.025127720087766647,
0.0318714901804924,
-0.007779527921229601,
0.008263474330306053,
0.022693702951073647,
-0.027245299890637398,
0.014905894175171852,
-0.03736501559615135,
0.04046400636434555,
-0.005587445572018623,
0.015488194301724434,
-0.02711998112499714,
0.011434509418904781,
-0.05107882246375084,
-0.055812835693359375,
-0.012126770801842213,
0.023793838918209076,
0.02735823020339012,
-0.03754536062479019,
0.007088547572493553,
0.006411977577954531,
-0.043535266071558,
-0.0035209651105105877,
-0.05961773917078972,
-0.004753544460982084,
0.005330882966518402,
0.0036418919917196035,
0.006289210636168718,
0.04749967157840729,
-0.036766115576028824,
0.060769591480493546,
0.022068621590733528,
0.02635590173304081,
0.06012442708015442,
0.03886942192912102,
0.017196282744407654,
-0.03165418654680252,
-0.025349827483296394,
0.017747923731803894,
-0.03250233083963394,
0.0014804466627538204,
0.09961535781621933,
0.02936095930635929,
0.06440528482198715,
-0.02858457714319229,
-0.01163717545568943,
0.03839626535773277,
0.06921105831861496,
0.04365655779838562,
0.051031265407800674,
-0.019611261785030365,
-0.031592268496751785,
0.07261139154434204,
-0.04145170748233795,
-0.005599010270088911,
-0.0012306816643103957,
-0.04930553585290909,
0.005781159736216068,
0.02211349457502365,
0.00933896191418171,
0.03753509745001793,
0.014612828381359577,
0.001621323637664318,
0.008405998349189758,
-0.02858663909137249,
0.015532529912889004,
0.06319452077150345,
0.02878010831773281,
-0.03024406172335148,
0.003236931748688221,
-0.030020086094737053,
-0.007551528513431549,
-0.060184676200151443,
0.01626032218337059,
0.021503765136003494,
-0.03939667344093323,
-0.028915075585246086,
0.04338373988866806,
0.0018692007288336754,
0.007124215364456177,
-0.0652945414185524,
-0.010855681262910366,
0.033923860639333725,
-0.012414825148880482,
-0.03405436500906944,
-0.049495454877614975,
-0.03471178188920021,
0.002505300333723426,
0.02583969011902809,
0.0759342759847641,
-0.010753164999186993,
-0.05793865770101547,
0.007360586430877447,
-0.04006744548678398,
-0.06340141594409943,
-0.0036029964685440063,
-0.014146975241601467,
-0.038174644112586975,
0.00883227214217186,
0.017824631184339523,
0.06156543269753456,
-0.0036509190686047077,
-0.04674435406923294,
-0.027243565768003464,
-0.06623409688472748,
0.021596098318696022,
-0.0015865849563851953,
-0.03414321318268776,
-0.0235529076308012,
-0.007406695745885372,
-0.05547080561518669,
-0.0131850466132164,
-0.005317743867635727,
-0.021244172006845474,
0.030985917896032333,
0.02236950770020485,
0.0789259597659111,
0.022987212985754013,
0.027561943978071213,
0.026436856016516685,
0.02421713061630726,
0.0063534448854625225,
0.006292589008808136,
-0.08343226462602615,
0.03937887027859688,
-0.0067866151221096516,
-0.01334405317902565,
0.03393520414829254,
0.03744679316878319,
-0.003965291194617748,
-0.010551323182880878,
0.014616177417337894,
0.010981266386806965,
0.013250592164695263,
0.02216007560491562,
0.060288794338703156,
0.09480919688940048,
0.03070584498345852,
0.014232490211725235,
-0.009534889832139015,
-0.05443660542368889,
0.014972575008869171,
0.033393457531929016,
0.02448049746453762,
-0.06940176337957382,
-0.03376662731170654,
0.013090179301798344,
0.01665915735065937,
0.0009181610657833517,
-0.000039556056435685605,
-0.005519229453057051,
-0.018187282606959343,
0.03453168645501137,
-0.028367187827825546,
-0.017305463552474976,
0.04204306751489639,
-0.039769917726516724,
0.03715982660651207,
-0.0381191149353981,
-0.01835348829627037,
0.02967800572514534,
0.002641283441334963,
0.0016842788318172097,
-0.005603928118944168,
-0.030489813536405563,
-0.0482574962079525,
0.03250718116760254,
-0.01989755406975746,
-0.007350685074925423,
-0.009522633627057076,
0.004438284784555435,
0.0380362793803215,
0.046730753034353256,
-0.025267481803894043,
-0.051184941083192825,
-0.01674336940050125,
0.001025770790874958,
-0.032255228608846664,
0.029333505779504776,
-0.048205967992544174,
-0.005065875593572855,
-0.023672113195061684,
-0.02061551809310913,
-0.030825208872556686,
-0.004300554282963276,
0.04527132958173752,
0.0030902863945811987,
0.013641574420034885,
0.05681609734892845,
0.015055477619171143,
-0.029075482860207558,
-0.07581255584955215
] |
<p>On pp 103 - 105 of <em>The Character of Physical Law</em>, Feynman draws this diagram to demonstrate that invariance under spatial translation leads to conservation of momentum:</p>
<p><img src="http://i.stack.imgur.com/BrYgE.jpg" alt="enter image description here"></p>
<p>To paraphrase Feynman's argument (if I understand it correctly), a particle's trajectory is the path AB. Space is horizontal; time vertical. </p>
<p>Because of spatial translation symmetry, the path CD has the same action as AB. Because AB has stationary action, ACDB has the same action as well.</p>
<p>That means the action of AC and BD are the same. (Note that they are traversed in opposite directions on the path ACDB.) This is a conserved quantity, and it turns out to be the momentum.</p>
<p>My question is about the meaning of the action of AC and BD. These paths aren't physical trajectories; they represent infinite velocity. I tried thinking of the trajectory as if the velocity, as a function of time, has two delta functions in it. However, because the Lagrangian depends on $v^2$, I think this leads to infinite action for the horizontal segments.</p>
<p>Mathematically, I see that the symmetry here implies $\frac{\partial L}{\partial x} = 0$. Least action implies $\frac{\partial L}{\partial x} = \frac{\mathrm{d}}{\mathrm{d}t}\frac{\partial L}{\partial \dot{x}}$. Combining these shows that the momentum $\frac{\partial L}{\partial \dot{x}}$ is constant, but I don't quite understand the connection to the picture.</p>
<p>Also, Feynman doesn't describe how he knows the conserved quantity is the momentum. Is there a way to get this from the picture? Finally, if momentum is being conserved, why isn't the trajectory a straight line?</p> | g4554 | [
0.059791501611471176,
-0.030822347849607468,
-0.019119182601571083,
-0.0005215650890022516,
0.10539853572845459,
0.039764195680618286,
0.08763712644577026,
0.035561032593250275,
-0.051644254475831985,
-0.030848097056150436,
0.003034146036952734,
-0.009208166971802711,
-0.010180968791246414,
-0.023558521643280983,
0.001976239960640669,
0.007975064218044281,
0.015460778959095478,
0.005745351780205965,
0.052614446729421616,
-0.017631778493523598,
-0.022265160456299782,
0.027159320190548897,
-0.012236364185810089,
0.00009352870256407186,
0.018544582650065422,
-0.04035525768995285,
0.0366935059428215,
-0.03422261402010918,
-0.0838753804564476,
-0.028171470388770103,
0.03359508514404297,
0.007857969962060452,
0.04032847285270691,
-0.04542430117726326,
-0.06054231896996498,
-0.050257302820682526,
0.046761639416217804,
-0.006278602872043848,
0.050621405243873596,
0.03890245035290718,
0.0372503437101841,
-0.020886341109871864,
-0.022606978192925453,
-0.0001747636270010844,
0.02428295649588108,
-0.023493202403187752,
-0.0599207803606987,
-0.057936958968639374,
-0.06153549998998642,
-0.010032884776592255,
-0.004724367521703243,
0.0254343394190073,
-0.0077693709172308445,
0.0006026951596140862,
0.019459843635559082,
0.033316630870103836,
0.04669132083654404,
-0.03814498335123062,
-0.01288587599992752,
0.03158969432115555,
0.0115324342623353,
-0.013707817532122135,
0.010901419445872307,
0.0386231429874897,
0.08588089793920517,
-0.07799173891544342,
-0.06913059949874878,
-0.032745569944381714,
-0.013182410970330238,
-0.010437246412038803,
0.04952139034867287,
-0.05273783951997757,
-0.004500989336520433,
-0.012506854720413685,
0.026272201910614967,
0.005650968290865421,
-0.03116060234606266,
-0.01933259144425392,
0.042320266366004944,
-0.02827964536845684,
-0.09037423878908157,
0.01376801822334528,
-0.0017902982654049993,
0.057256270200014114,
0.09016866981983185,
0.011788069270551205,
-0.008266638033092022,
0.0041845254600048065,
-0.06512197107076645,
-0.017431151121854782,
0.003729891963303089,
-0.03483162447810173,
0.029871314764022827,
0.025097794830799103,
-0.04512671381235123,
-0.03802856057882309,
-0.042265187948942184,
0.04123837500810623,
-0.004443219862878323,
-0.02691044844686985,
-0.03610474616289139,
0.001334114815108478,
-0.02567761205136776,
0.0005249562673270702,
0.05271805822849274,
0.00047611535410396755,
0.03441929444670677,
0.023571934551000595,
-0.002252725185826421,
0.005722359288483858,
0.011273892596364021,
-0.07060854882001877,
-0.06294478476047516,
-0.002501989947631955,
-0.024356883019208908,
-0.0179765447974205,
0.054023150354623795,
-0.020981473848223686,
0.008065763860940933,
0.07545433938503265,
0.03000614419579506,
-0.012961553409695625,
-0.00352921849116683,
0.028294071555137634,
-0.020620018243789673,
0.02285456284880638,
-0.06614872813224792,
0.01145199779421091,
0.045298296958208084,
0.018546270206570625,
-0.0036312087904661894,
-0.013494114391505718,
0.014369762502610683,
0.04596901312470436,
-0.005819389596581459,
-0.007700280752032995,
-0.001630206941626966,
0.055514413863420486,
0.017669910565018654,
0.01197310071438551,
-0.0027233122382313013,
0.004843251314014196,
-0.007050598505884409,
0.008785557001829147,
-0.028543030843138695,
0.04614955186843872,
-0.03390096127986908,
-0.010501998476684093,
0.03229307383298874,
-0.04845605045557022,
0.003899946575984359,
0.11027567833662033,
0.013419470749795437,
0.0064237406477332115,
0.017154935747385025,
-0.059495165944099426,
0.11457014828920364,
0.04368165507912636,
-0.038799066096544266,
0.0007584867416881025,
0.05861072987318039,
0.038854945451021194,
0.04492265358567238,
-0.04470203444361687,
-0.08009140193462372,
-0.025588562712073326,
0.012839037925004959,
-0.07272103428840637,
0.01854380965232849,
-0.05438818037509918,
-0.0813184306025505,
0.02871032804250717,
0.025723082944750786,
0.07217071205377579,
-0.003863008925691247,
0.01660413295030594,
-0.0953483060002327,
-0.011957604438066483,
0.029955048114061356,
-0.06685740500688553,
-0.040833890438079834,
0.009216997772455215,
0.06428582221269608,
0.02724272944033146,
0.002888676943257451,
0.02968773990869522,
0.009999707341194153,
0.0354444719851017,
-0.03619597107172012,
-0.0527803972363472,
0.02670450136065483,
0.009728936478495598,
-0.041335783898830414,
0.03985600173473358,
0.007659948896616697,
-0.013582242652773857,
0.005765638314187527,
-0.03585520014166832,
-0.0892505943775177,
0.008108772337436676,
-0.0024844943545758724,
0.029020458459854126,
0.06409618258476257,
0.00474808644503355,
0.024892771616578102,
0.04067060351371765,
-0.025973891839385033,
-0.009344825521111488,
0.012076550163328648,
0.030798600986599922,
0.05153505504131317,
-0.006314560770988464,
-0.012918077409267426,
-0.02219998463988304,
0.014780811965465546,
-0.02758210152387619,
-0.0033925906755030155,
0.028465580195188522,
-0.04183018207550049,
-0.013942716643214226,
-0.0300277266651392,
-0.05657791718840599,
0.01829966902732849,
-0.01285786833614111,
-0.041057392954826355,
0.04070983827114105,
-0.03590768203139305,
-0.02508717216551304,
-0.011858828365802765,
0.050617799162864685,
-0.022726694121956825,
0.0017710948595777154,
-0.039120741188526154,
-0.0006748448358848691,
0.023585906252264977,
-0.032048385590314865,
0.006358913145959377,
0.029420863837003708,
0.024116424843668938,
0.02742943912744522,
0.04094870388507843,
0.008004507049918175,
0.0004269665223546326,
-0.026845352724194527,
0.07635845988988876,
0.013721272349357605,
0.03860751911997795,
0.032402049750089645,
-0.011096091940999031,
0.030678143724799156,
0.013319386169314384,
0.017824295908212662,
0.021236004307866096,
-0.001842871424742043,
0.024588245898485184,
-0.004735197871923447,
0.011702173389494419,
0.010990873910486698,
-0.027376292273402214,
-0.048665229231119156,
-0.0005409404984675348,
-0.04415342956781387,
-0.012861578725278378,
0.03888298198580742,
-0.05250175669789314,
-0.010867428965866566,
-0.003579697571694851,
0.05004579573869705,
0.051199592649936676,
-0.00028904585633426905,
-0.015974853187799454,
0.08244495838880539,
-0.037599582225084305,
0.037254851311445236,
-0.023776303976774216,
-0.0044722165912389755,
0.0535750538110733,
-0.014974243938922882,
0.0031262622214853764,
-0.01356713380664587,
-0.007215413730591536,
0.03531433641910553,
-0.04511647671461105,
0.0245856661349535,
0.1158367395401001,
0.003128943732008338,
-0.022611742839217186,
0.012412882409989834,
-0.030169473960995674,
0.04512950778007507,
-0.0445987693965435,
0.0034026664216071367,
0.05505847558379173,
-0.004719321615993977,
-0.022279798984527588,
0.017236201092600822,
0.015181725844740868,
-0.05650452896952629,
-0.021006187424063683,
-0.04723413661122322,
-0.0391569621860981,
-0.00899758841842413,
0.009251770563423634,
0.035213809460401535,
0.016918761655688286,
0.04681564122438431,
-0.07031693309545517,
-0.025634774938225746,
-0.008160716854035854,
0.02707616053521633,
-0.0029951101168990135,
0.04991401359438896,
-0.06437209993600845,
-0.047076109796762466,
-0.0076681808568537235,
-0.026585420593619347,
-0.04610617086291313,
0.003273945301771164,
0.000801424088422209,
0.04602484777569771,
-0.04240145534276962,
-0.04107401892542839,
0.005994938313961029,
-0.015360305085778236,
0.045036330819129944,
-0.02868243120610714,
-0.06013171002268791,
-0.00785705354064703,
-0.03285893052816391,
-0.03808555006980896,
-0.044136546552181244,
-0.005362230818718672,
0.0119393989443779,
0.00793064758181572,
-0.0018037132686004043,
-0.03245486691594124,
-0.07714749872684479,
-0.01366762351244688,
0.06006293371319771,
-0.06804945319890976,
0.008465183898806572,
-0.030026065185666084,
-0.05047750100493431,
0.014813206158578396,
0.030805042013525963,
-0.009427213110029697,
0.0254889577627182,
0.04649671912193298,
0.04145156592130661,
0.0011008414439857006,
0.02515137568116188,
-0.020843561738729477,
0.005223346408456564,
0.0036840392276644707,
-0.01928844302892685,
0.0602099746465683,
0.027931101620197296,
0.0424480214715004,
-0.002898820675909519,
-0.022088203579187393,
-0.020968357101082802,
-0.0006990236579440534,
-0.029353130608797073,
0.03363838046789169,
-0.012170642614364624,
0.04363381862640381,
-0.05357545614242554,
-0.017734341323375702,
0.04048847407102585,
0.030164014548063278,
0.0010018645552918315,
-0.07199997454881668,
-0.04511535167694092,
0.018340233713388443,
0.006148754619061947,
-0.011781236156821251,
-0.010154970921576023,
-0.014212369918823242,
-0.06910993158817291,
0.027945732697844505,
0.010365797206759453,
0.06320308893918991,
0.03567167744040489,
0.030120601877570152,
0.03934277221560478,
0.06833270937204361,
-0.030766842886805534,
0.06867817789316177,
0.02708883211016655,
-0.0040379962883889675,
0.04540267959237099,
-0.036751940846443176,
0.017500417307019234,
-0.06673689931631088,
0.04072458669543266,
0.03268570080399513,
0.012937380000948906,
0.013328485190868378,
-0.02277912199497223,
-0.020362569019198418,
-0.03724685311317444,
-0.0004332262324169278,
-0.009896787814795971,
0.011758621782064438,
-0.013787521980702877,
0.037100788205862045,
0.036519501358270645,
-0.04916023463010788,
0.028221718966960907,
-0.023112522438168526,
0.020407432690262794,
-0.012813655659556389,
0.008050616830587387,
-0.043923571705818176,
-0.032247867435216904,
0.035308148711919785,
-0.05742217227816582,
-0.049283161759376526,
0.004654522053897381,
-0.004086489323526621,
0.09922568500041962,
0.0437166765332222,
0.04830401763319969,
-0.036844417452812195,
0.026397857815027237,
0.021810542792081833,
0.061367250978946686,
-0.028149591758847237,
-0.03309956192970276,
-0.02959868684411049,
0.0027858407702296972,
0.04144997522234917,
0.004317435435950756,
0.013612832874059677,
-0.06102081760764122,
0.03251596540212631,
-0.02485019527375698,
0.01028249692171812,
0.037170857191085815,
0.0863310843706131,
0.06915412098169327,
-0.01129408460110426,
0.009248888120055199,
-0.02655484899878502,
-0.04471205547451973,
0.03959262743592262,
0.03753812238574028,
-0.063395656645298,
-0.009543134830892086,
-0.031322408467531204,
0.009379731491208076,
0.07896235585212708,
-0.007382340729236603,
-0.06776449084281921,
0.039550259709358215,
-0.021032892167568207,
-0.039440613240003586,
0.020603777840733528,
0.059344641864299774,
-0.011097872629761696,
-0.11671391874551773,
0.018142519518733025,
0.009440065361559391,
-0.02487809956073761,
0.026698149740695953,
0.0033733618911355734,
-0.01742531917989254,
0.044376324862241745,
-0.03594852238893509,
-0.037208665162324905,
0.04408815875649452,
0.028926195576786995,
0.004960926249623299,
-0.018166206777095795,
0.03193717077374458,
-0.022565871477127075,
-0.00150057312566787,
0.02538466826081276,
0.009076200425624847,
-0.045829422771930695,
-0.02841530740261078,
0.0037332421634346247,
0.025094665586948395,
0.0015476858243346214,
0.004608002491295338,
-0.016583152115345,
-0.03489415720105171,
-0.014066418632864952,
-0.006968370638787746,
-0.05117855593562126,
0.017046963796019554,
-0.015234623104333878,
0.028456781059503555,
0.014657694846391678,
0.0019006585935130715,
-0.026100782677531242,
0.007723327726125717,
0.0011824289103969932,
-0.019953100010752678,
-0.009534088894724846,
-0.05169379711151123,
-0.044761206954717636,
0.014105679467320442,
-0.040254510939121246,
0.007414508610963821,
0.05649837478995323,
0.022108983248472214,
0.025588709861040115,
-0.07101192325353622,
-0.013988735154271126,
-0.01722644828259945,
0.011776208877563477,
-0.027119258418679237,
-0.004162950441241264,
0.011426430195569992,
0.00381109188310802,
0.03734381124377251,
-0.011656718328595161,
-0.03584682196378708,
-0.018033625558018684,
0.03091019205749035,
0.05066695436835289,
0.014551910571753979,
-0.05810097977519035,
0.06450632214546204,
0.005095642991364002,
-0.049788348376750946,
-0.04233032837510109,
0.00686689792200923,
0.08728711307048798,
0.011625879444181919,
0.0018170690163969994,
0.013772550970315933,
-0.0021858359687030315,
-0.07032101601362228,
-0.06524381041526794,
0.005600968841463327,
-0.03317531943321228,
0.046028632670640945,
-0.00012641519424505532,
-0.03244411572813988,
-0.05423090234398842,
-0.01156469527631998,
0.07962707430124283,
-0.025837751105427742,
0.008766679093241692,
-0.019070608541369438,
-0.03871910646557808,
-0.022737352177500725,
-0.009786990471184254,
-0.04107608646154404,
0.027325714007019997,
-0.02928077057003975,
-0.058346156030893326,
-0.022339409217238426,
0.005957505665719509,
-0.05167591571807861,
0.00899827666580677,
-0.012970306910574436,
-0.0010866186348721385,
0.05899342894554138,
0.06261637806892395,
0.02177434042096138,
-0.026510436087846756,
0.006985742598772049,
-0.027758963406085968,
0.011415974237024784,
0.03632780909538269,
0.05437956377863884,
0.0487339124083519,
-0.0006451485096476972,
0.03757550194859505,
-0.01964518055319786,
0.08724094182252884,
0.032746125012636185,
0.012443851679563522,
-0.05370275303721428,
-0.06421411782503128,
-0.09401588141918182,
-0.010882854461669922,
0.023687023669481277,
0.012077635154128075,
0.058316148817539215,
-0.022964615374803543,
-0.057657815515995026,
0.03627324849367142,
-0.040836580097675323,
-0.05545782297849655,
0.051237791776657104,
0.030301693826913834,
-0.05371929332613945,
0.026018794625997543,
-0.027362415567040443,
0.021750710904598236,
-0.0009298187796957791,
0.005100773181766272,
0.02060113474726677,
-0.04347294196486473,
-0.05677783861756325,
0.0020240156445652246,
0.018360882997512817,
0.01952272653579712,
-0.039485156536102295,
-0.03687960281968117,
-0.022609174251556396,
0.06500895321369171,
-0.03136845678091049,
-0.00516677089035511,
0.007758237887173891,
-0.007417644374072552,
-0.004262979608029127,
0.039495594799518585,
-0.021243011578917503,
0.03798185661435127,
-0.004877616185694933,
0.014296053908765316,
-0.01104780100286007,
0.031315017491579056,
-0.02893061935901642,
0.0061730085872113705,
0.0013673941139131784,
-0.0008973887306638062,
-0.04240569844841957,
-0.014078614301979542,
0.0685734823346138,
0.02756344899535179,
-0.026311667636036873,
0.06320804357528687,
0.010747828520834446,
0.050420235842466354,
-0.013423016294836998,
0.056695811450481415,
0.005493551027029753,
0.0306435264647007,
0.025613034144043922,
0.05840572342276573,
-0.0426165871322155,
0.032160334289073944,
0.02653229609131813,
0.005516294855624437,
-0.032897960394620895,
-0.020765116438269615,
0.04539310932159424,
0.012745519168674946,
-0.060715414583683014,
0.020398836582899094,
0.008253413252532482,
-0.03337627649307251,
-0.0781719759106636,
-0.007886557839810848,
-0.0171686802059412,
0.02008112706243992,
-0.032588399946689606,
0.029022252187132835,
-0.008072971366345882,
-0.01630556397140026,
-0.03467969968914986,
0.027352362871170044,
0.020368512719869614,
-0.06594093143939972,
-0.0093345632776618,
-0.03632093593478203,
0.027265286073088646,
-0.03731158375740051,
0.01977427862584591,
0.028771858662366867,
-0.03612852096557617,
-0.045526351779699326,
0.026301754638552666,
-0.023487618193030357,
-0.01610845886170864,
-0.019431376829743385,
0.019483335316181183,
0.05759552866220474,
0.006914365570992231,
0.03590497747063637,
0.01790154166519642,
0.039649732410907745,
-0.06199773773550987,
0.011917040683329105,
0.011693990789353848,
0.03414127975702286,
-0.014703713357448578,
-0.05457058176398277,
-0.02515813522040844,
-0.009803155437111855,
-0.019757749512791634,
0.023623814806342125,
-0.047798145562410355,
-0.03342922776937485,
-0.046027764678001404,
-0.012839632108807564,
0.01086624525487423,
-0.02689334563910961,
0.0222237017005682,
0.01001515332609415,
0.053102780133485794,
0.04467947781085968,
-0.017269650474190712,
0.02292291261255741,
0.046197496354579926,
-0.025833792984485626,
0.044656626880168915,
0.048743609338998795,
0.050660017877817154,
-0.04261181131005287,
0.01463274285197258,
-0.04423287883400917,
-0.018573768436908722,
-0.006926444359123707,
-0.00506706302985549,
0.017915235832333565,
0.02378731034696102,
0.010174408555030823,
0.021187450736761093,
0.015545642003417015,
-0.011176526546478271,
-0.0008280425681732595,
0.014844778925180435,
0.0087574552744627,
0.025602051988244057,
-0.003434366313740611,
-0.011720857582986355,
-0.08850689977407455,
-0.037301916629076004,
-0.026172330603003502,
-0.005494368728250265,
-0.011619099415838718,
0.022828539833426476,
0.002790930913761258,
-0.022386547178030014,
-0.014654393307864666,
-0.027351897209882736,
0.011686432175338268,
-0.010137701407074928,
-0.002864993177354336,
-0.010240147821605206,
-0.007118762470781803,
-0.006870674435049295,
0.017655596137046814,
0.011749781668186188,
-0.05731174349784851,
0.00002845274684659671,
0.013111636973917484,
-0.03186669945716858,
-0.02409241907298565,
-0.0035126639995723963,
0.009721769951283932,
0.029526229947805405,
-0.013063781894743443,
0.07748334854841232,
0.0347227044403553,
-0.006674634292721748,
0.006467445753514767,
-0.008555877953767776,
0.0020622077863663435,
0.032244179397821426,
0.012416365556418896,
0.048630598932504654,
0.05690915882587433,
-0.008096573874354362,
-0.005769610870629549,
0.02049444429576397,
-0.01944803074002266,
-0.054268233478069305,
-0.017999054864048958,
-0.059923090040683746,
0.03670995682477951
] |
<p>Imagine a vertical pipe (both ends opened) in the water. Drop several ping-pong balls into pipe and cover them with a cylinder. When you have enough balls, the cylinder will float. Now start adding weight into the top of a cylinder, and simultaneously start adding ping-pong balls via the bottom of pipe, to compensate the increasing weight. </p>
<p><img src="http://i.stack.imgur.com/Y3ZOT.jpg" alt="enter image description here"></p>
<p>At the some weight (and balls columng height) the topmost row of balls start crunching due the buoyancy pressure. <a href="http://physics.stackexchange.com/questions/8846/how-deep-in-the-ocean-can-a-ping-pong-ball-go-before-it-collapses-due-to-pressur">In this question</a> @mms <a href="http://physics.stackexchange.com/questions/8846/how-deep-in-the-ocean-can-a-ping-pong-ball-go-before-it-collapses-due-to-pressur/8851#8851">answered</a> than one ping-pong ball can withstand 3 atmosphere pressure.</p>
<p>The question is: how to approximate the maximum heigh of ball column (or maximum weight is possible float) for the pipe radius "R" before the topmost row of balls start crunching?</p>
<p>Or, maybe will start crunching not the topmost row, but somewhere else because the sum of buoyancy pressure (from the balls bellow) and water pressure will be more the 3atm. How to determine?</p> | g4555 | [
0.04163118824362755,
0.012277464382350445,
-0.005671103484928608,
-0.03879091516137123,
0.0644313246011734,
0.07052034139633179,
0.0283126812428236,
-0.015289164148271084,
-0.12582501769065857,
-0.006536722648888826,
-0.10278373956680298,
0.01261601597070694,
0.015867745503783226,
-0.03548363968729973,
0.03391154110431671,
0.0006836348329670727,
0.02041228674352169,
-0.07152517139911652,
-0.009781090542674065,
-0.059258099645376205,
-0.026889486238360405,
0.0038362503983080387,
-0.011753063648939133,
-0.036126814782619476,
-0.09176304936408997,
-0.0036075706593692303,
-0.012814206071197987,
0.011128883808851242,
-0.05939001962542534,
-0.0061323330737650394,
-0.031846046447753906,
0.01937350630760193,
-0.029581794515252113,
-0.06027628481388092,
0.03077814355492592,
-0.037445466965436935,
0.007429135497659445,
-0.03872472047805786,
-0.03795705363154411,
-0.015576876699924469,
-0.036534663289785385,
-0.05744583532214165,
0.06827853620052338,
0.02967059053480625,
-0.04633098840713501,
-0.026636717841029167,
0.014904345385730267,
0.04165883734822273,
-0.006879413966089487,
-0.06365392357110977,
0.025219205766916275,
-0.007369504310190678,
-0.05687481537461281,
-0.038493625819683075,
-0.03826380521059036,
0.043222442269325256,
0.019474128261208534,
-0.02688066102564335,
0.04732702299952507,
0.04578714072704315,
-0.043265797197818756,
0.038883060216903687,
-0.04006480798125267,
-0.02211163192987442,
0.0449497252702713,
0.006457707844674587,
-0.07973998785018921,
-0.03447645157575607,
0.012684532441198826,
-0.0010726924519985914,
0.08347953855991364,
-0.05074998736381531,
0.010988526977598667,
-0.03650198131799698,
-0.09361641854047775,
0.015248413197696209,
-0.04851572960615158,
0.007731591816991568,
0.027926713228225708,
-0.029562966898083687,
0.024481886997818947,
0.042767029255628586,
0.0016588406870141625,
-0.01274571567773819,
0.0056611886247992516,
-0.023687362670898438,
-0.020432496443390846,
-0.04517969861626625,
-0.05781680718064308,
0.03589017316699028,
-0.0550839863717556,
-0.02709284797310829,
0.08543650060892105,
0.02701914869248867,
0.0343715138733387,
-0.02585061453282833,
-0.020786244422197342,
0.06153158098459244,
0.006779637653380632,
0.0034199864603579044,
-0.0009432685910724103,
-0.017926998436450958,
0.03521928936243057,
-0.042387619614601135,
-0.04609982669353485,
0.03322965279221535,
0.08721587806940079,
0.026466989889740944,
0.03639713674783707,
-0.01974022388458252,
0.0035662357695400715,
-0.02750816009938717,
-0.017470240592956543,
-0.005245217587798834,
-0.017397407442331314,
-0.0030053851660341024,
0.07730401307344437,
0.07313699275255203,
-0.01806590147316456,
0.09468337893486023,
0.04293471574783325,
-0.01282489113509655,
0.08985322713851929,
0.015864429995417595,
0.0010624317219480872,
0.005969095975160599,
0.006643899716436863,
0.012464783154428005,
0.004392229486256838,
-0.03684401512145996,
-0.0020470116287469864,
0.03390078246593475,
-0.022791093215346336,
0.0031768435146659613,
-0.0058273617178201675,
0.014206882566213608,
-0.051457565277814865,
0.032590337097644806,
0.020697886124253273,
0.0017192719969898462,
-0.014024858362972736,
0.015268618240952492,
-0.00003980238761869259,
-0.00709943100810051,
-0.007953674532473087,
0.018385721370577812,
0.03757118433713913,
0.017898283898830414,
-0.02808898501098156,
0.03407548367977142,
-0.012890360318124294,
0.00539975892752409,
0.00507351104170084,
-0.03795638680458069,
0.07088013738393784,
0.032086893916130066,
0.0415598601102829,
-0.015523658134043217,
0.06908321380615234,
0.04849695414304733,
0.02679387666285038,
-0.021170388907194138,
0.012307274155318737,
0.025942690670490265,
-0.025938132777810097,
0.07386532425880432,
0.005753047298640013,
0.030546726658940315,
-0.07004692405462265,
0.0033032929059118032,
-0.0666293054819107,
-0.07020080834627151,
0.026959260925650597,
0.0015561137115582824,
0.019094867631793022,
0.034594349563121796,
0.026800863444805145,
-0.03072853572666645,
-0.009304235689342022,
0.023253047838807106,
0.07056071609258652,
-0.021687041968107224,
0.015857292339205742,
0.03711247816681862,
-0.01193855982273817,
-0.020696114748716354,
0.028196806088089943,
0.035546720027923584,
0.005145807284861803,
-0.03250013664364815,
-0.0358719527721405,
0.007390306331217289,
0.050356220453977585,
0.0076761129312217236,
0.008029580116271973,
-0.034075018018484116,
0.1223786473274231,
-0.05148206278681755,
-0.047432124614715576,
0.001154099591076374,
0.02792145498096943,
-0.007982458919286728,
0.06896470487117767,
-0.019376235082745552,
-0.02403164654970169,
0.025676675140857697,
-0.02494501695036888,
0.022763364017009735,
-0.011867852881550789,
0.04030666872859001,
0.023179473355412483,
0.00463399663567543,
0.033363599330186844,
-0.00915110670030117,
0.009452586993575096,
0.07144470512866974,
-0.04315416142344475,
0.041924331337213516,
-0.05039476603269577,
0.048297490924596786,
0.0158127099275589,
0.010994309559464455,
-0.005076573230326176,
-0.009905758313834667,
-0.004689972847700119,
-0.036575738340616226,
0.021698661148548126,
-0.014497444033622742,
0.003971701953560114,
0.0015389459440484643,
-0.0077903843484818935,
-0.014558031223714352,
0.01084174495190382,
-0.021009251475334167,
0.06030764803290367,
0.005320986267179251,
-0.018526488915085793,
0.03146950900554657,
0.020408442243933678,
0.029270639643073082,
0.035378627479076385,
0.034718550741672516,
-0.043247122317552567,
0.008706171996891499,
0.014226026833057404,
0.004735592752695084,
-0.03097953274846077,
-0.02943035587668419,
0.0035412830766290426,
0.08386722207069397,
-0.018998343497514725,
-0.028329288586974144,
-0.0024705491960048676,
0.021117279306054115,
0.01562703400850296,
-0.02481161057949066,
-0.01996884122490883,
0.05383218824863434,
-0.019307592883706093,
-0.04873320087790489,
-0.00963222049176693,
-0.018852844834327698,
-0.011845726519823074,
0.011744325049221516,
-0.059284426271915436,
0.002356274053454399,
-0.06784180551767349,
-0.06091669574379921,
0.017898553982377052,
0.0489499494433403,
-0.08252556622028351,
0.0233028382062912,
0.0349746011197567,
0.036290235817432404,
0.019279994070529938,
0.021950654685497284,
-0.0006936687859706581,
0.03196074441075325,
0.030723562464118004,
-0.03293223679065704,
-0.01245053205639124,
0.02584684267640114,
-0.05826501175761223,
-0.006324308924376965,
0.06484803557395935,
-0.031118668615818024,
0.007108204998075962,
0.0063309441320598125,
-0.017896972596645355,
0.030017169192433357,
0.024360090494155884,
-0.011446846649050713,
0.013726061210036278,
0.04999691992998123,
0.027903884649276733,
0.08230212330818176,
0.036756545305252075,
0.046014703810214996,
0.04261546954512596,
0.025179045274853706,
-0.010805039666593075,
-0.03381701558828354,
-0.016269782558083534,
0.009492326527833939,
0.009537425823509693,
0.058904100209474564,
0.0032461700029671192,
-0.013780368492007256,
-0.0017910852329805493,
0.016226472333073616,
-0.028589051216840744,
0.011425330303609371,
0.0223751962184906,
0.018934933468699455,
-0.06258392333984375,
-0.017732394859194756,
0.029535533860325813,
0.010507258586585522,
-0.01690744049847126,
-0.01053390558809042,
-0.0688050240278244,
-0.018645936623215675,
-0.006860172376036644,
-0.009880845434963703,
-0.04346996918320656,
0.028441980481147766,
-0.005646578501909971,
-0.012550371699035168,
-0.05150043964385986,
-0.028243085369467735,
0.031476836651563644,
0.0005420275847427547,
-0.007969798520207405,
-0.04497108608484268,
0.010558830574154854,
-0.030336668714880943,
0.0722624659538269,
0.006014189217239618,
0.030987560749053955,
-0.013569471426308155,
-0.04557590186595917,
-0.034699130803346634,
0.015957456082105637,
-0.03298725187778473,
-0.02147752232849598,
0.004692131653428078,
-0.0006033760728314519,
0.008051165379583836,
0.016436465084552765,
-0.021162964403629303,
0.042215362191200256,
-0.004929092712700367,
-0.0029900853987783194,
-0.022981155663728714,
0.02995564229786396,
0.016838690266013145,
0.04481926187872887,
0.04022151604294777,
-0.05868276581168175,
0.009707299992442131,
0.0062088738195598125,
-0.015811629593372345,
0.01693062297999859,
0.06638514250516891,
-0.020364556461572647,
-0.022128518670797348,
-0.04209272563457489,
0.013250229880213737,
-0.03634980320930481,
0.024635888636112213,
0.009189069271087646,
-0.030356571078300476,
-0.0023558479733765125,
-0.011598714627325535,
0.03160308673977852,
-0.06288973987102509,
-0.014468356035649776,
0.0025812347885221243,
0.009836816228926182,
0.017057469114661217,
0.03156101331114769,
0.005924535449594259,
0.03555655479431152,
-0.022191442549228668,
-0.041802454739809036,
0.0629221498966217,
-0.010881896130740643,
-0.008968769572675228,
-0.0010905459057539701,
-0.025717303156852722,
-0.0005795748438686132,
-0.04066875949501991,
-0.02836676314473152,
0.015633923932909966,
0.06322335451841354,
-0.008888031356036663,
-0.0029089206364005804,
0.0099730109795928,
-0.022020526230335236,
0.018053151667118073,
-0.0019460372859612107,
0.011195537634193897,
0.029207736253738403,
0.0036871822085231543,
-0.03830484300851822,
-0.02688705176115036,
0.06709350645542145,
-0.023454463109374046,
-0.054512377828359604,
-0.022127505391836166,
0.022230207920074463,
0.013473316095769405,
-0.017938124015927315,
-0.019777238368988037,
0.016411611810326576,
-0.035214103758335114,
0.02818874642252922,
0.03605502098798752,
-0.009899068623781204,
-0.006826875265687704,
0.03016328066587448,
-0.002220027381554246,
-0.028181305155158043,
-0.06837758421897888,
-0.06266602128744125,
0.005936298985034227,
-0.04284219443798065,
0.01982983946800232,
0.034931547939777374,
0.022620713338255882,
-0.015413309447467327,
-0.00005768908522441052,
0.009722346439957619,
0.045806191861629486,
0.04382742941379547,
0.020363373681902885,
0.024832723662257195,
-0.004070843569934368,
0.01047783624380827,
-0.01092133205384016,
0.03007822483778,
-0.0355985164642334,
-0.03985555097460747,
0.04198651388287544,
0.06128624826669693,
0.07614127546548843,
-0.03522687032818794,
-0.04408266767859459,
0.04625244811177254,
0.023929474875330925,
0.020554115995764732,
-0.04433097690343857,
0.0007864561630412936,
-0.021896973252296448,
-0.011294427327811718,
-0.026520434767007828,
0.027427131310105324,
0.01845376193523407,
-0.02473822794854641,
-0.03903171420097351,
-0.0006543885683640838,
-0.00011730979167623445,
-0.05579552799463272,
-0.010991406626999378,
-0.007907809689640999,
-0.04774260148406029,
-0.026507040485739708,
-0.04783676937222481,
0.009605550207197666,
0.03048940747976303,
0.0005423662369139493,
0.018261849880218506,
0.032882194966077805,
0.06578001379966736,
0.004434052389115095,
0.01702200248837471,
0.020013846457004547,
0.011760247871279716,
0.09990150481462479,
-0.10175676643848419,
0.03315933048725128,
0.023019984364509583,
-0.0978853777050972,
0.014677849598228931,
-0.01890423521399498,
0.026007477194070816,
-0.03637821599841118,
-0.03955285623669624,
0.020822875201702118,
0.09627155214548111,
-0.01881798915565014,
0.02089601196348667,
-0.01674971729516983,
0.05875273048877716,
-0.036256901919841766,
-0.06343353539705276,
0.021765820682048798,
0.012957620434463024,
-0.000830707373097539,
0.009189947508275509,
-0.049353357404470444,
-0.036991190165281296,
0.04098616540431976,
0.0022624297998845577,
-0.0547676607966423,
0.012323900125920773,
0.017215991392731667,
0.043927934020757675,
0.028206635266542435,
0.03036080300807953,
0.019305869936943054,
0.005453393794596195,
0.011540685780346394,
-0.022567233070731163,
0.032691359519958496,
-0.05354185402393341,
0.02986835688352585,
0.03631821274757385,
-0.025947127491235733,
0.012059502303600311,
0.06641464680433273,
-0.030214456841349602,
0.030146822333335876,
0.025701580569148064,
-0.040052954107522964,
0.019800497218966484,
-0.051592059433460236,
-0.026072749868035316,
0.03247736021876335,
-0.019980300217866898,
0.04009641706943512,
-0.03712842985987663,
0.030316688120365143,
-0.006124487146735191,
-0.08610645681619644,
-0.004232001956552267,
0.009932483546435833,
-0.03928708657622337,
0.06883527338504791,
0.0008782046497799456,
-0.04316994175314903,
0.016417935490608215,
0.03393837437033653,
0.07362382858991623,
0.01524374820291996,
-0.017364148050546646,
-0.11826308071613312,
0.045632313936948776,
0.04719598963856697,
-0.022305117920041084,
-0.0039434125646948814,
0.04009406641125679,
-0.0478355847299099,
0.014299494214355946,
0.010555797256529331,
-0.0004475275054574013,
0.04675092175602913,
-0.02284971810877323,
0.00047568351146765053,
-0.0017816915642470121,
0.030449479818344116,
-0.05040043592453003,
-0.020574238151311874,
-0.00011196667037438601,
-0.0014583944575861096,
-0.022446272894740105,
-0.04910312965512276,
0.030308613553643227,
0.03748304024338722,
0.02982875145971775,
0.00008486507431371137,
-0.004704935010522604,
0.03805217519402504,
0.002096005715429783,
0.020260212942957878,
0.00008290106779895723,
-0.014754103496670723,
0.03883998468518257,
0.008222698234021664,
-0.02632671222090721,
0.0032779620960354805,
0.013059648685157299,
0.04179976135492325,
-0.013623317703604698,
0.006252238526940346,
0.03952182084321976,
-0.022331904619932175,
-0.009115271270275116,
0.003109707497060299,
-0.03147577866911888,
-0.04959774762392044,
-0.0024385147262364626,
-0.01783410646021366,
-0.043483488261699677,
0.03469015657901764,
0.006503465585410595,
-0.02545853704214096,
-0.010936370119452477,
-0.036425430327653885,
0.05839117243885994,
0.019480599090456963,
0.03612612187862396,
0.01616288349032402,
-0.046523090451955795,
-0.006739952135831118,
0.016539117321372032,
0.014715004712343216,
-0.04667074605822563,
-0.030786048620939255,
-0.008541141636669636,
-0.0518624372780323,
0.01278654858469963,
0.06680106371641159,
0.0487249456346035,
-0.02474800869822502,
-0.03864134103059769,
0.06586400419473648,
0.005338409449905157,
0.00000905110027815681,
-0.03179529309272766,
0.008858137764036655,
-0.01217944361269474,
0.037282198667526245,
-0.09014932066202164,
0.05047374963760376,
-0.008793425746262074,
0.007552918046712875,
-0.029100211337208748,
0.011701446026563644,
-0.007746713701635599,
0.04234885796904564,
0.006371361203491688,
0.00029402473592199385,
0.02630162052810192,
-0.025105148553848267,
0.08404146879911423,
0.04052020236849785,
0.016592251136898994,
0.007462913636118174,
0.05869888886809349,
0.03991235792636871,
0.040182601660490036,
0.02390243113040924,
0.01271277479827404,
-0.057971447706222534,
0.029957715421915054,
0.0007465474773198366,
-0.044479139149188995,
0.002560886088758707,
0.05127844586968422,
-0.017643285915255547,
-0.04223780706524849,
-0.02952905185520649,
0.02827010676264763,
-0.03027803637087345,
-0.009857450611889362,
0.029369793832302094,
-0.04522039741277695,
0.036694690585136414,
0.016301937401294708,
-0.034221407026052475,
-0.053891994059085846,
0.0013128999853506684,
-0.04716144874691963,
-0.008009389042854309,
0.010594206862151623,
-0.031102636829018593,
-0.0856858417391777,
-0.029564768075942993,
-0.023429380729794502,
-0.002007392467930913,
-0.024471092969179153,
-0.07978153228759766,
-0.0049986024387180805,
0.039814580231904984,
-0.03034435771405697,
-0.045883141458034515,
-0.007566499058157206,
-0.030830226838588715,
0.07836241275072098,
-0.03077017515897751,
-0.02198299765586853,
-0.02141423709690571,
-0.03692551329731941,
0.02078724466264248,
0.009290406480431557,
0.006089959293603897,
0.03249383717775345,
0.026928596198558807,
0.024451827630400658,
-0.040577225387096405,
0.009944860823452473,
-0.012037442997097969,
-0.019029604271054268,
-0.016737891361117363,
0.03761943057179451,
0.019676104187965393,
-0.0018436717800796032,
0.04649614915251732,
-0.013549097813665867,
-0.026792066171765327,
-0.03302866593003273,
-0.011641431599855423,
-0.05874808505177498,
0.025207605212926865,
-0.012922550551593304,
-0.05124766752123833,
0.025044914335012436,
-0.017028095200657845,
-0.027277609333395958,
-0.006584225222468376,
0.07083456218242645,
-0.019467193633317947,
-0.060013704001903534,
-0.00699811102822423,
0.036712393164634705,
-0.0463910810649395,
0.00929737277328968,
0.006748687010258436,
0.009020970202982426,
-0.07562771439552307,
0.011829664930701256,
0.003213682444766164,
-0.07603028416633606,
-0.031096672639250755,
-0.03821209818124771,
-0.016565892845392227,
0.025837624445557594,
-0.05638830363750458,
-0.010016954503953457,
-0.019844597205519676,
-0.08010897785425186,
-0.05553572624921799,
0.029581788927316666,
0.01934536173939705,
0.03330781310796738,
-0.035343755036592484,
0.06653086096048355,
0.01393476128578186,
-0.007999657653272152,
-0.004804370924830437,
-0.006108046509325504,
-0.04037230834364891,
-0.023259952664375305,
0.022749433293938637,
-0.01857875846326351,
-0.006877593230456114,
0.0643281415104866,
0.04828547313809395,
-0.0654534101486206,
0.03251512721180916,
0.014471317641437054,
0.06906294077634811,
0.046901240944862366,
0.04006551578640938,
-0.0553211010992527,
-0.029200173914432526,
0.02727372944355011,
-0.004815994296222925,
-0.08313516527414322,
-0.028445523232221603,
0.0297052264213562,
0.035239268094301224,
-0.03315072879195213,
0.03424482420086861,
0.03097015805542469,
-0.0012085475027561188,
0.005478853825479746
] |
<p>My 8yo son is in the Cub Scouts.</p>
<p>He has a pinewood derby coming up next month and I would like to take this project and turn it into a fun, physics lesson for him. </p>
<p>For those not familiar, a pinewood derby is where you shape a block of wood into a car (or truck, or where ever your imagination leads you) and race it on a track against other cars.</p>
<p>The track looks something like this (not to scale):
<img src="http://i.stack.imgur.com/mo6UI.jpg" alt="Pinewood Derby"></p>
<p>The black curve represents the track. The peculiar, red triangle with wheels is the car. (<a href="http://scouting.org/scoutsource/CubScouts/Cub%20Scouts/ThingsToDo/PineDesign.aspx" rel="nofollow">Click this link</a> to see the various options for the block of wood.)</p>
<p>So, a few talking points that come to mind are as follows:</p>
<ol>
<li><strong>Gravity.</strong> Obviously w/o this the car would go nowhere when released. </li>
<li><strong>Friction.</strong> All wheels come with metal axles. We are allowed to use powered graphite to reduce the friction and make the car move quicker.</li>
<li><strong>Weight.</strong> The heaver it is, the faster it will move. However, there is a 5oz max weight the car can reach. Should the weight of the car be evenly distributed to maximize speed?</li>
<li><strong>Design.</strong> I imagine the design of the car is important to reduce drag...are there any designs from the previous link you would pick regarding that?</li>
</ol>
<p>Any thoughts on how to elaborate on the items above?</p>
<p>Is there anything I haven't listed that would be helpful to talk about?</p> | g4556 | [
0.005811556242406368,
0.054474011063575745,
0.01468272227793932,
-0.013229248113930225,
0.04940268024802208,
-0.02664855681359768,
-0.013871089555323124,
0.003175741294398904,
-0.05822277069091797,
-0.011994327418506145,
0.030570505186915398,
-0.05027596279978752,
0.03516293317079544,
0.016452066600322723,
0.08183508366346359,
0.03935667872428894,
-0.04385693371295929,
-0.05267275124788284,
0.040507249534130096,
0.017920387908816338,
0.050614628940820694,
0.030584946274757385,
-0.02156122773885727,
-0.001218561315909028,
-0.03143983334302902,
-0.0397799089550972,
-0.03650045394897461,
-0.032495126128196716,
-0.04888496920466423,
-0.005049103870987892,
0.026354314759373665,
-0.007619095500558615,
-0.018521418794989586,
-0.04829812049865723,
-0.10777197033166885,
0.044406771659851074,
-0.021222198382019997,
0.011522647924721241,
0.03143801540136337,
0.03970947116613388,
-0.0314127653837204,
-0.035176314413547516,
-0.03912097215652466,
-0.014847791753709316,
-0.009152279235422611,
-0.007880227640271187,
-0.013341424986720085,
-0.05439390987157822,
0.028829297050833702,
0.07853599637746811,
0.02576417662203312,
0.002462088130414486,
0.06873147934675217,
0.0021519947331398726,
0.0058092279359698296,
0.012005685828626156,
0.0209650918841362,
0.004887826275080442,
0.012388475239276886,
-0.01640058122575283,
-0.014796647243201733,
0.016261795535683632,
-0.04000188782811165,
0.026836704462766647,
0.008602124638855457,
-0.0052610402926802635,
0.009365178644657135,
-0.00015011962386779487,
0.04419192671775818,
0.016423553228378296,
0.08826763927936554,
0.012856478802859783,
0.0177291352301836,
-0.004130292218178511,
-0.012762533500790596,
0.010961959138512611,
-0.01134451013058424,
0.03400101140141487,
-0.001955231884494424,
0.023935513570904732,
0.000024516468329238705,
0.053757403045892715,
-0.07975856959819794,
-0.009305144660174847,
0.04871854931116104,
-0.045986611396074295,
-0.011623269878327847,
0.02654450759291649,
-0.06272588670253754,
-0.006277961656451225,
-0.03892452269792557,
-0.02012329176068306,
0.0574667826294899,
-0.013282401487231255,
0.03683598339557648,
-0.04140760749578476,
-0.02782721072435379,
0.02522578090429306,
0.04235510528087616,
0.08768963068723679,
-0.0379672534763813,
-0.03112694062292576,
0.03742622211575508,
0.0018633068539202213,
-0.010709051042795181,
-0.025435077026486397,
-0.04222368076443672,
0.047286421060562134,
-0.04308096691966057,
-0.00499721011146903,
-0.026790950447320938,
0.004729066509753466,
-0.08693064004182816,
-0.03651566058397293,
-0.04349762201309204,
-0.012343889102339745,
0.05060987547039986,
-0.014635622501373291,
-0.00467258645221591,
-0.02503477782011032,
0.0005346274119801819,
-0.04665609821677208,
-0.034560538828372955,
0.03645310923457146,
0.017576726153492928,
0.013923974707722664,
0.014833029359579086,
-0.026381947100162506,
-0.041087646037340164,
-0.06591086834669113,
0.017468690872192383,
-0.021014416590332985,
0.024277541786432266,
-0.02542477659881115,
0.002044604392722249,
0.03712889924645424,
-0.02325896918773651,
0.05517260730266571,
0.00030634202994406223,
-0.01677212491631508,
-0.011411059647798538,
0.0630929097533226,
-0.04625370725989342,
0.046083059161901474,
0.0035617814864963293,
0.029358189553022385,
-0.03427015617489815,
0.016958972439169884,
-0.0003539642202667892,
-0.024757960811257362,
0.04248537868261337,
-0.04533146321773529,
0.016075970605015755,
-0.014584183692932129,
-0.023568037897348404,
-0.01725616678595543,
0.06522087752819061,
0.0022135197650641203,
0.020092986524105072,
0.04968339577317238,
0.06205477938055992,
-0.027795562520623207,
-0.017349788919091225,
0.02931366115808487,
-0.054990485310554504,
0.0379510261118412,
0.017939623445272446,
-0.004350774455815554,
0.08034474402666092,
0.0448138564825058,
-0.04959356412291527,
-0.07974884659051895,
-0.013578317128121853,
0.08632668107748032,
-0.01741853728890419,
-0.052819713950157166,
0.07317434996366501,
-0.040057964622974396,
-0.029035400599241257,
0.04016588628292084,
0.003579377196729183,
-0.012395412661135197,
0.026262734085321426,
0.031684305518865585,
-0.07660164684057236,
0.011449495330452919,
-0.029312290251255035,
-0.009068496525287628,
-0.05132150277495384,
0.05238163843750954,
0.025664759799838066,
-0.045805465430021286,
0.009729642421007156,
-0.019134173169732094,
0.006052106153219938,
-0.0027252547442913055,
-0.009797392413020134,
-0.00635458342730999,
-0.007192600052803755,
-0.020866677165031433,
0.0013463215436786413,
-0.009222262538969517,
0.011524507775902748,
0.01658245362341404,
-0.006434578914195299,
-0.018146950751543045,
0.02530386485159397,
0.02083601988852024,
0.036307916045188904,
0.044078923761844635,
0.022540660575032234,
0.03135474771261215,
0.002377063501626253,
0.02196657657623291,
0.00004403280036058277,
0.03940486162900925,
-0.03152256831526756,
-0.003985710442066193,
-0.03514961525797844,
0.008517169393599033,
0.047691646963357925,
-0.005431678146123886,
-0.001967088086530566,
0.029362335801124573,
-0.00377481896430254,
-0.015997236594557762,
0.004139483440667391,
-0.010031984187662601,
0.03250032663345337,
0.013485613279044628,
0.013825338333845139,
-0.01007598266005516,
-0.019569847732782364,
-0.07056429982185364,
0.029990386217832565,
0.00980988796800375,
-0.005608811508864164,
-0.008913558907806873,
0.007174557540565729,
-0.04569108039140701,
0.016151370480656624,
-0.010102876462042332,
0.033166978508234024,
-0.063755564391613,
0.02099929377436638,
-0.079572394490242,
-0.022665681317448616,
0.0015966828214004636,
-0.015741800889372826,
-0.04010642319917679,
0.049861080944538116,
0.0511549673974514,
-0.05593375861644745,
-0.022987281903624535,
0.04472173750400543,
-0.00361829181201756,
-0.0021242958027869463,
-0.020644236356019974,
-0.042251236736774445,
-0.08870477229356766,
-0.02070360630750656,
-0.016449052840471268,
-0.050171781331300735,
0.005209692753851414,
-0.04317159578204155,
-0.05426633730530739,
-0.044717464596033096,
-0.10321125388145447,
0.02473248355090618,
-0.0054800971411168575,
-0.055633604526519775,
0.024676291272044182,
0.027070680633187294,
-0.05172692984342575,
0.0045408266596496105,
-0.07680333405733109,
0.0018101428868249059,
0.01366875134408474,
0.009573719464242458,
0.02323855273425579,
0.04205087572336197,
-0.009092575870454311,
-0.039399754256010056,
0.01404318306595087,
-0.016644280403852463,
0.04544658586382866,
0.003898604540154338,
-0.008053898811340332,
0.029942629858851433,
0.016913242638111115,
-0.07500379532575607,
0.03179844468832016,
0.05620839074254036,
-0.013738772831857204,
0.032512687146663666,
0.052339933812618256,
-0.03799159452319145,
0.023365940898656845,
0.023852063342928886,
-0.07308889925479889,
-0.03728606179356575,
0.04495476931333542,
-0.0036285591777414083,
0.020979221910238266,
0.0016595413908362389,
0.02418438345193863,
-0.024233845993876457,
0.012333715334534645,
0.00860032718628645,
0.026548154652118683,
0.01567745767533779,
-0.011767853982746601,
0.014260848052799702,
0.019214773550629616,
-0.1041519045829773,
-0.021352939307689667,
-0.002608631970360875,
0.027892325073480606,
0.02301451563835144,
-0.06916208565235138,
0.05140898376703262,
-0.0015879514394327998,
0.014617739245295525,
0.03407832607626915,
0.004143576603382826,
0.07567910850048065,
0.04199516400694847,
-0.017956525087356567,
0.023357728496193886,
0.02489941380918026,
0.03562299534678459,
0.05319053679704666,
-0.024256721138954163,
-0.0228918194770813,
-0.05082288011908531,
-0.03339055925607681,
-0.014022348448634148,
-0.03010237216949463,
-0.0020453741308301687,
-0.014136303216218948,
0.021075459197163582,
-0.028750915080308914,
-0.041748613119125366,
-0.047830745577812195,
-0.006632855162024498,
-0.001513760187663138,
0.05060918256640434,
-0.03295718505978584,
0.005057917907834053,
-0.02929737977683544,
0.03243507817387581,
-0.048782799392938614,
-0.04675799608230591,
-0.030335646122694016,
0.03248680755496025,
-0.009605185128748417,
-0.017129356041550636,
-0.0031210018787533045,
-0.00011975218512816355,
0.011433371342718601,
-0.004343398846685886,
0.032316092401742935,
-0.022438710555434227,
0.01657840609550476,
-0.05234520137310028,
-0.0530155710875988,
-0.0123772993683815,
-0.0032217351254075766,
-0.0156668983399868,
0.058941956609487534,
0.023497818037867546,
0.01009062584489584,
-0.02687571942806244,
-0.03797385096549988,
-0.03327435627579689,
0.01999395713210106,
0.06114804372191429,
0.008164401166141033,
-0.016841918230056763,
0.02022271789610386,
0.010621710680425167,
0.0916280597448349,
0.05607445538043976,
-0.03588232025504112,
-0.03292324021458626,
0.0037936235312372446,
0.012179655022919178,
0.02503572218120098,
0.03320854529738426,
0.03135007992386818,
-0.04956541955471039,
0.019670281559228897,
-0.056213054805994034,
-0.011791158467531204,
0.0017277543665841222,
0.03475425764918327,
-0.029367664828896523,
-0.053208138793706894,
-0.07689516246318817,
0.050198741257190704,
0.023410983383655548,
0.07655037939548492,
0.03292206674814224,
0.021156445145606995,
-0.016809634864330292,
0.001088970573619008,
0.018742574378848076,
0.010193934664130211,
-0.02403159625828266,
-0.0385877899825573,
0.0005609643994830549,
-0.06477206945419312,
0.018571170046925545,
-0.04088422283530235,
-0.012738929130136967,
-0.01140477042645216,
-0.012791456654667854,
0.06942608952522278,
-0.03002753108739853,
0.03819762542843819,
0.007530177943408489,
-0.0038375407457351685,
0.03519904240965843,
-0.03184307739138603,
-0.0007189742755144835,
0.010862324386835098,
0.01166874822229147,
-0.040362440049648285,
-0.037392597645521164,
-0.027573205530643463,
0.026292867958545685,
-0.04068434238433838,
0.0068906573578715324,
-0.012323964387178421,
0.010799064300954342,
0.0527280792593956,
-0.002582796849310398,
0.03330732882022858,
0.06250516325235367,
0.013031949289143085,
-0.07089005410671234,
0.046605922281742096,
0.04153476655483246,
-0.003238480305299163,
-0.05214507132768631,
0.02537623606622219,
-0.08119772374629974,
-0.008906163275241852,
-0.02123585157096386,
0.0254813265055418,
0.0034309751354157925,
0.003496191231533885,
-0.0330207496881485,
0.07237575203180313,
-0.0021698190830647945,
-0.005363161209970713,
-0.0599227137863636,
-0.011603099294006824,
0.05788709968328476,
0.01025070995092392,
0.00010193019988946617,
-0.0001806012005545199,
0.010863032191991806,
-0.0017410519067198038,
-0.014914006926119328,
-0.014601710252463818,
0.03522121533751488,
-0.0002980746212415397,
0.03863281384110451,
-0.04153504967689514,
-0.017975902184844017,
-0.023938437923789024,
0.038375794887542725,
0.0036153974942862988,
-0.0542370043694973,
0.06065145879983902,
0.00669869314879179,
0.012831787578761578,
0.054939236491918564,
-0.004001927096396685,
-0.023422161117196083,
0.05120822787284851,
0.023366723209619522,
-0.06421729177236557,
-0.0066954283975064754,
-0.04965769499540329,
-0.03958966210484505,
-0.00735119916498661,
-0.0045159985311329365,
0.028553416952490807,
0.015116754919290543,
0.021994149312376976,
-0.05445040017366409,
0.04088960960507393,
-0.018931956961750984,
-0.02807290479540825,
0.03962904214859009,
0.05548515170812607,
0.018654173240065575,
-0.05826830118894577,
0.012833262793719769,
0.02272718772292137,
0.00850149430334568,
-0.06494452804327011,
-0.015037193894386292,
0.0015178084140643477,
0.0524972602725029,
-0.03056912310421467,
-0.060529809445142746,
0.03990630805492401,
0.002428861102089286,
0.0659564808011055,
0.057343363761901855,
-0.005005855578929186,
-0.07478222995996475,
0.012944411486387253,
0.016182370483875275,
0.05009083449840546,
0.04244503006339073,
0.01071969885379076,
0.043825458735227585,
-0.015539241954684258,
-0.01012791134417057,
-0.08732041716575623,
-0.04341374337673187,
0.013088730163872242,
-0.028752101585268974,
-0.031161565333604813,
-0.03652229532599449,
-0.0056816223077476025,
-0.03609020635485649,
-0.029705967754125595,
-0.0038931078743189573,
0.018628042191267014,
-0.0796872079372406,
0.005903463810682297,
0.027460958808660507,
-0.04109624773263931,
0.0023709081578999758,
-0.004443510435521603,
-0.044782474637031555,
0.05052434280514717,
0.014985086396336555,
-0.012293277308344841,
-0.009375584311783314,
0.0007386893266811967,
0.005430975928902626,
-0.0007624280988238752,
0.03026540018618107,
-0.04972224682569504,
0.04227069392800331,
0.052138686180114746,
0.025932708755135536,
-0.03264302760362625,
0.023340508341789246,
-0.014587372541427612,
0.008767304010689259,
-0.03751881420612335,
0.013019785284996033,
-0.027031373232603073,
0.010290257632732391,
-0.003908406011760235,
0.022831646725535393,
0.030406581237912178,
0.04249441996216774,
-0.021116482093930244,
-0.045557182282209396,
-0.03649548813700676,
0.014115402474999428,
0.03174932673573494,
0.014516341499984264,
-0.010403425432741642,
0.020669762045145035,
0.03235374391078949,
0.07451878488063812,
-0.06333096325397491,
0.0055449483916163445,
-0.05240961164236069,
0.002177941147238016,
0.019459249451756477,
0.03989812359213829,
0.08065687865018845,
-0.025288349017500877,
-0.0022136487532407045,
-0.035988904535770416,
0.02515593357384205,
-0.05345837026834488,
-0.01987149566411972,
-0.02958052046597004,
-0.0433599129319191,
0.010468979366123676,
-0.006138008087873459,
-0.028077462688088417,
-0.004892964381724596,
-0.03353852406144142,
-0.006818657740950584,
-0.01811576448380947,
-0.016799313947558403,
0.035406485199928284,
0.023026015609502792,
-0.02521054819226265,
-0.005632744636386633,
-0.01824788749217987,
0.013218873180449009,
-0.05928073450922966,
0.033566709607839584,
0.031033167615532875,
-0.019195500761270523,
0.021480778232216835,
-0.018913261592388153,
-0.0335141085088253,
-0.003408946329727769,
-0.0019458051538094878,
0.025430992245674133,
0.016910696402192116,
0.05199027806520462,
0.04729137942194939,
-0.044459111988544464,
0.09591203182935715,
-0.02450552023947239,
-0.03419380635023117,
0.015058033168315887,
0.09391871839761734,
-0.05787336081266403,
-0.005365315359085798,
0.06751392036676407,
-0.05393148586153984,
0.02523869276046753,
0.03111940249800682,
0.004900563973933458,
0.025565573945641518,
-0.016142116859555244,
0.07177124172449112,
0.09419594705104828,
-0.0019305379828438163,
0.05901213362812996,
-0.011028935201466084,
0.06295950710773468,
-0.0016448587412014604,
0.02618125081062317,
0.010195539332926273,
0.03704124316573143,
-0.03977518901228905,
0.06250989437103271,
0.019088394939899445,
-0.012078143656253815,
0.0107249291613698,
-0.0315689854323864,
0.037977416068315506,
-0.00839407742023468,
-0.029322002083063126,
-0.03626419976353645,
-0.0037354372907429934,
-0.07303082197904587,
-0.04447709396481514,
0.04163355007767677,
-0.03725867718458176,
0.03821496665477753,
0.068666473031044,
0.0017185589531436563,
-0.029299059882760048,
-0.05537378787994385,
0.02856334112584591,
0.00021413917420431972,
-0.03881197050213814,
0.03595338761806488,
-0.010896154679358006,
0.06915175914764404,
-0.04573393985629082,
0.025212839245796204,
-0.019188785925507545,
-0.02373669296503067,
-0.0016952907899394631,
-0.01190129853785038,
-0.015702521428465843,
-0.033656902611255646,
-0.10562899708747864,
0.03308301791548729,
0.018955692648887634,
-0.03895842283964157,
0.014738979749381542,
0.02094300463795662,
-0.01819784753024578,
0.01702795922756195,
0.008779770694673061,
0.03185902535915375,
-0.05133454501628876,
0.02691277302801609,
0.03395574539899826,
0.01047282014042139,
0.024195613339543343,
0.020702676847577095,
0.01103084534406662,
0.020268062129616737,
-0.026544999331235886,
0.0007846648222766817,
-0.002520245499908924,
0.033600807189941406,
-0.03880473971366882,
0.017655087634921074,
-0.035097215324640274,
0.04791143909096718,
0.035531457513570786,
0.02376887947320938,
-0.015274605713784695,
-0.021657263860106468,
-0.08791931718587875,
-0.027233291417360306,
-0.07380606979131699,
-0.03238511085510254,
0.035465944558382034,
0.049494534730911255,
0.04184186831116676,
0.025475554168224335,
-0.016864417120814323,
0.04554779455065727,
0.05477575212717056,
0.006653785705566406,
-0.04654280096292496,
0.07446371763944626,
-0.04580828920006752,
0.023673351854085922,
0.00967742782086134,
0.03719015792012215,
0.028943030163645744,
-0.0721035972237587,
-0.0011038489174097776,
-0.06365726888179779,
0.024440843611955643,
0.04373125731945038,
-0.003854178125038743,
0.04736887663602829,
-0.0039618611335754395,
0.0067940158769488335,
-0.041980430483818054,
-0.012732351198792458,
-0.02979469858109951,
-0.016175219789147377,
-0.031044326722621918,
0.022784113883972168,
-0.019189361482858658,
-0.035292886197566986,
-0.012388920411467552,
-0.057047683745622635,
0.01310690026730299,
-0.0034317951649427414,
-0.00478871027007699,
0.11698605120182037,
-0.005404664669185877,
-0.00009053623944055289,
-0.007419336121529341,
0.05378536507487297,
-0.022341549396514893,
-0.0055165658704936504,
-0.00992241408675909,
0.007540506776422262,
0.015361014753580093,
0.042515646666288376,
0.02628537081182003,
-0.032147206366062164,
0.022609934210777283,
0.021811729297041893,
-0.010892292484641075,
-0.010367972776293755,
-0.00022979734058026224,
0.06417718529701233,
-0.01843455247581005,
-0.024153048172593117
] |
<p>When <code>taxpayers</code> pay <code>money</code> for expensive research (irrespective of the <code>partition-function</code> wheither a few projects worth <code>megabucks</code> [<code>M$</code>] or many smaller cheaper experiments), should the <code>raw data</code>/<code>designs</code>/... that result from it be <code>gratis</code> (as in linux), <code>opensource</code> (as in the source of beer) or even licensefree?</p>
<p>(the question is not intended as a binary one: it is more ethics of modern physics funding, assume it is possible)</p>
<p>this would also more easily allow people with or without diplomes to try processing the scientific data...</p>
<p>(<code>upvotes</code> if you can present your argument <code>completely formalized</code> in <code>deontologic</code> <code>Kripke semantics</code>)</p> | g4557 | [
0.0194377638399601,
0.07897164672613144,
0.01288776658475399,
-0.00149143161252141,
0.05542108044028282,
-0.008094974793493748,
-0.06710749864578247,
0.02905581332743168,
0.006463344674557447,
-0.017917310819029808,
0.04525657370686531,
0.02485557086765766,
0.06605151295661926,
-0.025194603949785233,
-0.05010545626282692,
-0.002063221763819456,
0.014000505208969116,
-0.03529123216867447,
-0.0052145966328680515,
0.03884298354387283,
-0.03303658589720726,
-0.008654028177261353,
-0.05338337644934654,
-0.07318516075611115,
-0.021749533712863922,
-0.052474815398454666,
0.004666091874241829,
-0.04362340271472931,
-0.03417832404375076,
-0.005316690541803837,
-0.013363541103899479,
-0.0033993313554674387,
0.045816417783498764,
0.026676593348383904,
-0.08382193744182587,
-0.021226119250059128,
0.0016783569008111954,
0.05965212732553482,
0.02656763419508934,
-0.051506444811820984,
0.014496969990432262,
0.0053876908496022224,
0.0023514714557677507,
-0.03456331044435501,
-0.009138301946222782,
0.01855071820318699,
0.012067276984453201,
-0.012720765545964241,
0.04421713575720787,
-0.060257673263549805,
0.007970583625137806,
0.03472767770290375,
-0.022421734407544136,
0.0773298442363739,
-0.00044460673234425485,
-0.021296225488185883,
-0.024485161527991295,
0.03380769118666649,
0.03184247761964798,
-0.04686151444911957,
0.011272675357758999,
0.027405764907598495,
-0.0226697139441967,
-0.00930281076580286,
0.07273344695568085,
0.027701828628778458,
-0.04337366297841072,
0.004550570156425238,
0.0813039168715477,
0.006041400600224733,
0.0062859999015927315,
-0.008512728847563267,
0.01608637161552906,
-0.08518806099891663,
-0.023015938699245453,
0.060115110129117966,
-0.016734037548303604,
-0.004456729628145695,
-0.02644992247223854,
0.058688897639513016,
-0.022434692829847336,
-0.008439532481133938,
-0.0007016506278887391,
0.036320075392723083,
0.06181446835398674,
-0.04297133535146713,
-0.0028816561680287123,
-0.023369096219539642,
0.0611509308218956,
0.08376815170049667,
0.0053388322703540325,
-0.06723223626613617,
0.039627574384212494,
0.0444522500038147,
-0.035764019936323166,
-0.0404486283659935,
0.006058398634195328,
-0.0007811429095454514,
-0.017746178433299065,
0.07817687094211578,
-0.012033361941576004,
-0.026703160256147385,
0.005331588909029961,
-0.005575467832386494,
0.01241410430520773,
-0.026528671383857727,
0.010797383263707161,
0.014897487126290798,
-0.019504329189658165,
0.017090339213609695,
-0.03955955430865288,
-0.002103701001033187,
-0.042568083852529526,
-0.013212891295552254,
-0.009663454256951809,
-0.03744053095579147,
0.08151926845312119,
-0.036433879286050797,
-0.021186312660574913,
0.0857902467250824,
0.026177452877163887,
-0.004490072373300791,
0.04162431135773659,
0.011592558585107327,
-0.03828372433781624,
0.009087390266358852,
-0.0003351596824359149,
0.021768473088741302,
0.008144439198076725,
-0.021042801439762115,
0.002539275446906686,
-0.04107316955924034,
-0.057276979088783264,
0.011580250225961208,
0.025024905800819397,
0.025626694783568382,
-0.03562051057815552,
-0.013434299267828465,
-0.026421809569001198,
-0.04616217315196991,
0.03246845304965973,
0.028563091531395912,
-0.021697470918297768,
0.031347937881946564,
-0.009601854719221592,
-0.009567187167704105,
0.00783319491893053,
-0.0017614528769627213,
0.054550349712371826,
0.050270963460206985,
-0.05039912462234497,
0.002399887191131711,
0.016647953540086746,
0.035511355847120285,
0.05529525876045227,
-0.014436348341405392,
0.02701745368540287,
-0.06925221532583237,
0.014467613771557808,
0.04396313801407814,
-0.02720506116747856,
-0.012770496308803558,
0.00748832942917943,
0.018573297187685966,
0.008796247653663158,
0.01820240169763565,
0.037492163479328156,
-0.02984623610973358,
-0.02938082255423069,
-0.012651612982153893,
-0.09881901741027832,
0.03041660413146019,
0.008860212750732899,
0.0793432667851448,
0.07566925883293152,
-0.00860141683369875,
-0.03446391969919205,
0.01569487899541855,
0.030433345586061478,
0.049574270844459534,
-0.027613069862127304,
0.03246311470866203,
0.04042891412973404,
0.004428179934620857,
0.004801271017640829,
-0.01780763640999794,
-0.011356080882251263,
-0.03769184648990631,
0.0018560102907940745,
-0.01965692825615406,
-0.024261703714728355,
-0.0040129004046320915,
-0.0443822517991066,
0.0006255317130126059,
-0.048452526330947876,
-0.018909193575382233,
-0.015375818125903606,
0.0362219400703907,
0.010103561915457249,
0.019689859822392464,
-0.010656467638909817,
0.056897491216659546,
-0.0023623814340680838,
0.0388011559844017,
-0.009339571930468082,
-0.009576414711773396,
-0.03360678628087044,
-0.013635761104524136,
0.016738800331950188,
-0.047715749591588974,
0.037184979766607285,
-0.03876695781946182,
-0.013538898900151253,
0.0052234213799238205,
-0.022263389080762863,
-0.02640184760093689,
-0.025047559291124344,
0.002460564486682415,
0.007939293049275875,
0.016455620527267456,
0.009392903186380863,
-0.011115137487649918,
0.022084126248955727,
0.000723017961718142,
-0.00817131157964468,
-0.07962200790643692,
-0.10023799538612366,
0.0014841388911008835,
-0.006195393390953541,
-0.046131033450365067,
0.0210295207798481,
-0.06358940154314041,
-0.014707114547491074,
-0.04965048283338547,
0.08163439482450485,
0.08945196121931076,
-0.025616878643631935,
-0.037279509007930756,
0.04406535252928734,
0.03991661220788956,
0.0007313223322853446,
0.022254982963204384,
-0.007378760725259781,
0.03573158383369446,
0.018367689102888107,
-0.003970939200371504,
0.026989690959453583,
0.008583657443523407,
-0.020950861275196075,
0.0047332728281617165,
-0.016814909875392914,
0.03952883556485176,
0.048873066902160645,
0.0018821563571691513,
-0.02647976018488407,
-0.013451813720166683,
-0.028635123744606972,
0.011272330768406391,
0.010854247026145458,
0.025662390515208244,
0.04654800891876221,
-0.0208835881203413,
-0.029632367193698883,
-0.04031222313642502,
0.013109877705574036,
0.0751505121588707,
-0.043975748121738434,
-0.06125042960047722,
-0.02634977176785469,
0.025172825902700424,
-0.014357675798237324,
0.054410237818956375,
0.014270270243287086,
0.021530866622924805,
0.07709064334630966,
0.02425108291208744,
0.048831403255462646,
-0.001891433261334896,
-0.013310257345438004,
-0.07806407660245895,
-0.07989466190338135,
-0.033075932413339615,
-0.052237313240766525,
0.004708021879196167,
0.044489894062280655,
-0.028570229187607765,
-0.045398127287626266,
-0.021899651736021042,
-0.005519528407603502,
-0.06282380223274231,
0.042125340551137924,
0.02597498521208763,
0.015090061351656914,
0.023292742669582367,
-0.04717668890953064,
0.0019104034872725606,
-0.008654199540615082,
0.007754109799861908,
0.03426163271069527,
0.011439437046647072,
-0.00042887942981906235,
-0.015834610909223557,
0.0636620819568634,
0.08701319247484207,
0.024616394191980362,
-0.048677168786525726,
-0.001286291517317295,
-0.023679349571466446,
-0.013503062538802624,
0.07002691924571991,
0.05979897826910019,
-0.0016483509680256248,
0.01703149639070034,
-0.012418773025274277,
-0.061650536954402924,
0.030081504955887794,
-0.007659476716071367,
-0.047732096165418625,
0.06242414936423302,
-0.09008362889289856,
0.007997912354767323,
-0.052490897476673126,
-0.0051217530854046345,
-0.05271158367395401,
-0.03610265627503395,
0.05280343070626259,
-0.07623392343521118,
-0.026938647031784058,
-0.02510443516075611,
-0.004739881027489901,
0.041363928467035294,
0.03102414682507515,
0.026582131162285805,
-0.04814702272415161,
-0.05140634998679161,
-0.054033391177654266,
0.051813870668411255,
-0.012374107725918293,
0.010224001482129097,
0.048569317907094955,
-0.046410832554101944,
-0.04095710068941116,
0.011737079359591007,
-0.03755388781428337,
-0.025087274610996246,
0.021443644538521767,
0.019611934199929237,
-0.032397426664829254,
0.012302362360060215,
-0.01747307926416397,
0.04609408974647522,
0.013567878864705563,
0.028519393876194954,
-0.03180355206131935,
-0.02534755878150463,
0.003348672529682517,
0.010952386073768139,
0.0022701146081089973,
0.01303869392722845,
0.0005435277707874775,
-0.03237353265285492,
0.032685235142707825,
0.006605794187635183,
-0.014830957166850567,
0.0015208871336653829,
0.078079454600811,
0.004641152918338776,
-0.032400187104940414,
-0.06131388619542122,
0.03078038990497589,
-0.007972592487931252,
0.05072886496782303,
-0.00154218846000731,
0.020578546449542046,
0.019612053409218788,
-0.026824329048395157,
0.00411478104069829,
0.007073608227074146,
0.010555218905210495,
0.026993785053491592,
0.05750858038663864,
0.0046890475787222385,
-0.006520095281302929,
-0.02995597943663597,
0.019032850861549377,
0.019676437601447105,
-0.01836213283240795,
-0.004286936949938536,
0.013474315404891968,
-0.00283647864125669,
0.012855369597673416,
0.0042484477162361145,
-0.025990158319473267,
0.024259867146611214,
-0.04916009679436684,
0.0024201099295169115,
-0.04555803909897804,
-0.02393963187932968,
0.039348479360342026,
0.05569799989461899,
-0.03646574541926384,
-0.03185851499438286,
-0.02901255339384079,
0.007232777774333954,
0.010814687237143517,
0.00041570101166144013,
-0.03651229664683342,
-0.07871494442224503,
-0.03937163203954697,
-0.06609319150447845,
-0.0017240275628864765,
-0.07062211632728577,
-0.018026769161224365,
-0.02121204137802124,
0.031001167371869087,
-0.042869165539741516,
-0.0011089921463280916,
-0.05212079733610153,
-0.014391097240149975,
0.0324823223054409,
0.03771686553955078,
-0.020161418244242668,
0.08690235763788223,
-0.018915947526693344,
0.01636267453432083,
0.00388138135895133,
0.03734879195690155,
-0.03545854240655899,
0.007443103939294815,
-0.03666433319449425,
0.06310231238603592,
0.030542941763997078,
-0.010316187515854836,
-0.01731768436729908,
-0.010469840839505196,
0.00819114688783884,
-0.013333546929061413,
-0.018910307437181473,
-0.08440205454826355,
-0.008358989842236042,
0.04041582718491554,
-0.014886274933815002,
-0.021844319999217987,
-0.07426151633262634,
-0.014048952609300613,
0.031072475016117096,
0.035978954285383224,
0.005074550863355398,
-0.005759118590503931,
-0.04578974470496178,
-0.008052420802414417,
-0.041977740824222565,
-0.0033584958873689175,
0.001538368291221559,
0.01759113185107708,
-0.018656050786376,
0.0038933211471885443,
-0.0400717668235302,
0.04334042966365814,
0.005847127176821232,
-0.03673330321907997,
-0.045723188668489456,
-0.0266050323843956,
0.036103349179029465,
0.033082377165555954,
-0.016628099605441093,
-0.044826705008745193,
-0.019493086263537407,
0.015489579178392887,
0.0033507782500237226,
-0.00173594756051898,
0.03769301250576973,
0.00869009830057621,
-0.008402782492339611,
0.002980054821819067,
0.017197996377944946,
0.005110356956720352,
-0.034069959074258804,
0.07531727850437164,
-0.024556610733270645,
-0.015267323702573776,
0.025031035766005516,
0.03599059581756592,
-0.022793790325522423,
0.027912020683288574,
0.03675079345703125,
-0.008161207661032677,
-0.055076733231544495,
-0.042241401970386505,
-0.059705283492803574,
0.03660498932003975,
0.006394688971340656,
0.06361556798219681,
-0.009340180084109306,
-0.03648305684328079,
0.019317761063575745,
-0.04271872341632843,
-0.004294607322663069,
0.0382225438952446,
-0.0017584743909537792,
0.003118527587503195,
-0.009845374152064323,
-0.017287034541368484,
0.007164000999182463,
0.025128765031695366,
0.02489398419857025,
0.09065384417772293,
0.03944675996899605,
-0.0193686094135046,
0.007014777977019548,
0.03685348480939865,
0.007279494311660528,
0.029318995773792267,
0.00900733470916748,
-0.006361809093505144,
0.004435849841684103,
-0.010221282951533794,
0.025045819580554962,
-0.0826181173324585,
-0.03960573300719261,
0.027110060676932335,
0.005880570504814386,
0.017505966126918793,
0.029582396149635315,
0.011534174904227257,
0.008184759877622128,
0.021184133365750313,
0.0302096139639616,
0.03730136901140213,
0.01706377975642681,
0.015953190624713898,
0.03540472313761711,
0.0039000515826046467,
0.043953441083431244,
-0.03832121193408966,
-0.005437103565782309,
-0.025235531851649284,
-0.0030330056324601173,
0.02317843586206436,
-0.0029181991703808308,
0.013357765972614288,
0.05039843171834946,
0.07934685051441193,
-0.0032159469556063414,
-0.014714568853378296,
-0.05902072787284851,
0.023170575499534607,
0.009159930050373077,
0.036460600793361664,
-0.13862143456935883,
-0.025510981678962708,
-0.03722061216831207,
0.012582844123244286,
-0.015020287595689297,
0.030927686020731926,
-0.002905571833252907,
-0.030528921633958817,
-0.020123278722167015,
0.0018027113983407617,
0.035503920167684555,
0.015704592689871788,
0.03295581042766571,
0.058902278542518616,
0.058960091322660446,
0.08340572565793991,
0.015113243833184242,
0.0027054455131292343,
-0.11247537285089493,
-0.009201224893331528,
0.05196868255734444,
-0.044711530208587646,
0.03513828665018082,
-0.008295099250972271,
-0.027073370292782784,
0.03371838107705116,
0.04460526630282402,
0.012808379717171192,
-0.0038693202659487724,
0.015178077854216099,
0.01067313551902771,
0.07737941294908524,
-0.026195799931883812,
-0.00496213324368,
0.03173961862921715,
-0.015195168554782867,
0.060283027589321136,
-0.04810270667076111,
0.006320679094642401,
-0.04902903735637665,
-0.04282412678003311,
-0.04854729026556015,
-0.07968615740537643,
-0.02529490739107132,
-0.004849177319556475,
-0.035857103765010834,
0.025462573394179344,
0.018131444230675697,
-0.036278754472732544,
-0.04396282136440277,
-0.041331253945827484,
-0.028628982603549957,
-0.026461338624358177,
0.019928425550460815,
0.02202836610376835,
-0.03435293585062027,
-0.04155942425131798,
-0.012464490719139576,
0.027248801663517952,
-0.013717741705477238,
-0.009689713828265667,
-0.04836951941251755,
-0.029692448675632477,
-0.04597222059965134,
-0.026483098044991493,
0.008811848238110542,
-0.03280605748295784,
0.013993825763463974,
-0.022574307397007942,
0.026027698069810867,
-0.01012377254664898,
0.011478278785943985,
0.010692287236452103,
0.012142348103225231,
-0.05448995903134346,
-0.008861967362463474,
0.047869905829429626,
-0.040213555097579956,
0.033142123371362686,
0.017160749062895775,
0.05229558050632477,
0.04223359003663063,
0.10549455136060715,
-0.00925078708678484,
-0.005826691631227732,
-0.08176141232252121,
0.031038327142596245,
-0.0388171561062336,
0.022909319028258324,
0.014934916980564594,
0.01962358132004738,
0.04746268689632416,
0.05152164027094841,
0.057584624737501144,
0.04320294409990311,
0.027540354058146477,
0.02497124671936035,
0.0311124287545681,
0.04050048068165779,
0.021362055093050003,
-0.010500253178179264,
-0.006052916403859854,
-0.011161313392221928,
0.012949769385159016,
-0.062283508479595184,
-0.010944326408207417,
0.03702657297253609,
0.005172706209123135,
0.056444622576236725,
0.0423235185444355,
-0.036726485937833786,
-0.0025146626867353916,
-0.034269239753484726,
-0.005564588122069836,
-0.002288893796503544,
-0.002165963174775243,
0.02875487506389618,
0.0043085492216050625,
0.034331630915403366,
0.05575186014175415,
0.027921149507164955,
0.03424873948097229,
0.010113916359841824,
-0.037944573909044266,
0.0017738350434228778,
0.03322484716773033,
-0.01355083379894495,
0.018603453412652016,
-0.01678282395005226,
-0.04698218032717705,
0.005868091247975826,
0.03502732515335083,
0.0001878825423773378,
0.027571482583880424,
-0.019338341429829597,
-0.1057330071926117,
-0.04127442091703415,
-0.023414472118020058,
0.016964200884103775,
0.003230997361242771,
-0.01723843812942505,
-0.017626632004976273,
0.010815960355103016,
0.04970920458436012,
-0.0038909490685909986,
-0.0005240956088528037,
-0.0073511432856321335,
-0.014133984223008156,
-0.016144312918186188,
0.03811195120215416,
0.0638948306441307,
0.03828875347971916,
-0.003456713631749153,
0.03239822760224342,
0.022786354646086693,
-0.01685389317572117,
0.052538398653268814,
0.06247006729245186,
0.004599226173013449,
-0.07395196706056595,
-0.08011310547590256,
0.015094045549631119,
0.010670839808881283,
-0.037047263234853745,
0.06282848119735718,
-0.013683849945664406,
0.002106190426275134,
-0.03990890458226204,
-0.005424796137958765,
0.0597364604473114,
-0.012650681659579277,
0.007937809452414513,
0.002161875367164612,
-0.04272274672985077,
-0.03317764028906822,
-0.04136941209435463,
-0.02659996971487999,
-0.0488274060189724,
-0.0394546203315258,
-0.04802463576197624,
0.02174404449760914,
-0.05653223395347595,
-0.02495315484702587,
-0.01081724651157856,
0.0734155923128128,
0.03251716494560242,
0.008818736299872398,
0.009414113126695156,
-0.005303629674017429,
-0.06230980157852173,
0.030495282262563705,
-0.033576734364032745,
-0.031386736780405045,
-0.0328788161277771,
0.058380838483572006,
-0.013358306139707565,
0.025043336674571037,
-0.0624103844165802,
0.017096923664212227,
0.011568306013941765,
0.0024360883980989456,
-0.012592420913279057,
-0.04365158826112747,
-0.013040597550570965,
0.04654432088136673,
0.04271889105439186,
0.0013177887303754687,
0.04417296126484871,
0.04634251073002815,
0.04172882065176964,
0.026682181283831596,
-0.018601644784212112,
-0.01984386332333088,
-0.0327305868268013,
0.05551972612738609,
-0.00634258845821023,
-0.07070764154195786,
0.02815576083958149,
0.02263246290385723
] |
<p>A <a href="http://en.wikipedia.org/wiki/Vortex_tube">Vortex Tube</a> takes a pressurized input stream, most typically of a gas, and creates two output streams with a temperature differential. <a href="http://www.exair.com/Cultures/en-US/Primary+Navigation/Products/Vortex+Tubes+and+Spot+Cooling/Vortex+Tubes/A+Phenomenon+of+Physics">Apparently, it has been described as a Maxwell's Demon</a>.</p>
<p>Both linked sources are scarce with information about how and why this works. Now, I have two questions:</p>
<ul>
<li><p>Why does it work, specifically why should the situation in the vortex lead to a transfer of thermal energy from the inner stream to the outer one?</p></li>
<li><p>How efficient can it be? </p></li>
<li><p>How do you define the efficiency of a device that may be closer to Maxwell's Demon than to a heat pump? My feeling is that any analysis should not only take into account the sum of input energy (thermal and mechanical energy instream) and sum output (thermal energies and pressures of both gas streams), but also the Temperature differential that is created - since that contains an ability to create work.*</p></li>
<li><p>If course it's pointless to create heat from high grade 8mech.) energy to transform it back to mech. energy - but it gives an idea on the worth of the output.</p></li>
</ul> | g316 | [
-0.006280970294028521,
0.023350834846496582,
-0.002769336337223649,
-0.0038918019272387028,
0.05905935540795326,
-0.01768101193010807,
0.05859699472784996,
0.044142674654722214,
-0.07931610941886902,
-0.04087943211197853,
-0.012678799219429493,
0.05599501356482506,
0.014791732653975487,
0.008800216019153595,
0.014199510216712952,
-0.017071694135665894,
0.01756533607840538,
-0.01255195215344429,
0.09139338880777359,
0.026442665606737137,
-0.024364158511161804,
0.02373637817800045,
0.02227597124874592,
-0.05432029440999031,
-0.009332092478871346,
-0.008684034459292889,
-0.005332436412572861,
0.03731607645750046,
-0.015610295347869396,
-0.004179768264293671,
0.040352098643779755,
0.022404581308364868,
0.014596221037209034,
-0.01483326405286789,
-0.0924353301525116,
0.04419538006186485,
0.024963296949863434,
0.0019354723626747727,
-0.001941631082445383,
-0.01736149564385414,
-0.01541056763380766,
-0.022114237770438194,
-0.012159405276179314,
-0.0379013828933239,
-0.06070780009031296,
0.07022333890199661,
-0.022288663312792778,
-0.039107274264097214,
-0.022634124383330345,
-0.001274024834856391,
0.011907847598195076,
0.014901825226843357,
0.059939537197351456,
0.02396724931895733,
0.06025967746973038,
-0.005164863541722298,
-0.039472416043281555,
-0.028951261192560196,
0.06538162380456924,
0.002885935828089714,
-0.01081747468560934,
0.0008391875308007002,
-0.001005134778097272,
0.021873729303479195,
-0.0028774954844266176,
-0.024527771398425102,
-0.00464241299778223,
0.0055635483004152775,
-0.024125773459672928,
0.027377715334296227,
-0.01147964596748352,
-0.03853640332818031,
0.01949136331677437,
-0.03725292906165123,
0.04379567876458168,
0.01489328220486641,
-0.006952651310712099,
-0.01678803190588951,
0.045920513570308685,
-0.038317374885082245,
-0.03701259195804596,
-0.004089601803570986,
-0.032842036336660385,
-0.01125227939337492,
0.04574096202850342,
-0.000044776305003324524,
-0.01427723653614521,
-0.009496835991740227,
-0.010090049356222153,
0.0019378475844860077,
-0.011260788887739182,
0.017157217487692833,
0.09951259940862656,
-0.01272699423134327,
-0.05006027594208717,
0.012484507635235786,
-0.012610998935997486,
0.03583808243274689,
0.01937243714928627,
0.005167640745639801,
0.018730223178863525,
-0.027167392894625664,
-0.006395488511770964,
0.006689032539725304,
0.04215048998594284,
-0.014316179789602757,
-0.03876379877328873,
0.003500767517834902,
-0.03710765391588211,
0.054629214107990265,
-0.07684854418039322,
-0.052570901811122894,
-0.05691080540418625,
0.023281432688236237,
-0.016054727137088776,
-0.042295366525650024,
0.021695159375667572,
0.04257058724761009,
-0.06000487878918648,
0.048120442777872086,
0.018784422427415848,
0.05067107081413269,
0.003234847681596875,
0.018769148737192154,
0.039815858006477356,
0.000654448987916112,
-0.005085476208478212,
-0.026996372267603874,
-0.0027338105719536543,
0.055324532091617584,
0.05419791489839554,
0.002015478676185012,
-0.031345926225185394,
0.03563659265637398,
0.07125295698642731,
0.05717882141470909,
-0.03739647567272186,
-0.055967651307582855,
0.024493159726262093,
-0.007456907071173191,
-0.02462121844291687,
-0.09390749037265778,
-0.046630073338747025,
-0.010178918950259686,
0.005254956427961588,
0.027802513912320137,
-0.07229941338300705,
-0.008198503404855728,
0.015395604074001312,
0.01824221946299076,
-0.04785657301545143,
0.09744308143854141,
0.030299155041575432,
0.012964176014065742,
0.042292892932891846,
-0.010696813464164734,
0.0709008276462555,
0.0018163438653573394,
0.006694937124848366,
-0.027574891224503517,
0.07437754422426224,
-0.054708193987607956,
0.07633890211582184,
-0.0036449215840548277,
-0.058359675109386444,
-0.07285412400960922,
0.02447887696325779,
-0.07502426207065582,
0.06464855372905731,
0.00030989275546744466,
-0.052377231419086456,
0.026197250932455063,
-0.0215135607868433,
0.0341346338391304,
0.027404872700572014,
0.014519485644996166,
0.060275908559560776,
0.022460144013166428,
-0.012722216546535492,
-0.04038185253739357,
-0.01834133453667164,
-0.016582578420639038,
0.05386753007769585,
-0.030912891030311584,
0.002969964873045683,
-0.0038565308786928654,
0.01214311458170414,
-0.027518685907125473,
-0.035721637308597565,
-0.029953608289361,
-0.04390605911612511,
-0.032621659338474274,
-0.011834654957056046,
0.05921349301934242,
-0.01836477592587471,
0.021774491295218468,
0.020283948630094528,
-0.027261408045887947,
-0.06629228591918945,
0.035130877047777176,
-0.0244109109044075,
-0.0012201820500195026,
0.04450397565960884,
0.0101500004529953,
0.029229138046503067,
0.07192401587963104,
-0.03631063923239708,
0.027736881747841835,
-0.013695704750716686,
-0.0363117977976799,
0.042330093681812286,
-0.0023617716506123543,
0.05454910174012184,
0.016766058281064034,
-0.06276046484708786,
0.003731201170012355,
-0.03354140371084213,
-0.034556981176137924,
-0.0024589928798377514,
-0.0261335801333189,
0.013106138445436954,
0.012763134203851223,
0.046879176050424576,
0.006840875372290611,
-0.06185381859540939,
-0.03481856733560562,
-0.02416101098060608,
-0.009523969143629074,
-0.030695796012878418,
0.00765920989215374,
-0.04865521565079689,
0.021302001550793648,
0.01598241925239563,
-0.06660571694374084,
0.030585143715143204,
-0.02097676508128643,
0.026637021452188492,
0.0050179134123027325,
-0.0035106120631098747,
0.039833564311265945,
0.023279331624507904,
-0.07963017374277115,
-0.006041320506483316,
-0.011193417012691498,
-0.007862702012062073,
-0.03911308944225311,
-0.005792128853499889,
-0.010014996863901615,
-0.01209135539829731,
-0.03796885907649994,
-0.01438573095947504,
-0.02257128246128559,
-0.02439807541668415,
0.024558307603001595,
-0.02974182367324829,
-0.07453922927379608,
-0.005384494084864855,
0.024214759469032288,
-0.0009076466085389256,
0.005261132959276438,
0.06647744029760361,
0.06850572675466537,
0.04789474979043007,
0.06509009003639221,
-0.05462710186839104,
0.009637361392378807,
-0.003630453022196889,
0.017277561128139496,
-0.021289881318807602,
-0.003647885285317898,
-0.031117858365178108,
0.05598795413970947,
-0.03282821178436279,
-0.004366274923086166,
0.047192178666591644,
0.0339486338198185,
-0.004222974646836519,
-0.029325246810913086,
0.020928284153342247,
-0.022178426384925842,
0.0048221140168607235,
-0.03748628497123718,
-0.05380500108003616,
0.04250645637512207,
0.011797060258686543,
-0.04994866997003555,
-0.00987109262496233,
0.022446611896157265,
-0.00451054610311985,
0.021497506648302078,
0.04613347351551056,
0.021877359598875046,
-0.026904093101620674,
0.0024222948122769594,
0.03153383731842041,
-0.04584905505180359,
0.01799839921295643,
-0.009418390691280365,
-0.015500621870160103,
-0.010561509989202023,
-0.019360823556780815,
-0.003429014701396227,
-0.0020122781861573458,
-0.00666650990024209,
-0.011425026692450047,
0.03397693485021591,
-0.039597731083631516,
-0.014015807770192623,
-0.04071136564016342,
0.008765948005020618,
0.04143235832452774,
-0.0059326523914933205,
0.006630449555814266,
-0.015194804407656193,
0.021172454580664635,
0.01497738342732191,
0.015021948143839836,
-0.015873774886131287,
0.0003406859759707004,
0.06082002446055412,
-0.04613758623600006,
-0.03561041131615639,
0.043821435421705246,
-0.05986569821834564,
0.002059551887214184,
0.019892843440175056,
-0.010494891554117203,
-0.06889616698026657,
-0.031127404421567917,
0.0006638608174398541,
0.004451109562069178,
-0.012501712888479233,
-0.024346938356757164,
-0.024677885696291924,
0.0022551717702299356,
-0.018920505419373512,
-0.08809451758861542,
0.0040370505303144455,
0.016971532255411148,
0.04520604386925697,
-0.05458627641201019,
0.00007743049354758114,
-0.05105811730027199,
0.020924938842654228,
0.028754375874996185,
0.03589142486453056,
-0.02362244389951229,
0.050684913992881775,
-0.02071227692067623,
0.0071578496135771275,
0.026217950507998466,
-0.008467292413115501,
0.05185050144791603,
0.02964150346815586,
0.006092649418860674,
-0.031513020396232605,
0.002837055828422308,
-0.005663123447448015,
0.041858069598674774,
0.05172520503401756,
0.009955217130482197,
-0.02017877995967865,
-0.039328739047050476,
-0.04241068288683891,
-0.017720293253660202,
0.012015317566692829,
0.06822160631418228,
0.006457654293626547,
-0.02817755565047264,
0.00045568286441266537,
-0.0375172458589077,
-0.020687341690063477,
-0.09985169023275375,
-0.022416945546865463,
0.041414231061935425,
-0.017062658444046974,
0.03613630682229996,
0.038081537932157516,
-0.02604796551167965,
0.03623615950345993,
0.005808393936604261,
0.03859260305762291,
-0.014311558566987514,
-0.001598846516571939,
0.018161067739129066,
0.002876209793612361,
-0.06020312383770943,
0.06592711806297302,
0.03022267296910286,
-0.07525967806577682,
-0.020470857620239258,
0.033078353852033615,
-0.02713717706501484,
-0.029023339971899986,
-0.01681244559586048,
0.00895336177200079,
0.06428752839565277,
-0.02405932918190956,
-0.00504949688911438,
0.0023842393420636654,
0.0385524183511734,
-0.01419282890856266,
0.032057154923677444,
0.016345994547009468,
-0.041837479919195175,
-0.016423041000962257,
0.013775688596069813,
-0.018358197063207626,
-0.008830959908664227,
-0.05150892212986946,
0.018111273646354675,
-0.025949101895093918,
0.011303296312689781,
-0.009973349049687386,
0.020311592146754265,
-0.03131645917892456,
-0.027206312865018845,
-0.009298130869865417,
0.04379437491297722,
0.020686529576778412,
0.02524392306804657,
0.0033747318666428328,
0.010180084966123104,
0.041434433311223984,
-0.0496041513979435,
0.012893405742943287,
0.04969000816345215,
0.06134572997689247,
-0.016973070800304413,
-0.0548446886241436,
0.01975177228450775,
0.004334051627665758,
-0.0473637692630291,
-0.02247333712875843,
-0.010708428919315338,
0.043109942227602005,
0.0007467254181392491,
0.00664736982434988,
-0.010495233349502087,
0.07612453401088715,
0.08543498069047928,
-0.01177707128226757,
-0.0304427407681942,
-0.04137397184967995,
0.0012944316258653998,
-0.0019086864776909351,
0.004317577928304672,
-0.0212783832103014,
-0.03844159469008446,
-0.03227091208100319,
-0.06273000687360764,
0.011856941506266594,
-0.004249097779393196,
-0.0902789905667305,
0.01822694204747677,
0.014715531840920448,
0.04773494973778725,
0.033912137150764465,
0.0105979572981596,
-0.023349056020379066,
-0.03929414227604866,
0.05248800292611122,
-0.06235681474208832,
0.025731168687343597,
0.009027187712490559,
-0.02832057513296604,
-0.03305250033736229,
-0.052013806998729706,
-0.03454494848847389,
-0.054063815623521805,
0.03781576827168465,
0.048907533288002014,
0.0213441401720047,
0.05081002041697502,
0.0314575731754303,
-0.04402481019496918,
0.041634004563093185,
-0.022258572280406952,
-0.003519294550642371,
-0.03238179534673691,
-0.0032134568318724632,
0.06322884559631348,
0.06897512078285217,
0.04834594205021858,
0.04038146883249283,
-0.030544355511665344,
-0.0801902711391449,
0.02410566247999668,
-0.015610050410032272,
-0.019290288910269737,
0.02696412429213524,
0.10160880535840988,
0.031293369829654694,
-0.06528297811746597,
-0.022996913641691208,
0.034427460283041,
0.09270703792572021,
-0.013999851420521736,
-0.05144713073968887,
0.011887392960488796,
-0.03682304546236992,
-0.046829793602228165,
-0.023089341819286346,
0.008596188388764858,
0.015278391540050507,
0.01015565451234579,
0.04486805573105812,
-0.004653445445001125,
0.022046558558940887,
0.05137861892580986,
-0.0025988940615206957,
0.00965191051363945,
-0.02984757162630558,
-0.0029129108879715204,
0.009283940307796001,
-0.014376913197338581,
0.022975176572799683,
-0.028786538168787956,
0.01443420723080635,
-0.005026401951909065,
0.03848688304424286,
-0.03891674801707268,
0.024008359760046005,
0.032333455979824066,
0.005827097687870264,
0.046445272862911224,
-0.05220135673880577,
-0.020364822819828987,
0.03647875040769577,
0.039608754217624664,
-0.012457648292183876,
0.01993921585381031,
0.0014946593437343836,
0.06524772197008133,
-0.040434133261442184,
-0.026696056127548218,
0.06223313882946968,
0.0006774644716642797,
0.044301554560661316,
-0.010029890574514866,
-0.01104214508086443,
-0.05063549056649208,
-0.011653956025838852,
0.04884268715977669,
0.05762159451842308,
-0.04497804865241051,
0.02759762480854988,
0.022350464016199112,
0.006637117825448513,
-0.012326771393418312,
-0.0878947302699089,
-0.020355282351374626,
0.07849420607089996,
-0.009257943369448185,
0.03797769919037819,
-0.006128445267677307,
0.036912549287080765,
-0.0008531887433491647,
0.0030529710929840803,
-0.002734938869252801,
0.048635758459568024,
0.04793568328022957,
0.015242548659443855,
0.008610649965703487,
0.045155901461839676,
-0.022406073287129402,
-0.02252967096865177,
0.01358499750494957,
0.033236611634492874,
0.04062846675515175,
0.002236153231933713,
-0.024019207805395126,
-0.02338130958378315,
-0.08905860036611557,
0.062013644725084305,
0.0005166353657841682,
-0.012449859641492367,
-0.03985559195280075,
-0.025074968114495277,
-0.005404239054769278,
0.022420795634388924,
-0.00011864924454130232,
0.047489989548921585,
-0.0021097047720104456,
0.017685016617178917,
0.03463052958250046,
-0.05642139911651611,
0.03583918511867523,
-0.01661461591720581,
0.004525309428572655,
0.03364495560526848,
-0.019683197140693665,
0.040317192673683167,
0.009138233959674835,
-0.010064692236483097,
-0.032906148582696915,
-0.0146871916949749,
-0.01772746443748474,
-0.028132598847150803,
-0.03635411337018013,
0.012379643507301807,
-0.039020270109176636,
-0.022799208760261536,
-0.01897541619837284,
0.001822901889681816,
0.0122471172362566,
-0.009060864336788654,
0.025845374912023544,
-0.0668773502111435,
0.00350542482919991,
-0.011504421010613441,
-0.006100981496274471,
-0.02206672914326191,
-0.013395469635725021,
-0.030074970796704292,
0.030459443107247353,
-0.04090673476457596,
-0.03551003336906433,
0.05625208839774132,
0.009054131805896759,
0.011933794245123863,
-0.017021454870700836,
0.024994676932692528,
-0.002451073145493865,
0.03770937770605087,
0.062065429985523224,
-0.07853935658931732,
0.016876081004738808,
0.04095782712101936,
0.06227165833115578,
-0.01568549871444702,
-0.027768103405833244,
-0.007875598967075348,
0.03696718066930771,
-0.03222687169909477,
-0.0012988700764253736,
-0.009880964644253254,
-0.006661615334451199,
0.05743921175599098,
0.06627581268548965,
-0.01449641864746809,
0.00321582262404263,
-0.0018797413213178515,
0.05568667873740196,
-0.043338239192962646,
-0.009929911233484745,
0.008766678161919117,
-0.006162147969007492,
-0.07302048057317734,
-0.03917854651808739,
-0.09305395931005478,
-0.054414428770542145,
-0.03620119020342827,
0.013563979417085648,
-0.05350371077656746,
-0.01979726366698742,
-0.010121053084731102,
0.06010250002145767,
-0.004061379469931126,
-0.028204936534166336,
0.048534560948610306,
0.006289348937571049,
0.02539939433336258,
0.08271697908639908,
0.06770492345094681,
0.030940931290388107,
-0.0529133602976799,
-0.02882927469909191,
0.0702076181769371,
-0.04446541517972946,
-0.0006402382277883589,
-0.0353054441511631,
-0.03322714567184448,
-0.017558420076966286,
-0.019406147301197052,
-0.08959029614925385,
-0.018079664558172226,
-0.027699775993824005,
-0.052077822387218475,
-0.03700249269604683,
-0.06464681029319763,
-0.011484581977128983,
-0.030270755290985107,
-0.04118841886520386,
-0.06346254795789719,
-0.008683795109391212,
-0.052929434925317764,
0.00532016484066844,
-0.022106437012553215,
-0.01457363273948431,
-0.007602888625115156,
0.07401401549577713,
0.029892001301050186,
-0.0006475896807387471,
-0.049128178507089615,
0.08986233919858932,
0.03826494514942169,
0.006095793563872576,
0.047074735164642334,
0.025378746911883354,
0.06209249049425125,
0.033747948706150055,
0.015585267916321754,
0.01730351708829403,
0.02694084867835045,
0.046233952045440674,
0.04547743871808052,
0.039893340319395065,
-0.02566465735435486,
0.04277887940406799,
0.015246269293129444,
-0.02576826699078083,
0.02064211294054985,
0.04117607697844505,
-0.0051661147736012936,
0.006610321346670389,
-0.01223034504801035,
0.032500408589839935,
-0.01633789949119091,
0.025661155581474304,
0.001955903833732009,
0.031742069870233536,
-0.019184622913599014,
-0.07651309669017792,
0.05157062038779259,
-0.03623002767562866,
0.011070274747908115,
0.004327329341322184,
-0.04223105311393738,
0.01790015585720539,
0.023743493482470512,
-0.012860522605478764,
0.007325790356844664,
-0.023239819332957268,
-0.015822310000658035,
-0.01792711578309536,
-0.005859544966369867,
0.034356169402599335,
0.024122901260852814,
0.0005810610018670559,
0.0697777047753334,
-0.03937462344765663,
-0.018983345478773117,
-0.09955981373786926,
-0.023769591003656387,
-0.05113307386636734,
-0.059226009994745255,
0.06465600430965424,
-0.0031991603318601847,
-0.009175081737339497,
0.03800200670957565,
-0.01796814613044262,
-0.04003505781292915,
-0.02060174196958542,
0.010835901834070683,
-0.029471110552549362,
-0.014764483086764812,
0.06430834531784058,
-0.02341906540095806,
0.03773921728134155,
-0.01172663364559412,
0.028542274609208107,
0.003056084271520376,
-0.01799844019114971,
-0.017588885501027107,
-0.014591075479984283,
0.01755053736269474,
-0.00963333435356617
] |
<p>Ive read a few courses on <strong>statistical mechanics</strong>, and while their textual explanations and example choices differ, the flow of information from microscopy to macroscopy seems the same, and reading between the lines you can see some mathematical construct. Has statistical mechanics been formalized in the sense that say analysis has been formalized (<em>down to quantifiers, sets, functions,...</em>) more rigorously? Where can one find a <strong>formal axiomatic approach</strong> to statistical mechanics as opposed to an introductory descriptory approach?</p> | g4558 | [
0.06847924739122391,
0.02420080453157425,
-0.010073753073811531,
-0.007227461319416761,
0.017921393737196922,
-0.040791261941194534,
0.009146537631750107,
-0.009730715304613113,
-0.011888128705322742,
-0.03914381563663483,
0.01212611049413681,
-0.03954485058784485,
0.13180086016654968,
-0.032729148864746094,
-0.04454631358385086,
-0.03736986219882965,
0.02737976424396038,
0.00561919342726469,
0.0714707151055336,
0.04019572585821152,
-0.016642846167087555,
0.053255707025527954,
0.027941254898905754,
-0.05715185031294823,
-0.04438189044594765,
-0.02993704378604889,
-0.01453893817961216,
-0.010198790580034256,
0.05965745821595192,
0.024220909923315048,
-0.004346565343439579,
-0.05251136049628258,
0.06267855316400528,
-0.039558686316013336,
0.013988344930112362,
-0.04637553542852402,
0.019809603691101074,
0.027508733794093132,
0.007499287836253643,
-0.04161066561937332,
0.06204809248447418,
0.02346404641866684,
0.01382265891879797,
-0.0321107842028141,
-0.03875608742237091,
0.005681313574314117,
-0.02147728204727173,
-0.04161832854151726,
-0.015296760015189648,
-0.011846589855849743,
-0.0054487804882228374,
0.03281943127512932,
0.08783756196498871,
0.01721838489174843,
0.046866584569215775,
0.02555890753865242,
-0.0023469682782888412,
0.005038436036556959,
0.034047480672597885,
-0.026667991653084755,
0.041689250618219376,
0.004620546009391546,
0.007431341800838709,
0.022233951836824417,
0.035255465656518936,
0.02453221008181572,
-0.03678227216005325,
-0.05154431611299515,
0.04687970131635666,
-0.0290803425014019,
-0.008685532957315445,
-0.07000192999839783,
-0.006512859836220741,
-0.046025000512599945,
-0.035320036113262177,
-0.02007639966905117,
-0.01479492336511612,
0.00940590538084507,
-0.022625349462032318,
-0.009157012216746807,
-0.077500119805336,
-0.008452050387859344,
-0.01477829273790121,
-0.022686585783958435,
0.029207440093159676,
0.01666107587516308,
0.0026234937831759453,
-0.008152641355991364,
0.07388074696063995,
0.026063529774546623,
0.05544232204556465,
0.026270905509591103,
0.009923310950398445,
0.00015751384489703923,
-0.04910488426685333,
-0.02373848296701908,
-0.06830618530511856,
0.014187668450176716,
-0.028551412746310234,
-0.002967263339087367,
-0.0085535179823637,
0.03979790583252907,
-0.007684222888201475,
-0.011351949535310268,
-0.03863169625401497,
0.011978080496191978,
-0.004951130133122206,
0.007185737602412701,
-0.010902782902121544,
0.009082785807549953,
0.0012122640619054437,
0.037544846534729004,
-0.03221422806382179,
0.06363419443368912,
-0.057059481739997864,
-0.021376648917794228,
0.10800237953662872,
-0.0025795064866542816,
-0.028345970436930656,
0.058015771210193634,
0.00537496991455555,
0.03548040986061096,
0.050002872943878174,
0.06922540813684464,
-0.06373297423124313,
-0.012395773082971573,
-0.013530812226235867,
0.03911278769373894,
0.023105626925826073,
0.0029820657800883055,
0.02979470044374466,
-0.013415716588497162,
-0.025288838893175125,
0.00041317782597616315,
0.00854607205837965,
0.04982445016503334,
-0.056478675454854965,
-0.03635120764374733,
-0.049914367496967316,
0.003216780489310622,
-0.07202707231044769,
0.019930656999349594,
-0.0012154292780905962,
0.025699203833937645,
-0.013143997639417648,
0.01760123483836651,
-0.004087499808520079,
0.01040724664926529,
0.04862168803811073,
-0.019387012347579002,
0.03162502869963646,
0.059124656021595,
-0.030774015933275223,
-0.09705542027950287,
-0.0075973086059093475,
-0.020611468702554703,
0.04638392850756645,
-0.020558085292577744,
0.017390286549925804,
0.013970740139484406,
0.03643110394477844,
0.028649158775806427,
0.009110854007303715,
-0.020562835037708282,
0.005656006745994091,
-0.022271163761615753,
0.009208516217768192,
-0.038314130157232285,
0.0520450621843338,
-0.033600419759750366,
-0.02555564045906067,
-0.04020313546061516,
0.011803043074905872,
-0.012409580871462822,
-0.0307447649538517,
0.029173389077186584,
-0.022320115938782692,
-0.008987742476165295,
0.005544443614780903,
0.017653262242674828,
-0.04231174662709236,
0.012059393338859081,
0.03551210090517998,
-0.03114328719675541,
0.0035049356520175934,
0.018201086670160294,
0.025153178721666336,
-0.04990345612168312,
-0.00030092691304162145,
0.022188028320670128,
-0.08070822060108185,
0.04520060494542122,
-0.012764997780323029,
0.051888708025217056,
0.044526681303977966,
-0.0036496783141046762,
0.009089901112020016,
-0.018353426828980446,
0.01980857364833355,
0.021000446751713753,
0.062298767268657684,
0.031000947579741478,
-0.010073534213006496,
0.06046842783689499,
-0.012155012227594852,
0.02882285788655281,
-0.020690351724624634,
0.029612712562084198,
-0.03225931152701378,
0.001301462878473103,
-0.007414442021399736,
0.022608557716012,
-0.014729000627994537,
-0.008596532978117466,
-0.004793707747012377,
-0.012810884043574333,
0.00042179779848083854,
-0.024865152314305305,
-0.02946169301867485,
0.025552760809659958,
-0.00568411173298955,
-0.034534942358732224,
0.018387984484434128,
0.052437737584114075,
0.01446338091045618,
0.028053782880306244,
-0.006900227628648281,
-0.0014470916939899325,
-0.04129257798194885,
0.026755083352327347,
-0.0902707427740097,
0.021444272249937057,
-0.019764795899391174,
-0.03503354266285896,
0.019009053707122803,
0.013176513835787773,
-0.004752985201776028,
-0.016211852431297302,
0.007893904112279415,
0.027471473440527916,
0.014653527177870274,
-0.0264601968228817,
-0.03312716260552406,
0.014242887496948242,
-0.02196410670876503,
-0.0172781553119421,
0.03315238282084465,
0.01600687950849533,
0.039659325033426285,
-0.006953202188014984,
-0.035642579197883606,
0.00041725169285200536,
-0.0065329670906066895,
-0.029559435322880745,
-0.013979262672364712,
-0.03968308866024017,
-0.026827996596693993,
0.017626499757170677,
-0.03920264169573784,
0.029889753088355064,
0.0011249231174588203,
0.05777193605899811,
0.0071674226783216,
-0.013781001791357994,
-0.03896985948085785,
-0.002042788080871105,
0.00024027399194892496,
-0.017803708091378212,
-0.03265058621764183,
-0.007388314697891474,
0.03709360584616661,
0.09504510462284088,
0.018351558595895767,
-0.023877041414380074,
0.02411869913339615,
-0.032253287732601166,
-0.006659808102995157,
-0.007500544190406799,
0.025742584839463234,
-0.05979825556278229,
0.0006401432328857481,
0.0009780325926840305,
-0.029537469148635864,
0.004559716209769249,
0.008012192323803902,
-0.0074950288981199265,
0.02350856177508831,
-0.02677394449710846,
0.013471049256622791,
-0.03167916461825371,
0.012239034287631512,
0.01940256543457508,
-0.008363230153918266,
-0.006804962642490864,
-0.12124928832054138,
0.021748952567577362,
0.007250847760587931,
-0.0377441830933094,
0.005453878082334995,
0.004796258639544249,
-0.05914106220006943,
-0.02279513329267502,
0.03378281742334366,
0.06841225922107697,
0.10888450592756271,
0.07202880084514618,
-0.0033237505704164505,
-0.08938057720661163,
-0.04527251422405243,
-0.002387766260653734,
-0.003112867707386613,
0.05091044679284096,
-0.0038097177166491747,
0.028505628928542137,
-0.049050312489271164,
-0.025006679818034172,
-0.009695657528936863,
0.013101761229336262,
-0.016462191939353943,
-0.06388785690069199,
-0.004883509129285812,
-0.056658122688531876,
0.025110891088843346,
-0.022482987493276596,
0.013837885111570358,
-0.056809112429618835,
-0.017958126962184906,
0.04418100044131279,
-0.10398150235414505,
0.0006470891530625522,
0.048192113637924194,
0.008129351772367954,
-0.009271128103137016,
-0.00973112229257822,
-0.07040300965309143,
-0.039108991622924805,
-0.056345902383327484,
-0.06319208443164825,
0.06024123355746269,
-0.07089116424322128,
0.022085346281528473,
-0.03896453604102135,
-0.024158092215657234,
-0.001908320700749755,
-0.00696896156296134,
0.0068513923324644566,
-0.02259412407875061,
-0.033844757825136185,
0.06690513342618942,
-0.03785193711519241,
-0.0160050205886364,
0.055301323533058167,
0.06430251151323318,
0.008595453575253487,
-0.04348310828208923,
0.0089419549331069,
0.09621233493089676,
0.02136259712278843,
0.06419619172811508,
-0.030488742515444756,
0.021096892654895782,
-0.05252614617347717,
-0.035464223474264145,
-0.011341245844960213,
-0.024978021159768105,
0.011407959274947643,
0.013266394846141338,
0.064082570374012,
0.0592050664126873,
0.014714337885379791,
-0.014061877503991127,
0.02473531663417816,
-0.04485327750444412,
0.04816058650612831,
-0.006673186086118221,
0.005555431358516216,
0.03786235675215721,
0.034522537142038345,
-0.027263974770903587,
-0.01789378933608532,
0.06593240797519684,
0.006707764230668545,
0.08633094280958176,
-0.006994145922362804,
0.027401721104979515,
0.015805713832378387,
-0.023765215650200844,
0.020355679094791412,
-0.011863653548061848,
-0.019351886585354805,
-0.0007072932203300297,
-0.06681398302316666,
-0.015874501317739487,
0.053468700498342514,
0.014435074292123318,
-0.02334797941148281,
0.03755483776330948,
0.020901495590806007,
-0.008778013288974762,
-0.002449383493512869,
-0.04783965274691582,
0.014452832750976086,
-0.023439686745405197,
0.010164756327867508,
-0.013779214583337307,
0.0393497459590435,
-0.02312970533967018,
-0.02824101224541664,
0.0048622558824718,
-0.025936679914593697,
0.013686181977391243,
-0.05151008814573288,
0.06375536322593689,
-0.023947840556502342,
-0.023739449679851532,
0.0018709483556449413,
-0.04748142510652542,
-0.007927155122160912,
0.003301083343103528,
0.04516176879405975,
-0.012773771770298481,
0.03683612123131752,
0.0033104598987847567,
-0.0017879806691780686,
-0.021090826019644737,
0.09763020277023315,
0.032239001244306564,
0.03181843087077141,
-0.003456834936514497,
-0.07252075523138046,
-0.018633520230650902,
0.01014351099729538,
0.03817563131451607,
0.06828334927558899,
-0.06867288798093796,
0.014946303330361843,
-0.0325312502682209,
0.0644073560833931,
-0.0007488701376132667,
0.016890404745936394,
0.04098518192768097,
-0.018210381269454956,
0.028080912306904793,
-0.015063611790537834,
0.053643714636564255,
0.00004860192711930722,
-0.0050603291019797325,
0.008712911047041416,
-0.03768065571784973,
-0.023511823266744614,
-0.049359291791915894,
0.04323858022689819,
-0.013083778321743011,
0.030964743345975876,
-0.07097062468528748,
-0.013606186024844646,
0.014986289665102959,
0.060835160315036774,
-0.021417200565338135,
-0.018580954521894455,
0.004748724400997162,
-0.03250475600361824,
0.01190502941608429,
-0.0014579821145161986,
-0.01646481826901436,
0.004230319056659937,
-0.08808747678995132,
0.03709716722369194,
-0.044207457453012466,
0.009447155520319939,
-0.009363120421767235,
0.03112109936773777,
-0.023860573768615723,
0.010079552419483662,
0.017758458852767944,
-0.009094093926250935,
0.000663394050206989,
-0.06284864991903305,
0.009995670057833195,
-0.04271944612264633,
0.022547347471117973,
-0.0435577929019928,
-0.0012713572941720486,
-0.021157963201403618,
0.02662034146487713,
-0.0009077953291125596,
-0.030434131622314453,
0.018426749855279922,
-0.05679762735962868,
-0.011319521814584732,
0.027366433292627335,
-0.015034306794404984,
0.016557252034544945,
-0.008579082787036896,
-0.05441749840974808,
-0.024546684697270393,
0.06086507439613342,
-0.021263163536787033,
-0.009256407618522644,
-0.04326500743627548,
-0.08104194700717926,
0.02537749707698822,
-0.03817444294691086,
0.058753106743097305,
0.007031416054815054,
0.02046792581677437,
0.05987715348601341,
-0.03213705122470856,
-0.10824231803417206,
0.04314948990941048,
0.0473899245262146,
0.037112463265657425,
-0.023688293993473053,
0.02230580523610115,
0.05249089002609253,
0.033558402210474014,
-0.005383635405451059,
0.064480260014534,
0.0011549708433449268,
-0.06081312522292137,
0.030842222273349762,
-0.009205939248204231,
-0.008516335859894753,
-0.0443744994699955,
-0.02437153272330761,
-0.0057619004510343075,
-0.04823886975646019,
-0.045420091599226,
0.03133494406938553,
0.01426620688289404,
-0.01803116872906685,
-0.012997915036976337,
0.0030728685669600964,
0.034270066767930984,
-0.0012991935946047306,
-0.005388571415096521,
0.01492790412157774,
0.03995823860168457,
-0.07903110235929489,
0.004222465213388205,
-0.004788131918758154,
0.027859466150403023,
0.01528217550367117,
0.042362600564956665,
0.02577309124171734,
-0.05016133934259415,
0.05768818408250809,
-0.053842391818761826,
0.08533582091331482,
-0.03084714524447918,
-0.033885084092617035,
-0.009212070144712925,
-0.015058395452797413,
-0.05539114400744438,
-0.05683746933937073,
0.06893578171730042,
0.0065519241616129875,
-0.06020234525203705,
-0.007596449926495552,
0.0033217789605259895,
0.005111199337989092,
0.0038799098692834377,
0.011119432747364044,
0.0069898380897939205,
0.017763884738087654,
-0.010925065726041794,
-0.030282266438007355,
-0.02379930391907692,
0.02814699523150921,
0.07453915476799011,
0.01178917195647955,
0.03426944836974144,
0.044203270226716995,
0.017968831583857536,
0.024441614747047424,
0.055723175406455994,
0.006211866158992052,
-0.03181472420692444,
0.003397237742319703,
-0.029687169939279556,
0.02491845190525055,
0.05924493446946144,
0.008949792943894863,
-0.04469146952033043,
-0.0696638971567154,
0.027985339984297752,
-0.031873174011707306,
-0.019057583063840866,
0.028104174882173538,
0.008488638326525688,
0.022142738103866577,
-0.03338468074798584,
-0.06144300475716591,
-0.00856067519634962,
-0.03338364511728287,
0.0008788321865722537,
0.07780066132545471,
-0.005027784965932369,
0.0182139053940773,
0.04523850604891777,
0.010148867033421993,
0.012113678269088268,
0.002652570139616728,
-0.06781712174415588,
0.08858668804168701,
0.027808556333184242,
0.007873653434216976,
0.01790578104555607,
0.03419627249240875,
-0.009625297039747238,
0.024335436522960663,
-0.011360365897417068,
-0.02541179768741131,
0.03783624246716499,
0.009010042995214462,
-0.06697307527065277,
-0.04527147859334946,
-0.0055162301287055016,
-0.013618210330605507,
-0.0036658807657659054,
0.004967281129211187,
-0.018153393641114235,
0.02225251868367195,
-0.03711966052651405,
-0.016257667914032936,
0.005182086024433374,
-0.016194794327020645,
0.0939227044582367,
0.06377694010734558,
-0.03262179717421532,
-0.016528375446796417,
0.02261371724307537,
-0.0006752436165697873,
-0.02695368602871895,
-0.025997186079621315,
0.007907502353191376,
-0.06800422072410583,
0.013456395827233791,
0.048821136355400085,
-0.01003194134682417,
-0.020784225314855576,
0.03286605328321457,
0.05886494740843773,
-0.051275383681058884,
-0.02047504298388958,
-0.04245273023843765,
0.02773052081465721,
0.03362487629055977,
-0.04537401720881462,
-0.028710391372442245,
0.04333677515387535,
0.031116126105189323,
-0.02564043365418911,
0.026707228273153305,
-0.0265529565513134,
0.08063670247793198,
0.06393507122993469,
-0.006773184984922409,
0.05261452496051788,
-0.052756182849407196,
0.032956212759017944,
0.002286188304424286,
-0.006708785425871611,
-0.06116300821304321,
0.014840069226920605,
0.05845842510461807,
-0.004198745358735323,
-0.0028847074136137962,
-0.04244855046272278,
-0.0430094413459301,
0.03348921239376068,
-0.035170942544937134,
-0.03719320893287659,
0.0018600707408040762,
0.03465195372700691,
-0.04858625307679176,
0.028754569590091705,
0.02290409244596958,
-0.0009765314171090722,
-0.03615277633070946,
0.018013542518019676,
0.029633792117238045,
0.03363018482923508,
0.0643719881772995,
-0.05492151156067848,
0.00362576125189662,
-0.03105107508599758,
-0.0017753331921994686,
-0.04238930344581604,
-0.00473334826529026,
-0.01640491932630539,
-0.07117515802383423,
0.0022037234157323837,
-0.010650687851011753,
0.020921025425195694,
-0.03245747461915016,
0.011882903054356575,
0.07052356004714966,
0.022467361763119698,
-0.0010530618019402027,
0.0037607247941195965,
0.015682311728596687,
-0.037655021995306015,
0.05193834379315376,
0.020762141793966293,
0.004564703907817602,
-0.050065841525793076,
-0.04209807515144348,
0.008403366431593895,
-0.00888086762279272,
-0.049530990421772,
-0.007382818032056093,
-0.004943632520735264,
-0.01067442074418068,
-0.002558172680437565,
-0.0184320081025362,
-0.013792917132377625,
-0.018512235954403877,
0.0452716201543808,
-0.010721922852098942,
-0.009481876157224178,
-0.020520886406302452,
-0.031811729073524475,
-0.004064046312123537,
0.007795744575560093,
0.03794161230325699,
-0.022643892094492912,
-0.02849746122956276,
-0.01866697147488594,
0.046973127871751785,
0.0011048286687582731,
0.0028215565253049135,
0.012112336233258247,
0.07825271040201187,
-0.054622501134872437,
0.040575653314590454,
0.071164071559906,
-0.005874414928257465,
-0.034427985548973083,
-0.010093672201037407,
0.042941223829984665,
-0.011502224020659924,
0.01514437049627304,
-0.0441552959382534,
-0.01771223172545433,
-0.00886854063719511,
-0.042612478137016296,
-0.013669505715370178,
0.0219598226249218,
-0.010494164191186428,
0.01329195685684681,
0.028696969151496887,
-0.015478825196623802,
0.04897451028227806,
-0.0483713373541832,
-0.056710656732320786,
0.032124873250722885,
0.006452105473726988,
0.06974662095308304,
-0.013346774503588676,
0.051589034497737885,
0.028443897143006325,
0.053926803171634674,
-0.01894773729145527,
-0.03212394192814827,
0.0039563425816595554,
-0.017260447144508362,
-0.00032239340362139046
] |
<p>Please move this if it's not in the right location.</p>
<p>I'm looking for the name of a device that I frequently see in many scenarios, specifically that of an office/library which can be described as having multiple rings that rotate in various directions. I was thinking it was a gyroscope or perhaps a celestial globe, but something tells me that it's not quite what I'm looking for. I recall that there is a movie production company which uses this device as their symbolic figure of their logo.</p> | g4559 | [
-0.035364460200071335,
0.06700687855482101,
-0.004820977803319693,
-0.050776395946741104,
-0.008777880109846592,
-0.015619957819581032,
0.04086374491453171,
-0.03965260460972786,
0.001989788841456175,
0.0025879384484142065,
0.020165208727121353,
0.007171601057052612,
0.03789033368229866,
-0.016839127987623215,
0.054499052464962006,
-0.07977471500635147,
0.04673057422041893,
-0.02167021483182907,
0.020815687254071236,
0.05170029029250145,
0.01582135260105133,
0.00024476664839312434,
0.00035726354690268636,
0.01933100074529648,
-0.04598234221339226,
0.059252116829156876,
0.007108402904123068,
-0.004824133589863777,
-0.050479739904403687,
-0.0348346009850502,
-0.05782128497958183,
-0.02398880571126938,
0.027273481711745262,
-0.026542022824287415,
-0.003755107754841447,
-0.001194171141833067,
0.01445167139172554,
0.020994793623685837,
0.020638495683670044,
-0.005863493774086237,
-0.004691751208156347,
-0.0334257036447525,
0.010201768949627876,
0.02058149129152298,
0.061796266585588455,
0.058184560388326645,
0.0072586508467793465,
0.00392150180414319,
0.051099784672260284,
-0.03538966923952103,
-0.04443538188934326,
0.02015281468629837,
0.01754058338701725,
-0.00890735350549221,
-0.01064857468008995,
0.03389241546392441,
-0.02774205058813095,
0.01889338158071041,
0.0016991941956803203,
0.022719064727425575,
0.013058548793196678,
0.06407926231622696,
0.001363452640362084,
-0.021749066188931465,
0.05416771396994591,
-0.017901871353387833,
0.014558637514710426,
-0.004724603146314621,
0.029917096719145775,
-0.04306185245513916,
0.02679027058184147,
-0.0017612091032788157,
0.06047486886382103,
0.0019557811319828033,
0.018222760409116745,
0.029883265495300293,
-0.045656345784664154,
-0.015738561749458313,
-0.025477338582277298,
0.06044802814722061,
-0.019549675285816193,
-0.006897596642374992,
-0.02792806178331375,
0.060447368770837784,
0.07323215156793594,
0.05298536643385887,
0.009894895367324352,
-0.017544446513056755,
0.008298179134726524,
0.029512638226151466,
0.02527393400669098,
0.0007913820445537567,
0.02314845100045204,
0.03814997151494026,
-0.048826176673173904,
0.000306440400891006,
0.01359164621680975,
0.02535352297127247,
0.011339900083839893,
0.012411369942128658,
-0.00647179689258337,
-0.04490158334374428,
0.03460562601685524,
-0.043326251208782196,
-0.024172265082597733,
0.023683860898017883,
-0.01183696836233139,
-0.014280609786510468,
-0.06769867986440659,
-0.048225078731775284,
0.004380738362669945,
0.005307158455252647,
-0.020183250308036804,
-0.0468546561896801,
-0.016810342669487,
-0.007218612357974052,
0.06890815496444702,
-0.014268058352172375,
0.05724387615919113,
0.028121380135416985,
0.006912203971296549,
-0.05744567885994911,
-0.02863774448633194,
0.05614185333251953,
-0.03703521564602852,
-0.00225792801938951,
0.01609514281153679,
-0.0577043779194355,
-0.001051748520694673,
0.015252985991537571,
0.04343995451927185,
-0.029620587825775146,
-0.008863245137035847,
-0.005620008334517479,
-0.01699027791619301,
0.048378899693489075,
-0.026072291657328606,
0.00013196560030337423,
-0.00412089005112648,
0.023079507052898407,
0.04630090296268463,
-0.10470272600650787,
0.019878363236784935,
-0.023803366348147392,
0.03444048389792442,
-0.010860526002943516,
0.03382371366024017,
-0.021060239523649216,
0.0902424156665802,
0.014552293345332146,
-0.006140463054180145,
0.03903668746352196,
-0.052600372582674026,
-0.03826599940657616,
0.00929200742393732,
-0.007133543957024813,
0.018175624310970306,
0.024910738691687584,
0.028463134542107582,
0.0010108654387295246,
0.022710319608449936,
0.004179499112069607,
-0.019466493278741837,
0.00942315999418497,
-0.0362527035176754,
-0.026724306866526604,
0.01696120761334896,
-0.016369709745049477,
-0.03488324210047722,
0.006408745888620615,
-0.025361057370901108,
-0.03978521004319191,
-0.00923194084316492,
0.016885366290807724,
0.016860218718647957,
0.03624719753861427,
0.06171288713812828,
-0.000946870306506753,
0.027537934482097626,
-0.0023298233281821012,
-0.031578321009874344,
-0.017010200768709183,
0.0063092587515711784,
0.009852440096437931,
-0.032385408878326416,
-0.010408936068415642,
-0.013479813933372498,
0.04846828803420067,
0.00827495101839304,
0.005932976491749287,
0.03583752363920212,
-0.027299225330352783,
-0.020913682878017426,
0.018299292773008347,
-0.002923561492934823,
-0.04739997535943985,
-0.01918427273631096,
-0.024052102118730545,
-0.019935129210352898,
0.008722842670977116,
0.043027717620134354,
-0.01718294434249401,
0.028082139790058136,
0.06486503034830093,
-0.03897777199745178,
-0.05590735003352165,
0.010192567482590675,
-0.0017492080805823207,
0.04651281237602234,
0.01430277805775404,
0.03023454174399376,
0.011874565854668617,
-0.02039964497089386,
-0.004340032581239939,
-0.014278778806328773,
-0.029919659718871117,
0.01819860190153122,
0.04795089736580849,
0.009623230434954166,
-0.0033993409015238285,
0.047211844474077225,
0.004582749679684639,
-0.02252892218530178,
-0.037971895188093185,
0.04425569623708725,
-0.0362962931394577,
-0.0031504614744335413,
-0.03596891835331917,
0.022238625213503838,
-0.007120577152818441,
-0.054082565009593964,
0.0019705507438629866,
0.09395813941955566,
0.024563929066061974,
0.08074178546667099,
-0.010786548256874084,
0.0016678320243954659,
-0.012708382681012154,
-0.02259976789355278,
0.018735194578766823,
0.014379524625837803,
0.013589982874691486,
-0.050303567200899124,
-0.042396243661642075,
0.025831272825598717,
-0.03803260251879692,
0.022302303463220596,
0.01143557857722044,
0.044580865651369095,
0.08607757836580276,
-0.011001036502420902,
-0.08178842812776566,
-0.0004870110424235463,
0.007791167590767145,
0.014868807047605515,
0.028092151507735252,
0.01904596947133541,
-0.015743738040328026,
-0.042725879698991776,
-0.027133725583553314,
-0.007898543030023575,
-0.05460337921977043,
0.08650467544794083,
0.014094914309680462,
0.09370952844619751,
-0.03942988067865372,
-0.030549250543117523,
-0.01590351201593876,
0.016183413565158844,
0.06770557165145874,
-0.03767311945557594,
-0.003902539610862732,
0.007669457700103521,
-0.006730084773153067,
-0.048159655183553696,
-0.051663029938936234,
0.001256458694115281,
0.02044922485947609,
-0.012317903339862823,
0.07156752794981003,
0.03432498127222061,
-0.01070789247751236,
-0.03312774375081062,
0.04101249948143959,
0.02812925912439823,
0.0183394867926836,
-0.024294331669807434,
0.09605363011360168,
-0.030622689053416252,
-0.017444025725126266,
-0.02275414764881134,
0.029230136424303055,
-0.01113547757267952,
-0.06500308960676193,
0.0019717267714440823,
-0.01763673685491085,
-0.010484620928764343,
0.04633259400725365,
-0.0336473323404789,
0.023783884942531586,
0.03295018523931503,
-0.0064584314823150635,
0.03881422430276871,
0.07638339698314667,
-0.01223781332373619,
0.03465316444635391,
0.005427325610071421,
-0.03302359580993652,
0.01985836587846279,
0.04627995565533638,
0.01577686332166195,
-0.013681634329259396,
-0.018796969205141068,
0.03764165937900543,
0.028930341824889183,
0.053936298936605453,
-0.00632847286760807,
0.008429636247456074,
-0.0331709198653698,
0.06525954604148865,
-0.027258489280939102,
-0.045878298580646515,
0.03626758232712746,
-0.021712299436330795,
-0.017052194103598595,
0.05512551590800285,
-0.03630298376083374,
-0.000019894956494681537,
0.033231452107429504,
-0.050895608961582184,
0.007473693694919348,
0.028368251398205757,
-0.0022620500531047583,
0.007309814915060997,
-0.03142256289720535,
0.042756564915180206,
-0.034732457250356674,
0.002052555326372385,
0.06404783576726913,
-0.0011220814194530249,
0.054400600492954254,
0.023932434618473053,
0.011632596142590046,
-0.04707934334874153,
0.008181198500096798,
0.038615308701992035,
-0.011229566298425198,
-0.008335428312420845,
-0.003195867408066988,
-0.011085429228842258,
0.005069121718406677,
0.013835042715072632,
0.01054784469306469,
-0.0468502901494503,
0.08075544983148575,
0.010175622999668121,
-0.013634438626468182,
-0.02599736489355564,
-0.017136218026280403,
0.017984559759497643,
-0.043633412569761276,
-0.004841185174882412,
-0.04610009118914604,
-0.0508410818874836,
0.05511479452252388,
0.014579402282834053,
0.027345631271600723,
0.009621143341064453,
-0.024391748011112213,
0.017960699275135994,
0.07489810138940811,
0.003174426732584834,
-0.044489536434412,
-0.033932290971279144,
0.028062133118510246,
-0.03813662752509117,
0.021694932132959366,
-0.03717401623725891,
-0.020635463297367096,
0.029690690338611603,
-0.01852802187204361,
0.01618797890841961,
0.015630511566996574,
0.03811730071902275,
-0.01436682976782322,
0.008471189998090267,
0.031115377321839333,
-0.040686413645744324,
-0.022735625505447388,
-0.056207068264484406,
0.008559861220419407,
-0.012328254990279675,
-0.01126996148377657,
0.006503963842988014,
0.002027624985203147,
-0.014736221171915531,
-0.0037317678797990084,
-0.010046853683888912,
-0.02700307033956051,
0.01261364109814167,
0.07156157493591309,
0.0019781675655394793,
0.014061051420867443,
0.035238832235336304,
-0.002561517059803009,
-0.018664855509996414,
0.008904569782316685,
-0.021777736023068428,
-0.018172040581703186,
-0.03989969566464424,
0.030765512958168983,
0.038910020142793655,
-0.002034662524238229,
-0.02556980960071087,
0.09851428121328354,
0.058403380215168,
0.004031953867524862,
0.03718608617782593,
-0.0020129126496613026,
0.06571915745735168,
-0.05446986109018326,
0.0830933228135109,
0.010761935263872147,
0.003063842887058854,
-0.06948921084403992,
-0.014161737635731697,
0.023640930652618408,
0.03773175925016403,
-0.04237079247832298,
0.00033008604077622294,
0.03681885451078415,
-0.013607222586870193,
0.021847404539585114,
-0.0041692135855555534,
0.014555824920535088,
-0.05059407651424408,
-0.009541102685034275,
-0.05126991495490074,
0.022249624133110046,
-0.014302389696240425,
0.03144197165966034,
-0.017497286200523376,
0.005171199329197407,
-0.059032805263996124,
-0.03442545607686043,
0.031076140701770782,
-0.06900452822446823,
0.031022360548377037,
-0.024900540709495544,
0.017630916088819504,
-0.0798344686627388,
-0.01976431906223297,
-0.028449134901165962,
-0.0161761287599802,
-0.01802942343056202,
-0.0012582916533574462,
0.013993832282721996,
-0.01728852279484272,
0.029028160497546196,
0.004114676266908646,
-0.02790423296391964,
-0.007080460898578167,
-0.07462359964847565,
0.014241536147892475,
-0.00420421315357089,
0.011085848324000835,
-0.010680364444851875,
-0.03822925686836243,
0.021214596927165985,
-0.029662197455763817,
-0.00824827328324318,
0.026222553104162216,
-0.01563122123479843,
0.06637980043888092,
-0.005295061506330967,
-0.04656143859028816,
-0.02427167259156704,
0.030210619792342186,
-0.023138653486967087,
-0.03217511624097824,
-0.07312292605638504,
0.06820173561573029,
0.02308488078415394,
-0.00639497023075819,
0.02271318808197975,
-0.055778585374355316,
0.020501796156167984,
-0.04070527106523514,
0.030613698065280914,
0.01956425979733467,
0.02114262618124485,
-0.012128470465540886,
0.016810333356261253,
-0.06958410143852234,
0.007538139820098877,
0.004603134468197823,
-0.006932476069778204,
-0.025459550321102142,
0.03437899053096771,
0.030327240005135536,
-0.030438268557190895,
0.012518073432147503,
0.025878967717289925,
-0.01693524606525898,
-0.022383078932762146,
0.03194200620055199,
-0.023047493770718575,
0.05716867372393608,
0.037531010806560516,
0.04934052377939224,
-0.05574905499815941,
-0.01655707322061062,
-0.07780333608388901,
0.029727395623922348,
-0.04082614183425903,
-0.02166997827589512,
-0.028631405904889107,
-0.0015879502752795815,
0.004050176125019789,
0.021663591265678406,
-0.018250225111842155,
-0.004863345064222813,
0.03189602866768837,
0.009561046026647091,
-0.006102302111685276,
0.04751712456345558,
0.04900682717561722,
0.029782354831695557,
0.05483321100473404,
0.08750750124454498,
0.01879299059510231,
-0.04291696101427078,
0.03733754903078079,
-0.011769335716962814,
0.027748562395572662,
-0.04141850024461746,
0.014155249111354351,
0.007744294591248035,
0.02111300826072693,
0.024207519367337227,
0.0019980950746685266,
-0.01665802113711834,
0.03999997675418854,
-0.026062320917844772,
-0.042160339653491974,
0.01831204444169998,
0.05077061429619789,
0.06909845024347305,
0.0068163094110786915,
0.025375109165906906,
0.022640636190772057,
0.034716542810201645,
-0.006285449489951134,
0.01827070862054825,
-0.01724149100482464,
-0.02121683768928051,
-0.008758623152971268,
-0.040152158588171005,
-0.05534161627292633,
-0.02131091058254242,
-0.030057422816753387,
0.00649287598207593,
0.011665108613669872,
-0.0024443387519568205,
-0.028029393404722214,
-0.04348830133676529,
-0.012199444696307182,
0.009043151512742043,
0.017855653539299965,
0.08064711838960648,
-0.023109348490834236,
-0.04562889039516449,
-0.10524946451187134,
0.03226667642593384,
0.061333492398262024,
0.002714188303798437,
0.030359208583831787,
-0.03212588280439377,
0.03790450468659401,
0.009426945820450783,
0.030280686914920807,
0.0650988444685936,
0.06363800913095474,
0.012926937080919743,
-0.01617399975657463,
0.02908921055495739,
-0.04107876121997833,
0.055808424949645996,
-0.0832814872264862,
-0.06079975888133049,
-0.01729952171444893,
0.004243139177560806,
-0.051901884377002716,
-0.0002839826629497111,
-0.03560779243707657,
0.03408398479223251,
-0.05909302830696106,
0.04012217000126839,
0.008721494115889072,
-0.04873146861791611,
-0.050721339881420135,
-0.036624275147914886,
0.029100516811013222,
-0.007204335182905197,
-0.004993418697267771,
0.043084800243377686,
-0.05097956955432892,
-0.0499924011528492,
0.015559995546936989,
-0.009412053972482681,
0.029778078198432922,
-0.005631793290376663,
0.02148905210196972,
0.05698222294449806,
0.019907252863049507,
0.02970816008746624,
0.016528090462088585,
-0.04186130315065384,
-0.022392354905605316,
-0.00950398575514555,
0.002423615427687764,
0.008750393986701965,
-0.015428231097757816,
-0.018441583961248398,
-0.02963602915406227,
-0.04218791052699089,
-0.022733520716428757,
-0.017975976690649986,
0.015001087449491024,
0.018528835847973824,
-0.09723715484142303,
-0.018259963020682335,
0.03655245155096054,
0.0382240004837513,
-0.020481878891587257,
0.0023918692022562027,
-0.06065301597118378,
-0.000261373003013432,
0.06362538039684296,
-0.00033116640406660736,
-0.010748487897217274,
-0.08394082635641098,
-0.0009565885411575437,
0.036842625588178635,
0.041466910392045975,
-0.0005771624273620546,
0.0252622552216053,
-0.0188610777258873,
0.029469773173332214,
-0.036034099757671356,
-0.047395676374435425,
-0.05459563061594963,
-0.0038535678759217262,
-0.011025403626263142,
-0.09203106164932251,
0.01156621053814888,
0.08790481090545654,
0.0017791833961382508,
-0.050304099917411804,
-0.05159822851419449,
-0.04539398476481438,
0.004899171646684408,
-0.06590186804533005,
0.009285943582654,
-0.0948684960603714,
0.029829174280166626,
-0.014426905661821365,
-0.0022275340743362904,
-0.02518261782824993,
-0.05620359256863594,
-0.012930034659802914,
0.055651403963565826,
-0.04208718612790108,
0.015620224177837372,
-0.012607155367732048,
0.06188807636499405,
0.060621477663517,
-0.0805765688419342,
-0.06721045076847076,
0.002120601013302803,
-0.07250170409679413,
0.016136623919010162,
-0.0064895679242908955,
-0.10178826004266739,
-0.0639018565416336,
-0.022968877106904984,
-0.05061880871653557,
0.02289104461669922,
-0.0037330761551856995,
-0.057601187378168106,
0.018431341275572777,
0.06525422632694244,
0.03471555933356285,
-0.022393114864826202,
0.0026749821845442057,
0.017606591805815697,
0.03631731867790222,
0.0048687029629945755,
-0.05206841230392456,
-0.020012114197015762,
-0.01756906695663929,
-0.0011814952595159411,
-0.041943058371543884,
0.03140099719166756,
0.03372244909405708,
-0.003306400729343295,
-0.007950608618557453,
0.05268118157982826,
0.02967684715986252,
0.050229646265506744,
-0.04945548251271248,
0.04057983309030533,
0.0065157450735569,
-0.05866655707359314,
0.017376955598592758,
0.0866992399096489,
0.009080181829631329,
0.06504972279071808,
0.020302528515458107,
0.004117818083614111,
0.015293749049305916,
0.02535531483590603,
-0.07609941065311432,
-0.03924719616770744,
-0.002599807921797037,
0.00197086064144969,
0.014703533612191677,
-0.03198909014463425,
0.023889439180493355,
-0.02499167062342167,
0.012425560504198074,
-0.007435723207890987,
-0.008977876976132393,
0.03295702114701271,
-0.01973617821931839,
-0.003035092493519187,
-0.05549554526805878,
-0.05595869570970535,
-0.04043232277035713,
-0.03347752243280411,
0.08497879654169083,
-0.08105694502592087,
-0.04680026322603226,
-0.02026323601603508,
-0.022521106526255608,
0.019356751814484596,
-0.03504335135221481,
-0.03031868487596512,
-0.007017115596681833,
-0.06505120545625687,
-0.05664720758795738,
0.0170979592949152,
0.04569348320364952,
-0.0612022764980793,
0.013799650594592094,
0.039621930569410324,
0.027479812502861023,
0.07079516351222992,
-0.06172233447432518,
-0.008881943300366402,
-0.04265586659312248,
-0.07037392258644104,
0.01730959862470627,
0.013238983228802681,
-0.0007600908284075558,
-0.010254373773932457,
-0.008151068352162838,
0.03965473175048828
] |
<p>Suppose we view fluids classically, i.e., as a collection of molecules (with some finite size) interacting via e&m and gravitational forces. Presumably we model fluids as continuous objects that satisfy some differential equation. What mathematical result says that modeling fluids as continuous objects can accurately predict the discrete behavior of the particles? I don't know anything about fluid mechanics, so my initial assumption may in itself be wrong.</p> | g187 | [
0.010424879379570484,
-0.014496189542114735,
0.0073964823968708515,
-0.06162218749523163,
0.031752001494169235,
-0.006582456640899181,
-0.021341441199183464,
0.01354586984962225,
-0.07844612747430801,
-0.07640564441680908,
0.029890544712543488,
-0.06246091052889824,
0.056207191199064255,
-0.04535498842597008,
-0.02214503288269043,
0.004639661870896816,
-0.015771962702274323,
-0.038429293781518936,
-0.03793017193675041,
0.008021770976483822,
0.043749354779720306,
0.028040792793035507,
0.0860244482755661,
-0.04044821858406067,
0.01757419854402542,
0.03936849161982536,
0.06532367318868637,
0.003949180245399475,
-0.041848815977573395,
0.05152497813105583,
0.0273283738642931,
0.025633184239268303,
0.020068276673555374,
-0.0317273773252964,
-0.005148041527718306,
-0.039030201733112335,
0.018443483859300613,
-0.008341089822351933,
0.026740625500679016,
-0.07263839244842529,
0.03464172035455704,
-0.0036521065048873425,
0.022841181606054306,
0.015651026740670204,
0.025228073820471764,
-0.04901207610964775,
0.012186896987259388,
-0.03692416474223137,
0.017239337787032127,
0.03352299705147743,
0.024968374520540237,
0.03532477840781212,
-0.023982707411050797,
0.013477637432515621,
-0.006709178909659386,
0.05601935088634491,
0.045535579323768616,
0.034916967153549194,
-0.01035496685653925,
-0.018373768776655197,
0.025750065222382545,
-0.02842828445136547,
-0.027756525203585625,
-0.02767135202884674,
0.0411851704120636,
-0.06749061495065689,
-0.0748729556798935,
-0.003926468081772327,
0.010189813561737537,
-0.01771235466003418,
0.0069276802241802216,
-0.06397715210914612,
0.033225659281015396,
-0.030568251386284828,
-0.04006321355700493,
0.027423040941357613,
-0.029791906476020813,
0.024089572951197624,
-0.022391052916646004,
-0.058611851185560226,
-0.014210396446287632,
0.058328744024038315,
0.032887306064367294,
-0.021082913503050804,
0.08211537450551987,
0.00846416037529707,
-0.025764595717191696,
-0.031171347945928574,
-0.0070730894804000854,
0.0043602134101092815,
-0.01131783239543438,
-0.03913084417581558,
0.007861606776714325,
0.015894051641225815,
0.015375975519418716,
-0.021176667883992195,
-0.03826996311545372,
0.05199228972196579,
-0.024903345853090286,
-0.0025249894242733717,
0.01823173463344574,
0.06041296571493149,
0.022176656872034073,
-0.026541145518422127,
-0.026074407622218132,
0.03448132053017616,
0.0024276580661535263,
0.08767184615135193,
-0.0019324118038639426,
-0.03968259319663048,
-0.026449553668498993,
0.009373128414154053,
-0.050886232405900955,
0.008797426708042622,
-0.019617725163698196,
0.004231711383908987,
0.004056685604155064,
0.00244549079798162,
-0.023021090775728226,
0.06122846528887749,
-0.007906567305326462,
0.03914337977766991,
0.05047046020627022,
0.08629712462425232,
-0.03915668651461601,
-0.0565328523516655,
-0.012821684591472149,
0.05510113760828972,
0.03423931077122688,
-0.014170509763062,
0.035577982664108276,
0.010179353877902031,
-0.022015981376171112,
-0.049219973385334015,
0.03993741050362587,
0.006316065788269043,
-0.018979186192154884,
-0.008496768772602081,
0.051544446498155594,
0.017580438405275345,
0.0670238807797432,
-0.019171183928847313,
0.016196276992559433,
-0.0034571343567222357,
-0.044493418186903,
-0.009558895602822304,
-0.019007371738553047,
-0.060509663075208664,
-0.02522386983036995,
0.02386997826397419,
-0.006415717303752899,
0.10095774382352829,
0.014220030978322029,
-0.013387818820774555,
0.00047659905976615846,
0.010377515107393265,
-0.008676528930664062,
-0.0011241593165323138,
-0.024452945217490196,
-0.056851621717214584,
0.07452230155467987,
-0.031079212203621864,
0.020602699369192123,
0.010052445344626904,
-0.06957103312015533,
0.03306407108902931,
-0.03531239554286003,
-0.07302569597959518,
0.009051086381077766,
-0.0020074304193258286,
-0.038795121014118195,
0.018210748210549355,
-0.0066111390478909016,
0.051026444882154465,
0.017832251265645027,
-0.005251710768789053,
0.016784746199846268,
-0.0633656308054924,
-0.0029904337134212255,
-0.035133156925439835,
0.02612285129725933,
0.005044323857873678,
0.012310359627008438,
0.0010328975040465593,
-0.028966767713427544,
0.08656191825866699,
-0.044798921793699265,
0.07137953490018845,
-0.03101525828242302,
-0.0346163734793663,
-0.0485009104013443,
0.020434333011507988,
-0.008757676929235458,
-0.009608596563339233,
0.06246679276227951,
-0.014202349819242954,
0.028925666585564613,
-0.05014245584607124,
-0.03606225177645683,
0.043492697179317474,
0.00048754835734143853,
0.05520687997341156,
0.04577534273266792,
0.02351970225572586,
0.003003097604960203,
-0.01714138500392437,
0.020926645025610924,
-0.02823401242494583,
0.021792396903038025,
-0.0013455956941470504,
0.05129730701446533,
-0.015662530437111855,
-0.03585636243224144,
0.01144515909254551,
-0.048136502504348755,
-0.052083346992731094,
-0.008511662483215332,
0.03380325436592102,
-0.002111775102093816,
-0.024941645562648773,
-0.0806097760796547,
-0.003468624781817198,
-0.011153778992593288,
0.028913352638483047,
-0.03693708777427673,
-0.005932965315878391,
0.06425058841705322,
0.0003761929110623896,
0.02601327933371067,
0.038842201232910156,
-0.051960017532110214,
-0.028640728443861008,
0.03605184704065323,
-0.024197760969400406,
0.05999108403921127,
0.03768723085522652,
-0.06884483247995377,
-0.001471951138228178,
0.06964854896068573,
0.024133337661623955,
0.022711865603923798,
-0.01693946309387684,
-0.03604475408792496,
-0.03744092956185341,
0.0179743729531765,
-0.03369065001606941,
0.003576916176825762,
-0.0005802829982712865,
0.020392868667840958,
0.06546454131603241,
0.007804553024470806,
0.0073461574502289295,
-0.030096501111984253,
0.027525819838047028,
0.0146388104185462,
-0.000013941800716565922,
-0.04237891733646393,
0.04378581419587135,
-0.008956830948591232,
0.009712904691696167,
-0.08714840561151505,
0.013632487505674362,
0.020649392157793045,
0.038214340806007385,
0.003326334757730365,
-0.06389511376619339,
-0.015795676037669182,
0.03567136079072952,
-0.003238104283809662,
0.002175211440771818,
0.030476894229650497,
-0.003453225130215287,
-0.008145173080265522,
0.035432182252407074,
-0.025649216026067734,
0.012629454955458641,
0.021541813388466835,
0.006022545974701643,
-0.0038766725920140743,
-0.011500289663672447,
-0.01448123063892126,
-0.010737276636064053,
-0.052836596965789795,
0.023480918258428574,
0.040942128747701645,
-0.04457225650548935,
-0.015615380369126797,
0.02158532664179802,
-0.004733883775770664,
0.020369306206703186,
0.060811594128608704,
0.1029038205742836,
-0.017727507278323174,
0.005564219783991575,
-0.07848171144723892,
0.046301666647195816,
0.014512180350720882,
0.023030344396829605,
-0.02616100385785103,
0.06343303620815277,
-0.022834163159132004,
0.006722633261233568,
0.018199915066361427,
0.026592116802930832,
0.005246337968856096,
-0.011744830757379532,
-0.07251172512769699,
-0.0199130792170763,
0.006739327684044838,
-0.10280346125364304,
0.0669359564781189,
0.06091457977890968,
-0.04882684722542763,
-0.0018673829035833478,
-0.03375149145722389,
-0.03435902297496796,
-0.012019248679280281,
0.02247968502342701,
-0.005074245389550924,
-0.04079297184944153,
0.03385614603757858,
-0.04035094007849693,
0.03206436336040497,
-0.04272022470831871,
0.03435701131820679,
0.03176605701446533,
-0.06531024724245071,
-0.02128797583281994,
0.056364987045526505,
0.03953202813863754,
0.0516238771378994,
-0.01344486977905035,
0.04492631554603577,
0.008393201045691967,
-0.007108259946107864,
-0.05145400017499924,
-0.06669587641954422,
-0.024274108931422234,
0.038723912090063095,
-0.008583161048591137,
-0.012739384546875954,
-0.006401836406439543,
-0.030988968908786774,
-0.03747731074690819,
-0.049588702619075775,
0.024002186954021454,
-0.026550859212875366,
0.014260571449995041,
0.02451212704181671,
-0.02414429746568203,
-0.020253252238035202,
-0.04259147495031357,
0.04380868747830391,
-0.0036227013915777206,
-0.02590091899037361,
-0.015926087275147438,
0.0676424503326416,
0.025786690413951874,
0.02920282818377018,
0.005020682699978352,
-0.01735607348382473,
-0.020280545577406883,
0.00824512168765068,
0.0518178716301918,
0.05144011601805687,
0.016367390751838684,
0.005382123403251171,
0.04149049147963524,
-0.0016386108472943306,
-0.039537571370601654,
-0.05087330564856529,
0.007013517897576094,
-0.018425002694129944,
0.010603358969092369,
0.06586722284555435,
-0.015782220289111137,
0.028575468808412552,
-0.017618481069803238,
-0.008368671871721745,
-0.021473169326782227,
0.044927287846803665,
0.07916826009750366,
-0.0072813499718904495,
0.04569258913397789,
-0.0020315402653068304,
0.03544888272881508,
-0.013319948688149452,
-0.06306546926498413,
0.016322938725352287,
-0.029071537777781487,
0.021154221147298813,
-0.05231897905468941,
0.027185164391994476,
0.02351999096572399,
-0.017227357253432274,
-0.013110247440636158,
0.007891449145972729,
0.031407810747623444,
0.017590338364243507,
0.016230568289756775,
0.004094989039003849,
-0.015487585216760635,
-0.05459968373179436,
-0.020358463749289513,
0.03958721458911896,
-0.015778673812747,
-0.0012096753343939781,
-0.017802048474550247,
-0.035516612231731415,
-0.038977958261966705,
0.03262973949313164,
-0.0011519441613927484,
-0.003437178675085306,
-0.0416366383433342,
-0.030139967799186707,
0.028167879208922386,
-0.011939030140638351,
-0.04553491249680519,
0.01427410263568163,
0.016757523640990257,
0.07041224837303162,
0.0017375304596498609,
-0.06568196415901184,
0.031518034636974335,
-0.02287529781460762,
-0.0008304377552121878,
0.021742597222328186,
0.031854502856731415,
-0.09747417271137238,
-0.07437130063772202,
-0.004019291140139103,
-0.0021600755862891674,
0.012688455171883106,
0.07677730172872543,
-0.02453557401895523,
0.03520150110125542,
-0.018694167956709862,
0.033240508288145065,
0.018564041703939438,
-0.01691647432744503,
0.006148786284029484,
0.01811087131500244,
0.021888509392738342,
-0.041780419647693634,
0.006074666045606136,
0.09169845283031464,
-0.04593962803483009,
-0.01966945081949234,
-0.0188978873193264,
-0.008439063094556332,
-0.015730371698737144,
0.009832180105149746,
-0.0332486629486084,
0.007773172575980425,
0.0006193122244440019,
-0.007622578181326389,
-0.015026851557195187,
-0.0022829605732113123,
0.02172502689063549,
0.028631415218114853,
-0.03960946947336197,
0.001102757640182972,
-0.007975276559591293,
0.06593801081180573,
-0.0046654073521494865,
0.0029228515923023224,
-0.015650838613510132,
-0.022762011736631393,
-0.024655716493725777,
-0.03210790455341339,
-0.03681923449039459,
0.05191193148493767,
0.03390177711844444,
-0.024643829092383385,
-0.012433579191565514,
-0.04300345107913017,
-0.0263676717877388,
0.03098948858678341,
0.05969619378447533,
-0.03125162050127983,
-0.02408592775464058,
-0.00919032096862793,
0.04398733749985695,
0.019213082268834114,
-0.013184093870222569,
0.036245208233594894,
0.009959602728486061,
0.03159092739224434,
-0.03278375789523125,
0.07586029917001724,
0.03928786888718605,
-0.044568564742803574,
0.0329892635345459,
-0.05944380164146423,
-0.06749691814184189,
-0.046515125781297684,
-0.009138028137385845,
-0.034861497581005096,
0.02725185453891754,
0.049454279243946075,
-0.07483818382024765,
0.0018946320051327348,
0.031206408515572548,
-0.012819668278098106,
0.0024676239117980003,
0.10649368911981583,
0.03494955226778984,
-0.04159336909651756,
-0.028340646997094154,
0.047221146523952484,
0.015759525820612907,
0.019703183323144913,
0.04270007461309433,
0.06830541789531708,
-0.020948734134435654,
0.007109435740858316,
-0.051155347377061844,
-0.004057370126247406,
-0.014667845331132412,
-0.03122027777135372,
0.015179362148046494,
0.015133228152990341,
-0.0007578967488370836,
0.05298445746302605,
-0.02241497114300728,
0.025407826527953148,
-0.008949694223701954,
0.01359574869275093,
0.01571349985897541,
0.06328184902667999,
0.04508234187960625,
0.0403587743639946,
-0.054761141538619995,
-0.01069555338472128,
-0.0311223566532135,
0.023873327299952507,
0.000012884297575510573,
0.02934064157307148,
0.03912064805626869,
0.008001796901226044,
-0.0318353995680809,
0.024527238681912422,
0.026627056300640106,
0.023476475849747658,
0.05810099467635155,
0.043110527098178864,
0.014702343381941319,
0.04832431674003601,
0.07423780113458633,
-0.009553090669214725,
-0.027523959055542946,
0.04676707834005356,
-0.014667919836938381,
0.004738357849419117,
0.04346374049782753,
0.0211564339697361,
0.023326070979237556,
-0.03810223937034607,
0.0024433229118585587,
0.024190397933125496,
-0.03263965621590614,
0.01903306506574154,
0.007369298953562975,
-0.028050202876329422,
0.026218755170702934,
-0.0619845949113369,
0.05440809577703476,
0.010553542524576187,
0.014183416031301022,
0.041167352348566055,
-0.026868535205721855,
0.004802927374839783,
0.05243420600891113,
-0.013941740617156029,
-0.01466036681085825,
-0.02394697815179825,
-0.04088497534394264,
-0.03874390944838524,
-0.04774889722466469,
0.010991265997290611,
0.06070316582918167,
-0.04387691989541054,
-0.015739865601062775,
-0.023952079936861992,
0.031073501333594322,
0.048842497169971466,
-0.0665433257818222,
-0.03888808190822601,
0.014749068766832352,
0.0036404249258339405,
0.034257419407367706,
-0.04180238023400307,
-0.0318436436355114,
-0.054402269423007965,
0.001690406585112214,
-0.02452453039586544,
0.02594258449971676,
0.050266291946172714,
-0.04058143123984337,
0.013712944462895393,
-0.00008314130536746234,
0.0635295882821083,
0.013497534207999706,
0.004213820677250624,
0.01680910587310791,
0.003068190533667803,
-0.05165573209524155,
0.011756617575883865,
0.024795720353722572,
0.003990683704614639,
-0.0568929947912693,
0.005163068883121014,
0.010098489001393318,
-0.0032831698190420866,
0.001475474564358592,
-0.051752831786870956,
-0.014866137877106667,
0.01823771744966507,
0.03550351411104202,
-0.009617313742637634,
-0.02211465686559677,
0.015285738743841648,
-0.008285732008516788,
-0.10991242527961731,
-0.0032962255645543337,
-0.0062004579231143,
-0.039803631603717804,
0.009582659229636192,
0.07328857481479645,
0.02856019325554371,
-0.026003431528806686,
-0.00849349144846201,
0.0153920603916049,
0.0582125149667263,
-0.017877981066703796,
0.002502261195331812,
-0.0703105628490448,
0.012215428054332733,
0.023622704669833183,
0.029514649882912636,
0.05166138708591461,
0.027143290266394615,
0.03332449123263359,
-0.02573058381676674,
-0.047848451882600784,
-0.04193701222538948,
0.06190848723053932,
0.04361187666654587,
-0.08240926265716553,
-0.023875966668128967,
0.014370455406606197,
-0.029262693598866463,
0.02713451348245144,
-0.022127626463770866,
-0.014285308308899403,
0.03714078664779663,
0.017476314678788185,
-0.044052813202142715,
0.015255948528647423,
-0.023451711982488632,
-0.020046288147568703,
-0.027355268597602844,
-0.049842964857816696,
-0.008205654099583626,
-0.013459054753184319,
-0.01610676757991314,
-0.008159440010786057,
-0.026708127930760384,
0.032608531415462494,
-0.03253454342484474,
0.0362681970000267,
-0.04980377480387688,
-0.01741904579102993,
0.0523001030087471,
0.016896270215511322,
-0.05977046862244606,
-0.013237996026873589,
0.0479465052485466,
0.06272096186876297,
0.024883324280381203,
0.052080683410167694,
0.09054498374462128,
0.04136946424841881,
0.04695825278759003,
-0.03917514532804489,
0.037329621613025665,
0.00414934242144227,
-0.038921307772397995,
-0.028436828404664993,
-0.01914825290441513,
-0.009907282888889313,
-0.010228382423520088,
-0.018043747171759605,
-0.03990299627184868,
-0.040655020624399185,
-0.010774758644402027,
0.04246904328465462,
0.023930976167321205,
0.035381980240345,
0.01847880706191063,
-0.024767018854618073,
0.0005340302595868707,
0.000899246777407825,
-0.061865948140621185,
0.01624808833003044,
0.0017482615076005459,
-0.026713402941823006,
-0.024891041219234467,
-0.002702034078538418,
-0.02678583562374115,
-0.051870957016944885,
-0.03188832104206085,
0.021402273327112198,
0.003835309064015746,
0.022709565237164497,
-0.029587848111987114,
-0.05630616471171379,
-0.05089437589049339,
0.04657447710633278,
-0.02477041818201542,
-0.02842092141509056,
-0.006361188367009163,
0.00161726213991642,
-0.021122759208083153,
-0.015964433550834656,
-0.06231020763516426,
-0.08162203431129456,
-0.04731350764632225,
-0.006308040115982294,
0.025066331028938293,
-0.08414663374423981,
0.008799702860414982,
-0.009958121925592422,
-0.019058825448155403,
-0.0018342379480600357,
0.041424453258514404,
0.019052861258387566,
0.013033946044743061,
0.002608273411169648,
-0.012625849805772305,
-0.012923164293169975,
-0.026315711438655853,
0.0319657027721405,
0.0250846054404974,
0.028367429971694946,
-0.033360082656145096,
-0.030841778963804245,
-0.023602116852998734,
0.045194171369075775,
0.0692577138543129,
0.03409599885344505,
0.0032478212378919125,
0.022007979452610016,
0.011000573635101318,
0.03458131477236748,
-0.10417667031288147,
-0.05210783705115318,
0.038634371012449265,
-0.04246152192354202,
-0.03565748408436775,
-0.03876655176281929,
0.00006215302710188553,
0.003993503749370575,
0.009237655438482761,
-0.03801753744482994,
-0.017642904072999954,
-0.0005560718709602952,
0.06124980375170708
] |
<blockquote>
<p>If it takes work W to stretch a Hooke’s-law spring (F = kx) a distance d from its unstressed length, determine the extra work required to stretch it an additional distance d (Hint: draw a graph and give answer in terms of W!).</p>
</blockquote>
<p>I don't understand why the answer is not 2W since Force is proportional to x, or even how to begin using a graph to disprove why the answer is not 2W. Any help would be greatly appreciated.</p> | g4560 | [
0.05436130613088608,
0.07149390131235123,
0.012524392455816269,
0.008138919249176979,
-0.004144309554249048,
-0.007192334625869989,
0.030392536893486977,
-0.03154429793357849,
-0.02869276888668537,
-0.058067142963409424,
-0.037003517150878906,
-0.017237447202205658,
0.013299588114023209,
-0.04000213369727135,
0.04828347638249397,
0.05487123876810074,
0.06500836461782455,
-0.05947279557585716,
0.03219416365027428,
-0.0049535720609128475,
-0.027546057477593422,
0.01925409585237503,
-0.010857507586479187,
-0.0486900731921196,
-0.014967507682740688,
-0.06718744337558746,
0.02737639658153057,
-0.025860924273729324,
-0.10913904756307602,
-0.00801554974168539,
0.026516903191804886,
0.005593557376414537,
0.007304388098418713,
-0.10144075751304626,
-0.06907729804515839,
0.051471441984176636,
0.031865525990724564,
0.04216236248612404,
0.027498258277773857,
0.02973746322095394,
-0.022997071966528893,
-0.023116357624530792,
0.022160643711686134,
0.009778140112757683,
-0.0010599675588309765,
-0.03816085681319237,
-0.03939209505915642,
0.07108699530363083,
0.049750786274671555,
-0.005684876348823309,
-0.009594142436981201,
0.05439361557364464,
0.017828531563282013,
-0.020180098712444305,
-0.0014094185316935182,
0.024595417082309723,
0.06564407795667648,
-0.0759364664554596,
0.05577494949102402,
0.0012977896258234978,
-0.02391323260962963,
0.01420740969479084,
0.02148454636335373,
-0.03555794060230255,
0.006395318079739809,
-0.024517914280295372,
0.0459340363740921,
-0.016171278432011604,
0.02433396689593792,
0.03124312311410904,
-0.01437948364764452,
-0.04757723957300186,
0.03836072236299515,
-0.011683977209031582,
-0.06513294577598572,
-0.0015286648413166404,
0.0068184491246938705,
0.07323279976844788,
-0.02726721204817295,
-0.023373132571578026,
0.01435712818056345,
0.007008744403719902,
-0.034117165952920914,
0.012405015528202057,
0.057509083300828934,
0.018971510231494904,
0.007087247911840677,
0.005562121514230967,
0.010450364090502262,
0.06122932955622673,
-0.01896420493721962,
-0.011050825007259846,
0.08436036854982376,
0.00677513750270009,
-0.041794050484895706,
-0.0658501461148262,
0.012276756577193737,
0.05987473577260971,
0.012397894635796547,
0.013149570673704147,
-0.015644021332263947,
-0.03633985295891762,
-0.022750766947865486,
-0.04667109251022339,
-0.03625881299376488,
-0.012377590872347355,
0.06423711031675339,
0.020103756338357925,
-0.003963921219110489,
-0.03031042218208313,
-0.03099377639591694,
-0.028318051248788834,
0.012385488487780094,
0.022135421633720398,
-0.0026607851032167673,
-0.019767586141824722,
0.04178645834326744,
-0.05415200814604759,
0.015135243535041809,
0.01745784282684326,
0.027970725670456886,
-0.002040636260062456,
0.0548575259745121,
-0.009497934952378273,
-0.03258417919278145,
-0.03774365037679672,
0.036358870565891266,
0.035814572125673294,
0.01221480406820774,
-0.056303441524505615,
0.013507012277841568,
0.06697679311037064,
0.0029708787333220243,
0.02430664747953415,
-0.07176125049591064,
0.019464809447526932,
-0.025136085227131844,
0.009627409279346466,
0.006134441122412682,
0.03741021081805229,
-0.06092659384012222,
-0.014738271944224834,
0.01335233822464943,
-0.021314196288585663,
-0.026027798652648926,
0.0539676696062088,
-0.044427599757909775,
-0.016313202679157257,
0.032169073820114136,
-0.038651783019304276,
-0.031636469066143036,
0.07424957305192947,
-0.003639299189671874,
-0.026673197746276855,
0.04701061174273491,
-0.019127150997519493,
0.041629113256931305,
-0.008446754887700081,
0.013779417611658573,
0.005862557794898748,
0.04409826919436455,
-0.04336291551589966,
-0.016804609447717667,
0.0053009712137281895,
-0.028330307453870773,
0.007768872659653425,
-0.004679951351135969,
0.015546701848506927,
-0.012478022836148739,
-0.06931859254837036,
-0.07393280416727066,
-0.01887245662510395,
0.050221849232912064,
0.012253882363438606,
-0.0464676134288311,
-0.01040700450539589,
0.013472492806613445,
-0.0007837560842745006,
0.015669217333197594,
0.021535325795412064,
-0.03258061781525612,
0.02321506291627884,
0.04146727919578552,
0.02724236249923706,
-0.04406771808862686,
0.025833962485194206,
0.007746491115540266,
-0.0378350205719471,
-0.03359713405370712,
-0.04064393416047096,
-0.02134399116039276,
0.0001197518504341133,
-0.024596529081463814,
0.02164154127240181,
-0.011918590404093266,
-0.01420328114181757,
0.05173216387629509,
-0.02709229663014412,
0.014335542917251587,
-0.00627782242372632,
0.022349338978528976,
0.04352959990501404,
-0.0004734021204058081,
0.017438111826777458,
-0.006158888805657625,
0.03293281048536301,
-0.03436655178666115,
0.00026728337979875505,
0.06280095875263214,
0.014609121717512608,
0.02018010802567005,
-0.03794759139418602,
0.037978414446115494,
0.025635454803705215,
-0.041461944580078125,
-0.060999397188425064,
-0.020354310050606728,
0.04089457914233208,
-0.021333040669560432,
0.006933417171239853,
-0.014030072838068008,
-0.028259331360459328,
0.02258635126054287,
0.01792365126311779,
-0.03399183601140976,
-0.02659650705754757,
0.0007809392409399152,
-0.017889391630887985,
-0.03730592131614685,
0.01578124612569809,
0.012313101440668106,
-0.041899289935827255,
-0.03701893985271454,
0.007319137454032898,
0.05320672690868378,
0.058642808347940445,
0.010512648150324821,
0.024130595847964287,
-0.004478329326957464,
0.0022864106576889753,
0.0969681367278099,
-0.04554428905248642,
0.022318445146083832,
-0.019647426903247833,
0.05273338779807091,
-0.009497787803411484,
0.0456358902156353,
0.049320146441459656,
0.01901797391474247,
0.05261943116784096,
-0.0047025601379573345,
0.003753948723897338,
-0.02329718880355358,
0.005316905677318573,
0.030217336490750313,
0.029176702722907066,
-0.01103490125387907,
0.013369059190154076,
-0.0252891443669796,
-0.06625813245773315,
-0.008790520951151848,
-0.029461095109581947,
-0.0016295122914016247,
-0.023298759013414383,
-0.07985718548297882,
0.0031114283483475447,
-0.04149843752384186,
-0.01988953910768032,
0.04846815764904022,
-0.027715306729078293,
0.006273288745433092,
0.022755436599254608,
-0.05777447670698166,
-0.016526594758033752,
-0.005243720021098852,
-0.04314744472503662,
0.0164523683488369,
-0.03791782259941101,
0.0068154423497617245,
0.04635239392518997,
0.02015186846256256,
-0.011477532796561718,
-0.032134972512722015,
0.040893517434597015,
0.011249339208006859,
-0.016623642295598984,
0.005850621033459902,
-0.015829620882868767,
-0.04259506240487099,
-0.052797164767980576,
-0.029270300641655922,
0.04890584945678711,
0.047480687499046326,
0.003908302169293165,
0.024178965017199516,
0.06273166090250015,
-0.011785031296312809,
-0.021209169179201126,
-0.009989801794290543,
-0.006738762836903334,
-0.017742840573191643,
-0.05193895474076271,
-0.009339614771306515,
0.02791040763258934,
0.022699406370520592,
0.028517870232462883,
-0.023341050371527672,
-0.0664176419377327,
-0.006183051969856024,
0.07459638267755508,
-0.026252813637256622,
0.017310328781604767,
0.0754401683807373,
-0.03604752942919731,
-0.08067026734352112,
-0.020978597924113274,
-0.012097344733774662,
0.002726217033341527,
-0.015205406583845615,
-0.042739905416965485,
0.04232658073306084,
-0.044348523020744324,
0.01932471990585327,
0.008822561241686344,
-0.03210137411952019,
0.03537246957421303,
-0.040960732847452164,
0.023183735087513924,
-0.04148513078689575,
-0.0073051149956882,
-0.004123271442949772,
-0.032733820378780365,
0.012179558165371418,
-0.07746584713459015,
-0.038984354585409164,
-0.10224144160747528,
0.04587671905755997,
0.036411091685295105,
0.015644697472453117,
0.07873734831809998,
-0.05627889931201935,
-0.025510340929031372,
-0.08178377151489258,
-0.0033828679006546736,
-0.0036927475593984127,
0.02214326336979866,
0.014146821573376656,
0.023420361801981926,
0.06165868043899536,
-0.022378627210855484,
0.0005437558284029365,
-0.039173394441604614,
-0.03140014782547951,
0.007344848942011595,
0.0694965198636055,
0.0023895243648439646,
0.023046154528856277,
-0.01854543201625347,
-0.043684981763362885,
-0.013349383138120174,
0.06647737324237823,
0.016897954046726227,
-0.047639649361371994,
0.005070259794592857,
-0.023210298269987106,
0.011279751546680927,
0.05434712767601013,
0.08196079730987549,
-0.014621790498495102,
0.0008465765276923776,
0.025664040818810463,
-0.09641725569963455,
0.03874969482421875,
0.057461630553007126,
0.05540972203016281,
-0.00861251913011074,
0.011467239819467068,
0.02810811810195446,
-0.006245308555662632,
0.02382318116724491,
0.030335962772369385,
0.04552662745118141,
-0.004617925733327866,
-0.018038151785731316,
-0.025589946657419205,
-0.05543572083115578,
-0.021985188126564026,
-0.008168389089405537,
0.024842988699674606,
0.019029177725315094,
-0.02784329652786255,
-0.0629810243844986,
-0.05338102951645851,
0.000868737231940031,
0.017715943977236748,
-0.013735483400523663,
-0.012504138983786106,
0.01742568425834179,
-0.019733188673853874,
-0.002480176743119955,
-0.0075672990642488,
0.04965643584728241,
-0.026631882414221764,
0.0668102279305458,
-0.008044048212468624,
-0.011729896999895573,
0.032790135592222214,
-0.03579694777727127,
0.028885867446660995,
0.004640894941985607,
0.02566535957157612,
-0.05858961120247841,
0.0013387913350015879,
-0.0728711187839508,
0.013370230793952942,
-0.05840853229165077,
0.056335218250751495,
-0.0004563132824841887,
-0.031033292412757874,
0.02342495135962963,
0.028499513864517212,
0.029344307258725166,
0.022716322913765907,
-0.010277485474944115,
0.019137326627969742,
0.045508574694395065,
-0.008083479478955269,
-0.03024282678961754,
0.025205526500940323,
-0.017548443749547005,
-0.06396514177322388,
0.023659737780690193,
0.002183484612032771,
-0.006049323361366987,
-0.02252323180437088,
0.040242984890937805,
0.024171294644474983,
0.08254072815179825,
-0.06602028012275696,
0.038290783762931824,
-0.028114652261137962,
-0.002564874943345785,
0.017254265025258064,
0.02064874768257141,
-0.03002992831170559,
0.00619125971570611,
-0.044590141624212265,
-0.06186389550566673,
-0.020907795056700706,
0.03642570599913597,
-0.04185192659497261,
-0.031497757881879807,
0.027890658006072044,
-0.012386169284582138,
0.029971128329634666,
0.030435066670179367,
-0.002224075375124812,
0.008583000861108303,
-0.0011676459107547998,
0.029873128980398178,
-0.009896652773022652,
-0.004557720851153135,
0.0403030626475811,
0.029683317989110947,
0.0023345076479017735,
0.02550274319946766,
-0.060099147260189056,
-0.015497163869440556,
-0.03887278586626053,
0.04536910727620125,
0.019758371636271477,
0.005200935527682304,
-0.001679571345448494,
-0.017700189724564552,
0.05269642174243927,
0.021209388971328735,
0.03345802426338196,
0.034712426364421844,
0.0024796335492283106,
-0.02061108872294426,
-0.014006287790834904,
-0.004936472978442907,
-0.022267121821641922,
-0.036536216735839844,
0.05776038020849228,
0.0063869585283100605,
-0.02611450105905533,
-0.00020069212769158185,
0.027177149429917336,
-0.000247458228841424,
0.06973117589950562,
0.09818841516971588,
0.007139088120311499,
0.0224063228815794,
-0.010896711610257626,
0.025189537554979324,
0.03917780891060829,
0.03532823920249939,
0.03785480186343193,
-0.011596334166824818,
-0.015258826315402985,
0.038812581449747086,
0.00701234070584178,
0.0062267673201859,
-0.026563577353954315,
0.0675828829407692,
0.03587062284350395,
0.025220949202775955,
0.005628408398479223,
0.010158654302358627,
-0.013950134627521038,
0.0054986728355288506,
0.02918975241482258,
-0.007454968988895416,
0.018211711198091507,
0.023067891597747803,
0.031218571588397026,
-0.011840201914310455,
-0.04345892369747162,
0.023687833920121193,
0.14607013761997223,
0.05074477195739746,
0.05744660273194313,
-0.019361842423677444,
-0.009713729843497276,
0.03471159562468529,
-0.04559667035937309,
-0.07174349576234818,
-0.03337021917104721,
0.004177954979240894,
0.024615244939923286,
0.043705444782972336,
-0.029356172308325768,
-0.05116153135895729,
-0.0002850483579095453,
-0.05244652181863785,
0.057999104261398315,
-0.029599184170365334,
-0.02400207705795765,
-0.05149836838245392,
-0.025105293840169907,
-0.040406111627817154,
0.08500860631465912,
0.011794469319283962,
-0.04876117408275604,
-0.0050148251466453075,
-0.0016756349941715598,
-0.026507705450057983,
0.013284768909215927,
-0.011291226372122765,
-0.04291129112243652,
0.014990316703915596,
-0.039070405066013336,
0.030287476256489754,
-0.028438614681363106,
0.00415185047313571,
0.06348691880702972,
-0.0887640193104744,
0.027185723185539246,
0.013794488273561,
0.015029153786599636,
0.030036309733986855,
-0.032278332859277725,
0.0048521095886826515,
0.042994655668735504,
-0.09267337620258331,
-0.055739156901836395,
0.04187401011586189,
0.07614657282829285,
0.042025357484817505,
-0.02320544235408306,
-0.015257702209055424,
-0.005327151622623205,
0.06481891125440598,
0.01121376920491457,
0.014776840806007385,
-0.021415799856185913,
-0.03243372589349747,
-0.017849590629339218,
-0.01029765885323286,
-0.059575341641902924,
0.0023169906344264746,
0.005229712463915348,
-0.03852035105228424,
-0.00903434306383133,
0.034848134964704514,
-0.019493594765663147,
-0.015457258559763432,
0.06127753108739853,
-0.02333720214664936,
-0.04604335129261017,
-0.011811005882918835,
-0.002309973118826747,
0.010282976552844048,
-0.026287280023097992,
0.004359595477581024,
0.04572261497378349,
0.04514927789568901,
-0.006504562217742205,
0.004499063361436129,
0.027202701196074486,
0.06602752208709717,
0.0916193425655365,
-0.0634605661034584,
0.02938763052225113,
-0.002924860455095768,
-0.019738147035241127,
-0.018802549690008163,
0.00278610922396183,
-0.041609026491642,
-0.035961251705884933,
0.0887010395526886,
0.03280654922127724,
0.028405986726284027,
-0.0051003810949623585,
-0.010514670982956886,
0.009376882575452328,
-0.03351004421710968,
-0.029276167973876,
-0.04277908802032471,
0.027637524530291557,
-0.049381185322999954,
0.016619998961687088,
-0.024138193577528,
0.03571832552552223,
0.013375886715948582,
-0.052117448300123215,
-0.019664382562041283,
0.001961803762242198,
0.028430648148059845,
0.020646365359425545,
0.04579675570130348,
-0.06359537690877914,
0.018612690269947052,
0.003170877229422331,
0.07117253541946411,
-0.0175066739320755,
0.07578275352716446,
0.03844833746552467,
0.07710539549589157,
-0.056014157831668854,
-0.00728917820379138,
-0.031564053148031235,
-0.01412287075072527,
-0.03847946226596832,
-0.042370639741420746,
0.016341015696525574,
-0.0141914626583457,
-0.0666118636727333,
0.03725045919418335,
0.0042340438812971115,
0.04654626175761223,
-0.0316472053527832,
-0.03638906031847,
0.000005616362159344135,
-0.014772926457226276,
0.005081243347376585,
-0.05212797224521637,
0.009945192374289036,
-0.014653898775577545,
-0.05949389934539795,
-0.02116389200091362,
0.03996511921286583,
0.0030795445200055838,
-0.037480805069208145,
0.08003201335668564,
-0.028400959447026253,
0.04049009829759598,
-0.03511851653456688,
0.00852853711694479,
0.009779118932783604,
0.001509939436800778,
0.0069116572849452496,
-0.007691884413361549,
0.048354584723711014,
0.0035419086925685406,
0.006701767910271883,
-0.008454442955553532,
-0.004604321904480457,
-0.031151970848441124,
0.018744101747870445,
0.02831856720149517,
-0.04457712918519974,
-0.0254204161465168,
-0.023276232182979584,
0.039007123559713364,
-0.00858352892100811,
0.018344666808843613,
0.0309965331107378,
0.012757601216435432,
-0.03279924765229225,
0.04583999142050743,
-0.027958909049630165,
-0.014668489806354046,
0.013744236901402473,
0.020260892808437347,
0.019303852692246437,
-0.01472646463662386,
0.0312555693089962,
-0.01727195829153061,
0.03450759872794151,
0.006252756807953119,
-0.0451633594930172,
0.04018644243478775,
0.006789019796997309,
0.011586380191147327,
-0.058315251022577286,
-0.012575581669807434,
-0.08090945333242416,
-0.06399103254079819,
0.011515779420733452,
-0.010493890382349491,
-0.011169414967298508,
-0.01550520583987236,
0.050988901406526566,
0.0017864868277683854,
0.01034532394260168,
-0.009786687791347504,
0.008926892653107643,
-0.07797492295503616,
-0.006844579242169857,
-0.021811969578266144,
0.018380803987383842,
-0.03261546045541763,
-0.0423116534948349,
-0.048377301543951035,
-0.0253535695374012,
-0.018825111910700798,
-0.04377976804971695,
0.00477704918012023,
0.008567873388528824,
-0.06906438618898392,
0.03492307662963867,
-0.015809621661901474,
-0.058075692504644394,
-0.004738371819257736,
0.024610096588730812,
0.0013710205676034093,
0.027754366397857666,
0.029972681775689125,
-0.034912411123514175,
0.004649267997592688,
-0.03522710129618645,
-0.03553885221481323,
0.02013704739511013,
-0.05117963254451752,
-0.013864281587302685,
0.05620710179209709,
0.07109319418668747,
-0.0007763017201796174,
0.002736164489760995,
-0.00882051419466734,
0.04623347520828247,
-0.0061157215386629105,
-0.018972957506775856,
-0.04392346367239952,
-0.029674768447875977,
0.026534004136919975,
0.03974771872162819,
-0.00750013766810298,
-0.061256829649209976,
0.01741265505552292,
-0.024018315598368645,
0.026606019586324692,
0.025074413046240807,
-0.017543256282806396,
-0.010105680674314499,
0.0030746294651180506
] |
<p>Is it possible to reclaim nuclear waste from commercial reactors for useful purposes, if not necessarily energy production?</p> | g4561 | [
0.019421739503741264,
0.04660410061478615,
0.004617707803845406,
0.009234294295310974,
-0.00012521306052803993,
-0.029347075149416924,
-0.009854277595877647,
0.030258534476161003,
0.0024329652078449726,
-0.005427679046988487,
0.03209099918603897,
0.026775365695357323,
0.011873909272253513,
-0.03581644967198372,
-0.03473694622516632,
-0.008281965740025043,
0.022160964086651802,
-0.04142994433641434,
-0.012455936521291733,
0.10338311642408371,
0.023990802466869354,
-0.07080438733100891,
-0.025865737348794937,
-0.04810871183872223,
-0.06289710104465485,
-0.0018304396653547883,
-0.00465949485078454,
-0.03243742138147354,
-0.04172543063759804,
-0.03231357783079147,
-0.023555107414722443,
-0.06438366323709488,
0.02262873947620392,
0.02003062702715397,
-0.06703386455774307,
-0.06184294447302818,
-0.03459476679563522,
-0.037100084125995636,
0.07660673558712006,
-0.031055305153131485,
-0.04914727434515953,
0.014782746322453022,
0.0033932134974747896,
-0.015012510120868683,
-0.026395214721560478,
0.07378058135509491,
0.025943342596292496,
0.02739003300666809,
-0.04182372987270355,
-0.011600364930927753,
0.033542390912771225,
-0.01935955323278904,
-0.01881122589111328,
0.022891787812113762,
-0.0357355922460556,
-0.038842473179101944,
0.04366416856646538,
-0.010749253444373608,
0.033717334270477295,
0.03197135031223297,
-0.006803032476454973,
0.07451607286930084,
0.030769670382142067,
0.006390188354998827,
0.044523872435092926,
0.01843949779868126,
-0.037523891776800156,
0.037015143781900406,
0.012081652879714966,
0.045192401856184006,
0.03189651295542717,
0.03699126094579697,
0.005778960417956114,
-0.0008312601712532341,
-0.05725641921162605,
0.03715827688574791,
0.0022539200726896524,
0.004231113940477371,
-0.029907751828432083,
0.017062688246369362,
-0.05023251846432686,
-0.033200155943632126,
-0.0236312597990036,
0.03896986320614815,
-0.026867901906371117,
0.01836901716887951,
0.005214267875999212,
0.01349108200520277,
0.02240918204188347,
0.011557744815945625,
0.08314474672079086,
0.0410187654197216,
0.05156087502837181,
0.00691009359434247,
0.03306132182478905,
-0.0036059871781617403,
-0.04319708049297333,
-0.021756496280431747,
-0.04432359337806702,
0.06040261313319206,
0.007081141695380211,
-0.02451799064874649,
0.01754351519048214,
-0.040249746292829514,
0.03595921769738197,
-0.02327890135347843,
0.04324972629547119,
-0.001673879218287766,
0.022672895342111588,
-0.013706996105611324,
0.0806749239563942,
-0.00016311246145050973,
-0.020401351153850555,
0.028170840814709663,
0.0032481553498655558,
-0.0036946143954992294,
-0.009285139851272106,
-0.01024702936410904,
-0.04288536310195923,
0.07417744398117065,
0.08865991979837418,
0.0010333374375477433,
-0.032373517751693726,
0.0016258946852758527,
0.023117514327168465,
0.027556531131267548,
-0.040839117020368576,
0.006644268985837698,
0.07564684748649597,
0.02484414353966713,
-0.013672729954123497,
-0.027322527021169662,
-0.02970384806394577,
-0.01523037999868393,
0.08055170625448227,
0.03321797400712967,
-0.04185548797249794,
0.004512213636189699,
0.0477064810693264,
0.0003738096565939486,
0.04777814820408821,
0.006096838973462582,
0.013937604613602161,
0.0657641664147377,
-0.03184747323393822,
0.03362845256924629,
0.006299304310232401,
0.037934791296720505,
-0.03490765765309334,
0.060462500900030136,
-0.054079387336969376,
-0.0029187046457082033,
0.039434853941202164,
-0.0702081024646759,
0.015801478177309036,
0.013996136374771595,
-0.021162528544664383,
-0.054332632571458817,
-0.010228361003100872,
-0.04222472384572029,
0.0668829008936882,
0.025074969977140427,
0.033118899911642075,
-0.031981877982616425,
-0.02099653333425522,
-0.04036516696214676,
0.022776685655117035,
-0.03541691601276398,
-0.02961661107838154,
0.0016479763435199857,
-0.06741435825824738,
-0.015874335542321205,
0.0013315132819116116,
0.027361592277884483,
-0.0034486819058656693,
-0.047444868832826614,
0.052686210721731186,
0.006599998101592064,
0.0022770303767174482,
-0.030077071860432625,
0.0011086774757131934,
0.011599691584706306,
-0.005703210365027189,
-0.03647720813751221,
0.056992530822753906,
0.008679886348545551,
-0.005752420984208584,
0.00473966496065259,
-0.024411534890532494,
0.02834470383822918,
0.05315057933330536,
0.04624878615140915,
0.006043175235390663,
0.014349289238452911,
-0.06303168088197708,
0.021169060841202736,
-0.06460945308208466,
0.020347656682133675,
0.035552214831113815,
0.06676939129829407,
0.03698991984128952,
-0.020840654149651527,
0.00707536144182086,
-0.07766810804605484,
0.0247457604855299,
-0.07852331548929214,
-0.023552102968096733,
-0.048247214406728745,
-0.0343133918941021,
0.0023888838477432728,
0.019558584317564964,
-0.014036317355930805,
-0.005935916677117348,
-0.017583008855581284,
-0.02323688007891178,
-0.03335994482040405,
-0.07059253752231598,
-0.0014552510110661387,
0.018820416182279587,
-0.0009280713275074959,
-0.03402399644255638,
-0.015871688723564148,
0.0186991635710001,
0.045011255890131,
0.026216058060526848,
0.014662262052297592,
0.006867186166346073,
-0.011992779560387135,
0.024309242144227028,
-0.017526699230074883,
0.015014910139143467,
-0.03683523088693619,
-0.02362094074487686,
-0.057200707495212555,
0.033347681164741516,
0.03655269742012024,
0.03643719479441643,
0.014623891562223434,
-0.019295908510684967,
0.00826549157500267,
-0.03487900644540787,
-0.0018294195178896189,
-0.05111243575811386,
0.023087987676262856,
-0.026192275807261467,
-0.05303972214460373,
0.010979601182043552,
0.014452585019171238,
0.019792156293988228,
-0.08157709240913391,
0.03109571523964405,
0.06657008081674576,
0.043646637350320816,
-0.015293446369469166,
0.018225621432065964,
-0.02763928659260273,
0.039184920489788055,
0.03804238513112068,
0.009717689827084541,
0.019718825817108154,
-0.038077328354120255,
-0.022723006084561348,
0.04000547155737877,
0.0070143709890544415,
0.019430849701166153,
0.01631147228181362,
-0.0446435883641243,
0.018506145104765892,
-0.006461024284362793,
-0.003445378039032221,
-0.041059985756874084,
-0.06500235944986343,
0.030592147260904312,
0.03728216886520386,
-0.0247972309589386,
-0.028795959427952766,
0.03745238482952118,
-0.014214306138455868,
0.04531450197100639,
-0.015663955360651016,
0.01756194233894348,
0.03114360198378563,
0.005030662287026644,
-0.019089244306087494,
-0.00736714992672205,
0.017424099147319794,
-0.1134115606546402,
-0.05280459672212601,
0.030012162402272224,
0.04617340862751007,
-0.020053107291460037,
-0.021038303151726723,
0.02390354499220848,
-0.017279349267482758,
-0.04087008163332939,
0.00029491554596461356,
-0.002478200476616621,
0.0029813554137945175,
-0.026288220658898354,
-0.004569801036268473,
-0.005352697800844908,
-0.041114114224910736,
-0.0011352845467627048,
0.052060093730688095,
-0.08778654038906097,
0.01628348045051098,
-0.053192734718322754,
0.053589604794979095,
0.030460020527243614,
-0.01396914478391409,
-0.029253192245960236,
0.03484354913234711,
-0.0027252929285168648,
0.027071673423051834,
0.012055560946464539,
0.013863939791917801,
0.058419231325387955,
-0.08300897479057312,
0.10517597198486328,
0.007681507617235184,
-0.00779043510556221,
-0.009406326338648796,
0.00868772529065609,
0.025593800470232964,
-0.0093951765447855,
-0.007088929880410433,
0.02091270126402378,
-0.02254999801516533,
0.06359934061765671,
-0.024808408692479134,
-0.0010715340031310916,
-0.005302954465150833,
-0.011769426055252552,
-0.04368109628558159,
-0.01573980040848255,
-0.0025644581764936447,
0.036564383655786514,
0.024260180070996284,
0.021063808351755142,
-0.017442408949136734,
0.03856867179274559,
0.04594792425632477,
-0.012478690594434738,
0.014341904781758785,
-0.036480579525232315,
-0.006523742340505123,
-0.03668884187936783,
-0.06312245875597,
-0.0709175318479538,
0.014539874158799648,
-0.0025272779166698456,
-0.045326005667448044,
-0.008564108982682228,
-0.004168706014752388,
0.01007461454719305,
0.029483797028660774,
0.006541925948113203,
0.051656175404787064,
0.026966027915477753,
0.027203869074583054,
-0.04630788788199425,
0.02859673835337162,
0.05267486721277237,
-0.01931954175233841,
0.03155595809221268,
0.0541323721408844,
0.014208529144525528,
0.0029635101091116667,
-0.036854878067970276,
-0.0028746759053319693,
-0.02923346497118473,
0.00038754954584874213,
0.05270190164446831,
-0.032361019402742386,
-0.05060630664229393,
0.0027169384993612766,
0.03432604297995567,
0.03527407348155975,
-0.02908562310039997,
0.01761275716125965,
-0.01606154814362526,
-0.044986601918935776,
-0.07660838216543198,
-0.01492247823625803,
-0.046333517879247665,
-0.020191913470625877,
-0.031281329691410065,
-0.02056710235774517,
-0.045545656234025955,
0.002570421900600195,
-0.016903609037399292,
-0.02913123369216919,
-0.05383889749646187,
0.014360303990542889,
-0.030965406447649002,
-0.016750823706388474,
-0.011017207987606525,
-0.04918959364295006,
0.01876295544207096,
0.020972909405827522,
-0.02928980626165867,
0.007352316286414862,
-0.008788402192294598,
-0.015093136578798294,
-0.006315426900982857,
-0.01649666205048561,
-0.009784472174942493,
-0.014711735770106316,
-0.07330062240362167,
-0.04113999754190445,
-0.0005476580117829144,
-0.019381415098905563,
0.004354724194854498,
-0.011097706854343414,
0.0019434518180787563,
-0.050309427082538605,
-0.044896479696035385,
-0.02023208886384964,
0.05313137173652649,
0.06645433604717255,
-0.010200247168540955,
-0.01548109669238329,
-0.007444411516189575,
0.06358931958675385,
0.024024931713938713,
0.06398957967758179,
-0.019208446145057678,
-0.06774920970201492,
0.00778379337862134,
-0.01776769384741783,
0.0686902105808258,
-0.010091997683048248,
-0.016751931980252266,
-0.02302788384258747,
0.018608111888170242,
0.047721486538648605,
-0.05585898831486702,
0.03157219663262367,
0.061847370117902756,
-0.023489994928240776,
0.09329114854335785,
0.01991444267332554,
-0.03226151317358017,
0.056738898158073425,
-0.006916011217981577,
0.03060937114059925,
0.0681539997458458,
-0.02948966808617115,
-0.02840385213494301,
-0.037797775119543076,
0.008726092055439949,
-0.034624453634023666,
-0.022183816879987717,
0.029643651098012924,
-0.00293299020268023,
-0.015501996502280235,
0.022642571479082108,
-0.02328900247812271,
-0.022132225334644318,
0.024813370779156685,
0.02604098618030548,
-0.042636580765247345,
0.05767123028635979,
-0.06613557785749435,
0.0017690203385427594,
-0.012180769816040993,
-0.023203695192933083,
0.026180868968367577,
0.03682031109929085,
-0.002832291414961219,
-0.02936861664056778,
-0.014148358255624771,
0.043937209993600845,
0.0029810278210788965,
-0.01735006459057331,
-0.040146537125110626,
0.011773799546062946,
-0.0443049892783165,
-0.02024945430457592,
0.029275430366396904,
-0.039795927703380585,
0.013773724436759949,
-0.07737672328948975,
0.052993450313806534,
0.023747518658638,
-0.0327468067407608,
-0.00016217544907703996,
-0.008234185166656971,
0.060276903212070465,
0.0011904120910912752,
-0.009938504546880722,
0.03105558454990387,
-0.0022931667044758797,
-0.024733291938900948,
0.02616727352142334,
-0.003690145444124937,
0.0062767635099589825,
-0.02722548134624958,
-0.059931058436632156,
-0.03125572204589844,
0.04104316979646683,
-0.0334852896630764,
-0.031210824847221375,
0.028412964195013046,
0.011835562996566296,
0.021260367706418037,
0.018904883414506912,
0.040847983211278915,
-0.02130783535540104,
0.024203892797231674,
0.03959672525525093,
-0.038930896669626236,
-0.0742545872926712,
0.00009399846021551639,
0.0510585643351078,
-0.02040361613035202,
-0.026942992582917213,
-0.03722115606069565,
0.011869867332279682,
-0.004855320323258638,
-0.055327970534563065,
0.020465649664402008,
0.09405655413866043,
-0.0443417988717556,
-0.06930771470069885,
-0.009569671005010605,
-0.07100634276866913,
0.06490078568458557,
0.010213157162070274,
0.0360165499150753,
0.049597952514886856,
-0.020744455978274345,
-0.0044967480935156345,
0.024759143590927124,
-0.01631101779639721,
0.04123782366514206,
-0.099977508187294,
0.04320354387164116,
0.04923124238848686,
0.01903725415468216,
0.05851839855313301,
-0.026516593992710114,
0.026356911286711693,
-0.0016803023172542453,
0.0073140887543559074,
-0.008361191488802433,
-0.012744099833071232,
0.013920769095420837,
-0.07293862104415894,
-0.039254289120435715,
0.031512439250946045,
0.017721299082040787,
-0.014964978210628033,
-0.05573272332549095,
0.08096054941415787,
-0.003908794838935137,
0.058314066380262375,
0.052971888333559036,
0.03974693641066551,
-0.04455580189824104,
-0.007091652601957321,
0.05077606067061424,
0.032951902598142624,
0.04069104418158531,
0.033740900456905365,
-0.037895843386650085,
-0.014304977841675282,
0.02514674700796604,
0.00236368365585804,
0.035866912454366684,
0.02953946590423584,
0.019190218299627304,
-0.014448052272200584,
0.018912246450781822,
-0.004985318519175053,
-0.06199895218014717,
0.005414607003331184,
0.035878121852874756,
0.029279405251145363,
-0.01669771410524845,
-0.016771553084254265,
-0.05306079238653183,
0.013671436347067356,
-0.032461993396282196,
-0.002594755031168461,
0.009763686917722225,
0.016217032447457314,
0.005412627477198839,
-0.09098835289478302,
0.02766641229391098,
-0.0034545876551419497,
-0.028184419497847557,
0.022503769025206566,
-0.022368796169757843,
0.02699756808578968,
-0.014740262180566788,
-0.0637693852186203,
0.029523933306336403,
0.004653552081435919,
-0.01914033479988575,
-0.07488983869552612,
0.028327960520982742,
0.03727027028799057,
-0.04726419225335121,
-0.018387820571660995,
-0.006438064854592085,
-0.013438602909445763,
0.0037852986715734005,
0.01166780199855566,
-0.0347696952521801,
-0.005990163888782263,
0.035251062363386154,
0.011137129738926888,
0.0003392657090444118,
-0.057449810206890106,
-0.050633639097213745,
0.04796374961733818,
-0.0038398192264139652,
0.038137517869472504,
-0.0014313856372609735,
0.06874570995569229,
-0.0016520210774615407,
0.04327398166060448,
-0.03075806051492691,
0.004646177403628826,
0.0020194086246192455,
-0.07611024379730225,
0.012893388979136944,
0.09953121095895767,
0.060186196118593216,
0.001910060760565102,
0.0475001186132431,
0.008829617872834206,
-0.042316734790802,
-0.029541950672864914,
0.04302611202001572,
0.0033984193578362465,
-0.018858226016163826,
-0.011819415725767612,
-0.06160818785429001,
-0.013720774091780186,
0.010757186450064182,
-0.012362871319055557,
-0.005315470043569803,
-0.07787565886974335,
0.06061558425426483,
0.07412909716367722,
0.06761162728071213,
-0.012032626196742058,
0.02535642497241497,
0.005426221992820501,
0.002086441498249769,
0.005710546392947435,
-0.04816504940390587,
-0.051763176918029785,
0.0030353206675499678,
-0.05954328551888466,
0.009324583224952221,
-0.007573653943836689,
0.00035369826946407557,
0.06126461923122406,
0.003328913589939475,
0.0036371215246617794,
-0.05446258559823036,
0.04739397391676903,
-0.021462827920913696,
0.02347317710518837,
0.03664007782936096,
0.04883837327361107,
-0.0011974606895819306,
0.011235596612095833,
-0.06284395605325699,
-0.05695858225226402,
0.0034855033736675978,
0.045609503984451294,
-0.013471119105815887,
0.03293550759553909,
0.03158644214272499,
-0.0029138748068362474,
-0.007124247029423714,
0.027975929901003838,
-0.006920399609953165,
0.004569891840219498,
-0.020868485793471336,
-0.02040332742035389,
0.0007115578628145158,
-0.017568841576576233,
0.003839091630652547,
0.06830523163080215,
0.03524184599518776,
-0.020881440490484238,
0.05681835114955902,
0.10121568292379379,
-0.05032152310013771,
-0.05258888751268387,
-0.028849167749285698,
0.004972643684595823,
-0.0029704042244702578,
-0.015523592010140419,
0.03732110559940338,
0.01228672731667757,
0.03382192179560661,
-0.03521773964166641,
-0.0409361869096756,
-0.03725401312112808,
0.03223908320069313,
-0.023952003568410873,
-0.03691320866346359,
-0.006552547682076693,
0.06757226586341858,
0.012084320187568665,
0.011284749954938889,
-0.002991259563714266,
0.050446778535842896,
0.012563745491206646,
-0.010999043472111225,
-0.0043077245354652405,
-0.023947186768054962,
0.06626777350902557,
0.013225272297859192,
-0.019712146371603012,
-0.012373335659503937,
-0.057700999081134796,
0.03529001772403717,
-0.014392650686204433,
0.0024041240103542805,
-0.02259214222431183,
-0.029696933925151825,
-0.051728665828704834,
0.030302803963422775,
0.007485867477953434,
0.0327637642621994,
0.01735066808760166,
-0.0067359223030507565,
0.09795305132865906,
-0.04273151606321335,
-0.009124253876507282,
-0.01987203024327755,
-0.028104715049266815,
0.007466551847755909,
0.03770849481225014,
0.013810217380523682,
-0.01313698012381792,
0.025604579597711563,
0.0005698786117136478,
0.031057141721248627,
-0.03641211614012718,
0.028035175055265427,
-0.04892902076244354,
-0.016799965873360634,
0.001973747042939067,
-0.019914111122488976,
0.032645612955093384,
0.07539724558591843,
0.06584089994430542,
-0.03564511984586716,
-0.01589384488761425,
0.02997671812772751,
-0.04789595678448677,
0.013284189626574516,
-0.011695878580212593,
0.014408576302230358,
-0.0074655404314398766,
-0.056337758898735046,
0.009427620097994804,
-0.04773165285587311,
-0.015888025984168053,
0.00011769231059588492
] |
<p>Case 1: two people wake up in spaceships accelerating at 1g. They can measure or observe anything inside the room but not outside. They couldn't determine if they were on a spaceship or on earth. If they ever communicated in the future they would be the same age. Is this correct?</p>
<p>Case 2: one person wakes up in a room on earth, another on a spaceship accelerating 1g. Same measuring restrictions. Again neither could determine if they were on a spaceship or earth. However now if they communicated in the future they would find they are different ages. Is this correct?</p>
<p>I've heard acceleration from a rocket or gravity are the same (e.g. time slows down near a black hole). But case 2 above seems there is a difference?</p> | g4562 | [
-0.0005581737495958805,
0.029032520949840546,
0.0011092000640928745,
0.010086243972182274,
0.008182630874216557,
0.06556466221809387,
0.011756328865885735,
-0.04305877909064293,
-0.04873053357005119,
-0.004084629472345114,
0.07396518439054489,
-0.03096301667392254,
0.010432342998683453,
0.05197346955537796,
-0.009099526330828667,
-0.04132428392767906,
0.09589436650276184,
-0.06090180575847626,
-0.061632633209228516,
-0.026486076414585114,
0.024498973041772842,
-0.01442653313279152,
-0.059362463653087616,
-0.018875401467084885,
-0.03168036416172981,
-0.061878036707639694,
0.004635718185454607,
-0.024532858282327652,
-0.09093260020017624,
-0.048323724418878555,
0.06014012545347214,
0.002264148322865367,
0.0444181002676487,
-0.06399500370025635,
-0.00727885402739048,
-0.05683765560388565,
0.003884689649567008,
-0.0165291465818882,
-0.019858181476593018,
0.037304021418094635,
0.04945835471153259,
-0.03666502982378006,
-0.0027239068876951933,
-0.03836587816476822,
0.00903137493878603,
0.03330747410655022,
0.00013038984616287053,
-0.01859278604388237,
0.12310206890106201,
0.011548069305717945,
-0.003458786755800247,
-0.0059922668151557446,
0.018004583194851875,
0.031074078753590584,
-0.008013583719730377,
0.05207919329404831,
0.0036532811354845762,
0.0075669256038963795,
0.054487429559230804,
0.001605504541657865,
-0.041807059198617935,
-0.021773817017674446,
0.023867690935730934,
0.006634852383285761,
0.079620361328125,
0.011561093851923943,
-0.019786274060606956,
0.02342691831290722,
0.002913303207606077,
-0.03549579530954361,
0.046375907957553864,
-0.02794966846704483,
-0.07461090385913849,
-0.03844963386654854,
-0.018545133993029594,
0.030889326706528664,
-0.02893405593931675,
-0.02917644940316677,
-0.00955491978675127,
0.07616541534662247,
-0.01781638339161873,
-0.005320106633007526,
0.016471045091748238,
0.0022746827453374863,
0.07268442958593369,
0.0591319277882576,
-0.025168737396597862,
-0.008466796018183231,
0.030174292623996735,
0.04456114396452904,
0.06501847505569458,
-0.029140273109078407,
0.09290380030870438,
0.03257753700017929,
-0.04628535732626915,
0.03978075459599495,
0.020913442596793175,
0.06222833693027496,
0.04650716483592987,
0.04339109733700752,
-0.059792038053274155,
0.010820725001394749,
0.019494397565722466,
0.03017682395875454,
0.02354656718671322,
-0.03862766921520233,
0.012264648452401161,
-0.00950213335454464,
-0.027049420401453972,
-0.06999611109495163,
-0.04380781203508377,
-0.07529731839895248,
-0.034902725368738174,
-0.027069903910160065,
-0.00030528046772815287,
-0.057650838047266006,
0.018276970833539963,
0.047323811799287796,
-0.015650566667318344,
0.014369143173098564,
0.012701660394668579,
0.025310823693871498,
0.030409419909119606,
0.02384263090789318,
0.0008665041532367468,
0.005825386382639408,
-0.02808225341141224,
-0.0427071750164032,
-0.01673242822289467,
0.0021196086890995502,
-0.005908135790377855,
0.03697913885116577,
-0.0007864078506827354,
0.03336343169212341,
-0.04482797533273697,
0.026187462732195854,
0.001175092882476747,
0.03399570658802986,
0.009232341311872005,
0.0014774550218135118,
0.022616080939769745,
-0.07525516301393509,
-0.04105108231306076,
-0.022568197920918465,
-0.010626017116010189,
0.02377467043697834,
-0.0009806709131225944,
0.00583788612857461,
-0.009360753931105137,
0.04835348203778267,
-0.0016445175278931856,
0.09728250652551651,
-0.0017644373001530766,
0.016152989119291306,
0.014257334172725677,
0.006259504705667496,
-0.028884824365377426,
0.019707655534148216,
0.018763257190585136,
0.038129497319459915,
0.028435243293642998,
0.007097570691257715,
0.025323573499917984,
0.07441367954015732,
-0.035937219858169556,
0.010774652473628521,
-0.0050148447044193745,
-0.059250690042972565,
0.01508693303912878,
-0.021134182810783386,
-0.026790345087647438,
-0.02991625852882862,
0.021233798936009407,
0.03452037647366524,
0.041394587606191635,
0.03982732072472572,
0.04933835193514824,
-0.08618433773517609,
-0.04630892351269722,
0.000373235932784155,
-0.026897132396697998,
-0.058574166148900986,
-0.048774354159832,
-0.012596284970641136,
-0.017637884244322777,
-0.03998945653438568,
0.0029647524934262037,
-0.0007113679894246161,
-0.08550749719142914,
0.01955728977918625,
-0.0542612262070179,
-0.055687274783849716,
-0.056139033287763596,
0.021599367260932922,
-0.03472009673714638,
-0.033971112221479416,
0.01641305722296238,
0.07278993725776672,
0.003928346559405327,
0.029177449643611908,
-0.0038955402560532093,
0.0028774309903383255,
0.04037502780556679,
-0.014846145175397396,
0.04343612492084503,
0.013674418441951275,
0.008553793653845787,
-0.008746295236051083,
0.045929450541734695,
-0.029485531151294708,
0.016967104747891426,
0.023555701598525047,
0.005939606577157974,
-0.005052412860095501,
0.003964256029576063,
0.00441349484026432,
0.01074201986193657,
0.04029905050992966,
0.026644786819815636,
-0.042868874967098236,
-0.015024525113403797,
-0.07806581258773804,
0.05683169141411781,
-0.04879317432641983,
-0.005463579203933477,
-0.056290555745363235,
-0.012472819536924362,
-0.050770025700330734,
-0.013144231401383877,
0.0559348464012146,
-0.06639246642589569,
-0.0008162502199411392,
-0.005697239190340042,
-0.01754390075802803,
0.023564886301755905,
0.02098885178565979,
0.01577357016503811,
0.05413879081606865,
0.032397475093603134,
0.0006475094123743474,
0.01854967139661312,
0.032392919063568115,
-0.04701049253344536,
0.006224184762686491,
0.04873868077993393,
-0.028992455452680588,
0.011039851233363152,
-0.016407480463385582,
-0.02008674480021,
0.024629389867186546,
-0.017214419320225716,
0.032672349363565445,
-0.06958005577325821,
0.01607515662908554,
-0.015464264899492264,
-0.06625157594680786,
0.003336078254505992,
0.04067767411470413,
-0.07605930417776108,
0.0021043571177870035,
0.02048494480550289,
-0.028388816863298416,
-0.04352661594748497,
0.018875963985919952,
0.009614543057978153,
-0.01995573192834854,
-0.028914181515574455,
0.0032633482478559017,
0.004042068496346474,
-0.0282010305672884,
-0.009868739172816277,
-0.02090548165142536,
-0.002277216874063015,
0.06034460663795471,
0.007098974194377661,
-0.026021109893918037,
0.014964893460273743,
-0.017002763226628304,
0.044717200100421906,
0.03631897270679474,
-0.027532564476132393,
-0.025122594088315964,
-0.065195232629776,
-0.001069870195351541,
0.04638427123427391,
0.020761365070939064,
0.019466908648610115,
0.005823249462991953,
-0.028587184846401215,
0.021491624414920807,
0.028192313387989998,
0.05882365256547928,
0.07097364217042923,
0.048382315784692764,
-0.017863651737570763,
0.05910603702068329,
-0.012752490118145943,
0.03590575233101845,
-0.04275655373930931,
-0.022643832489848137,
0.05576976016163826,
-0.048102788627147675,
0.00732297170907259,
0.06916497647762299,
0.06451821327209473,
-0.0625433400273323,
-0.053664155304431915,
-0.025505464524030685,
0.033022720366716385,
-0.021368471905589104,
-0.011234262958168983,
0.0013461181661114097,
-0.01676461473107338,
-0.02492869645357132,
0.05378589779138565,
0.009943638928234577,
-0.021887175738811493,
0.04111102968454361,
0.009643426164984703,
0.019135870039463043,
-0.04616246372461319,
-0.006371343974024057,
-0.011836034245789051,
-0.009607159532606602,
0.023777471855282784,
0.029084771871566772,
-0.023443574085831642,
-0.003505977336317301,
-0.03616500273346901,
-0.010442860424518585,
-0.023492885753512383,
-0.01204445119947195,
-0.020580198615789413,
-0.020805438980460167,
0.0036033804062753916,
-0.017968347296118736,
-0.02118416130542755,
0.04464986175298691,
0.0075335693545639515,
0.037650059908628464,
0.03040531650185585,
-0.04098879545927048,
0.015438015572726727,
0.04047516733407974,
0.032009419053792953,
-0.0012728767469525337,
0.015550535172224045,
0.009518387727439404,
-0.0312737412750721,
0.0009368374012410641,
0.010516942478716373,
-0.055914729833602905,
0.013467730022966862,
0.022658860310912132,
-0.023301005363464355,
0.0028416684363037348,
-0.0026103102136403322,
-0.01251530647277832,
-0.014126492664217949,
-0.01679186150431633,
-0.037877295166254044,
0.053202513605356216,
-0.03039786033332348,
0.012985668145120144,
-0.019830605015158653,
-0.024581167846918106,
0.03169965744018555,
0.007411070168018341,
0.03960122913122177,
-0.03376119211316109,
0.024080630391836166,
0.06406225264072418,
-0.012670569121837616,
-0.039541054517030716,
0.07025676220655441,
-0.07483605295419693,
0.014314861036837101,
-0.03460955247282982,
0.014571665786206722,
0.009967772290110588,
0.06530988961458206,
-0.009816533885896206,
-0.003235230688005686,
-0.008650045841932297,
0.06809582561254501,
-0.000058005334722111,
-0.004572000820189714,
-0.02523304708302021,
-0.023282520473003387,
-0.08548736572265625,
0.027381647378206253,
-0.03406965360045433,
-0.03783087804913521,
0.024056589230895042,
0.01372550055384636,
0.0019824004266411066,
-0.010233447887003422,
-0.01557463500648737,
0.03295530006289482,
0.01092823687940836,
0.006239120848476887,
0.04834403470158577,
0.007868832908570766,
0.021171463653445244,
-0.026859350502490997,
0.010549348779022694,
-0.00586733128875494,
-0.04806727543473244,
-0.007132808677852154,
0.028557471930980682,
0.012944327667355537,
0.0458301417529583,
-0.021935682743787766,
-0.06607434153556824,
0.00011548693873919547,
-0.011155124753713608,
0.021132295951247215,
-0.009365711361169815,
0.042375992983579636,
0.0374588668346405,
0.016037730500102043,
0.05735813081264496,
-0.01205301284790039,
-0.04434627667069435,
-0.00044060530490241945,
0.08724711090326309,
-0.008142450824379921,
0.03818806633353233,
0.00357865821570158,
-0.024479025974869728,
0.027442073449492455,
0.029625074937939644,
-0.014540697447955608,
0.03200945258140564,
-0.050578806549310684,
0.06469883024692535,
0.034294355660676956,
0.005423010792583227,
0.05161745846271515,
-0.0021834445651620626,
0.050259191542863846,
0.0024697703775018454,
-0.014504526741802692,
-0.018905550241470337,
0.03250066190958023,
0.10673128068447113,
-0.0717473030090332,
-0.04050992429256439,
-0.0027901274152100086,
0.024131784215569496,
-0.03413498401641846,
0.04730983451008797,
-0.009725198149681091,
-0.038194045424461365,
0.010241168551146984,
-0.023341599851846695,
0.015164373442530632,
-0.00761799793690443,
0.04046507552266121,
-0.004220343194901943,
-0.03770554065704346,
-0.001900227158330381,
0.02745174430310726,
-0.026670506224036217,
-0.030002381652593613,
-0.0011345805833116174,
-0.07658793777227402,
-0.04052210971713066,
-0.0403648279607296,
0.033459048718214035,
-0.051449984312057495,
-0.03609210625290871,
0.004446449689567089,
0.04606727138161659,
-0.03524385392665863,
0.04206642508506775,
0.03880989924073219,
-0.024844298139214516,
-0.008783632889389992,
-0.04001116007566452,
-0.033720459789037704,
0.022138694301247597,
0.026157567277550697,
0.00033671403070911765,
0.0009233221644535661,
-0.0034059493336826563,
0.002444860991090536,
0.031310368329286575,
0.06622487306594849,
-0.019793525338172913,
0.04450637847185135,
-0.062316350638866425,
-0.0003417869738768786,
-0.005433961749076843,
-0.05993252992630005,
-0.008081388659775257,
-0.015262201428413391,
-0.04248257726430893,
-0.02249090000987053,
0.037955719977617264,
-0.04672098904848099,
0.024599270895123482,
0.028477387502789497,
-0.01566053368151188,
-0.02216087281703949,
0.03504472225904465,
0.041662946343421936,
-0.055849503725767136,
0.010841527953743935,
0.08016283065080643,
-0.055692750960588455,
-0.0011800494976341724,
0.005280263721942902,
0.05217763036489487,
0.045261871069669724,
-0.022917017340660095,
0.043119657784700394,
0.0317741259932518,
0.0021276555489748716,
0.028997059911489487,
0.04374612867832184,
-0.001333938562311232,
0.03268628567457199,
0.06265251338481903,
0.023903802037239075,
-0.014507132582366467,
-0.02042500674724579,
-0.02755308523774147,
0.04756760969758034,
0.02012653462588787,
0.0570024736225605,
0.05297275260090828,
0.00396301131695509,
-0.04456751048564911,
0.0012321561807766557,
-0.002598579041659832,
-0.011222321540117264,
-0.03226146847009659,
0.060272760689258575,
-0.029043950140476227,
-0.046326495707035065,
-0.016027821227908134,
-0.02808864414691925,
0.030469391494989395,
-0.01694035530090332,
0.02697993442416191,
-0.05779505521059036,
-0.030185725539922714,
-0.0011088232276961207,
0.010339131578803062,
-0.03354152664542198,
-0.02077888511121273,
0.005283011589199305,
0.025370996445417404,
-0.02178201638162136,
0.06563138961791992,
0.008327510207891464,
0.0003796967212110758,
-0.026745129376649857,
0.03483550250530243,
0.042456723749637604,
0.004837303422391415,
0.021989140659570694,
-0.03846478462219238,
-0.0011664158664643764,
-0.052298061549663544,
-0.008866505697369576,
-0.024751415476202965,
-0.012808282859623432,
-0.029231222346425056,
0.015005694702267647,
-0.023321645334362984,
0.009752776473760605,
-0.004825484938919544,
-0.02868083119392395,
-0.02685670182108879,
-0.039165351539850235,
0.009604543447494507,
-0.05291000381112099,
0.007411620579659939,
-0.007675201632082462,
0.014047671109437943,
0.013893299736082554,
-0.010872882790863514,
0.042385611683130264,
0.05239200219511986,
-0.011133374646306038,
-0.03406844660639763,
0.04474131762981415,
-0.03253534808754921,
-0.02933819591999054,
-0.07264877110719681,
0.008047438226640224,
-0.04308827221393585,
-0.13876843452453613,
0.005228010937571526,
0.028081603348255157,
-0.03235168009996414,
-0.0636398047208786,
0.022841759026050568,
-0.012299194931983948,
-0.0077276332303881645,
0.06498976051807404,
0.014315148815512657,
0.014337144792079926,
-0.006126968655735254,
-0.05183204635977745,
0.018516452983021736,
0.08179761469364166,
-0.08453630656003952,
-0.029394393786787987,
0.03289857506752014,
0.011076471768319607,
0.03342339023947716,
0.03207394480705261,
0.03258895128965378,
0.003410403151065111,
-0.037758298218250275,
-0.024519119411706924,
-0.0026584623847156763,
0.10736265033483505,
-0.03181275352835655,
-0.009778381325304508,
-0.049642421305179596,
0.013413664884865284,
0.04296552389860153,
-0.03723466396331787,
0.009802991524338722,
0.0077471681870520115,
0.04546504095196724,
0.0032272597309201956,
-0.017257243394851685,
-0.0014045481802895665,
0.05022911727428436,
0.06511302292346954,
0.017763031646609306,
0.03141774982213974,
0.06782460957765579,
-0.04169200360774994,
0.004083271604031324,
0.054527416825294495,
0.02919488400220871,
0.01573800854384899,
0.03100169450044632,
0.004794484470039606,
0.0052534774877130985,
0.045998986810445786,
-0.027909640222787857,
-0.04819687083363533,
-0.010237949900329113,
-0.032308418303728104,
-0.06217789277434349,
-0.05693493038415909,
0.028061237186193466,
0.0015682980883866549,
0.0016702581197023392,
0.0021806247532367706,
-0.04570141062140465,
0.023668203502893448,
-0.03843563422560692,
0.00757663743570447,
-0.012985887005925179,
-0.0527849905192852,
0.052241597324609756,
-0.046922098845243454,
0.03724250942468643,
-0.005623792763799429,
-0.053551919758319855,
-0.03469296544790268,
-0.00358084705658257,
0.005031628999859095,
-0.009545547887682915,
-0.03977340832352638,
-0.012152853421866894,
-0.02123238332569599,
0.0166068933904171,
-0.03240584209561348,
-0.034837786108255386,
-0.01679026521742344,
0.018884113058447838,
0.038273707032203674,
-0.0013732925290241838,
-0.023160593584179878,
0.026897070929408073,
0.014339243993163109,
0.06429048627614975,
-0.04837318882346153,
-0.035369135439395905,
0.013457364402711391,
-0.03862830623984337,
-0.05314211547374725,
-0.0033787668216973543,
-0.010265923105180264,
0.0386512391269207,
-0.020173095166683197,
0.010088683106005192,
-0.025829242542386055,
0.08716714382171631,
-0.03026796504855156,
-0.01766185276210308,
-0.008550150319933891,
0.0258179921656847,
0.008581127971410751,
0.03778029605746269,
-0.02553911879658699,
-0.05484430864453316,
-0.03595815226435661,
-0.02190835401415825,
-0.005864415783435106,
-0.02794792503118515,
0.009264868684113026,
0.017323428764939308,
0.028913626447319984,
0.007764602545648813,
0.018147451803088188,
-0.008662653155624866,
-0.030436072498559952,
-0.005448183510452509,
0.034533705562353134,
0.015455703251063824,
0.050598081201314926,
-0.03982003405690193,
-0.008065707981586456,
-0.07905858755111694,
-0.04182092845439911,
-0.009127803146839142,
-0.0011939549585804343,
0.03522820770740509,
0.011048498563468456,
-0.06039600819349289,
-0.024474268779158592,
0.021504711359739304,
-0.01680554263293743,
0.027304833754897118,
-0.001255182782188058,
0.06753552705049515,
0.008157235570251942,
0.03157864883542061,
-0.07798755168914795,
0.0037884812336415052,
-0.06720136851072311,
0.011451305821537971,
0.00074315897654742,
0.05382265895605087,
-0.016298072412610054,
0.0049185180105268955,
-0.006537238135933876,
0.05116031691431999,
0.028014719486236572,
-0.048248350620269775,
0.0171133391559124,
0.0045609017834067345,
-0.09609542042016983,
0.07286644726991653,
0.011709684506058693,
0.0054034884087741375,
0.031324855983257294,
0.022705430164933205,
-0.017939584329724312,
-0.06254883110523224,
-0.027986181899905205,
0.03270939365029335,
-0.024479815736413002,
-0.010851350612938404,
-0.06709831953048706,
-0.015453891828656197,
-0.005016984883695841,
0.008959928527474403
] |
<p>I just want a book on classical mechanics that covers the same ground as Goldstein's book but is more on the line of DJ Griffiths's Classical Electrodynamics. I mean less formal and more conversational. </p> | g98 | [
0.042645104229450226,
0.01810041442513466,
-0.000964723527431488,
-0.056489963084459305,
0.015691278502345085,
0.01338773500174284,
0.026771487668156624,
-0.038404468446969986,
0.01198693085461855,
0.01080949418246746,
0.05135605111718178,
-0.042105793952941895,
-0.013445810414850712,
-0.00836372934281826,
0.006302976049482822,
-0.009442126378417015,
0.004107424523681402,
0.053267017006874084,
0.016721460968255997,
-0.02426663041114807,
0.002818713430315256,
0.024106374010443687,
-0.011751721613109112,
-0.01619509607553482,
-0.038407281041145325,
-0.0008449060842394829,
0.0013122553937137127,
-0.02287900261580944,
0.022404849529266357,
0.00039836452924646437,
-0.036635756492614746,
-0.018313778564333916,
0.018623564392328262,
-0.036731671541929245,
-0.011404325254261494,
0.012211373075842857,
0.012951473705470562,
-0.036406293511390686,
-0.0027255541644990444,
0.0005841003148816526,
0.04586656764149666,
0.008837866596877575,
-0.006648406386375427,
0.028068166226148605,
0.05024716630578041,
-0.06322953850030899,
0.010622366331517696,
0.035678472369909286,
-0.06586640328168869,
0.01604631170630455,
0.045417670160532,
0.012615452520549297,
0.05885031819343567,
-0.017342500388622284,
0.049360912293195724,
0.029888218268752098,
-0.0015523581532761455,
0.039183471351861954,
-0.04588533565402031,
-0.018857359886169434,
0.010580949485301971,
0.02246687561273575,
-0.019165853038430214,
-0.016048915684223175,
0.005596857517957687,
-0.03301585465669632,
0.04640999436378479,
-0.05256820470094681,
-0.002497381530702114,
-0.017691893503069878,
-0.022919554263353348,
-0.03494301065802574,
0.016892483457922935,
-0.01013114582747221,
0.01589244417846203,
0.004799924325197935,
0.062129907310009,
-0.009546017274260521,
0.05679446831345558,
-0.06373460590839386,
-0.07535459846258163,
-0.04895002767443657,
-0.015459991991519928,
-0.03958199545741081,
0.08196862787008286,
-0.022721512243151665,
-0.020003464072942734,
-0.0062571363523602486,
0.0047951857559382915,
-0.06277500092983246,
0.016260888427495956,
-0.02136996202170849,
0.052248094230890274,
-0.05741428583860397,
-0.017746517434716225,
-0.008257421664893627,
-0.026073329150676727,
-0.017026685178279877,
0.004446512553840876,
-0.025392068549990654,
-0.017844505608081818,
0.008828883059322834,
0.049928031861782074,
-0.0020324892830103636,
-0.03784232586622238,
0.009405633434653282,
-0.023441817611455917,
-0.038015179336071014,
-0.014353816397488117,
0.0051522585563361645,
0.008175835013389587,
-0.025370841845870018,
0.019097499549388885,
-0.021620050072669983,
-0.024138426408171654,
0.07016918808221817,
0.08207092434167862,
-0.045957714319229126,
0.0003493795229587704,
0.05215054005384445,
0.01568131148815155,
0.001969427103176713,
0.03341640904545784,
0.0020501965191215277,
-0.016735907644033432,
-0.016515880823135376,
0.04423431307077408,
0.01929168775677681,
0.025686156004667282,
-0.0035633929073810577,
0.06472182273864746,
0.042190928012132645,
-0.057946037501096725,
-0.027760028839111328,
-0.03260314464569092,
0.08538638055324554,
0.03810947760939598,
-0.031957656145095825,
0.030710414052009583,
-0.012036553584039211,
0.04725956171751022,
-0.033620670437812805,
-0.004181795287877321,
-0.029240921139717102,
0.017788534983992577,
0.02746192365884781,
-0.008484850637614727,
0.010932395234704018,
0.00038301965105347335,
0.0032145457807928324,
0.029833270236849785,
0.0024134237319231033,
0.027415873482823372,
-0.009800921194255352,
0.007494048215448856,
0.04006480053067207,
0.02210257016122341,
0.03529076278209686,
0.016967590898275375,
0.00002043994390987791,
0.0008619915461167693,
-0.025158725678920746,
-0.01589708961546421,
0.029601985588669777,
0.025870976969599724,
0.07527142763137817,
-0.023625651374459267,
-0.08000930398702621,
0.01884426176548004,
0.004622845910489559,
0.009390498511493206,
0.0006447548512369394,
0.04529358446598053,
0.09852248430252075,
-0.05040992796421051,
0.09580554813146591,
-0.1104741021990776,
-0.06268048286437988,
-0.02400594763457775,
-0.03492847457528114,
0.004926564637571573,
-0.07200554758310318,
0.06276771426200867,
-0.00205339421518147,
-0.0669993981719017,
0.06738998740911484,
0.012783556245267391,
0.021032825112342834,
-0.046660277992486954,
0.014091790653765202,
0.013178365305066109,
0.029386242851614952,
0.007415004074573517,
0.08378353714942932,
0.0052391840144991875,
0.01037180982530117,
-0.009430207312107086,
-0.048871442675590515,
-0.023406023159623146,
0.08090044558048248,
0.04327339306473732,
0.05874321609735489,
0.05698632821440697,
0.012064981274306774,
-0.01290105190128088,
0.03970595821738243,
0.015202878974378109,
0.017752503976225853,
0.06350629776716232,
-0.0724397748708725,
0.00977477990090847,
-0.03627986088395119,
0.017810238525271416,
-0.01019421499222517,
0.03395220637321472,
-0.04477435722947121,
-0.004227892030030489,
0.009646455757319927,
0.00485163414850831,
0.012694088742136955,
-0.017845042049884796,
-0.03892316669225693,
-0.04752042144536972,
0.014766913838684559,
0.013277372345328331,
-0.05981370434165001,
0.04617168754339218,
-0.0060156723484396935,
0.02067391760647297,
-0.01074057538062334,
-0.07773958891630173,
-0.011967970989644527,
0.007741173729300499,
-0.007605956867337227,
0.05472337082028389,
0.09293080121278763,
-0.001328981714323163,
-0.038016531616449356,
0.05627688392996788,
-0.03547700494527817,
0.07078340649604797,
-0.016647277399897575,
0.018604066222906113,
-0.024424752220511436,
-0.03116484172642231,
-0.006237458437681198,
0.048044927418231964,
0.01565585285425186,
0.03969348222017288,
-0.0005563421291299164,
0.02372502163052559,
-0.01731063425540924,
-0.0811251848936081,
-0.00842154398560524,
0.006634078454226255,
0.03351706638932228,
-0.014270690269768238,
0.0717143565416336,
0.02103351429104805,
-0.009190792217850685,
0.0009558164165355265,
-0.004012034274637699,
-0.004138614982366562,
0.022593585774302483,
-0.006665372755378485,
0.02059403620660305,
-0.004405337851494551,
0.0264135655015707,
-0.03905267268419266,
-0.04948718845844269,
0.004663036670535803,
0.06011725217103958,
0.017782000824809074,
-0.00803174264729023,
0.007173982914537191,
-0.028651950880885124,
0.010474334470927715,
-0.03551819920539856,
0.014911605045199394,
-0.05627293512225151,
-0.000031947052775649354,
-0.016139686107635498,
0.051108844578266144,
0.01431186217814684,
-0.004497275687754154,
-0.08820085972547531,
-0.021087590605020523,
0.015612018294632435,
0.0013998327776789665,
0.00008168890053639188,
0.030879219993948936,
0.07855862379074097,
0.006842828821390867,
-0.010464854538440704,
-0.037134673446416855,
0.06774337589740753,
-0.034158553928136826,
0.021114656701683998,
-0.049168430268764496,
-0.014384427107870579,
-0.0009928593644872308,
-0.036639463156461716,
-0.016414957121014595,
0.05025101825594902,
-0.012666182592511177,
0.005861994344741106,
-0.0227865781635046,
-0.028508946299552917,
0.030542848631739616,
-0.02193615585565567,
0.022746548056602478,
-0.01163632795214653,
0.005251175723969936,
0.02404845505952835,
-0.08061771839857101,
-0.011681195348501205,
0.01628684811294079,
0.0024911973159760237,
-0.0008856744971126318,
0.0015133259585127234,
-0.015729686245322227,
-0.01821686513721943,
0.07184439152479172,
-0.053107403218746185,
0.03522532805800438,
0.041907165199518204,
-0.04054781422019005,
-0.03421135991811752,
0.0019121328368782997,
0.011950238607823849,
0.04360063001513481,
-0.05875681713223457,
0.0035894992761313915,
-0.03794984146952629,
-0.049117311835289,
-0.043393414467573166,
-0.0008238576701842248,
0.012710757553577423,
0.027433548122644424,
-0.003240627935156226,
0.012970014475286007,
-0.03724119812250137,
0.004546756390482187,
-0.017393596470355988,
-0.03767793998122215,
-0.013900809921324253,
0.04193630814552307,
-0.017806578427553177,
0.04112200438976288,
-0.05430883914232254,
0.03854823485016823,
-0.001392997452057898,
0.01072975154966116,
-0.039503470063209534,
-0.06458801031112671,
-0.030015448108315468,
0.012761124409735203,
0.04602329432964325,
0.0803694948554039,
-0.022023579105734825,
-0.015828752890229225,
0.006741990800946951,
-0.018812663853168488,
-0.07588483393192291,
0.013315277174115181,
0.01822306029498577,
-0.028397703543305397,
0.009454352781176567,
-0.019672511145472527,
-0.0003584162041079253,
-0.024805165827274323,
0.03704245388507843,
0.09159507602453232,
0.02176232449710369,
0.019818874076008797,
-0.08454899489879608,
0.052950937300920486,
0.06092977523803711,
-0.043997928500175476,
-0.006749376188963652,
-0.058193057775497437,
0.005717596039175987,
0.023374633863568306,
0.028746604919433594,
0.03921167179942131,
0.013555610552430153,
-0.013728453777730465,
0.004082599189132452,
-0.014929477125406265,
-0.009860294871032238,
0.01300677191466093,
-0.029154809191823006,
-0.04405698925256729,
0.01447293534874916,
0.014708753675222397,
-0.003064377699047327,
0.047199610620737076,
0.005926445126533508,
-0.0034550288692116737,
0.00485603092238307,
-0.005061302799731493,
0.02582399919629097,
-0.00750688835978508,
0.019972683861851692,
-0.0008392833406105638,
0.00345164118334651,
0.03327798843383789,
-0.009435255080461502,
0.028435859829187393,
-0.018229098990559578,
0.01881510019302368,
-0.06051165610551834,
0.03485919162631035,
-0.024078909307718277,
0.04166743904352188,
0.038988374173641205,
-0.03309806436300278,
-0.07721175253391266,
0.036574263125658035,
0.013632087036967278,
-0.07332313805818558,
0.011977607384324074,
-0.045092273503541946,
-0.06193123757839203,
0.0432906374335289,
0.04640224203467369,
0.0644172951579094,
0.00011315548181300983,
-0.021721243858337402,
-0.017196454107761383,
-0.0009817949030548334,
-0.04510175436735153,
-0.043428756296634674,
0.0302956011146307,
-0.036185942590236664,
0.01577863283455372,
0.007642216514796019,
0.03996516764163971,
-0.0009913804242387414,
0.010545019991695881,
0.05967649817466736,
0.011731859296560287,
-0.010241487063467503,
0.015283958986401558,
-0.008250080049037933,
0.07087662070989609,
-0.04070337861776352,
-0.00555237103253603,
-0.028462866321206093,
-0.05683170631527901,
-0.012760229408740997,
0.008281570859253407,
0.006878085900098085,
0.04398609325289726,
-0.07702219486236572,
-0.026400934904813766,
-0.05527535825967789,
0.0015272407326847315,
0.02924763597548008,
0.016554683446884155,
-0.039238933473825455,
0.008217970840632915,
-0.01559877023100853,
0.06201600283384323,
0.020574074238538742,
0.007921896874904633,
-0.05792328715324402,
0.03231273218989372,
-0.06361062079668045,
-0.050189998000860214,
0.012597231194376945,
0.007066548336297274,
-0.019042717292904854,
-0.043924104422330856,
0.01480951253324747,
-0.01431380957365036,
0.02846117690205574,
-0.05927537754178047,
0.024762257933616638,
-0.018802277743816376,
-0.005645175464451313,
0.01568576879799366,
-0.03459390252828598,
0.05764812231063843,
-0.014526888728141785,
-0.034547824412584305,
0.01955488696694374,
0.028346439823508263,
-0.06256324052810669,
-0.026126081123948097,
0.06263218820095062,
-0.02425011806190014,
0.026670025661587715,
-0.042651426047086716,
-0.06770650297403336,
0.06351958215236664,
0.05766179785132408,
-0.052179187536239624,
-0.007339962292462587,
0.05000898987054825,
-0.08732950687408447,
0.016151616349816322,
-0.05469333007931709,
-0.006089531816542149,
0.02346278913319111,
0.015768427401781082,
-0.006403725128620863,
0.05064121261239052,
-0.05504980310797691,
0.044825728982686996,
0.032966289669275284,
0.021999716758728027,
-0.02384079061448574,
0.061155956238508224,
0.029000284150242805,
0.022610576823353767,
-0.009095386601984501,
-0.03636559844017029,
0.028633255511522293,
0.008067728020250797,
-0.0026943001430481672,
-0.05098544806241989,
0.009752322919666767,
-0.021491339430212975,
-0.04871362820267677,
0.030392125248908997,
-0.05466841533780098,
-0.023545755073428154,
-0.026396211236715317,
0.03620591759681702,
0.00846837181597948,
-0.026404190808534622,
-0.016299080103635788,
-0.0291447713971138,
-0.01845005713403225,
0.031477924436330795,
-0.03813750669360161,
0.05420151352882385,
-0.039786383509635925,
0.0026573382783681154,
-0.02229534648358822,
0.029279524460434914,
0.04568727687001228,
-0.011968976818025112,
-0.0050545041449368,
0.004876351449638605,
0.02602999284863472,
-0.007062927819788456,
0.0960211232304573,
-0.06364276260137558,
0.015222535468637943,
-0.02121773175895214,
-0.04906415194272995,
-0.015114112757146358,
-0.012667220085859299,
0.014074227772653103,
-0.016397809609770775,
-0.007341146469116211,
0.02903207577764988,
0.04322498291730881,
-0.01460077054798603,
0.00730123883113265,
-0.00046782431309111416,
0.042907968163490295,
0.04424815997481346,
0.003430415177717805,
-0.04006751999258995,
-0.025639532133936882,
0.08610024303197861,
-0.011383590288460255,
-0.01965130865573883,
0.005518756806850433,
-0.007045691832900047,
0.006410653702914715,
-0.01973794773221016,
0.030817916616797447,
-0.06143194064497948,
-0.06979440897703171,
0.00064481032313779,
-0.019078567624092102,
0.0366666242480278,
0.0018295054323971272,
0.0733959823846817,
-0.026563778519630432,
-0.0033287631813436747,
0.03327002376317978,
-0.023548999801278114,
0.04523254558444023,
-0.023041149601340294,
0.07183283567428589,
-0.008423472754657269,
-0.01569255255162716,
-0.01940404810011387,
-0.015869056805968285,
0.006999354809522629,
0.023342326283454895,
0.00951107032597065,
0.06688319891691208,
0.09027544409036636,
0.04161734879016876,
-0.023977994918823242,
0.02901109866797924,
0.05307776853442192,
-0.01703582890331745,
0.06390295922756195,
0.049130748957395554,
-0.00294885179027915,
-0.03803163021802902,
0.024921156466007233,
0.011318673379719257,
-0.0035327745135873556,
-0.02858899161219597,
0.03123384527862072,
-0.03740554302930832,
-0.009874127805233002,
-0.07290671020746231,
-0.0353204719722271,
0.0320790633559227,
-0.03540343418717384,
-0.030637692660093307,
0.007371057756245136,
-0.012901457026600838,
0.028206510469317436,
-0.037465836852788925,
-0.06933499872684479,
0.022673610597848892,
-0.05200948193669319,
0.010732069611549377,
0.0636431947350502,
-0.0002759421768132597,
-0.005104799289256334,
0.02453906275331974,
0.0025417525321245193,
0.07840661704540253,
0.017705058678984642,
0.020289786159992218,
-0.04421847686171532,
-0.0032187141478061676,
0.02172277309000492,
-0.047380562871694565,
0.0044416156597435474,
0.03768543154001236,
0.09923560172319412,
-0.05744999647140503,
-0.028486911207437515,
-0.06800263375043869,
0.0005606709746643901,
-0.01051015593111515,
-0.08292020857334137,
0.036581799387931824,
0.07105515897274017,
0.03068387508392334,
0.0029837957117706537,
-0.049362145364284515,
0.014182783663272858,
0.030064648017287254,
0.07253530621528625,
0.02116984874010086,
0.05345099791884422,
-0.053762923926115036,
-0.0038192905485630035,
0.047821324318647385,
-0.007017231546342373,
0.0438903346657753,
-0.02111048437654972,
0.04810589179396629,
-0.001093024155125022,
-0.046770233660936356,
-0.018463315442204475,
-0.013895566575229168,
-0.006157012656331062,
-0.036563631147146225,
-0.041094180196523666,
0.005247333087027073,
-0.025776002556085587,
0.004334587138146162,
0.018822191283106804,
0.026818208396434784,
-0.012494266033172607,
-0.025310643017292023,
0.0037914372514933348,
0.05476255342364311,
0.019521966576576233,
-0.015134846791625023,
-0.06040102243423462,
0.03375901281833649,
-0.006712914444506168,
-0.03781548887491226,
-0.007338318042457104,
0.023390576243400574,
0.0005615827976725996,
-0.02294272370636463,
-0.039252400398254395,
-0.03018718585371971,
-0.012689136900007725,
-0.019525686278939247,
0.002557518659159541,
0.03776613622903824,
0.025564901530742645,
-0.03523372486233711,
-0.01744348555803299,
0.027904268354177475,
-0.0413893423974514,
0.017405197024345398,
-0.019952354952692986,
-0.03811820223927498,
0.011534711346030235,
-0.05459513142704964,
0.020335674285888672,
0.014909964054822922,
0.03360826522111893,
-0.020610472187399864,
-0.019438577815890312,
0.06447792798280716,
0.023625439032912254,
0.010055774822831154,
-0.02853994444012642,
0.05776722729206085,
0.010624146088957787,
-0.027251169085502625,
0.03192872554063797,
-0.06492062658071518,
-0.01848018728196621,
-0.030039584264159203,
-0.06500112265348434,
-0.05814192444086075,
-0.01794920302927494,
-0.01584346406161785,
0.0072234757244586945,
0.03872678801417351,
-0.021665723994374275,
-0.00573223689571023,
-0.009333182126283646,
-0.009584043174982071,
-0.03933611512184143,
-0.007116739172488451,
-0.006296920590102673,
-0.020076803863048553,
0.0035733815748244524,
0.018267374485731125,
0.021039459854364395,
-0.09565505385398865,
-0.021692592650651932,
-0.007192349061369896,
-0.0008026904542930424,
-0.07978203892707825,
-0.032897137105464935,
-0.005619863513857126,
0.031105272471904755,
0.0237980168312788,
-0.053429245948791504,
0.030325664207339287,
0.02229463681578636,
-0.041210416704416275,
0.029140140861272812,
-0.07017336040735245,
0.020036349073052406,
-0.0016389546217396855,
0.0010742421727627516,
-0.006198922637850046,
0.013217996805906296,
-0.061446886509656906,
0.04887102544307709,
-0.011771081015467644,
-0.053811460733413696,
0.02161754108965397,
0.014362731017172337,
0.0014300512848421931
] |
<p>In QFT we associate to each Gauge theory a continuous group of local transformations (a Gauge group), and then we require\define fermion fields to be irreducible representations belonging to the fundamental representation of this Gauge group.</p>
<ol>
<li><p>What is the <a href="http://en.wikipedia.org/wiki/Fundamental_representation" rel="nofollow">fundamental representation</a>, and why do we require fermions to be in it?</p></li>
<li><p>What does it mean for a field to <em>belong to a certain <a href="http://en.wikipedia.org/wiki/Group_representation" rel="nofollow">representation</a></em>? Is this just a way of stating that the fields are the "targets" of the Gauge transformations we introduced, meaning that they belong to the vector space where the representation of these transformations act?</p></li>
<li><p>A Gauge transformation must by definition not change the physics. This means that given any field $\psi$ we have to identify as a single physical entity all the fields that can be obtained by $\psi$ by means of any element of the Gauge group. Is the formalization of this concept the reason we require fields to belong to <a href="http://en.wikipedia.org/wiki/Irreducible_representation" rel="nofollow">irreducible</a> representations? Is there any other justification for it?</p></li>
</ol> | g4563 | [
0.02563885599374771,
0.01419108547270298,
-0.03314961865544319,
-0.10250627994537354,
0.10449635237455368,
0.0014916234649717808,
-0.009745858609676361,
0.05538163334131241,
-0.026018192991614342,
-0.028210191056132317,
-0.012026749551296234,
0.00980778131633997,
-0.029061561450362206,
-0.00840688031166792,
-0.02035490982234478,
0.015704285353422165,
0.03713967651128769,
0.021775798872113228,
0.07346299290657043,
-0.07577713578939438,
-0.02304946444928646,
0.05951619893312454,
0.04652692750096321,
-0.054091207683086395,
-0.031555116176605225,
0.004300308879464865,
0.1083502471446991,
-0.03810654208064079,
0.007018387783318758,
-0.01299254596233368,
0.004299364052712917,
0.0420600026845932,
0.06265239417552948,
-0.060130778700113297,
0.03485497459769249,
-0.051899783313274384,
0.06748435646295547,
0.05635479465126991,
0.024926388636231422,
-0.011867267079651356,
0.03294399753212929,
-0.00533265108242631,
-0.030528098344802856,
-0.03620333597064018,
-0.029585035517811775,
0.05196934938430786,
0.0033243352081626654,
-0.029799001291394234,
-0.05184962972998619,
0.036334916949272156,
0.032839734107255936,
-0.029006173834204674,
0.005391317419707775,
0.016480011865496635,
0.04528431221842766,
0.0013899434125050902,
0.05118218809366226,
0.017040874809026718,
0.044367630034685135,
-0.047194600105285645,
-0.023180967196822166,
0.033591680228710175,
-0.007454500533640385,
0.015063212253153324,
-0.0076450807973742485,
0.01890529692173004,
-0.03629087656736374,
0.013567132875323296,
-0.01832188479602337,
-0.020674927160143852,
-0.030325986444950104,
-0.022403044626116753,
-0.015781981870532036,
0.08001817017793655,
0.006836192216724157,
0.029555706307291985,
0.0011704955250024796,
-0.01236986555159092,
0.016400208696722984,
-0.007528713438659906,
-0.0003075401473324746,
-0.017459889873862267,
0.021298084408044815,
-0.0007224935689009726,
0.021321753039956093,
0.004890406504273415,
-0.02610964886844158,
0.00748953502625227,
0.0525338277220726,
0.011000927537679672,
-0.031193720176815987,
0.036704886704683304,
0.05468481779098511,
0.034463100135326385,
-0.0185030996799469,
0.012408865615725517,
0.00029872142476961017,
0.057935602962970734,
-0.06977994740009308,
0.005697582848370075,
-0.03522505983710289,
0.010781538672745228,
0.03631910681724548,
-0.033065877854824066,
-0.031047653406858444,
-0.006964307744055986,
0.05034278333187103,
0.026691904291510582,
0.008683741092681885,
0.01893831230700016,
-0.018641600385308266,
0.03515844792127609,
-0.03375352919101715,
0.0005993339000269771,
-0.028384167701005936,
-0.023800840601325035,
0.08380146324634552,
0.0035417815670371056,
-0.008453692309558392,
0.049446117132902145,
0.016794191673398018,
-0.012230361811816692,
0.14238829910755157,
0.026929078623652458,
-0.009462442249059677,
-0.07788096368312836,
0.0017200969159603119,
0.03070339374244213,
0.04153626412153244,
-0.03821779042482376,
-0.02807077206671238,
-0.03223423659801483,
-0.042110905051231384,
-0.0030847627203911543,
0.002840194385498762,
-0.0317377895116806,
-0.007917743176221848,
0.03663397580385208,
-0.00365998107008636,
0.056841082870960236,
-0.0028859039302915335,
0.02290240488946438,
0.001212179777212441,
-0.01842459663748741,
0.03687667101621628,
-0.05760573968291283,
0.04260138422250748,
-0.041986022144556046,
0.06025424227118492,
-0.011005209758877754,
0.01941458322107792,
0.0466851070523262,
-0.01897154375910759,
-0.047250065952539444,
0.038401082158088684,
-0.036834459751844406,
0.061946578323841095,
0.008663445711135864,
0.0070014470256865025,
-0.002368649234995246,
0.01713082753121853,
0.023740727454423904,
0.02315952070057392,
-0.023478396236896515,
-0.024924203753471375,
-0.029569195583462715,
0.02004624903202057,
-0.021926982328295708,
0.008709140121936798,
-0.02070315182209015,
-0.00781464483588934,
0.0589253194630146,
-0.021151326596736908,
0.026233453303575516,
-0.016381070017814636,
0.034210436046123505,
-0.0355130210518837,
-0.008570550009608269,
-0.014226040802896023,
-0.03216148912906647,
-0.052832819521427155,
-0.006404307205229998,
0.06944862753152847,
-0.010209726169705391,
0.0023081758990883827,
0.016387710347771645,
-0.07875900715589523,
0.03621244430541992,
-0.0623154379427433,
0.043303024023771286,
-0.021000513806939125,
-0.010347403585910797,
0.005808109417557716,
0.04105101153254509,
0.021034177392721176,
0.024531744420528412,
0.0037917322479188442,
-0.10111325979232788,
-0.04289345070719719,
-0.027987472712993622,
0.053904399275779724,
0.0069668046198785305,
0.0017901055980473757,
-0.02132001891732216,
0.04065254330635071,
0.052187200635671616,
-0.04786596819758415,
-0.03311821445822716,
0.011032961308956146,
-0.038909912109375,
-0.001965891569852829,
-0.0362677127122879,
0.04134226590394974,
0.008546287193894386,
-0.016935132443904877,
-0.049647942185401917,
-0.014809614978730679,
0.017825273796916008,
-0.042930521070957184,
0.05830024182796478,
-0.0010722295846790075,
0.004878206644207239,
0.02907112054526806,
0.012406918220221996,
-0.035472333431243896,
-0.011129293590784073,
0.018339471891522408,
0.006938715931028128,
-0.019323337823152542,
0.051207464188337326,
-0.05483139306306839,
0.020355356857180595,
-0.06234773248434067,
-0.00418698787689209,
-0.023746639490127563,
0.06092357635498047,
-0.019869599491357803,
0.013010738417506218,
0.028998617082834244,
0.0511259064078331,
0.016413578763604164,
-0.047151751816272736,
0.006556249689310789,
0.02436675876379013,
0.005591226276010275,
0.010983875021338463,
0.04132087528705597,
-0.017692619934678078,
-0.05050763115286827,
0.04722123593091965,
-0.03511007875204086,
-0.03337938338518143,
-0.03271562233567238,
0.012960580177605152,
-0.021261066198349,
-0.035959865897893906,
0.0216082651168108,
0.02053326927125454,
-0.01916925236582756,
0.032665859907865524,
0.004355788230895996,
-0.011507654562592506,
0.0036777551285922527,
0.06372598558664322,
-0.04273628816008568,
-0.016860079020261765,
0.008542743511497974,
0.062043558806180954,
-0.05444527044892311,
-0.05236072465777397,
-0.06067398935556412,
0.03354067727923393,
0.002851055935025215,
-0.0003195356111973524,
0.031195705756545067,
-0.05492740496993065,
-0.010802204720675945,
0.0022777519188821316,
-0.03099939227104187,
-0.000532467442099005,
0.006600798107683659,
-0.033559318631887436,
-0.0684499517083168,
0.0018013992812484503,
-0.032736651599407196,
-0.03406571224331856,
0.0011604215251281857,
-0.03233898803591728,
0.010914142243564129,
0.00027155171846970916,
0.043120138347148895,
0.004590827040374279,
0.008091438561677933,
0.022733768448233604,
-0.013918734155595303,
-0.006630438845604658,
-0.00010815814312081784,
-0.08495678752660751,
0.002926412969827652,
0.08333176374435425,
0.01193210482597351,
-0.021929899230599403,
-0.01452853437513113,
-0.016198432072997093,
0.08570665121078491,
-0.04650337994098663,
-0.055498044937849045,
-0.029737135395407677,
-0.09090127795934677,
-0.007326364051550627,
0.0021579416934400797,
0.017495304346084595,
-0.0012606285745278,
0.019539274275302887,
-0.0625070109963417,
0.019833052530884743,
-0.009626482613384724,
0.01589335687458515,
0.018577953800559044,
-0.05836109817028046,
-0.05382431671023369,
-0.00494815967977047,
0.055396780371665955,
0.0004952949821017683,
0.09528591483831406,
0.04677531495690346,
-0.004713079426437616,
0.01581382378935814,
0.04886571690440178,
-0.054707322269678116,
0.046333976089954376,
0.0007098388159647584,
-0.01509205624461174,
-0.0229419507086277,
-0.01914915069937706,
-0.0003818834957201034,
-0.07307467609643936,
-0.021087883040308952,
0.009064559824764729,
-0.03111276775598526,
0.000759443617425859,
-0.02120187133550644,
-0.0828666239976883,
0.03123580850660801,
0.015515961684286594,
-0.003978063818067312,
0.02392205409705639,
-0.01583698019385338,
0.0034303022548556328,
-0.01970004104077816,
-0.046613335609436035,
0.014012778177857399,
0.02991889789700508,
0.01153989601880312,
-0.02481885999441147,
-0.024627983570098877,
0.025954946875572205,
0.0007131247548386455,
-0.012562562711536884,
0.01825789175927639,
-0.019902298226952553,
-0.029906481504440308,
-0.005893034860491753,
0.014275777153670788,
-0.030221525579690933,
-0.014768284745514393,
-0.015055173076689243,
-0.007535382639616728,
0.004321154206991196,
0.01960422657430172,
0.0538332499563694,
-0.0415317639708519,
-0.06719662994146347,
0.06572256982326508,
-0.04364166408777237,
-0.05514100193977356,
0.019716843962669373,
-0.012922941707074642,
-0.05594884604215622,
-0.01460268720984459,
0.0002793150197248906,
0.03810041397809982,
0.027278169989585876,
0.01986042782664299,
0.02942984737455845,
-0.006046729627996683,
-0.01496133767068386,
0.024102864786982536,
-0.0011935833608731627,
0.052074067294597626,
-0.03237537667155266,
-0.00599519070237875,
0.025271527469158173,
0.024842731654644012,
-0.021769283339381218,
0.008468741551041603,
0.004491893108934164,
-0.03985336422920227,
0.037709735333919525,
0.04067748039960861,
0.0017098800744861364,
-0.013910332694649696,
0.011053179390728474,
-0.003016379429027438,
0.04296397417783737,
-0.008052511140704155,
-0.0017694280249997973,
-0.05497530475258827,
0.02102186717092991,
-0.055297210812568665,
-0.031663425266742706,
0.0052400315180420876,
0.022824028506875038,
-0.060727138072252274,
0.01869053952395916,
0.0047623044811189175,
-0.03838134929537773,
-0.09943623095750809,
-0.018269522115588188,
-0.04224640503525734,
0.03861279413104057,
-0.004487723112106323,
0.07298130542039871,
0.020891185849905014,
0.0371382050216198,
0.0545126348733902,
0.025197701528668404,
0.004191766493022442,
-0.02661384455859661,
-0.05679365247488022,
-0.02676544152200222,
0.05687063932418823,
0.02355862222611904,
0.004605783149600029,
-0.05175701156258583,
0.0055198995396494865,
-0.08055605739355087,
0.023819997906684875,
0.013727773912250996,
0.022754669189453125,
0.06770889461040497,
-0.04275801032781601,
-0.02472824603319168,
-0.007976625114679337,
-0.04391641169786453,
0.026009924709796906,
-0.0641195997595787,
0.04106604680418968,
-0.018213775008916855,
-0.03996642306447029,
0.0018866138998419046,
0.016009587794542313,
-0.022098766639828682,
0.009129890240728855,
0.02380560338497162,
0.0016892601270228624,
0.0009341157856397331,
-0.05999644100666046,
0.010280259884893894,
-0.03715522214770317,
-0.06297339498996735,
-0.01958896778523922,
-0.032110657542943954,
0.006317410618066788,
0.025789042934775352,
-0.01614026166498661,
-0.031570013612508774,
0.002289473544806242,
-0.025323854759335518,
-0.051686014980077744,
0.056232526898384094,
-0.045845355838537216,
-0.0030401526018977165,
-0.01959805376827717,
0.035927146673202515,
0.05797109007835388,
0.0318257212638855,
-0.0286647230386734,
-0.01664809137582779,
-0.02392365038394928,
0.01131159346550703,
-0.05180392041802406,
0.06566180288791656,
0.02977966144680977,
-0.00440503703430295,
0.016293928027153015,
-0.002294873585924506,
0.029290737584233284,
-0.014901431277394295,
-0.0055839065462350845,
-0.019039763137698174,
0.004234401974827051,
0.03244532644748688,
0.0182541161775589,
0.00658593513071537,
0.021880632266402245,
-0.011430170387029648,
-0.019760746508836746,
0.005586074199527502,
-0.018746942281723022,
-0.004520527087152004,
0.05395814776420593,
0.09146609157323837,
0.015814252197742462,
-0.016998140141367912,
0.02768181636929512,
0.10160055011510849,
0.015177898108959198,
-0.009760729968547821,
-0.01646219566464424,
0.035873476415872574,
-0.005750199314206839,
0.01583980768918991,
-0.04255477711558342,
0.032516200095415115,
0.014577358029782772,
-0.057042445987463,
-0.014416826888918877,
-0.06349437683820724,
-0.0366511270403862,
-0.006980603095144033,
0.013673179782927036,
-0.011152567341923714,
-0.0720597505569458,
0.0062577989883720875,
0.04538893699645996,
0.013040085323154926,
-0.06008356437087059,
0.006566721946001053,
0.07874057441949844,
0.02296140231192112,
-0.016455309465527534,
0.02353488840162754,
-0.030274895951151848,
0.02408706396818161,
-0.0022803745232522488,
0.07400374114513397,
-0.0001934105239342898,
0.042110733687877655,
0.006976970471441746,
-0.05622190982103348,
0.028654737398028374,
-0.0021605168003588915,
0.009629175066947937,
0.04478786140680313,
-0.004884354770183563,
0.03563748300075531,
-0.0006128308596089482,
-0.014999170787632465,
-0.043592046946287155,
0.008662303909659386,
-0.037403132766485214,
0.022113297134637833,
-0.03913058713078499,
0.01745949499309063,
-0.013909083791077137,
-0.021250931546092033,
-0.022719362750649452,
-0.006368192378431559,
-0.022418158128857613,
0.020650282502174377,
0.016155723482370377,
-0.01048305444419384,
-0.00777196791023016,
0.038017310202121735,
0.00417275819927454,
0.011588691733777523,
-0.045310959219932556,
0.08844468742609024,
0.012784088030457497,
-0.00023756468726787716,
0.015259642153978348,
0.02755737490952015,
0.0036487856414169073,
-0.06483115255832672,
-0.016551613807678223,
0.008421256206929684,
-0.033554378896951675,
-0.013079090043902397,
0.00471129734069109,
0.0030409276951104403,
-0.022832559421658516,
-0.00033737911144271493,
-0.08454693108797073,
0.024290096014738083,
0.01263661403208971,
-0.10003705322742462,
-0.039676688611507416,
0.013727053068578243,
0.024375032633543015,
0.0035202763974666595,
0.042054515331983566,
0.012403137050569057,
0.03764490410685539,
-0.017688404768705368,
0.01780962198972702,
-0.0043511707335710526,
0.02680475451052189,
-0.009821519255638123,
-0.013312301598489285,
-0.015341933816671371,
0.0259544737637043,
0.05926626920700073,
0.055672209709882736,
0.04398798942565918,
0.07431641221046448,
-0.04881799593567848,
-0.03934368118643761,
-0.002728976309299469,
0.0016417896840721369,
0.0009779171086847782,
-0.02469654381275177,
-0.02657247520983219,
-0.03300085663795471,
0.007603276055306196,
-0.022191686555743217,
-0.028558790683746338,
0.024499453604221344,
-0.02995966002345085,
0.04900019243359566,
0.017811840400099754,
-0.03811381012201309,
0.008702512830495834,
0.006996159441769123,
-0.027266962453722954,
0.09888127446174622,
-0.04858872666954994,
0.04411955550312996,
0.05519622191786766,
-0.029685737565159798,
-0.03001992776989937,
0.011928106658160686,
-0.0031999668572098017,
0.0036722004879266024,
-0.023768097162246704,
0.007876166142523289,
-0.03897544741630554,
0.010493263602256775,
0.021414637565612793,
0.02552984654903412,
-0.025677919387817383,
0.021149085834622383,
0.046916663646698,
0.0033298321068286896,
-0.05207452178001404,
-0.013793929480016232,
0.02376881241798401,
-0.02747923694550991,
-0.08979077637195587,
0.033775828778743744,
0.014339997433125973,
0.07558378577232361,
-0.018829431384801865,
-0.03423912450671196,
-0.032969389110803604,
0.0413065031170845,
-0.022028779610991478,
0.053743693977594376,
-0.03925325348973274,
-0.029529299587011337,
-0.037720657885074615,
-0.0403425469994545,
-0.0388852022588253,
0.011209331452846527,
0.012257376685738564,
0.02132410556077957,
-0.007601270452141762,
-0.037610143423080444,
0.08580197393894196,
0.0028573242016136646,
-0.005492002237588167,
-0.0015679962234571576,
0.04603259637951851,
-0.025439584627747536,
-0.022297870367765427,
-0.02684389054775238,
0.00037400826113298535,
0.10665199160575867,
0.016894856467843056,
-0.009820442646741867,
-0.07374749332666397,
0.09180906414985657,
0.04267282783985138,
-0.04416026920080185,
-0.06165486201643944,
-0.027468804270029068,
0.026941968128085136,
0.01808692142367363,
0.04613572731614113,
-0.0023692299146205187,
0.037421755492687225,
-0.03230355679988861,
0.010287578217685223,
-0.030623851343989372,
-0.020501600578427315,
0.0038539045490324497,
0.0612625814974308,
-0.014496956951916218,
0.02071521431207657,
-0.04056241735816002,
0.07924534380435944,
-0.039950769394636154,
-0.0418192595243454,
0.0071541545912623405,
0.031029222533106804,
-0.02219885028898716,
0.01670394279062748,
-0.01770278438925743,
-0.02672768570482731,
0.040108442306518555,
-0.035333406180143356,
0.04694138839840889,
0.07431437075138092,
0.034149445593357086,
0.028663190081715584,
0.030716007575392723,
0.0050120544619858265,
0.02888076938688755,
-0.032971009612083435,
-0.02316759154200554,
0.06958665698766708,
-0.008948796428740025,
-0.04181980341672897,
-0.010006089694797993,
-0.03201691433787346,
-0.0015247937990352511,
0.022355224937200546,
-0.04653998836874962,
0.03838939964771271,
-0.024759460240602493,
-0.03636204078793526,
0.024734893813729286,
-0.025911372154951096,
0.029804054647684097,
-0.05753442645072937,
0.047865480184555054,
-0.004010794218629599,
-0.03434307500720024,
-0.019311949610710144,
-0.00861423835158348,
0.021812546998262405,
-0.039446424692869186,
-0.014783523045480251,
0.05548667907714844,
-0.0450352281332016,
-0.040948137640953064,
-0.020551316440105438,
0.01346669439226389,
-0.0038653570227324963,
0.004140755161643028,
0.028896182775497437,
0.02516200579702854,
-0.005993329919874668,
0.03818511590361595,
0.023438096046447754,
-0.05502334237098694,
-0.03471308946609497,
0.03346901386976242,
0.06211600452661514,
0.012425502762198448,
0.009493126533925533,
0.0021504187025129795,
0.012884372845292091,
0.030438411980867386,
-0.0770096555352211,
-0.03790995851159096,
-0.02619936875998974,
0.0415138304233551
] |
<p>How does one see it as obvious that</p>
<p>$$\int_S \frac{\partial A_i}{\partial x^j} dS^{ji} = \int_S\frac{1}{2}(\frac{\partial A_j}{\partial x^i} - \frac{\partial A_i}{\partial x^j})dS^{ij}$$</p>
<p>where $d S^{ij} = dx^i dx^{j*} - dx^j dx^{i*} $</p>
<p>From <a href="http://books.google.ie/books?id=X18PF4oKyrUC&lpg=PP1&pg=PA22#v=onepage&q&f=false" rel="nofollow">Landau's CToF</a>.</p> | g4564 | [
0.04798082262277603,
0.06200644001364708,
-0.01965010166168213,
-0.03730640932917595,
-0.03621341288089752,
-0.02206236682832241,
0.043838370591402054,
0.03969171643257141,
-0.015712030231952667,
0.015350471250712872,
-0.04714621976017952,
0.040990885347127914,
0.04603717848658562,
-0.012177716009318829,
-0.03846970573067665,
-0.02838028222322464,
-0.00037532506394200027,
0.017728110775351524,
0.035288337618112564,
-0.023021535947918892,
-0.034318190068006516,
-0.021033555269241333,
0.038805220276117325,
-0.04376047104597092,
0.03501641005277634,
-0.004395929630845785,
0.012307695113122463,
0.017126811668276787,
-0.05345118045806885,
0.02412496507167816,
0.0024879092816263437,
0.026495961472392082,
0.05661650374531746,
-0.030339263379573822,
-0.010102462023496628,
0.005627909209579229,
0.05990920960903168,
-0.014048636890947819,
0.03042471781373024,
-0.05289078503847122,
-0.0446440652012825,
-0.02461744286119938,
-0.039721108973026276,
0.03645232319831848,
-0.009375589899718761,
0.009994055144488811,
-0.05891181901097298,
-0.008697648532688618,
-0.05921643599867821,
-0.024915866553783417,
-0.019927021116018295,
0.1022525206208229,
0.0123282540589571,
-0.024370865896344185,
-0.004409782122820616,
0.03627290576696396,
-0.01794627495110035,
-0.038044996559619904,
0.09386615455150604,
0.022018110379576683,
0.005130194127559662,
0.011628507636487484,
0.014505122788250446,
0.02393743023276329,
0.01058375183492899,
-0.01813550293445587,
0.031708408147096634,
-0.05765576288104057,
0.007558270823210478,
-0.020778844133019447,
0.005018739961087704,
-0.014450791291892529,
0.052010126411914825,
-0.03294504061341286,
-0.038837771862745285,
-0.007391848601400852,
0.056199394166469574,
-0.0008733276044949889,
0.01793358474969864,
-0.008165981620550156,
0.030098386108875275,
-0.05912978947162628,
0.0407966747879982,
-0.016787877306342125,
0.027464138343930244,
-0.004384123720228672,
0.0256660059094429,
0.016986722126603127,
0.004950738977640867,
0.06350149214267731,
-0.07394268363714218,
0.001996082253754139,
-0.030959146097302437,
0.03910309821367264,
0.016087466850876808,
-0.01966262049973011,
-0.003885004436597228,
0.04045666381716728,
-0.014586657285690308,
-0.04000123217701912,
0.009851512499153614,
0.0485772043466568,
0.023165326565504074,
0.0355948731303215,
-0.060879383236169815,
0.015708833932876587,
-0.02696225605905056,
-0.01846308261156082,
0.030391324311494827,
-0.053186386823654175,
-0.018564658239483833,
0.03197184205055237,
-0.052479419857263565,
-0.04640970379114151,
0.010800287127494812,
-0.010595767758786678,
-0.024398257955908775,
-0.023031696677207947,
-0.07177355885505676,
-0.010689637623727322,
0.007777179125696421,
-0.0635315552353859,
0.061754122376441956,
0.04068100452423096,
0.03884216398000717,
0.0424887090921402,
-0.012891444377601147,
0.030996648594737053,
0.056917060166597366,
-0.0009264869149774313,
-0.07878025621175766,
-0.002788042649626732,
0.04834117367863655,
0.0159017164260149,
0.028437260538339615,
0.02049063891172409,
-0.02093455009162426,
0.02094689942896366,
-0.03617557883262634,
0.011876014992594719,
-0.006735535338521004,
0.011848930269479752,
-0.055290043354034424,
-0.04440317675471306,
0.015277842991054058,
0.0013836491852998734,
-0.037681445479393005,
-0.022267287597060204,
-0.009673445485532284,
0.008964300155639648,
0.0061079273000359535,
0.05587827414274216,
-0.021645784378051758,
-0.022452088072896004,
-0.037461377680301666,
0.036472078412771225,
0.07377459853887558,
-0.00390610215254128,
-0.016500450670719147,
-0.04118214547634125,
0.00658708019182086,
0.016863828524947166,
0.0020140090491622686,
0.04788989573717117,
-0.04586614668369293,
-0.002002166584134102,
0.06290245801210403,
-0.04725795239210129,
-0.007188485004007816,
0.0088137062266469,
-0.018357159569859505,
-0.0012045159237459302,
0.04301545396447182,
0.03426734358072281,
-0.010389314964413643,
0.03538195416331291,
-0.015509149059653282,
-0.01333322748541832,
0.06848157942295074,
0.02533734031021595,
0.03753237426280975,
0.0005309124826453626,
-0.05720432475209236,
-0.0032649654895067215,
-0.018677212297916412,
-0.006997368764132261,
-0.010080238804221153,
0.039000462740659714,
-0.009641396813094616,
0.004906428046524525,
0.008890409022569656,
0.008870583027601242,
0.022238198667764664,
0.05337949097156525,
0.04338183254003525,
-0.026930563151836395,
-0.011116387322545052,
-0.024371935054659843,
-0.04508756846189499,
-0.015205617994070053,
0.006287324707955122,
0.007861737161874771,
0.03991683945059776,
-0.011432153172791004,
0.010509699583053589,
0.0009228477138094604,
-0.0025777658447623253,
-0.01627192273736,
0.00039820701931603253,
0.041339483112096786,
-0.02758626639842987,
-0.03619803860783577,
-0.011842606589198112,
0.0358784981071949,
-0.002655188087373972,
-0.014072819612920284,
-0.03241229057312012,
-0.03976210579276085,
-0.025454076007008553,
0.030133388936519623,
-0.04496462643146515,
-0.009203008376061916,
0.027420736849308014,
0.01371886394917965,
-0.017385762184858322,
0.016952216625213623,
0.01210090983659029,
0.02473677322268486,
-0.027334310114383698,
-0.002089480869472027,
-0.06056147441267967,
-0.08521348983049393,
-0.041635166853666306,
0.05970059335231781,
0.046441297978162766,
0.007089797407388687,
-0.03527672961354256,
-0.028647596016526222,
0.050523992627859116,
0.06848561018705368,
-0.03461238369345665,
-0.036548759788274765,
-0.031962208449840546,
-0.0029548811726272106,
0.014883790165185928,
0.02532566711306572,
0.019171422347426414,
0.002071149181574583,
0.01843361370265484,
-0.0026719027664512396,
-0.039786409586668015,
-0.025631133466959,
0.005709948483854532,
0.016956953331828117,
0.011519190855324268,
-0.0336601622402668,
0.01696246676146984,
-0.0012343249982222915,
0.04296281561255455,
-0.004609989933669567,
-0.004492579959332943,
-0.05088460445404053,
-0.012241525575518608,
0.020627237856388092,
-0.09565455466508865,
0.0041189719922840595,
0.054428670555353165,
-0.03679470717906952,
-0.00012326784781180322,
-0.011329195462167263,
0.0390937365591526,
0.06400902569293976,
-0.00931454822421074,
0.04227575287222862,
-0.030865482985973358,
-0.013477387838065624,
0.007146175485104322,
-0.042412105947732925,
-0.024234281852841377,
-0.012253263965249062,
0.009245923720300198,
0.01464136503636837,
-0.02989531122148037,
0.05487445369362831,
0.054163165390491486,
-0.04922438785433769,
-0.022420428693294525,
0.0650273934006691,
-0.03144355118274689,
0.03330378606915474,
0.010235369205474854,
0.056568704545497894,
-0.030695360153913498,
0.009602680802345276,
-0.028582757338881493,
-0.03329525515437126,
0.013773526065051556,
-0.029758576303720474,
0.011480809189379215,
0.08170672506093979,
0.044192273169755936,
0.01251626294106245,
-0.00027837351080961525,
0.014845848083496094,
0.01578289456665516,
-0.015043225139379501,
0.05084656924009323,
0.00420400220900774,
-0.008303032256662846,
-0.06308946013450623,
0.06674645096063614,
0.02256927825510502,
0.04807915538549423,
-0.01824791356921196,
-0.03511190786957741,
-0.02136172167956829,
0.001678995555266738,
-0.021502545103430748,
-0.009221699088811874,
-0.011503823101520538,
0.0055914586409926414,
-0.0208292119204998,
-0.019907990470528603,
0.008663591928780079,
0.053357381373643875,
-0.035895947366952896,
-0.06431504338979721,
0.034661777317523956,
-0.054876264184713364,
-0.006920553743839264,
0.013321517035365105,
-0.00852748192846775,
0.0041412608698010445,
-0.031633589416742325,
-0.07384955137968063,
-0.05651053413748741,
-0.054697416722774506,
0.07237061858177185,
0.047386109828948975,
0.02244734764099121,
-0.03566230088472366,
0.03459290415048599,
-0.036363035440444946,
0.05681620165705681,
-0.013080848380923271,
-0.03262259066104889,
0.007884648628532887,
0.06932173669338226,
0.001430507400073111,
-0.006145486608147621,
-0.02936019003391266,
0.03964530676603317,
0.030884338542819023,
0.009254198521375656,
-0.046521496027708054,
0.04184048995375633,
0.05803119018673897,
0.06401793658733368,
-0.006069576367735863,
0.012045115232467651,
0.08941097557544708,
-0.041251085698604584,
-0.01352077629417181,
0.00430340925231576,
0.022655615583062172,
-0.027091048657894135,
-0.02935185842216015,
0.027445292100310326,
-0.01992075890302658,
-0.0020329102408140898,
-0.028714582324028015,
-0.02453319914638996,
0.06256429105997086,
0.03646358102560043,
0.016936754807829857,
-0.09876649081707001,
-0.0807534009218216,
0.016333332285284996,
0.05843402072787285,
-0.006229176186025143,
0.05484748259186745,
0.041491590440273285,
0.0247682835906744,
-0.05742371082305908,
-0.0018041032599285245,
0.011779773980379105,
-0.04615608975291252,
-0.010765126906335354,
0.007542810402810574,
-0.04400336742401123,
0.030954908579587936,
0.012646102346479893,
-0.0640501156449318,
0.01105333212763071,
-0.03201855719089508,
0.04407399147748947,
-0.015891075134277344,
0.02874615229666233,
-0.08141735941171646,
0.0407731868326664,
-0.013794679194688797,
-0.03224632516503334,
-0.01717035099864006,
-0.046418771147727966,
0.01883815787732601,
0.006389321759343147,
0.053590983152389526,
-0.047609563916921616,
0.08798813074827194,
-0.03329891711473465,
-0.047561921179294586,
-0.048958711326122284,
0.02372223697602749,
-0.049911390990018845,
-0.038651756942272186,
0.03869004175066948,
0.021782295778393745,
-0.039600569754838943,
0.05538921803236008,
-0.03500215336680412,
0.02444363757967949,
0.013493699952960014,
-0.02383258566260338,
-0.026350999251008034,
-0.00041116485954262316,
0.0833650752902031,
0.01623021438717842,
-0.0028038800228387117,
-0.02655738778412342,
-0.004251027945429087,
-0.03672432526946068,
0.066901296377182,
-0.04779940843582153,
0.00630586314946413,
-0.07026489078998566,
0.03293899819254875,
0.005892822984606028,
0.049270547926425934,
-0.040617700666189194,
0.08863049000501633,
0.005486994981765747,
-0.0018341708928346634,
-0.017708567902445793,
-0.028220372274518013,
0.05124334245920181,
0.00829364825040102,
0.01415774691849947,
-0.028611907735466957,
-0.0034049577079713345,
-0.0465831458568573,
-0.03927285969257355,
0.027762824669480324,
0.002145296661183238,
-0.024940358474850655,
0.07623939216136932,
-0.025627681985497475,
-0.08107072860002518,
0.01287097204476595,
0.001245104125700891,
-0.012843865901231766,
-0.015212452970445156,
-0.021440526470541954,
-0.01873672381043434,
-0.0038217841647565365,
0.03837708756327629,
0.051136504858732224,
-0.011749956756830215,
-0.037747275084257126,
-0.02130064368247986,
-0.026871241629123688,
0.05797526240348816,
0.024900170043110847,
-0.03911209478974342,
-0.044909968972206116,
0.0678168386220932,
-0.023005040362477303,
-0.023242659866809845,
-0.01168014295399189,
0.006020271219313145,
-0.005306823644787073,
0.04131852090358734,
0.039151351898908615,
-0.00018775211356114596,
-0.011707074008882046,
0.00610164413228631,
0.03476771339774132,
-0.013928410597145557,
-0.03781663998961449,
-0.04453491047024727,
-0.04889427870512009,
0.08611040562391281,
-0.010157808661460876,
-0.00592420157045126,
0.010019714944064617,
-0.035590872168540955,
0.03243635222315788,
0.04971807450056076,
-0.011752787977457047,
-0.02439896948635578,
0.021683432161808014,
-0.058088257908821106,
-0.0655905082821846,
0.03458426892757416,
0.036398086696863174,
-0.021201390773057938,
0.07755783945322037,
0.06976111233234406,
-0.030458219349384308,
0.009344984777271748,
0.03746924176812172,
0.013124706223607063,
-0.02163294143974781,
0.010712998919188976,
-0.025415074080228806,
0.08203571289777756,
0.021003643050789833,
-0.014885627664625645,
-0.018559642136096954,
-0.03167298436164856,
-0.09125916659832001,
0.08316484838724136,
0.010480417869985104,
-0.0013608575100079179,
0.007963796146214008,
-0.0033027473837137222,
-0.007816316559910774,
-0.06344766169786453,
-0.0864860936999321,
-0.0044318679720163345,
0.03043435513973236,
-0.04579203203320503,
-0.056544434279203415,
-0.001275558490306139,
-0.006673133000731468,
0.019993271678686142,
0.018230443820357323,
-0.02919170632958412,
0.010075454600155354,
0.041233453899621964,
0.008448311127722263,
0.003502350300550461,
0.03179699555039406,
-0.0035503532271832228,
0.005439735017716885,
-0.05966353788971901,
0.015481854788959026,
0.026618480682373047,
0.01873704046010971,
0.04605976119637489,
-0.07294317334890366,
-0.004169305320829153,
0.008970197290182114,
-0.037221163511276245,
-0.024954967200756073,
0.07113342732191086,
0.0003568563552107662,
-0.0031444670166820288,
0.007048831786960363,
0.008145703934133053,
-0.010430867783725262,
-0.006185723934322596,
0.01878892071545124,
-0.0584225170314312,
-0.03621769696474075,
-0.004062195774167776,
-0.07526175677776337,
0.01707117259502411,
0.05320775508880615,
0.048172321170568466,
-0.025048283860087395,
-0.01595231331884861,
0.0022813589312136173,
0.024452926591038704,
0.002808107528835535,
-0.006363634020090103,
0.08443329483270645,
-0.05575750023126602,
-0.05528634786605835,
0.020563919097185135,
-0.05223485827445984,
-0.03323278948664665,
0.00219413498416543,
0.07649193704128265,
0.002922558458521962,
-0.015930598601698875,
-0.005053457338362932,
-0.039940863847732544,
-0.013095364905893803,
0.029028940945863724,
0.10813970118761063,
-0.05086982995271683,
-0.00478695472702384,
-0.04751291498541832,
-0.039148859679698944,
-0.0023894370533525944,
-0.04742412641644478,
-0.00007891566201578826,
0.05559145286679268,
0.023863213136792183,
0.0201158057898283,
-0.0009906635386869311,
0.005114855244755745,
0.031655605882406235,
0.025760384276509285,
0.03907664865255356,
0.007602513302117586,
-0.020969804376363754,
0.012642971239984035,
-0.026391692459583282,
0.061494164168834686,
-0.03710987791419029,
0.033982180058956146,
0.006110860500484705,
0.05619310215115547,
0.020154383033514023,
-0.04525589570403099,
0.008516518399119377,
0.021580668166279793,
0.02600696124136448,
-0.04887458309531212,
0.03414662554860115,
-0.013509942218661308,
-0.03337549790740013,
0.0005542926373891532,
0.01922939345240593,
0.04228951409459114,
0.019668003544211388,
-0.014585171826183796,
0.03626124560832977,
0.03509095683693886,
-0.005419529974460602,
-0.007961916737258434,
-0.028624961152672768,
0.006275181658565998,
-0.01929129846394062,
0.015740079805254936,
-0.041749391704797745,
0.06533950567245483,
0.05232987552881241,
0.05217490345239639,
-0.04738568514585495,
0.008356846868991852,
0.00851726345717907,
-0.019916050136089325,
-0.05124034732580185,
-0.015317508950829506,
-0.003031723201274872,
-0.0060067796148359776,
-0.12044022977352142,
0.022011684253811836,
0.05751644819974899,
0.031890131533145905,
-0.00013095860776957124,
-0.034886572510004044,
-0.021113479509949684,
-0.04162004962563515,
0.054019734263420105,
-0.04424247890710831,
0.055467039346694946,
-0.07994603365659714,
-0.030589910224080086,
0.00890295673161745,
0.0038154483772814274,
0.00044188270112499595,
-0.029674788936972618,
0.02092411369085312,
0.03677583485841751,
-0.028437331318855286,
0.008344560861587524,
-0.057131391018629074,
-0.004399517551064491,
0.004449580330401659,
0.019819993525743484,
0.04250474274158478,
0.019093066453933716,
0.019007163122296333,
0.004106592386960983,
0.023688044399023056,
-0.007708885706961155,
0.031988393515348434,
0.03371894732117653,
0.03534853085875511,
0.019394956529140472,
-0.03559640422463417,
-0.03228642791509628,
0.015188108198344707,
0.005115777254104614,
-0.07942312955856323,
0.02248738519847393,
0.04570349305868149,
0.025201914831995964,
0.012414054945111275,
0.06329721957445145,
0.005295003764331341,
-0.0056018587201833725,
0.008796744979918003,
0.03083176165819168,
0.010035323910415173,
0.0036521153524518013,
0.09803802520036697,
0.0034923870116472244,
0.00961831584572792,
0.006212787237018347,
0.0029366915114223957,
0.0028547965921461582,
0.0301810409873724,
0.05467650294303894,
-0.0007263731095008552,
-0.009269101545214653,
-0.060257017612457275,
0.03803027421236038,
-0.01901857554912567,
-0.029701000079512596,
-0.009452234022319317,
0.02087262272834778,
-0.010891369543969631,
-0.015629295259714127,
0.028840981423854828,
0.006633758544921875,
-0.02623806707561016,
0.02150176838040352,
-0.04065367579460144,
-0.007097224239259958,
-0.05518722161650658,
-0.030167976394295692,
-0.03218041732907295,
-0.0009291694732382894,
0.014660857617855072,
-0.043194662779569626,
0.037504784762859344,
-0.051238518208265305,
0.04114338383078575,
-0.010699606500566006,
-0.00006593116995645687,
-0.03480071946978569,
0.010095293633639812,
0.02900821901857853,
-0.06446826457977295,
-0.032197657972574234,
0.06570655852556229,
-0.020978618413209915,
0.002888073679059744,
-0.027306953445076942,
-0.031603384763002396,
-0.036728668957948685,
-0.023297585546970367,
-0.04669513553380966,
-0.0034084084909409285,
0.028224455192685127,
-0.027760600671172142,
0.0007633171044290066,
-0.02474016137421131,
0.004625970963388681,
-0.002745900070294738,
0.0356990322470665,
-0.0019691395573318005,
0.015899846330285072,
0.05369805917143822,
0.009564968757331371,
-0.01318529061973095,
-0.03244219347834587,
-0.002399189630523324,
-0.07350623607635498,
0.047917261719703674,
-0.018811946734786034,
-0.07417043298482895,
-0.012174248695373535,
-0.01961175911128521
] |
<p>Suppose you have an 1-dimensional system with a charge distribution $\rho(x)$ (not given) moving with an speed $v(x)$ (not given), calculate the potential $\phi(x)$ and the charge distribution $\rho(x)$ in the quasistatic limit $\frac{d}{dt}=0$. </p>
<p>Hints:</p>
<p>$\frac{d^{2} \phi}{dx^{2}}=-\rho/ \varepsilon_{0}$ (Poisson equation)</p>
<p>$j=\rho v$</p>
<p>$\frac{d}{dx}(\rho v)=0$ (Continuity equation)</p>
<p>$\frac{1}{2} mv^{2}=q\phi$(Energy Conservation)</p>
<p>My attempt for solving it was:
From the energy conservation equation we get that
$$\frac{1}{v}=\sqrt{\frac{m}{2q}} \phi^{-1/2}$$
Continuity equation tells us that $j$ is constant, then
$$ \rho = \frac{j}{v}=j\sqrt{\frac{m}{2q}} \phi^{-1/2}$$
Using Laplace equation
$$-\varepsilon_{0}\frac{d^{2} \phi}{dx^{2}}=j\sqrt{\frac{m}{2q}} \phi^{-1/2}$$
Then
$$\frac{d^{2} \phi}{dx^{2}}+\frac{j}{\varepsilon_{0}}\sqrt{\frac{m}{2q}} \phi^{-1/2}=0$$
This is just an equation of the form
$$ f^{\prime\prime}+kf^{-1/2}=0$$
Multiplying by $f^{\prime}$ and integrating
$$ \int f^{\prime}f^{\prime\prime}dx+k\int f^{\prime}f^{-1/2}dx=0$$
$$ \frac{1}{2}(f^{\prime})^2+2k\sqrt{f}=0$$
$$ (f^{\prime})^2=-4k\sqrt{f}$$
$$ f^{\prime}=\sqrt{-4k} f^{1/4}$$
And here is my problem, i have the $\sqrt{-4k}$ term that in general is not real!
$$ \frac{df}{f^{1/4}}=\sqrt{-4k}dx $$
$$ \frac{4}{3} f^{3/4}=\sqrt{-4k}x +C $$
$$ f={\frac{3}{4}[\sqrt{-4k}x +C]}^{4/3} $$</p> | g4565 | [
0.029719533398747444,
0.05529015511274338,
-0.019830036908388138,
-0.0020126765593886375,
0.043160974979400635,
0.003017827169969678,
-0.0012138830497860909,
-0.035697951912879944,
0.008932861499488354,
0.015017305500805378,
-0.036195747554302216,
0.021935556083917618,
-0.05777975916862488,
0.039671048521995544,
-0.004902427550405264,
0.02869519591331482,
0.07069016993045807,
-0.017796024680137634,
-0.032126687467098236,
-0.006833668798208237,
-0.0638812780380249,
-0.052201248705387115,
0.03184955194592476,
0.012756255455315113,
0.02046627178788185,
0.040085285902023315,
0.007914677262306213,
0.0028611277230083942,
-0.04443780332803726,
-0.042353056371212006,
0.0007360898307524621,
-0.0058005452156066895,
-0.0282873697578907,
-0.017867909744381905,
-0.03247379511594772,
-0.013681227341294289,
0.0908505916595459,
-0.04883313924074173,
0.04679717868566513,
-0.055959053337574005,
-0.02903035655617714,
-0.08067663013935089,
0.06348781287670135,
0.020195510238409042,
0.002890064148232341,
-0.006511398125439882,
-0.03948405757546425,
-0.022086527198553085,
-0.04539922624826431,
0.035623371601104736,
0.04179608076810837,
0.07882630079984665,
0.04558958858251572,
0.012243824079632759,
-0.014679738320410252,
0.006535849068313837,
0.020917488262057304,
-0.029883911833167076,
-0.04032076150178909,
0.038354936987161636,
0.004469738807529211,
0.010787022300064564,
0.021137608215212822,
-0.006625975016504526,
0.07854664325714111,
-0.04174011945724487,
-0.057117924094200134,
-0.02055330015718937,
0.04168951138854027,
-0.003912055864930153,
0.030064387246966362,
-0.024784456938505173,
-0.028407664969563484,
-0.014737414196133614,
0.018254024907946587,
0.010239395312964916,
0.046135369688272476,
-0.029752230271697044,
0.012566187418997288,
-0.03335847705602646,
-0.03408884257078171,
-0.008233960717916489,
0.06564061343669891,
0.004576328210532665,
0.06097158417105675,
-0.008047862909734249,
0.009841463528573513,
0.015927819535136223,
0.000604988366831094,
-0.01460869237780571,
-0.0626874566078186,
0.009701933711767197,
-0.029981203377246857,
-0.0010473940055817366,
0.012491538189351559,
0.005944167263805866,
-0.019231801852583885,
0.04792436584830284,
-0.02271614596247673,
-0.058420490473508835,
0.008801241405308247,
0.017510442063212395,
-0.017933551222085953,
0.014273503795266151,
0.005838376935571432,
-0.015157136134803295,
-0.020167673006653786,
0.03285492584109306,
0.012866637669503689,
-0.006509703118354082,
0.03394690155982971,
-0.04016002640128136,
-0.013849574141204357,
-0.06233769282698631,
0.0001767642970662564,
-0.015423201024532318,
0.03960249572992325,
-0.04000994190573692,
-0.0452299602329731,
-0.0030203720089048147,
-0.025414807721972466,
0.022150546312332153,
0.040561433881521225,
0.06738079339265823,
0.018049731850624084,
-0.0051155732944607735,
-0.004307406954467297,
0.004930512979626656,
-0.004230549093335867,
0.005941901355981827,
-0.06032661721110344,
-0.03138703480362892,
0.07921706885099411,
0.0021487309131771326,
-0.0453219935297966,
0.03867880627512932,
-0.018510727211833,
0.03514181077480316,
0.03164342790842056,
-0.026411959901452065,
0.010150723159313202,
-0.03389551863074303,
0.0030796362552791834,
-0.019643738865852356,
-0.04084911197423935,
-0.023772643879055977,
-0.0032701001036912203,
-0.04867167770862579,
-0.025344213470816612,
-0.001983975525945425,
0.01002613827586174,
0.05764821916818619,
-0.05918916314840317,
0.033365070819854736,
0.0128121767193079,
0.005472865886986256,
0.028214849531650543,
0.025359617546200752,
-0.00198264024220407,
-0.014088836498558521,
-0.005763151682913303,
0.04894866794347763,
-0.005998330656439066,
0.016849854961037636,
-0.00800550077110529,
-0.009963786229491234,
0.023626936599612236,
-0.012900881469249725,
0.017344916239380836,
-0.042703866958618164,
-0.0014217711286619306,
-0.019035683944821358,
0.04543767124414444,
0.03583693504333496,
0.015591752715408802,
-0.043896544724702835,
0.0009343646815977991,
-0.020300932228565216,
0.014799725264310837,
-0.011821999214589596,
0.021370498463511467,
-0.007074800319969654,
0.03865787759423256,
-0.028473764657974243,
-0.057346828281879425,
0.03446495160460472,
-0.03854828327894211,
0.07215174287557602,
0.012621568515896797,
0.000605548731982708,
-0.04215314984321594,
-0.0006514216656796634,
-0.021373523399233818,
0.03105061501264572,
-0.04434993863105774,
0.029810719192028046,
0.0016127793351188302,
-0.028601450845599174,
-0.021646099165081978,
-0.02990902215242386,
-0.004431186709553003,
0.003746005706489086,
0.0767660066485405,
-0.012061034329235554,
0.11721035838127136,
-0.07293340563774109,
0.004494799766689539,
-0.04201024770736694,
0.07405106723308563,
0.010437347926199436,
-0.02632172591984272,
-0.07625488936901093,
-0.04070476442575455,
0.07517138868570328,
0.05641971528530121,
-0.07690417766571045,
0.008904414251446724,
-0.003554452210664749,
-0.04131041839718819,
0.019802583381533623,
-0.08814418315887451,
0.020453887060284615,
0.023343902081251144,
0.012555461376905441,
-0.042937032878398895,
0.03275702893733978,
0.0059168413281440735,
0.008680032566189766,
-0.06913606822490692,
0.03169482201337814,
-0.00521473353728652,
0.0000186108718480682,
-0.014986362308263779,
0.02498702146112919,
0.03056483156979084,
0.019028769806027412,
-0.05655674636363983,
-0.0026845396496355534,
-0.007955549284815788,
-0.021303558722138405,
-0.039265453815460205,
0.024732176214456558,
0.027532733976840973,
0.030818862840533257,
0.05575431138277054,
0.06058966740965843,
0.02823958545923233,
-0.010937146842479706,
0.027379289269447327,
0.015144150704145432,
0.07754549384117126,
0.020220786333084106,
0.010248423554003239,
-0.03452407568693161,
0.01188301295042038,
-0.045033566653728485,
-0.019506098702549934,
0.011941594071686268,
0.03072967380285263,
-0.03793801739811897,
-0.05267607420682907,
0.06660563498735428,
-0.05895928293466568,
-0.01988976262509823,
-0.010610558092594147,
0.021734213456511497,
-0.017384668812155724,
0.06710349023342133,
0.04763539880514145,
0.005238895770162344,
0.01991875469684601,
0.03680039197206497,
0.012468098662793636,
0.04036734625697136,
0.0024417375680059195,
-0.03824847564101219,
0.0011468470329418778,
-0.06833542883396149,
0.027903418987989426,
-0.015272397547960281,
-0.0023989686742424965,
-0.03869437426328659,
0.027872363105416298,
0.04211375489830971,
0.013749429024755955,
-0.0612170584499836,
0.07779008895158768,
0.026259563863277435,
0.004097932018339634,
-0.011736479587852955,
-0.020093154162168503,
0.024618523195385933,
0.03512885421514511,
-0.0051128980703651905,
-0.033046696335077286,
0.0749225988984108,
0.033408209681510925,
-0.08405939489603043,
0.029979098588228226,
-0.003835587529465556,
0.04025372862815857,
-0.038708120584487915,
-0.007767885457724333,
0.08038126677274704,
0.057525940239429474,
0.02604445070028305,
-0.01600082404911518,
-0.014030908234417439,
0.05105806142091751,
-0.01667228899896145,
0.03618312627077103,
0.03345964103937149,
0.027115989476442337,
0.019618472084403038,
-0.0486062727868557,
0.013888118788599968,
0.034402765333652496,
-0.03520222380757332,
-0.010199054144322872,
-0.010556817054748535,
0.013280599378049374,
-0.03783813491463661,
-0.016275273635983467,
0.00801308173686266,
-0.002881945576518774,
0.07888779789209366,
-0.08349921554327011,
0.00578926969319582,
0.015760373324155807,
0.013506350107491016,
0.016987551003694534,
0.04245825111865997,
0.08101890236139297,
-0.05176175385713577,
-0.06380306929349899,
-0.03196173533797264,
-0.021782971918582916,
0.05542841926217079,
0.051935791969299316,
-0.042382676154375076,
-0.05023302510380745,
0.031230736523866653,
-0.02192103862762451,
0.025953277945518494,
-0.03597303852438927,
-0.034865718334913254,
-0.006647246424108744,
0.03144292160868645,
-0.01351935788989067,
-0.0014430648880079389,
0.01076684519648552,
0.023662494495511055,
0.06285729259252548,
0.02346799336373806,
-0.04848175495862961,
0.019008982926607132,
-0.01205525454133749,
0.042047228664159775,
-0.05224717780947685,
0.008087190799415112,
0.012156021781265736,
-0.06633983552455902,
0.0099174864590168,
0.03321400657296181,
0.029566314071416855,
-0.005106078460812569,
0.008912468329071999,
-0.008528475649654865,
-0.009820505976676941,
-0.033496737480163574,
0.025509405881166458,
0.013707748614251614,
0.026653962209820747,
0.06723286956548691,
-0.011026953347027302,
-0.016982560977339745,
-0.026867400854825974,
-0.052075378596782684,
-0.05307355895638466,
-0.010250401683151722,
0.035505495965480804,
-0.009374353103339672,
0.04126446694135666,
0.017508497461676598,
0.03903606906533241,
0.013093479909002781,
0.0028817851562052965,
-0.031401313841342926,
0.03311443328857422,
-0.020911281928420067,
0.03660774603486061,
-0.020902294665575027,
-0.027979491278529167,
0.038280609995126724,
-0.018546678125858307,
-0.022755570709705353,
0.03251958638429642,
-0.0328415222465992,
-0.06415916979312897,
-0.013620720244944096,
-0.014000673778355122,
-0.05962004140019417,
0.0011016435455530882,
-0.041845809668302536,
0.008210941217839718,
-0.0014207207132130861,
0.003924306482076645,
-0.011373763903975487,
0.018206460401415825,
-0.013728073798120022,
-0.023005204275250435,
-0.0467572845518589,
0.05615069344639778,
-0.020940938964486122,
-0.02748042531311512,
-0.048938408493995667,
-0.005233380943536758,
0.04024334251880646,
-0.00013680050324182957,
-0.0008328358526341617,
0.0410107783973217,
0.004088446963578463,
0.01748342253267765,
0.012224800884723663,
0.028395410627126694,
-0.011015409603714943,
0.054952073842287064,
-0.004931456875056028,
-0.013788048177957535,
-0.021401578560471535,
-0.0014399413485080004,
0.03602954000234604,
-0.001612387364730239,
-0.006061298307031393,
-0.030795477330684662,
0.0547136627137661,
-0.05503387004137039,
-0.019034940749406815,
-0.042302731424570084,
0.06252383440732956,
0.018157243728637695,
0.055007610470056534,
0.022916749119758606,
0.004713360220193863,
0.025117043405771255,
0.04716799035668373,
0.015355588868260384,
-0.048040978610515594,
0.020662199705839157,
-0.028726670891046524,
-0.023731786757707596,
0.018095219507813454,
0.01327000092715025,
-0.004212100524455309,
0.0706334263086319,
-0.052318770438432693,
-0.09498082846403122,
-0.03635672852396965,
0.015684854239225388,
0.03291749954223633,
-0.04090644419193268,
0.0457148402929306,
0.04290324077010155,
-0.004251347854733467,
0.009537635371088982,
-0.03527273237705231,
-0.04261159896850586,
-0.004749849904328585,
-0.03677188977599144,
-0.061622150242328644,
-0.0036194752901792526,
0.014444801025092602,
0.04464910179376602,
-0.01059227716177702,
0.012701139785349369,
-0.03365803882479668,
-0.007000155746936798,
0.03221413120627403,
0.022600475698709488,
-0.027802960947155952,
0.043535176664590836,
0.0366988405585289,
-0.02877025492489338,
0.03007376566529274,
0.030363667756319046,
0.016834260895848274,
-0.019513864070177078,
-0.0026505200657993555,
-0.019985122606158257,
-0.016575505957007408,
0.02961749956011772,
0.021629702299833298,
-0.01854660175740719,
0.04602230712771416,
0.05275198817253113,
0.04930752143263817,
0.036595817655324936,
0.004261529538780451,
-0.007885494269430637,
0.03273174539208412,
-0.027090707793831825,
-0.0545785017311573,
-0.023938817903399467,
-0.003892487147822976,
0.047666896134614944,
0.07377759367227554,
0.06663218140602112,
-0.028270332142710686,
0.015668626874685287,
0.02655818685889244,
-0.001037153648212552,
0.05264796316623688,
0.08882385492324829,
-0.010541588068008423,
0.0032734479755163193,
-0.01897905021905899,
-0.0466199591755867,
0.03949231281876564,
-0.001124704722315073,
-0.06996723264455795,
0.074886754155159,
-0.003976522013545036,
0.01563907228410244,
0.01038977038115263,
0.01945538818836212,
-0.02708416059613228,
-0.0450018048286438,
-0.10733943432569504,
-0.023006431758403778,
0.059291813522577286,
-0.010913163423538208,
-0.05316353961825371,
-0.05123964697122574,
-0.03571835905313492,
-0.05196971446275711,
0.02409364841878414,
-0.04466316103935242,
-0.03783723711967468,
0.020678158849477768,
-0.03477868437767029,
0.000003122116368103889,
-0.037092722952365875,
-0.002172484528273344,
0.004982694983482361,
-0.07974006235599518,
0.04340852424502373,
-0.07496563345193863,
-0.020353879779577255,
-0.006082573905587196,
-0.07314789295196533,
0.0613476000726223,
0.003209327580407262,
-0.059526268392801285,
-0.08734074234962463,
0.037840649485588074,
-0.008250832557678223,
0.03520086407661438,
-0.00865991972386837,
-0.028218965977430344,
0.03504965826869011,
-0.011898152530193329,
-0.00610846234485507,
0.01383152138441801,
0.028695963323116302,
0.0018339876551181078,
-0.05830400809645653,
0.04921635240316391,
0.013900414109230042,
0.0331416055560112,
0.04475611075758934,
-0.019916821271181107,
0.059109922498464584,
-0.005395379848778248,
-0.011479242704808712,
0.0654095932841301,
-0.039683714509010315,
0.008509577251970768,
-0.0547260120511055,
-0.07331221550703049,
-0.009983261115849018,
-0.056002575904130936,
0.02266325056552887,
0.05075101926922798,
0.0006467612693086267,
-0.014997901394963264,
0.061130404472351074,
0.026847949251532555,
-0.05769140645861626,
0.016443749889731407,
-0.02814161218702793,
0.019814137369394302,
-0.002673806855455041,
-0.014034764841198921,
-0.03126741945743561,
-0.060348909348249435,
-0.026347137987613678,
0.033750735223293304,
-0.04534224420785904,
-0.0446702279150486,
0.058341190218925476,
0.018856529146432877,
0.018939057365059853,
-0.0361308716237545,
-0.03568932041525841,
-0.014898701570928097,
-0.0308036208152771,
-0.0027167017105966806,
0.025008831173181534,
-0.06300117075443268,
0.027927007526159286,
-0.0029408675618469715,
0.07668811082839966,
-0.004702868405729532,
-0.010334956459701061,
0.0394541434943676,
-0.03223475441336632,
0.03848463296890259,
0.06261086463928223,
0.010179294273257256,
-0.007496329955756664,
0.04321788251399994,
-0.007136476691812277,
-0.006948002614080906,
-0.04821256920695305,
0.0423792339861393,
-0.007811466697603464,
-0.008706641383469105,
0.008347964845597744,
0.07317086309194565,
0.009072361513972282,
0.06577171385288239,
-0.04576222971081734,
-0.04540880769491196,
0.049299195408821106,
0.004047159571200609,
0.016270603984594345,
0.005519989877939224,
0.020797288045287132,
0.017153698951005936,
-0.024430768564343452,
-0.000757140398491174,
0.03301601856946945,
0.0343516506254673,
-0.0182590764015913,
-0.03175927698612213,
-0.002288406016305089,
0.02229156345129013,
0.03885103389620781,
-0.03585648164153099,
-0.0400480255484581,
0.05896979942917824,
0.0023020266089588404,
-0.01785343885421753,
-0.01655595190823078,
-0.030321218073368073,
0.04356981813907623,
0.025619851425290108,
0.020989196375012398,
0.01012593973428011,
-0.027876852080225945,
0.02284737303853035,
-0.025715036317706108,
0.004988128785043955,
0.004863997455686331,
0.014711200259625912,
0.04090634733438492,
-0.0006524038617499173,
-0.0582675077021122,
0.01617676578462124,
-0.06853079795837402,
0.027205713093280792,
0.028520453721284866,
-0.023833895102143288,
0.03140733763575554,
0.04111947491765022,
0.032859012484550476,
0.05123131722211838,
0.03369482234120369,
-0.023959947749972343,
-0.01757965423166752,
-0.0018631156999617815,
-0.008003837428987026,
-0.06985988467931747,
-0.018393300473690033,
-0.00923127681016922,
-0.0032357233576476574,
-0.08074323832988739,
-0.03780695050954819,
0.0037821566220372915,
0.10126230120658875,
-0.013638535514473915,
-0.043255217373371124,
0.018832912668585777,
-0.003305359510704875,
0.014435172080993652,
0.007831432856619358,
-0.02624308317899704,
0.018622035160660744,
0.03042192943394184,
0.009621310979127884,
0.006754857487976551,
-0.02677212283015251,
-0.021247658878564835,
0.02567065879702568,
-0.021494222804903984,
-0.03711601346731186,
-0.01445010770112276,
-0.06607627868652344,
0.026250462979078293,
0.008768445812165737,
0.0130940405651927,
-0.03480807691812515,
-0.009028670378029346,
-0.008537526242434978,
0.057353582233190536,
-0.01725325547158718,
-0.04996428266167641,
0.027969704940915108,
-0.005895702634006739,
-0.009146442636847496,
-0.0322771817445755,
-0.04144132882356644,
-0.032931603491306305,
-0.06690549850463867,
0.010040792636573315,
-0.02631891705095768,
-0.02556677721440792,
-0.02259903773665428,
-0.0025238015223294497,
-0.008255217224359512,
-0.05941404774785042,
-0.029330676421523094,
-0.025385987013578415,
-0.0018856496317312121,
-0.03675759956240654,
-0.04368703439831734,
-0.003119761124253273,
-0.00947652105242014,
0.02706841006875038,
0.018117861822247505,
-0.03218064457178116,
-0.0377039834856987,
0.00454320153221488,
0.004514437634497881,
0.03352808579802513,
-0.025825660675764084,
-0.026830419898033142,
0.030687343329191208,
0.08040346950292587,
0.005318838637322187,
0.05439045652747154,
-0.02508121356368065,
-0.07044759392738342,
0.03131749480962753,
0.04948025569319725,
-0.0040123662911355495,
0.02473602443933487,
0.03647556155920029,
-0.018816493451595306,
-0.0013277664547786117,
-0.04475174844264984,
-0.09882138669490814,
0.004903232213109732,
0.038813333958387375,
0.028047846630215645,
-0.060014694929122925,
0.004467506427317858,
0.006683452054858208
] |
<p>Photons have no charge. Light is a form of electromagnetic energy.</p>
<p>All spectroscopic effects (to my knowledge) are due to changes in electron state, induced either through an interior or exterior EM (Electro-Magnetic) field. EM forces may affect that state, which in turn affects the light emitted during the change of state, e.g. the Zeeman effect, etc. </p>
<p>However, if we <strong><em>exclude</strong> all such spectroscopic phenomena</em>, and consider EM fields purely energetically on the one side, and light energy on the other, are there any know <strong>direct</strong> effects of EM fields on light itself? </p>
<p>(I'd really like to hear from physicists with hands on knowledge - and please keep all the Tags as is because I have reasons for selecting them, thx.)</p> | g4566 | [
0.02532937563955784,
0.008971230126917362,
0.01370906364172697,
0.034455183893442154,
0.012366891838610172,
-0.0002865681890398264,
-0.009516742080450058,
0.038107726722955704,
0.026928259059786797,
-0.03147925063967705,
0.02320338785648346,
-0.025859786197543144,
0.00017642135208006948,
-0.008099053986370564,
-0.059565551578998566,
0.003964031580835581,
0.1008017510175705,
0.045771174132823944,
0.02786477841436863,
0.029671093448996544,
-0.08014648407697678,
-0.03918438032269478,
-0.025815442204475403,
-0.05805462598800659,
-0.05954187363386154,
-0.010525320656597614,
0.05739390850067139,
-0.04436742514371872,
0.004896278027445078,
-0.03252105414867401,
-0.013395879417657852,
-0.040100838989019394,
0.04595649242401123,
0.0035904927644878626,
-0.04759867861866951,
-0.024722332134842873,
0.03581429645419121,
0.0639738142490387,
-0.022281154990196228,
0.02595124952495098,
0.024028906598687172,
0.03714831918478012,
0.033872347325086594,
-0.03645338490605354,
-0.007671652361750603,
-0.01684468984603882,
-0.00134927942417562,
0.02137865498661995,
0.012035232968628407,
-0.03348865360021591,
-0.019548414275050163,
-0.03548505902290344,
0.04892018809914589,
0.0009762853151187301,
0.08200101554393768,
-0.04147370532155037,
-0.018001845106482506,
0.02894512005150318,
0.09855010360479355,
-0.004029750358313322,
0.016554562374949455,
-0.02575068548321724,
-0.008489353582262993,
0.0356474369764328,
-0.039638321846723557,
-0.03099660575389862,
-0.03922364115715027,
-0.053408183157444,
0.02813686989247799,
0.062399476766586304,
0.01325919944792986,
0.016516543924808502,
-0.08883532136678696,
0.003958674147725105,
0.07941633462905884,
-0.01966489665210247,
-0.012088102288544178,
-0.018189843744039536,
0.03474925085902214,
-0.013140308670699596,
-0.013548891991376877,
-0.07213746011257172,
0.045049697160720825,
-0.01733122393488884,
0.032494496554136276,
-0.06119299307465553,
0.024446530267596245,
0.0487276092171669,
0.03325163200497627,
-0.027367504313588142,
0.034053996205329895,
-0.0032745618373155594,
0.03850657120347023,
0.026982663199305534,
-0.008100836537778378,
-0.02445082925260067,
0.08169569820165634,
0.04942721128463745,
0.025616355240345,
-0.020163148641586304,
-0.04954925552010536,
0.020235124975442886,
-0.03741707280278206,
0.016031712293624878,
0.03952215611934662,
-0.021715553477406502,
0.029428953304886818,
0.02883719839155674,
-0.029902243986725807,
0.0035706255584955215,
-0.034481946378946304,
0.013432099483907223,
-0.04776086285710335,
-0.023714987561106682,
-0.051073215901851654,
-0.01771453768014908,
0.02252429910004139,
-0.08677150309085846,
-0.053501371294260025,
0.056815020740032196,
0.0770639032125473,
0.014013644307851791,
0.03530064597725868,
0.03468431159853935,
-0.0063061947003006935,
0.006538619752973318,
0.0149639081209898,
0.022580260410904884,
-0.0007607938023284078,
-0.05501788482069969,
-0.01870412565767765,
-0.027568208053708076,
-0.015010399743914604,
0.0038753494154661894,
-0.005622268654406071,
0.014133095741271973,
0.0251480545848608,
-0.02063685469329357,
0.009327920153737068,
-0.039034806191921234,
0.05474335700273514,
0.02150467410683632,
-0.0014228770742192864,
0.00016817900177557021,
0.016328252851963043,
0.009665903635323048,
0.024923574179410934,
-0.012558206915855408,
0.07568075507879257,
0.037941962480545044,
0.08729685097932816,
-0.027502072975039482,
-0.015750214457511902,
-0.06271389126777649,
0.03391416743397713,
-0.01944711059331894,
0.012910275720059872,
-0.03763439878821373,
-0.053437650203704834,
0.011596547439694405,
0.028155462816357613,
0.05964518338441849,
0.029109220951795578,
-0.027408434078097343,
0.013656488619744778,
-0.05979260429739952,
0.017381584271788597,
-0.035120703279972076,
-0.012162033468484879,
0.008730792440474033,
-0.025396788492798805,
-0.019311441108584404,
0.007518445607274771,
0.028047239407896996,
-0.04778730124235153,
0.0033787558786571026,
0.03642110526561737,
-0.02664485014975071,
0.04840271174907684,
0.003996170125901699,
-0.03960857540369034,
0.010686742141842842,
-0.00667200330644846,
-0.030544856563210487,
0.020069073885679245,
-0.03283859044313431,
-0.04145233705639839,
0.022312870249152184,
-0.055985696613788605,
0.04524371773004532,
-0.04416155815124512,
0.02048734948039055,
0.054629988968372345,
-0.00027635859441943467,
-0.02580634318292141,
-0.030469872057437897,
-0.0147037198767066,
0.010430123656988144,
-0.010193315334618092,
0.006635203957557678,
-0.07386387139558792,
0.07125124335289001,
-0.03804789111018181,
0.024228470399975777,
0.011791467666625977,
0.030084891244769096,
0.03346490114927292,
-0.05137503892183304,
0.008837888948619366,
-0.018983161076903343,
0.05322091281414032,
0.002314426237717271,
0.034118399024009705,
0.003062179544940591,
0.021739305928349495,
-0.019041985273361206,
-0.06358993798494339,
-0.029965830966830254,
0.0216650553047657,
0.03761940449476242,
-0.04673285037279129,
0.02914150059223175,
0.01318467315286398,
0.01736314594745636,
-0.05222075432538986,
-0.03479260951280594,
-0.003958479501307011,
0.040664609521627426,
0.004955051001161337,
0.003891804488375783,
-0.07001575827598572,
0.03852011263370514,
0.02873537875711918,
0.010956400074064732,
0.03191893547773361,
0.02711893990635872,
-0.05964961647987366,
-0.008659955114126205,
0.031963709741830826,
-0.017503561452031136,
0.012322735972702503,
-0.05210765451192856,
-0.007615336682647467,
-0.0024775078054517508,
-0.020919203758239746,
-0.05665406584739685,
0.009892746806144714,
0.05246889591217041,
-0.009326721541583538,
-0.06552374362945557,
0.02486160397529602,
-0.019643941894173622,
-0.009201002307236195,
0.02790425345301628,
-0.013971672393381596,
-0.024355150759220123,
-0.005465251859277487,
0.033008746802806854,
-0.035656172782182693,
0.008283449336886406,
-0.018835119903087616,
0.0067210085690021515,
-0.03731143847107887,
0.025335505604743958,
-0.0023815641179680824,
-0.023156633600592613,
-0.003292125416919589,
0.028423292562365532,
0.023304946720600128,
-0.0023513096384704113,
-0.050779666751623154,
0.10184737294912338,
-0.035219695419073105,
-0.005690799094736576,
0.0630778819322586,
0.016306359320878983,
-0.04235028475522995,
0.037338703870773315,
0.02208736725151539,
-0.08545579016208649,
-0.01266500260680914,
-0.021175064146518707,
-0.0385325625538826,
0.017548952251672745,
0.04344730079174042,
-0.06298423558473587,
-0.004265878349542618,
-0.05086127668619156,
-0.011497466824948788,
-0.035014186054468155,
-0.005236014723777771,
0.02405571937561035,
0.07276579737663269,
-0.008729705587029457,
-0.03615277633070946,
-0.06563093513250351,
-0.015949714928865433,
-0.00982315931469202,
-0.023940352723002434,
0.05038756877183914,
0.02655186504125595,
0.01255079172551632,
0.004624424036592245,
0.04344126582145691,
0.04413926228880882,
-0.007241634652018547,
-0.08525516092777252,
-0.07547852396965027,
0.036324650049209595,
0.009700821712613106,
-0.05444273725152016,
0.05275489389896393,
-0.0070448159240186214,
0.051204174757003784,
-0.04640625789761543,
0.04045207425951958,
-0.008004950359463692,
0.0031179417856037617,
-0.015422835014760494,
0.00594021612778306,
0.02585335448384285,
-0.029254255816340446,
-0.005799659062176943,
-0.03251938149333,
0.05466645583510399,
0.012277786619961262,
0.016609538346529007,
-0.009274939075112343,
-0.03158978372812271,
0.015987755730748177,
0.005412451922893524,
-0.022048091515898705,
0.006910837255418301,
-0.012893645092844963,
-0.08364421874284744,
0.07485684752464294,
-0.03951374441385269,
-0.030054112896323204,
0.026250047609210014,
0.0010267662582919002,
0.04261081665754318,
-0.015042517334222794,
-0.08993232250213623,
-0.0049568163231015205,
0.014463391155004501,
-0.0009166607051156461,
-0.036324743181467056,
-0.0936708077788353,
-0.0011432274477556348,
0.0022472250275313854,
0.05881265178322792,
0.0066152107901871204,
-0.01584533415734768,
0.014445644803345203,
-0.029937388375401497,
-0.014620453119277954,
0.05433431640267372,
0.057886961847543716,
0.0007450541597791016,
-0.01438251044601202,
-0.06446082890033722,
-0.01737947203218937,
0.02729993872344494,
-0.07529842853546143,
-0.016783487051725388,
0.025473514571785927,
-0.019819946959614754,
0.005243970546871424,
0.041193608194589615,
-0.0032970025204122066,
0.0014114452060312033,
0.0019181962125003338,
0.010935339145362377,
0.03127322345972061,
-0.02828321047127247,
-0.006262560375034809,
0.057055097073316574,
-0.048380497843027115,
-0.033860087394714355,
0.024285800755023956,
0.038213226944208145,
0.023086564615368843,
0.06896914541721344,
0.04584658145904541,
0.01930215395987034,
-0.0006401471327990294,
-0.031772613525390625,
0.023840658366680145,
-0.05580275133252144,
0.03444228693842888,
0.004369032569229603,
-0.044732991605997086,
-0.021863263100385666,
0.03896030783653259,
-0.025368938222527504,
-0.023132892325520515,
0.04046657308936119,
-0.06205592676997185,
-0.03210347145795822,
-0.010916410014033318,
0.039543475955724716,
0.017577677965164185,
0.0031982630025595427,
-0.006139559205621481,
0.002941486658528447,
0.00011738611647160724,
0.013191725127398968,
-0.025962289422750473,
-0.05878014117479324,
-0.026010477915406227,
0.038591064512729645,
-0.04372863098978996,
-0.03149411827325821,
-0.006920831277966499,
-0.037264999002218246,
-0.008052991703152657,
-0.04454108700156212,
0.0013951255241408944,
0.04757982864975929,
-0.02535225823521614,
0.050820302218198776,
0.022419391199946404,
-0.005650146398693323,
0.011306741274893284,
-0.0231639314442873,
0.08323023468255997,
0.020682653412222862,
-0.017499588429927826,
0.020146513357758522,
0.0313868448138237,
0.030486343428492546,
0.0453023687005043,
-0.03560035303235054,
-0.010448938235640526,
0.006503673270344734,
0.0645127072930336,
-0.03499336913228035,
-0.010684262029826641,
0.011141221970319748,
0.00430681137368083,
0.10305928438901901,
0.06427519023418427,
0.030967790633440018,
0.022223692387342453,
-0.022897494956851006,
0.026382355019450188,
-0.05551644787192345,
0.00870069582015276,
-0.0022865580394864082,
-0.027182115241885185,
-0.011905179359018803,
0.008720235899090767,
-0.03622780740261078,
-0.0383765883743763,
-0.011594370007514954,
-0.0029762079939246178,
-0.030882645398378372,
0.004454907029867172,
-0.042554885149002075,
0.03876439854502678,
-0.009237580001354218,
-0.021596234291791916,
0.04103738069534302,
0.04079773649573326,
0.01358431950211525,
-0.008932993747293949,
-0.07640305161476135,
-0.008786281570792198,
-0.05805569887161255,
-0.011994631960988045,
-0.0005088744219392538,
-0.016367832198739052,
0.03934868052601814,
-0.04697265848517418,
-0.018229451030492783,
0.0007908489205874503,
-0.06490623205900192,
-0.03651309385895729,
-0.039048995822668076,
-0.056769680231809616,
0.00243762438185513,
-0.03754223883152008,
0.03829067572951317,
0.019592642784118652,
-0.016686007380485535,
0.005439839791506529,
0.004347759764641523,
0.08873216062784195,
-0.03439707309007645,
-0.08021513372659683,
-0.06613047420978546,
0.01419238280504942,
-0.06834407150745392,
-0.03963642939925194,
-0.03364938497543335,
0.04723400995135307,
0.003230275819078088,
0.019368186593055725,
0.0010790276573970914,
0.016507070511579514,
0.0069653550162911415,
-0.016588754951953888,
0.011599150486290455,
-0.008345168083906174,
-0.037030111998319626,
-0.030113786458969116,
0.008750352077186108,
-0.013546711765229702,
-0.022484060376882553,
-0.0001260192657355219,
-0.08016707748174667,
-0.011647193692624569,
0.01740458980202675,
0.01573319546878338,
-0.004540476016700268,
0.010111295618116856,
-0.013935287483036518,
0.05856310576200485,
0.048821188509464264,
-0.033058881759643555,
-0.034183960407972336,
-0.005579243414103985,
0.05291170999407768,
-0.020904911682009697,
0.06260848045349121,
0.022352907806634903,
0.00015676612383686006,
0.07280784845352173,
0.05970371514558792,
-0.004587061703205109,
-0.0001174632998299785,
0.014523312449455261,
0.030751783400774002,
0.018505094572901726,
0.009415030479431152,
-0.07996921986341476,
0.038742199540138245,
0.02905830554664135,
-0.027400175109505653,
0.036123622208833694,
0.010306382551789284,
-0.029160991311073303,
0.01665908470749855,
0.04903697222471237,
-0.03872458264231682,
0.00548067782074213,
-0.027297452092170715,
-0.04712371528148651,
0.0288519486784935,
0.0014426197158172727,
0.021273605525493622,
-0.030054936185479164,
-0.0272243432700634,
-0.027767842635512352,
-0.025905735790729523,
0.05577385425567627,
0.0007127239950932562,
0.0000521956171724014,
-0.04637834057211876,
-0.013554307632148266,
0.06323792785406113,
0.04641512408852577,
0.013482371345162392,
0.03232289478182793,
0.02475438453257084,
0.04772565886378288,
0.0500793419778347,
-0.07471373677253723,
-0.0030354864429682493,
0.006202791351824999,
0.04180142283439636,
0.031230518594384193,
0.0028385454788804054,
-0.04721299931406975,
-0.013170633465051651,
-0.011828253977000713,
0.0075810691341757774,
0.023013297468423843,
-0.08980156481266022,
-0.01847553439438343,
-0.007269348483532667,
0.013142082840204239,
0.0914764553308487,
-0.05755380541086197,
-0.01010964997112751,
0.019703445956110954,
-0.005911975167691708,
0.04947494715452194,
0.06305394321680069,
-0.019959058612585068,
-0.012601974420249462,
-0.0018426673486828804,
0.008072041906416416,
-0.012511693872511387,
-0.021034037694334984,
-0.03745526075363159,
0.01424814946949482,
0.009925752878189087,
-0.014084508642554283,
0.04403891786932945,
0.05818333849310875,
-0.019174380227923393,
0.014400660060346127,
-0.023489316925406456,
0.0419665090739727,
0.05270478129386902,
-0.027462266385555267,
-0.0007316329283639789,
0.002956556621938944,
0.021257398650050163,
-0.04162469133734703,
-0.07967881113290787,
-0.035798683762550354,
-0.0337335541844368,
-0.023330083116889,
-0.07214660197496414,
0.006994122639298439,
0.012668336741626263,
0.015409430488944054,
-0.010769722983241081,
-0.06540552526712418,
-0.08985262364149094,
0.07172626256942749,
0.000790837686508894,
0.029503973200917244,
0.10798223316669464,
-0.08524508029222488,
0.027395660057663918,
0.000007047753570077475,
-0.02324717678129673,
0.0046629831194877625,
0.00016604221309535205,
0.0009019437711685896,
-0.003333844244480133,
0.001508869114331901,
0.06241877004504204,
0.0013403085758909583,
-0.054338619112968445,
0.02807597629725933,
-0.03491587191820145,
-0.001206149929203093,
0.042936041951179504,
0.05095420777797699,
-0.012238485738635063,
-0.03454671800136566,
0.013731706887483597,
-0.028381820768117905,
-0.008584301918745041,
0.011727230623364449,
0.05865047127008438,
-0.021397169679403305,
-0.036794513463974,
0.016368042677640915,
-0.004412571433931589,
0.037463877350091934,
0.0247694980353117,
-0.010527429170906544,
0.012282024137675762,
0.0036321785300970078,
-0.06435757130384445,
0.02640058845281601,
-0.0036514848470687866,
-0.03292696923017502,
-0.02122480608522892,
0.01664004474878311,
0.011168100871145725,
0.03292207792401314,
-0.04495793581008911,
-0.0035547323059290648,
0.03857918456196785,
0.032953303307294846,
-0.05343084782361984,
-0.02455984055995941,
0.015737691894173622,
-0.022604839876294136,
-0.008217999711632729,
-0.04083750396966934,
0.06108008697628975,
-0.01068459264934063,
-0.015497618354856968,
-0.02985352836549282,
0.07169173657894135,
-0.00021300528896972537,
0.03197995200753212,
-0.013562469743192196,
0.010567896068096161,
-0.02992192655801773,
0.0395025759935379,
-0.016855726018548012,
-0.06072583049535751,
0.006596631836146116,
-0.04007852450013161,
-0.019278932362794876,
0.005013375077396631,
-0.045556437224149704,
-0.0436226986348629,
0.015989741310477257,
0.029872531071305275,
0.035514891147613525,
-0.0035791685804724693,
-0.03282603248953819,
0.00046630616998299956,
0.008397109806537628,
-0.04247141629457474,
0.03902219608426094,
0.024394799023866653,
0.0026846674736589193,
-0.03517596051096916,
-0.017411300912499428,
0.050289664417505264,
0.01425890438258648,
0.042568139731884,
0.021328797563910484,
0.0072881197556853294,
0.04174569249153137,
0.0163619052618742,
0.031285662204027176,
0.024999380111694336,
0.03489601984620094,
0.056191034615039825,
-0.05127335339784622,
0.00655393535271287,
-0.04959513247013092,
0.024397484958171844,
0.011072862893342972,
0.02244020812213421,
0.029003962874412537,
-0.005935913883149624,
0.07799335569143295,
-0.0013869514223188162,
0.03662556782364845,
-0.0026779749896377325,
-0.020259641110897064,
0.021421797573566437,
-0.022904042154550552,
0.01493629440665245,
0.024248972535133362,
0.00839495100080967,
0.046084608882665634,
-0.021778427064418793,
0.0009550023241899908,
-0.049122001975774765,
-0.052707821130752563,
-0.03384093940258026,
0.014285187236964703,
-0.005982907488942146,
0.012169335037469864,
0.023666735738515854,
0.010047320276498795,
0.06483223289251328,
-0.010685054585337639,
0.024666614830493927,
-0.027808984741568565,
0.07074002176523209,
0.05262498930096626,
-0.08056846261024475,
-0.023880610242486,
-0.03927282616496086,
0.01744094118475914,
0.02878294512629509,
-0.014340639114379883,
0.012690580449998379,
-0.020823033526539803,
-0.015534688718616962,
0.03009030409157276,
-0.03398069366812706,
-0.003958721179515123,
0.011362635530531406
] |
<p>For years I have been very fascinated by the "mystery" aspect of gravity. Functionally, we understand it perfectly for our all applications, but in my (limited to undergrad General Physics 3 quarters) understanding, we don't know WHY it exists or HOW the "pull" works. </p>
<p>I'm very sorry for what is surely trite pop-science term use, but, to provide an example of what I mean: there has to be SOME "measurable material" of gravity between say the earth and the moon -- some kind of 'graviton' (not that it needs to be a particle or anything, I have <em>zero</em> claims as to the nature of how gravity does what it does). The [butchered] saying of "pluck a flower and move the furthest moon," because gravity in theory, has an infinite range (?) and moving a flower on earth could maybe move an atom on jupiter ever so slightly (?)."</p>
<p>Anyway, similar to how we had "very good" hypotheses about the existence of higgs-boson that the LHC 99%+ confirmed, do we have any "very good" hypotheses in regards to the fundamental way how gravity does what we have long-known it to do?</p> | g4567 | [
0.02204345539212227,
0.06687460094690323,
-0.004469363950192928,
-0.009810267016291618,
0.014059185981750488,
0.006012002471834421,
-0.012449664995074272,
-0.016554851084947586,
-0.012019791640341282,
-0.09276297688484192,
0.022830171510577202,
-0.024948369711637497,
0.08665081858634949,
-0.008054750971496105,
-0.027533892542123795,
0.0030267639085650444,
0.013424558565020561,
-0.013713907450437546,
0.036235298961400986,
0.0022365893237292767,
0.021945610642433167,
0.0011402219533920288,
0.03832358866930008,
-0.027272962033748627,
-0.13222767412662506,
-0.025748135522007942,
0.029326163232326508,
-0.015892770141363144,
-0.005979249719530344,
-0.02117280662059784,
-0.004622538108378649,
-0.0509282723069191,
0.053182292729616165,
-0.059069614857435226,
-0.04004718363285065,
-0.0441451333463192,
-0.0036326732952147722,
0.0022024326026439667,
0.0041969940066337585,
-0.0008135922253131866,
-0.0100833335891366,
-0.026826350018382072,
0.0047399564646184444,
-0.019155962392687798,
0.019570987671613693,
0.024707473814487457,
-0.007665438577532768,
-0.005050087813287973,
0.024218730628490448,
-0.05739425867795944,
-0.013764225877821445,
0.044024258852005005,
0.055553849786520004,
0.05214511975646019,
-0.010226927697658539,
-0.021754557266831398,
0.10864689946174622,
0.06305045634508133,
0.06647306680679321,
-0.004490710329264402,
0.009101788513362408,
0.03163149207830429,
0.020979274064302444,
-0.0018821201520040631,
0.01838991604745388,
0.02844122052192688,
-0.03321137651801109,
0.029776794835925102,
-0.022999068722128868,
0.005990495439618826,
0.02155635692179203,
-0.06185648962855339,
0.02928740344941616,
-0.008230937644839287,
-0.04655913636088371,
0.03006323054432869,
-0.04558491334319115,
0.04412563890218735,
0.007162999827414751,
-0.07423052936792374,
0.0004993707407265902,
-0.055062878876924515,
-0.0324941948056221,
-0.010428221896290779,
0.04974135383963585,
-0.009766935370862484,
-0.03180151432752609,
-0.010643047280609608,
0.03287661075592041,
0.04070842266082764,
0.03189077973365784,
-0.00566080491989851,
0.01637035608291626,
0.010004318319261074,
-0.010211684741079807,
-0.03441425785422325,
0.024348124861717224,
0.01502959057688713,
-0.049834515899419785,
-0.02020048163831234,
-0.03940340504050255,
-0.016652224585413933,
0.01176612451672554,
0.0013637141091749072,
0.021977074444293976,
0.0055175600573420525,
0.011235247366130352,
0.030365021899342537,
0.0480794683098793,
-0.010588369332253933,
-0.022960031405091286,
0.07194608449935913,
0.04212496429681778,
-0.027295459061861038,
0.03162318468093872,
-0.043927110731601715,
0.05092518776655197,
0.048441361635923386,
-0.00495208939537406,
0.0466102659702301,
-0.058818839490413666,
0.04938352853059769,
0.0035896096378564835,
0.030449025332927704,
-0.033189401030540466,
-0.06765398383140564,
0.01909194514155388,
0.0010489721316844225,
-0.02518361061811447,
0.012062938883900642,
-0.019026700407266617,
0.0011590959038585424,
-0.036429982632398605,
0.03911352902650833,
-0.024321604520082474,
0.04880082979798317,
0.02466893568634987,
0.03525688499212265,
0.018461499363183975,
0.022546863183379173,
-0.0444384403526783,
-0.029282221570611,
-0.029591085389256477,
-0.017795918509364128,
-0.005276287440210581,
0.03877514228224754,
-0.006175737362354994,
0.003131663193926215,
-0.054717112332582474,
-0.041932594031095505,
0.008191611617803574,
0.07154735177755356,
0.056942250579595566,
-0.07959651201963425,
-0.004182104952633381,
0.006781519390642643,
0.012577391229569912,
-0.06862503290176392,
-0.029539838433265686,
0.013431841507554054,
0.060654234141111374,
-0.0393172986805439,
0.007197021506726742,
-0.03103715181350708,
-0.031712476164102554,
0.06366340070962906,
-0.008709466084837914,
-0.017565591260790825,
0.009389529936015606,
0.04402103275060654,
-0.11960885673761368,
-0.037210818380117416,
0.014078726060688496,
0.09479746967554092,
0.04025134816765785,
-0.015258051455020905,
0.08356791734695435,
-0.019576508551836014,
-0.0019944633822888136,
0.020997200161218643,
0.0021251975558698177,
-0.03454777970910072,
0.03488965705037117,
-0.002142093377187848,
-0.01766885444521904,
0.0015942519530653954,
0.0027015076484531164,
-0.012705210596323013,
-0.006233417894691229,
0.01063211914151907,
-0.07813157141208649,
-0.023275226354599,
0.02938888594508171,
0.004201479256153107,
0.00730576366186142,
-0.04391026496887207,
-0.015251357108354568,
-0.04052431136369705,
-0.0390152707695961,
0.033987823873758316,
-0.07072034478187561,
0.02194940485060215,
0.03721226006746292,
-0.019458109512925148,
0.015258146449923515,
-0.005717047955840826,
0.02435648813843727,
0.03147124499082565,
0.023518813773989677,
0.020759914070367813,
0.04030995815992355,
-0.03364446386694908,
0.036005668342113495,
0.059189118444919586,
-0.0011101450072601438,
-0.006311002187430859,
-0.0744933933019638,
-0.014830885455012321,
0.021672582253813744,
0.016695933416485786,
0.004796219058334827,
-0.01664249412715435,
0.02933928743004799,
0.03031846694648266,
0.0006585207884199917,
-0.005462377332150936,
-0.0250899326056242,
-0.025039806962013245,
-0.019055316224694252,
0.03064853698015213,
-0.00504416273906827,
0.02597837708890438,
0.0418831929564476,
-0.0043694148771464825,
0.027230514213442802,
0.016458697617053986,
0.016084300354123116,
-0.06308858096599579,
0.0376058854162693,
0.08776824921369553,
0.03122626803815365,
-0.08573296666145325,
-0.026898927986621857,
-0.03421921655535698,
0.028221404179930687,
0.012402846477925777,
0.03560402989387512,
0.011147938668727875,
-0.01926310546696186,
0.005045733880251646,
0.03270919248461723,
-0.022807994857430458,
-0.056580550968647,
-0.03825582191348076,
-0.0011801301734521985,
-0.006071124225854874,
0.027795331552624702,
0.07519976049661636,
-0.03461339697241783,
-0.018877172842621803,
0.014604752883315086,
-0.07457403093576431,
0.029292449355125427,
0.051930129528045654,
-0.03323078155517578,
-0.05390644818544388,
-0.09275847673416138,
0.025632141157984734,
-0.04984450340270996,
0.00862906128168106,
-0.02877521887421608,
0.034258704632520676,
0.007273346185684204,
0.01736968755722046,
-0.0355457067489624,
0.04002486541867256,
0.004104773513972759,
-0.010541335679590702,
0.057561855763196945,
-0.025154348462820053,
-0.024499408900737762,
-0.018980730324983597,
-0.051607176661491394,
-0.013263280503451824,
-0.011671951040625572,
0.027004778385162354,
-0.06036851555109024,
-0.023725049570202827,
-0.018590006977319717,
0.0014300055336207151,
0.010372083634138107,
0.0015272954478859901,
0.038533009588718414,
0.018177777528762817,
-0.02756941132247448,
0.013699428178369999,
-0.006501187104731798,
0.007897965610027313,
-0.045450784265995026,
-0.02706906758248806,
0.004614314530044794,
0.0009090686216950417,
0.03295841068029404,
0.031072959303855896,
-0.05444555729627609,
0.00485075730830431,
-0.04352410510182381,
-0.01452755369246006,
0.032823726534843445,
-0.017048915848135948,
0.007439288776367903,
0.07910813391208649,
0.012478627264499664,
0.03552223742008209,
0.006142734549939632,
-0.0156719870865345,
0.0005355224129743874,
0.044440995901823044,
-0.012569052167236805,
-0.016689153388142586,
0.046534642577171326,
-0.012210242450237274,
-0.023314334452152252,
-0.03987319767475128,
0.047366928309202194,
0.06719446182250977,
-0.09372250735759735,
0.04414328560233116,
-0.0600954033434391,
-0.013359349220991135,
0.0663720965385437,
-0.03963359072804451,
-0.05276069417595863,
0.009224599227309227,
-0.032806940376758575,
0.007580214645713568,
0.03387736529111862,
0.043844074010849,
0.08343423902988434,
-0.005286934319883585,
-0.0325067974627018,
0.007988996803760529,
-0.04199999198317528,
0.03979693353176117,
0.0050895968452095985,
0.055852010846138,
-0.008033535443246365,
-0.033504288643598557,
0.019097447395324707,
0.017337391152977943,
0.049875155091285706,
-0.025462234392762184,
-0.030487308278679848,
-0.05575110763311386,
0.022584935650229454,
0.015517689287662506,
0.011328838765621185,
-0.026649342849850655,
0.02469741180539131,
-0.039128150790929794,
-0.02642754465341568,
0.04005405679345131,
0.002225634176284075,
0.025113388895988464,
0.006484627723693848,
-0.033490683883428574,
0.0011705412762239575,
0.052770234644412994,
-0.035143207758665085,
-0.017125878483057022,
0.024423981085419655,
0.05018286779522896,
-0.012387142516672611,
0.04530254378914833,
0.01692313142120838,
-0.06803206354379654,
0.023574866354465485,
0.00892637949436903,
-0.011554253287613392,
0.002095344942063093,
0.056120604276657104,
0.061877645552158356,
0.036740660667419434,
0.05867975205183029,
0.004457533825188875,
0.0025465013459324837,
-0.0869559720158577,
-0.034094974398612976,
0.02618858590722084,
-0.021739719435572624,
-0.05896425619721413,
0.02894456684589386,
0.0038601229898631573,
-0.02494342066347599,
-0.0013356314739212394,
-0.058348577469587326,
-0.006972952745854855,
0.004098348785191774,
0.03457624092698097,
-0.04863152652978897,
-0.01607939600944519,
0.04864837974309921,
0.02595994807779789,
-0.03182554990053177,
-0.033078063279390335,
-0.04393292963504791,
0.03201327100396156,
-0.00436668936163187,
0.013787847943603992,
-0.0025646761059761047,
0.07099570333957672,
0.025104127824306488,
0.03159981220960617,
-0.06953006237745285,
0.022735334932804108,
-0.0465204119682312,
-0.021042605862021446,
-0.022588899359107018,
0.059397436678409576,
-0.01804010570049286,
0.0788688063621521,
0.08170615136623383,
0.01508201565593481,
-0.006942189298570156,
-0.021705565974116325,
0.0736817941069603,
0.044850826263427734,
0.009786365553736687,
-0.04905937239527702,
-0.012710440903902054,
0.007688539568334818,
0.013192386366426945,
0.050089411437511444,
0.006797583308070898,
0.012188260443508625,
0.03584231808781624,
-0.09385935962200165,
0.06658979505300522,
-0.05077409744262695,
0.01888580434024334,
0.08370918780565262,
-0.011629785411059856,
0.03431385010480881,
0.009592276066541672,
0.04486185312271118,
0.0487808994948864,
0.017463449388742447,
-0.004873467143625021,
-0.012216096743941307,
0.032787322998046875,
-0.02846907079219818,
-0.022394569590687752,
-0.0800570696592331,
-0.02419501729309559,
-0.02700699493288994,
0.05283518135547638,
0.02861967496573925,
0.00308783445507288,
0.00863258633762598,
-0.012807995080947876,
-0.08475898951292038,
-0.03854276239871979,
-0.009503083303570747,
0.058530863374471664,
-0.006961293052881956,
-0.04906732216477394,
-0.02759438008069992,
-0.03196537494659424,
0.008876534178853035,
-0.00755054596811533,
0.012040778063237667,
0.03480488434433937,
0.07716459780931473,
0.020498478785157204,
0.011171015910804272,
0.04106416925787926,
-0.007352134678512812,
0.02179933339357376,
-0.016082914546132088,
-0.04267251491546631,
-0.010362996719777584,
0.013523676432669163,
-0.012680741026997566,
-0.054013680666685104,
-0.06150099262595177,
-0.029609808698296547,
-0.08402284234762192,
0.010417488403618336,
-0.04034528136253357,
-0.04474635422229767,
-0.015996787697076797,
-0.05165574699640274,
0.04516007751226425,
-0.05308442562818527,
-0.009993901476264,
-0.10088025778532028,
-0.004815943073481321,
0.024759510532021523,
-0.010861123912036419,
-0.03264879062771797,
-0.02245522476732731,
0.057782966643571854,
0.03803117200732231,
-0.00971580296754837,
0.05425181984901428,
0.014407101087272167,
0.0401911586523056,
-0.012513404712080956,
-0.01940484158694744,
0.03718708083033562,
-0.02532307058572769,
-0.01934593729674816,
-0.051833607256412506,
0.03748425468802452,
0.043737925589084625,
0.02997501939535141,
0.0031871236860752106,
-0.013108115643262863,
-0.0390593521296978,
0.07845068722963333,
-0.03332027420401573,
-0.0197118129581213,
0.04257001355290413,
0.01936590112745762,
0.07203654944896698,
0.03854912146925926,
-0.06907467544078827,
-0.018274793401360512,
0.023104334250092506,
-0.011545371264219284,
0.010874519124627113,
-0.026546938344836235,
0.05693606287240982,
-0.005448522511869669,
0.019737068563699722,
0.01527993194758892,
0.04891570284962654,
0.005421710200607777,
0.018942665308713913,
-0.052413925528526306,
-0.026837067678570747,
-0.011336388066411018,
-0.018888672813773155,
0.06094402074813843,
-0.013900529593229294,
0.006137822289019823,
-0.03745991736650467,
-0.0008240601746365428,
0.06866227090358734,
-0.04733002930879593,
-0.04722240939736366,
0.020415011793375015,
0.028031915426254272,
0.026375634595751762,
0.022053208202123642,
-0.026673533022403717,
-0.029363349080085754,
-0.022296082228422165,
-0.021037569269537926,
0.008511717431247234,
-0.0016498935874551535,
0.03804410621523857,
-0.025858044624328613,
-0.034830331802368164,
0.03053649328649044,
0.005465319845825434,
0.034173574298620224,
-0.0566638819873333,
0.027043022215366364,
0.014983534812927246,
-0.057170312851667404,
-0.013810180127620697,
0.013764015398919582,
-0.0053568328730762005,
-0.0037141209468245506,
-0.019693715497851372,
-0.03261631727218628,
0.03232305124402046,
-0.04694502800703049,
-0.023800773546099663,
0.08798171579837799,
-0.030426867306232452,
0.01085137203335762,
-0.0515623539686203,
-0.049800898879766464,
0.029906149953603745,
-0.07147952169179916,
-0.01834702119231224,
0.06038239970803261,
-0.019429150968790054,
0.009555669501423836,
0.04195652902126312,
0.010379904881119728,
-0.01745707541704178,
-0.0455995611846447,
-0.04526769369840622,
0.07609206438064575,
-0.02851990982890129,
-0.019379880279302597,
-0.017987770959734917,
0.013530159369111061,
0.016122471541166306,
0.05986601114273071,
0.01891506090760231,
0.06873048096895218,
0.03804238140583038,
-0.02683880552649498,
0.019116168841719627,
0.01608847826719284,
-0.01829264685511589,
-0.05970900133252144,
0.023420818150043488,
-0.009691109880805016,
-0.002042809734120965,
-0.032793182879686356,
-0.0770493596792221,
-0.04592909291386604,
-0.014568891376256943,
-0.033972129225730896,
-0.013409226201474667,
-0.00941498950123787,
0.010830341838300228,
0.025118550285696983,
-0.06768583506345749,
0.053722552955150604,
-0.0001907191181089729,
0.007780519314110279,
0.019667482003569603,
0.00860061775892973,
-0.02479303441941738,
-0.010051465593278408,
0.03237052261829376,
0.0013646251754835248,
-0.0022732496727257967,
-0.03712565451860428,
0.044347383081912994,
-0.027969572693109512,
0.036448992788791656,
0.015518337488174438,
-0.02349226363003254,
-0.04250699281692505,
0.029669376090168953,
0.003928221296519041,
0.036213040351867676,
0.008403989486396313,
-0.04932845011353493,
-0.011582957580685616,
0.006584286689758301,
-0.04890512302517891,
0.05009095370769501,
-0.007661254145205021,
-0.05977006256580353,
0.01051320880651474,
0.0075201294384896755,
-0.02080608904361725,
0.027216127142310143,
-0.004041718319058418,
-0.005520957987755537,
0.015072168782353401,
-0.07833666354417801,
-0.06812842190265656,
-0.013780280016362667,
0.016525978222489357,
-0.012122733518481255,
-0.03731754794716835,
0.023475406691432,
0.020452870056033134,
0.004092778544872999,
-0.02230539172887802,
0.03974093496799469,
0.04618325084447861,
-0.028073478490114212,
-0.015558206476271152,
0.01968858763575554,
-0.011645065620541573,
-0.027494102716445923,
-0.043850675225257874,
0.0020624035969376564,
0.00477176858112216,
-0.01640755869448185,
-0.03028695099055767,
0.07614708691835403,
0.025499192997813225,
0.039012741297483444,
-0.03458676487207413,
0.004611121024936438,
-0.022427337244153023,
0.029082396999001503,
-0.056773047894239426,
0.003364460775628686,
0.005839787423610687,
-0.004984070546925068,
0.002374522853642702,
-0.005657960195094347,
0.007907900027930737,
0.00686359778046608,
-0.021578161045908928,
-0.0037755249068140984,
0.00674060545861721,
0.0205520112067461,
-0.020439786836504936,
-0.04213595390319824,
-0.00338154099881649,
-0.050794001668691635,
0.042123861610889435,
0.04576511308550835,
-0.03937866538763046,
-0.0046495418064296246,
-0.07322506606578827,
0.04878984019160271,
0.037708427757024765,
0.04883429780602455,
0.022161919623613358,
-0.0025265179574489594,
0.022964216768741608,
0.013165026903152466,
0.0031611439771950245,
0.009202652610838413,
-0.011449038982391357,
0.007308377884328365,
-0.0021228124387562275,
-0.029243502765893936,
0.026734067127108574,
-0.04140125587582588,
-0.06012614443898201,
0.019084075465798378,
-0.01942082867026329,
-0.03131852671504021,
-0.00033135857665911317,
-0.014687377959489822,
0.027071846649050713,
-0.014453966170549393,
0.033440522849559784,
-0.0639311820268631,
-0.026081958785653114,
0.018149754032492638,
0.01164837647229433,
-0.020497597754001617,
0.007549367379397154,
0.03136121481657028,
0.006962379440665245,
-0.04972420632839203,
0.004552442580461502,
-0.0026583883445709944,
0.01309641357511282,
-0.0367225706577301,
0.020108357071876526,
0.05783966928720474,
0.011801333166658878,
-0.03991512209177017,
0.0091404402628541,
0.03047453984618187,
-0.012469013221561909,
0.04809475690126419,
0.03110375441610813,
-0.04001474753022194,
-0.013019576668739319,
0.034113988280296326,
0.029216155409812927,
-0.025400681421160698,
0.006116216536611319,
-0.008802237920463085,
-0.015177206136286259,
0.042326558381319046,
-0.014443443156778812,
0.015237103216350079,
-0.032921791076660156,
0.022484730929136276
] |
<p>Depending on the theories, the center of our galaxy is a super massive black hole, this is easy to accept as a truth, but what I couldn't simply devour is how the solar system is orbiting around it while not getting absorbed to the inside ? It's simple to understand how earth orbits the sun, but the black hole is something more energetic and at most pulls everything to it's center.
By looking to this image for example:
<img src="http://i.stack.imgur.com/MXn7W.jpg" alt="enter image description here"></p>
<p>If we follow the bright lines it looks like everything is really going to the true center like a vortex.
If you have any simple ways to enlighten me or any references to read I will be thankful, because sometimes I don't know what topic should I search for to find answers without posting questions like this one.</p>
<p>And also, would our galaxy run out of stars since the black hole devours them fast while they take too long to reproduce ?</p> | g4568 | [
0.013883518986403942,
0.07043078541755676,
0.021213095635175705,
0.004835566971451044,
0.01869480311870575,
0.009056166745722294,
0.0264128390699625,
0.01663740538060665,
0.04487527906894684,
-0.033652208745479584,
0.03675377368927002,
-0.01697487197816372,
0.06438945978879929,
0.0025292448699474335,
0.059669338166713715,
-0.052339717745780945,
-0.014970032498240471,
0.005590478423982859,
0.019841086119413376,
0.014268319122493267,
0.018410904332995415,
-0.04925528168678284,
0.050714053213596344,
-0.05067155137658119,
-0.09551043063402176,
-0.0005782709340564907,
0.005831757560372353,
0.030969012528657913,
-0.00935328658670187,
-0.042932625859975815,
0.0142693892121315,
-0.011264684610068798,
-0.02692718245089054,
-0.06492238491773605,
0.00938610453158617,
0.021622663363814354,
0.006163583602756262,
-0.008334985002875328,
0.012569216080009937,
0.005414857529103756,
-0.02074526622891426,
-0.07431931048631668,
0.003808311652392149,
-0.00644494267180562,
-0.03567143902182579,
-0.02942485921084881,
0.04963276535272598,
-0.00032276284764520824,
0.009224934503436089,
-0.04997197911143303,
-0.01972353644669056,
-0.0056764534674584866,
0.04244654253125191,
0.018225956708192825,
0.001491543254815042,
0.04944365471601486,
0.03910273686051369,
-0.004054631106555462,
-0.023482779040932655,
0.02138005942106247,
-0.03272357955574989,
0.007828271016478539,
0.049775104969739914,
0.02345307171344757,
-0.0015158046735450625,
-0.026640422642230988,
0.0015266214031726122,
0.013656986877322197,
-0.06895459443330765,
-0.019314264878630638,
0.03535192087292671,
0.01561724953353405,
-0.012698915787041187,
-0.06370623409748077,
-0.012016154825687408,
0.048712506890296936,
-0.013634052127599716,
0.04681796208024025,
0.030409136787056923,
-0.011747173964977264,
-0.00977402925491333,
-0.015968773514032364,
-0.061455223709344864,
-0.0015672565205022693,
0.1135065108537674,
-0.0003946224460378289,
-0.020803697407245636,
-0.033136624842882156,
-0.0014615020481869578,
0.021925369277596474,
0.0539499968290329,
-0.01523821335285902,
0.06529948115348816,
0.01796076074242592,
0.015824224799871445,
0.009275705553591251,
0.0038450045976787806,
0.021074580028653145,
-0.02251075766980648,
0.014977050945162773,
-0.0514860600233078,
0.04210206866264343,
-0.008466269820928574,
-0.03661911189556122,
0.05036402866244316,
-0.0000221775899262866,
0.01958548091351986,
0.05355782061815262,
0.025839298963546753,
0.04773604869842529,
-0.0033226870000362396,
-0.06860988587141037,
-0.0013026901287958026,
0.0037432806566357613,
-0.03102293238043785,
-0.009861454367637634,
0.12895922362804413,
0.052647657692432404,
0.024595487862825394,
0.039715226739645004,
0.04669007658958435,
0.036350879818201065,
0.030976803973317146,
0.036562275141477585,
0.018769316375255585,
-0.10090121626853943,
0.04776604101061821,
-0.022264620289206505,
-0.007966021075844765,
0.020317358896136284,
-0.030479194596409798,
-0.024179359897971153,
-0.02161451056599617,
0.049894072115421295,
0.009989527054131031,
0.002144459169358015,
-0.019738877192139626,
-0.013770653866231441,
-0.046308357268571854,
0.0068047852255403996,
0.006042954977601767,
0.0063375141471624374,
0.024545319378376007,
0.003710937686264515,
-0.057828471064567566,
0.041812434792518616,
-0.007758635096251965,
-0.02853378839790821,
0.05555161088705063,
-0.005104349460452795,
0.026185017079114914,
0.07308384031057358,
-0.01253579556941986,
-0.03635688126087189,
0.01050692331045866,
-0.04053168743848801,
0.03563731536269188,
-0.006838436704128981,
-0.009271854534745216,
-0.0003500648308545351,
0.0437973290681839,
-0.04648572951555252,
-0.001965445000678301,
0.023202085867524147,
-0.02117590233683586,
-0.015303613618016243,
0.0197187177836895,
-0.09098260849714279,
0.04315151646733284,
0.03531050309538841,
-0.029427366331219673,
0.004758132621645927,
-0.030689282342791557,
0.07137229293584824,
0.009560111910104752,
0.02765544131398201,
0.05652884393930435,
-0.0016059151384979486,
-0.008374889381229877,
0.05562569946050644,
-0.00028750489582307637,
0.015781624242663383,
-0.019067171961069107,
-0.017352662980556488,
-0.002791209612041712,
-0.02059074304997921,
0.008850558660924435,
0.04631456732749939,
0.02652944251894951,
0.02823086641728878,
-0.010788082145154476,
0.016996227204799652,
0.10703576356172562,
0.06775244325399399,
-0.015482083894312382,
-0.0058967010118067265,
0.011951045133173466,
-0.02550867386162281,
-0.026823440566658974,
0.027319971472024918,
-0.02238459698855877,
-0.018938647583127022,
-0.0024015961680561304,
0.035263266414403915,
0.031705085188150406,
0.014280632138252258,
-0.038134876638650894,
0.016263339668512344,
-0.0030472741927951574,
0.03467617556452751,
0.038625165820121765,
0.001823195954784751,
-0.024423152208328247,
0.06782224029302597,
-0.04498354718089104,
0.05192727595567703,
-0.08908259868621826,
0.03698596730828285,
0.007039494812488556,
0.027139119803905487,
-0.03135045990347862,
-0.059203244745731354,
-0.008151906542479992,
-0.020404737442731857,
-0.002729938831180334,
0.05318981781601906,
-0.04242860525846481,
-0.07447933405637741,
0.031060904264450073,
0.01696287840604782,
-0.033817678689956665,
-0.0010286641772836447,
0.03415459394454956,
-0.00020819138444494456,
0.026525404304265976,
0.026066187769174576,
0.0017967522144317627,
0.018843358382582664,
-0.031055500730872154,
0.025639547035098076,
0.004735253751277924,
-0.018225789070129395,
-0.013833240605890751,
-0.04101848602294922,
0.05505910515785217,
-0.01825040392577648,
0.026349028572440147,
-0.026594573631882668,
-0.06192826107144356,
0.0053151315078139305,
0.0297673549503088,
-0.03616985306143761,
-0.005616713315248489,
-0.03553270548582077,
-0.00968958344310522,
-0.03266938775777817,
0.013932907953858376,
0.03291032835841179,
-0.028910808265209198,
-0.06497112661600113,
-0.030471179634332657,
0.00178056419827044,
0.04051477834582329,
0.006530820392072201,
-0.019726933911442757,
-0.013033089227974415,
-0.049176864326000214,
-0.0166188832372427,
0.030425766482949257,
0.01702813431620598,
-0.00944510567933321,
0.021010354161262512,
0.028418440371751785,
0.04263561964035034,
-0.002113513881340623,
0.03585425391793251,
-0.00744525995105505,
0.014397876337170601,
0.06167981028556824,
0.011358346790075302,
0.021321341395378113,
0.01518968679010868,
-0.03449161723256111,
0.033558446913957596,
0.008414684794843197,
-0.014344403520226479,
-0.048798177391290665,
0.04359183460474014,
-0.03651375323534012,
-0.02796931192278862,
0.046640630811452866,
-0.022710207849740982,
0.01944759115576744,
0.08700801432132721,
-0.03423603996634483,
0.02841806970536709,
0.041138600558042526,
-0.026243159547448158,
-0.039581503719091415,
0.028562922030687332,
0.042924001812934875,
0.00004542015813058242,
0.023386768996715546,
0.0795440822839737,
-0.02449941635131836,
0.0636569932103157,
-0.004290561657398939,
-0.031030192971229553,
0.02224106155335903,
-0.05281767621636391,
0.0160079188644886,
-0.008204644545912743,
-0.01665220595896244,
0.07839573919773102,
0.000019579516447265632,
0.010203462094068527,
-0.04798257723450661,
-0.011856856755912304,
0.06035352870821953,
0.003166514215990901,
-0.03354434296488762,
0.013024838641285896,
-0.06278324872255325,
0.019086435437202454,
0.011689679697155952,
0.04512401297688484,
-0.02793259732425213,
-0.05966884642839432,
-0.04957211762666702,
0.005945886950939894,
-0.01969820261001587,
-0.010915671475231647,
-0.08760099858045578,
0.04709305986762047,
-0.013736092485487461,
-0.016010422259569168,
-0.025967465713620186,
0.008028888143599033,
0.051777515560388565,
-0.0007013828144408762,
-0.046747881919145584,
-0.012980681844055653,
0.005820726975798607,
-0.0040985532104969025,
-0.003278253134340048,
-0.019204426556825638,
0.004261281341314316,
-0.08405771106481552,
0.010102872736752033,
-0.06925135850906372,
0.05859867110848427,
-0.0037875899579375982,
-0.021893752738833427,
-0.004763473756611347,
-0.04326043650507927,
0.023658357560634613,
0.043366577476263046,
0.007451371755450964,
-0.0010757369454950094,
0.006120207253843546,
0.006739174481481314,
-0.009076721966266632,
0.04742814972996712,
0.004669600166380405,
0.036198701709508896,
-0.0027478463016450405,
-0.002840987639501691,
-0.052191514521837234,
-0.008273664861917496,
0.018329765647649765,
-0.027562811970710754,
0.02694210410118103,
-0.010352239944040775,
0.0161131601780653,
0.03773238882422447,
-0.06281321495771408,
0.049972712993621826,
0.05869940295815468,
-0.006579046603292227,
0.005334979854524136,
0.039991892874240875,
0.001906800433062017,
0.0029376621823757887,
-0.01891719363629818,
-0.00879117101430893,
0.033024176955223083,
0.012100886553525925,
-0.05343717336654663,
-0.027455758303403854,
-0.010429085232317448,
0.014829309657216072,
-0.023085974156856537,
0.0406947135925293,
-0.06746388226747513,
0.06204277276992798,
-0.05794772505760193,
-0.006359852850437164,
0.015072437934577465,
-0.012143289670348167,
-0.019228460267186165,
0.05731336027383804,
0.028315480798482895,
0.05659248307347298,
-0.019233636558055878,
0.023707067593932152,
0.021423207595944405,
-0.0018614184809848666,
-0.03550170361995697,
-0.03780920431017876,
-0.023280315101146698,
0.06608352065086365,
0.010783717967569828,
0.05539017915725708,
0.010692707262933254,
0.08774647861719131,
-0.005032889079302549,
-0.006880868226289749,
0.018125277012586594,
-0.018276803195476532,
0.004030815325677395,
0.050368666648864746,
0.021494902670383453,
-0.04020591080188751,
-0.009182635694742203,
-0.021595798432826996,
-0.0020612028893083334,
-0.04582126811146736,
0.032506149262189865,
-0.005238603334873915,
0.06263183802366257,
0.029932856559753418,
-0.009760212153196335,
0.016273248940706253,
0.030192507430911064,
-0.06415126472711563,
0.04225459322333336,
-0.07255291193723679,
0.03610672429203987,
-0.028700031340122223,
0.011720608919858932,
0.027275325730443,
-0.02116643823683262,
0.004685260821133852,
0.00923676136881113,
-0.00018980535969603807,
0.000568991235923022,
0.007573909591883421,
0.028173310682177544,
-0.005943079013377428,
-0.04416344687342644,
-0.022900205105543137,
0.0069615705870091915,
-0.04381472244858742,
-0.01946393772959709,
-0.05577418953180313,
-0.0017541045090183616,
-0.04586310684680939,
0.04901817813515663,
-0.02871389500796795,
0.027202384546399117,
-0.05174877122044563,
-0.020652491599321365,
0.048951826989650726,
0.028283609077334404,
0.019098958000540733,
-0.06135817989706993,
-0.028059231117367744,
-0.011638661846518517,
0.013685327023267746,
0.01584857515990734,
-0.02590750902891159,
0.029712148010730743,
0.03357238322496414,
0.024630507454276085,
-0.018678974360227585,
0.021268533542752266,
-0.026077168062329292,
-0.05622108280658722,
0.04313107952475548,
-0.07472927868366241,
-0.015283371321856976,
-0.025069642812013626,
0.03716795891523361,
0.03087964653968811,
0.026673292741179466,
0.039844006299972534,
-0.045586541295051575,
-0.006657807156443596,
-0.051324017345905304,
0.021643273532390594,
-0.04937763512134552,
-0.02528628148138523,
-0.023880967870354652,
-0.05052398145198822,
-0.021458161994814873,
-0.028716254979372025,
-0.033602118492126465,
-0.08630168437957764,
0.022379374131560326,
-0.01574067957699299,
-0.02401401847600937,
0.03981451690196991,
-0.029361648485064507,
0.011916188523173332,
0.009862803854048252,
0.01843423955142498,
0.0219494067132473,
-0.02055085077881813,
-0.005296836141496897,
0.07537882030010223,
-0.030716169625520706,
0.05121289938688278,
-0.016351858153939247,
-0.007797105237841606,
0.02850993722677231,
-0.07679928094148636,
0.0012370465556159616,
0.01191413588821888,
0.07568297535181046,
0.026165466755628586,
-0.049105204641819,
0.0077687837183475494,
-0.0011990866623818874,
0.030229821801185608,
0.09319370239973068,
0.02004479616880417,
-0.04151621460914612,
0.010593029670417309,
0.07480777055025101,
-0.029993649572134018,
0.01847916468977928,
-0.01873381994664669,
0.014723447151482105,
0.02342795953154564,
0.030449695885181427,
-0.013549549505114555,
0.038746390491724014,
-0.0029814697336405516,
0.08379808813333511,
-0.058890920132398605,
0.007285345811396837,
-0.02107253298163414,
0.002595206955447793,
0.04678931459784508,
-0.03812506049871445,
0.020609112456440926,
-0.05215275660157204,
0.01128064189106226,
0.022315040230751038,
-0.030823608860373497,
-0.08279839903116226,
0.05321343615651131,
0.020636335015296936,
0.033919431269168854,
-0.07122558355331421,
0.0468977726995945,
0.016360195353627205,
0.010254431515932083,
-0.049498483538627625,
-0.07620622217655182,
-0.04297109693288803,
0.011816401965916157,
-0.018020909279584885,
-0.019929993897676468,
0.052906155586242676,
-0.009925048798322678,
0.007906446233391762,
-0.0410124808549881,
0.04924285411834717,
0.004121521487832069,
-0.017138756811618805,
-0.03265027701854706,
0.025725768879055977,
0.047125332057476044,
0.05585714057087898,
-0.022445790469646454,
-0.017753414809703827,
0.03923540934920311,
-0.031756430864334106,
-0.05939248576760292,
0.07230678200721741,
-0.07438431680202484,
0.0377226360142231,
-0.07447871565818787,
0.06407947093248367,
0.036613598465919495,
-0.01556293573230505,
0.07413194328546524,
0.022840045392513275,
-0.009819299913942814,
-0.008249275386333466,
0.019009172916412354,
0.024960530921816826,
-0.018253518268465996,
-0.05758396163582802,
-0.029621953144669533,
0.010519306175410748,
-0.04214028641581535,
0.01852303370833397,
-0.05067393183708191,
-0.031793706119060516,
0.024816378951072693,
-0.012616054154932499,
-0.042532555758953094,
-0.001301336451433599,
-0.05084777623414993,
0.03082461655139923,
-0.03986886888742447,
-0.0021671471185982227,
0.014426710084080696,
0.0603828988969326,
0.03060510940849781,
-0.0002608134818729013,
-0.02181011252105236,
0.005871667992323637,
-0.021309996023774147,
-0.031677912920713425,
-0.0026726366486400366,
0.05632118508219719,
0.012604613788425922,
-0.033453140407800674,
0.006617747247219086,
-0.002556651597842574,
-0.038633573800325394,
0.05445432662963867,
0.0419028177857399,
-0.03494742512702942,
0.007370577659457922,
0.04416701942682266,
0.010803856886923313,
0.06969565898180008,
0.07879737764596939,
-0.002606659894809127,
0.011891419999301434,
0.07108698785305023,
0.03570723533630371,
-0.057008933275938034,
0.0042814575135707855,
-0.032121337950229645,
-0.0014482219703495502,
-0.009038034826517105,
-0.06126506254076958,
-0.017138762399554253,
0.03546668961644173,
-0.04756947606801987,
0.03225954994559288,
-0.013217058964073658,
-0.0428987517952919,
-0.05431880056858063,
-0.004052880685776472,
0.019737770780920982,
-0.06818260997533798,
-0.028200650587677956,
-0.054603785276412964,
-0.015637800097465515,
-0.02307538129389286,
-0.00553126260638237,
-0.0012276245979592204,
-0.0630037933588028,
-0.08698579668998718,
0.021009210497140884,
0.002950813854113221,
-0.05297490209341049,
0.008951771073043346,
0.0050349244847893715,
-0.00297025078907609,
0.059171874076128006,
-0.020986182615160942,
-0.030693285167217255,
-0.009717991575598717,
-0.0035421960055828094,
-0.05126788467168808,
-0.06024888530373573,
0.0181709136813879,
-0.07678022980690002,
-0.03558872640132904,
-0.052051011472940445,
-0.017522642388939857,
0.008744756691157818,
0.06285182386636734,
0.014143376611173153,
0.015455704182386398,
0.023543706163764,
0.03032822348177433,
-0.011956616304814816,
-0.022098099812865257,
-0.06766414642333984,
-0.013130527921020985,
-0.026440594345331192,
-0.02693239413201809,
-0.04568668454885483,
0.04036456346511841,
-0.025944743305444717,
0.018323557451367378,
-0.006691371090710163,
-0.012178795412182808,
-0.011811730451881886,
0.024139225482940674,
-0.005436302628368139,
-0.005228548776358366,
0.004448804073035717,
0.008666475303471088,
0.025179358199238777,
-0.03994947671890259,
0.03972119837999344,
0.014625894837081432,
-0.053496845066547394,
-0.02523052878677845,
-0.04705870524048805,
0.07945186644792557,
0.06175883114337921,
0.01566375605762005,
-0.026529652997851372,
-0.03775046765804291,
-0.046070583164691925,
-0.007237537298351526,
0.018410110846161842,
0.052935872226953506,
-0.05987058952450752,
-0.0106858154758811,
-0.025877662003040314,
0.01664712466299534,
0.002643142594024539,
-0.00597807765007019,
-0.0006038681021891534,
0.019546207040548325,
0.038921814411878586,
-0.03502899408340454,
-0.010004048235714436,
-0.04111857712268829,
-0.010428903624415398,
-0.013966514728963375,
0.01840946450829506,
-0.030693156644701958,
-0.01294222753494978,
0.0371110737323761,
-0.04657996445894241,
-0.05263589322566986,
-0.03202042728662491,
-0.029668595641851425,
-0.007717529311776161,
-0.054179705679416656,
-0.03494328632950783,
-0.05827515572309494,
0.006064793094992638,
0.0024121939204633236,
-0.024523764848709106,
0.021293288096785545,
0.06462666392326355,
-0.011101087555289268,
0.05511955916881561,
-0.009751369245350361,
-0.014776983298361301,
-0.007440583314746618,
-0.002003374742344022,
-0.04427725076675415,
-0.007138177286833525,
-0.010231224820017815,
-0.07008751481771469,
0.018582573160529137,
-0.01956644281744957,
-0.004134741611778736,
-0.00822083093225956,
-0.006359901279211044,
0.04231658950448036,
-0.04646856710314751,
-0.021683815866708755,
0.030916133895516396
] |
<p>Suppose I have plenty of food I want to heat (which will provide load) in the microwave, and one item I don't want to heat. What properties would make a material a a good shield, to reduce or prevent heating of that item? I know metal can work as a barrier in the form of a Faraday cage, but that there are also potential issues with arcing. Presumably some kind of smoothly flexible metal mesh would be a good candidate - what properties would it need to be effective? (For example, we might consider mesh spacing, wire diameter, and the choice of metal.)</p>
<p><sub>(Note: this is based on <a href="http://cooking.stackexchange.com/q/33871/1672">this question</a>, which was recently migrated over to Seasoned Advice (food and cooking), but I think that it could really use physics expertise, so this is a rephrased version, addressing the complaints I saw leading to that question's migration.)</sub></p> | g4569 | [
0.05462140589952469,
0.027799442410469055,
0.026615247130393982,
-0.007626446429640055,
0.00839309487491846,
-0.015054055489599705,
-0.026039008051156998,
0.008396629244089127,
-0.0377650186419487,
-0.048595454543828964,
0.043396513909101486,
0.04699644073843956,
-0.03740283101797104,
0.04301552474498749,
0.029955081641674042,
0.008656498976051807,
0.0243427325040102,
0.027044016867876053,
0.028366753831505775,
0.07520491629838943,
-0.01759996823966503,
-0.017580941319465637,
-0.023476390168070793,
-0.005247053224593401,
-0.04344513639807701,
0.008060706779360771,
0.03490353375673294,
0.027294913306832314,
0.0012639636406674981,
-0.018069999292492867,
-0.03506315499544144,
-0.055810779333114624,
-0.023592086508870125,
-0.049144163727760315,
-0.053176503628492355,
0.020968789234757423,
-0.003815221833065152,
0.009826980531215668,
-0.06320882588624954,
-0.011988397687673569,
0.0111272307112813,
0.016043847426772118,
0.011037050746381283,
0.0343136228621006,
0.050167765468358994,
0.07316523045301437,
-0.040113624185323715,
0.01348953414708376,
0.028002433478832245,
-0.02709820866584778,
-0.0066290744580328465,
-0.04070939123630524,
0.02512548118829727,
-0.09623662382364273,
-0.005708395969122648,
-0.06846005469560623,
-0.039335984736680984,
0.013841137290000916,
0.04504481330513954,
-0.02972196787595749,
-0.009645659476518631,
0.05647712200880051,
-0.08116143196821213,
-0.050463560968637466,
-0.0053960164077579975,
0.024398865178227425,
-0.06408723443746567,
0.003751652082428336,
0.016837652772665024,
0.05649251863360405,
0.01001000590622425,
0.03721777722239494,
-0.0018655994208529592,
-0.02211015671491623,
0.036601051688194275,
0.002750278217718005,
-0.07272855192422867,
0.04571273922920227,
0.04151453822851181,
-0.013971051201224327,
-0.009037555195391178,
0.03155539184808731,
-0.021662099286913872,
-0.014155757613480091,
-0.005192853044718504,
0.0020458754152059555,
-0.009072946384549141,
-0.042140208184719086,
-0.02188309095799923,
0.0013480931520462036,
-0.02560892514884472,
0.015396656468510628,
0.05437129735946655,
0.002921886509284377,
0.0332767628133297,
0.08382383733987808,
-0.014828497543931007,
-0.020511209964752197,
-0.034738946706056595,
-0.021374911069869995,
0.08466064929962158,
-0.035138119012117386,
0.058599360287189484,
-0.0003824887389782816,
-0.0455951951444149,
0.01833033747971058,
0.039096906781196594,
0.055801428854465485,
-0.0020902010146528482,
0.025693707168102264,
-0.03752952441573143,
0.000585583271458745,
-0.08871354907751083,
-0.02587917260825634,
0.016127809882164,
0.011249544098973274,
0.08492665737867355,
0.03855406120419502,
0.04631685093045235,
0.04797365516424179,
0.01762959361076355,
0.02381402626633644,
0.03335554525256157,
0.025227949023246765,
-0.00935834925621748,
0.0031622201204299927,
0.0028084623627364635,
0.011765848845243454,
0.020196087658405304,
-0.013214746490120888,
0.004764783661812544,
-0.005735210608690977,
-0.038302917033433914,
0.03185517340898514,
-0.02725299820303917,
0.014540743082761765,
-0.004577346611768007,
-0.012431184761226177,
0.0051427544094622135,
-0.019991764798760414,
0.04487786814570427,
-0.03837805241346359,
0.009392250329256058,
-0.0366659089922905,
-0.006914109457284212,
0.02737722359597683,
-0.036869119852781296,
0.015893561765551567,
0.02333351969718933,
0.011283669620752335,
0.01864703558385372,
0.07312022894620895,
-0.018476102501153946,
-0.015310528688132763,
-0.00795146357268095,
-0.026063883677124977,
0.05174792930483818,
-0.034407924860715866,
0.09109020978212357,
0.013411241583526134,
0.05039791762828827,
0.0402764230966568,
-0.017070140689611435,
-0.03913705423474312,
-0.018864599987864494,
0.04255867749452591,
-0.0298153143376112,
0.008008433505892754,
0.03330015763640404,
-0.0019801899325102568,
-0.004565607290714979,
-0.023564845323562622,
-0.027628479525446892,
0.057695530354976654,
-0.03347953408956528,
-0.03192787244915962,
0.08756718784570694,
-0.012426072731614113,
0.04331059008836746,
-0.06793511658906937,
-0.017061738297343254,
-0.050628796219825745,
0.07827429473400116,
0.01966020278632641,
-0.04725363105535507,
0.0245272908359766,
0.06277509778738022,
-0.004487867932766676,
-0.06683836877346039,
0.05679449811577797,
-0.012198631651699543,
-0.032076284289360046,
-0.0031929947435855865,
0.0040586101822555065,
-0.0011591961374506354,
-0.0232984758913517,
0.031478285789489746,
0.035974591970443726,
0.00263597397133708,
-0.04733939841389656,
-0.000817230436950922,
-0.007601152174174786,
0.043733078986406326,
0.056715697050094604,
-0.01772025227546692,
0.011598465964198112,
0.0005475320504046977,
-0.014465440064668655,
0.011872085742652416,
-0.06581052392721176,
0.057139959186315536,
0.04040611535310745,
-0.0028143974486738443,
-0.0236723143607378,
0.0650925412774086,
0.050738219171762466,
-0.04625771939754486,
0.007650638930499554,
-0.036435529589653015,
0.014054342173039913,
0.01156332716345787,
-0.03770747035741806,
0.0069979592226445675,
-0.01132106501609087,
-0.00021143084450159222,
-0.02438153140246868,
0.01155246701091528,
-0.013277932070195675,
-0.03885282203555107,
0.011527931317687035,
-0.05123068764805794,
-0.03686722740530968,
0.040966279804706573,
-0.044400498270988464,
0.01782180368900299,
0.00031142073567025363,
0.03177984431385994,
0.018690789118409157,
-0.048029668629169464,
-0.030763741582632065,
0.03020010143518448,
-0.02898435667157173,
0.000017775859305402264,
-0.04706389829516411,
0.05996431037783623,
-0.05667053535580635,
-0.010885246098041534,
0.009158061817288399,
0.060669127851724625,
-0.003618768183514476,
0.022484706714749336,
-0.03083060309290886,
-0.06047465279698372,
0.03678898513317108,
-0.04919307306408882,
-0.036530498415231705,
0.016279609873890877,
0.001122439163736999,
0.011898176744580269,
0.0086012352257967,
-0.0013442635536193848,
-0.09816242009401321,
0.011446741409599781,
0.004885443951934576,
-0.050804704427719116,
-0.03672439604997635,
-0.069826640188694,
0.0009068147046491504,
0.03605912625789642,
0.045703399926424026,
-0.01842312701046467,
-0.0052711027674376965,
0.03636447340250015,
0.01751919463276863,
-0.0018468346679583192,
-0.04989442601799965,
0.02973250113427639,
-0.026841748505830765,
0.050297293812036514,
0.0189284048974514,
0.026118049398064613,
-0.007955058477818966,
-0.007358103059232235,
0.03134044632315636,
0.01965312846004963,
0.02410712279379368,
-0.026764031499624252,
0.047880809754133224,
-0.004812759812921286,
0.01694377139210701,
-0.0514705590903759,
0.0007717734551988542,
0.016842877492308617,
0.024799125269055367,
-0.034296873956918716,
-0.02318277768790722,
-0.006650786381214857,
0.012967483140528202,
-0.008777746930718422,
-0.08101261407136917,
-0.04092736914753914,
0.01353493519127369,
-0.05707646533846855,
-0.04486836493015289,
-0.006171782035380602,
0.03714510798454285,
-0.034465283155441284,
-0.03766370564699173,
0.0587196908891201,
-0.0034173806197941303,
0.028195498511195183,
0.005907779559493065,
0.02812327817082405,
0.010399449616670609,
-0.05134081095457077,
0.00863663386553526,
-0.00499045941978693,
-0.018796324729919434,
0.030844125896692276,
0.03142434358596802,
0.016267171129584312,
0.017317986115813255,
0.0051535931415855885,
-0.08677097409963608,
0.006455986760556698,
0.06469950824975967,
0.0345940887928009,
-0.024051522836089134,
-0.01487504132091999,
-0.01668539084494114,
0.029786832630634308,
-0.009692723862826824,
-0.019870329648256302,
-0.04393966495990753,
-0.0780356153845787,
0.03667062520980835,
-0.015499083325266838,
0.018332453444600105,
0.02921832911670208,
0.011182857677340508,
-0.012923258356750011,
-0.06325386464595795,
0.022795971482992172,
-0.0547930970788002,
0.008345598354935646,
0.03472820296883583,
-0.0026643825694918633,
-0.013631857000291348,
-0.015788476914167404,
-0.022263983264565468,
0.03031851351261139,
0.04278991371393204,
0.022002391517162323,
0.0014153843512758613,
-0.0065451133996248245,
0.031773969531059265,
0.03272617608308792,
-0.008940950967371464,
0.017911028116941452,
0.024464089423418045,
-0.03886495903134346,
-0.047683198004961014,
-0.039162714034318924,
-0.07997947186231613,
0.024743417277932167,
0.03550740331411362,
0.0367804616689682,
0.0543951615691185,
0.0014819290954619646,
-0.006762841250747442,
0.013363276608288288,
-0.038247112184762955,
-0.03491993620991707,
-0.008580612950026989,
0.04467775300145149,
0.049193356186151505,
-0.019630249589681625,
0.003187946043908596,
-0.02078077383339405,
-0.041189298033714294,
-0.05956392362713814,
-0.0008759018965065479,
-0.01971156895160675,
0.0010576533386483788,
-0.012021909467875957,
0.0027237716130912304,
0.061353765428066254,
0.04740634933114052,
-0.036341216415166855,
-0.06583574414253235,
0.0013369345106184483,
-0.04634838551282883,
-0.012673621065914631,
0.006376467179507017,
0.020941514521837234,
-0.03142878785729408,
-0.02310056798160076,
-0.05241858959197998,
0.0025723509024828672,
0.031607866287231445,
0.06292308866977692,
0.07758449018001556,
-0.02975824475288391,
-0.00645696185529232,
0.0037460923194885254,
-0.05983630195260048,
0.07386140525341034,
-0.024643225595355034,
-0.023297853767871857,
-0.05977838113903999,
-0.006222487427294254,
-0.07468073070049286,
-0.020690811797976494,
-0.020256120711565018,
0.005823735147714615,
-0.055624764412641525,
-0.01776379905641079,
-0.010425835847854614,
0.02007986791431904,
-0.022409195080399513,
-0.03812851384282112,
0.029897496104240417,
0.0021593321580439806,
0.023440567776560783,
-0.00467079458758235,
0.05833350494503975,
0.017466746270656586,
-0.04685843735933304,
-0.0004828458768315613,
0.02372305653989315,
0.005311089567840099,
0.012055442668497562,
-0.0811939612030983,
-0.05624945089221001,
0.05623947083950043,
-0.003953143022954464,
-0.0685022845864296,
-0.04263102635741234,
-0.050639912486076355,
0.035123955458402634,
-0.021039558574557304,
0.010227182880043983,
0.01635843515396118,
-0.029362786561250687,
-0.023851076140999794,
0.022100234404206276,
-0.04155070707201958,
0.02737397886812687,
-0.01813923940062523,
0.022052790969610214,
0.00822378695011139,
-0.048113226890563965,
-0.025746379047632217,
-0.046652283519506454,
-0.04313318431377411,
-0.006733056623488665,
-0.008972615003585815,
-0.013311267830431461,
0.11472437530755997,
0.004482517018914223,
-0.056304339319467545,
-0.002390920417383313,
-0.05153791606426239,
0.005374799948185682,
0.013514328747987747,
-0.012632985599339008,
0.039423443377017975,
0.00021520399604924023,
0.012744552455842495,
0.06838136911392212,
0.0002481756964698434,
0.05202643945813179,
-0.009942889213562012,
0.008992902934551239,
0.019949838519096375,
0.01602931320667267,
-0.019450347870588303,
-0.02254432626068592,
-0.03395915776491165,
-0.026521049439907074,
-0.02192840538918972,
0.07462453097105026,
0.01910077966749668,
0.02851501666009426,
0.025077039375901222,
-0.03516959026455879,
-0.010616851970553398,
0.06019320711493492,
0.021697938442230225,
-0.0025394707918167114,
0.019520344212651253,
0.004401123616844416,
0.02943073958158493,
0.02675088495016098,
-0.0010707275941967964,
0.010137662291526794,
0.0740881860256195,
-0.038403209298849106,
-0.053085144609212875,
0.017246698960661888,
0.0013996288180351257,
-0.019625525921583176,
-0.014294520951807499,
-0.010681455954909325,
-0.01559029333293438,
0.004828887991607189,
0.045765120536088943,
-0.04730282351374626,
0.04996649920940399,
-0.03634921833872795,
-0.0014913111226633191,
-0.01298525184392929,
-0.03499766066670418,
-0.04965470731258392,
0.018546313047409058,
0.003902353113517165,
-0.002581386361271143,
-0.07649601995944977,
-0.021724972873926163,
-0.042445339262485504,
-0.027519552037119865,
0.00995152723044157,
0.0028649228624999523,
0.03450675681233406,
0.018540391698479652,
-0.016911569982767105,
-0.013184970244765282,
0.0035592638887465,
-0.031001821160316467,
0.055895544588565826,
0.04441600665450096,
0.00991721823811531,
-0.024165291339159012,
-0.013069992884993553,
-0.040099743753671646,
0.049593571573495865,
0.013610859401524067,
0.032569222152233124,
0.030080394819378853,
0.005860805511474609,
-0.03310375288128853,
-0.02035108208656311,
0.05955061316490173,
0.04391525685787201,
0.0022253557108342648,
-0.03603454306721687,
-0.000022238808014662936,
0.05121955648064613,
0.029743753373622894,
0.03036533296108246,
0.017270555719733238,
-0.003076833439990878,
0.05147620663046837,
-0.05373146012425423,
0.07450242340564728,
0.0890069305896759,
0.04544096067547798,
0.010511568747460842,
0.05733710154891014,
-0.035542771220207214,
0.013767548836767673,
0.01394953578710556,
0.018955891951918602,
0.00913326907902956,
0.024980710819363594,
-0.03582175076007843,
-0.05529071390628815,
-0.019553545862436295,
0.04750461503863335,
0.03607017174363136,
0.0044022053480148315,
-0.017870696261525154,
0.0020211415830999613,
-0.005275885108858347,
-0.03261799365282059,
0.00928238034248352,
-0.0653170719742775,
-0.027863454073667526,
-0.013321524485945702,
0.01350472867488861,
0.01484654750674963,
0.047057028859853745,
0.013898112811148167,
-0.019588224589824677,
-0.02849424071609974,
0.02462352253496647,
-0.01532745361328125,
-0.010805627331137657,
0.007169707212597132,
-0.05316173657774925,
0.031553976237773895,
-0.005346100311726332,
0.03417833149433136,
0.07508029788732529,
0.046018335968256,
-0.02096681483089924,
0.00871532503515482,
0.007265271618962288,
0.012860908173024654,
0.0807504653930664,
0.04087240993976593,
-0.062042172998189926,
-0.003919730428606272,
-0.05507846921682358,
0.02207096852362156,
0.07955767214298248,
0.07858215272426605,
-0.005222741514444351,
0.0065074278973042965,
-0.006475004833191633,
0.03059961460530758,
0.004862585570663214,
0.0350111685693264,
0.0044336202554404736,
0.0014375759055837989,
-0.013093954883515835,
-0.027875786647200584,
-0.028007248416543007,
-0.04471396654844284,
0.035949207842350006,
-0.012335021048784256,
-0.012838112190365791,
-0.03523030877113342,
-0.005198993254452944,
-0.016616372391581535,
-0.005538080353289843,
-0.02698301151394844,
0.03483359143137932,
0.05497501790523529,
-0.04605494439601898,
-0.020913511514663696,
-0.008559473790228367,
0.04538819566369057,
-0.026198919862508774,
-0.03348810225725174,
0.020082896575331688,
0.000007885013474151492,
0.0283108651638031,
-0.02226812206208706,
0.016506005078554153,
-0.064209945499897,
0.012300532311201096,
0.06010745093226433,
0.10268286615610123,
-0.02800413779914379,
0.013520929962396622,
-0.02303982339799404,
0.016098039224743843,
-0.039185430854558945,
0.0028743857983499765,
-0.06078140437602997,
0.007246390450745821,
-0.07335012406110764,
-0.004533896688371897,
0.006160525605082512,
-0.025950249284505844,
-0.03926306217908859,
0.009112880565226078,
0.03631671518087387,
-0.004371775779873133,
0.012876459397375584,
-0.03801900893449783,
0.05417313054203987,
-0.0484468936920166,
-0.02753707766532898,
0.034876566380262375,
-0.02477455511689186,
-0.021440986543893814,
-0.027722854167222977,
-0.03202027454972267,
0.003887222381308675,
-0.014412290416657925,
0.005366733763366938,
-0.019588565453886986,
0.028282707557082176,
-0.034065306186676025,
-0.031818509101867676,
-0.03736386075615883,
0.005508736241608858,
-0.015303459949791431,
-0.058527372777462006,
0.030815718695521355,
0.04036913067102432,
-0.03264749050140381,
0.011788493022322655,
0.014725943095982075,
0.0026791878044605255,
0.05932098627090454,
0.0256004948168993,
0.013921273872256279,
-0.006814708933234215,
0.034491900354623795,
0.01249011978507042,
0.02904606983065605,
-0.025928635150194168,
0.012110375799238682,
0.04673835262656212,
0.005028643645346165,
0.012649263255298138,
-0.015984678640961647,
-0.00021102902246639132,
0.01915222965180874,
0.009833136573433876,
-0.027214184403419495,
0.06256148964166641,
0.09167535603046417,
-0.01145901158452034,
0.027089936658740044,
-0.054787781089544296,
-0.009405743330717087,
0.07548590749502182,
0.07509106397628784,
0.033678069710731506,
0.018433766439557076,
0.007631485350430012,
-0.0033857920207083225,
-0.09168919920921326,
0.03757292404770851,
0.010174312628805637,
0.0024135129060596228,
-0.009669279679656029,
0.013708874583244324,
0.031693652272224426,
-0.01863042637705803,
0.026402214542031288,
-0.024459686130285263,
0.005269069690257311,
-0.005866379477083683,
0.0024183066561818123,
0.023992428556084633,
0.05046173557639122,
-0.026863928884267807,
-0.013777842745184898,
0.019217096269130707,
-0.02912481687963009,
-0.06821180880069733,
0.039396077394485474,
-0.003531750990077853,
0.020162386819720268,
0.06522378325462341,
0.07119560241699219,
0.054029680788517,
-0.062105048447847366,
-0.07543383538722992,
-0.011446744203567505,
0.0017729675164446235,
-0.05418654903769493,
0.04743590205907822,
0.002772210631519556,
-0.035021815448999405,
-0.09288300573825836,
-0.05721447244286537,
-0.0934615507721901,
-0.04750419780611992,
-0.014809021726250648,
-0.030415192246437073,
-0.07889623939990997,
-0.03642474487423897,
0.03616594150662422,
-0.0022062682546675205,
0.028443876653909683,
-0.02311187982559204,
0.007077536080032587,
0.032430101186037064,
-0.01678064465522766,
-0.0043953657150268555,
0.010364804416894913,
-0.07627522945404053
] |
<p>I'm trying to introduce myself to QFT following <a href="http://www.damtp.cam.ac.uk/user/tong/qft.html" rel="nofollow">these lectures</a> by David Tong. I've started with lecture 1 (Classical Field Theory) and I'm trying to prove that under an infinitesimal Lorentz transformation of the form</p>
<p>$$\tag{1.49} {\Lambda^\mu}_\nu={\delta^\mu}_\nu+{\omega^\mu}_\nu,$$</p>
<p>where $\omega$ is antisymmetric, the variation of the Lagrangian density $\mathcal{L}$ is</p>
<p>$$\tag{1.53} \delta\mathcal{L}=-\partial_\mu({\omega^\mu}_\nu{x}^\nu\mathcal{L}).$$</p>
<p>Using $\mathcal{L}=\mathcal{L}(\phi,\partial_\mu\phi)$, I've tried computing $\delta\mathcal{L}$ directly using</p>
<p>$$\tag{1.52} \delta\phi=-{\omega^\mu}_\nu{x}^\nu\partial_\mu\phi$$</p>
<p>[which I obtained earlier computing explicitly $\phi(x)\to\phi(\Lambda^{-1}x)$], however, I get
$$\delta\mathcal{L}=-\partial_\mu({\omega^\mu}_\nu{x}^\nu\mathcal{L})-\frac{\partial\mathcal{L}}{\partial(\partial_\mu\phi)}{\omega^\sigma}_\mu\partial_\sigma\phi$$
The extra term arises when I compute
$$\partial_\mu(\delta\phi)=-{\omega^\sigma}_\nu\left[{\delta^\nu}_\mu\partial_\sigma\phi+x^\nu\partial_{\mu\sigma}\phi\right]=-{\omega^\sigma}_\mu\partial_{\sigma}\phi-{\omega^\sigma}_\nu{x}^\nu\partial_{\mu\sigma}\phi$$</p>
<p>[because I'm assuming $\partial_\mu(\delta\phi)=\delta(\partial_\mu\phi)$]; I thought I'd get rid of it just replacing $\phi$ with $\partial_\sigma\phi$ in $(1.52)$, however $\partial_\mu(\delta\phi)=\delta(\partial_\mu\phi)$ should still hold, ain't it? I also tried using (the previous expression to) 1.27 in the lectures, namely that the derivatives of the field transform as</p>
<p>$$\tag{1.26b} \partial_\mu\phi(x)\to{(\Lambda^{-1})^\nu}_\mu\partial_\nu\phi(\Lambda^{-1}x),$$</p>
<p>but I still get (to the first order in $\omega$),</p>
<p>\begin{align}{(\Lambda^{-1})^\nu}_\mu\partial_\nu\phi(\Lambda^{-1}x)&=({\delta^\nu}_\mu-{\omega^\nu}_\mu)\partial_\nu\phi(x^\sigma-{\omega^\sigma}_\rho{x}^\rho)\\&=({\delta^\nu}_\mu-{\omega^\nu}_\mu)\left[\partial_\nu\phi(x)-{\omega^\sigma}_\rho{x}^\rho\partial_{\sigma\nu}\phi(x)\right]\\&=\partial_\mu\phi-{\omega^\sigma}_\rho{x}^\rho\partial_{\sigma\mu}\phi-{\omega^\nu}_\mu\partial_\nu\phi\end{align} </p>
<p>I'm resisting the idea that ${\omega^\nu}_\mu\partial_\nu\phi=0$, but I don't understand what I'm doing wrong.</p> | g4570 | [
0.04084538668394089,
-0.012927178293466568,
-0.013204035349190235,
-0.06116707995533943,
0.02959783747792244,
-0.009186120703816414,
0.033523079007864,
0.012106815353035927,
-0.030693521723151207,
-0.04398193582892418,
-0.03902026265859604,
0.07178738713264465,
-0.002429269254207611,
0.04197605699300766,
0.03430929780006409,
0.04443718120455742,
0.019547060132026672,
-0.00022906977392267436,
0.0187112707644701,
-0.06081203371286392,
-0.0662454217672348,
0.05073046684265137,
0.050835903733968735,
-0.05361507833003998,
0.038766756653785706,
-0.02081421948969364,
-0.004508296027779579,
0.031485773622989655,
-0.04868585243821144,
-0.001317875343374908,
-0.027400271967053413,
0.01055760309100151,
0.0013639412354677916,
0.007069379556924105,
-0.014493212103843689,
-0.009918026626110077,
0.0430874228477478,
0.024283040314912796,
0.04428201541304588,
0.0024461273569613695,
0.0049476842395961285,
-0.010193121619522572,
0.05580383166670799,
0.03971630707383156,
-0.03500402346253395,
-0.02188786119222641,
-0.06140488013625145,
0.012483805418014526,
-0.04999374598264694,
0.06263615936040878,
0.009433580562472343,
0.05030706524848938,
0.052800312638282776,
-0.059227559715509415,
-0.04893684387207031,
0.003063302021473646,
0.03759673237800598,
-0.044471804052591324,
0.023203914985060692,
0.01833127997815609,
0.011920304037630558,
-0.0543300099670887,
0.002872176468372345,
-0.03800908476114273,
0.02118713967502117,
-0.005248309578746557,
0.016908474266529083,
-0.02186201512813568,
-0.05062185972929001,
0.0050895982421934605,
-0.022234471514821053,
-0.014593666419386864,
0.0198113564401865,
0.005037736613303423,
0.00654230173677206,
0.018482755869627,
-0.03659787029027939,
0.020510058850049973,
0.031924132257699966,
-0.03237292915582657,
-0.039486147463321686,
-0.037446435540914536,
-0.021463515236973763,
0.03295771777629852,
0.049507733434438705,
-0.01661042682826519,
-0.014966455288231373,
0.014450183138251305,
0.01997283287346363,
0.004341815132647753,
-0.03572845831513405,
-0.017926158383488655,
-0.007965117692947388,
-0.049422409385442734,
0.004859196953475475,
-0.021752674132585526,
0.0059808529913425446,
0.014417996630072594,
-0.022846076637506485,
-0.049025557935237885,
-0.0025867456570267677,
0.08054759353399277,
0.013222482986748219,
0.06705141067504883,
-0.035013340413570404,
0.040764037519693375,
0.03768393397331238,
-0.0022744631860405207,
-0.009107597172260284,
0.037063635885715485,
-0.04606519266963005,
0.017123199999332428,
0.04403921589255333,
-0.03684591129422188,
-0.028221070766448975,
-0.025437526404857635,
-0.0065676430240273476,
0.0014791380381211638,
-0.002805344993248582,
0.0635635256767273,
-0.0035863476805388927,
-0.03505479544401169,
0.10511825978755951,
0.025770798325538635,
0.02661595493555069,
-0.013626880012452602,
-0.01062716729938984,
0.025848310440778732,
0.05016494542360306,
-0.031983632594347,
0.02699749730527401,
0.038250893354415894,
-0.006464426405727863,
0.01907980814576149,
-0.005095951724797487,
0.018055999651551247,
-0.0266822911798954,
0.03020785190165043,
0.0014283446362242103,
0.011903826147317886,
0.012428674846887589,
-0.013588915579020977,
-0.03259808197617531,
-0.02496829256415367,
0.03269731253385544,
0.024261340498924255,
0.029959063977003098,
-0.0971345603466034,
-0.03164136782288551,
-0.038523636758327484,
-0.017032833769917488,
0.06695587188005447,
0.009307639673352242,
0.091715008020401,
0.015509063377976418,
0.006223536562174559,
0.06438768655061722,
-0.037849873304367065,
-0.008830697275698185,
-0.027962520718574524,
0.027721941471099854,
-0.00894198752939701,
0.0323692224919796,
-0.06721906363964081,
0.012110214680433273,
0.029362162575125694,
0.04206182435154915,
-0.04972173273563385,
-0.045552484691143036,
-0.039430879056453705,
-0.019557498395442963,
-0.011802325956523418,
0.02722114883363247,
-0.0014183031162247062,
0.01784389838576317,
0.0258956216275692,
-0.02383682318031788,
-0.00949417520314455,
0.00496981805190444,
0.015713879838585854,
-0.03570740297436714,
-0.026267508044838905,
-0.010395883582532406,
0.0040915245190262794,
0.01044307742267847,
-0.021855400875210762,
-0.007013339549303055,
0.005034645088016987,
-0.008192385546863079,
0.021036427468061447,
-0.06079339236021042,
0.018874645233154297,
-0.028667999431490898,
0.01617804542183876,
0.00702700624242425,
0.04295630753040314,
0.03222713619470596,
-0.09215125441551208,
-0.07531167566776276,
-0.02851105108857155,
-0.02338334545493126,
0.018231108784675598,
0.05230603367090225,
-0.012732229195535183,
0.014615464024245739,
-0.008837149478495121,
-0.018333904445171356,
-0.02241295576095581,
-0.004297219682484865,
-0.018469534814357758,
0.0007296764524653554,
-0.09212843328714371,
-0.02234233170747757,
0.007152642589062452,
-0.01665305718779564,
-0.011435097083449364,
0.019736088812351227,
0.0037857741117477417,
-0.043008528649806976,
0.07834793627262115,
0.013057361356914043,
-0.00020285957725718617,
0.06357797235250473,
0.0020679370500147343,
-0.06601204723119736,
0.03779936581850052,
0.05293784290552139,
0.015189353376626968,
-0.014767090789973736,
0.009182673878967762,
-0.04288662597537041,
0.03643353655934334,
0.0011182855814695358,
0.010406535118818283,
-0.007240588776767254,
-0.008641050197184086,
-0.05497613921761513,
0.02664191462099552,
0.006949826143682003,
0.053749892860651016,
0.05620007589459419,
0.04683779552578926,
-0.025641974061727524,
0.0034838945139199495,
0.023734712973237038,
-0.0476699061691761,
0.052137717604637146,
0.06398464739322662,
-0.0017980833072215319,
0.005780278705060482,
0.0017996709793806076,
-0.01719500683248043,
0.022572044283151627,
-0.006364009343087673,
0.03218074142932892,
0.0023349919356405735,
-0.032014694064855576,
-0.022108756005764008,
0.036955997347831726,
-0.03267321735620499,
-0.010934202931821346,
-0.007191207259893417,
-0.0028249025344848633,
0.005000598728656769,
-0.05591081827878952,
0.0015577046433463693,
-0.02411905862390995,
0.03398820757865906,
-0.01685284823179245,
-0.0014956771628931165,
0.0032489753793925047,
0.07487045973539352,
0.06030014902353287,
0.05231991410255432,
-0.007519426289945841,
0.018496284261345863,
-0.05393274500966072,
-0.018807996064424515,
0.028862066566944122,
0.021763445809483528,
0.06409244239330292,
-0.0005367062985897064,
0.023370491340756416,
0.07195952534675598,
0.0054123420268297195,
-0.06846339255571365,
0.008501730859279633,
0.019022833555936813,
-0.03042810969054699,
0.023275507614016533,
0.0015717544592916965,
0.03225983306765556,
0.016915297135710716,
-0.025167087092995644,
-0.02243896760046482,
0.04314322769641876,
-0.011847982183098793,
-0.08461948484182358,
-0.019730761647224426,
0.022668126970529556,
-0.006918051745742559,
0.010791188105940819,
0.01637125387787819,
0.04702163487672806,
0.06147228181362152,
0.006789581384509802,
-0.04473712295293808,
0.003113432787358761,
0.012208913452923298,
-0.00732405437156558,
0.02310827560722828,
-0.024087734520435333,
0.019550075754523277,
-0.10395234078168869,
-0.04163464158773422,
-0.03368910402059555,
0.04450798034667969,
0.008930757641792297,
0.0032955387141555548,
0.006937447004020214,
-0.012955371290445328,
-0.08537942171096802,
-0.02313338778913021,
0.0024239718914031982,
0.05776384472846985,
0.015702124685049057,
-0.04511192440986633,
0.002339289290830493,
-0.04881243035197258,
-0.048994217067956924,
0.025302009657025337,
0.014367136172950268,
-0.005129956174641848,
-0.030288558453321457,
-0.07316618412733078,
0.0067287590354681015,
-0.0832572802901268,
0.004902826156467199,
0.010387285612523556,
-0.011708507314324379,
-0.07688500732183456,
-0.020240819081664085,
-0.02473551593720913,
0.028667978942394257,
0.03539438173174858,
-0.054017577320337296,
0.022241821512579918,
0.025013351812958717,
0.019210990518331528,
0.030280131846666336,
-0.025732090696692467,
-0.011802781373262405,
0.015134298242628574,
-0.0006118247983977199,
0.006538851652294397,
0.037329815328121185,
0.051223624497652054,
0.010398351587355137,
0.07098019868135452,
-0.021657289937138557,
0.0342475064098835,
-0.04519530013203621,
-0.04915419593453407,
0.01656290329992771,
-0.015387151390314102,
0.03231904283165932,
0.022678285837173462,
-0.022099904716014862,
-0.04705425724387169,
0.036217499524354935,
0.07235533744096756,
-0.026461509987711906,
0.02787824533879757,
0.04497789219021797,
-0.025243597105145454,
-0.07447676360607147,
0.012382682412862778,
0.03964890167117119,
-0.026084721088409424,
0.059184730052948,
-0.0075671779923141,
0.02508062683045864,
-0.006156047806143761,
-0.0017037318320944905,
0.004791999235749245,
0.033242374658584595,
-0.011076981201767921,
-0.0004939470090903342,
0.020397059619426727,
0.02461799420416355,
-0.008573997765779495,
-0.0030001183040440083,
0.000568361661862582,
-0.0027877422980964184,
-0.013792402110993862,
-0.03343401476740837,
0.04569967836141586,
0.007067536003887653,
-0.055323753505945206,
-0.0026554458308964968,
-0.050667256116867065,
0.0156873632222414,
-0.009871997870504856,
-0.03419565409421921,
-0.020355168730020523,
-0.011716860346496105,
0.04410777986049652,
0.0005618292489089072,
0.053004637360572815,
-0.03940318524837494,
-0.016360685229301453,
-0.026280460879206657,
0.02671511471271515,
-0.04739193618297577,
0.017979193478822708,
0.014413570053875446,
0.02138572558760643,
-0.0812198743224144,
-0.039408739656209946,
-0.02420555241405964,
-0.001874734996818006,
0.03477850556373596,
-0.009634153917431831,
-0.013496911153197289,
0.016138114035129547,
0.039662912487983704,
0.08752315491437912,
0.03489142283797264,
0.005595676135271788,
-0.06825215369462967,
-0.0038047758862376213,
0.0785093754529953,
-0.02706235460937023,
0.05435726046562195,
-0.09660430997610092,
-0.001156546175479889,
-0.07927075773477554,
0.07451929897069931,
-0.02045365981757641,
0.03732354938983917,
0.04447387531399727,
-0.001794125186279416,
0.017564985901117325,
-0.012271037325263023,
-0.01053622830659151,
0.034432750195264816,
-0.051628001034259796,
-0.04144313558936119,
0.011144429445266724,
-0.00854505505412817,
-0.02230810932815075,
-0.024380987510085106,
0.033143870532512665,
-0.007864288054406643,
0.027081361040472984,
-0.028775127604603767,
0.00533274793997407,
-0.012901687994599342,
0.007937144488096237,
0.023040039464831352,
-0.041869305074214935,
0.007641275878995657,
-0.04443049058318138,
0.01119181327521801,
0.05624411255121231,
-0.017655206844210625,
-0.0575692392885685,
0.015910634770989418,
-0.045687563717365265,
-0.022332843393087387,
0.03342604637145996,
0.005629232618957758,
0.032822124660015106,
-0.0720740556716919,
-0.01428921613842249,
0.05466888099908829,
-0.04638195037841797,
-0.04007190838456154,
-0.01654927060008049,
-0.05311528965830803,
0.038620397448539734,
-0.029552152380347252,
-0.0064008524641394615,
-0.021841702982783318,
-0.03158041834831238,
0.04385507479310036,
-0.004095657728612423,
-0.002697473159059882,
-0.009592410176992416,
-0.03581203892827034,
0.007135389838367701,
-0.005837193224579096,
0.05773487687110901,
0.0089042279869318,
-0.027674676850438118,
0.013853784650564194,
-0.016181647777557373,
-0.007802774664014578,
0.005056250840425491,
-0.05197514593601227,
-0.09729816764593124,
0.043449100106954575,
-0.016537752002477646,
-0.07737275213003159,
0.008986198343336582,
0.0464114286005497,
0.036920201033353806,
0.07054278999567032,
0.011177881620824337,
0.03209526091814041,
0.029624680057168007,
0.035371966660022736,
0.024508275091648102,
-0.025783803313970566,
0.0030853552743792534,
0.01445166114717722,
0.007363624405115843,
-0.04241349920630455,
-0.0030578686855733395,
-0.07174845039844513,
0.06203291192650795,
0.024327510967850685,
-0.061056576669216156,
-0.03940654546022415,
0.0459008514881134,
0.060829855501651764,
-0.05224303528666496,
-0.0815473273396492,
-0.05641915649175644,
-0.0022748990450054407,
0.003288982203230262,
0.02438756637275219,
0.0029420030768960714,
-0.040281493216753006,
0.006285097450017929,
-0.027724185958504677,
0.03336593508720398,
-0.011987545527517796,
0.0057887425646185875,
0.016099998727440834,
-0.05353529006242752,
-0.026185132563114166,
0.03050396591424942,
0.008582298643887043,
-0.05514197796583176,
0.02117236889898777,
0.03668414428830147,
-0.01824415847659111,
0.006805906537920237,
0.010037112981081009,
-0.012289372272789478,
0.02155592478811741,
-0.019764183089137077,
0.02428680658340454,
-0.0361286923289299,
0.01763359270989895,
-0.008551051840186119,
-0.035015325993299484,
-0.056971851736307144,
0.008732614107429981,
-0.019718220457434654,
-0.011987372301518917,
-0.00709701469168067,
-0.009056535549461842,
0.00712707731872797,
-0.015450255014002323,
0.007455518934875727,
-0.06569116562604904,
0.029355406761169434,
-0.01570025645196438,
-0.027738409116864204,
0.05702773481607437,
0.012787489220499992,
0.007415431551635265,
0.01655867137014866,
0.043549202382564545,
-0.0348733551800251,
-0.05590870976448059,
-0.01662278175354004,
-0.014034129679203033,
-0.022913752123713493,
0.05917200818657875,
-0.03150572627782822,
-0.029106104746460915,
-0.026872817426919937,
0.01437052059918642,
-0.027630703523755074,
-0.040017660707235336,
0.040444932878017426,
0.02482152357697487,
-0.02078375220298767,
0.0016408665105700493,
-0.033753398805856705,
0.021429136395454407,
-0.0034421165473759174,
0.03673893213272095,
0.044688887894153595,
-0.011977184563875198,
-0.000609855109360069,
0.00011449944577179849,
0.08909894526004791,
-0.0006171987042762339,
0.028375351801514626,
-0.01865173690021038,
0.027109509333968163,
0.0105427335947752,
-0.016427991911768913,
0.03607545420527458,
-0.008546711876988411,
-0.02406667172908783,
0.011991473846137524,
0.017024610191583633,
-0.05317237973213196,
0.012228650972247124,
0.04338961839675903,
-0.026041187345981598,
-0.036974065005779266,
0.07762449234724045,
-0.02971292845904827,
0.04125655069947243,
0.029699916020035744,
0.010429305024445057,
-0.052732113748788834,
-0.03764142841100693,
0.030228614807128906,
0.03618995100259781,
0.029428744688630104,
-0.006026892457157373,
0.01157232467085123,
-0.02036537416279316,
0.07088551670312881,
0.022434836253523827,
0.0016694188816472888,
0.03696821630001068,
-0.006384627427905798,
0.05799657478928566,
-0.03665776550769806,
0.08364425599575043,
0.036905013024806976,
0.060394369065761566,
0.006108783185482025,
0.004965655505657196,
0.06980138272047043,
-0.043929632753133774,
-0.03862009570002556,
-0.016849150881171227,
-0.03263022378087044,
0.01887638121843338,
-0.13627870380878448,
0.0025506082456558943,
0.08948299288749695,
0.012963359244167805,
-0.013183469884097576,
-0.001631443970836699,
0.0095264483243227,
0.019634949043393135,
0.008671801537275314,
0.017848894000053406,
-0.019321143627166748,
-0.06327206641435623,
-0.030986865982413292,
-0.033596910536289215,
0.025529222562909126,
0.025139013305306435,
0.02407204359769821,
0.012736405245959759,
0.006061026826500893,
-0.03478969261050224,
0.031213931739330292,
-0.022600924596190453,
-0.025847958400845528,
-0.030954785645008087,
-0.020921414718031883,
0.005306942388415337,
0.04375366121530533,
-0.007614315953105688,
0.06797342747449875,
0.05373765528202057,
-0.04328041523694992,
0.02686484344303608,
-0.04948817193508148,
-0.008829772472381592,
-0.0798281729221344,
-0.02236778475344181,
-0.025490563362836838,
-0.04883807152509689,
0.0032048956491053104,
-0.015815241262316704,
0.020468125119805336,
0.07120196521282196,
-0.015703286975622177,
-0.025019733235239983,
-0.06595145910978317,
0.035074926912784576,
-0.05779505893588066,
0.05383085086941719,
0.005531157832592726,
0.01739051192998886,
0.055706899613142014,
0.08061478286981583,
0.07564376294612885,
-0.02662416361272335,
-0.03235761076211929,
0.01338625606149435,
0.03722730651497841,
0.0015729618025943637,
0.027409955859184265,
-0.0335395522415638,
-0.03450899198651314,
0.017882002517580986,
0.04712724685668945,
-0.005353161133825779,
0.017125312238931656,
-0.021737294271588326,
0.0816068947315216,
0.02201017364859581,
0.005060533527284861,
0.03295706957578659,
0.008357388898730278,
0.002672396134585142,
0.025041788816452026,
0.059083957225084305,
0.009236607700586319,
-0.0625755563378334,
-0.005897358525544405,
-0.014028428122401237,
-0.04026079550385475,
-0.0456652007997036,
-0.014061232097446918,
0.024200135841965675,
-0.03731680288910866,
-0.0313730351626873,
-0.05879981070756912,
-0.023564880713820457,
-0.0327993705868721,
0.0013465933734551072,
-0.008838529698550701,
-0.057589273899793625,
0.06663703173398972,
0.0032437893096357584,
-0.023293130099773407,
-0.010242472402751446,
0.011131349951028824,
-0.0008644693298265338,
-0.0288363229483366,
-0.003355346852913499,
-0.018780909478664398,
0.01157156378030777,
0.004103953950107098,
0.0168465506285429,
-0.0436747707426548,
0.08191476762294769,
0.014014705084264278,
0.059166718274354935,
0.0017369166016578674,
-0.017721105366945267,
0.008620411157608032,
0.013933761976659298,
0.0748809427022934,
0.0038632117211818695,
-0.040008194744586945,
-0.0981486439704895,
0.03254197910428047,
0.0301671139895916,
-0.002553528407588601,
-0.03800758346915245,
-0.008072469383478165,
-0.043280262500047684
] |
<p>In proving that the action $$S\equiv \int^{t_2}_{t_1}L(x, x',t)dt$$ has a has a stationary point $x_0$ that satisfies the following:
$$\frac{d}{dt}(\frac{\partial L}{\partial x'_0})=\frac{\partial L}{\partial x_0}$$
My textbook finds the action of $$x_a(t)\equiv x_0(t)+a\beta (t)$$ differentiated with respect a to the first order to reach the expression:
$$\frac{\partial}{\partial a} S[x_a(t)]=\int^{t_2}_{t_1}(\frac{\partial L}{\partial x_a} - \frac{d}{dt}(\frac{\partial L}{\partial x'_a}))\beta dt$$
It then says that the only way this can be 0 for all $\beta$ is if the expression in the parentheses evaluated at $a=0$ is identically equal to zero. I don't understand why we can evaluate it at 0, please could someone explain? (I would understand if the thing in the parentheses had to be 0 for all $a$ but why does been it been 0 for $a=0$ imply it is 0 for all $a$?)</p> | g4571 | [
0.03119058348238468,
-0.0457780547440052,
-0.01400667242705822,
-0.022554904222488403,
0.08275606483221054,
-0.03322448953986168,
0.09062423557043076,
0.03288477286696434,
-0.07524333894252777,
-0.024336084723472595,
-0.08330632746219635,
0.08745448291301727,
-0.006093762349337339,
0.009338116273283958,
0.018917808309197426,
-0.00921574980020523,
0.009382993914186954,
-0.019330227747559547,
-0.034649334847927094,
-0.013090825639665127,
0.016820833086967468,
0.09813104569911957,
-0.0028786153998225927,
-0.034920018166303635,
0.057981833815574646,
-0.0036435716319829226,
0.008221713826060295,
0.021920504048466682,
-0.07009515166282654,
-0.002340312348678708,
0.016462400555610657,
-0.0008947676396928728,
0.03921159356832504,
0.023967210203409195,
0.013655557297170162,
-0.055275190621614456,
0.06505916267633438,
0.011723062954843044,
0.011014778167009354,
-0.05753578245639801,
0.0036153695546090603,
0.01618950627744198,
-0.00941489264369011,
0.005330381449311972,
-0.01591235212981701,
-0.04006850719451904,
-0.01507171243429184,
0.03783109411597252,
-0.010509397834539413,
0.0016242226120084524,
0.044852085411548615,
-0.02749251015484333,
0.007600603625178337,
-0.07969794422388077,
-0.031233971938490868,
0.038892343640327454,
-0.046281445771455765,
-0.019320134073495865,
-0.014842487871646881,
0.035121601074934006,
-0.050887443125247955,
-0.032096873968839645,
0.03585829585790634,
0.030883705243468285,
0.02419896051287651,
-0.05276712775230408,
0.020163007080554962,
-0.035625047981739044,
-0.020216748118400574,
0.014221730642020702,
-0.022811301052570343,
-0.03224113583564758,
0.004395981784909964,
0.010846349410712719,
-0.019373171031475067,
-0.02366076037287712,
-0.0015054185641929507,
-0.01899365335702896,
-0.0038974485360085964,
-0.011642416007816792,
-0.03178708255290985,
0.005799890495836735,
0.06201111152768135,
0.023336593061685562,
0.007914156652987003,
-0.006931622978299856,
0.01368196215480566,
-0.02294114977121353,
-0.03135982155799866,
0.057474467903375626,
0.03882351890206337,
-0.0004498928610701114,
0.04338345304131508,
0.03550000116229057,
-0.020128952339291573,
-0.0182041022926569,
0.03086468018591404,
-0.009868210181593895,
-0.030068788677453995,
-0.050346676260232925,
0.011058228090405464,
0.06132470816373825,
0.013980966061353683,
0.06333066523075104,
-0.0004222604038659483,
-0.024993721395730972,
0.0014869030565023422,
-0.012401718646287918,
-0.01805870793759823,
-0.06970062851905823,
0.03625508397817612,
0.05177381634712219,
-0.10016936808824539,
-0.02984776347875595,
-0.004726121202111244,
0.005357455927878618,
0.03194228932261467,
0.008618097752332687,
-0.040635645389556885,
-0.000522854330483824,
-0.006524438504129648,
0.0002935804659500718,
-0.03712648153305054,
0.08131168782711029,
0.0030093456152826548,
0.03938945755362511,
-0.051942575722932816,
0.11020353436470032,
0.01967201568186283,
-0.0025684924330562353,
-0.02398041822016239,
0.03954952210187912,
0.025436250492930412,
-0.026291776448488235,
0.03987753018736839,
0.030490228906273842,
-0.03889152407646179,
-0.013958845287561417,
-0.004275268875062466,
-0.021152488887310028,
-0.07883509993553162,
-0.030663304030895233,
-0.07290267944335938,
0.03270990028977394,
0.017143966630101204,
0.002652771770954132,
0.0009795899968594313,
-0.010611987672746181,
0.02695508860051632,
0.00909336470067501,
-0.014193391427397728,
0.05144742131233215,
0.038999103009700775,
-0.006233911029994488,
-0.0061032953672111034,
0.02095722407102585,
0.05197476968169212,
0.01939091831445694,
-0.033739615231752396,
-0.013051125220954418,
0.02205927111208439,
0.059553422033786774,
0.026751434430480003,
0.02365223318338394,
-0.12300827354192734,
0.05253840237855911,
-0.05737930163741112,
-0.016413182020187378,
0.01834142953157425,
-0.05837063491344452,
-0.03922684118151665,
0.09521134942770004,
0.034685369580984116,
0.03265674412250519,
-0.00010878838656935841,
0.030264558270573616,
-0.019504254683852196,
-0.013771477155387402,
-0.004206689540296793,
0.002871348289772868,
-0.030393080785870552,
-0.0500500425696373,
-0.02316388115286827,
-0.03798212483525276,
-0.022853296250104904,
-0.02909044735133648,
0.0013695125235244632,
-0.01192489918321371,
-0.049503859132528305,
-0.021682754158973694,
-0.003681579139083624,
0.024076445028185844,
-0.005207862704992294,
0.006851358339190483,
-0.02711378037929535,
0.036134615540504456,
0.0013684266014024615,
-0.07965176552534103,
-0.0070812334306538105,
-0.027178853750228882,
-0.015679314732551575,
0.031188609078526497,
-0.0005480209947563708,
0.009612483903765678,
-0.06354030221700668,
0.02672724612057209,
0.00904285628348589,
-0.006223662756383419,
0.015432901680469513,
0.07400763779878616,
-0.027241501957178116,
-0.07203750312328339,
-0.024602094665169716,
0.027972212061285973,
-0.00493220891803503,
-0.07891850173473358,
0.022066043689846992,
0.028071563690900803,
0.006345234811306,
-0.07211389392614365,
-0.041912078857421875,
-0.019476335495710373,
-0.005396266933530569,
0.003935409709811211,
-0.05979529395699501,
0.031959690153598785,
0.012055221945047379,
-0.00286308117210865,
-0.02775711379945278,
0.05179418995976448,
-0.05966902896761894,
-0.04443281888961792,
-0.03355982154607773,
-0.04368162527680397,
0.013223420828580856,
-0.06093675270676613,
-0.0015424974262714386,
-0.046659018844366074,
0.030035611242055893,
0.07803291827440262,
-0.002472272142767906,
0.0016209916211664677,
-0.04966023191809654,
0.051416005939245224,
0.026187129318714142,
-0.027270182967185974,
0.004271277226507664,
0.01817561313509941,
-0.013843710534274578,
0.005513402633368969,
-0.06084015592932701,
0.05128604173660278,
0.03023773990571499,
0.023312067613005638,
0.013889187015593052,
-0.048389896750450134,
0.016406312584877014,
-0.009240834042429924,
0.05309091508388519,
0.011800029315054417,
-0.02474011853337288,
-0.00790315493941307,
0.011924322694540024,
0.05225668475031853,
-0.04787330701947212,
0.035825759172439575,
0.008992530405521393,
-0.04136142507195473,
0.05926596373319626,
-0.028089705854654312,
0.004374067299067974,
0.017894243821501732,
0.021297121420502663,
0.07180695980787277,
-0.053505416959524155,
-0.018763091415166855,
0.0001174339558929205,
0.0007343198521994054,
0.03937676176428795,
0.012874339707195759,
0.039447180926799774,
-0.002507119905203581,
0.017649173736572266,
0.06530090421438217,
0.0431082658469677,
-0.03428331017494202,
0.015438918955624104,
0.02914712019264698,
-0.01656796969473362,
-0.06456459313631058,
0.011514050886034966,
0.009435193613171577,
-0.014453931711614132,
-0.024823077023029327,
0.04435468092560768,
0.00014649647346232086,
-0.04436668008565903,
-0.08245845884084702,
0.023588478565216064,
-0.008579755201935768,
-0.022074785083532333,
0.026478741317987442,
-0.0007302882731892169,
-0.03166104853153229,
0.0407632477581501,
-0.03820598125457764,
0.039960265159606934,
-0.05758415162563324,
-0.014556880109012127,
0.04953130707144737,
-0.03231381997466087,
0.04781779646873474,
-0.026297597214579582,
-0.08776140958070755,
-0.0070844185538589954,
0.02667396329343319,
-0.011543049477040768,
-0.003337863367050886,
0.04451891779899597,
0.01280070561915636,
0.02720613032579422,
-0.0384523943066597,
0.017639024183154106,
-0.017778826877474785,
0.01718217320740223,
-0.04458838701248169,
-0.0277960654348135,
0.027276327833533287,
-0.09496667981147766,
-0.022160271182656288,
0.02661290392279625,
-0.0023991845082491636,
0.01562829688191414,
0.013453353196382523,
0.04686644300818443,
-0.012762189842760563,
-0.06383901089429855,
0.059628672897815704,
0.02846849150955677,
-0.003437930252403021,
-0.0666353702545166,
0.0055605326779186726,
-0.041316188871860504,
0.05714885890483856,
0.04719911888241768,
-0.04163238778710365,
0.0028478503227233887,
0.06188106909394264,
0.04602392390370369,
0.011287092231214046,
0.026561761274933815,
-0.018061695620417595,
0.00601211516186595,
-0.019852032884955406,
-0.007184291258454323,
0.010432690382003784,
0.07691625505685806,
0.05247761681675911,
-0.0033214387949556112,
-0.02869240939617157,
0.04827073588967323,
0.002818814944475889,
-0.023203840479254723,
0.03356679156422615,
0.06478815525770187,
0.010926262475550175,
-0.013899545185267925,
0.044291410595178604,
-0.03808628395199776,
0.04201023653149605,
0.025652287527918816,
-0.021724414080381393,
0.035334695130586624,
0.0040769740007817745,
0.015473181381821632,
-0.047255732119083405,
-0.04417425021529198,
0.016483809798955917,
-0.008474824018776417,
0.07760225236415863,
0.033034030348062515,
0.046255700290203094,
0.0028006513603031635,
-0.00003382374416105449,
0.015549384988844395,
0.014166516251862049,
-0.014423193410038948,
0.0035918650683015585,
0.04471058398485184,
-0.03404634818434715,
0.043982770293951035,
0.03709634393453598,
-0.0013320731231942773,
-0.014968172647058964,
-0.03337247669696808,
-0.010284729301929474,
0.012725370936095715,
-0.00009471557132201269,
-0.008174901828169823,
0.03853794187307358,
-0.02211572416126728,
-0.04452608898282051,
0.03614073246717453,
-0.01273440383374691,
-0.008517771027982235,
-0.030043423175811768,
0.03247381001710892,
0.0177590474486351,
0.05074619874358177,
-0.01746918261051178,
-0.04369872435927391,
-0.04457886517047882,
-0.01435679942369461,
-0.020468899980187416,
-0.011122564785182476,
0.030127380043268204,
0.02207791619002819,
-0.05055614933371544,
0.041090261191129684,
-0.05114646255970001,
0.047852929681539536,
0.005164313595741987,
-0.04878881573677063,
-0.04870131239295006,
0.06275731325149536,
0.08892341703176498,
0.05383487045764923,
0.024084698408842087,
0.008386213332414627,
-0.004994626622647047,
-0.07293952256441116,
0.01337310578674078,
-0.027102341875433922,
0.08905957639217377,
-0.050353799015283585,
0.06494544446468353,
-0.053223978728055954,
0.05888773128390312,
0.005236269440501928,
0.010977831669151783,
0.016465816646814346,
-0.00862240232527256,
-0.037816472351551056,
0.046225033700466156,
0.0208356361836195,
0.011565012857317924,
-0.013322785496711731,
-0.08790843933820724,
0.009165744297206402,
-0.018311500549316406,
-0.02960227057337761,
0.05456898733973503,
0.031214192509651184,
-0.045451123267412186,
0.03379515931010246,
-0.013087509199976921,
0.003608360653743148,
-0.024665245786309242,
-0.02195032313466072,
-0.020754819735884666,
-0.011421751230955124,
-0.03180839121341705,
0.044387590140104294,
0.03110184147953987,
0.08148116618394852,
0.01243407279253006,
-0.006220384035259485,
-0.003154524601995945,
-0.04162076488137245,
-0.01616119220852852,
0.029302256181836128,
0.03191707655787468,
0.040527746081352234,
0.02161155827343464,
0.003088126890361309,
-0.04370242357254028,
-0.00989601667970419,
-0.0033788320142775774,
-0.027628153562545776,
-0.03566562756896019,
-0.03510409966111183,
-0.012779893353581429,
-0.0069205136969685555,
-0.00987438764423132,
0.023391108959913254,
0.022088613361120224,
-0.03998490422964096,
-0.04575565084815025,
0.007868500426411629,
-0.006125363055616617,
0.05455421656370163,
-0.0034796802792698145,
0.05715456232428551,
-0.03639436885714531,
-0.006278535351157188,
-0.013159467838704586,
0.029293091967701912,
0.02580598182976246,
-0.012308607809245586,
-0.02159143052995205,
-0.060516200959682465,
-0.016025716438889503,
0.0008920504478737712,
-0.012713106349110603,
0.015298929996788502,
0.05385206639766693,
0.028559722006320953,
-0.0019371586386114359,
-0.00011181347508681938,
-0.006677572149783373,
0.012109129689633846,
0.0662602111697197,
0.014009032398462296,
0.010810152627527714,
-0.0022665960714221,
0.021195104345679283,
-0.00937675591558218,
-0.02592220902442932,
-0.04855102673172951,
0.0009508990915492177,
0.0405859611928463,
0.01817421428859234,
-0.01627493090927601,
-0.01293671503663063,
0.05523988977074623,
-0.015256274491548538,
-0.0371902771294117,
-0.062434859573841095,
-0.06699199974536896,
0.01437334530055523,
-0.0012663055676966906,
0.03814607486128807,
-0.03769451752305031,
-0.058200906962156296,
-0.0022733111400157213,
0.015421682968735695,
-0.00563756562769413,
0.014997868798673153,
0.01082640141248703,
-0.009859146550297737,
-0.05746578052639961,
-0.013059129938483238,
-0.019333183765411377,
0.057231079787015915,
-0.07473050802946091,
-0.004757996648550034,
-0.05321219563484192,
0.013605042360723019,
-0.020901042968034744,
-0.05653946101665497,
-0.054612770676612854,
0.0399281270802021,
-0.0279134102165699,
-0.01460504624992609,
-0.01170026883482933,
0.021736912429332733,
-0.06258957087993622,
0.008570416830480099,
-0.018191112205386162,
-0.05402678996324539,
-0.004596062004566193,
0.010118476115167141,
0.01689670793712139,
-0.005289582069963217,
0.03262120857834816,
-0.07186111062765121,
0.00477126007899642,
0.016830597072839737,
0.010593358427286148,
0.004006961360573769,
0.0412653349339962,
0.03924728184938431,
0.031018517911434174,
0.018014516681432724,
0.014775995165109634,
-0.006292365957051516,
0.0025743430014699697,
-0.008296347223222256,
0.005331299267709255,
-0.012055966071784496,
-0.029108379036188126,
0.031651515513658524,
0.008490178734064102,
-0.008225435391068459,
-0.004899903666228056,
0.04007124900817871,
-0.01052012573927641,
-0.02085454948246479,
0.04024789482355118,
0.03163828328251839,
-0.0037980915512889624,
0.008212154731154442,
-0.011987381614744663,
-0.003789351787418127,
0.02985050529241562,
-0.020376499742269516,
0.03142709285020828,
0.030960308387875557,
0.02726753242313862,
-0.04491204768419266,
0.004637097008526325,
0.03750201687216759,
-0.000709734798874706,
-0.03479461371898651,
-0.0013487840769812465,
0.046915240585803986,
-0.035151079297065735,
-0.015389923937618732,
0.039709340780973434,
0.04410466551780701,
-0.02737751044332981,
0.03611134737730026,
0.022164320573210716,
0.003955105319619179,
0.008475965820252895,
-0.02989502251148224,
-0.04748781397938728,
0.009890721179544926,
-0.03169041499495506,
-0.009261248633265495,
0.08735927939414978,
-0.006161211524158716,
-0.033202946186065674,
-0.007506328169256449,
0.0447566956281662,
0.019629614427685738,
-0.003652943531051278,
0.017596660181879997,
-0.019559264183044434,
0.01987638883292675,
-0.024425949901342392,
0.021067891269922256,
-0.055345386266708374,
0.04226041957736015,
-0.028339076787233353,
0.020944315940141678,
-0.04028364270925522,
0.04238762706518173,
0.004825602285563946,
0.022609833627939224,
-0.02037012204527855,
0.07494058459997177,
-0.024142244830727577,
-0.015093863010406494,
-0.01238293293863535,
0.04393544793128967,
0.019210075959563255,
-0.004247627686709166,
-0.11155274510383606,
0.005016460549086332,
0.10926920175552368,
0.06361930817365646,
-0.011998790316283703,
-0.0002715559967327863,
-0.027619803324341774,
-0.016996072605252266,
-0.011101075448095798,
-0.00008684978092787787,
-0.05911170691251755,
-0.034837283194065094,
0.0037671304307878017,
0.004180108662694693,
-0.027482813224196434,
0.021590281277894974,
0.0008295336156152189,
-0.0011560344137251377,
0.018765773624181747,
-0.046645186841487885,
0.03352436423301697,
-0.03837163746356964,
0.04317886382341385,
0.014149649068713188,
-0.004156573675572872,
0.03757266327738762,
0.05222610384225845,
0.0698375254869461,
0.02213640883564949,
0.01802126318216324,
0.016093671321868896,
0.020442048087716103,
0.02282499335706234,
-0.017057592049241066,
0.03006821870803833,
-0.06435805559158325,
-0.04846404492855072,
0.011987556703388691,
0.009114440530538559,
-0.010151653550565243,
-0.007826968096196651,
-0.015096345916390419,
0.005847109481692314,
-0.006992217618972063,
0.03566299006342888,
-0.0045007625594735146,
0.023646606132388115,
-0.05159484222531319,
-0.020377447828650475,
0.0345827154815197,
-0.047004155814647675,
0.013263382017612457,
0.035984721034765244,
-0.040057431906461716,
-0.03874848037958145,
-0.005829766858369112,
0.012251380831003189,
0.011752596125006676,
0.024178389459848404,
0.02488800138235092,
-0.015524058602750301,
-0.0670768991112709,
0.01474173553287983,
0.00671057403087616,
-0.04265638068318367,
-0.030622148886322975,
0.02703990414738655,
-0.011638190597295761,
-0.023821137845516205,
-0.010470897890627384,
0.033144064247608185,
-0.040444355458021164,
0.02204786241054535,
-0.0179391261190176,
-0.01499012392014265,
-0.11057977378368378,
-0.03380727395415306,
-0.026931630447506905,
-0.054263561964035034,
0.018615880981087685,
0.050125207751989365,
0.031221115961670876,
-0.022614168003201485,
-0.016660409048199654,
0.011499782092869282,
0.05650024861097336,
-0.012732038274407387,
0.06025201454758644,
0.029637863859534264,
-0.07708480954170227,
-0.06129482015967369,
0.02547176368534565,
-0.1130346804857254,
-0.016631154343485832,
-0.0026197615079581738,
0.034738484770059586,
0.02090569958090782,
0.016570329666137695,
0.011366471648216248,
0.02736799791455269,
0.04328250512480736,
-0.04197390377521515,
0.02446480095386505,
0.026680484414100647,
-0.056026801466941833,
0.003515667049214244,
-0.0037455817218869925,
-0.0039091394282877445,
0.004729699809104204,
-0.0024906813632696867,
0.03402070701122284,
0.037604060024023056,
-0.04241915047168732,
0.060098662972450256,
-0.02398466132581234,
0.024025222286581993,
-0.033027492463588715,
-0.08744999766349792,
0.028263401240110397,
-0.022531701251864433
] |
<p>I am looking for a device to provide variable excitation voltage (30VDC to 200VDC) to a Transducer for a variable time (10 to 20 milliseconds).</p>
<p>Can someone please advise how I could achieve this using an off the shelf product? </p> | g4572 | [
0.06454543769359589,
0.02802211232483387,
-0.005684276577085257,
-0.06477931141853333,
-0.00825949851423502,
-0.034882016479969025,
-0.026768401265144348,
-0.07073045521974564,
-0.02075156755745411,
0.0073070223443210125,
-0.03885413333773613,
0.013314616866409779,
-0.05668887123465538,
0.01875261589884758,
0.02352866902947426,
-0.01019436027854681,
0.0019053596770390868,
-0.008546452037990093,
0.021254241466522217,
0.020911436527967453,
0.015110422857105732,
-0.04541517049074173,
-0.009959938004612923,
-0.004388816654682159,
-0.017235904932022095,
-0.014876918867230415,
0.03874653950333595,
0.04331783205270767,
-0.04606441408395767,
0.015635017305612564,
-0.05880245566368103,
-0.018660617992281914,
0.02904033102095127,
0.06593190133571625,
-0.007925097830593586,
0.03459266945719719,
-0.010164457373321056,
-0.012401649728417397,
0.026656460016965866,
0.013041163794696331,
-0.005504034925252199,
0.028735941275954247,
0.022640246897935867,
-0.02991269715130329,
0.0782776027917862,
0.01782754622399807,
0.01576772890985012,
-0.010133710689842701,
-0.07111110538244247,
-0.022670870646834373,
-0.014714798890054226,
-0.052471768110990524,
0.016802167519927025,
0.026657510548830032,
0.008154220879077911,
0.009606425650417805,
-0.07123980671167374,
-0.004833607003092766,
-0.019564645364880562,
-0.015213577076792717,
0.008779649622738361,
0.0016972302692010999,
0.02087268978357315,
-0.07846958190202713,
0.028223460540175438,
-0.026195090264081955,
-0.0076736207120120525,
-0.06552448123693466,
-0.004211741965264082,
0.06825477629899979,
0.038044217973947525,
-0.008610306307673454,
0.04218121990561485,
-0.02253110520541668,
0.07628179341554642,
-0.019426140934228897,
0.020496532320976257,
-0.04666533321142197,
0.016899721696972847,
-0.007898461073637009,
-0.008853483945131302,
0.02333468198776245,
-0.020902885124087334,
-0.015529502183198929,
-0.020017065107822418,
-0.0393218919634819,
-0.008862247690558434,
0.08048068732023239,
0.03078637272119522,
-0.031811852008104324,
-0.009988972917199135,
-0.0002771915460471064,
-0.00042650813702493906,
0.05209504812955856,
-0.07145489752292633,
-0.022856589406728745,
0.0013544185785576701,
0.05443234741687775,
-0.020726341754198074,
0.024922387674450874,
0.022500373423099518,
-0.034266505390405655,
0.035300131887197495,
-0.011601273901760578,
-0.06165572255849838,
0.010747102089226246,
0.02684427611529827,
-0.007319488096982241,
0.03029547818005085,
-0.022269081324338913,
0.005214206874370575,
-0.0598534420132637,
-0.03945949301123619,
-0.030336590483784676,
-0.024483030661940575,
-0.0006947150686755776,
-0.025919610634446144,
0.040318042039871216,
-0.07799377292394638,
-0.05113504081964493,
0.010159087367355824,
0.029994215816259384,
-0.04989861696958542,
0.029753711074590683,
-0.021317174658179283,
0.0076226438395679,
-0.006822232622653246,
-0.003293978748843074,
0.009308074600994587,
0.03997143357992172,
0.04362243413925171,
-0.02440767176449299,
-0.017027825117111206,
0.026285186409950256,
-0.029009731486439705,
0.005299929995089769,
0.057962797582149506,
-0.009384927339851856,
0.00364994490519166,
0.03716089576482773,
0.0014295863220468163,
-0.01592455804347992,
-0.018638847395777702,
-0.023381667211651802,
-0.012370982207357883,
0.018126871436834335,
0.0040038106963038445,
-0.024814192205667496,
0.035385243594646454,
-0.025412967428565025,
0.04487408697605133,
-0.0009442249429412186,
-0.009325622580945492,
0.009963016025722027,
-0.036397870630025864,
-0.001141114393249154,
0.01107598003000021,
-0.00895138829946518,
-0.020631566643714905,
-0.03847656026482582,
0.006941783241927624,
0.032769978046417236,
-0.01273942831903696,
-0.005683754570782185,
0.017812766134738922,
-0.04838471859693527,
0.060511358082294464,
-0.011132564395666122,
0.012763838283717632,
-0.01582762412726879,
-0.0689842700958252,
0.01225191354751587,
0.04821139946579933,
-0.008238089270889759,
-0.04546089470386505,
-0.01402951218187809,
-0.012614080682396889,
0.012275472283363342,
-0.03443587198853493,
0.00017165078315883875,
-0.061536241322755814,
-0.011103293858468533,
0.002833309583365917,
-0.05183384567499161,
-0.014076109044253826,
0.03203194960951805,
0.0036482741124927998,
-0.017030738294124603,
0.012804997153580189,
-0.0005596753326244652,
-0.01570269837975502,
-0.04141531512141228,
-0.04974237456917763,
0.05606270954012871,
-0.05025375634431839,
0.012633102014660835,
0.03731415420770645,
-0.04115525260567665,
0.002127649262547493,
-0.0053314585238695145,
0.060503676533699036,
0.024418139830231667,
0.06789608299732208,
0.054435715079307556,
0.04795996472239494,
-0.014456123113632202,
-0.041158996522426605,
-0.049024004489183426,
0.00006612772267544642,
0.031577061861753464,
0.03148284927010536,
0.035949528217315674,
-0.032866206020116806,
0.015922844409942627,
-0.07772050052881241,
-0.08743426203727722,
-0.009717903099954128,
0.012031259015202522,
0.02731958217918873,
0.005097716581076384,
0.028083287179470062,
0.06600924581289291,
0.05200539901852608,
-0.020200200378894806,
0.007519838400185108,
-0.018886243924498558,
-0.026527229696512222,
-0.018049977719783783,
0.037098828703165054,
-0.04427308589220047,
0.024284759536385536,
-0.0005851280293427408,
0.028386244550347328,
-0.04489900544285774,
0.03937618434429169,
0.030603468418121338,
-0.01233306247740984,
-0.056209128350019455,
-0.030993947759270668,
-0.013494129292666912,
-0.010061617009341717,
-0.019734350964426994,
0.0530446395277977,
-0.014317022636532784,
-0.06176915019750595,
-0.07350928336381912,
0.051977068185806274,
0.003273208159953356,
0.0671120434999466,
0.012152637355029583,
0.00665044691413641,
0.011408564634621143,
-0.001158584258519113,
0.008820583112537861,
-0.03007781319320202,
-0.022941360250115395,
0.026171891018748283,
0.06452849507331848,
-0.04790721833705902,
-0.025716586038470268,
-0.042845387011766434,
0.07612168043851852,
0.05398011580109596,
0.06072660908102989,
0.02016390487551689,
-0.02745860069990158,
-0.029335547238588333,
0.05518677830696106,
0.01455505657941103,
-0.016426926478743553,
0.008352100849151611,
-0.0038047153502702713,
-0.024990897625684738,
-0.00643360149115324,
-0.01790875941514969,
0.005109221674501896,
0.0578487291932106,
0.020307058468461037,
0.02382391318678856,
-0.022088628262281418,
-0.006327774375677109,
-0.03623722121119499,
0.05254228413105011,
0.02850320376455784,
-0.01917138323187828,
-0.017024172469973564,
0.00862040463835001,
-0.023627035319805145,
-0.011023450642824173,
-0.0012624645605683327,
-0.01634419523179531,
-0.020860251039266586,
-0.08360031247138977,
-0.027690406888723373,
0.023695170879364014,
-0.019041111692786217,
-0.021337680518627167,
0.010849511250853539,
0.01170505303889513,
0.032370198518037796,
-0.02674751728773117,
-0.022834256291389465,
-0.002863992704078555,
-0.008865403942763805,
-0.036001790314912796,
-0.06345387548208237,
0.04622229188680649,
-0.0143510727211833,
-0.033308323472738266,
0.02818256802856922,
-0.004750238731503487,
-0.0553072914481163,
-0.001618679380044341,
-0.00787467323243618,
-0.05991053208708763,
0.019208794459700584,
0.011519218795001507,
0.027545303106307983,
-0.006631505209952593,
0.018970543518662453,
0.032673999667167664,
-0.023364704102277756,
0.04198191314935684,
0.03940717875957489,
-0.013619683682918549,
0.00038381884223781526,
0.05057332292199135,
0.024712642654776573,
-0.06318269670009613,
-0.0023101535625755787,
0.007727157790213823,
0.006575506646186113,
-0.02416309341788292,
0.03370092436671257,
0.033782701939344406,
-0.06509483605623245,
-0.06761669367551804,
0.0715104416012764,
-0.010650748386979103,
0.024217093363404274,
0.04342668503522873,
0.005727116018533707,
-0.08802735805511475,
-0.016955869272351265,
0.0021998616866767406,
-0.006489255465567112,
-0.02174074575304985,
0.038711920380592346,
-0.027959542348980904,
-0.04874124750494957,
0.04151792451739311,
0.03010849468410015,
0.00020936274086125195,
0.011141841299831867,
0.036681413650512695,
0.031206510961055756,
0.015040924772620201,
0.016485728323459625,
-0.05658182129263878,
-0.003638653550297022,
-0.018607672303915024,
0.00919606164097786,
0.05653886869549751,
-0.01655096374452114,
0.0011402900563552976,
0.050865206867456436,
0.043515145778656006,
0.0516088642179966,
-0.004234750289469957,
0.0019413793925195932,
0.025072697550058365,
0.04234949126839638,
-0.01026976853609085,
-0.006903188303112984,
-0.04308333620429039,
-0.03428349643945694,
-0.00039411522448062897,
-0.021668680012226105,
-0.07222407311201096,
0.06283222138881683,
-0.039446715265512466,
0.028291935101151466,
0.017153015360236168,
-0.00976735819131136,
-0.0026190613862127066,
-0.04068346321582794,
-0.03625868633389473,
0.03659816086292267,
0.03580450639128685,
-0.04040485620498657,
0.012016642838716507,
-0.07181750982999802,
-0.03175429627299309,
0.041120342910289764,
-0.027951132506132126,
0.007737354841083288,
0.04951751232147217,
-0.05294265225529671,
0.01585417054593563,
-0.04692131280899048,
0.019549917429685593,
0.009717226959764957,
0.028911324217915535,
0.03200919181108475,
0.012667178176343441,
-0.018443305045366287,
0.032570067793130875,
-0.06507058441638947,
-0.01793147251009941,
0.009400691837072372,
-0.024940503761172295,
-0.07512465864419937,
0.01625647023320198,
0.0037299690302461386,
-0.006571435369551182,
0.04559798538684845,
0.08354272693395615,
-0.0021260057110339403,
0.028421059250831604,
0.004271253943443298,
-0.04357259348034859,
0.00156909239012748,
0.03795730695128441,
-0.0032315400894731283,
-0.00583600765094161,
0.030552692711353302,
0.0027369067538529634,
-0.04136280342936516,
0.027934256941080093,
0.014185567386448383,
-0.047940272837877274,
-0.0397183857858181,
0.005902249366044998,
-0.03621212765574455,
-0.03365541994571686,
0.044529836624860764,
0.027484769001603127,
-0.03221438080072403,
0.013408954255282879,
0.017630979418754578,
0.0755554586648941,
-0.039165206253528595,
-0.0192466601729393,
0.0001825986400945112,
-0.02422301098704338,
0.05975241959095001,
-0.06483826786279678,
-0.028120674192905426,
0.06481710076332092,
-0.01427859254181385,
-0.01792694441974163,
0.017448317259550095,
-0.04651447385549545,
-0.05530966445803642,
0.05087348446249962,
0.012684307061135769,
0.02729087322950363,
-0.021311860531568527,
0.07840201258659363,
0.017921043559908867,
-0.0557076521217823,
-0.01802491769194603,
-0.038380034267902374,
0.00006852550723124295,
-0.003344108583405614,
0.011623403057456017,
-0.015887659043073654,
-0.04057211056351662,
-0.02192877233028412,
-0.003324793418869376,
-0.013983183540403843,
0.023432394489645958,
-0.006913549266755581,
0.11006253212690353,
0.05355830490589142,
-0.0005368527490645647,
0.0169020127505064,
-0.03337857872247696,
-0.011052282527089119,
-0.016317158937454224,
-0.05922241508960724,
0.03415808081626892,
-0.009173874743282795,
0.009446244686841965,
0.06493569910526276,
-0.0427488349378109,
-0.05824176222085953,
-0.010167958214879036,
0.03444203361868858,
-0.027816032990813255,
0.04812963306903839,
0.02977328561246395,
0.01735064573585987,
-0.0006809025071561337,
-0.012450340203940868,
-0.011027615517377853,
0.005434193182736635,
-0.09948605298995972,
-0.016232406720519066,
0.0032830804120749235,
-0.006160174496471882,
0.0193296167999506,
-0.07449594140052795,
0.021669939160346985,
-0.002494666026905179,
-0.011818732134997845,
-0.06149794161319733,
0.11371153593063354,
-0.015811072662472725,
0.0800452008843422,
-0.030177325010299683,
0.02350732870399952,
0.040925972163677216,
-0.024447830393910408,
-0.028943853452801704,
0.06369561702013016,
-0.02767920307815075,
-0.009210536256432533,
-0.04479388892650604,
0.008214008063077927,
0.019599998369812965,
-0.04197161644697189,
0.0312991626560688,
0.02475357986986637,
-0.056928716599941254,
0.03799282759428024,
-0.028531111776828766,
-0.0107803363353014,
0.0013356545241549611,
0.006369223352521658,
0.05830895155668259,
-0.0006123197381384671,
-0.043135229498147964,
-0.035812538117170334,
-0.033164750784635544,
-0.001510752597823739,
-0.016132201999425888,
0.018910791724920273,
-0.08453477919101715,
-0.04509515315294266,
-0.028375281020998955,
-0.033726610243320465,
0.055309802293777466,
-0.006745893973857164,
0.02979147806763649,
0.034243013709783554,
-0.0031704967841506004,
0.03661288321018219,
0.016621019691228867,
-0.009088730439543724,
0.0012856455286964774,
0.048084139823913574,
0.010264075361192226,
0.04415296018123627,
0.047485481947660446,
0.0017550704069435596,
-0.019848383963108063,
0.010963646695017815,
-0.05031457915902138,
-0.03889131918549538,
0.017773592844605446,
0.0020077661611139774,
-0.04301277920603752,
0.02871457301080227,
-0.041142020374536514,
0.047361139208078384,
0.02556263655424118,
0.06317029148340225,
-0.004238525405526161,
0.02983897179365158,
0.004654239863157272,
-0.019900618121027946,
0.018691467121243477,
-0.026627903804183006,
0.013277354650199413,
-0.02276669815182686,
0.05769442766904831,
-0.0531143881380558,
0.046100735664367676,
-0.004559907130897045,
-0.006171898450702429,
0.029094597324728966,
-0.06658006459474564,
0.029451513662934303,
0.014002262614667416,
-0.008587353862822056,
-0.04112790897488594,
-0.014930060133337975,
-0.07838458567857742,
-0.013489481061697006,
0.03253862261772156,
0.02221253700554371,
-0.017776113003492355,
-0.007886972278356552,
0.02264147810637951,
0.009580641984939575,
-0.037150729447603226,
0.04994087293744087,
0.044439882040023804,
0.01840566284954548,
-0.025116635486483574,
0.03569197282195091,
-0.0311164278537035,
-0.020755579695105553,
-0.03609991446137428,
-0.00782929826527834,
-0.023104794323444366,
-0.009042187593877316,
0.027090802788734436,
-0.03405793011188507,
0.035384777933359146,
-0.033568158745765686,
0.010104299522936344,
-0.003394995117560029,
-0.017173342406749725,
0.051058877259492874,
0.0028809031937271357,
-0.0021741336677223444,
0.038584139198064804,
0.04844846948981285,
0.054886434227228165,
0.040938928723335266,
0.013497849926352501,
0.06505724787712097,
-0.0077088987454771996,
0.04762708395719528,
-0.04091682657599449,
-0.054870352149009705,
0.049125418066978455,
0.013930472545325756,
-0.05367256700992584,
0.03752175346016884,
0.043395910412073135,
-0.018345661461353302,
-0.060897860676050186,
0.049518901854753494,
0.04804148152470589,
0.011427783407270908,
0.021721772849559784,
0.014459764584898949,
0.008633526973426342,
0.01798519864678383,
-0.010925882495939732,
0.026706423610448837,
0.03448706865310669,
0.05901879072189331,
0.030216624960303307,
0.041155487298965454,
0.011109143495559692,
0.03528604283928871,
0.05995393544435501,
-0.000010529126484470908,
0.01076152641326189,
0.08421771228313446,
0.0019374701660126448,
0.050710562616586685,
0.03759968280792236,
-0.014635801315307617,
0.02577267400920391,
-0.01622753217816353,
-0.03414053097367287,
-0.04999920725822449,
-0.02093360386788845,
-0.01294525247067213,
0.016751132905483246,
0.030690696090459824,
-0.06471438705921173,
-0.038771264255046844,
-0.02917465753853321,
-0.026731839403510094,
0.01440400816500187,
-0.018562067300081253,
-0.023581627756357193,
0.0013492329744622111,
0.0073908185586333275,
-0.049748871475458145,
-0.03725787252187729,
0.050630711019039154,
-0.058667656034231186,
0.01582893542945385,
-0.050896357744932175,
-0.05210446938872337,
-0.001563170226290822,
-0.0057555013336241245,
-0.029660489410161972,
-0.0031244230922311544,
-0.022704871371388435,
0.04900133237242699,
0.07204887270927429,
0.06577523052692413,
0.0020760975312441587,
0.024888215586543083,
0.043921805918216705,
-0.06676819175481796,
0.022765252739191055,
-0.005591377150267363,
0.012008920311927795,
-0.0487997829914093,
0.03247908502817154,
0.0640602707862854,
0.05408067628741264,
0.0352448970079422,
-0.026577427983283997,
0.04045647382736206,
-0.005743524059653282,
0.04581587389111519,
0.0199049711227417,
-0.06582576781511307,
0.028694581240415573,
0.03767429292201996,
-0.0012939618900418282,
0.045807525515556335,
-0.025980647653341293,
0.022177787497639656,
-0.02876146137714386,
0.020955033600330353,
-0.07653544843196869,
0.06788481026887894,
0.0029654966201633215,
0.0015795272774994373,
-0.01915411837399006,
0.016075048595666885,
-0.00349509553052485,
-0.015598868951201439,
0.03644021227955818,
-0.09387004375457764,
-0.10482699424028397,
0.04128159582614899,
-0.017475154250860214,
-0.04932069778442383,
0.025431044399738312,
-0.053096625953912735,
0.024611033499240875,
0.05511811003088951,
-0.020336488261818886,
-0.011897644028067589,
-0.0020658799912780523,
0.012505797669291496,
-0.04807192087173462,
0.06410115212202072,
0.0605425201356411,
-0.05970026180148125,
-0.0994439423084259,
0.03844917193055153,
0.0096479132771492,
0.051673322916030884,
-0.00876663625240326,
0.04414482042193413,
0.014806229621171951,
-0.0317625030875206,
-0.04410737752914429,
-0.021308768540620804,
-0.07623741775751114,
-0.008825931698083878,
0.02692040242254734,
-0.03304964676499367,
0.06700441986322403,
0.037854693830013275,
-0.030758613720536232,
-0.024061929434537888,
-0.061069704592227936,
0.020868077874183655,
0.00607515312731266,
0.021375291049480438,
-0.0003449835639912635,
0.027267588302493095,
-0.025305815041065216,
0.005326573271304369
] |
<p>I know that if the Helmholtz free energy, $A$, is expressed as a function $A\sim A(N,V,T)$, then this function contains all thermodynamic information about the system. For instance, the pressure of the system is given by:</p>
<p>$$P(N,V,T) = -\frac{\partial A}{\partial V}\Bigg|_{n,T}$$</p>
<p>Indeed, if we imagine $N$ and $T$ are fixed, then this in effect gives us pressure as a function of volume:</p>
<p>$$P\sim f(V).$$</p>
<p>My question relates to the inverse of this equation. If we are given $P$ rather than $V$ (still with $T$ and $N$ fixed and known) then either numerically or analytically we can solve this to find $V$. But if the equation is complicated enough, <em>there maybe multiple values of $V$ for a given $P$, $T$ and $N$</em>.</p>
<p>This didn't seem too unreasonable to me (perhaps physically this represents a gas and a liquid co-existing at the same $T$, $P$ and $N$ at equilibrium), until I realised that, if we worked with the Gibbs free energy instead, and found values of $G(T,P,N)$, then in that case</p>
<p>$$V(T,P,N) = \frac{\partial G}{\partial P} \Bigg|_{N,T}$$</p>
<p>and this gives us an explicit, <em>single-valued</em> equation for $V$ as a function of $P$, $T$ and $N$ (though perhaps the inverse $P(V)$ is now multi-valued?).</p>
<p>What's going on here? One formulation of thermodynamics gives me an EOS in which there can exist multiple values of $V$ for a given $P$, and the other says I can have multiple values of $P$ for a given $V$! </p> | g4573 | [
0.02453470602631569,
-0.02564549818634987,
-0.032747700810432434,
-0.003085128730162978,
0.010164971463382244,
-0.009316394105553627,
-0.03455575928092003,
0.013234110549092293,
-0.03463426232337952,
0.005532813258469105,
-0.04859171807765961,
-0.0034853899851441383,
0.043576717376708984,
0.004570105113089085,
0.004334331955760717,
-0.013926330953836441,
0.08599430322647095,
-0.02164439484477043,
-0.00197348790243268,
0.0194074846804142,
-0.0170421302318573,
-0.016963740810751915,
0.015505016781389713,
-0.05242200568318367,
0.011743244715034962,
-0.030041217803955078,
0.014864709228277206,
0.01439947821199894,
-0.045415934175252914,
0.004083055071532726,
-0.03742140531539917,
0.027188144624233246,
0.03250905126333237,
-0.03341706842184067,
-0.08463505655527115,
-0.0050979978404939175,
0.07458382099866867,
0.012127065099775791,
0.013824937865138054,
0.0024746349081397057,
-0.020695794373750687,
-0.025739111006259918,
0.00836497638374567,
0.03964993357658386,
-0.032839588820934296,
0.008363720029592514,
-0.02423184923827648,
0.041165791451931,
-0.07315927743911743,
-0.03483149781823158,
0.08271004259586334,
0.046137839555740356,
-0.0027477967087179422,
0.0010957230115309358,
-0.037834133952856064,
-0.0317826084792614,
-0.004878656007349491,
0.05884907394647598,
0.00020405120449140668,
0.06380915641784668,
0.005410565994679928,
0.015164673328399658,
0.0025810205843299627,
0.020693909376859665,
0.032298892736434937,
0.0069637661799788475,
-0.019921820610761642,
-0.0038623253349214792,
0.013915074057877064,
-0.03639952838420868,
0.032848116010427475,
-0.008143803104758263,
-0.015285697765648365,
-0.023587891831994057,
0.004889339208602905,
0.0014894630294293165,
0.004481391981244087,
-0.015964126214385033,
0.01608230173587799,
0.001270074164494872,
0.01108573842793703,
0.007153424434363842,
0.07027266174554825,
-0.017561709508299828,
0.04030121490359306,
-0.02187999151647091,
0.042278993874788284,
-0.03007708117365837,
-0.04697727411985397,
0.010454372502863407,
-0.017829466611146927,
0.02963404357433319,
0.08397596329450607,
0.005269492045044899,
0.025982104241847992,
0.022173745557665825,
-0.01733742468059063,
0.027553599327802658,
-0.056889165192842484,
-0.012335839681327343,
-0.016597198322415352,
-0.0007933948072604835,
0.00015542481560260057,
-0.019690461456775665,
0.029874732717871666,
-0.05309237539768219,
0.05450912192463875,
0.029614850878715515,
-0.021159755066037178,
-0.03360600396990776,
-0.013944958336651325,
0.036218300461769104,
0.018552178516983986,
0.014810238964855671,
-0.022250764071941376,
-0.05619169771671295,
0.07401754707098007,
-0.021036680787801743,
-0.049274176359176636,
0.04170319437980652,
-0.009341035969555378,
0.01639566943049431,
0.0216139517724514,
0.051427360624074936,
0.006013648118823767,
0.010479209944605827,
0.0073179323226213455,
-0.020598111674189568,
0.013933099806308746,
-0.03837679699063301,
0.011776228435337543,
0.009402502328157425,
0.0010449170367792249,
0.027695797383785248,
0.041653815656900406,
0.008681927807629108,
-0.053951576352119446,
0.02783909998834133,
-0.03559984639286995,
0.053912218660116196,
0.0035836598835885525,
-0.03486315906047821,
-0.0328882560133934,
0.0031290759798139334,
0.03347313031554222,
-0.00981177855283022,
-0.014081120491027832,
-0.0075049614533782005,
0.02263234555721283,
-0.018726607784628868,
-0.022246353328227997,
0.05497671663761139,
0.035537172108888626,
0.03269527480006218,
-0.015717417001724243,
-0.025160405784845352,
0.0006369385519064963,
-0.048381906002759933,
-0.025987330824136734,
0.01612779311835766,
0.021673066541552544,
-0.015197942033410072,
0.08960702270269394,
0.032564643770456314,
0.02950899675488472,
0.07879700511693954,
0.005792183335870504,
-0.06970681995153427,
-0.010005208663642406,
-0.025738036260008812,
-0.033939894288778305,
0.039228327572345734,
-0.005215945187956095,
0.04036033898591995,
0.03302573412656784,
0.0002160637523047626,
0.032841768115758896,
0.00773780420422554,
-0.018952205777168274,
0.046041470021009445,
-0.008969854563474655,
0.02840116061270237,
0.01563311740756035,
-0.012090370990335941,
-0.003349236911162734,
0.026946857571601868,
-0.02029925025999546,
0.04200280085206032,
0.0012140873586758971,
0.04527390003204346,
-0.031494662165641785,
0.060484837740659714,
-0.010308773256838322,
0.056858595460653305,
0.059991504997015,
-0.001560170203447342,
0.012156372889876366,
-0.06707371771335602,
-0.04357842355966568,
0.014936600811779499,
-0.00349768646992743,
0.03694412484765053,
0.04630016162991524,
0.0444602333009243,
0.04164395108819008,
0.07445865869522095,
-0.0015708081191405654,
-0.02832493931055069,
0.027639834210276604,
-0.005054471082985401,
-0.020679699257016182,
-0.05746229365468025,
-0.023443613201379776,
0.03831595554947853,
0.053414247930049896,
-0.07719863951206207,
0.04459671303629875,
0.02614719606935978,
-0.0028983433730900288,
-0.021034467965364456,
-0.011254662647843361,
0.060670606791973114,
-0.022876564413309097,
-0.007632242515683174,
-0.01839684695005417,
-0.006757055409252644,
-0.011042308993637562,
-0.026576247066259384,
-0.07228615134954453,
0.006076158490031958,
-0.00473698740825057,
0.011568122543394566,
0.06519385427236557,
-0.025068607181310654,
-0.0013053345028311014,
0.0741579607129097,
0.0016855901340022683,
-0.00121799495536834,
0.010143141262233257,
0.09711320698261261,
0.0018762380350381136,
-0.039970800280570984,
-0.04265400767326355,
0.07705650478601456,
0.02617586962878704,
0.050330374389886856,
-0.01979040913283825,
0.0392167828977108,
0.012630478478968143,
0.028721310198307037,
-0.05080518499016762,
-0.006646472495049238,
0.0270064827054739,
-0.00144917459692806,
-0.028713015839457512,
-0.00591186573728919,
0.0061684828251600266,
-0.005836620926856995,
-0.04438335821032524,
0.023211805149912834,
0.0266175027936697,
0.03090035542845726,
0.0019298422848805785,
0.03283047676086426,
0.012274028733372688,
0.0030257985927164555,
0.040373317897319794,
-0.003315276699140668,
-0.0040856958366930485,
0.020578594878315926,
0.05738217383623123,
0.05319393053650856,
0.00018266955157741904,
0.03210350126028061,
0.008793271146714687,
-0.01808793470263481,
-0.021440602838993073,
-0.06341750919818878,
0.06368892639875412,
-0.042804501950740814,
-0.058393627405166626,
0.013839992694556713,
-0.03571668267250061,
0.040854718536138535,
0.012323413975536823,
-0.05715445056557655,
0.08372494578361511,
-0.019196147099137306,
0.040899164974689484,
-0.018297526985406876,
-0.003711084369570017,
0.014181459322571754,
-0.01428886316716671,
0.03312911465764046,
-0.07219965755939484,
-0.030562451109290123,
-0.012659108266234398,
-0.0801258310675621,
-0.013118364848196507,
0.012313048355281353,
-0.015316563658416271,
-0.038320016115903854,
0.007037799805402756,
0.009151951409876347,
-0.0010452474234625697,
-0.014926078729331493,
-0.0754343718290329,
-0.044802118092775345,
0.013739479705691338,
-0.0052320887334644794,
0.009570461697876453,
0.018572673201560974,
0.013672416098415852,
-0.00748278247192502,
-0.05723383277654648,
0.06474217772483826,
0.00860451627522707,
-0.05016559734940529,
0.035163283348083496,
-0.025054235011339188,
-0.057190798223018646,
-0.06884638965129852,
0.02652190998196602,
-0.03147411346435547,
0.01682262495160103,
-0.03364737331867218,
-0.0667487382888794,
-0.02202528342604637,
0.017961779609322548,
-0.007068711798638105,
0.03904976695775986,
0.0128754498437047,
0.03955003246665001,
-0.02269367128610611,
0.034702885895967484,
-0.021704476326704025,
-0.020701497793197632,
0.013957108370959759,
0.038458202034235,
-0.0004801756876986474,
0.008461765944957733,
-0.04058534651994705,
-0.04625769332051277,
0.021404452621936798,
-0.03160237893462181,
-0.016163192689418793,
-0.0789584219455719,
0.025901781395077705,
-0.0002524068404454738,
-0.06097770482301712,
0.009853840805590153,
-0.025667252019047737,
0.008255998603999615,
0.01141718402504921,
0.02216160297393799,
0.00013215496437624097,
0.04213165119290352,
0.012003089301288128,
0.054867785423994064,
0.015034857206046581,
0.00933641754090786,
-0.05983696132898331,
0.05173414945602417,
0.02364707924425602,
0.04321146756410599,
0.006914951838552952,
0.025510454550385475,
0.02852240949869156,
-0.07508061081171036,
-0.07303625345230103,
0.030024124309420586,
-0.052542030811309814,
0.0358395054936409,
-0.003083092626184225,
0.04224935173988342,
-0.030320964753627777,
-0.011165718547999859,
-0.004974068142473698,
-0.02401982620358467,
0.02438819780945778,
0.08817150443792343,
-0.042441513389348984,
0.009511045180261135,
0.006570560857653618,
0.02716466784477234,
-0.010741017758846283,
-0.021579032763838768,
0.013049274682998657,
0.03391055762767792,
-0.012594233267009258,
0.0029530308675020933,
0.026607051491737366,
-0.06276372075080872,
0.09058402478694916,
0.008618961088359356,
0.0224552471190691,
0.03488721698522568,
-0.06302820891141891,
-0.043593697249889374,
0.051637664437294006,
0.0031776034738868475,
-0.046909481287002563,
0.010182336904108524,
-0.05204688385128975,
0.016848301514983177,
0.013247926719486713,
0.060600899159908295,
-0.0708106979727745,
-0.04231293499469757,
-0.012443928979337215,
0.009383006952702999,
-0.04256385937333107,
0.06834806501865387,
-0.008706871420145035,
0.008101049810647964,
0.002836893079802394,
0.006320031825453043,
-0.05757474526762962,
0.0773426741361618,
-0.004119248129427433,
0.03383660316467285,
-0.029230525717139244,
0.0330980084836483,
-0.009853997267782688,
-0.06309840828180313,
-0.0038605642039328814,
0.05836360529065132,
0.020471516996622086,
-0.050746768712997437,
-0.06624604016542435,
0.02914363145828247,
-0.008938144892454147,
0.041708216071128845,
0.023728154599666595,
0.008200629614293575,
0.03051672875881195,
-0.01894485205411911,
0.008566736243665218,
-0.0700942724943161,
0.055271901190280914,
0.009302644059062004,
0.008727636188268661,
0.002158443909138441,
-0.020314782857894897,
0.007850263267755508,
-0.01607177034020424,
0.034857556223869324,
0.004586992785334587,
-0.03576875105500221,
-0.04583973437547684,
0.0007584199775010347,
-0.009060007520020008,
-0.023525409400463104,
0.027461275458335876,
-0.010650310665369034,
-0.01977464370429516,
-0.02510235086083412,
-0.009817833080887794,
0.03714928776025772,
-0.007826633751392365,
-0.021603038534522057,
-0.03212505951523781,
0.020254889503121376,
0.029197024181485176,
0.02248801663517952,
-0.06112516298890114,
-0.06744188815355301,
0.055995043367147446,
-0.01787257380783558,
-0.012455975636839867,
0.02659795805811882,
0.016922328621149063,
0.027245374396443367,
0.0025154417380690575,
0.006291573867201805,
-0.012168945744633675,
-0.003414359875023365,
-0.02947360649704933,
-0.0012837802059948444,
-0.06426524370908737,
0.001503805280663073,
0.052023060619831085,
-0.004395166877657175,
0.04424740746617317,
-0.027628054842352867,
0.004797162022441626,
-0.031720586121082306,
-0.016681073233485222,
0.018809931352734566,
0.017992820590734482,
-0.009298139251768589,
0.06961625814437866,
0.040422216057777405,
0.008896552957594395,
-0.06448625028133392,
-0.012943999841809273,
-0.006850607693195343,
-0.057225581258535385,
0.02370534837245941,
0.028470201417803764,
-0.054510004818439484,
-0.00896645151078701,
0.021610664203763008,
0.033177830278873444,
0.042757727205753326,
0.06835250556468964,
0.029169967398047447,
-0.014279398135840893,
-0.03664851933717728,
0.05275394767522812,
0.06037629768252373,
-0.07782111316919327,
-0.01776996999979019,
-0.015359182842075825,
-0.02045874297618866,
-0.058761294931173325,
-0.05031070485711098,
-0.017138764262199402,
-0.012370730750262737,
-0.035132791846990585,
0.03669191151857376,
-0.01132959220558405,
0.010803849436342716,
0.016993632540106773,
-0.0037177742924541235,
-0.02503722533583641,
-0.05898110941052437,
-0.06106795370578766,
0.00028963020304217935,
0.03750268742442131,
-0.03339334949851036,
0.02816913090646267,
0.0263470821082592,
0.024935195222496986,
-0.02525569498538971,
-0.0070167225785553455,
-0.07898395508527756,
0.014079106040298939,
0.07405703514814377,
-0.03825102001428604,
0.05233227089047432,
-0.046554163098335266,
0.008744015358388424,
0.051549121737480164,
0.003020884934812784,
-0.01492422353476286,
-0.014198141172528267,
-0.03231985867023468,
0.014822762459516525,
0.04818900674581528,
-0.021494800224900246,
0.00032475750776939094,
-0.062233816832304,
-0.02677752822637558,
0.018995868042111397,
-0.00003474553159321658,
0.02970079332590103,
-0.03098597563803196,
0.015332264825701714,
0.012521618977189064,
-0.024466905742883682,
0.040497347712516785,
-0.005476700142025948,
0.03821880370378494,
-0.03612491488456726,
-0.03700032830238342,
0.018199404701590538,
0.015240955166518688,
-0.02360842376947403,
0.0605953112244606,
-0.0013766693882644176,
-0.029116438701748848,
0.03254381939768791,
-0.05323874205350876,
0.042866967618465424,
-0.012150377035140991,
-0.04538390785455704,
-0.0526847317814827,
0.029018627479672432,
0.003424105467274785,
-0.07471165806055069,
-0.035435449331998825,
0.0246420931071043,
0.02562067285180092,
0.03993711620569229,
0.04602848365902901,
-0.0033341937232762575,
-0.0483553521335125,
0.019823357462882996,
0.024961072951555252,
0.040573619306087494,
-0.06580344587564468,
-0.06064556911587715,
-0.006359547842293978,
0.002770529594272375,
0.0025207451544702053,
0.04294061288237572,
-0.02801908738911152,
-0.020533375442028046,
0.061060067266225815,
-0.009471803903579712,
0.06075797975063324,
0.06779275089502335,
-0.11101331561803818,
-0.018524859100580215,
0.011187280528247356,
-0.026058383285999298,
0.03096677176654339,
-0.05291750282049179,
0.011038246564567089,
-0.040028706192970276,
-0.023130133748054504,
-0.03964440897107124,
-0.0384259857237339,
0.030753837898373604,
0.040424566715955734,
0.0017192234518006444,
0.016285371035337448,
0.048652514815330505,
0.02198966033756733,
0.007828854955732822,
-0.024516331031918526,
-0.023955626413226128,
-0.01324545405805111,
0.053920965641736984,
-0.02973211742937565,
-0.04093103110790253,
0.03568824380636215,
-0.02500770427286625,
0.023923823609948158,
0.0824170634150505,
-0.026567433029413223,
-0.011816425248980522,
0.06551937758922577,
-0.03669615462422371,
0.03343359753489494,
-0.06400614976882935,
0.004702813923358917,
0.001991609111428261,
-0.008096420206129551,
-0.02792106382548809,
-0.012747082859277725,
0.035708632320165634,
0.04785486310720444,
-0.059752654284238815,
0.031671371310949326,
0.04846695065498352,
-0.018147118389606476,
-0.12142815440893173,
0.04003079980611801,
0.020559005439281464,
-0.009990307502448559,
-0.06446440517902374,
0.06060592457652092,
-0.035237234085798264,
0.019332928583025932,
0.0000794790466898121,
0.029821718111634254,
-0.004048746079206467,
0.012055618688464165,
0.012714151293039322,
0.024694425985217094,
0.01073892880231142,
0.03597589209675789,
-0.0006554669234901667,
0.0870937630534172,
0.06698515266180038,
-0.09231434017419815,
0.029990043491125107,
-0.03328102454543114,
0.0007303440943360329,
-0.05056396499276161,
-0.0576837919652462,
0.0393097810447216,
-0.03465447947382927,
-0.007806374225765467,
0.04024611786007881,
0.011875477619469166,
-0.02284594252705574,
-0.005855696275830269,
-0.01662978157401085,
0.021504435688257217,
-0.006613036151975393,
-0.0072958809323608875,
-0.019714294001460075,
-0.03256138414144516,
-0.05878068879246712,
0.0169499721378088,
-0.07163725793361664,
0.02081446908414364,
-0.03091127797961235,
-0.04773432016372681,
0.0493914894759655,
-0.0011995184468105435,
-0.054061152040958405,
0.017718292772769928,
0.05737610161304474,
0.044050801545381546,
0.0074479482136666775,
-0.027539320290088654,
0.03964310884475708,
-0.007677851710468531,
-0.007949878461658955,
-0.031073061749339104,
0.020338034257292747,
0.03580759838223457,
-0.0030632971320301294,
-0.0055143143981695175,
-0.012420713901519775,
-0.001873429981060326,
-0.029880624264478683,
-0.04300105944275856,
-0.012286868877708912,
0.04522565007209778,
0.03592903912067413,
-0.00012267869897186756,
-0.06357140094041824,
-0.01612679846584797,
-0.0030508346389979124,
-0.06049530580639839,
-0.034156542271375656,
-0.02513880655169487,
-0.05915534123778343,
-0.06947652995586395,
-0.03784441575407982,
-0.011187202297151089,
-0.048333171755075455,
0.014027450233697891,
0.014898949302732944,
0.046245332807302475,
-0.026898778975009918,
-0.015038051642477512,
0.010154422372579575,
0.007047966122627258,
0.018887246027588844,
-0.020776212215423584,
0.08430573344230652,
-0.04940364882349968,
0.04107454791665077,
-0.0006607358809560537,
0.005538247991353273,
-0.03561290353536606,
0.06185203045606613,
-0.026342613622546196,
0.017596492543816566,
-0.022058766335248947,
-0.07392099499702454,
0.0074935550801455975,
0.051689326763153076,
-0.04765750467777252,
-0.015259012579917908,
-0.022535715252161026,
0.037748370319604874,
-0.006147006060928106,
0.003162992186844349,
-0.037527598440647125,
0.02513526938855648,
0.013454076834022999,
-0.01485257688909769,
0.05075455084443092,
-0.04914139211177826,
0.03646280989050865,
-0.010081346146762371,
0.005580402910709381,
-0.006522131152451038,
-0.06300776451826096,
-0.009156078100204468,
0.0312829315662384
] |
<p>Eq (1.137) in Negele and Orland gives the following identity for a normal-ordered operator $A(a_i^\dagger,a_i)$:</p>
<p>$$\langle \phi|A(a_i^\dagger,a_i)|\phi'\rangle=A(\phi_i^*,\phi'_i)e^{\sum \phi_i^*\phi'_i}$$</p>
<p>For the coherent (boson) states $|\phi\rangle=e^{\sum\phi_ia^\dagger_i}|0\rangle $. When I try to prove this I get a factor of 1/2 in the exponent. I'm going to take a simple example $A=a_i^\dagger a_i$ to try and find my mistake. First I define $\eta'=\sum \phi'_ia_i^\dagger$, and use the identity</p>
<p>$$a_i\eta'^n=n\phi'_i\eta'^{n-1}+\eta'^n a_i.$$</p>
<p>Then I can show</p>
<p>$$a_i|\phi'\rangle=(e^{\eta'}a_i+\phi'_ie^{\eta'})|0\rangle$$</p>
<p>One term of which kills the vacuum so I have shown</p>
<p>$$\langle \phi |a^\dagger_i a_i|\phi'\rangle=\langle 0| \phi^*_i\phi'_ie^{\eta^*}e^{\eta'}|0\rangle$$</p>
<p>Then I want to use the Baker-Campbell-Hausdorf formula. The commutator </p>
<p>\begin{equation}
[\eta^*,\eta']=[\sum\phi^*_ia_i,\sum\phi_ja^\dagger_j]=\sum[\phi^*_ia_i,\phi_i'a_i^\dagger]+\sum_{i\neq j}[\phi^*_ia_i,\phi_ja^\dagger_j]=\sum\phi_i^*\phi'_i,\qquad (1)
\end{equation}
and when you commute everything through the second term and kill the vacuum. Since this is a scalar, the BCH formula gives</p>
<p>$$\ln(e^{\eta^*}e^{\eta'})=\eta^*+\eta'+\frac{1}{2}\sum\phi_i^*\phi_i'$$</p>
<p>Rearrange the sum, exponentiate, kill some more vacuum and I get the right expression but with a factor of 1/2!</p>
<p>What am I doing wrong? My first guess is in equation (1), maybe there is some dobule-counting I don't see but you can write things like</p>
<p>$$[\sum,\sum]=[1,\sum]+[2,\sum]+...=[1,1]+[1,\sum_{\neq 1}]+[2,2]+[2,\sum_{\neq 2}]+...$$
$$=\sum[i,i]+\sum_{i\neq j}[i,j].$$</p> | g4574 | [
-0.02752717025578022,
-0.03196173161268234,
0.004439297132194042,
0.012061377055943012,
0.06250239163637161,
-0.03598736226558685,
0.04641176760196686,
0.015263919718563557,
0.050120387226343155,
0.00430724024772644,
-0.06088775768876076,
0.016177723184227943,
0.020525677129626274,
0.02883169986307621,
-0.016778435558080673,
0.015713458880782127,
0.023287206888198853,
0.007753279060125351,
0.027677908539772034,
-0.0035510018933564425,
-0.05719868466258049,
0.028019849210977554,
0.033815108239650726,
-0.07401657849550247,
0.09960202872753143,
-0.02214600332081318,
0.06252671778202057,
0.00866716168820858,
-0.06420177221298218,
-0.038579538464546204,
0.009527516551315784,
0.06105813384056091,
-0.014907757751643658,
0.004395242314785719,
-0.03745037689805031,
-0.00991748832166195,
0.07802698761224747,
0.06531969457864761,
0.043510064482688904,
-0.013701902702450752,
-0.03677507862448692,
0.03506173565983772,
0.03633328527212143,
-0.023436080664396286,
-0.021480200812220573,
0.015803394839167595,
-0.020352544263005257,
-0.012176111340522766,
-0.02779175341129303,
-0.05038296803832054,
-0.0016025315271690488,
0.001853106077760458,
0.05434669181704521,
-0.029791973531246185,
-0.03388907387852669,
0.07663172483444214,
-0.027758078649640083,
-0.09617330133914948,
0.007388127036392689,
0.055163733661174774,
-0.02449379302561283,
-0.08212579041719437,
0.04832698777318001,
-0.020209399983286858,
0.025736110284924507,
-0.007704231888055801,
-0.0000011657583627311396,
0.046072959899902344,
-0.01967943087220192,
-0.038892727345228195,
-0.03433747962117195,
-0.06482808291912079,
0.046718910336494446,
-0.01778663508594036,
-0.011727932840585709,
0.016681278124451637,
0.0016617841320112348,
-0.015842968598008156,
0.023425579071044922,
-0.0035434369929134846,
-0.03963260352611542,
-0.03603924810886383,
-0.009603678248822689,
0.06056174635887146,
0.010728457011282444,
-0.05532269924879074,
0.016203923150897026,
-0.02215864509344101,
0.03935990855097771,
-0.026876196265220642,
-0.021281719207763672,
-0.004860051441937685,
-0.002001109067350626,
0.04704599827528,
0.024848340079188347,
-0.0164367463439703,
0.018227286636829376,
0.0540173202753067,
-0.029941154643893242,
0.0007750465883873403,
-0.03709984943270683,
0.015102693811058998,
-0.031990356743335724,
-0.07383272796869278,
0.021503295749425888,
0.006124460604041815,
0.0477229543030262,
-0.04535742849111557,
-0.054776281118392944,
-0.009392458014190197,
-0.02427194081246853,
-0.04105005040764809,
-0.0574965700507164,
-0.04350036755204201,
0.02759549953043461,
0.02984662353992462,
0.0006419166456907988,
-0.006305421702563763,
-0.00845961831510067,
0.03114817477762699,
0.00567441014572978,
-0.03215000405907631,
0.021166913211345673,
0.004350943490862846,
-0.00419347919523716,
-0.026817459613084793,
0.021921880543231964,
0.041231703013181686,
0.056233249604701996,
0.06802106648683548,
-0.02084595151245594,
-0.027325160801410675,
0.024092689156532288,
0.06433812528848648,
0.021391097456216812,
0.029876770451664925,
0.030888574197888374,
0.012356340885162354,
0.03176853060722351,
-0.05292845517396927,
0.002924867207184434,
0.009026280604302883,
0.008862310089170933,
-0.0000985250881058164,
-0.006479539442807436,
-0.018256645649671555,
0.007266641594469547,
-0.05069351941347122,
-0.009826436638832092,
0.006799227092415094,
-0.024628719314932823,
0.033575475215911865,
-0.02434854581952095,
0.010677408427000046,
-0.006892476696521044,
0.03878729045391083,
0.03086911141872406,
-0.017939778044819832,
-0.0621240958571434,
0.0017586760222911835,
-0.04006197676062584,
0.02546899951994419,
-0.00409064581617713,
0.05270539969205856,
-0.028883211314678192,
-0.0077391681261360645,
0.043383412063121796,
-0.03808686509728432,
-0.014392812736332417,
-0.014397951774299145,
0.016977345570921898,
0.03593479469418526,
0.0717199444770813,
-0.0008338092593476176,
0.07297103852033615,
0.06654351949691772,
-0.030955424532294273,
0.051533959805965424,
0.03189476951956749,
0.015992777422070503,
-0.00679418770596385,
0.028378169983625412,
0.0528460294008255,
0.006764077115803957,
-0.030771715566515923,
0.03541308641433716,
-0.03332066535949707,
0.030360421165823936,
-0.01031283475458622,
0.04007516801357269,
0.014614523388445377,
0.07657438516616821,
-0.04002666100859642,
0.037644896656274796,
-0.025102488696575165,
0.012850544415414333,
-0.03479992598295212,
-0.08717943727970123,
0.015123717486858368,
-0.03130048140883446,
-0.02762037329375744,
-0.002261308953166008,
0.008801787160336971,
0.006975085008889437,
-0.002299490151926875,
-0.0895063653588295,
0.012345288880169392,
-0.009737899526953697,
0.007565786130726337,
-0.008747493848204613,
0.02693081460893154,
-0.05051753669977188,
-0.048554688692092896,
0.0630415603518486,
0.03622298315167427,
-0.030038341879844666,
0.01982252672314644,
-0.03654766455292702,
-0.03719398379325867,
-0.0032840489875525236,
-0.030894050374627113,
-0.009792398661375046,
0.02669348195195198,
-0.05747424066066742,
-0.03169970586895943,
0.0024940967559814453,
0.032828688621520996,
0.010951487347483635,
-0.027285365387797356,
-0.02296340838074684,
-0.0582999624311924,
0.024076316505670547,
-0.04731741547584534,
-0.07164610922336578,
0.025112565606832504,
-0.0016574794426560402,
0.016316263005137444,
0.00970515888184309,
0.05730224773287773,
0.07867896556854248,
-0.047310106456279755,
-0.040538251399993896,
-0.028472239151597023,
-0.0016676897648721933,
-0.025864779949188232,
0.005602346733212471,
0.0111182676628232,
-0.007304356899112463,
-0.013874534517526627,
0.04380934685468674,
-0.012294597923755646,
-0.039622899144887924,
-0.0033257766626775265,
0.006517072673887014,
0.01394153106957674,
-0.028131194412708282,
0.007397728506475687,
-0.015586026012897491,
0.0439193993806839,
0.06650970131158829,
-0.013449699617922306,
-0.04083701968193054,
0.015630794689059258,
0.061370860785245895,
-0.06218281388282776,
-0.039454586803913116,
-0.05000859498977661,
0.024775011464953423,
0.05523580685257912,
0.009768151678144932,
-0.002542132046073675,
-0.00045675813453271985,
-0.007861698977649212,
0.03052123263478279,
-0.045630402863025665,
-0.033184174448251724,
0.00773158622905612,
-0.012571379542350769,
0.05663137137889862,
0.024485116824507713,
-0.02828681282699108,
0.04381275177001953,
-0.04337715357542038,
0.013837866485118866,
-0.004147369414567947,
-0.007389761507511139,
0.007893945090472698,
0.047085557132959366,
-0.02115059643983841,
0.029045403003692627,
0.010817324742674828,
0.03153182938694954,
-0.008046346716582775,
-0.01026324275881052,
0.0066610523499548435,
0.01595449075102806,
-0.006934349425137043,
-0.03476935625076294,
0.052952904254198074,
0.04011973366141319,
0.05417300760746002,
-0.0278677549213171,
0.007122301030904055,
-0.026316698640584946,
-0.01584876887500286,
-0.03266734629869461,
-0.02738482877612114,
-0.05764024332165718,
0.05855163186788559,
0.0030284458771348,
0.014313099905848503,
0.02239723689854145,
-0.021269796416163445,
-0.02788776345551014,
0.038876019418239594,
0.010477040894329548,
-0.013578949496150017,
-0.027721602469682693,
0.02504413016140461,
-0.01631283573806286,
-0.05483821779489517,
-0.05507345870137215,
-0.0015980454627424479,
-0.030970796942710876,
-0.010645025409758091,
-0.002545426832512021,
-0.08074144273996353,
0.021802421659231186,
-0.044165417551994324,
-0.024611175060272217,
-0.013901080936193466,
0.003964316565543413,
0.026566844433546066,
-0.044433917850255966,
-0.0533444918692112,
-0.040742747485637665,
0.014615118503570557,
0.029252618551254272,
0.0232646856456995,
0.02104465290904045,
0.008229922503232956,
-0.030358653515577316,
0.03695591166615486,
0.02799607627093792,
-0.03325965255498886,
-0.07211115211248398,
0.005049474071711302,
0.06556280702352524,
0.018369443714618683,
0.009620945900678635,
0.010655786842107773,
-0.0013116258196532726,
0.055295947939157486,
0.002691184636205435,
-0.04449913650751114,
0.0013343276223167777,
0.027226831763982773,
-0.02990756928920746,
0.03863966092467308,
-0.007002969738095999,
0.029058916494250298,
-0.014434301294386387,
-0.03390062227845192,
-0.00037153298035264015,
0.02248435840010643,
0.006178405601531267,
0.01754176616668701,
0.048297930508852005,
-0.002864518901333213,
0.03333449736237526,
0.012995248660445213,
0.027524683624505997,
0.020960733294487,
-0.027173416689038277,
-0.006649472285062075,
-0.02839067578315735,
0.005801022052764893,
0.029376721009612083,
0.03161303699016571,
0.025250107049942017,
0.01983499713242054,
-0.028499877080321312,
0.00983973778784275,
-0.03912702947854996,
-0.0016248739557340741,
0.03769202530384064,
-0.014066246338188648,
-0.04811982810497284,
0.0511811263859272,
-0.028090106323361397,
0.03204171359539032,
0.01519110519438982,
0.0037187128327786922,
0.02414035238325596,
0.055792927742004395,
0.025487393140792847,
-0.018433423712849617,
0.006551101803779602,
-0.11516115069389343,
0.027020419016480446,
0.014187929220497608,
-0.06565608829259872,
0.04401072487235069,
0.00946775171905756,
-0.029904456809163094,
0.010536485351622105,
0.04398362711071968,
0.015108908526599407,
0.020008055493235588,
-0.040295056998729706,
-0.042796988040208817,
0.0073453024961054325,
-0.025506986305117607,
0.0069631473161280155,
0.003896981943398714,
-0.04181132838129997,
0.06360195577144623,
0.010209362022578716,
-0.03533351793885231,
0.0017642203019931912,
0.048021793365478516,
-0.0014402685919776559,
-0.04690167307853699,
-0.04125802591443062,
-0.007484322879463434,
0.07342991977930069,
0.008362486027181149,
0.01384861208498478,
0.026647528633475304,
-0.0011304243234917521,
-0.009260803461074829,
0.06562362611293793,
-0.010890770703554153,
0.06221384182572365,
-0.029035523533821106,
-0.0007558189099654555,
-0.0657636895775795,
0.015246258117258549,
0.015402909368276596,
0.08472581952810287,
-0.02512321248650551,
-0.0335809551179409,
-0.05327962711453438,
-0.019911354407668114,
0.060043562203645706,
-0.012102361768484116,
-0.01123142708092928,
-0.07117872685194016,
0.019078070297837257,
-0.02696388214826584,
0.007193567231297493,
0.05727892369031906,
0.02142498828470707,
-0.04097334295511246,
0.04264020919799805,
-0.0013113290769979358,
-0.019461434334516525,
-0.01472546812146902,
0.020181434229016304,
-0.016401851549744606,
-0.0036505276802927256,
-0.022994011640548706,
0.030339978635311127,
-0.018664168193936348,
0.048904482275247574,
0.06366374343633652,
-0.04309162497520447,
0.024109192192554474,
0.02249119244515896,
-0.05903278663754463,
0.07784219831228256,
0.02229437418282032,
0.016963347792625427,
-0.05190938711166382,
-0.022292492911219597,
0.0306867528706789,
-0.006872450467199087,
0.0058236271142959595,
-0.06950188428163528,
0.06690116971731186,
-0.008405810222029686,
-0.04624522849917412,
-0.03633759543299675,
-0.010867170058190823,
-0.014936462976038456,
0.017035966739058495,
-0.006444993894547224,
0.02698052115738392,
0.008362611755728722,
-0.02826600708067417,
0.020598817616701126,
-0.0041068256832659245,
0.01758543588221073,
-0.03471949324011803,
-0.012872938066720963,
-0.010301700793206692,
0.02063686028122902,
-0.03541946038603783,
0.00374258472584188,
0.08256673067808151,
-0.08060678094625473,
0.04558773338794708,
-0.004790592007339001,
0.0129594337195158,
0.0011255786521360278,
0.0063781291246414185,
0.026906238868832588,
0.06167146936058998,
0.022334197536110878,
0.023691391572356224,
0.000021415344235720113,
-0.05314194783568382,
0.0790330320596695,
-0.01940305344760418,
0.02483079768717289,
0.02273756079375744,
-0.006245066877454519,
-0.0032162212301045656,
-0.05929640308022499,
-0.03167073428630829,
0.023414548486471176,
0.03326431289315224,
0.021222278475761414,
0.008514022454619408,
-0.018252070993185043,
0.026505019515752792,
-0.04966389015316963,
-0.1138966828584671,
-0.023637354373931885,
-0.003659767098724842,
-0.008586941286921501,
0.027804860845208168,
-0.004503507167100906,
-0.03837623819708824,
0.06370776891708374,
-0.022488411515951157,
-0.04436322674155235,
0.02831958793103695,
-0.029885126277804375,
-0.03581659495830536,
0.009905309416353703,
-0.022583745419979095,
-0.024303961545228958,
0.004458528943359852,
-0.015422041527926922,
0.014159058220684528,
-0.02806946262717247,
-0.0357457771897316,
0.06836919486522675,
-0.008277501910924911,
-0.012903057970106602,
-0.005414208397269249,
-0.016627373173832893,
-0.045596037060022354,
0.023749317973852158,
0.01708459109067917,
0.05143464729189873,
-0.007151538506150246,
-0.05768854543566704,
0.008472882211208344,
0.009775840677320957,
0.005311897490173578,
0.004659214988350868,
0.0049769156612455845,
0.004513928666710854,
-0.03989402949810028,
0.04888595640659332,
0.03830384090542793,
-0.043387170881032944,
0.013888007961213589,
-0.00930052436888218,
0.012390214018523693,
-0.04567984491586685,
-0.0235027726739645,
0.053512729704380035,
0.06349704414606094,
-0.09045267105102539,
-0.07710397243499756,
-0.011553308926522732,
0.006090868730098009,
-0.042938437312841415,
-0.00971412193030119,
0.034840166568756104,
-0.03612159565091133,
-0.04613456130027771,
0.04943821579217911,
-0.03253776207566261,
-0.023607956245541573,
0.07646418362855911,
0.01496866811066866,
-0.029584908857941628,
0.012804490514099598,
-0.0285573098808527,
-0.017027564346790314,
-0.026070380583405495,
0.0643668845295906,
0.03979916498064995,
0.006384271662682295,
-0.015437841415405273,
0.005239055957645178,
0.045187123119831085,
0.0013935539172962308,
0.007073818705976009,
-0.012425431981682777,
-0.07253679633140564,
0.04196763411164284,
-0.09277839213609695,
0.053753312677145004,
-0.03011253848671913,
0.03679092600941658,
-0.004410355817526579,
0.0034405833575874567,
0.009062574245035648,
-0.013668905012309551,
-0.03986581787467003,
-0.025854500010609627,
0.017597438767552376,
0.057684049010276794,
0.009276018477976322,
0.05448843166232109,
0.044302795082330704,
-0.023836825042963028,
0.006540203467011452,
0.030554428696632385,
0.03580239415168762,
0.00574658066034317,
-0.021588729694485664,
-0.0155029296875,
0.027636542916297913,
0.016237255185842514,
0.007420450448989868,
0.004477237816900015,
-0.04992740601301193,
0.0020863956306129694,
0.004008921328932047,
-0.04287908226251602,
-0.04897971823811531,
0.08443725854158401,
0.005732299294322729,
0.06057558208703995,
-0.05780074745416641,
0.04526380077004433,
0.050244979560375214,
-0.03386273607611656,
-0.06743375211954117,
0.028552010655403137,
0.006119200959801674,
0.022312356159090996,
-0.06124197691679001,
0.008893236517906189,
0.0063899727538228035,
0.022500023245811462,
0.036774396896362305,
0.029904680326581,
0.020894745364785194,
-0.025639034807682037,
0.09263887256383896,
0.037772100418806076,
-0.017573660239577293,
-0.015681494027376175,
-0.006677411496639252,
0.03657227009534836,
0.001728129805997014,
0.007714873179793358,
0.0052478983998298645,
-0.01180721540004015,
0.01568884775042534,
-0.012733069248497486,
0.06937915086746216,
-0.025955554097890854,
-0.004641697276383638,
-0.03963608667254448,
-0.046575650572776794,
-0.007844208739697933,
-0.051598697900772095,
0.03154531866312027,
0.03158948943018913,
0.043633848428726196,
-0.013547418639063835,
-0.0054051848128438,
0.021501749753952026,
0.02143058367073536,
-0.029543213546276093,
-0.02034641243517399,
-0.0014834613539278507,
0.07286009192466736,
-0.012702872976660728,
0.0018371762707829475,
0.09394338726997375,
0.028203334659337997,
0.007659628055989742,
-0.018897753208875656,
0.05245533213019371,
0.0051402500830590725,
0.03620960935950279,
0.008209124207496643,
-0.04669306427240372,
0.00960802473127842,
0.010300356894731522,
0.030073590576648712,
0.029082853347063065,
-0.0035092567559331656,
-0.020858656615018845,
-0.07046524435281754,
-0.05346705764532089,
0.002476033754646778,
0.040982820093631744,
0.014173301868140697,
0.01730588637292385,
0.016638869419693947,
-0.01616423949599266,
-0.02825196459889412,
-0.04484489560127258,
-0.011523805558681488,
0.03576695919036865,
-0.027406243607401848,
-0.053013406693935394,
-0.02032153680920601,
0.004618144128471613,
0.004804190248250961,
-0.019818169996142387,
0.005853953771293163,
-0.0299368966370821,
0.005418061278760433,
-0.028473366051912308,
-0.05654364824295044,
-0.028936706483364105,
0.0153629370033741,
-0.0019060273189097643,
0.05629512295126915,
-0.018522633239626884,
-0.0821906179189682,
-0.07090426981449127,
-0.0270487442612648,
-0.00601796293631196,
-0.0651414543390274,
0.01748218946158886,
-0.06476319581270218,
0.041909679770469666,
-0.02685587853193283,
-0.025746045634150505,
-0.04421262815594673,
0.009451506659388542,
-0.03105238266289234,
0.05867096036672592,
-0.09555554389953613,
-0.026755718514323235,
-0.02057386189699173,
0.03713726997375488,
0.012213988229632378,
0.03760095685720444,
0.0279111098498106,
-0.04235977679491043,
0.052609361708164215,
0.07827030122280121,
-0.015340288169682026,
0.08069951087236404,
0.029742499813437462,
0.03715277463197708,
0.00954990740865469,
-0.01623714156448841,
-0.05625376105308533,
-0.03590483218431473,
0.01882726326584816,
-0.06940023601055145,
-0.06385008245706558,
0.012330192141234875,
0.006880918983370066
] |
<p>Can we generate a pulse , transmit it and after that can we record it's response time ?</p>
<p>I am curious because I want to know that is it possible to make a mapping device (like SLAM) which uses this technique.
I have done a little search but didn't get the satisfying result .
If any one has any idea about this or where I can get more knowledge about it please share it.</p> | g4575 | [
0.0101978350430727,
0.007125662174075842,
0.005650822073221207,
0.0067213596776127815,
0.0039772214367985725,
-0.02506675012409687,
0.03485889360308647,
0.03755710646510124,
0.015240930952131748,
-0.02216937020421028,
-0.05530787631869316,
0.04141081124544144,
0.051151055842638016,
-0.015023530460894108,
-0.0534946508705616,
-0.06933408975601196,
0.08301489055156708,
-0.014242292381823063,
-0.019117996096611023,
0.030847208574414253,
0.05034615471959114,
0.008369163610041142,
-0.023042647168040276,
-0.01935591921210289,
-0.04557810723781586,
-0.02789866365492344,
0.036096639931201935,
0.009210126474499702,
-0.07546620815992355,
-0.00406233686953783,
-0.026581408455967903,
-0.0564400888979435,
0.014178555458784103,
0.03285142406821251,
-0.01084472332149744,
-0.018683940172195435,
-0.078364297747612,
-0.05834810808300972,
0.009605765342712402,
0.033299900591373444,
0.002767168218269944,
-0.055532071739435196,
0.043463826179504395,
0.015843423083424568,
0.01165550947189331,
0.007399783469736576,
0.04583950340747833,
-0.00210889196023345,
0.01762293465435505,
-0.029880767688155174,
-0.050659023225307465,
-0.048369698226451874,
0.013222083449363708,
-0.010461624711751938,
0.033377889543771744,
0.01792992651462555,
-0.00804633367806673,
-0.014120281673967838,
0.05752639099955559,
-0.032126303762197495,
-0.023470474407076836,
-0.013686064630746841,
0.01959666982293129,
0.04086550697684288,
0.0859612450003624,
-0.013015319593250751,
-0.045975640416145325,
0.012224216014146805,
-0.05774373188614845,
0.05664718523621559,
0.005558705423027277,
-0.006800447124987841,
-0.03568154200911522,
-0.049351319670677185,
0.07813713699579239,
-0.0006855326937511563,
0.05110126733779907,
-0.04983007162809372,
-0.02995976246893406,
0.06271356344223022,
-0.0022255168296396732,
-0.020075133070349693,
-0.026773249730467796,
-0.02763465791940689,
0.06565318256616592,
-0.02146020159125328,
0.009012945927679539,
0.01269647479057312,
-0.005708164069801569,
0.012734496034681797,
0.008566692471504211,
-0.017363404855132103,
0.09379725158214569,
0.010515334084630013,
0.00020833547750953585,
0.02641092799603939,
-0.059032004326581955,
0.04754621908068657,
0.03947245329618454,
0.03603878617286682,
-0.018845155835151672,
-0.025180354714393616,
0.01859675720334053,
-0.02574160322546959,
-0.024028651416301727,
-0.03682960942387581,
0.008534364402294159,
-0.03770209103822708,
0.006649128161370754,
-0.03281955420970917,
0.004848420154303312,
-0.05517243221402168,
0.010280949994921684,
0.05967926234006882,
-0.03686414659023285,
-0.02310432307422161,
0.041429415345191956,
0.005356824491173029,
-0.03039279766380787,
0.07044968008995056,
0.032959915697574615,
-0.03314261510968208,
-0.07884534448385239,
0.00327923777513206,
0.022336723282933235,
0.0494147352874279,
0.003442055080085993,
0.004219500347971916,
0.01640426553785801,
0.06509554386138916,
-0.005876405164599419,
0.009156264364719391,
-0.0509585477411747,
0.046636078506708145,
0.0051787244156003,
0.046536870300769806,
0.014086776413023472,
-0.007276721764355898,
0.002023163018748164,
0.03347393497824669,
-0.0020638678688555956,
-0.08202724158763885,
-0.03598150238394737,
-0.020717734470963478,
0.01438415702432394,
0.0513397715985775,
0.01186890248209238,
-0.018424639478325844,
0.02493978850543499,
0.033132102340459824,
-0.017932001501321793,
-0.0031352464575320482,
-0.012480242177844048,
0.0039013500791043043,
0.06644843518733978,
0.020070264115929604,
-0.03397412970662117,
-0.04293882101774216,
-0.012583255767822266,
0.010077516548335552,
-0.008023313246667385,
-0.03954184427857399,
0.0078014200553298,
0.009381101466715336,
0.01541565079241991,
-0.0620230995118618,
0.03702949360013008,
-0.0012719467049464583,
0.03759642317891121,
-0.0726771205663681,
-0.020303094759583473,
0.008414420299232006,
-0.006498085800558329,
-0.002743672812357545,
0.06605333834886551,
0.01400113943964243,
-0.026347585022449493,
-0.006928862072527409,
0.016888249665498734,
-0.01581752300262451,
-0.05137968063354492,
-0.0004697296826634556,
-0.059402212500572205,
-0.05616816133260727,
0.010162970051169395,
0.03244590386748314,
0.000297253456665203,
-0.03340675309300423,
-0.02840665727853775,
-0.005869959481060505,
-0.048400573432445526,
-0.06804422289133072,
-0.023712974041700363,
0.012672617100179195,
0.0003411043144296855,
0.00886996928602457,
0.03993390500545502,
-0.0655067190527916,
0.036665141582489014,
0.022963477298617363,
0.023858243599534035,
-0.0010560735827311873,
0.07288084924221039,
-0.015957657247781754,
0.016505658626556396,
-0.03919102996587753,
0.01877201534807682,
-0.018065577372908592,
-0.021678831428289413,
0.018706031143665314,
0.05385243520140648,
0.04066234454512596,
0.006946953944861889,
0.02896873466670513,
-0.017723167315125465,
-0.023277536034584045,
-0.013125993311405182,
0.011030284687876701,
0.07778806984424591,
-0.011900963261723518,
-0.008947317488491535,
0.024541212245821953,
0.018271470442414284,
-0.02525087632238865,
-0.059979528188705444,
0.02226794883608818,
-0.031804122030735016,
-0.006056979764252901,
-0.04705627262592316,
0.04617473483085632,
0.0004183406999800354,
-0.030073633417487144,
0.023856637999415398,
-0.08171236515045166,
0.014573866501450539,
0.06686193495988846,
0.005631124600768089,
0.04596460983157158,
-0.05775459483265877,
-0.00794567633420229,
-0.02614673413336277,
-0.06933736801147461,
-0.0063987174071371555,
0.012662854976952076,
-0.012771728448569775,
-0.05568932741880417,
0.02667473629117012,
0.02845597080886364,
0.015162122435867786,
0.010621354915201664,
-0.032384730875492096,
-0.04251920431852341,
-0.04070734977722168,
-0.042709313333034515,
-0.010217824950814247,
-0.08711335808038712,
0.07856733351945877,
0.03081088326871395,
-0.06046512350440025,
-0.04677221179008484,
-0.015706421807408333,
0.01141776330769062,
-0.008023874834179878,
0.003874602960422635,
-0.015278935432434082,
-0.040507785975933075,
0.025175048038363457,
0.03817057982087135,
-0.009984314441680908,
0.0471331886947155,
-0.04129169508814812,
-0.0063540143892169,
0.040874600410461426,
0.048854805529117584,
-0.033383559435606,
0.012790657579898834,
0.044699978083372116,
-0.041545044630765915,
0.02707863040268421,
-0.02878965437412262,
-0.05268167704343796,
-0.0548018217086792,
-0.06916721165180206,
0.03784601017832756,
-0.01826978102326393,
-0.07463274896144867,
-0.003314586356282234,
0.04618750140070915,
-0.010348338633775711,
0.04576469212770462,
-0.037045806646347046,
-0.05334000289440155,
0.0020498509984463453,
0.03947500139474869,
-0.09198696166276932,
0.06077279895544052,
0.07490505278110504,
-0.031753119081258774,
0.09706804156303406,
0.005672122351825237,
0.027438193559646606,
-0.018074695020914078,
0.035575419664382935,
-0.030305691063404083,
0.04882209748029709,
-0.023549756035208702,
-0.03470316901803017,
-0.035122793167829514,
-0.01310206949710846,
0.0762651190161705,
0.012873167172074318,
0.04929319769144058,
-0.037338826805353165,
0.011853999458253384,
0.009495592676103115,
0.004446332808583975,
-0.002012111945077777,
0.002252087462693453,
0.012089035473763943,
0.011049898341298103,
-0.030243556946516037,
-0.08915604650974274,
-0.020553700625896454,
0.004138809163123369,
0.015184727497398853,
0.04508025571703911,
-0.0289156474173069,
0.017673976719379425,
-0.03063647449016571,
-0.0017081140540540218,
0.0021069361828267574,
0.023650700226426125,
0.004536019638180733,
-0.006161625497043133,
0.0014930329052731395,
-0.03614482656121254,
-0.03992109000682831,
0.058545175939798355,
0.032879140228033066,
0.020906411111354828,
-0.007961394265294075,
-0.017945054918527603,
-0.04439996927976608,
-0.020323719829320908,
0.01210203766822815,
0.050416022539138794,
-0.03338199481368065,
0.024714186787605286,
-0.00893942080438137,
-0.047758325934410095,
0.05378815531730652,
0.03096020594239235,
0.00547608220949769,
-0.034902431070804596,
0.04091738536953926,
0.05639827996492386,
0.01692158170044422,
0.0503828302025795,
-0.031379323452711105,
-0.06410018354654312,
-0.03610420972108841,
0.016297413036227226,
0.05749455466866493,
0.011639394797384739,
0.01987849548459053,
0.017520872876048088,
0.03697850555181503,
0.0521509125828743,
-0.013898387551307678,
0.011057237163186073,
0.029452072456479073,
-0.07110680639743805,
-0.01916544698178768,
0.010057471692562103,
-0.010464408434927464,
-0.056929830461740494,
-0.013516003265976906,
-0.0052562374621629715,
-0.019625777378678322,
0.05823875963687897,
-0.033320728689432144,
0.03588305786252022,
0.10176372528076172,
-0.03830037638545036,
0.0009908381616696715,
-0.0202683974057436,
0.020857760682702065,
0.00008610854274593294,
-0.009723072871565819,
-0.040810033679008484,
0.017478736117482185,
-0.06815155595541,
-0.04549098759889603,
0.031232213601469994,
0.031159231439232826,
-0.01931721903383732,
-0.03917897492647171,
-0.028413688763976097,
-0.04574836790561676,
-0.0005054828361608088,
0.020015956833958626,
0.04458945617079735,
0.012628293596208096,
-0.035986848175525665,
-0.007624385412782431,
-0.03920086473226547,
0.008730453439056873,
-0.003025504993274808,
-0.013323702849447727,
-0.0345204658806324,
-0.03646164759993553,
-0.058272067457437515,
-0.039485324174165726,
-0.04490596801042557,
0.008924259804189205,
0.04506964609026909,
0.06749217212200165,
0.05764983966946602,
0.03903142735362053,
0.01471460796892643,
-0.04227650538086891,
0.07671525329351425,
0.0027828975580632687,
0.010166187770664692,
-0.053673382848501205,
0.04865375533699989,
0.023451197892427444,
-0.046811461448669434,
0.03398624807596207,
-0.019744984805583954,
0.04024564102292061,
0.01817270740866661,
0.048849329352378845,
0.049059852957725525,
-0.001659795525483787,
0.004019950050860643,
-0.01726042479276657,
0.005639431066811085,
0.03581515699625015,
0.03512059152126312,
0.031237715855240822,
-0.06788576394319534,
0.037728678435087204,
-0.027461029589176178,
-0.03694281727075577,
0.09779098629951477,
-0.04128633812069893,
-0.054426159709692,
-0.005362840369343758,
-0.023975512012839317,
0.0062183537520468235,
0.023328540846705437,
-0.010677901096642017,
-0.034093547612428665,
-0.0107443667948246,
-0.0116619523614645,
-0.018302466720342636,
0.01581306755542755,
0.04680512100458145,
0.0368804931640625,
-0.011781716719269753,
0.008785570040345192,
0.029339082539081573,
-0.008084384724497795,
0.014757906086742878,
-0.027330415323376656,
-0.05171147733926773,
-0.021688437089323997,
-0.06274175643920898,
-0.05633675307035446,
-0.0014148519840091467,
-0.0167311392724514,
0.028049355372786522,
0.09276733547449112,
-0.018345102667808533,
-0.06502130627632141,
0.014869089238345623,
-0.008406051434576511,
0.06662255525588989,
-0.03166097775101662,
-0.00651754392310977,
0.02115173265337944,
-0.057743024080991745,
-0.015873191878199577,
0.02886783331632614,
0.002487079706043005,
-0.05790715292096138,
0.03266596049070358,
0.013177882879972458,
-0.03240428864955902,
0.06271641701459885,
0.026436515152454376,
0.05043498054146767,
-0.030110731720924377,
0.005238065496087074,
-0.0636790469288826,
0.005585395265370607,
-0.006540221627801657,
-0.043124809861183167,
-0.0021255798637866974,
-0.028821879997849464,
-0.029672497883439064,
-0.02811814472079277,
0.037501685321331024,
-0.020130986347794533,
0.008689026348292828,
0.00910878274589777,
0.02745503932237625,
-0.028666509315371513,
0.013244669884443283,
-0.0339936688542366,
0.0232158862054348,
-0.07673147320747375,
-0.024680044502019882,
0.007639595773071051,
-0.05607997626066208,
-0.032325442880392075,
-0.00699453242123127,
-0.021321678534150124,
0.035542912781238556,
-0.005879803095012903,
-0.026706505566835403,
0.09571628272533417,
0.0620405450463295,
-0.02257927879691124,
-0.011225415393710136,
-0.036441002041101456,
0.030630655586719513,
0.03732403367757797,
0.0022540048230439425,
0.01428753137588501,
-0.0028973801527172327,
-0.01593318022787571,
-0.06197081878781319,
-0.019164826720952988,
0.0002537420950829983,
0.013865411281585693,
0.021646996960043907,
0.01582217775285244,
-0.03286285325884819,
-0.004565659444779158,
-0.04646715521812439,
0.05907132849097252,
0.004304301925003529,
0.05002174153923988,
-0.014145863242447376,
0.010308274999260902,
0.018924249336123466,
-0.04988597705960274,
-0.014884092845022678,
0.006910931784659624,
0.007019117474555969,
-0.030986838042736053,
-0.02786651812493801,
0.021569019183516502,
0.01668090932071209,
-0.03548917546868324,
-0.03950265049934387,
0.05007736012339592,
-0.005232243798673153,
0.03390512987971306,
0.0422133170068264,
0.04330574721097946,
0.026582060381770134,
0.019445421174168587,
-0.013394495472311974,
0.028606420382857323,
0.056645575910806656,
0.02648610807955265,
0.031823452562093735,
0.039564620703458786,
-0.09056488424539566,
-0.003464785637333989,
-0.020150387659668922,
-0.022179465740919113,
-0.009845058433711529,
0.05219995230436325,
0.03384646028280258,
0.022573068737983704,
0.0018413260113447905,
-0.04519106075167656,
-0.0022044049110263586,
0.04037901386618614,
0.05373749881982803,
0.02929276041686535,
-0.008841299451887608,
0.021158523857593536,
0.07498784363269806,
-0.004588294308632612,
-0.0084806177765131,
-0.04130050167441368,
-0.0053878105245530605,
0.021437853574752808,
-0.023598700761795044,
-0.010854439809918404,
0.04308407008647919,
-0.010337213054299355,
0.014973794110119343,
0.04352937266230583,
0.048780351877212524,
-0.07014673948287964,
0.002703859470784664,
0.002025032415986061,
-0.03821235150098801,
-0.07544088363647461,
0.03534586355090141,
0.024581683799624443,
-0.007407959084957838,
0.06930951029062271,
0.007505679037421942,
-0.06516699492931366,
-0.030960753560066223,
0.031207984313368797,
-0.016205769032239914,
0.008948348462581635,
-0.018106114119291306,
0.030797505751252174,
-0.06098885461688042,
0.034116197377443314,
0.022662514820694923,
0.024884384125471115,
-0.011362572200596333,
0.02530471794307232,
0.009998248890042305,
-0.016481827944517136,
-0.011300885118544102,
0.019525282084941864,
0.02759678103029728,
0.017385469749569893,
0.009491329081356525,
-0.010244124568998814,
0.0018504662439227104,
-0.037163130939006805,
0.04569301754236221,
-0.029604241251945496,
0.07749693840742111,
-0.012021721340715885,
0.03161925449967384,
0.05201398581266403,
-0.018188457936048508,
0.07231708616018295,
0.04459015652537346,
-0.05614718049764633,
0.02254721336066723,
-0.021631602197885513,
0.009506477043032646,
0.04156705364584923,
0.003487045643851161,
-0.017319567501544952,
-0.006661724299192429,
-0.020112568512558937,
-0.003520515514537692,
-0.06813541054725647,
-0.028968973085284233,
-0.009305193088948727,
0.054607462137937546,
0.04155444726347923,
0.012984436936676502,
-0.02357206866145134,
-0.03225570172071457,
-0.02117743529379368,
-0.042819708585739136,
-0.0445859357714653,
-0.05684399604797363,
0.030807705596089363,
-0.003459337865933776,
-0.00999104231595993,
-0.0027297213673591614,
-0.017215272411704063,
-0.023316901177167892,
-0.004397975280880928,
-0.005322066135704517,
0.026156118139624596,
0.026962976902723312,
-0.004578657913953066,
-0.04736555367708206,
0.03170660138130188,
0.043748125433921814,
-0.051329806447029114,
0.005835096351802349,
-0.04812188446521759,
-0.05143698677420616,
-0.01600046269595623,
-0.017219847068190575,
-0.012947877869009972,
0.04768335819244385,
-0.07622113823890686,
0.015555066056549549,
0.0009273148025386035,
-0.07282479852437973,
-0.023410610854625702,
0.02915775775909424,
0.021742241457104683,
0.028583765029907227,
0.006852622143924236,
-0.0019968654960393906,
-0.029602574184536934,
0.040853966027498245,
-0.048975612968206406,
-0.0028563733212649822,
-0.005935461260378361,
0.026505768299102783,
0.011179509572684765,
0.03842359036207199,
0.018157031387090683,
-0.043151505291461945,
-0.010780688375234604,
-0.027423642575740814,
0.001729526906274259,
-0.03309701010584831,
-0.005887462757527828,
0.02134973183274269,
-0.050021082162857056,
0.03617656230926514,
-0.026225430890917778,
0.028009427711367607,
-0.007612212561070919,
0.05857697129249573,
0.010926461778581142,
0.032320719212293625,
0.0429832823574543,
0.014017116278409958,
0.019338270649313927,
-0.005728399381041527,
0.022184252738952637,
-0.00913641694933176,
-0.0006246480625122786,
0.01374967209994793,
0.028394334018230438,
-0.003856436815112829,
0.07700656354427338,
0.000826613511890173,
0.01522440928965807,
-0.0025637922808527946,
-0.021834231913089752,
-0.06622503697872162,
0.006233082618564367,
0.04793794825673103,
-0.030134746804833412,
0.07727042585611343,
0.01307464949786663,
-0.013305066153407097,
-0.03934581205248833,
-0.03350277617573738,
0.05343009531497955,
-0.03158621862530708,
-0.05192642658948898,
0.06314633041620255,
0.06047605350613594,
-0.011513009667396545,
-0.013205161318182945,
-0.0005199742736294866,
-0.0526396706700325,
0.024230748414993286,
0.02648659236729145,
-0.022646266967058182,
-0.010515226982533932,
0.025002699345350266,
0.03298734128475189,
-0.06722761690616608,
0.00010098530765390024,
0.027087770402431488,
-0.015316333621740341,
0.04800301045179367,
-0.00868374202400446,
0.029000457376241684,
-0.014999670907855034,
-0.022560108453035355
] |
<p>In the book "A Briefer History of Time" Stephen Hawking wrote:</p>
<blockquote>
<p>The unpredictable, random element comes in only when we try to
interpret the wave in terms of the positions and velocities of
particles. But maybe that is our mistake: maybe there are no particle
positions and velocities, but only waves. It is just that we try to
fit the waves to our preconceived ideas of positions and velocities.
The resulting mismatch is the cause of the apparent unpredictability.</p>
</blockquote>
<p>Are there evidences that disprove this hypothesis? </p>
<p>If true, would it eliminate most of the apparent quantum paradoxes, and necessity to <a href="http://en.wikipedia.org/wiki/Copenhagen_interpretation#Alternatives" rel="nofollow">"Shut up and calculate!"</a> for those who attempt to interpret quantum physics with common sense?</p>
<p><strong>Edit:</strong> I assume that S. Hawking is aware of Standard Model, and he considers this statement as a legitimate hypothesis. Are there evidences that prove that it's not? In other words, is it a philosophical or scientific question?</p> | g4576 | [
0.05094272270798683,
0.08202347159385681,
0.01571027748286724,
0.006145219784229994,
0.016917170956730843,
0.0005793764139525592,
0.0370769277215004,
0.027881721034646034,
0.022504158318042755,
-0.016552617773413658,
0.005472181830555201,
-0.026025133207440376,
0.014770491048693657,
0.04884800687432289,
-0.015458553098142147,
0.009015854448080063,
0.07051951438188553,
-0.04526679590344429,
0.005623084492981434,
0.02396266534924507,
0.015932224690914154,
-0.020085753872990608,
0.0032341359183192253,
-0.0224594883620739,
-0.08808756619691849,
-0.02705146186053753,
-0.022753044962882996,
-0.11078550666570663,
0.011169185861945152,
-0.016226237639784813,
0.06320976465940475,
0.00725568737834692,
0.04418120160698891,
-0.07438499480485916,
-0.07364456355571747,
-0.0007226380985230207,
0.04034828767180443,
-0.03985839709639549,
-0.02076810784637928,
0.015927737578749657,
0.008594444021582603,
-0.010658569633960724,
-0.010344854556024075,
-0.00412321649491787,
-0.0072111631743609905,
0.006944502238184214,
0.005981074646115303,
0.050003863871097565,
0.005065281875431538,
-0.031593553721904755,
-0.04282093420624733,
0.030619505792856216,
0.1279280036687851,
0.05650937184691429,
0.05088449642062187,
0.1009332537651062,
0.06268477439880371,
0.009745199233293533,
0.0342121385037899,
0.03612899407744408,
0.020000381395220757,
0.019296105951070786,
0.007466078735888004,
-0.005063932854682207,
0.05573965236544609,
0.03620981052517891,
-0.04691613093018532,
-0.026760779321193695,
0.026732804253697395,
-0.020723914727568626,
0.041747722774744034,
-0.08471474051475525,
-0.014681062661111355,
0.019215716049075127,
-0.025466935709118843,
0.05472133308649063,
0.013269535265862942,
0.02250710502266884,
0.01976679638028145,
0.001397816464304924,
-0.04044455289840698,
-0.03985297307372093,
-0.0008832914172671735,
-0.010976419784128666,
0.08277405053377151,
-0.011791148222982883,
0.019796069711446762,
0.005235386546701193,
0.017429538071155548,
0.0006826820899732411,
0.0008263320196419954,
-0.0318308025598526,
0.03999181091785431,
-0.007424091454595327,
-0.017078742384910583,
-0.004788021557033062,
-0.05166831240057945,
0.04316683113574982,
-0.07757452875375748,
0.04681534692645073,
-0.0911913588643074,
0.07111244648694992,
-0.04647213965654373,
-0.01744036003947258,
-0.05295637995004654,
-0.03651122376322746,
-0.03134928643703461,
-0.008927388116717339,
0.0004242153081577271,
-0.045459482818841934,
-0.03692203015089035,
-0.013340501114726067,
0.004351758863776922,
0.011244679801166058,
-0.026829881593585014,
-0.03452277183532715,
0.07563784718513489,
0.01802775263786316,
-0.014325995929539204,
0.03982623293995857,
-0.03885061666369438,
0.033715032041072845,
-0.028769513592123985,
0.06918683648109436,
-0.02333715185523033,
-0.006814715452492237,
0.00768303032964468,
-0.03078518621623516,
0.009596106596291065,
0.006252748426049948,
0.011958440765738487,
0.03530428186058998,
-0.013414404354989529,
0.070366770029068,
0.020573357120156288,
0.022480694577097893,
0.051599010825157166,
0.007470557000488043,
0.016931524500250816,
0.04438834264874458,
0.04488189518451691,
0.012655811384320259,
0.011339406482875347,
-0.050384197384119034,
0.012468794360756874,
-0.013105932623147964,
-0.03707485273480415,
-0.0024507290218025446,
-0.03244737163186073,
0.0035491299349814653,
-0.0372530072927475,
0.05416958034038544,
-0.043329764157533646,
0.018006380647420883,
-0.054512668401002884,
0.020679080858826637,
0.03107624314725399,
0.044471029192209244,
-0.008205348625779152,
0.005830071400851011,
0.07605394721031189,
-0.029872136190533638,
0.01098468154668808,
0.007439393550157547,
-0.0402500182390213,
0.003791855415329337,
0.025678876787424088,
-0.002356438199058175,
-0.027150088921189308,
-0.038303572684526443,
-0.048081930726766586,
0.025694886222481728,
0.0025490294210612774,
0.03976203873753548,
-0.01172207947820425,
0.030563607811927795,
-0.0002303500659763813,
-0.02843429520726204,
-0.05170072615146637,
-0.0054780906066298485,
0.01172473095357418,
0.031845033168792725,
0.0022600817028433084,
-0.045047175139188766,
-0.005703137256205082,
0.01138385757803917,
-0.011310146190226078,
0.027061857283115387,
-0.020038152113556862,
-0.02142985351383686,
0.015903258696198463,
-0.06289394199848175,
0.015072386711835861,
0.049087025225162506,
0.0319623164832592,
-0.03562018647789955,
-0.011926611885428429,
0.018089445307850838,
-0.04327283054590225,
0.011778897605836391,
-0.002398743527010083,
0.0324334092438221,
0.007054803892970085,
-0.02495390921831131,
0.008893818594515324,
0.0226910300552845,
0.019152943044900894,
0.010659793391823769,
0.03822087496519089,
-0.04822402074933052,
0.0861639529466629,
0.0004010807315353304,
-0.038232870399951935,
0.02837592177093029,
-0.01110854372382164,
-0.003478233702480793,
0.023949962109327316,
0.010013878345489502,
0.003236353863030672,
-0.016589432954788208,
-0.016533568501472473,
-0.004240226000547409,
-0.025884078815579414,
0.010526089929044247,
0.012895877473056316,
0.025281036272644997,
-0.0764470100402832,
-0.10014849156141281,
-0.04833335429430008,
0.047711633145809174,
-0.03704078495502472,
-0.04411027207970619,
-0.021639199927449226,
0.014686799608170986,
0.10027875006198883,
0.028658073395490646,
0.05339203029870987,
-0.023231273517012596,
0.0662301555275917,
0.019494010135531425,
0.031113993376493454,
-0.021452507004141808,
-0.09614229202270508,
-0.03391876816749573,
0.021211769431829453,
-0.04372140020132065,
0.015298060141503811,
-0.09056058526039124,
0.018099986016750336,
0.007308101747184992,
0.002029824536293745,
-0.04292039945721626,
-0.04121892899274826,
-0.02328968234360218,
0.036450907588005066,
0.01779317297041416,
-0.008950728923082352,
0.03744114562869072,
-0.06713365018367767,
-0.01888960786163807,
-0.028033602982759476,
0.044171057641506195,
0.014621034264564514,
0.03278021141886711,
-0.020430486649274826,
-0.005717149004340172,
-0.011984240263700485,
0.00620812363922596,
-0.0561390221118927,
-0.039566703140735626,
0.04488076642155647,
-0.015140539035201073,
0.07789144665002823,
0.04301128163933754,
-0.04791833087801933,
0.005665617063641548,
-0.04550039395689964,
-0.04991801828145981,
-0.02252606675028801,
0.009173054248094559,
-0.07039900869131088,
0.018151212483644485,
-0.0048270998522639275,
0.04015025496482849,
0.03282993286848068,
-0.05988290160894394,
-0.011606949381530285,
0.003615015186369419,
0.01595950685441494,
0.011298004537820816,
-0.025054272264242172,
0.04364670440554619,
0.015495016239583492,
0.08790779113769531,
-0.059027280658483505,
0.045182909816503525,
-0.000754323264118284,
-0.00693292822688818,
-0.011804082430899143,
0.02344902604818344,
-0.003498674603179097,
-0.0143405357375741,
-0.03575785458087921,
0.027231208980083466,
0.023310402408242226,
0.05437162518501282,
0.007046682294458151,
0.0000564423571631778,
0.013917459174990654,
-0.04573254659771919,
0.006982005666941404,
0.0959501564502716,
-0.05017244815826416,
0.03725250065326691,
-0.050150103867053986,
0.016053587198257446,
-0.012049210257828236,
0.018905803561210632,
0.04684491828083992,
-0.038762398064136505,
-0.03064367175102234,
-0.03762366622686386,
-0.047824613749980927,
-0.034395478665828705,
0.053525857627391815,
0.03314589709043503,
-0.017516741529107094,
0.0014794652815908194,
-0.0716039389371872,
-0.022582747042179108,
0.027258707210421562,
-0.04501625895500183,
0.017886267974972725,
0.01376175694167614,
-0.08006717264652252,
-0.1280275583267212,
0.05487683415412903,
0.07210857421159744,
0.042131535708904266,
-0.015895063057541847,
0.022689582780003548,
-0.00499412277713418,
-0.04502453655004501,
0.04946049302816391,
-0.004088273271918297,
0.008387614041566849,
0.02199915051460266,
-0.024242157116532326,
0.030958956107497215,
-0.021411240100860596,
0.008595943450927734,
0.012564385309815407,
0.032931260764598846,
0.04263286665081978,
-0.02751200646162033,
0.07607908546924591,
0.04932108521461487,
0.019595669582486153,
0.041728533804416656,
0.015055607073009014,
-0.01735776662826538,
-0.030639423057436943,
0.02179911360144615,
0.0009925458580255508,
-0.008954020217061043,
0.02231191284954548,
-0.06441625207662582,
0.07078222185373306,
0.025883173570036888,
-0.014787966385483742,
-0.007569081149995327,
-0.003939469810575247,
0.009074053727090359,
0.0044067432172596455,
0.053476445376873016,
0.00882024597376585,
0.05689655616879463,
0.05250643193721771,
-0.00929179321974516,
-0.022140825167298317,
0.02386944554746151,
0.04030710086226463,
0.017290083691477776,
-0.0017058185767382383,
0.02527496963739395,
-0.058546099811792374,
-0.04063236713409424,
-0.020764676854014397,
-0.030909905210137367,
-0.023509066551923752,
-0.014032998122274876,
0.013331236317753792,
-0.01810530759394169,
0.029451444745063782,
0.011234931647777557,
0.058902282267808914,
0.004304368514567614,
-0.013630091212689877,
0.019330905750393867,
0.058867473155260086,
0.019752822816371918,
-0.06384348124265671,
-0.07638466358184814,
0.03879678621888161,
-0.008370568975806236,
0.033838123083114624,
0.049235615879297256,
-0.002697997959330678,
0.0017755043227225542,
-0.027407396584749222,
0.0007291670190170407,
-0.0035242284648120403,
0.015144532546401024,
-0.03923298418521881,
-0.02593291737139225,
0.0307709239423275,
-0.018098685890436172,
-0.046638939529657364,
0.04225824773311615,
0.015957649797201157,
-0.005739311687648296,
0.06474654376506805,
0.024415571242570877,
-0.009851664304733276,
0.0026636337861418724,
0.022274186834692955,
0.037080906331539154,
-0.007335972040891647,
-0.031676411628723145,
-0.01587827131152153,
0.06652052700519562,
-0.0010004955111071467,
-0.020003272220492363,
0.03877605125308037,
-0.02023267187178135,
-0.013081335462629795,
0.021255919709801674,
0.026379602029919624,
-0.020615460351109505,
0.010391024872660637,
-0.02089524455368519,
0.00039211157127283514,
0.03300420939922333,
0.027830306440591812,
-0.020668121054768562,
0.04057956486940384,
-0.05397391691803932,
-0.008681191131472588,
-0.006093353498727083,
-0.00393466604873538,
-0.03826231509447098,
0.022558556869626045,
0.0002602870517875999,
-0.0069245845079422,
0.010408803820610046,
-0.03192059323191643,
-0.05361371859908104,
0.07582112401723862,
-0.03788166493177414,
0.006495255045592785,
-0.03268382325768471,
0.030895104631781578,
0.012429721653461456,
0.07606296986341476,
0.008028017356991768,
0.02563507668673992,
-0.0487246960401535,
-0.03964318335056305,
-0.030400851741433144,
-0.048054810613393784,
0.006453303154557943,
0.02288145013153553,
0.03809201344847679,
0.04603450745344162,
-0.022769633680582047,
-0.04621947556734085,
0.02382485382258892,
0.009625205770134926,
-0.03230341896414757,
0.011766483075916767,
0.01026124320924282,
0.007717628497630358,
0.03943830728530884,
-0.0000748933816794306,
-0.012800194323062897,
-0.00482579693198204,
-0.011210082098841667,
0.008999376557767391,
-0.008281868882477283,
-0.012054666876792908,
0.05070328339934349,
-0.03587469831109047,
0.006020112428814173,
-0.048922326415777206,
-0.014794284477829933,
-0.028078796342015266,
0.036240242421627045,
0.03382062166929245,
-0.03624601662158966,
0.03529905527830124,
-0.05248891934752464,
0.042522769421339035,
0.012037470936775208,
-0.014737778343260288,
-0.012653421610593796,
0.028253240510821342,
0.016264989972114563,
0.034574225544929504,
-0.04582186043262482,
0.019523346796631813,
0.013857045210897923,
0.004894735291600227,
-0.044153839349746704,
0.018685726448893547,
0.020967312157154083,
-0.011410042643547058,
-0.04372747614979744,
-0.03456391394138336,
0.0043619051575660706,
-0.036448780447244644,
0.020611729472875595,
0.022634029388427734,
-0.015054920688271523,
-0.03430144488811493,
0.0013824691995978355,
-0.033886272460222244,
-0.0527687631547451,
-0.021230706945061684,
-0.011885768733918667,
0.06224968284368515,
0.04597575217485428,
0.028404774144291878,
0.04623972624540329,
-0.0019275583326816559,
0.012155786156654358,
0.04269488528370857,
-0.012328214012086391,
0.023471292108297348,
0.005815296433866024,
-0.004628912545740604,
-0.07271331548690796,
0.005674917716532946,
0.05485693737864494,
0.023955659940838814,
0.013965442776679993,
0.01733696274459362,
-0.047761932015419006,
0.027938030660152435,
0.01899677701294422,
-0.1428828090429306,
-0.011873594485223293,
0.007222782354801893,
-0.04834529012441635,
-0.014837809838354588,
0.0038220807909965515,
-0.004907533992081881,
-0.017031509429216385,
-0.04524639993906021,
-0.013211963698267937,
0.017908429726958275,
0.0384347066283226,
0.022974258288741112,
-0.0022528041154146194,
0.020450370386242867,
0.00702668959274888,
0.0216184314340353,
-0.04079747572541237,
0.002895825309678912,
-0.0008124132873490453,
0.035933468490839005,
-0.05066012218594551,
0.07364846765995026,
0.013547132723033428,
0.02613234519958496,
0.0145206144079566,
-0.02833932638168335,
0.005442032590508461,
-0.016636094078421593,
-0.05502081662416458,
-0.016559114679694176,
-0.037077635526657104,
-0.008412864990532398,
0.03687942400574684,
-0.021845854818820953,
-0.04106419160962105,
0.003422902198508382,
-0.062133532017469406,
0.03877631947398186,
-0.008922946639358997,
0.04562493413686752,
0.006045799236744642,
0.034257788211107254,
-0.051351290196180344,
-0.061157796531915665,
-0.03442616015672684,
-0.06518354266881943,
0.033723752945661545,
-0.02357504330575466,
-0.07117194682359695,
0.0025152096059173346,
-0.040774282068014145,
-0.0615934319794178,
0.030618971213698387,
-0.017378509044647217,
0.003254731185734272,
0.029138563200831413,
-0.013044421561062336,
-0.009074155241250992,
0.012608364224433899,
0.011269204318523407,
-0.01337275467813015,
0.02161441557109356,
0.05056791380047798,
0.02301196940243244,
-0.03272028639912605,
-0.023553971201181412,
-0.034553587436676025,
-0.009961034171283245,
-0.06879882514476776,
-0.011860553175210953,
0.1292215883731842,
0.008411120623350143,
-0.040867459028959274,
-0.008007541298866272,
0.014264518395066261,
0.0003602842625696212,
-0.01758197508752346,
-0.03392200917005539,
0.06549492478370667,
0.013150899671018124,
0.0069247824139893055,
-0.022114034742116928,
0.046930890530347824,
0.0106576606631279,
-0.01073397509753704,
0.0424281470477581,
-0.04798635467886925,
0.030964480713009834,
-0.008350623771548271,
0.02129591628909111,
-0.0021852338686585426,
0.004823777824640274,
0.03985544666647911,
-0.04246032238006592,
-0.057808324694633484,
-0.00892330426722765,
0.0634506419301033,
0.034770041704177856,
-0.07277340441942215,
-0.013700434006750584,
0.00037221459206193686,
0.016782982274889946,
-0.019177217036485672,
-0.0529489703476429,
0.035978950560092926,
0.0041897716000676155,
0.011317587457597256,
0.020805146545171738,
0.062246471643447876,
-0.03743232786655426,
-0.026396548375487328,
-0.027778996154665947,
-0.005345978774130344,
-0.027508355677127838,
-0.04266643524169922,
0.022385885939002037,
-0.02878766506910324,
-0.027708854526281357,
-0.04551498964428902,
-0.03201984614133835,
0.005753460340201855,
-0.053113777190446854,
-0.04093243554234505,
-0.011329774744808674,
0.008171542547643185,
-0.04221230745315552,
-0.02377922087907791,
0.03464336693286896,
0.008600791916251183,
0.0036200780887156725,
0.05766436085104942,
0.05951835587620735,
0.0038304224144667387,
0.05930449068546295,
-0.019795209169387817,
0.03366638347506523,
0.013977241702377796,
-0.03718546777963638,
-0.044495705515146255,
-0.012805504724383354,
0.012417457066476345,
0.0022659199312329292,
0.01963329128921032,
-0.04928826540708542,
0.020854633301496506,
0.01679088920354843,
0.04979350417852402,
0.055488601326942444,
-0.027475761249661446,
0.03557002916932106,
-0.06524024158716202,
-0.014599110931158066,
-0.03677050396800041,
0.020685728639364243,
-0.041680894792079926,
0.027492474764585495,
0.004262163303792477,
0.011274978518486023,
-0.09398900717496872,
0.007409963756799698,
0.027169298380613327,
-0.00965340156108141,
-0.015259644016623497,
-0.010655265301465988,
0.0197649747133255,
-0.03673626855015755,
0.026569517329335213,
-0.007818099111318588,
0.048341866582632065,
-0.01596427522599697,
-0.015423671342432499,
-0.0391494520008564,
-0.01821487955749035,
0.015519806183874607,
0.007474473677575588,
-0.020161956548690796,
-0.038145214319229126,
-0.01658346690237522,
0.013374687172472477,
0.025260739028453827,
0.014597873203456402,
-0.05296700820326805,
-0.022113163024187088,
0.028373172506690025,
-0.014819293282926083,
0.04846770316362381,
0.008100341074168682,
0.05056598782539368,
-0.03516005724668503,
0.025956157594919205,
-0.01916668564081192,
0.021048249676823616,
-0.014473793096840382,
-0.013917749747633934,
-0.054396484047174454,
-0.06230654940009117,
-0.025462718680500984,
0.019288256764411926,
-0.03550393879413605,
-0.04455222561955452,
0.008821721188724041,
0.06352271139621735,
-0.05049477890133858,
0.015169761143624783,
0.03821305185556412,
-0.05222058668732643,
-0.0016715612728148699,
0.003017251379787922,
0.002768375677987933,
-0.01654023677110672,
0.029039941728115082,
-0.04011664539575577,
0.05112720653414726,
-0.007816904224455357,
-0.02300332486629486,
-0.035502925515174866,
-0.009855075739324093,
0.002053872449323535
] |
<p>What happens if I charged a capacitor then i touch the 2 poles in same time?</p> | g4577 | [
0.060975581407547,
-0.003857143921777606,
0.00011370480206096545,
-0.010110571049153805,
0.07586394995450974,
0.033107414841651917,
0.03352304548025131,
-0.01124273519963026,
-0.018898295238614082,
-0.03814918175339699,
-0.10840335488319397,
0.012700917199254036,
-0.026050152257084846,
0.007507801055908203,
0.02113529108464718,
-0.02057625912129879,
0.07264412194490433,
0.004081368912011385,
-0.010234345681965351,
0.03569476678967476,
-0.027555225417017937,
-0.017584456130862236,
-0.037195730954408646,
-0.06304958462715149,
-0.052012547850608826,
-0.028024276718497276,
-0.04287533089518547,
-0.022551119327545166,
-0.057729896157979965,
-0.06258267164230347,
-0.009510918520390987,
0.07030224055051804,
-0.0068181478418409824,
0.007144771981984377,
-0.06500682979822159,
-0.049510907381772995,
0.05847642570734024,
-0.03422616794705391,
-0.038398757576942444,
-0.01686830446124077,
0.04028230905532837,
0.02275945246219635,
0.09022720903158188,
-0.02720841020345688,
0.023305743932724,
-0.061053432524204254,
-0.014025028795003891,
0.0012175962328910828,
-0.012107211165130138,
0.0006678072968497872,
-0.0386461541056633,
-0.01469262596219778,
0.02041199989616871,
0.00835558120161295,
0.055142637342214584,
0.02546289749443531,
0.018121622502803802,
-0.0662267729640007,
0.04687253758311272,
0.061620716005563736,
-0.0022139137145131826,
0.029790116474032402,
-0.00020363242947496474,
0.003917524591088295,
-0.01888764649629593,
-0.013101913034915924,
0.019126903265714645,
-0.005055589135736227,
0.02764534018933773,
0.02125389128923416,
-0.011231894604861736,
-0.03063063696026802,
0.041276704519987106,
-0.058213971555233,
0.010167619213461876,
0.06045357137918472,
0.09491068869829178,
0.001727417460642755,
-0.024728834629058838,
0.011116772890090942,
-0.041383467614650726,
-0.00733707332983613,
0.023325115442276,
-0.018515339121222496,
-0.04764942824840546,
-0.02181718870997429,
0.0001470283605158329,
-0.00033502394217066467,
-0.05479668080806732,
-0.048430703580379486,
-0.033851467072963715,
-0.08787412196397781,
0.005249090492725372,
0.029064271599054337,
0.01553528942167759,
-0.03688598424196243,
0.03238190338015556,
0.01943439617753029,
0.022167155519127846,
-0.0030110867228358984,
-0.031111637130379677,
0.033238768577575684,
0.004246954340487719,
0.008582506328821182,
0.0051888395100831985,
-0.012188930064439774,
0.07832149416208267,
-0.005540395155549049,
-0.01492825336754322,
-0.0296167004853487,
-0.00011852895841002464,
-0.04255273938179016,
-0.012854685075581074,
0.05220901966094971,
-0.019829917699098587,
-0.028250044211745262,
0.03125498816370964,
-0.05545271560549736,
0.018793033435940742,
0.050869815051555634,
0.04036393761634827,
-0.0419929139316082,
-0.0008739380864426494,
0.022382505238056183,
0.02678205445408821,
-0.02643723413348198,
0.07756856828927994,
0.0008919439278542995,
-0.006798914168030024,
-0.015969054773449898,
0.011658539064228535,
-0.03774474933743477,
-0.01571444235742092,
0.02376454509794712,
0.013389898464083672,
-0.04164525866508484,
0.06375382095575333,
-0.049389928579330444,
0.007965209893882275,
-0.03930290788412094,
0.006428481079638004,
-0.03533145412802696,
-0.00007745296170469373,
-0.003990671597421169,
0.02637978456914425,
-0.024045025929808617,
0.0023186826147139072,
-0.061185017228126526,
0.02147800475358963,
-0.019777100533246994,
0.007812540978193283,
-0.012465900741517544,
0.0054549588821828365,
-0.044630762189626694,
0.02078345976769924,
0.02690812572836876,
0.04956094175577164,
0.015378028154373169,
0.04803059250116348,
0.026354124769568443,
0.01681980863213539,
-0.01829018071293831,
0.031013429164886475,
0.024480437859892845,
-0.05297531187534332,
0.05147389695048332,
0.012430604547262192,
-0.011822620406746864,
0.016122888773679733,
-0.04404468089342117,
-0.01112802792340517,
-0.03498693183064461,
0.022926677018404007,
0.0256784800440073,
0.04166577756404877,
-0.008700222708284855,
-0.0689752995967865,
0.013671210035681725,
0.05603336542844772,
-0.021687384694814682,
-0.033657532185316086,
0.026461921632289886,
-0.048564691096544266,
-0.011786111630499363,
-0.022163189947605133,
-0.0233590267598629,
-0.06107545644044876,
0.07612693309783936,
-0.012218896299600601,
0.02704373002052307,
-0.07091957330703735,
-0.046331100165843964,
-0.026070378720760345,
0.027247348800301552,
-0.010941211134195328,
-0.03021901845932007,
0.05978895351290703,
0.0050432407297194,
0.006959149613976479,
-0.06751636415719986,
0.018167026340961456,
-0.012095896527171135,
0.08322785049676895,
0.005826227832585573,
0.019467102363705635,
0.03228311240673065,
0.01844744384288788,
-0.01966293528676033,
0.064729705452919,
-0.02001117914915085,
0.03611484542489052,
0.049759168177843094,
0.001066642813384533,
0.046932369470596313,
-0.07296457141637802,
-0.06011662259697914,
-0.023775633424520493,
0.03428494557738304,
-0.05526789277791977,
0.02498697116971016,
-0.019638631492853165,
0.023873591795563698,
0.07088553160429001,
-0.04396397992968559,
-0.01644132286310196,
0.0075545054860413074,
-0.027997879311442375,
-0.008517437614500523,
-0.024298863485455513,
0.0009263530955649912,
-0.012464162893593311,
-0.03727914020419121,
0.011542607098817825,
-0.0012809195322915912,
-0.05140410736203194,
0.061796583235263824,
0.02046050690114498,
-0.024944882839918137,
0.011144105345010757,
-0.03630297631025314,
-0.019002148881554604,
-0.062099020928144455,
0.05837811529636383,
0.02629345841705799,
-0.02370956540107727,
0.02877272479236126,
0.024239763617515564,
0.0020781648345291615,
-0.010347048752009869,
0.023144882172346115,
0.06251679360866547,
0.031860943883657455,
0.004066061694175005,
0.06695417314767838,
-0.06632652878761292,
-0.029664667323231697,
0.014720053412020206,
0.011629177257418633,
-0.03959920257329941,
-0.046445511281490326,
0.003793082432821393,
-0.03590286150574684,
-0.017252381891012192,
0.026265660300850868,
-0.0604003369808197,
-0.03263917192816734,
-0.06168784573674202,
0.008534307591617107,
0.03689631074666977,
-0.04056740552186966,
-0.01406667847186327,
0.06783398985862732,
-0.0032334523275494576,
0.014506223611533642,
-0.007713109254837036,
-0.031498074531555176,
-0.0039988551288843155,
-0.09292895346879959,
-0.0003002618614118546,
-0.04993307590484619,
-0.047936443239450455,
-0.0036581121385097504,
0.00023419223725795746,
-0.021244054660201073,
0.047388706356287,
-0.0249500535428524,
-0.040070854127407074,
-0.020367110148072243,
-0.0296681746840477,
0.003282691817730665,
-0.049667391926050186,
0.007061933167278767,
0.1086413562297821,
-0.06965389847755432,
0.03513267636299133,
0.023232202976942062,
0.023181727156043053,
0.0028941540513187647,
0.0050487578846514225,
0.02598968893289566,
0.04720547795295715,
-0.01785343326628208,
-0.04598822444677353,
-0.0213329941034317,
0.042143821716308594,
0.03909904882311821,
0.0017967944731935859,
-0.024007337167859077,
0.054328225553035736,
0.017977798357605934,
-0.025074182078242302,
0.03352045267820358,
0.0186061542481184,
-0.004410767462104559,
-0.017275825142860413,
-0.0020246633794158697,
-0.009255829267203808,
-0.013826897367835045,
0.010075796395540237,
-0.032126449048519135,
-0.006282667629420757,
-0.03734549134969711,
0.0019326444016769528,
0.05090673267841339,
-0.03844780474901199,
-0.021909428760409355,
0.009163748472929,
0.03126323223114014,
0.021206874400377274,
0.08235704898834229,
-0.02067641355097294,
0.07210696488618851,
-0.019033581018447876,
-0.04133656620979309,
0.023128479719161987,
-0.001208398025482893,
-0.014756973832845688,
0.05454239994287491,
0.0184920746833086,
0.04116133973002434,
-0.034600526094436646,
-0.02677805908024311,
-0.03724197670817375,
-0.10283822566270828,
-0.009159181267023087,
0.025149548426270485,
0.05092284455895424,
-0.02163630537688732,
0.05922163277864456,
0.013310788199305534,
0.04815637692809105,
0.005608852487057447,
-0.003680621040984988,
0.023504741489887238,
0.02121894434094429,
0.00046243020915426314,
-0.021077638491988182,
0.06801655143499374,
-0.028445767238736153,
0.019562752917408943,
0.052034784108400345,
-0.015513438731431961,
0.04000923037528992,
-0.008858580142259598,
0.0330515131354332,
-0.00293061719276011,
-0.03670882061123848,
0.04766428843140602,
-0.0031962248031049967,
-0.012641673907637596,
-0.007307569961994886,
0.017395375296473503,
-0.019189119338989258,
0.030578838661313057,
0.03327930346131325,
0.003082255134359002,
0.007927121594548225,
-0.025714974850416183,
-0.019922567531466484,
0.051643647253513336,
0.009760760702192783,
-0.027957934886217117,
-0.0024229553528130054,
0.016182629391551018,
0.025082701817154884,
0.022591378539800644,
0.024579141288995743,
-0.004425174091011286,
-0.014741993509232998,
-0.028374919667840004,
-0.017101602628827095,
-0.005896759685128927,
-0.0039048506878316402,
-0.0170858446508646,
0.044648971408605576,
-0.04129621386528015,
-0.019435355439782143,
-0.03469189256429672,
0.03142131492495537,
-0.03413742408156395,
-0.06264475733041763,
-0.004897116217762232,
-0.033310990780591965,
-0.03307536989450455,
-0.015970412641763687,
-0.020830657333135605,
0.028348593041300774,
0.0029891703743487597,
0.054762937128543854,
0.01760532706975937,
-0.006330436561256647,
-0.02043536864221096,
0.015352754853665829,
-0.012936949729919434,
-0.013986226171255112,
-0.02214953862130642,
0.09356828778982162,
0.03613322600722313,
0.009088278748095036,
0.01921970397233963,
0.01340110320597887,
0.024858642369508743,
-0.01660815067589283,
-0.017977505922317505,
-0.01445811428129673,
-0.04242926463484764,
0.04032038152217865,
-0.02569115161895752,
-0.023301392793655396,
-0.02202189527451992,
-0.011723145842552185,
-0.02153157815337181,
0.0016263051657006145,
-0.014575065113604069,
-0.015788251534104347,
0.08748375624418259,
-0.010469313710927963,
0.05390966311097145,
-0.005512252915650606,
0.09011327475309372,
0.05658403038978577,
0.011891381815075874,
-0.04436285048723221,
0.002635488286614418,
0.04010319709777832,
0.055320851504802704,
-0.0038788754027336836,
-0.03674538806080818,
0.016168782487511635,
-0.06240842491388321,
-0.09630096703767776,
-0.003230080474168062,
-0.04614395275712013,
-0.031456708908081055,
0.008359670639038086,
-0.0002082607097690925,
0.05080590769648552,
-0.0019643830601125956,
-0.050819650292396545,
-0.03524656221270561,
-0.029118573293089867,
0.0057736532762646675,
0.03764680027961731,
-0.07042219489812851,
0.005610435735434294,
-0.06559932231903076,
-0.03683434799313545,
-0.06085900589823723,
-0.07307672500610352,
-0.030643466860055923,
0.02956182323396206,
0.008325162343680859,
0.0010223763529211283,
0.01741008460521698,
0.026059960946440697,
-0.0164338331669569,
0.06414172053337097,
0.07359719276428223,
-0.02660501003265381,
-0.007122949697077274,
0.007975411601364613,
0.027814704924821854,
-0.0207307618111372,
-0.02889830991625786,
-0.02785004861652851,
-0.050938379019498825,
-0.01668502204120159,
0.008542210794985294,
0.04379232972860336,
0.013337818905711174,
0.014978253282606602,
0.015001323074102402,
0.014349058270454407,
0.05593787878751755,
-0.009196413680911064,
0.06221775710582733,
-0.06195424869656563,
-0.0023527119774371386,
-0.032558243721723557,
0.012447196990251541,
0.03497758135199547,
-0.037741485983133316,
-0.013296931982040405,
0.03017980232834816,
0.01475009135901928,
0.07001348584890366,
0.01423653680831194,
-0.035657960921525955,
0.057673607021570206,
0.04033783823251724,
-0.031714532524347305,
0.018442096188664436,
0.06256022304296494,
0.09699118882417679,
0.04265090450644493,
0.04349777474999428,
-0.02571048215031624,
-0.04210823401808739,
-0.03719369322061539,
-0.035837966948747635,
0.06752713024616241,
-0.0015578399179503322,
-0.021941088140010834,
0.023047544062137604,
-0.048709239810705185,
-0.012919067405164242,
-0.024732647463679314,
0.018496477976441383,
0.04081929475069046,
0.08351712673902512,
0.006242254748940468,
0.017983142286539078,
-0.002773288171738386,
-0.01828010566532612,
0.046546194702386856,
-0.03396524116396904,
-0.024295782670378685,
-0.026232775300741196,
0.014250279404222965,
0.014541670680046082,
-0.023042991757392883,
-0.02471497468650341,
0.03232062980532646,
0.03230651095509529,
-0.009721003472805023,
-0.010714590549468994,
0.014988036826252937,
0.0450172983109951,
0.04631859064102173,
-0.011724457144737244,
0.008564232848584652,
-0.022445492446422577,
-0.014448252506554127,
0.014227312989532948,
0.06888173520565033,
0.010550416074693203,
-0.013822220265865326,
-0.04409850388765335,
0.06137362867593765,
0.008852560073137283,
-0.00010960248619085178,
-0.005582856945693493,
0.02883581630885601,
-0.025006674230098724,
0.027399994432926178,
-0.021208198741078377,
-0.014634701423346996,
0.05215435102581978,
0.05601055175065994,
-0.0164656862616539,
0.008682278916239738,
-0.011398430913686752,
0.033152446150779724,
-0.0645102709531784,
0.01542016863822937,
0.05633655562996864,
0.00609030993655324,
0.0971497967839241,
0.05288621783256531,
-0.023626191541552544,
-0.013475533574819565,
-0.060305625200271606,
0.010861854068934917,
0.01852046139538288,
0.04752134531736374,
0.0265444777905941,
0.040787845849990845,
-0.05006852373480797,
0.08699840307235718,
0.012519845739006996,
-0.03426690399646759,
-0.0303109772503376,
0.05851159989833832,
-0.006323708686977625,
0.01649061031639576,
-0.014889695681631565,
0.010627852752804756,
0.05859530717134476,
0.033800940960645676,
0.0648941919207573,
0.011900506913661957,
-0.03614448383450508,
0.029122330248355865,
-0.05815993621945381,
-0.04268390312790871,
0.0031293241772800684,
-0.011768897995352745,
-0.0468376986682415,
-0.0028515916783362627,
-0.011456513777375221,
-0.058289285749197006,
-0.048790059983730316,
-0.0015972137916833162,
-0.00036139367148280144,
-0.05023397505283356,
0.0034364834427833557,
0.037977028638124466,
-0.014677096158266068,
-0.006352532655000687,
0.02536344900727272,
0.07298140972852707,
0.015991196036338806,
-0.0031510957051068544,
-0.03195863962173462,
-0.024276671931147575,
0.004212384112179279,
0.0395754836499691,
-0.005057410802692175,
0.01248569879680872,
-0.01799372024834156,
-0.028362300246953964,
0.017589686438441277,
-0.022156136110424995,
0.05559614300727844,
0.018747925758361816,
0.06601943075656891,
0.0312671884894371,
-0.06263914704322815,
0.011508381925523281,
-0.016444308683276176,
0.031737539917230606,
0.06479564309120178,
-0.01628824695944786,
0.008250607177615166,
-0.0008550711208954453,
-0.007647015154361725,
0.007245505694299936,
-0.044121984392404556,
-0.043242499232292175,
0.03849303349852562,
-0.03647581487894058,
-0.012134408578276634,
0.007364749908447266,
0.05728507041931152,
-0.015503007918596268,
-0.018978582695126534,
0.03066638484597206,
0.04070287570357323,
-0.025323649868369102,
0.02093476988375187,
0.0029586199671030045,
-0.0040540373884141445,
-0.105259969830513,
-0.01790531724691391,
0.0054488349705934525,
0.009988127276301384,
0.03836479038000107,
-0.019051508978009224,
0.026281539350748062,
-0.053110625594854355,
-0.03721831366419792,
-0.028321973979473114,
-0.030624739825725555,
0.0169281754642725,
-0.012840515933930874,
-0.016204383224248886,
0.06073814630508423,
-0.04837319254875183,
-0.01062692329287529,
0.002338133053854108,
0.045295074582099915,
-0.04335403814911842,
0.02653118595480919,
-0.03222423046827316,
-0.05388808995485306,
0.026303373277187347,
0.012840475887060165,
0.019487939774990082,
0.0424940250813961,
-0.02278381586074829,
0.041053950786590576,
0.0012531623942777514,
0.043219439685344696,
-0.012774072587490082,
-0.013857186771929264,
-0.030224893242120743,
-0.029423551633954048,
-0.005648199003189802,
-0.036763593554496765,
-0.007673052605241537,
0.04666322097182274,
0.001421761349774897,
-0.02071041241288185,
-0.025268858298659325,
-0.05216333642601967,
0.036891065537929535,
-0.03264184668660164,
-0.029971303418278694,
-0.012966012582182884,
-0.010902630165219307,
-0.007357283495366573,
0.04347427561879158,
0.0196627676486969,
0.03055068850517273,
0.026633795350790024,
0.015424416400492191,
-0.031097324565052986,
0.026165777817368507,
0.036924779415130615,
0.024506457149982452,
-0.06962642073631287,
-0.027246715500950813,
-0.025570807978510857,
-0.06666569411754608,
-0.026611246168613434,
0.007250703871250153,
-0.015441762283444405,
0.04316043481230736,
-0.007742446381598711,
-0.030672667548060417,
0.039063598960638046,
-0.05212754011154175,
0.0019645458087325096,
-0.01040145754814148,
-0.019429007545113564,
-0.03229779750108719,
0.02278103493154049,
0.040862787514925,
0.037784699350595474,
-0.026924021542072296,
-0.045015256851911545,
-0.08640638738870621,
-0.040886737406253815,
0.019815299659967422,
0.01544363982975483,
0.010935933329164982,
0.010951949283480644,
0.0296794343739748,
0.04396899417042732,
-0.005165262147784233,
0.009069220162928104,
-0.05021337419748306,
-0.06650616973638535,
0.031063618138432503,
0.05442247912287712,
-0.03329724818468094,
-0.060181763023138046,
0.02553616836667061,
0.0067686219699680805,
0.0025422496255487204,
-0.03702031075954437,
-0.007353831082582474,
-0.053960878401994705,
-0.04782138392329216,
0.04301698878407478,
-0.023689543828368187,
-0.023082144558429718,
0.0002409374574199319
] |
<p>This question is a follow-up to <a href="http://physics.stackexchange.com/users/2190/david-bar-moshe">David Bar Moshe</a>'s answer to my earlier question on the <a href="http://physics.stackexchange.com/questions/34990/aharonov-bohm-effect-and-flux-quantization-in-superconductors">Aharonov-Bohm effect and flux-quantization</a>. What I forgot was that it is not the <em>wavefunction</em> that must be single-valued, but rather, the <em>probability density</em> (wavefunction-squared).</p>
<p>But if that is so, how do I justify the quantization condition $m=\{\ldots,-1,0,1\ldots\}$ based on the boundary condition on the azimuthal part of spherically symmetric wavefunctions $\psi(x,y,z)\sim R(r)\Theta(\theta)\Phi(\phi)$:</p>
<p>$$\Phi(\phi)\sim e^{im\phi}$$</p>
<p>whose square (probability density) is unity, independent of $m$?</p> | g4578 | [
0.023821411654353142,
0.01691359467804432,
-0.0104284156113863,
-0.006555150728672743,
0.06852594763040543,
0.014309059828519821,
0.08824755251407623,
0.021894216537475586,
0.008609257638454437,
0.003902990370988846,
-0.03577939420938492,
0.056085240095853806,
-0.021854275837540627,
0.02212955802679062,
-0.011785177513957024,
0.004804664291441441,
-0.03313806653022766,
0.04366668313741684,
0.012403571978211403,
0.024881966412067413,
-0.04596662148833275,
-0.010412107221782207,
0.002665351377800107,
-0.049399640411138535,
0.05667615681886673,
-0.025400007143616676,
0.0036324241664260626,
-0.033203043043613434,
0.032640937715768814,
0.05244218185544014,
0.010717371478676796,
-0.002178163966163993,
0.07588762789964676,
0.031052879989147186,
0.02859625220298767,
0.031456246972084045,
0.01695629581809044,
0.0012226123362779617,
0.06022609770298004,
-0.028682712465524673,
0.019873127341270447,
-0.0137704499065876,
0.007216901518404484,
-0.011404543183743954,
-0.07869036495685577,
0.05068734660744667,
-0.04433358460664749,
0.0391346774995327,
-0.0038954864721745253,
0.0015915717231109738,
0.04845013841986656,
-0.029601529240608215,
0.07051333785057068,
0.009343334473669529,
-0.04526583477854729,
0.0289608221501112,
0.047209374606609344,
0.001984088448807597,
-0.033432431519031525,
0.06758157908916473,
-0.004967294167727232,
0.07082458585500717,
-0.022697357460856438,
-0.03136197105050087,
0.0480467714369297,
0.07421091198921204,
-0.011932631023228168,
-0.0003927326761186123,
-0.09127214550971985,
0.019674217328429222,
0.005310072563588619,
-0.03738910332322121,
-0.07076909393072128,
0.036567676812410355,
-0.037975143641233444,
0.0501607209444046,
0.027076050639152527,
0.01442026812583208,
0.04904382303357124,
-0.042336344718933105,
-0.10874734073877335,
-0.03302524983882904,
0.04565328359603882,
-0.0201611015945673,
0.008567998185753822,
-0.017998073250055313,
0.03526342287659645,
-0.02062217704951763,
-0.02728882245719433,
0.0003577684401534498,
-0.01005521509796381,
-0.05550730228424072,
-0.020657522603869438,
0.039135731756687164,
0.0005224795313552022,
0.013075904920697212,
0.008604701608419418,
0.010166103951632977,
-0.0303818192332983,
0.01303242240101099,
-0.0814429521560669,
0.047177255153656006,
-0.002059167018160224,
-0.00495885731652379,
-0.013396160677075386,
-0.018050944432616234,
0.0072335717268288136,
0.0012183745857328176,
0.041751205921173096,
-0.004572057165205479,
-0.03903389722108841,
0.015294457785785198,
0.003812792943790555,
0.034376293420791626,
-0.046366624534130096,
-0.004245285410434008,
0.06613797694444656,
-0.014602665789425373,
-0.013450984843075275,
0.014666181989014149,
-0.023370351642370224,
0.0432220920920372,
-0.012303952127695084,
0.053720906376838684,
0.004427628125995398,
0.03834100440144539,
-0.040352705866098404,
0.01074845902621746,
0.017930151894688606,
0.0033029993064701557,
0.03538089618086815,
-0.005296893883496523,
-0.029268035665154457,
0.029026692733168602,
-0.027088724076747894,
0.027400681748986244,
-0.00820095743983984,
0.00845060683786869,
-0.016051560640335083,
-0.008802652359008789,
-0.013197941705584526,
-0.028396151959896088,
0.06794437766075134,
-0.04888320714235306,
-0.0076115853153169155,
0.006956865545362234,
0.020268389955163002,
-0.07380924373865128,
0.0009934232803061604,
0.006773011758923531,
0.009183858521282673,
0.07308482378721237,
-0.04145050421357155,
0.010664339177310467,
-0.007107104174792767,
0.02179190330207348,
0.033062372356653214,
0.011627966538071632,
-0.018876465037465096,
-0.02854127809405327,
0.047686029225587845,
0.044206440448760986,
0.01629292592406273,
-0.02615443989634514,
-0.028940051794052124,
0.007756521459668875,
0.02945149503648281,
-0.03554561734199524,
-0.0019168062135577202,
-0.0488845556974411,
-0.02197800949215889,
0.00040245859418064356,
-0.0027979130391031504,
0.02616172470152378,
0.009045647457242012,
0.034060314297676086,
-0.051906224340200424,
0.05064311996102333,
0.010058303363621235,
0.020779628306627274,
-0.0019379218574613333,
0.021771684288978577,
0.0225139819085598,
-0.06340529024600983,
0.049873076379299164,
0.004722606390714645,
0.030661413446068764,
0.016282008960843086,
-0.07288307696580887,
0.046028587967157364,
0.00538657559081912,
0.004710067994892597,
-0.05468367412686348,
-0.006379926111549139,
0.004524449352174997,
0.0038486896082758904,
0.04562138020992279,
-0.012902419082820415,
0.007358702830970287,
0.01958475634455681,
-0.006917440798133612,
0.06684678047895432,
0.0838073268532753,
-0.005279059521853924,
0.05914262309670448,
0.023418476805090904,
-0.00387726747430861,
0.016743745654821396,
0.0084836445748806,
-0.017666494473814964,
0.020993264392018318,
-0.0734323114156723,
-0.0036234771832823753,
0.005330918822437525,
-0.04116346687078476,
0.012198456563055515,
-0.03138158097863197,
0.04762950539588928,
-0.05377790331840515,
-0.02986821159720421,
-0.016307812184095383,
0.0130602503195405,
0.06012411415576935,
0.0016238883836194873,
-0.0045410869643092155,
0.029501302167773247,
-0.007711777463555336,
-0.025425059720873833,
0.0026094086933881044,
0.01661605015397072,
-0.07946464419364929,
-0.0040599689818918705,
-0.021191710606217384,
-0.023134665563702583,
-0.03289853408932686,
0.08280064910650253,
-0.048542577773332596,
0.01038280688226223,
0.006487224251031876,
0.022963743656873703,
0.019877690821886063,
0.0265180803835392,
-0.025685157626867294,
0.0030066086910665035,
0.07208415865898132,
-0.05820516496896744,
-0.016669761389493942,
0.023242564871907234,
0.045339904725551605,
-0.008748465217649937,
-0.005642757751047611,
-0.06767793744802475,
0.02988629974424839,
-0.009231706149876118,
0.0382220484316349,
-0.01567963883280754,
-0.02724909782409668,
0.014525686390697956,
-0.020538603886961937,
-0.0034441917669028044,
-0.0352407805621624,
-0.06413225084543228,
0.05103892832994461,
-0.033828169107437134,
-0.05152301862835884,
-0.004050309769809246,
-0.08089672774076462,
0.06730743497610092,
0.03334837034344673,
-0.01896854303777218,
0.03524037450551987,
0.09779410064220428,
0.0017995858797803521,
0.04148374870419502,
0.02206861786544323,
0.02368377335369587,
-0.009909247048199177,
-0.01647065207362175,
0.02389679104089737,
-0.029811596497893333,
-0.07086954265832901,
-0.02035125158727169,
0.02357461489737034,
0.008494863286614418,
0.01623501628637314,
-0.08180411905050278,
0.026836508885025978,
-0.03745388612151146,
0.0007430319674313068,
0.01166816707700491,
-0.05543334782123566,
0.022146424278616905,
0.026245256885886192,
0.029146425426006317,
0.009023725986480713,
-0.00740407407283783,
0.009142008610069752,
-0.0627429410815239,
0.013928426429629326,
0.045304153114557266,
-0.015985624864697456,
-0.034329380840063095,
-0.002355716424062848,
0.0034994282759726048,
0.06551941484212875,
0.05338495969772339,
-0.06727883964776993,
-0.0535416454076767,
-0.040348246693611145,
-0.0080984802916646,
0.014119564555585384,
0.03585038706660271,
-0.03703904524445534,
-0.009665076620876789,
-0.01319847535341978,
0.010408627800643444,
0.022563859820365906,
-0.057498931884765625,
0.03209533169865608,
-0.06856495887041092,
-0.04824883118271828,
-0.0076641482301056385,
0.012634765356779099,
-0.044113416224718094,
0.05174856260418892,
0.014848808757960796,
-0.012904271483421326,
-0.0529341995716095,
-0.04463839530944824,
-0.037290722131729126,
0.017679281532764435,
0.015147955156862736,
-0.01719573698937893,
-0.005150936543941498,
-0.05558764189481735,
-0.049678537994623184,
-0.037154871970415115,
-0.04283111169934273,
-0.02221786417067051,
0.04682216793298721,
-0.015030836686491966,
-0.022631283849477768,
0.018015839159488678,
-0.029489897191524506,
0.002540305955335498,
-0.03028244338929653,
-0.017848720774054527,
0.0461658276617527,
0.05738721787929535,
0.015969155356287956,
-0.01166739221662283,
-0.04110809415578842,
0.07287157326936722,
0.034933216869831085,
0.016141055151820183,
0.025404514744877815,
0.09521927684545517,
0.004788478836417198,
0.020155904814600945,
-0.026974627748131752,
-0.012147161178290844,
-0.050235241651535034,
-0.001152021693997085,
-0.02504223957657814,
0.017687391489744186,
-0.07349266111850739,
0.03618121147155762,
0.045453350991010666,
-0.051021501421928406,
-0.032051362097263336,
-0.018104402348399162,
-0.015425339341163635,
0.03380191698670387,
0.026558704674243927,
0.06486385315656662,
-0.050100766122341156,
0.016658388078212738,
0.030936218798160553,
-0.022196723148226738,
0.025295505300164223,
0.04309559985995293,
0.02225455455482006,
0.012677585706114769,
-0.00197869841940701,
-0.00035868576378561556,
0.04515288025140762,
-0.00931109581142664,
-0.019602932035923004,
-0.004851275123655796,
-0.03424087539315224,
0.020968599244952202,
-0.020132867619395256,
-0.011361537501215935,
0.0064468830823898315,
0.0071547143161296844,
-0.030325401574373245,
0.024613764137029648,
-0.07346754521131516,
0.013055488467216492,
0.04309142008423805,
-0.0007439062464982271,
-0.007189139258116484,
-0.02278333529829979,
-0.04219149425625801,
0.02784905768930912,
-0.03186648339033127,
0.026369608938694,
-0.00656443415209651,
-0.004433488007634878,
-0.0806448832154274,
-0.0315152108669281,
-0.017613014206290245,
0.0018917893758043647,
-0.07511794567108154,
0.020546071231365204,
0.010083415545523167,
0.005388056393712759,
-0.064799465239048,
-0.03011969104409218,
-0.005242917221039534,
0.038389403373003006,
-0.009142800234258175,
-0.025314997881650925,
-0.012903331778943539,
-0.04405364766716957,
0.04467879608273506,
0.08314011991024017,
-0.013714894652366638,
0.03180176764726639,
-0.0391414538025856,
-0.018232185393571854,
0.04468661546707153,
0.03301876410841942,
0.0423056036233902,
-0.08153899759054184,
-0.013850928284227848,
-0.031026359647512436,
0.04923319071531296,
0.01482151634991169,
0.05161590129137039,
0.005582044366747141,
-0.00250298366881907,
0.016602419316768646,
-0.024084040895104408,
0.058915894478559494,
0.022534826770424843,
-0.06303767114877701,
-0.07050219178199768,
0.05691411718726158,
-0.019219834357500076,
-0.08406205475330353,
-0.020653029903769493,
-0.01959632895886898,
-0.018698155879974365,
0.020364800468087196,
-0.045202404260635376,
-0.005976167973130941,
0.035058461129665375,
0.023960944265127182,
0.017525726929306984,
-0.02840210311114788,
0.00031903787748888135,
-0.03054836578667164,
-0.009994054213166237,
0.0481523722410202,
0.0004302320594433695,
-0.05246036499738693,
0.04348241165280342,
-0.016621647402644157,
-0.008684959262609482,
-0.012663044966757298,
0.031329553574323654,
0.07079417258501053,
0.018224788829684258,
0.005391774233430624,
0.01037733443081379,
0.03400145843625069,
0.00845268927514553,
0.002546906704083085,
-0.02215537056326866,
-0.02291233465075493,
0.010877854190766811,
0.033727873116731644,
0.0058407047763466835,
-0.021260753273963928,
0.03053625300526619,
0.009374108165502548,
-0.0011666512582451105,
-0.017313266173005104,
0.0007877300377003849,
-0.022616161033511162,
-0.06163999065756798,
0.009763974696397781,
0.015224521048367023,
0.013691072352230549,
-0.08990947902202606,
0.021956786513328552,
-0.05790393427014351,
-0.011417686007916927,
0.006781062111258507,
-0.035868965089321136,
-0.031168613582849503,
-0.002997262869030237,
0.010931800119578838,
-0.0021917729172855616,
-0.011065270751714706,
-0.014775769785046577,
0.02463006041944027,
-0.020322101190686226,
-0.014762683771550655,
-0.018063673749566078,
-0.0020674096886068583,
0.030246103182435036,
-0.012599457986652851,
0.013905532658100128,
0.03307592123746872,
-0.02889353781938553,
0.056708164513111115,
-0.0545048862695694,
0.019114943221211433,
0.0448622852563858,
0.04405583068728447,
0.026221098378300667,
-0.025825627148151398,
0.032778482884168625,
0.005349988117814064,
-0.06854094564914703,
-0.07191964238882065,
0.025761589407920837,
0.06922914832830429,
-0.03844698145985603,
0.008022948168218136,
0.018969671800732613,
-0.02865363471210003,
0.007463592104613781,
-0.020300913602113724,
0.0015292593743652105,
-0.004947198089212179,
0.015307564288377762,
0.06365709751844406,
0.02149229496717453,
-0.011224085465073586,
0.015638241544365883,
0.02806643210351467,
-0.05306239798665047,
0.016650265082716942,
-0.035312484949827194,
0.027684509754180908,
-0.01714879274368286,
0.009209571406245232,
-0.06490077823400497,
-0.02929205633699894,
-0.05906309187412262,
-0.039493121206760406,
0.03333194926381111,
0.008255609311163425,
-0.021571017801761627,
0.02666633389890194,
-0.0021373324561864138,
-0.003338519250974059,
0.028868945315480232,
-0.008921881206333637,
0.05080980807542801,
-0.06066853180527687,
-0.0033869773615151644,
-0.019833315163850784,
0.010763739235699177,
0.026906102895736694,
0.001392676611430943,
0.03488227352499962,
-0.01327685546129942,
0.010730917565524578,
0.038450613617897034,
-0.03147969767451286,
0.03740694746375084,
0.0772688016295433,
0.002535628154873848,
-0.06835372000932693,
-0.0513005293905735,
0.01121068187057972,
-0.028674671426415443,
0.037693798542022705,
0.051122721284627914,
-0.11759890615940094,
0.015832383185625076,
0.05479178577661514,
-0.02256496623158455,
-0.050362929701805115,
0.061795853078365326,
-0.0069039929658174515,
-0.03611231595277786,
-0.06590425968170166,
0.0236796997487545,
0.014526707120239735,
-0.041774947196245193,
0.04800323396921158,
-0.004359046462923288,
0.019946379587054253,
-0.05001530423760414,
0.014950000680983067,
0.03171352297067642,
-0.009133328683674335,
0.00832617748528719,
-0.022161925211548805,
0.05375618487596512,
0.025360489264130592,
0.029051952064037323,
0.0006425900501199067,
-0.045684635639190674,
0.03463687375187874,
-0.019504524767398834,
-0.017330626025795937,
-0.037103310227394104,
0.02822825126349926,
0.02393740974366665,
-0.05031725391745567,
-0.02222229726612568,
0.041929420083761215,
-0.029088109731674194,
0.011172400787472725,
0.0505543015897274,
-0.004763927776366472,
-0.02316935732960701,
-0.006907403003424406,
0.03923414647579193,
0.05919688194990158,
0.035632357001304626,
-0.013801923021674156,
0.05138256400823593,
0.01705910451710224,
0.006744157988578081,
0.021342046558856964,
-0.015161055140197277,
-0.01704641617834568,
0.005884646903723478,
0.02968185395002365,
-0.008725385181605816,
-0.06868980824947357,
0.0003698405926115811,
-0.028020063415169716,
-0.019328510388731956,
0.034200821071863174,
0.07995305210351944,
-0.0009368557948619127,
-0.10308516025543213,
-0.003133086021989584,
0.03594525530934334,
0.03680865094065666,
-0.10255113989114761,
0.03667427599430084,
0.03400339558720589,
0.022495349869132042,
-0.04076444357633591,
-0.035996999591588974,
-0.017412440851330757,
-0.012601480819284916,
-0.008708789944648743,
0.05598936975002289,
0.015683425590395927,
0.012781364843249321,
0.03694911673665047,
-0.029700547456741333,
-0.028313731774687767,
-0.023910291492938995,
0.03426118195056915,
0.029508480802178383,
-0.004399644210934639,
0.0004534678009804338,
0.0006761184195056558,
-0.08109316229820251,
0.0028298860415816307,
0.012961859814822674,
-0.03949068486690521,
0.018018849194049835,
-0.0006917126593180001,
0.0025237477384507656,
0.011173266917467117,
0.062247149646282196,
-0.0014308292884379625,
-0.04807187616825104,
0.01963151805102825,
-0.016194764524698257,
0.020418748259544373,
-0.031048474833369255,
-0.04364539682865143,
-0.010467621497809887,
-0.0054255384020507336,
-0.03115948662161827,
0.0013571155723184347,
0.06352265179157257,
0.005924217402935028,
-0.02254033274948597,
0.025293385609984398,
0.0043717725202441216,
-0.05211113020777702,
0.027790505439043045,
0.07988167554140091,
0.04255496338009834,
0.06987618654966354,
0.06354027986526489,
0.018164699897170067,
-0.012858341448009014,
-0.03239127993583679,
-0.022511979565024376,
0.07426843792200089,
-0.016762379556894302,
-0.002433654386550188,
-0.030089400708675385,
-0.0002031742042163387,
-0.03239471837878227,
0.030544141307473183,
0.029879072681069374,
-0.011737298220396042,
0.007889334112405777,
0.021839845925569534,
0.02481207065284252,
-0.06817197799682617,
0.0006189123960211873,
-0.01009997446089983,
-0.03470657020807266,
-0.034505560994148254,
0.027050169184803963,
-0.012373778969049454,
-0.012266654521226883,
-0.004167370498180389,
-0.04742478206753731,
-0.04634103551506996,
-0.014518923126161098,
0.03900562599301338,
-0.012272226624190807,
-0.035403378307819366,
-0.023316236212849617,
-0.03487466648221016,
0.0007057655020616949,
-0.07927975058555603,
-0.025878624990582466,
0.01067396905273199,
0.05977257713675499,
0.040886327624320984,
-0.011051631532609463,
0.02060350775718689,
-0.08974497765302658,
0.021178152412176132,
-0.035934701561927795,
-0.015707407146692276,
0.05388451740145683,
-0.06875339895486832,
-0.01002095453441143,
0.05688616633415222,
0.03209306672215462,
-0.001965022413060069,
-0.03927159309387207,
-0.0027853769715875387,
0.03035249374806881,
0.0012367427116259933,
-0.049382127821445465,
0.027535293251276016,
-0.02369033172726631,
0.059367310255765915,
-0.002855493687093258,
-0.02125728130340576,
-0.07306861877441406,
0.009413467720150948,
0.03204668313264847,
-0.04427005350589752,
-0.04309108108282089,
0.008055757731199265,
0.054996058344841
] |
<p>I would like to point to the beautiful section 4.3 (page 42) of <a href="http://www.people.fas.harvard.edu/~xiyin/253b_Lectures.pdf">these lecture notes.</a> I think this is the most educative exposition I have ever seen anywhere about Yang-Mill's beta function. What I love best about it is that it does it without using diagramatics (and its confusing combinatorics)(..though of course these are equivalent..but I find this language most comfortable..) </p>
<p>I have the following questions in relation to the above, </p>
<ul>
<li><p>In the above the author has picked out the terms quadratic in the fluctuations in equation 4.40 and evaluated the determinant and that gives the 1-loop effective action. </p>
<p>What would one do in this method if one had to go to 2-loops or higher?
What is the relationship between how many orders one keeps in the fluctuation field and how many loop result it translates into? (..if there a reference which shows going to higher loops in this method?..) </p></li>
<li><p>Can I use the method in these notes to evaluate the corrected gauge or the Fermion propagator? If someone could outline the steps.. </p>
<p>Here the author has chosen a constant and static background gauge (why?) and hence he has in 4.40 no term which is a derivative of the background gauge field left. I guess one would have to lift this restriction if one had to calculate the gauge field propagator correction. With this assumption about the background gauge field lifted I guess that one would have to then compute the $\Gamma^{1-loop}$ as defined in equation 4.41 and pick out the terms quadratic in the gauge field in it and invert that. </p></li>
<li><p>In the above the author has picked out from $\Gamma^{1-loop}$ only the terms quartic in the gauge field and and calculated the divergent contribution to it which is the shift in the gauge coupling constant. But the gauge coupling constant is also multiplying the term cubic in the gauge field and there is a 1-loop shift even there. What about that? Is there some theorem which guarantees that the beta-function derived by tacking the cubic term would have been the same? </p></li>
</ul>
<p>I guess that since even after choosing a constant and static gauge field one can track a change in the gauge coupling constant through a quartic term, it makes sense. But if one were in a theory (or in light-cone gauge!) where the gauge coupling constant were existing only in a term which has derivatives of the gauge field then I guess this choice of a background would not work. </p>
<p>I would like to know of a precise way of understanding the above. (...there is also the issue of whether the 1-loop effective action done this way can throw up terms that were removed by a gauge choice..and then what would one do..) </p> | g4579 | [
0.01693236455321312,
-0.07275029271841049,
-0.02615426480770111,
-0.06245701387524605,
0.08273594826459885,
0.030388908460736275,
0.07663007825613022,
-0.012776797637343407,
0.013480564579367638,
-0.03030671365559101,
-0.044523995369672775,
0.05596032738685608,
0.05991402268409729,
0.045544713735580444,
0.04443946108222008,
-0.00748081598430872,
0.0729733407497406,
0.011895238421857357,
-0.013955851085484028,
-0.05968967825174332,
0.040166087448596954,
0.05537240579724312,
0.004968585446476936,
-0.06057161092758179,
-0.04310567304491997,
-0.0019960340578109026,
0.03013761341571808,
0.01663328893482685,
-0.029066698625683784,
-0.009145678021013737,
-0.008094608783721924,
-0.01803593896329403,
0.052804648876190186,
-0.02749788388609886,
-0.018873609602451324,
0.07634278386831284,
0.06562261283397675,
0.04544008523225784,
0.01878342591226101,
0.02379225380718708,
-0.021006353199481964,
-0.041764695197343826,
0.04109584912657738,
-0.0262038204818964,
0.02171088382601738,
0.036861028522253036,
-0.03752831742167473,
-0.00947767123579979,
0.03786080330610275,
0.04462267830967903,
-0.013257339596748352,
0.013992213644087315,
0.05978277698159218,
0.013123185373842716,
0.009651370346546173,
0.0580245777964592,
0.03505624085664749,
0.03060625120997429,
0.017912281677126884,
0.030385076999664307,
-0.009566809982061386,
-0.0012301468523219228,
0.07743795961141586,
-0.022528026252985,
0.0192766934633255,
-0.029889455065131187,
-0.026837104931473732,
-0.013053401373326778,
-0.08675681799650192,
0.04011274129152298,
-0.011332756839692593,
-0.04990886524319649,
-0.029530266299843788,
0.00024569264496676624,
-0.026516763493418694,
0.06331515312194824,
0.033384229987859726,
-0.029111331328749657,
-0.06617524474859238,
-0.034137409180402756,
-0.0869300365447998,
-0.042308054864406586,
0.04354019835591316,
0.023290008306503296,
0.09034138172864914,
-0.0522698275744915,
0.0019791829399764538,
-0.01766284555196762,
-0.07025649398565292,
-0.06954705715179443,
-0.032685596495866776,
-0.04415399953722954,
0.012975171208381653,
0.03298497945070267,
-0.029911864548921585,
0.017063599079847336,
-0.009340424090623856,
-0.013458143919706345,
0.008155353367328644,
0.0003683519607875496,
-0.03845304623246193,
0.0334814228117466,
0.003400391200557351,
0.0245684627443552,
-0.07603345066308975,
-0.006904613226652145,
0.06626749038696289,
-0.03648489713668823,
-0.008048774674534798,
-0.022839460521936417,
-0.05976662412285805,
-0.012019607238471508,
-0.0003204050299245864,
-0.05592556297779083,
-0.05206530913710594,
-0.03468669578433037,
0.09229103475809097,
-0.039241429418325424,
-0.014189769513905048,
-0.005414803512394428,
-0.04520449414849281,
0.036478109657764435,
0.013660449534654617,
0.020661160349845886,
0.029326334595680237,
-0.03048086166381836,
-0.09148886799812317,
0.047662317752838135,
0.024922002106904984,
-0.054358504712581635,
0.04577893391251564,
-0.04477480426430702,
0.030179014429450035,
0.008986212313175201,
0.00454955268651247,
-0.03661510348320007,
0.011134467087686062,
0.0313439816236496,
-0.015277651138603687,
-0.003914752509444952,
-0.05795234069228172,
-0.05806576460599899,
0.005490263924002647,
-0.009873258881270885,
-0.02651471644639969,
0.07822157442569733,
-0.007835502736270428,
-0.006889305543154478,
-0.0029833109583705664,
-0.050325747579336166,
0.08372344821691513,
0.09181956201791763,
0.03703742101788521,
0.0016544327372685075,
0.018941620364785194,
0.01618940755724907,
0.07579116523265839,
-0.04494251310825348,
-0.017700759693980217,
0.013942118734121323,
0.05388936027884483,
-0.05975597724318504,
0.028667304664850235,
0.024954846128821373,
-0.05637418106198311,
0.040529344230890274,
-0.015990586951375008,
-0.0034369330387562513,
-0.022680245339870453,
-0.04651231691241264,
-0.05598526448011398,
0.032430846244096756,
0.028105340898036957,
-0.035014327615499496,
0.01916860230267048,
0.05505876988172531,
-0.008448746986687183,
-0.04935117065906525,
-0.018890636041760445,
-0.03002530336380005,
0.016787460073828697,
0.011951611377298832,
-0.029544314369559288,
-0.01678021438419819,
-0.03217727690935135,
-0.03978034481406212,
0.0222892165184021,
0.008886829949915409,
0.02082645706832409,
-0.0337088368833065,
-0.02771148458123207,
-0.04202036187052727,
-0.04034778103232384,
0.0259291660040617,
-0.06383683532476425,
-0.010132284834980965,
0.027771059423685074,
-0.05569559335708618,
0.023057570680975914,
-0.01258800644427538,
-0.033953070640563965,
0.023312518373131752,
0.025220170617103577,
-0.0704708993434906,
0.013949343003332615,
0.002240420551970601,
0.026207802817225456,
-0.005298099014908075,
-0.03568693622946739,
-0.04088649898767471,
0.014851951040327549,
-0.056767020374536514,
0.013821512460708618,
-0.009166485629975796,
-0.017015282064676285,
-0.017672576010227203,
0.024260008707642555,
0.04005584493279457,
-0.05559495836496353,
0.007598317228257656,
-0.01470304187387228,
-0.007699577137827873,
0.04871681332588196,
0.010892082005739212,
-0.013141043484210968,
0.028391795232892036,
0.011448247358202934,
0.013753261417150497,
-0.007687297184020281,
0.0703749731183052,
-0.0803980827331543,
0.02180422469973564,
-0.10318166017532349,
-0.058090921491384506,
0.0028417117428034544,
0.03177393227815628,
0.027056356891989708,
-0.032773423939943314,
0.030012281611561775,
0.0007180513348430395,
0.01626616343855858,
0.06749702244997025,
-0.017889808863401413,
0.03128809481859207,
0.01842322014272213,
0.038067061454057693,
0.0769055038690567,
0.0449310764670372,
-0.03898352384567261,
-0.015023265033960342,
0.017422473058104515,
0.020851610228419304,
-0.03678872063755989,
0.042133878916502,
-0.015558143146336079,
-0.05851982533931732,
0.0026799910701811314,
0.03982635959982872,
-0.0414581261575222,
-0.002330629387870431,
0.033862195909023285,
-0.041052017360925674,
0.012618445791304111,
0.03517637774348259,
0.0015982616459950805,
0.0026016286574304104,
-0.008492117747664452,
-0.053002629429101944,
-0.01039400976151228,
-0.01275268942117691,
-0.008582733571529388,
-0.00182875688187778,
0.010166501626372337,
0.0345478393137455,
-0.038220591843128204,
-0.04416081681847572,
-0.0004870443372055888,
0.0018435943638905883,
0.061918701976537704,
-0.00425936933606863,
0.04031379148364067,
-0.019869495183229446,
-0.03193061798810959,
-0.007837725803256035,
0.07099589705467224,
-0.037469759583473206,
0.005748380441218615,
-0.038212671875953674,
0.025076476857066154,
0.006782799027860165,
-0.05225304514169693,
-0.009602765552699566,
-0.0025289778131991625,
-0.007143508177250624,
0.002161736600100994,
-0.030271530151367188,
0.04793045297265053,
-0.035231489688158035,
0.028696754947304726,
0.04415547475218773,
-0.00004778845686814748,
-0.0011317386524751782,
-0.03210971876978874,
-0.01847854256629944,
0.03873548284173012,
-0.007102177944034338,
-0.039945684373378754,
0.019223621115088463,
-0.004474422428756952,
0.0599050372838974,
0.012818536721169949,
-0.014771468937397003,
-0.023673299700021744,
-0.055737998336553574,
0.026139136403799057,
0.013824855908751488,
0.022640634328126907,
0.0015033421805128455,
0.012269287370145321,
0.022871706634759903,
-0.013906129635870457,
-0.015862155705690384,
0.037181466817855835,
-0.011008568108081818,
-0.01485852524638176,
0.01733868196606636,
-0.024481069296598434,
0.006002229638397694,
-0.05330159515142441,
-0.0016423225170001388,
0.058458298444747925,
-0.031321510672569275,
-0.014727835543453693,
-0.03261284530162811,
0.035865314304828644,
-0.06577335298061371,
-0.0817589983344078,
0.007328739855438471,
0.003910242114216089,
-0.0319940447807312,
-0.02243725396692753,
0.006063305772840977,
-0.043715741485357285,
0.010544250719249249,
-0.006513104308396578,
-0.02316167764365673,
-0.0038022147491574287,
-0.008420570753514767,
-0.02679395116865635,
-0.018162548542022705,
0.0441986545920372,
-0.06234199181199074,
-0.013341149315237999,
0.014202061109244823,
0.065754234790802,
-0.02992856316268444,
0.031630560755729675,
0.10552015155553818,
0.007075615227222443,
-0.014427482150495052,
-0.002753174165263772,
-0.001339078415185213,
0.018524231389164925,
-0.0025666949804872274,
-0.07008350640535355,
0.015400196425616741,
-0.003649880178272724,
0.029633061960339546,
-0.015597132034599781,
-0.01507310476154089,
0.018977154046297073,
-0.013974537141621113,
-0.0010384778724983335,
0.019735051319003105,
0.00042395104537718,
0.009212072007358074,
0.016432171687483788,
0.03167606517672539,
-0.049827925860881805,
0.05989767983555794,
0.01646260730922222,
0.016714464873075485,
0.050142064690589905,
0.046339359134435654,
-0.034052737057209015,
0.05273899435997009,
-0.0423823706805706,
-0.023125117644667625,
-0.0031301931012421846,
0.005607207305729389,
0.01665375381708145,
0.03274238482117653,
-0.03167509287595749,
-0.020190032199025154,
0.015723856166005135,
-0.018871279433369637,
0.008109703660011292,
0.043296534568071365,
0.021667148917913437,
0.00888964906334877,
0.016600679606199265,
-0.023269306868314743,
0.03292073681950569,
-0.028791295364499092,
-0.019743937999010086,
-0.031697217375040054,
-0.01316225714981556,
-0.005025271791964769,
0.04693952947854996,
-0.03375234454870224,
-0.04039149358868599,
0.08256615698337555,
0.015349255874752998,
-0.07848422229290009,
0.039782095700502396,
-0.034681081771850586,
0.0276727806776762,
-0.03747795522212982,
0.019152695313096046,
-0.07392287254333496,
0.04669502004981041,
0.0193489920347929,
-0.04242854192852974,
-0.036197587847709656,
0.01895284838974476,
0.060508932918310165,
0.05110357329249382,
-0.0009655249887146056,
0.012024919502437115,
-0.07547171413898468,
0.021916551515460014,
0.05140870437026024,
-0.033699411898851395,
0.050387416034936905,
-0.0453924760222435,
0.052407532930374146,
-0.015271899290382862,
0.028754571452736855,
-0.007021151017397642,
0.04896740987896919,
0.05336882546544075,
-0.012210560031235218,
0.024298513308167458,
0.010307297110557556,
-0.026673048734664917,
0.00256266794167459,
-0.033394843339920044,
-0.019389338791370392,
-0.019236765801906586,
0.01383232418447733,
0.02101072669029236,
0.04972388595342636,
0.00268196570686996,
-0.01807994581758976,
0.03728420287370682,
-0.07871678471565247,
0.014613673090934753,
0.06023397296667099,
-0.030630260705947876,
-0.003112926846370101,
-0.031238604336977005,
-0.014724278822541237,
0.04704151675105095,
0.011195504106581211,
0.021953541785478592,
-0.010451317764818668,
-0.013621998019516468,
-0.013336422853171825,
-0.05889536067843437,
0.006018401123583317,
0.012255617417395115,
0.011260691098868847,
0.0511951819062233,
-0.04348047822713852,
-0.02038031443953514,
-0.011796293780207634,
-0.018421636894345284,
0.007395374588668346,
0.0013734219828620553,
-0.06104334071278572,
-0.03627265244722366,
-0.026409292593598366,
0.03654233366250992,
0.005786243826150894,
-0.012460999190807343,
-0.01814757101237774,
-0.010783144272863865,
-0.040513209998607635,
0.02400224842131138,
-0.027654100209474564,
0.04786349833011627,
0.010229860432446003,
0.0631033182144165,
-0.03718690574169159,
0.03493940457701683,
0.008119381032884121,
0.05971129983663559,
0.06283067911863327,
0.0043249973095953465,
-0.017388965934515,
-0.049844931811094284,
0.02833578921854496,
-0.03971711918711662,
-0.008180760778486729,
-0.014918388798832893,
0.0646122470498085,
0.08645014464855194,
-0.012483742088079453,
0.01802276447415352,
-0.002358432859182358,
-0.024582212790846825,
-0.00013660914555657655,
-0.018483037129044533,
-0.002926100976765156,
0.023948276415467262,
0.019522981718182564,
0.0028709545731544495,
-0.015415412373840809,
-0.005069719161838293,
-0.036248475313186646,
0.05823429301381111,
0.04385269805788994,
0.006096961908042431,
-0.0209346953779459,
-0.014916694723069668,
-0.011868647299706936,
-0.04762890934944153,
-0.0468178428709507,
0.01686299964785576,
-0.024167532101273537,
-0.0005456035141833127,
0.026852238923311234,
0.009025579318404198,
0.015821991488337517,
0.01421105582267046,
-0.0041178022511303425,
0.017478885129094124,
-0.013587532564997673,
0.036225832998752594,
0.04655488580465317,
0.04231719672679901,
0.015550936572253704,
0.05904300883412361,
0.050794824957847595,
-0.05561612546443939,
-0.06642787903547287,
-0.022930962964892387,
-0.007427677046507597,
0.019261343404650688,
-0.03932049497961998,
-0.048527635633945465,
0.013307943008840084,
0.03359222784638405,
0.007220889441668987,
-0.07505232840776443,
0.03274089843034744,
0.014106081798672676,
-0.02466190606355667,
-0.026040269061923027,
-0.024184145033359528,
-0.003896530717611313,
-0.005519380327314138,
0.058419812470674515,
-0.01442671474069357,
0.04358520731329918,
-0.031262561678886414,
0.004437467083334923,
-0.07442791014909744,
-0.004581016022711992,
0.042391322553157806,
0.025236431509256363,
-0.015201703645288944,
-0.012261468917131424,
0.07094895094633102,
0.013076779432594776,
0.032455042004585266,
-0.008675201795995235,
-0.04169667139649391,
-0.01568610593676567,
-0.0016247162129729986,
-0.055123500525951385,
0.04469704255461693,
-0.04287640005350113,
-0.031205013394355774,
-0.009714317508041859,
0.08493863046169281,
-0.03772382065653801,
0.021927447989583015,
0.023223066702485085,
-0.06088186055421829,
-0.013838347047567368,
-0.017255153506994247,
0.035608869045972824,
0.026662278920412064,
-0.0011936231749132276,
0.006611870601773262,
-0.019044654443860054,
0.0199199877679348,
0.023397931829094887,
-0.01196214184165001,
0.029482828453183174,
0.03410792350769043,
-0.013984535820782185,
-0.04488154500722885,
0.00026041167438961565,
0.03509068489074707,
-0.01264949794858694,
-0.002199275651946664,
0.019025014713406563,
-0.019833886995911598,
0.020738082006573677,
0.008854863233864307,
-0.007304982282221317,
0.006731268018484116,
-0.019024640321731567,
-0.03515133261680603,
-0.026083486154675484,
0.04891984537243843,
-0.0029171747155487537,
-0.025864925235509872,
0.041617944836616516,
0.02243747003376484,
0.03500422090291977,
-0.04916789382696152,
0.02676740474998951,
0.005540492944419384,
0.05224179849028587,
-0.05591137334704399,
0.03797610104084015,
0.0063390713185071945,
0.02562674880027771,
0.03664148226380348,
-0.03581271320581436,
0.051689356565475464,
-0.01995524950325489,
0.07705305516719818,
-0.03820224106311798,
0.0013740520225837827,
-0.026356086134910583,
0.058383602648973465,
-0.07711970061063766,
0.08068303763866425,
0.03126827999949455,
0.014273152686655521,
0.005372351035475731,
-0.025707315653562546,
0.024031514301896095,
0.06348685920238495,
-0.03938309848308563,
0.03062407858669758,
0.027395673096179962,
-0.006197878625243902,
-0.034046705812215805,
0.028138842433691025,
-0.09531994163990021,
0.006613452918827534,
0.014929723925888538,
0.052551671862602234,
-0.009019147604703903,
-0.06851251423358917,
-0.015354925766587257,
-0.07136550545692444,
0.010977145284414291,
-0.0039054243825376034,
0.01003951858729124,
0.02897750772535801,
-0.043257929384708405,
0.00810732040554285,
0.02147672511637211,
0.01158666517585516,
-0.002521510934457183,
-0.011821187101304531,
0.014364289119839668,
0.02043931744992733,
0.025360699743032455,
-0.032306037843227386,
-0.045582935214042664,
0.011442366987466812,
-0.035979609936475754,
0.03114246390759945,
0.0058896541595458984,
-0.022247735410928726,
0.010321957059204578,
-0.05655284970998764,
-0.08936551213264465,
-0.003849649103358388,
-0.03616918623447418,
0.014874192886054516,
0.010850725695490837,
-0.017186416313052177,
0.014690821059048176,
-0.03676458075642586,
-0.009416119195520878,
-0.021130837500095367,
-0.020817464217543602,
0.03995203599333763,
0.028028514236211777,
-0.007892909459769726,
0.023006882518529892,
0.032647039741277695,
0.027699926868081093,
-0.026817845180630684,
-0.05248379334807396,
-0.019447539001703262,
0.10724489390850067,
0.005644825752824545,
-0.006548143457621336,
-0.04812070354819298,
-0.05175395309925079,
-0.04134869948029518,
-0.010506965219974518,
0.021547866985201836,
-0.015182754956185818,
0.02729266881942749,
0.06595909595489502,
0.024650312960147858,
-0.014656721614301205,
0.022754516452550888,
-0.02745930664241314,
0.050879303365945816,
-0.014900989830493927,
0.047910094261169434,
-0.05142964422702789,
-0.03865114226937294,
-0.03704512119293213,
-0.015225359238684177,
0.0059737637639045715,
-0.029384054243564606,
-0.010973585769534111,
0.007881974801421165,
-0.029511457309126854,
-0.0010043287184089422,
-0.0778064951300621,
0.009226557798683643,
-0.03658000007271767,
0.06708847731351852,
0.014135856181383133,
0.015958430245518684,
0.024638546630740166,
0.034794606268405914,
-0.008406671695411205,
-0.041523534804582596,
0.02747783623635769,
-0.009261734783649445,
0.007720435503870249,
-0.02871629036962986,
0.03498009219765663,
-0.0005454401252791286,
0.034618645906448364,
-0.016461055725812912,
-0.03069491498172283,
0.034510884433984756,
-0.025506265461444855,
0.03535943478345871,
0.06475245952606201,
-0.0372220017015934,
-0.0059295822866261005,
-0.02753266878426075,
0.0194315854460001,
0.01654159277677536,
-0.0011448602890595794,
-0.0009796813828870654,
0.014835208654403687,
0.08252537995576859,
-0.02201569825410843,
0.00935392826795578,
-0.02305564470589161,
-0.02950385771691799
] |
<p>I've looked in and out the forum, and found no precise definition of the meaning of <a href="http://en.wikipedia.org/wiki/Fine-tuning" rel="nofollow">fine-tuning</a> in physics.</p>
<p><strong>QUESTION</strong></p>
<p>Is it possible to give a precise definition of fine-tuning?</p>
<p>Of course, I guess most of us understand the empirical meaning of the phrase... but it seem so ethereal, that's the reason behind my question.</p> | g4580 | [
0.018388066440820694,
0.05363998934626579,
-0.003256017342209816,
0.004694577306509018,
0.019608642905950546,
-0.025185637176036835,
0.04821661487221718,
0.022730208933353424,
0.005525333806872368,
-0.06598377227783203,
-0.03647351637482643,
0.009234958328306675,
0.04842368885874748,
0.0024176116567105055,
-0.018302666023373604,
0.020032214000821114,
0.08199635148048401,
0.04295971989631653,
0.103143610060215,
-0.010654551908373833,
0.012335573323071003,
0.010390304028987885,
0.016254283487796783,
-0.04361740127205849,
-0.01819860190153122,
-0.02067132666707039,
-0.0037499088793992996,
-0.07612613588571548,
-0.01916622743010521,
-0.018080269917845726,
0.0017475764034315944,
-0.013537361286580563,
0.00742154847830534,
0.024307699874043465,
0.01220385916531086,
-0.008073005825281143,
-0.0026187412440776825,
0.05775737389922142,
0.045204002410173416,
0.030393440276384354,
-0.027703190222382545,
0.011549338698387146,
0.011944811791181564,
-0.0662674605846405,
-0.02259749360382557,
-0.011212087236344814,
-0.007494975812733173,
-0.02914942055940628,
-0.010603209026157856,
-0.0431319922208786,
0.027952108532190323,
0.031944457441568375,
0.042287375777959824,
0.04089023917913437,
0.0754421055316925,
0.018103862181305885,
0.07404408603906631,
0.049526698887348175,
0.011260333471000195,
-0.006751113571226597,
-0.009200622327625751,
-0.014879729598760605,
0.024518607184290886,
0.011323942802846432,
0.048107538372278214,
0.006249043624848127,
-0.0077193924225866795,
-0.01949784904718399,
-0.012247392907738686,
-0.004579266998916864,
-0.009648467414081097,
-0.05590338259935379,
-0.030575459823012352,
-0.04727586358785629,
-0.04181109368801117,
-0.015801336616277695,
-0.033680371940135956,
-0.006497673224657774,
0.047418657690286636,
-0.023544805124402046,
-0.004111718852072954,
-0.0011843971442431211,
-0.052159424871206284,
0.04219656437635422,
0.03535454347729683,
0.014270012266933918,
-0.025376591831445694,
0.0039268918335437775,
0.07234836369752884,
0.05562334135174751,
0.04549575597047806,
0.02450043149292469,
0.009215306490659714,
-0.020867377519607544,
-0.003298909403383732,
-0.005958591587841511,
-0.06059717759490013,
0.06633403897285461,
0.005260678939521313,
0.028995299711823463,
-0.040627699345350266,
-0.020772410556674004,
-0.02559525892138481,
-0.017297083511948586,
0.010487416759133339,
0.02581731788814068,
-0.002595217665657401,
0.000739542709197849,
-0.03274038806557655,
-0.01734718680381775,
-0.023728830739855766,
0.0020226112101227045,
-0.025479210540652275,
-0.01115224789828062,
-0.03723369538784027,
-0.001564181293360889,
0.05672202259302139,
0.053255945444107056,
0.019423475489020348,
0.07220494747161865,
0.012762986123561859,
0.00683567114174366,
0.07946014404296875,
0.0874546617269516,
-0.04287854954600334,
-0.006410045083612204,
0.01562642864882946,
-0.021555688232183456,
-0.043983712792396545,
-0.015292433090507984,
0.009918393567204475,
-0.06455373018980026,
0.005032429005950689,
-0.04540512338280678,
0.010329197160899639,
0.013085804879665375,
0.028736170381307602,
0.029889069497585297,
0.02917066216468811,
0.022358078509569168,
0.01616254262626171,
-0.06871654093265533,
0.047697827219963074,
-0.05405846983194351,
0.0019400980090722442,
-0.008549897000193596,
-0.027416331693530083,
0.04285302385687828,
0.07545769214630127,
-0.013454235158860683,
0.004395945463329554,
0.020763734355568886,
0.025174455717206,
-0.06336542218923569,
-0.01164662092924118,
0.01598496176302433,
-0.006368805188685656,
0.013357508927583694,
0.010650969110429287,
0.024510053917765617,
0.004431205336004496,
0.009406154975295067,
-0.05311812832951546,
0.028035512194037437,
-0.041795890778303146,
0.0209735669195652,
-0.00907605979591608,
0.009696662425994873,
-0.027722258120775223,
-0.023080648854374886,
-0.06646575033664703,
-0.028341496363282204,
0.05285970866680145,
0.00030542287277057767,
0.0492466539144516,
0.08134371042251587,
0.06727280467748642,
-0.005236777476966381,
-0.009575274772942066,
0.0040166317485272884,
-0.03935299813747406,
0.0027448057662695646,
-0.0077192955650389194,
-0.005788357928395271,
-0.017337245866656303,
-0.0013466833624988794,
0.016659419983625412,
-0.048808980733156204,
-0.03748096898198128,
-0.0005449809250421822,
-0.022840600460767746,
-0.004614074248820543,
-0.014272782951593399,
0.045118000358343124,
0.01448926143348217,
-0.04023096710443497,
-0.0408051572740078,
-0.07086002826690674,
-0.003761579282581806,
-0.006032486911863089,
-0.015798749402165413,
-0.01694646291434765,
0.045300085097551346,
0.009497489780187607,
-0.027749234810471535,
-0.007828217931091785,
-0.018540456891059875,
-0.030394116416573524,
-0.015744077041745186,
0.03464241325855255,
0.03360463306307793,
0.03598899766802788,
0.02756856195628643,
0.03143838420510292,
-0.01884506642818451,
-0.04242583364248276,
0.008627783507108688,
-0.05155089497566223,
-0.02820640802383423,
0.02836490049958229,
-0.0007204641005955637,
-0.0052788350731134415,
0.00036595945130102336,
0.03503875061869621,
-0.011223753914237022,
-0.02499711513519287,
0.0014685369096696377,
-0.000807900563813746,
-0.0021656916942447424,
-0.008324902504682541,
-0.00407892931252718,
-0.040282245725393295,
-0.02831404097378254,
-0.0039483970031142235,
0.04854099079966545,
0.02393098920583725,
-0.018782388418912888,
-0.0019342843443155289,
-0.003611762775108218,
0.06995103508234024,
0.002271931618452072,
-0.08011816442012787,
-0.04074353724718094,
-0.04821857064962387,
-0.010000742971897125,
0.004202798940241337,
0.04233842343091965,
-0.010307773016393185,
-0.010819658637046814,
-0.04440870136022568,
0.007650881540030241,
-0.013529025949537754,
0.02840239740908146,
-0.004780232440680265,
0.009808128699660301,
-0.0041768597438931465,
-0.04366958141326904,
0.028824592009186745,
-0.022195808589458466,
0.03706212341785431,
0.020832352340221405,
-0.025036582723259926,
0.019093092530965805,
-0.07930267602205276,
-0.006292793434113264,
-0.019976336508989334,
-0.035636916756629944,
-0.01898046024143696,
-0.015214337967336178,
0.003975133877247572,
-0.0012798439711332321,
-0.007257690187543631,
0.025465069338679314,
0.034585241228342056,
-0.06815081834793091,
0.04014916345477104,
-0.03838467225432396,
-0.005037164315581322,
0.051131412386894226,
0.0013704008888453245,
-0.03614905849099159,
0.0340939462184906,
-0.03472086787223816,
0.025727178901433945,
-0.0004789591475855559,
0.004848208278417587,
-0.0006833127699792385,
0.015146847814321518,
-0.0214084405452013,
0.04319155216217041,
-0.026011109352111816,
-0.059309206902980804,
0.06220056116580963,
0.036258358508348465,
-0.06892108917236328,
0.04148252680897713,
0.05019101873040199,
-0.009300719946622849,
-0.0027370061725378036,
0.0644276961684227,
0.01966925524175167,
0.025049183517694473,
0.005735362879931927,
0.022537454962730408,
0.03159056231379509,
0.04755505174398422,
0.01105966605246067,
-0.07711576670408249,
-0.0134739326313138,
0.05841612070798874,
-0.02297423779964447,
0.032618358731269836,
0.013678253628313541,
0.027113527059555054,
-0.047463539987802505,
0.01129709929227829,
-0.018992843106389046,
0.05285648629069328,
0.05223070830106735,
-0.07030299305915833,
0.024767247959971428,
-0.033781830221414566,
0.026195866987109184,
-0.00024878355907276273,
0.015162201598286629,
-0.02619306370615959,
-0.03563208132982254,
-0.05546048656105995,
-0.025625748559832573,
-0.0687638446688652,
0.04587600752711296,
-0.006265765521675348,
-0.06527506560087204,
-0.01801973581314087,
-0.051337629556655884,
0.014514042064547539,
-0.010905672796070576,
0.007891573943197727,
0.06781050562858582,
0.0074792709201574326,
-0.02715209685266018,
-0.07413017004728317,
-0.013175311498343945,
-0.025768078863620758,
-0.023810725659132004,
0.07750670611858368,
-0.03366824612021446,
-0.010482316836714745,
0.043046895414590836,
0.008294595405459404,
0.056003767997026443,
0.011323664337396622,
-0.06332685798406601,
-0.050083696842193604,
-0.027374759316444397,
-0.030216822400689125,
0.03955455124378204,
-0.02277924120426178,
-0.03168555721640587,
-0.015460452996194363,
0.007574161980301142,
0.0009443386225029826,
0.019655270501971245,
0.00034846627386286855,
-0.054917577654123306,
0.04115913435816765,
-0.029675927013158798,
0.06997138261795044,
-0.028052471578121185,
0.0009688215795904398,
-0.04355103522539139,
-0.030513718724250793,
-0.044719256460666656,
0.08723824471235275,
-0.04660054296255112,
-0.0177015233784914,
0.029232719913125038,
0.031409598886966705,
-0.0893457755446434,
0.009215065278112888,
0.04414231330156326,
0.06683100014925003,
0.00007986166019691154,
-0.0009004949824884534,
0.046896882355213165,
-0.029104359447956085,
-0.011364972218871117,
-0.06818422675132751,
0.03544871509075165,
0.03560217469930649,
0.02424841932952404,
-0.02127681113779545,
-0.03693360462784767,
0.02895188331604004,
0.021937085315585136,
-0.04432728886604309,
0.03483228385448456,
-0.020105881616473198,
-0.043084774166345596,
0.09012839943170547,
0.0137924924492836,
0.0029633285012096167,
-0.010543694719672203,
0.012968778610229492,
-0.015120431780815125,
-0.01610802300274372,
0.000578513543587178,
-0.011339790187776089,
-0.013631260953843594,
-0.03592250496149063,
-0.012159186415374279,
-0.0481664203107357,
0.009538127109408379,
-0.03367943316698074,
-0.0030275778844952583,
0.030958514660596848,
-0.007710687816143036,
-0.02718040719628334,
0.010897273197770119,
0.009149022400379181,
0.0073712351731956005,
0.02995913103222847,
0.018041394650936127,
-0.022699523717164993,
-0.03806481882929802,
0.011487280949950218,
-0.013632488436996937,
0.04379305988550186,
0.03533579409122467,
-0.031157832592725754,
0.008897049352526665,
0.0042978147976100445,
0.02018580213189125,
0.03906137868762016,
-0.028897222131490707,
-0.013828275725245476,
-0.025598688051104546,
0.003953251522034407,
0.014632177539169788,
0.03887204825878143,
0.009174101054668427,
0.012331495992839336,
-0.01619577407836914,
0.010569924488663673,
-0.02916686236858368,
0.030895739793777466,
-0.0358307771384716,
0.03177078813314438,
0.005833457689732313,
-0.02765050157904625,
-0.05182889848947525,
0.026303056627511978,
-0.0009052374516613781,
0.027589276432991028,
-0.012668302282691002,
0.010831437073647976,
0.008897433988749981,
-0.03905271738767624,
0.009931420907378197,
0.0010610894532874227,
-0.05107388645410538,
-0.041496433317661285,
0.02069324254989624,
0.025011494755744934,
0.0010106745176017284,
0.011271441355347633,
0.004643036052584648,
-0.10201765596866608,
-0.09560924768447876,
-0.024083608761429787,
-0.024052726104855537,
-0.014686428010463715,
0.051802199333906174,
0.06806504726409912,
0.006740916054695845,
-0.028450967743992805,
0.05053063482046127,
0.010766662657260895,
-0.05223404988646507,
0.015365907922387123,
-0.006965077482163906,
-0.013216366991400719,
0.08176196366548538,
-0.019666170701384544,
0.02369590662419796,
-0.011610899120569229,
-0.04773682728409767,
0.027901222929358482,
-0.008268864825367928,
0.027709033340215683,
0.03047637827694416,
0.02749086730182171,
0.02860204502940178,
-0.019948692992329597,
-0.011900672689080238,
-0.0486677922308445,
0.005101436283439398,
0.007781758438795805,
0.00041553896153345704,
-0.019429363310337067,
-0.02720021829009056,
0.021245617419481277,
-0.00039950618520379066,
0.030100369825959206,
-0.014041995629668236,
0.0472671240568161,
0.027271313592791557,
-0.07706797868013382,
-0.010265246964991093,
0.021858181804418564,
-0.030205613002181053,
0.024805285036563873,
-0.01200088206678629,
-0.05974508449435234,
0.050655923783779144,
0.01740272156894207,
0.028509212657809258,
0.026357699185609818,
-0.023154374212026596,
-0.03469764441251755,
0.01925918646156788,
0.05789811164140701,
-0.03588082641363144,
-0.014470924623310566,
-0.010577980428934097,
-0.06364921480417252,
-0.034774765372276306,
0.0408867709338665,
0.008198653347790241,
0.05230921134352684,
0.01362787839025259,
0.08298066258430481,
0.006341830361634493,
0.021209675818681717,
0.04690517485141754,
-0.0393192283809185,
0.028721505776047707,
-0.027454329654574394,
-0.10727895051240921,
0.009773166850209236,
-0.018668295815587044,
0.0904294103384018,
-0.022134141996502876,
0.06459181755781174,
0.0382680706679821,
-0.025559749454259872,
-0.029708631336688995,
0.011882159858942032,
0.06436609476804733,
-0.0005297261523082852,
-0.030424660071730614,
-0.06991530954837799,
-0.05019048601388931,
-0.030188651755452156,
0.006507941987365484,
0.07298001646995544,
-0.00025396261480636895,
-0.062211327254772186,
0.02968617156147957,
-0.05998694896697998,
-0.021813781931996346,
0.008116651326417923,
-0.0230302382260561,
0.04490625858306885,
-0.010030888020992279,
-0.029875554144382477,
-0.06407530605792999,
-0.05437062680721283,
0.025079062208533287,
0.05004869028925896,
-0.029968803748488426,
0.012881002388894558,
0.01655495911836624,
-0.010497279465198517,
0.019080746918916702,
0.004661775194108486,
-0.09733794629573822,
0.02651919610798359,
-0.03255176544189453,
-0.0467289574444294,
0.01705971173942089,
-0.002594855148345232,
0.08868485689163208,
-0.021753497421741486,
-0.03520597890019417,
0.010469341650605202,
-0.02911541983485222,
0.045530810952186584,
0.010630280710756779,
0.011739498004317284,
-0.03760132938623428,
0.011765955947339535,
-0.04735506698489189,
0.05028668791055679,
-0.04286180064082146,
0.0025774084497243166,
-0.022973427549004555,
-0.0019824723713099957,
-0.06303949654102325,
0.0785539299249649,
-0.007291895337402821,
-0.02403159625828266,
-0.013692162930965424,
0.05573727935552597,
-0.0015594179276376963,
0.03092464990913868,
0.013266081921756268,
0.06239115074276924,
-0.06994671374559402,
0.025099659338593483,
-0.03370260074734688,
0.03485185652971268,
0.04184254631400108,
-0.012799374759197235,
-0.11747754365205765,
-0.03811381384730339,
0.012378932908177376,
-0.021321846172213554,
-0.044468626379966736,
0.0038271250668913126,
0.05154286324977875,
-0.028614871203899384,
0.013975902460515499,
-0.00965814758092165,
-0.004510580096393824,
0.05705924704670906,
-0.014110992662608624,
0.0010790126398205757,
0.049480803310871124,
-0.06042666733264923,
-0.012904824689030647,
-0.00860466156154871,
-0.01683657430112362,
-0.005094039253890514,
-0.021273603662848473,
0.062179699540138245,
-0.06670023500919342,
-0.009100117720663548,
0.04915517568588257,
0.006874856539070606,
-0.050823505967855453,
0.07835830003023148,
0.06469038873910904,
-0.019135206937789917,
-0.05962859094142914,
-0.04401520639657974,
-0.0071034664288163185,
-0.016606895253062248,
-0.016743073239922523,
0.01394811924546957,
0.049161866307258606,
-0.015244750306010246,
-0.04632535204291344,
0.03411472961306572,
0.0382593534886837,
0.0782063826918602,
-0.013900788500905037,
0.0977015495300293,
-0.011420599184930325,
-0.06618169695138931,
-0.032484009861946106,
0.0536920540034771,
0.037399593740701675,
0.0007561469683423638,
-0.016273874789476395,
0.05590160936117172,
-0.03863741457462311,
-0.05525427684187889,
-0.03139875456690788,
-0.023251973092556,
0.05015871301293373,
0.004737615119665861,
0.011691788211464882,
-0.004997132811695337,
0.06490898132324219,
-0.046711329370737076,
-0.015217830426990986,
0.08044364303350449,
0.0017458308720961213,
-0.014276335015892982,
0.05960133299231529,
0.003944140858948231,
0.0070086028426885605,
-0.0008948899921961129,
-0.08869045972824097,
0.017467239871621132,
-0.018510404974222183,
0.014326049946248531,
0.0008632823592051864,
-0.00450156582519412,
-0.01955001801252365,
0.025782035663723946,
-0.03993827477097511,
-0.028890429064631462,
-0.04049372673034668,
0.008093519136309624,
0.03522162511944771,
-0.012661777436733246,
0.024841781705617905,
-0.013042690232396126,
0.024392392486333847,
0.04721786081790924,
-0.035044115036726,
0.04095081612467766,
0.030553361400961876,
0.021073609590530396,
-0.04601719602942467,
-0.01757175289094448,
-0.00869398657232523,
-0.0035199117846786976,
-0.016192134469747543,
-0.011042198166251183,
0.02538757584989071,
0.02426336333155632,
0.043572064489126205,
0.005363802891224623,
0.05752469226717949,
-0.07184834033250809,
-0.06515827775001526,
0.04620073363184929,
-0.029002217575907707,
0.006318225525319576,
0.048651356250047684,
0.01751522533595562,
-0.03644338995218277,
0.028981462121009827,
-0.02362636663019657,
0.013148104771971703,
-0.027478182688355446,
0.027407946065068245,
-0.014076663181185722,
-0.0041832756251096725,
0.04706624895334244,
0.05962153524160385,
-0.03620836138725281,
-0.0053305248729884624,
0.019798683002591133,
0.06423401832580566,
0.006098979152739048,
0.020865466445684433,
-0.0022035965230315924,
-0.011133645661175251,
-0.025596145540475845,
-0.004884935449808836,
0.024410583078861237,
-0.008935920894145966,
0.015444457530975342,
0.04850056394934654,
-0.026858782395720482,
-0.061587583273649216,
-0.029547380283474922,
0.0636858344078064,
-0.03615279123187065,
0.03125934302806854,
0.03997522220015526,
-0.029980311170220375,
0.019805345684289932,
0.008968609385192394,
0.038237400352954865,
0.010938282124698162,
-0.014678220264613628,
0.024409055709838867,
-0.011887898668646812,
-0.025442976504564285,
-0.03356190025806427,
-0.06685919314622879,
0.004047361668199301,
0.010288487188518047
] |
<p>I've come across a problem with finding the energy stored in time/frequency electric field. In space/time we have (taking $\epsilon = 1$)</p>
<p>$$ Energy = \frac{1}{2} \int_V |\mathbf{E}(\mathbf{x},t)|^2 \;d^3x $$ </p>
<p>But, I presume that the formula is different for a frequency-dependent electric field. I've searched Griffiths and Jackson but can't quite find what I'm looking for...</p>
<p>I've also tried to Fourier transform my expression for the electric field back to space/time, but my electric field is a fairly gruesome expression - I couldn't FT it easily. I was hoping to compute the energy from $E(\mathbf{x},\omega)$ via computational integral, once I find an expression for the energy.</p> | g4581 | [
0.05416165292263031,
0.04211493209004402,
-0.038515422493219376,
-0.05593204125761986,
0.001627594232559204,
-0.04909084737300873,
0.010228263214230537,
0.023662181571125984,
-0.07326975464820862,
0.0015338461380451918,
-0.0011325943050906062,
0.0152104701846838,
0.0020970057230442762,
-0.029433157294988632,
-0.04573795944452286,
0.04572462663054466,
0.060165099799633026,
0.052156731486320496,
-0.051432039588689804,
-0.0018304572440683842,
-0.023152900859713554,
-0.010703624226152897,
0.023569345474243164,
-0.011813132092356682,
0.030683275312185287,
-0.019325071945786476,
0.08760536462068558,
-0.017437346279621124,
-0.022610481828451157,
-0.08436496555805206,
-0.02474689856171608,
0.042725782841444016,
0.0454632043838501,
0.01167675293982029,
-0.05160112679004669,
-0.01973382569849491,
0.008702035062015057,
-0.005627584643661976,
0.0652301087975502,
0.014936826191842556,
-0.001214593998156488,
-0.006346102803945541,
-0.0088470708578825,
0.04818182438611984,
-0.02166125550866127,
-0.024069173261523247,
-0.04137705639004707,
0.01881486549973488,
-0.023645665496587753,
0.002427811501547694,
-0.010240936651825905,
0.04971816763281822,
0.06189734861254692,
-0.024450410157442093,
-0.0035636359825730324,
-0.03971574455499649,
0.04991646483540535,
-0.014645086601376534,
0.019987650215625763,
0.006288993638008833,
0.010512413457036018,
-0.07805079221725464,
-0.03219237178564072,
-0.000967527914326638,
0.020277297124266624,
-0.03404027968645096,
-0.009679809212684631,
-0.0011569735361263156,
-0.029492147266864777,
-0.026946768164634705,
-0.011143703013658524,
-0.0013540990184992552,
0.01323031447827816,
-0.012177500873804092,
0.0011758505133911967,
0.01362407673150301,
0.04718048870563507,
-0.003911315929144621,
-0.01977447234094143,
-0.018256815150380135,
-0.006134734023362398,
0.033979080617427826,
-0.017294885590672493,
-0.003902006195858121,
-0.010808693245053291,
-0.05969323590397835,
-0.006659179460257292,
0.04156815633177757,
0.04441789910197258,
-0.003945855889469385,
-0.04376787319779396,
0.05584750324487686,
0.0649070292711258,
-0.044794369488954544,
0.019830888137221336,
-0.010977028869092464,
-0.02265104651451111,
0.03987903147935867,
-0.02629006654024124,
-0.030593134462833405,
0.014831079170107841,
-0.062257908284664154,
0.02586267702281475,
-0.014559410512447357,
-0.007143077440559864,
-0.04569071903824806,
0.0036651832051575184,
-0.019482707604765892,
-0.03736221417784691,
-0.021143000572919846,
-0.008082998916506767,
-0.029829325154423714,
-0.017034895718097687,
-0.03930574283003807,
-0.04451235011219978,
0.0005401282687671483,
0.01567121408879757,
-0.05860816687345505,
-0.018368853256106377,
0.018259722739458084,
-0.030024453997612,
-0.022917939350008965,
0.05406992509961128,
0.04332185909152031,
-0.028329432010650635,
0.03376005217432976,
-0.0006423271261155605,
0.036094047129154205,
-0.008691840805113316,
-0.01470342930406332,
-0.004477058071643114,
-0.00729003269225359,
0.03701135143637657,
-0.006802860647439957,
-0.015093524008989334,
0.047689348459243774,
-0.049499429762363434,
0.02107151411473751,
0.006208212114870548,
0.02002168633043766,
-0.013431424275040627,
-0.023486388847231865,
0.009666507132351398,
-0.004699359182268381,
-0.04584428668022156,
0.044529810547828674,
-0.07374601811170578,
-0.14123551547527313,
0.049005020409822464,
0.01604229211807251,
0.02263787016272545,
0.07204549759626389,
-0.033987950533628464,
-0.035737358033657074,
0.037386175245046616,
-0.015575317665934563,
0.022234993055462837,
0.013287504203617573,
-0.025200065225362778,
0.0035993147175759077,
0.06518743932247162,
0.058043234050273895,
0.029221834614872932,
-0.027423005551099777,
0.0068637654185295105,
-0.0040476503781974316,
0.010599611327052116,
-0.04803550988435745,
-0.015470098704099655,
-0.06821368634700775,
-0.037187445908784866,
0.0024388229940086603,
0.041520047932863235,
-0.003668497782200575,
-0.0008386921836063266,
0.08077769726514816,
-0.010314134880900383,
-0.037904150784015656,
-0.014194880612194538,
-0.011849002912640572,
0.013723966665565968,
-0.016270475462079048,
0.0338909849524498,
-0.02255816012620926,
0.048005666583776474,
-0.016475794836878777,
-0.00041916617192327976,
0.008535830304026604,
-0.06616729497909546,
0.03562282398343086,
0.0031991656869649887,
0.061474286019802094,
0.02205875888466835,
0.04664856195449829,
-0.00556535180658102,
0.06392417848110199,
-0.02487253211438656,
-0.07873043417930603,
-0.028183579444885254,
0.005530481692403555,
0.032629817724227905,
-0.0017656791023910046,
0.10277369618415833,
0.029780268669128418,
0.06707032024860382,
0.016133703291416168,
-0.001807530876249075,
-0.06329290568828583,
0.0081650884822011,
-0.01762736216187477,
-0.016100766137242317,
-0.03613099455833435,
-0.02223300375044346,
0.06205255910754204,
0.06725619733333588,
-0.0034457470756024122,
-0.042664963752031326,
-0.020152119919657707,
-0.034231431782245636,
-0.0017441506497561932,
-0.04504711925983429,
-0.014633589424192905,
0.07162253558635712,
-0.021397318691015244,
-0.017038708552718163,
-0.006178090814501047,
-0.015019578859210014,
-0.057634033262729645,
-0.08765971660614014,
0.014205383136868477,
-0.04097607359290123,
0.04164343699812889,
-0.027292976155877113,
-0.04983541741967201,
0.04997725412249565,
0.008594131097197533,
-0.04020419716835022,
-0.020606590434908867,
0.03876914456486702,
0.028177063912153244,
-0.01639513112604618,
0.01134115643799305,
0.044666267931461334,
-0.012891728430986404,
-0.0012202708749100566,
-0.023494314402341843,
0.06917553395032883,
0.017567336559295654,
0.013553514145314693,
-0.010152553208172321,
0.0017152565997093916,
-0.010885055176913738,
-0.06653933227062225,
0.004670746624469757,
-0.03316885605454445,
-0.008337251842021942,
-0.013441650196909904,
0.029962074011564255,
-0.037455298006534576,
-0.04921978339552879,
-0.02946864254772663,
-0.022918764501810074,
0.008149019442498684,
0.05945373699069023,
-0.0032773283310234547,
-0.020582349970936775,
-0.0049676899798214436,
0.02748049981892109,
0.015344429761171341,
-0.020010946318507195,
-0.011761958710849285,
0.04026038944721222,
0.019467521458864212,
-0.017809422686696053,
0.06598450243473053,
-0.09808466583490372,
-0.006605631206184626,
-0.04836361110210419,
0.05188414454460144,
-0.02023947797715664,
-0.020662562921643257,
-0.052012816071510315,
0.009530778974294662,
0.0826060026884079,
-0.03736719861626625,
-0.03782636299729347,
0.0299653522670269,
0.012400610372424126,
-0.0018361103720963001,
-0.00846140831708908,
0.0012557973386719823,
0.005693566519767046,
-0.03377116844058037,
-0.04196426272392273,
-0.05903596431016922,
0.03625209629535675,
0.025071633979678154,
-0.029961062595248222,
0.030417155474424362,
0.054448992013931274,
0.03316420316696167,
0.0036130540538579226,
0.03405364975333214,
0.007702197413891554,
0.009922454133629799,
-0.005877085495740175,
-0.0486392080783844,
-0.03828851878643036,
0.03985362872481346,
-0.010125523433089256,
0.002171768806874752,
0.010213848203420639,
0.03999275714159012,
-0.016116824001073837,
-0.08940336108207703,
0.026679715141654015,
0.0024921901058405638,
-0.07767607271671295,
0.0018375087529420853,
-0.02559341862797737,
-0.017073294147849083,
-0.024491678923368454,
0.016244618222117424,
-0.024484140798449516,
-0.002131030196323991,
0.048098813742399216,
-0.03876715525984764,
0.0031655204948037863,
-0.03333105146884918,
-0.01917770877480507,
-0.033369459211826324,
-0.024490797892212868,
0.043618008494377136,
-0.020316865295171738,
0.015776680782437325,
-0.0016502063954249024,
-0.061928294599056244,
0.03129925578832626,
0.006977192126214504,
-0.028483746573328972,
0.0044438899494707584,
0.033600762486457825,
-0.03562946245074272,
-0.011976671405136585,
-0.010603235103189945,
-0.014635070227086544,
-0.022833559662103653,
0.026585306972265244,
0.007861096411943436,
-0.005654696375131607,
-0.03848716616630554,
-0.04421220347285271,
0.027804691344499588,
0.007615826558321714,
-0.0004136840580031276,
0.017657823860645294,
0.007444343995302916,
0.025513963773846626,
0.0212421752512455,
0.007740802131593227,
-0.008331154473125935,
-0.061942726373672485,
0.030436107888817787,
-0.03193723410367966,
-0.02370871789753437,
-0.07035215944051743,
-0.013816106133162975,
0.0371704064309597,
-0.030039047822356224,
-0.009168695658445358,
0.027198631316423416,
0.004441832657903433,
0.06174468994140625,
0.019756903871893883,
-0.027702491730451584,
-0.09774821251630783,
-0.013059165328741074,
0.0021759162191301584,
-0.016808535903692245,
0.022847652435302734,
0.001232284470461309,
-0.012665877118706703,
0.05019387602806091,
0.01830533891916275,
0.046163756400346756,
-0.022583626210689545,
0.00032080902019515634,
0.04531322792172432,
0.0004481594078242779,
0.01668749563395977,
0.009717007167637348,
-0.025823460891842842,
-0.008706335909664631,
0.015734698623418808,
-0.0231479462236166,
-0.05321091413497925,
0.03980327025055885,
-0.02861417829990387,
-0.04086390510201454,
0.010920947417616844,
0.11015781760215759,
-0.022969501093029976,
0.009832869283854961,
0.005965107586234808,
-0.009735483676195145,
0.019785074517130852,
0.08419244736433029,
-0.07739084213972092,
-0.009463601745665073,
-0.039303991943597794,
-0.03689032047986984,
-0.06738421320915222,
0.04813283681869507,
-0.06807689368724823,
-0.04693112149834633,
0.014811038039624691,
0.03348538652062416,
-0.03733593225479126,
0.09324730932712555,
-0.005808705929666758,
0.0024440251290798187,
0.017905408516526222,
-0.009799551218748093,
-0.01721540279686451,
-0.02042095549404621,
0.06389615684747696,
0.05910699442028999,
0.011748780496418476,
-0.02760719321668148,
0.038468845188617706,
0.012636067345738411,
0.04277649521827698,
-0.04371509701013565,
0.004449770320206881,
-0.07194556295871735,
0.03790386766195297,
-0.016151612624526024,
0.00806983932852745,
0.013462758623063564,
0.025261199101805687,
0.09603975713253021,
-0.02381649985909462,
0.0026538160163909197,
-0.00699639692902565,
-0.03229057416319847,
0.04332667961716652,
-0.057069264352321625,
-0.06398560106754303,
0.02691693976521492,
0.00124658877030015,
0.037761587649583817,
0.05142786353826523,
0.006080779246985912,
-0.004189244005829096,
0.02435184083878994,
-0.013086535967886448,
-0.041130468249320984,
-0.001860083662904799,
0.05918261781334877,
0.027178075164556503,
-0.054882168769836426,
-0.0007803362677805126,
-0.05583313852548599,
0.02998683601617813,
0.057252004742622375,
0.01792415976524353,
-0.043714672327041626,
-0.03857661411166191,
0.012759890407323837,
-0.007186913397163153,
0.057642560452222824,
-0.009766287170350552,
0.004308315459638834,
-0.019798099994659424,
0.027612337842583656,
0.004233716521412134,
0.01070413738489151,
-0.04443908482789993,
-0.018625352531671524,
-0.045966893434524536,
-0.014548377133905888,
-0.04027869179844856,
0.015444457530975342,
0.06835339963436127,
-0.018357379361987114,
0.012554332613945007,
-0.02476949617266655,
0.033489130437374115,
0.024765409529209137,
-0.015244707465171814,
0.01570437103509903,
0.07890596240758896,
0.03621036931872368,
-0.04489550366997719,
0.02220950461924076,
0.02541661448776722,
-0.005161608569324017,
0.012760613113641739,
-0.020548228174448013,
0.00292736804112792,
-0.004521071445196867,
0.04001124948263168,
-0.0803905501961708,
-0.010280424728989601,
0.021028758957982063,
0.041190989315509796,
0.04838385060429573,
0.0573597215116024,
-0.03891228139400482,
0.02257607877254486,
0.015572930686175823,
-0.012478108517825603,
0.03295948728919029,
0.02753240428864956,
0.04673469066619873,
-0.03314526751637459,
-0.009050766006112099,
-0.005257098004221916,
0.020236587151885033,
-0.049350012093782425,
0.031147850677371025,
0.02724476344883442,
0.021343881264328957,
-0.022083912044763565,
0.05048195272684097,
0.0473976656794548,
-0.03719170764088631,
-0.07721728086471558,
-0.0030733414459973574,
0.0078038666397333145,
-0.02087664231657982,
-0.00737728551030159,
-0.055018264800310135,
-0.03804919868707657,
0.021501844748854637,
0.003851398127153516,
-0.03111322782933712,
-0.044845256954431534,
0.001721670269034803,
0.01862499676644802,
-0.008435873314738274,
-0.007608039304614067,
0.004884358029812574,
-0.05472623556852341,
-0.051829829812049866,
0.01396667305380106,
0.02484169229865074,
-0.056643690913915634,
0.03911383077502251,
0.0034104487858712673,
0.05374353006482124,
-0.025856776162981987,
0.004474332090467215,
-0.058828774839639664,
0.04374202340841293,
0.039564330130815506,
0.03166267275810242,
-0.008406016044318676,
-0.0558200404047966,
0.0016943361843004823,
-0.004841503221541643,
-0.01807061955332756,
0.010210330598056316,
-0.010848511010408401,
0.05565675348043442,
0.00313235423527658,
0.07629024982452393,
0.022955017164349556,
0.028359107673168182,
0.00007019854092504829,
0.042928751558065414,
0.016331445425748825,
-0.0029535130597651005,
0.000912421615794301,
0.0375080443918705,
-0.0031809434294700623,
-0.014193128794431686,
-0.04509761929512024,
-0.014749933034181595,
-0.016120294108986855,
0.020782992243766785,
-0.03657257556915283,
0.0316583625972271,
-0.002256502863019705,
-0.011013070121407509,
0.015699146315455437,
-0.02205963246524334,
-0.06066134199500084,
0.06946276873350143,
-0.03749225288629532,
-0.0016443103086203337,
0.015002409927546978,
0.026284482330083847,
0.013002948835492134,
0.002660823054611683,
-0.02365829236805439,
0.016873976215720177,
0.0012600707123056054,
0.04645989462733269,
0.06090643256902695,
-0.010689636692404747,
0.006488346029073,
0.022213157266378403,
-0.05013950169086456,
0.05377865210175514,
0.022427139803767204,
-0.0008736693416722119,
0.005641469731926918,
-0.005682447925209999,
0.0069858618080616,
0.0022449304815381765,
-0.016692200675606728,
0.024059252813458443,
-0.006972407456487417,
-0.06153039634227753,
-0.018589889630675316,
0.04111003503203392,
0.037036068737506866,
0.016960205510258675,
0.021237164735794067,
0.04974433407187462,
-0.002334123943001032,
-0.05246008187532425,
-0.005386390257626772,
0.03445613384246826,
0.030031265690922737,
-0.04318609833717346,
0.013223882764577866,
0.03142299875617027,
-0.06843072175979614,
0.039647769182920456,
0.027855828404426575,
-0.023496506735682487,
0.05175398290157318,
0.01861298643052578,
-0.03256184980273247,
-0.0144776850938797,
0.03585680574178696,
-0.03659011423587799,
0.04564381018280983,
-0.05653582885861397,
0.042181700468063354,
0.03254518285393715,
0.005820669699460268,
-0.04282163828611374,
-0.017575327306985855,
0.016982663422822952,
0.015097918920218945,
-0.02745787799358368,
0.021506085991859436,
0.06559089571237564,
0.005469811614602804,
-0.003527768887579441,
-0.030933398753404617,
-0.044906582683324814,
-0.009916040115058422,
0.005561535246670246,
-0.01912914216518402,
0.02741009183228016,
-0.04480389505624771,
0.023524999618530273,
-0.044423192739486694,
-0.049024637788534164,
0.04254288971424103,
0.008656607940793037,
0.04735086113214493,
0.041899897158145905,
-0.027139244601130486,
0.06370382755994797,
-0.050976626574993134,
0.01791091449558735,
-0.03137938678264618,
-0.013226713985204697,
-0.0035980839747935534,
-0.05805549398064613,
-0.01830301433801651,
-0.0024653743021190166,
0.0813635066151619,
-0.06249804422259331,
-0.002740683499723673,
-0.05159467086195946,
-0.004334343131631613,
-0.06654438376426697,
0.007138258311897516,
0.025508899241685867,
0.040776871144771576,
-0.05101862549781799,
-0.01292884349822998,
0.011418763548135757,
0.07992012798786163,
-0.04437852278351784,
0.04264974594116211,
0.004162597004324198,
-0.006903181783854961,
-0.007128937169909477,
-0.048427764326334,
0.051377542316913605,
0.01974157989025116,
0.0730515569448471,
0.03422359377145767,
0.013369922526180744,
-0.052948959171772,
0.037861019372940063,
-0.006728651933372021,
-0.029148995876312256,
0.002910635666921735,
-0.005454014986753464,
-0.03368619456887245,
-0.03450412675738335,
0.05211656913161278,
0.03844809904694557,
0.005630859639495611,
0.029583292081952095,
0.04095464572310448,
0.09186852723360062,
-0.026839951053261757,
-0.0254665557295084,
0.0429222546517849,
0.006850717589259148,
-0.02103743888437748,
-0.01713826321065426,
-0.011114506050944328,
-0.03302547335624695,
-0.0018200203776359558,
0.06767260283231735,
0.022513968870043755,
-0.08795251697301865,
-0.017804592847824097,
0.10617749392986298,
-0.03621247783303261,
-0.0025568464770913124,
-0.0008756110910326242,
0.002901501953601837,
-0.015149378217756748,
0.031944818794727325,
0.005211646668612957,
0.021590590476989746,
-0.0254267118871212,
0.020508719608187675,
0.024492500349879265,
0.05085255205631256,
-0.014418627135455608,
-0.026284435763955116,
-0.023657696321606636,
-0.006409324239939451,
-0.011568277142941952,
-0.06416898965835571,
0.006299667526036501,
0.06396813690662384,
-0.027898328378796577,
0.041792016476392746,
-0.043707750737667084,
-0.059764571487903595,
0.027178235352039337,
0.06221408769488335,
-0.04545871913433075,
0.02684957906603813,
-0.01879946142435074,
0.04431767016649246,
0.020964378491044044,
-0.008344450034201145,
0.006563310511410236,
-0.022996840998530388,
0.03136688843369484,
0.022508390247821808,
-0.07132332026958466,
0.060818396508693695,
0.05519996955990791
] |
<p>I was watching a youtube video the other day where an economist said that he challenged his physics professor on this question back when he was in school. His professor said each scenario is the same, while he said that they are different, and he said he supplied a proof showing otherwise.</p>
<p>He didn't say whether or not the cars are the same mass, but I assumed they were. To state it more clearly, in the first instance each car is traveling at 50mph in the opposite direction and they collide with each other. In the second scenario, a car travels at 100 mph and crashes into a brick wall. Which one is "worse"?</p>
<p>When I first heard it, I thought, "of course they're the same!" But then I took a step back and thought about it again. It seems like in the first scenario the total energy of the system is the KE of the two cars, or $\frac{1}{2}mv^2 + \frac{1}{2}mv^2 = mv^2$. In the second scenario, it's the KE of the car plus wall, which is $\frac{1}{2}m(2v)^2 + 0 = 2mv^2$. So the car crashing into the wall has to absorb (and dissipate via heat) twice as much energy, so crashing into the wall is in fact worse.</p>
<p>Is this correct?</p>
<p>To clarify, I'm not concerned with the difference between a wall and a car, and I don't think that's what the question is getting at. Imagine instead that in the second scenario, a car is crashing at 100mph into the same car sitting there at 0mph (with it's brakes on of course). First scenario is the same, two of the same cars going 50mph in opposite directions collide. Are those two situations identical?</p> | g58 | [
0.07517026364803314,
0.005177817773073912,
0.024625316262245178,
0.036737482994794846,
0.05074061080813408,
-0.025673506781458855,
0.030910521745681763,
0.0011326551903039217,
-0.08156182616949081,
-0.012815337628126144,
-0.0009892783127725124,
-0.03344270586967468,
0.010379085317254066,
0.019061440601944923,
-0.0018634253647178411,
-0.02082870714366436,
0.10844127088785172,
-0.03884589672088623,
-0.0005677837762050331,
0.048064231872558594,
-0.03007914125919342,
0.0023574824444949627,
-0.026969941332936287,
0.013666399754583836,
-0.02162879705429077,
-0.013505837880074978,
-0.04595772549510002,
-0.022080235183238983,
-0.060892801731824875,
-0.02635704167187214,
0.06621410697698593,
0.005716253072023392,
0.04392305016517639,
-0.06884808093309402,
-0.08450787514448166,
0.0015722262905910611,
0.01665383018553257,
-0.05006095767021179,
-0.026817305013537407,
-0.013864889740943909,
0.07930531352758408,
-0.03350582718849182,
0.0549958311021328,
-0.024350440129637718,
0.0016378900036215782,
-0.046952780336141586,
-0.03211648762226105,
-0.008772161789238453,
0.0022034826688468456,
0.049733713269233704,
-0.018291085958480835,
0.039149943739175797,
0.04252730682492256,
0.06022239848971367,
0.04445572942495346,
-0.01608441397547722,
0.044975560158491135,
-0.01446318905800581,
0.05316644161939621,
0.04699685797095299,
-0.03094351850450039,
0.01573932357132435,
-0.020837316289544106,
-0.06193294748663902,
0.027453824877738953,
0.010286744683980942,
0.001123060006648302,
0.06545697152614594,
0.04154633358120918,
-0.038020357489585876,
0.03882396221160889,
0.021077420562505722,
-0.0403834767639637,
-0.05401929095387459,
0.030735312029719353,
-0.07038456201553345,
0.010044557973742485,
-0.04248611256480217,
0.08730563521385193,
0.019413866102695465,
-0.036653853952884674,
0.040372785180807114,
0.012218671850860119,
0.018790455535054207,
0.04687495529651642,
0.021434875205159187,
-0.0178220234811306,
0.029798736795783043,
0.006817392073571682,
0.02273632399737835,
0.01610419899225235,
-0.018485449254512787,
0.06744381785392761,
0.027062559500336647,
-0.059195626527071,
-0.007888981141149998,
-0.03744073212146759,
0.04544958099722862,
0.02951056696474552,
0.0430091992020607,
0.006935940124094486,
-0.031652115285396576,
-0.00947651732712984,
0.04142080619931221,
-0.011282520368695259,
-0.019995752722024918,
0.01385608222335577,
0.0226672925055027,
-0.04562896490097046,
-0.05973678082227707,
-0.017778905108571053,
-0.07272450625896454,
-0.03159097954630852,
-0.023837633430957794,
-0.03590315952897072,
0.03337644040584564,
0.09184424579143524,
0.020480383187532425,
-0.012755491770803928,
0.03789540007710457,
-0.010511258617043495,
0.07483980059623718,
-0.020975079387426376,
0.007460915949195623,
0.018673229962587357,
0.0038964273408055305,
-0.03364184498786926,
0.011129793711006641,
0.025253282859921455,
-0.026903100311756134,
-0.0349908173084259,
0.014347431249916553,
0.04567328467965126,
-0.04517973214387894,
-0.008821794763207436,
0.07440269738435745,
-0.007077912800014019,
0.02928195521235466,
-0.009231551550328732,
0.014070961624383926,
0.06636705994606018,
0.04299212247133255,
-0.02296007052063942,
0.05091789737343788,
-0.08290749788284302,
0.022340334951877594,
-0.04807350039482117,
-0.038199182599782944,
-0.009915541857481003,
0.008097046986222267,
0.02163248136639595,
0.016022317111492157,
-0.03301021084189415,
-0.016559241339564323,
0.05310150608420372,
-0.002230392536148429,
-0.0012721584644168615,
0.004386078100651503,
-0.014732525683939457,
0.010225789621472359,
0.016632171347737312,
-0.018863026052713394,
0.05971868336200714,
-0.04268711805343628,
-0.008315620943903923,
-0.004154849797487259,
-0.005395097192376852,
0.005898716859519482,
-0.00473004300147295,
0.001522601000033319,
-0.03397180512547493,
-0.03352445363998413,
-0.04795290157198906,
0.11304610967636108,
-0.007548630703240633,
-0.029125932604074478,
0.018999239429831505,
-0.05425902456045151,
0.017292998731136322,
-0.015139967203140259,
0.040246907621622086,
0.0031294869258999825,
0.006873477250337601,
-0.0168007779866457,
0.04657070338726044,
-0.03596684709191322,
0.013075037859380245,
0.07175556570291519,
-0.0904955044388771,
0.03286236897110939,
-0.05224044248461723,
-0.037400417029857635,
-0.04194837063550949,
0.03678779676556587,
-0.01953163370490074,
0.0030418301466852427,
-0.018258672207593918,
0.022007012739777565,
-0.0283662136644125,
0.006265989504754543,
0.0295324195176363,
0.019372666254639626,
0.014161122031509876,
0.0007052301662042737,
-0.0009761581313796341,
0.09756742417812347,
-0.06322473287582397,
0.0004482948570512235,
0.0540752150118351,
-0.057785920798778534,
-0.0015259388601407409,
0.014787377789616585,
-0.008814973756670952,
0.012185754254460335,
0.01829361915588379,
-0.03355172649025917,
0.04375792667269707,
0.041922006756067276,
-0.022323060780763626,
-0.04868123680353165,
0.007100553717464209,
-0.006008083000779152,
0.048632871359586716,
-0.08606123924255371,
-0.023763878270983696,
-0.008569453842937946,
-0.06731300055980682,
-0.048016469925642014,
-0.01271865889430046,
0.04509630799293518,
-0.03797140717506409,
0.009940137155354023,
0.04148949682712555,
-0.027399327605962753,
0.018963368609547615,
0.0409139022231102,
0.04516058415174484,
-0.004690296482294798,
0.022937551140785217,
-0.04391750320792198,
0.036220114678144455,
-0.004842990543693304,
-0.03764060139656067,
-0.0031483317725360394,
0.05751044303178787,
-0.03506889194250107,
-0.005594584625214338,
-0.016872959211468697,
0.06132498383522034,
0.07012735307216644,
-0.013744816184043884,
0.01498898770660162,
-0.06382884085178375,
-0.017706746235489845,
0.055071793496608734,
-0.02132538892328739,
0.004335653968155384,
-0.02365979179739952,
-0.023364853113889694,
0.04118938371539116,
0.028867099434137344,
-0.0718536451458931,
-0.03265107050538063,
0.049132585525512695,
-0.03400518000125885,
0.0112648019567132,
0.016387036070227623,
-0.0009470829972997308,
0.01128494180738926,
-0.03770367056131363,
0.014596608467400074,
0.004535605665296316,
-0.010326498188078403,
0.023377155885100365,
0.01419887226074934,
-0.021301589906215668,
0.05077795311808586,
-0.05983102694153786,
-0.002826692769303918,
-0.04025157913565636,
-0.04692372679710388,
0.015186204575002193,
-0.01713334396481514,
0.03983142226934433,
0.07522076368331909,
-0.06740710884332657,
-0.011755326762795448,
0.03069620579481125,
-0.020042231306433678,
0.03230386599898338,
-0.07902452349662781,
0.05280439555644989,
0.06562192738056183,
-0.0052103386260569096,
0.0007145546842366457,
0.0882965475320816,
0.012839341536164284,
-0.0270784143358469,
-0.01981993392109871,
-0.07062683999538422,
-0.013256597332656384,
-0.006120237056165934,
-0.046893343329429626,
0.042021896690130234,
0.09825646132230759,
0.0485164038836956,
-0.05615653097629547,
-0.03133884444832802,
-0.014699225313961506,
-0.0327652245759964,
0.03745822608470917,
-0.0038068690337240696,
-0.0035405231174081564,
0.0010077435290440917,
-0.05229765549302101,
0.002786672906950116,
0.014809858985245228,
-0.0009838658152148128,
0.05731877312064171,
0.04648734629154205,
-0.04233410209417343,
-0.027285663411021233,
0.03517276048660278,
0.012442720122635365,
-0.04617895558476448,
0.04509386420249939,
-0.026615450158715248,
0.04826267436146736,
-0.01994081400334835,
-0.051627662032842636,
0.003846152452751994,
0.05228522792458534,
-0.011644993908703327,
-0.031892240047454834,
0.017316056415438652,
-0.010505697689950466,
-0.02175670862197876,
0.007215326651930809,
0.014247997663915157,
0.03269658610224724,
-0.012787384912371635,
0.06366420537233353,
0.01845068670809269,
-0.0008311833953484893,
0.02267071045935154,
0.037141166627407074,
0.04400875046849251,
0.025335535407066345,
-0.005157805513590574,
-0.060457080602645874,
0.03240314498543739,
-0.0032326639629900455,
0.023575181141495705,
0.009777269326150417,
-0.10172241926193237,
-0.06520301103591919,
-0.030737154185771942,
0.006844904273748398,
0.01766345277428627,
0.0802614837884903,
0.026988117024302483,
-0.007199650164693594,
0.006519796792417765,
-0.005824083928018808,
-0.009296106174588203,
-0.019187428057193756,
-0.02871180698275566,
-0.015895234420895576,
-0.030036138370633125,
-0.044826652854681015,
-0.0009722248651087284,
0.029052989557385445,
0.013274623081088066,
0.03563714399933815,
0.03385410085320473,
-0.03229942172765732,
0.02749166078865528,
-0.04029252380132675,
0.009201333858072758,
0.033128779381513596,
0.07165206223726273,
-0.01219517644494772,
0.013302301056683064,
0.014301227405667305,
0.04708092659711838,
-0.06289017200469971,
-0.02233470231294632,
-0.03198249265551567,
-0.006494597531855106,
0.03177940472960472,
-0.0022121660877019167,
0.008125849068164825,
-0.022072551771998405,
0.038271304219961166,
0.02860875241458416,
0.01414186879992485,
-0.0023820961359888315,
-0.005210148636251688,
0.01140112616121769,
0.03978878632187843,
-0.00971370842307806,
0.019805995747447014,
-0.01107451319694519,
-0.013744162395596504,
0.0029698784928768873,
0.004847640171647072,
0.017054829746484756,
-0.010135456919670105,
-0.019565001130104065,
-0.02179912105202675,
0.015277157537639141,
-0.03176132217049599,
-0.008003754541277885,
-0.021170318126678467,
0.0072253188118338585,
0.03575940430164337,
-0.024379394948482513,
0.04175403341650963,
0.04911961406469345,
0.018057556822896004,
-0.04318084940314293,
0.01635894738137722,
-0.09410910308361053,
-0.0189412422478199,
0.04411569982767105,
0.008800788782536983,
0.03516574949026108,
0.012882825918495655,
-0.04181268438696861,
-0.010843704454600811,
0.051186349242925644,
-0.000928345019929111,
-0.04185349866747856,
-0.0033945045433938503,
-0.013866350054740906,
0.03129676729440689,
-0.0019124558893963695,
0.008117259480059147,
0.04735209420323372,
0.008797596208751202,
0.00020065905118826777,
0.004987698048353195,
-0.07389234006404877,
0.02677399478852749,
0.04818996042013168,
0.017743173986673355,
-0.011133389547467232,
-0.029842399060726166,
-0.028347399085760117,
-0.02627880685031414,
-0.02350994013249874,
0.009268180467188358,
0.013533770106732845,
-0.018024412915110588,
-0.017817582935094833,
-0.035054031759500504,
-0.022707901895046234,
0.022622115910053253,
-0.006710770074278116,
-0.013792409561574459,
0.0011375885223969817,
0.028679601848125458,
0.021591754630208015,
-0.012682073749601841,
0.007584697566926479,
-0.022250451147556305,
-0.010093732737004757,
0.012133697979152203,
-0.06664726883172989,
-0.0011823337990790606,
0.010671853087842464,
-0.023923639208078384,
-0.023942910134792328,
-0.038873668760061264,
0.07842160016298294,
-0.025803212076425552,
0.0006689593428745866,
0.005287573207169771,
0.009499404579401016,
-0.08081188797950745,
-0.04057791456580162,
-0.04316357895731926,
0.018187321722507477,
-0.029530363157391548,
-0.006255614571273327,
0.009161806665360928,
-0.034091297537088394,
0.008073527365922928,
0.0873049646615982,
-0.003199551021680236,
0.020604003220796585,
0.019253702834248543,
-0.05407041683793068,
-0.03852890804409981,
0.038280244916677475,
0.028353990986943245,
0.05135882645845413,
-0.03248181566596031,
-0.04188110679388046,
0.001909616868942976,
-0.07144477963447571,
0.0171091016381979,
0.008164490573108196,
-0.05584597960114479,
0.022617876529693604,
0.040455423295497894,
0.026111189275979996,
0.011014667339622974,
-0.016554679721593857,
0.07630566507577896,
-0.054015859961509705,
0.017058366909623146,
0.0570039264857769,
0.01190896611660719,
0.012572848238050938,
-0.013696116395294666,
0.0002612961397971958,
-0.013973886147141457,
0.052219122648239136,
-0.05227239429950714,
0.03632128983736038,
-0.029886092990636826,
-0.046494074165821075,
0.018013646826148033,
-0.01602059416472912,
-0.02720571681857109,
-0.0018360016401857138,
-0.08342429250478745,
-0.012707225978374481,
0.014013850130140781,
0.04215983301401138,
0.018131962046027184,
0.039473023265600204,
0.05165920779109001,
-0.04881715774536133,
0.014269988983869553,
-0.03604377433657646,
-0.02275335229933262,
0.06518804281949997,
0.019501667469739914,
0.005700285080820322,
-0.031499918550252914,
0.052201323211193085,
0.08145016431808472,
-0.014811912551522255,
0.015199764631688595,
-0.017554771155118942,
-0.018777063116431236,
0.009966694749891758,
-0.050514452159404755,
-0.03262405842542648,
0.005519425496459007,
-0.02419096976518631,
-0.03262707591056824,
0.03146883100271225,
0.013716679997742176,
0.02973632700741291,
0.0003605434321798384,
-0.0027527206111699343,
0.004801766015589237,
0.03955322131514549,
-0.01953030377626419,
0.020602311939001083,
-0.009370614774525166,
0.07998301088809967,
-0.0310305617749691,
-0.04418663680553436,
0.018696501851081848,
0.03823209926486015,
0.012642355635762215,
0.061030060052871704,
-0.0351332426071167,
0.03465263545513153,
-0.004102345090359449,
0.04976094886660576,
-0.015313204377889633,
-0.02040615677833557,
-0.029503658413887024,
0.006330694071948528,
-0.02239726111292839,
0.02975710853934288,
-0.022693734616041183,
-0.010244786739349365,
0.015727074816823006,
0.01423147227615118,
-0.009131635539233685,
-0.03109041415154934,
-0.0013559228973463178,
0.03610145300626755,
-0.022630875930190086,
-0.02692226879298687,
-0.04606398567557335,
0.009260902181267738,
0.028194984421133995,
-0.004183617886155844,
0.005683710798621178,
-0.01595211774110794,
-0.006805827375501394,
-0.050913006067276,
0.08496661484241486,
-0.011638264171779156,
-0.022659730166196823,
0.047038812190294266,
-0.016019856557250023,
-0.0033993932884186506,
0.018947847187519073,
0.013915513642132282,
0.06015742942690849,
-0.024993766099214554,
0.005763387307524681,
-0.02320554107427597,
0.04537070170044899,
0.00645468570291996,
0.027492523193359375,
0.006999802775681019,
0.02417284995317459,
-0.0977092981338501,
-0.012059497646987438,
-0.0011389683932065964,
-0.023646704852581024,
0.018348246812820435,
-0.048071105033159256,
0.01250012032687664,
-0.08382036536931992,
0.03392443060874939,
0.027446793392300606,
-0.04223140701651573,
0.057726066559553146,
0.05697689205408096,
-0.006362069398164749,
0.007753672078251839,
-0.05653482675552368,
0.019775642082095146,
0.039230428636074066,
-0.006160419434309006,
0.0008962709689512849,
-0.021330667659640312,
0.011935203336179256,
-0.011444727890193462,
-0.017170283943414688,
0.013354313559830189,
0.029106317088007927,
-0.005242608021944761,
0.03864039480686188,
-0.0702698677778244,
-0.030823931097984314,
0.033482614904642105,
-0.029278608039021492,
-0.029587607830762863,
0.018344895914196968,
-0.061080530285835266,
-0.01045105792582035,
-0.06446269154548645,
-0.027646388858556747,
-0.05665925145149231,
0.012843369506299496,
-0.011648573912680149,
-0.006966743618249893,
0.07214660942554474,
-0.011255708523094654,
0.01294462289661169,
0.025489086285233498,
0.0022185088600963354,
0.0257484819740057,
-0.019595319405198097,
-0.0017402669182047248,
0.0010024328948929906,
-0.05501924827694893,
0.0006781448028050363,
0.01845311000943184,
0.027268115431070328,
-0.024803364649415016,
-0.04212573543190956,
0.002811624901369214,
-0.009705445729196072,
-0.01778528094291687,
-0.02025829255580902,
0.038409147411584854,
0.02104087732732296,
-0.012262464500963688,
0.09048875421285629,
-0.031890831887722015,
0.010984523221850395,
0.021220214664936066,
0.050230130553245544,
-0.0010756560368463397,
-0.020047105848789215,
0.01620214246213436,
-0.04927484691143036,
-0.06716059148311615,
0.014668065123260021,
-0.026487374678254128,
0.04418187215924263,
0.053431715816259384,
-0.014709229581058025,
0.021283965557813644,
-0.015268709510564804,
0.037130340933799744,
-0.029672255739569664,
-0.03644175082445145,
-0.02977593243122101,
0.023903390392661095,
0.03734590485692024,
0.01959642954170704,
-0.05025723949074745,
-0.00826014019548893,
0.02458552084863186,
-0.025754455476999283,
-0.06499802321195602,
-0.034686341881752014,
0.0411321297287941,
0.024953989312052727,
0.037001945078372955,
0.01956210471689701,
0.003183783032000065,
-0.04099423810839653,
0.00012535834684967995,
-0.013791659846901894,
0.021163467317819595,
0.046034522354602814,
0.0016660288674756885,
-0.07067472487688065,
0.03131755068898201,
-0.1040964126586914,
0.029301732778549194,
-0.02473960816860199,
-0.0006047316710464656,
-0.007707615382969379,
-0.08542054891586304,
-0.010021181777119637,
-0.03677237406373024,
0.04040481522679329,
0.0015192886348813772,
-0.00018475089746061713,
-0.0357857346534729,
0.009807725436985493,
0.00527114188298583,
0.01512316707521677,
-0.06272609531879425,
-0.005169501528143883,
-0.02525685913860798,
-0.02945539727807045,
-0.03219052776694298,
0.023431768640875816,
-0.03460705652832985,
-0.008642859756946564,
-0.029174892231822014,
0.05039099603891373,
0.01458196435123682,
-0.07396064698696136,
0.03562849387526512,
-0.015987128019332886,
-0.058618057519197464,
0.027345072478055954,
0.03836233168840408,
0.0043525081127882,
0.0017592298099771142,
0.008812333457171917,
-0.028459670022130013,
0.05238424986600876,
0.022413089871406555,
-0.02547244168817997,
-0.03043404407799244,
-0.07960373163223267,
0.011722967959940434,
-0.034819986671209335,
-0.021121293306350708,
-0.005703394766896963
] |
<p>Are all <a href="http://en.wikipedia.org/wiki/Wave" rel="nofollow">waves</a> in the universe the same as <a href="http://en.wikipedia.org/wiki/Electromagnetic_waves" rel="nofollow">electromagnetic waves</a>?</p>
<p>Basically, my question arises from an equation I found in my chemistry textbook:</p>
<p>$$\lambda \nu ~=~ c.$$</p>
<p>This states that the wavelength (distance from crest to crest) times the frequency (amount of times the wave passes the center point) equals the speed of light. Now, I know this applies in a vacuum and that the speed of light changes based on density. However, does this apply to all waves? If so, does this apply to a wave in water?</p>
<p>It seems as though it should. You have a high frequency of light that is incredibly high compared to water, but you have a incredibly small wavelength which causes that value to be lower. In the case of water, if you considered only the wavelength, the value would be too high, but if you also consider that the frequency is going to be orders of magnitude lower than light, you can see where I might arrive at this conclusion.</p>
<p>If we measure the crest of a <a href="http://en.wikipedia.org/wiki/Surface_wave" rel="nofollow">wave</a> of water and the frequency of that wave (I assume from the surface of the body of water) and consider the density of the water in our calculation (as some other variable that is normally used when calculating this), would the result also be the speed of light? In addition, if water was within a vacuum and we were to create a wave, how would this react? If we could create a wave in water in this vacuum, would our values reflect $c$ or a variation of $c$ based on the density of the water?</p>
<p>If $\lambda \nu ~=~ c$ is valid for all waves, what other attributes must be supplied within the equation to make the math work out to give the correct answer of $c$?</p> | g4582 | [
0.04915117472410202,
0.012131123803555965,
-0.013717287220060825,
-0.028849216178059578,
0.09873243421316147,
0.04015025123953819,
0.022754371166229248,
0.018675366416573524,
-0.028695283457636833,
-0.05278392508625984,
-0.006645936984568834,
0.06255383789539337,
0.035966016352176666,
0.07259280979633331,
-0.043804071843624115,
-0.006836160086095333,
0.03757159411907196,
-0.0465497151017189,
0.03052063286304474,
-0.021624160930514336,
-0.0039720693603158,
-0.011807705275714397,
-0.020715733990073204,
-0.03775162994861603,
-0.061226602643728256,
0.003673750441521406,
0.05249984934926033,
-0.047677360475063324,
0.011075503192842007,
-0.006458332762122154,
-0.03119897097349167,
0.0644519031047821,
0.035659462213516235,
-0.005309129133820534,
0.0014691319083794951,
0.015967411920428276,
-0.06573647260665894,
0.031120091676712036,
0.017725205048918724,
0.06313085556030273,
-0.0061394209042191505,
0.05111745744943619,
-0.04227784276008606,
-0.014516339637339115,
0.028631024062633514,
0.0035411084536463022,
-0.04760230332612991,
0.010067693889141083,
0.0043166582472622395,
-0.048152659088373184,
0.025182774290442467,
-0.046743378043174744,
-0.0014578377595171332,
0.02598479390144348,
-0.0034011907409876585,
0.016427498310804367,
0.026465050876140594,
-0.02585187740623951,
0.0631261095404625,
0.010983332991600037,
-0.004022468812763691,
-0.038477394729852676,
0.0491458959877491,
0.029997706413269043,
0.03659878298640251,
-0.00804546196013689,
-0.011744426563382149,
-0.041492193937301636,
-0.0011433440959081054,
-0.007673680782318115,
-0.03595499321818352,
-0.06396794319152832,
-0.06550024449825287,
-0.07264664024114609,
-0.030529318377375603,
0.01238991878926754,
0.0051222932524979115,
0.004706688690930605,
0.015886826440691948,
0.000931785034481436,
-0.0066576190292835236,
0.0494556725025177,
0.010066797025501728,
0.06382724642753601,
-0.0056986333802342415,
-0.007888230495154858,
-0.018488161265850067,
0.028392314910888672,
0.013587920926511288,
0.01598396897315979,
-0.008120172657072544,
0.009854604490101337,
0.033381685614585876,
-0.042892973870038986,
-0.013234582729637623,
-0.03656679764389992,
-0.008703484199941158,
0.019505789503455162,
-0.019270088523626328,
0.031111815944314003,
-0.041690632700920105,
0.01442593615502119,
0.04992358013987541,
-0.013407633639872074,
0.013833587057888508,
-0.004696941468864679,
0.019363965839147568,
0.001910485909320414,
-0.02794346585869789,
-0.010827815160155296,
-0.0486508272588253,
-0.07293568551540375,
-0.024069203063845634,
-0.024185696616768837,
-0.08438871800899506,
-0.079062320291996,
0.04271818697452545,
0.04204905405640602,
-0.015114507637917995,
0.0540771558880806,
0.03964054957032204,
0.027349555864930153,
0.0008790057036094368,
0.03951135277748108,
0.01070511806756258,
-0.0018582604825496674,
-0.04265131801366806,
0.03803880140185356,
0.05037310719490051,
0.03463159501552582,
-0.0011442250106483698,
0.02133898437023163,
-0.06250268965959549,
0.008124856278300285,
-0.027149492874741554,
-0.009661175310611725,
0.01570162922143936,
-0.0015187409007921815,
0.02835075370967388,
0.0002752539876382798,
0.02086830884218216,
-0.034432366490364075,
0.03965548798441887,
-0.039240505546331406,
-0.014199570752680302,
0.013358492404222488,
-0.03897546976804733,
-0.016452230513095856,
0.03580406680703163,
-0.022548288106918335,
0.01089327223598957,
0.07501709461212158,
0.0089895473793149,
-0.0066849831491708755,
-0.011871477589011192,
0.04086582362651825,
-0.015292634256184101,
0.0014789564302191138,
-0.02655094303190708,
-0.035525742918252945,
0.05633644387125969,
-0.005565212573856115,
0.03503693267703056,
0.029350612312555313,
0.00758748222142458,
-0.005871820263564587,
0.027851607650518417,
-0.018518518656492233,
-0.04584231600165367,
-0.06835030019283295,
-0.018164943903684616,
-0.01521883811801672,
-0.03514106944203377,
-0.013162044808268547,
0.027956092730164528,
0.025255007669329643,
0.05988120287656784,
-0.01099272258579731,
-0.030163107439875603,
0.024784453213214874,
-0.08667026460170746,
-0.027574172243475914,
0.0014992756769061089,
-0.05167549476027489,
0.02152932807803154,
0.0007404547650367022,
0.023081522434949875,
-0.05563767999410629,
-0.09044934064149857,
0.004582520108669996,
-0.04880703613162041,
-0.050364021211862564,
-0.034016646444797516,
0.050558604300022125,
0.02993539534509182,
0.01762496866285801,
0.003107335651293397,
-0.015630247071385384,
-0.03574809804558754,
0.028279846534132957,
-0.021220721304416656,
0.052402157336473465,
0.06477311253547668,
0.0006256841588765383,
0.04147360101342201,
0.02887215092778206,
0.04201565310359001,
-0.018360650166869164,
0.02230743318796158,
-0.020814446732401848,
0.02123572863638401,
-0.0037196900229901075,
-0.0066560618579387665,
0.040323350578546524,
-0.05025617033243179,
0.04582910239696503,
-0.058818452060222626,
0.02673976868391037,
-0.004071520641446114,
0.020461207255721092,
-0.04839997738599777,
0.026901016011834145,
0.00021703122183680534,
-0.014795107766985893,
0.020753610879182816,
0.013687366619706154,
-0.058113470673561096,
-0.02738170325756073,
0.07101941853761673,
0.011443785391747952,
0.07021702826023102,
0.014106779359281063,
-0.01148142945021391,
-0.01534439716488123,
0.011025134474039078,
0.05094234272837639,
-0.040592651814222336,
0.024726977571845055,
0.02310979925096035,
-0.02484167367219925,
0.03676629066467285,
-0.014708256348967552,
-0.06225886940956116,
0.026500748470425606,
0.02051238715648651,
-0.05874232202768326,
-0.005080096889287233,
-0.02735181897878647,
0.002680791774764657,
0.07442621886730194,
0.04273518547415733,
0.012751593254506588,
0.03511475399136543,
0.043318744748830795,
0.011372202076017857,
-0.00659566093236208,
-0.013439078815281391,
0.03282925486564636,
-0.05213165283203125,
0.0031518947798758745,
0.02087716944515705,
-0.0008713874849490821,
0.024584507569670677,
-0.03352586179971695,
-0.03883781656622887,
-0.004549728706479073,
-0.03312921151518822,
0.03631146252155304,
-0.0107630779966712,
0.006682817358523607,
-0.05808969587087631,
0.048578646034002304,
-0.006192021071910858,
-0.0042469981126487255,
-0.02335282787680626,
-0.03718625754117966,
-0.002198989037424326,
-0.059871282428503036,
0.031035691499710083,
-0.010689351707696915,
-0.009710656479001045,
-0.022779250517487526,
-0.07801364362239838,
0.009908167645335197,
0.004423357080668211,
-0.042223818600177765,
0.004881284665316343,
-0.004114117473363876,
-0.00013414218847174197,
0.044858478009700775,
0.004317573271691799,
0.020853225141763687,
-0.039190057665109634,
0.08362650126218796,
-0.018773868680000305,
0.02436046488583088,
0.049705278128385544,
-0.0280557069927454,
-0.020686034113168716,
0.012931524775922298,
0.042553044855594635,
-0.03415297344326973,
0.01602349616587162,
0.008768167346715927,
-0.027117643505334854,
0.03333320841193199,
-0.023990944027900696,
-0.06458993256092072,
0.03681963309645653,
-0.01588808186352253,
0.014253677800297737,
0.060189139097929,
0.0092186089605093,
-0.011174975894391537,
-0.03786133974790573,
0.037377361208200455,
-0.012047362513840199,
-0.024830183014273643,
-0.009631330147385597,
-0.004491743631660938,
-0.030472993850708008,
-0.012114189565181732,
0.0010254736989736557,
-0.032935284078121185,
0.03128185495734215,
0.024681732058525085,
-0.001494726282544434,
0.02612842619419098,
-0.04331681504845619,
-0.03635665774345398,
0.03786138445138931,
-0.0235024094581604,
-0.008390293456614017,
-0.017677243798971176,
0.009946757927536964,
-0.06573735922574997,
0.017691606655716896,
0.004382613580673933,
0.06732520461082458,
0.07738357037305832,
-0.04929663985967636,
-0.06921496242284775,
-0.034402236342430115,
0.0008284081122837961,
0.0008924336871132255,
0.03144300729036331,
-0.0026673302054405212,
0.018164265900850296,
-0.06044768542051315,
0.0013191552134230733,
0.03610330447554588,
-0.010939497500658035,
-0.019144903868436813,
-0.03118186816573143,
0.028691191226243973,
0.0507572703063488,
0.046915069222450256,
0.024638112634420395,
0.04766346886754036,
-0.036178700625896454,
0.014680158346891403,
-0.05652806535363197,
0.03769184648990631,
-0.029569178819656372,
-0.03285985812544823,
-0.029029691591858864,
0.0007814259734004736,
0.04627499729394913,
-0.044324930757284164,
0.019314197823405266,
0.02188403531908989,
-0.03132609277963638,
0.01489426288753748,
0.03537335619330406,
0.041064657270908356,
-0.020387372002005577,
0.047381654381752014,
-0.00843213964253664,
-0.025056714192032814,
0.055943720042705536,
0.056445229798555374,
0.006798853632062674,
0.05589809641242027,
-0.1061175987124443,
-0.011605162173509598,
-0.032608114182949066,
-0.0652044415473938,
-0.061249736696481705,
0.05528181046247482,
-0.031029056757688522,
-0.03777799382805824,
-0.04285315424203873,
-0.02848009206354618,
0.009221374057233334,
0.011775747872889042,
-0.005756134167313576,
0.03037002868950367,
-0.02819187380373478,
-0.07160688191652298,
0.07384249567985535,
0.030498338863253593,
-0.0236153956502676,
0.021969961002469063,
0.009036147966980934,
-0.01746600680053234,
0.02567337080836296,
0.06800542026758194,
-0.03345063328742981,
-0.016659993678331375,
-0.016845859587192535,
-0.021986333653330803,
-0.05773307755589485,
0.014541011303663254,
-0.07087838649749756,
-0.024574706330895424,
0.054903920739889145,
0.025199158117175102,
-0.0738130435347557,
-0.020484140142798424,
0.056239355355501175,
0.02215781807899475,
0.0206073559820652,
-0.0025555817410349846,
0.011399841867387295,
-0.04688147082924843,
0.013581044040620327,
0.08683065325021744,
0.01786741614341736,
-0.006347909569740295,
-0.02124132588505745,
0.0065749455243349075,
0.013451259583234787,
0.008840183727443218,
0.06207964941859245,
0.05261833965778351,
0.004850807134062052,
-0.009837860241532326,
-0.010600857436656952,
0.031207332387566566,
-0.0430915392935276,
0.006543997675180435,
0.022668957710266113,
-0.0025242578703910112,
0.003099913941696286,
-0.02180211804807186,
0.06580741703510284,
-0.056163858622312546,
-0.023639826104044914,
-0.044808998703956604,
-0.046485986560583115,
-0.08396030217409134,
0.10318750888109207,
0.027438415214419365,
-0.04949551075696945,
-0.018703540787100792,
-0.0005566789768636227,
0.008071603253483772,
-0.00852946750819683,
0.06768966466188431,
0.027764994651079178,
-0.05569399520754814,
0.021206006407737732,
0.003417416475713253,
-0.030486995354294777,
0.07962972670793533,
-0.059942521154880524,
-0.012391782365739346,
0.003855261020362377,
-0.04442073404788971,
0.033319976180791855,
0.048687148839235306,
-0.01992993801832199,
0.022302521392703056,
0.013135869055986404,
0.034722648561000824,
0.026190411299467087,
0.010887877084314823,
-0.011351353488862514,
-0.0363653227686882,
-0.0590750090777874,
-0.006319573614746332,
-0.03421996906399727,
0.011279139667749405,
0.013670213520526886,
-0.0205675195902586,
0.05831437557935715,
-0.055403679609298706,
0.07778270542621613,
0.015209943987429142,
-0.0670042559504509,
0.011299715377390385,
-0.031793270260095596,
-0.023535089567303658,
0.014285297133028507,
-0.04936321824789047,
-0.0017012167954817414,
0.0039612241089344025,
-0.02051667310297489,
-0.012470238842070103,
-0.03835000842809677,
-0.017983295023441315,
0.026670247316360474,
-0.02345212921500206,
-0.037803299725055695,
-0.011544621549546719,
0.032448478043079376,
0.06779476255178452,
0.03223705291748047,
-0.004617094062268734,
0.07075046747922897,
0.07646352797746658,
-0.014824816025793552,
-0.007371022831648588,
0.026547957211732864,
0.035303253680467606,
-0.05755304545164108,
-0.048758190125226974,
0.05832119658589363,
0.004583998583257198,
-0.011984122917056084,
0.012587767094373703,
0.0007296885596588254,
0.043510161340236664,
0.015033350326120853,
0.04687226191163063,
-0.012793970294296741,
-0.0613768994808197,
-0.021741770207881927,
0.0018177387537434697,
-0.013427086174488068,
0.017682891339063644,
0.032039280980825424,
0.05142607167363167,
-0.04903753846883774,
0.013448648154735565,
-0.03616777062416077,
0.009889104403555393,
-0.011202641762793064,
0.03445829451084137,
0.02403678186237812,
0.0048591503873467445,
0.019297555088996887,
0.00551749998703599,
0.05094806104898453,
-0.009930924512445927,
0.01419304683804512,
0.023406188935041428,
-0.014908453449606895,
-0.002696405630558729,
0.045471686869859695,
-0.04078144207596779,
-0.00920176412910223,
0.03210083767771721,
0.0567348450422287,
-0.040065836161375046,
0.03185868263244629,
-0.0021378640085458755,
-0.022443007677793503,
-0.03526289016008377,
-0.0765974223613739,
0.04907339811325073,
0.03846706822514534,
0.019764283671975136,
-0.00579771539196372,
-0.005947386845946312,
-0.05623028799891472,
0.0010319369612261653,
-0.025420570746064186,
0.10036920011043549,
0.004607319366186857,
-0.014600615948438644,
-0.04708165302872658,
-0.01863844133913517,
-0.0615556426346302,
-0.010545444674789906,
-0.033326148986816406,
0.05783529952168465,
-0.04313427954912186,
-0.04535173252224922,
-0.005899334326386452,
0.02356843091547489,
-0.05112122744321823,
0.02171017974615097,
-0.03750710189342499,
0.03090672567486763,
-0.0394638366997242,
0.004420557525008917,
-0.024896178394556046,
0.07308415323495865,
-0.021107589825987816,
0.009486345574259758,
0.010150357149541378,
-0.013285739347338676,
-0.006217458285391331,
0.013038727454841137,
-0.06897794455289841,
-0.014054308645427227,
-0.038049161434173584,
-0.035737987607717514,
0.04732270911335945,
0.028479665517807007,
0.01142480131238699,
0.041331443935632706,
0.04780955612659454,
0.02623833529651165,
-0.0026563501451164484,
-0.01622588559985161,
-0.03046705573797226,
0.023436767980456352,
-0.01376190036535263,
-0.029236692935228348,
0.05692455917596817,
-0.02393091283738613,
-0.03859737887978554,
-0.07100021094083786,
-0.05672844871878624,
0.03414912894368172,
-0.03874496743083,
-0.013736079446971416,
0.059238698333501816,
0.06308820098638535,
-0.039308059960603714,
-0.011484634131193161,
0.0018664798699319363,
0.001952601596713066,
0.09305407851934433,
-0.03682604059576988,
0.028580840677022934,
0.07010594010353088,
-0.014182736165821552,
0.06897252798080444,
-0.029679980129003525,
-0.010420739650726318,
0.06794241815805435,
-0.019070614129304886,
0.039603836834430695,
-0.0004782799514941871,
0.008662614040076733,
0.06558281928300858,
0.0033509531058371067,
0.0372331328690052,
-0.011691251769661903,
0.043373193591833115,
0.02850847877562046,
-0.0567755363881588,
0.023913947865366936,
0.05357261002063751,
-0.085850790143013,
-0.027321169152855873,
-0.0027133652474731207,
0.021844903007149696,
0.026857612654566765,
-0.01571420021355152,
0.04384267330169678,
0.025368213653564453,
0.04223525524139404,
-0.06500780582427979,
0.04892421141266823,
-0.08874830603599548,
-0.02503889426589012,
-0.054492708295583725,
0.003659785259515047,
0.021499551832675934,
-0.002441129647195339,
0.008089504204690456,
0.05886029079556465,
0.011525694280862808,
-0.05950445681810379,
-0.015226200222969055,
0.02314111217856407,
0.0273455660790205,
-0.027022819966077805,
-0.014539074152708054,
-0.0033782650716602802,
0.008869943208992481,
0.03440188616514206,
-0.04647018760442734,
0.04921973496675491,
0.015385700389742851,
-0.005825018044561148,
0.007204936817288399,
0.01754104346036911,
0.00824171956628561,
-0.06238603591918945,
-0.005297972820699215,
0.018982214853167534,
-0.05216638371348381,
-0.014531990513205528,
0.06313309818506241,
-0.06589363515377045,
-0.035054679960012436,
-0.01718631573021412,
0.012574886903166771,
-0.03108764812350273,
-0.015935560688376427,
-0.004381148144602776,
0.02544693648815155,
0.011762110516428947,
0.023629499599337578,
-0.02790543995797634,
-0.01289911288768053,
-0.025158770382404327,
0.003326765261590481,
-0.018566066399216652,
0.049808330833911896,
0.021329175680875778,
-0.04047568142414093,
-0.016969453543424606,
0.0012462716549634933,
0.0009729268494993448,
-0.0011677858419716358,
0.01535606849938631,
-0.03369886800646782,
-0.017055300995707512,
0.05347532778978348,
-0.005944970529526472,
-0.021112043410539627,
0.003695422550663352,
-0.03849693387746811,
-0.052618976682424545,
-0.07875871658325195,
-0.030061854049563408,
-0.009051920846104622,
-0.05910078436136246,
0.05744815990328789,
0.020282717421650887,
0.0014820783399045467,
-0.0009572483832016587,
-0.03278280794620514,
0.02205401286482811,
-0.017351791262626648,
-0.05942348763346672,
-0.014767088927328587,
-0.03996561840176582,
0.010625829920172691,
0.008766192011535168,
0.011304750107228756,
0.060821063816547394,
-0.01250985637307167,
-0.02489629201591015,
0.03385615348815918,
-0.0015378108946606517,
-0.03251618891954422,
-0.0027731468435376883,
-0.000283058121567592,
-0.01270959060639143,
-0.030719809234142303,
-0.0108735840767622,
0.040431417524814606,
-0.050230611115694046,
0.013319588266313076,
0.054610732942819595,
-0.01879524625837803,
0.055558498948812485,
0.015362652018666267,
-0.027577007189393044,
0.03935401886701584,
0.013867436908185482,
0.02440665476024151,
-0.008545617572963238,
-0.013721344992518425,
0.00618122098967433,
0.02575550600886345,
0.010415718890726566,
-0.007333484012633562,
-0.04763854667544365,
-0.04492415487766266,
-0.005289087072014809
] |
<p>I'm creating a simple astronomy simulator that should use Newtonian physics to simulate movement of plants in a system (or any objects, for that matter). All the bodies are circles in an Euclidean plane, that have properties such as position, velocity, mass, radius and the resultant force.</p>
<p>I want to update the universe in small time steps, usually a few milliseconds, but I'm not sure how to correctly calculate the changes in position.</p>
<p>The force is simple: <code>fr = sum(G * body.m * bodyi.m / dist(body, bodyi)^2)</code>.</p>
<p>But how do I go on from there?</p>
<p>I could do this:</p>
<pre><code>a = Fr/body.m
v += a*dt
position += v*dt
</code></pre>
<p>But that would, of course, be false. Maybe if I added <code>0.5</code> as a factor in position calculation?</p> | g4583 | [
0.003857725765556097,
-0.03290178254246712,
-0.015143012627959251,
-0.05758693814277649,
-0.016950706019997597,
-0.03316215053200722,
0.0020543490536510944,
-0.035272009670734406,
-0.04008267819881439,
0.0019978955388069153,
-0.01769028790295124,
0.026786169037222862,
0.04519937187433243,
0.004846468102186918,
0.007538261357694864,
0.027730576694011688,
0.040290769189596176,
-0.0011674728011712432,
0.015124129131436348,
0.035933028906583786,
0.011449838057160378,
-0.015409098006784916,
0.016919517889618874,
-0.06906480342149734,
0.009141863323748112,
0.018574897199869156,
0.0648089125752449,
0.07100920379161835,
-0.06945369392633438,
0.03282686695456505,
0.01764095202088356,
0.01651635393500328,
0.02276821807026863,
-0.027504848316311836,
-0.01708347164094448,
0.012450139969587326,
0.03664405271410942,
-0.019279720261693,
0.05300096049904823,
-0.05213572829961777,
0.004333299119025469,
-0.06096517667174339,
0.03978482261300087,
0.012445543892681599,
0.04265056923031807,
-0.07446844130754471,
0.024959610775113106,
-0.04786757007241249,
0.00896073505282402,
-0.00549337500706315,
-0.042535021901130676,
-0.0025797795969992876,
-0.004774090833961964,
-0.007788143120706081,
-0.020472189411520958,
0.08397237956523895,
-0.012261982075870037,
-0.06347671151161194,
0.05758684501051903,
0.011763351038098335,
-0.01548757404088974,
-0.014997294172644615,
0.04081427678465843,
-0.01180014107376337,
0.03607778623700142,
0.04955916106700897,
-0.061524100601673126,
0.0037372196093201637,
-0.06948995590209961,
-0.039895832538604736,
-0.024239610880613327,
-0.030938219279050827,
0.009409151040017605,
-0.0647176057100296,
-0.0735403373837471,
0.011730879545211792,
-0.007877088151872158,
-0.002639730228111148,
-0.04019768908619881,
-0.027394285425543785,
-0.006053888704627752,
0.03317446634173393,
0.018686868250370026,
-0.0020909251179546118,
-0.005041082389652729,
-0.052293404936790466,
-0.018236350268125534,
0.05746721476316452,
-0.0023652289528399706,
0.005836311727762222,
0.006553446874022484,
0.015522612258791924,
0.07165364176034927,
0.02989109605550766,
0.012982514686882496,
-0.04886346682906151,
-0.11326189339160919,
0.07639973610639572,
0.061375729739665985,
0.03543679416179657,
-0.0249747633934021,
-0.03421705216169357,
0.019814234226942062,
-0.01824064366519451,
-0.03271406143903732,
0.014242159202694893,
0.01756567880511284,
0.006531937047839165,
0.00518003897741437,
-0.016950100660324097,
-0.021587077528238297,
-0.10072469711303711,
-0.01705341972410679,
-0.04983837902545929,
-0.036101486533880234,
-0.044193513691425323,
0.023281944915652275,
0.0027311607263982296,
0.033767491579055786,
0.05659439414739609,
-0.05605073645710945,
0.04757940396666527,
0.03855350241065025,
0.015035719610750675,
-0.049490369856357574,
-0.08352668583393097,
-0.05738958716392517,
0.032539550215005875,
0.08008932322263718,
-0.02744172140955925,
0.0008954642107710242,
-0.028868332505226135,
-0.012809991836547852,
0.035630788654088974,
-0.0324091836810112,
0.05202455073595047,
0.0165144931524992,
-0.02324453927576542,
-0.026760701090097427,
-0.013009030371904373,
-0.00246987072750926,
-0.02775369957089424,
0.03466800972819328,
-0.020112307742238045,
-0.04410744085907936,
0.037030357867479324,
-0.008912933059036732,
-0.014757772907614708,
0.021168973296880722,
-0.019139651209115982,
0.09241926670074463,
0.096634142100811,
-0.03418596088886261,
-0.009236159734427929,
0.0391034260392189,
-0.012665108777582645,
0.024749327450990677,
0.038503970950841904,
-0.026881353929638863,
-0.0559002086520195,
0.0424630269408226,
-0.004277012310922146,
0.0036034435033798218,
-0.019564680755138397,
-0.03317951038479805,
0.1027182787656784,
-0.0253960769623518,
-0.051275599747896194,
-0.04416685178875923,
-0.02559053525328636,
-0.00575799448415637,
-0.0593380406498909,
0.020679425448179245,
0.015816833823919296,
-0.011873654089868069,
0.058971889317035675,
0.0023063330445438623,
-0.03312889486551285,
-0.028061674907803535,
0.016952114179730415,
0.05795016884803772,
-0.0012184102088212967,
0.05078570172190666,
0.02845207042992115,
-0.021756965667009354,
-0.008207585662603378,
0.01685275137424469,
0.015640782192349434,
-0.04944339394569397,
-0.017261650413274765,
-0.052218109369277954,
-0.019382433965802193,
-0.01312238723039627,
0.029235854744911194,
-0.027456434443593025,
0.010456489399075508,
0.02517876960337162,
-0.015346050262451172,
-0.021855797618627548,
0.08681139349937439,
0.022110195830464363,
0.03659334406256676,
0.008035450242459774,
0.059300657361745834,
0.01692756824195385,
-0.014509051106870174,
0.020855005830526352,
0.02949010394513607,
-0.009340102784335613,
-0.006359010003507137,
0.052107974886894226,
0.03607339784502983,
-0.02144196443259716,
-0.021839095279574394,
-0.03466235101222992,
0.0006526376237161458,
-0.029517371207475662,
-0.04074379429221153,
-0.017342546954751015,
0.060094598680734634,
-0.010690032504498959,
-0.015022938139736652,
0.05136796459555626,
-0.01607745699584484,
-0.0015820786356925964,
-0.02926485985517502,
0.0024278678465634584,
0.017089465633034706,
0.006127743516117334,
0.014295240864157677,
-0.03596046566963196,
0.06823375076055527,
-0.06696557253599167,
-0.012060891836881638,
0.058969371020793915,
0.012799488380551338,
0.00038894376484677196,
0.03000081330537796,
0.052309222519397736,
0.05091409012675285,
0.015334214083850384,
-0.007180179934948683,
0.008830760605633259,
-0.03212994337081909,
0.049302659928798676,
-0.03645538538694382,
0.0813097283244133,
-0.029537048190832138,
-0.03428241237998009,
0.053881846368312836,
0.0003698773216456175,
-0.035676516592502594,
-0.01739017479121685,
-0.003519203746691346,
-0.029824478551745415,
0.023100003600120544,
-0.07507535815238953,
-0.00683498103171587,
0.016539789736270905,
-0.026260701939463615,
0.0011614032555371523,
0.00832405686378479,
0.03375072777271271,
0.040983233600854874,
0.003777638077735901,
0.014808139763772488,
-0.03317577764391899,
-0.0031395666301250458,
0.005368271842598915,
-0.024491354823112488,
0.0025171362794935703,
-0.003188803791999817,
0.0190639179199934,
0.05037931725382805,
-0.028860779479146004,
-0.023490704596042633,
0.07195619493722916,
-0.040099456906318665,
0.011031693778932095,
0.03154853358864784,
-0.030108392238616943,
-0.04870132356882095,
-0.03332618623971939,
0.039241623133420944,
0.03154157102108002,
-0.058327604085206985,
0.0025722694117575884,
0.0015530093805864453,
-0.0336572490632534,
-0.031409524381160736,
0.007964657619595528,
0.05553773045539856,
0.004009862430393696,
-0.0033272909931838512,
0.024470455944538116,
0.06442993134260178,
0.030965644866228104,
-0.027067475020885468,
0.024749113246798515,
0.03184015676379204,
-0.006543654482811689,
0.008159362711012363,
0.03155558556318283,
0.03507014736533165,
-0.01987573131918907,
-0.012340240180492401,
0.025746438652276993,
-0.03050689585506916,
0.0012268248246982694,
-0.023340431973338127,
0.0224924236536026,
0.0384901687502861,
-0.04333968088030815,
-0.027578826993703842,
-0.05197184532880783,
0.0039274441078305244,
0.007031147368252277,
0.00450494047254324,
0.014132172800600529,
0.02962009236216545,
0.010138197802007198,
-0.04081207141280174,
-0.002318060491234064,
-0.003615383058786392,
0.06423196196556091,
0.08820470422506332,
0.0005421453970484436,
-0.01384006254374981,
-0.045897819101810455,
-0.01895570568740368,
0.0262064840644598,
0.008641079068183899,
-0.01440300140529871,
-0.01223356556147337,
-0.053005918860435486,
-0.0603458546102047,
-0.016611911356449127,
-0.04003799334168434,
-0.016277603805065155,
-0.03345179185271263,
-0.01907224953174591,
-0.02534867264330387,
-0.01223787572234869,
0.02213909849524498,
0.013570999726653099,
0.006534253712743521,
0.07225672155618668,
0.03944670036435127,
-0.001603532931767404,
-0.016822822391986847,
-0.009889462031424046,
-0.05660174787044525,
0.03750406578183174,
-0.0369858518242836,
0.0288911871612072,
0.021754393354058266,
0.005183754954487085,
-0.029795540496706963,
-0.05348684638738632,
0.021391985937952995,
-0.026003899052739143,
-0.058188509196043015,
-0.03205229341983795,
0.09767864644527435,
-0.015959689393639565,
0.020519820973277092,
0.009785554371774197,
0.03401369974017143,
0.003483367385342717,
0.012042052112519741,
0.004392670467495918,
0.0007014911388978362,
-0.02236354723572731,
-0.0535515733063221,
0.058605607599020004,
-0.037281546741724014,
0.05607298016548157,
-0.041196104139089584,
0.03904455900192261,
0.01670326106250286,
0.03654131293296814,
0.00540169095620513,
0.021943064406514168,
0.009948867373168468,
-0.012230297550559044,
0.041007351130247116,
-0.004618092440068722,
-0.03077939711511135,
0.0835203230381012,
0.014666224829852581,
0.021613655611872673,
-0.06679082661867142,
0.000911311770323664,
-0.008729246445000172,
0.020268777385354042,
-0.048650920391082764,
0.015020417049527168,
0.025649115443229675,
-0.024934280663728714,
-0.017217667773365974,
0.007290880661457777,
-0.004134946968406439,
0.013302633538842201,
0.029534436762332916,
-0.04030753672122955,
0.040096964687108994,
0.025913428515195847,
-0.03461149334907532,
0.02158023789525032,
-0.010548015125095844,
0.027658134698867798,
0.015486018732190132,
0.0510016605257988,
-0.05383150652050972,
0.011684534139931202,
0.011759703978896141,
0.06398266553878784,
-0.016334621235728264,
-0.026572570204734802,
0.011804753914475441,
-0.03238612785935402,
0.08834077417850494,
0.011610401794314384,
-0.044349461793899536,
0.009600796736776829,
0.06132484972476959,
0.017170652747154236,
-0.03250380605459213,
0.07807962596416473,
-0.021648947149515152,
-0.017518242821097374,
0.050031520426273346,
0.03898925334215164,
0.040641967207193375,
-0.03698156774044037,
0.04967285692691803,
0.014932084828615189,
-0.010711395181715488,
-0.013975614681839943,
0.017404841259121895,
0.020806139335036278,
0.012120953761041164,
-0.010096055455505848,
-0.02226942405104637,
-0.01518463995307684,
0.0418267622590065,
-0.10339146107435226,
-0.06113195791840553,
-0.02245781384408474,
-0.021120376884937286,
-0.022341005504131317,
0.048493318259716034,
0.038173481822013855,
0.02676539123058319,
0.013646695762872696,
0.010931591503322124,
-0.02014201320707798,
0.02334746904671192,
0.008914836682379246,
-0.002421299461275339,
-0.06271745264530182,
0.042586732655763626,
-0.0794767215847969,
0.007320931181311607,
-0.01614428497850895,
0.05486990511417389,
-0.009326236322522163,
0.0294154342263937,
0.01750352419912815,
0.021831557154655457,
0.033285073935985565,
-0.03511912748217583,
0.020055770874023438,
0.014533953741192818,
-0.001770700910128653,
0.023868922144174576,
-0.0065886592492461205,
0.001894198008812964,
0.07516929507255554,
0.031207123771309853,
-0.038088440895080566,
0.02107883058488369,
0.017881855368614197,
-0.009378337301313877,
0.020058181136846542,
-0.01993272826075554,
-0.011092293076217175,
-0.013493468053638935,
0.002543869661167264,
-0.023039812222123146,
-0.011007349006831646,
0.03070296160876751,
0.04647742956876755,
-0.025456884875893593,
-0.036640465259552,
0.06485229730606079,
0.001546402694657445,
-0.04288949817419052,
-0.00016341744048986584,
0.01896434836089611,
-0.0745336040854454,
0.04022083058953285,
0.029185205698013306,
0.0014642144087702036,
-0.02244175598025322,
0.02814578264951706,
0.03280065953731537,
4.59878918945833e-7,
0.0025636220816522837,
0.026929013431072235,
0.04399183392524719,
0.06907735764980316,
0.02678169496357441,
0.028293658047914505,
-0.039847370237112045,
-0.05311066657304764,
0.009231693111360073,
-0.01597614586353302,
-0.08782614767551422,
-0.059466611593961716,
0.05617012456059456,
0.00966548640280962,
0.07063668221235275,
0.030370516702532768,
0.03595341742038727,
0.03607122600078583,
0.0057735564187169075,
-0.029492035508155823,
-0.050797395408153534,
-0.006017476785928011,
-0.003878014162182808,
-0.008658181875944138,
0.000712006411049515,
0.010905591771006584,
-0.05618242174386978,
-0.021588314324617386,
-0.004125489853322506,
-0.05155622214078903,
0.040762778371572495,
-0.020333779975771904,
-0.021772580221295357,
0.02078257128596306,
0.004757964983582497,
-0.013291588053107262,
-0.08229857683181763,
-0.0031021046452224255,
0.002600803505629301,
0.045899588614702225,
0.044801920652389526,
-0.031316034495830536,
-0.00850825384259224,
0.0443754717707634,
0.018916506320238113,
-0.051481492817401886,
-0.048839833587408066,
0.02854504995048046,
-0.052006568759679794,
-0.05477200075984001,
-0.007599386386573315,
-0.026865413412451744,
0.005799373611807823,
-0.035423971712589264,
-0.0044309226796031,
0.00587550550699234,
0.003736501093953848,
-0.035457294434309006,
0.010102478787302971,
0.013014876283705235,
0.05804726481437683,
0.013590806163847446,
-0.051385167986154556,
0.005710499361157417,
-0.01820724457502365,
-0.021652566269040108,
0.008899804204702377,
-0.019415277987718582,
0.012719782069325447,
-0.007982473820447922,
-0.037954941391944885,
0.04974972456693649,
-0.04646049439907074,
0.008034313097596169,
0.006378257647156715,
-0.049843452870845795,
0.008466925472021103,
0.04550598934292793,
-0.0323416031897068,
0.00421374524012208,
0.052957501262426376,
-0.01858488656580448,
-0.011485788971185684,
-0.011190163902938366,
-0.009383517317473888,
-0.036800410598516464,
-0.005325854290276766,
0.009903023019433022,
-0.015577363781630993,
0.049226824194192886,
0.022976361215114594,
0.059789855033159256,
-0.019245166331529617,
-0.05135175585746765,
0.04873087257146835,
-0.09514390677213669,
-0.022277137264609337,
-0.0019851874094456434,
-0.09325490891933441,
0.021062949672341347,
0.05626627802848816,
-0.04197803884744644,
0.006870728451758623,
-0.036673568189144135,
0.010617837309837341,
0.07549863308668137,
0.009694328531622887,
-0.03543698042631149,
0.05060027167201042,
0.030208515003323555,
0.022907741367816925,
-0.010525344870984554,
-0.009776490740478039,
-0.010092567652463913,
0.027334177866578102,
-0.028603753075003624,
0.03539370000362396,
0.0025023554917424917,
-0.08693695068359375,
0.020688874647021294,
0.04430815950036049,
-0.03494299203157425,
0.023150691762566566,
-0.026403719559311867,
-0.0430791974067688,
0.062349189072847366,
-0.011970791034400463,
0.0174595657736063,
-0.0230144914239645,
0.047006431967020035,
-0.0017555787926539779,
0.05979093536734581,
-0.024490157142281532,
0.006527226883918047,
0.028824742883443832,
-0.017632709816098213,
-0.015022610314190388,
-0.06465896964073181,
0.03874149173498154,
0.03442511335015297,
0.026875125244259834,
0.025743629783391953,
-0.0077741933055222034,
-0.007073065731674433,
0.03840676695108414,
0.06923557817935944,
-0.03423943743109703,
0.027149228379130363,
-0.015700308606028557,
0.00040222867392003536,
-0.003219492733478546,
-0.05579715594649315,
-0.03548513725399971,
-0.045226093381643295,
-0.045332130044698715,
-0.01679190993309021,
0.050914499908685684,
0.05592302978038788,
-0.008259930647909641,
0.03233151137828827,
0.012282409705221653,
-0.04390941187739372,
-0.0029677944257855415,
0.0118734585121274,
-0.055701643228530884,
0.07652657479047775,
0.011004908941686153,
0.02258523926138878,
-0.021159304305911064,
0.000008682466614118312,
-0.023597953841090202,
0.009167585521936417,
-0.007121853530406952,
-0.0004941729712300003,
-0.006801517680287361,
0.04647035896778107,
-0.019377639517188072,
0.04601602628827095,
-0.03076903522014618,
0.03762776032090187,
0.017591707408428192,
-0.029638515785336494,
0.032969728112220764,
0.054044757038354874,
-0.04610036313533783,
-0.015474606305360794,
0.004172068554908037,
-0.01277233101427555,
0.02592226304113865,
-0.024649368599057198,
0.05822575464844704,
-0.050755199044942856,
-0.02891187183558941,
-0.049541834741830826,
0.042806755751371384,
-0.02779960073530674,
-0.01687241531908512,
-0.01635022647678852,
-0.051465004682540894,
0.01141918171197176,
-0.006813955958932638,
-0.0036984325852245092,
-0.0016285220626741648,
0.020034076645970345,
0.00499194348230958,
0.008402706123888493,
-0.012455853633582592,
0.01363586075603962,
-0.0065953996963799,
0.02455245330929756,
0.008976482786238194,
0.01964137889444828,
-0.07438866049051285,
-0.006185461301356554,
-0.027527911588549614,
-0.05479206517338753,
-0.03352607786655426,
-0.0495159886777401,
-0.0663248673081398,
-0.030683280900120735,
-0.0028782712761312723,
-0.06844006478786469,
0.00855033379048109,
-0.06415911763906479,
-0.011530941352248192,
0.02000834234058857,
0.049506984651088715,
0.010478817857801914,
-0.04516630992293358,
-0.05488915368914604,
-0.0251211766153574,
0.007730220444500446,
-0.015240159817039967,
-0.10673453658819199,
0.040498167276382446,
0.036581091582775116,
0.03124481998383999,
-0.014066271483898163,
-0.04196994751691818,
0.08526831865310669,
0.019535034894943237,
0.01149306632578373,
-0.03909752890467644,
0.062132641673088074,
-0.02291371114552021,
-0.03306572884321213,
-0.03415842354297638,
0.0024861404672265053,
-0.021800238639116287,
0.01905377395451069,
0.029508380219340324,
-0.060525696724653244,
-0.022772256284952164,
0.030027257278561592,
-0.01396294217556715,
-0.004149138927459717,
0.04212313890457153,
-0.029079273343086243,
0.033294547349214554,
0.04988110437989235
] |
<p>We know that space-time dimensions are 3+1 macroscopically, but what if 2+2?
Obviously it is tough to imagine two time dimensions, but mathematically we can always imagine as either having two parameters $t_1$ and $t_2$ or else in Lorentz matrix
$$\eta_{00} = \eta_{11} = -1$$ and, $$\eta_{22} = \eta_{33} = 1.$$</p>
<p>Is there any physical reason for not taking this, like the norms become negative or something else? </p> | g4584 | [
-0.01882356032729149,
0.050933923572301865,
0.002877028426155448,
0.012732846662402153,
-0.008397160097956657,
0.0358399972319603,
-0.009710087440907955,
0.002956983633339405,
-0.04870019108057022,
0.0032073352485895157,
0.03831414878368378,
0.022980187088251114,
0.06673432141542435,
0.015000581741333008,
0.0006219923961907625,
-0.031141240149736404,
0.04521457478404045,
0.005597993731498718,
0.016714563593268394,
0.0053958650678396225,
-0.01653238944709301,
-0.01760549657046795,
0.0019773796666413546,
-0.04881150647997856,
0.02189030312001705,
-0.008911033160984516,
0.07094909250736237,
-0.006113275419920683,
-0.01904122158885002,
0.007496871519833803,
0.043314989656209946,
-0.00019007829541806132,
-0.025429606437683105,
-0.02198883332312107,
-0.00887792743742466,
-0.05839945748448372,
0.04166825860738754,
0.02612706460058689,
0.007278753910213709,
0.014919611625373363,
0.013991639949381351,
-0.011497491970658302,
-0.04212133586406708,
-0.009999994188547134,
0.014230334199965,
0.013358629308640957,
0.012184507213532925,
0.007237372454255819,
0.043973859399557114,
-0.008969474583864212,
0.001963014481589198,
-0.003183144610375166,
0.042331937700510025,
0.021267956122756004,
0.019409865140914917,
0.0010947645641863346,
0.0783894881606102,
-0.03827747330069542,
0.10722962766885757,
0.034404102712869644,
-0.048233240842819214,
-0.037248071283102036,
0.05233145132660866,
0.03728509321808815,
0.01393375638872385,
-0.0009659907664172351,
-0.0548868291079998,
-0.002820110647007823,
0.03459499031305313,
-0.001840586424805224,
-0.023341694846749306,
-0.02217154949903488,
0.017844855785369873,
-0.022844862192869186,
0.014052767306566238,
0.07438753545284271,
0.005984128452837467,
0.03667674958705902,
0.005667583085596561,
0.04155771806836128,
-0.06375771760940552,
0.037673402577638626,
-0.011951242573559284,
-0.035626910626888275,
0.05892755463719368,
0.0032866462133824825,
0.031056953594088554,
0.010742354206740856,
0.04211286082863808,
0.05307412147521973,
0.03552116081118584,
-0.0551854632794857,
0.05027622729539871,
0.007001549005508423,
0.0076379296369850636,
-0.017442340031266212,
0.03130073845386505,
0.06277915835380554,
0.012606257572770119,
0.008666717447340488,
0.05512337386608124,
0.0733121931552887,
0.028292028233408928,
-0.004375687800347805,
-0.0358988493680954,
0.0324389711022377,
0.00393624696880579,
0.00526558980345726,
-0.01460924744606018,
-0.02399802766740322,
-0.026015015318989754,
0.018708065152168274,
-0.010322424583137035,
-0.022306246683001518,
0.024574527516961098,
-0.013506680727005005,
0.04315073788166046,
-0.0372295081615448,
-0.023592349141836166,
0.07051530480384827,
0.0339852012693882,
-0.05432312190532684,
0.04226681962609291,
0.008806014433503151,
0.011577984318137169,
0.0034332762006670237,
-0.014596851542592049,
0.02529979683458805,
0.028334565460681915,
-0.08354390412569046,
0.008302660658955574,
0.03800474479794502,
0.048812929540872574,
-0.006909139920026064,
-0.061986517161130905,
0.03617352992296219,
-0.016069451346993446,
-0.024188455194234848,
-0.01552831195294857,
0.026013674214482307,
-0.024516334757208824,
-0.061898671090602875,
0.026846328750252724,
-0.00846902560442686,
-0.04182368144392967,
-0.0007468370604328811,
0.010774866677820683,
-0.031616631895303726,
0.04692528769373894,
0.015729740262031555,
-0.04322265461087227,
0.08002660423517227,
0.05178282782435417,
-0.02354954369366169,
-0.010842344723641872,
0.0006370980991050601,
0.027810515835881233,
0.015000236220657825,
0.02587730437517166,
-0.023365911096334457,
0.03875529766082764,
0.0027407498564571142,
-0.03493252769112587,
-0.002218530047684908,
-0.00895922165364027,
-0.017745256423950195,
0.001006013946607709,
-0.024058792740106583,
-0.03493349626660347,
-0.04863302409648895,
-0.03230242058634758,
-0.030269805341959,
0.00330028822645545,
0.03129146620631218,
0.023001406341791153,
0.06342937052249908,
-0.09123138338327408,
0.052786216139793396,
-0.050741471350193024,
0.02298738621175289,
-0.037525929510593414,
-0.04643528535962105,
-0.028095657005906105,
-0.04625559598207474,
0.035193368792533875,
-0.055008891969919205,
0.011482960544526577,
0.08909445255994797,
-0.10283558815717697,
0.04348796606063843,
0.02223067358136177,
0.004832619801163673,
0.03506677225232124,
0.03242878243327141,
0.012852773070335388,
-0.015445801429450512,
0.05289241671562195,
0.01829659752547741,
-0.009243462234735489,
0.0780671015381813,
0.02444102242588997,
0.04362965375185013,
0.04617007449269295,
-0.016075368970632553,
-0.017458172515034676,
-0.011501840315759182,
-0.018742091953754425,
0.04655323550105095,
-0.0059851352125406265,
-0.020635707303881645,
0.06975452601909637,
-0.011237986385822296,
-0.017348209396004677,
-0.003154365811496973,
-0.046272117644548416,
-0.030793381854891777,
-0.0021958602592349052,
0.01197904348373413,
-0.010647391900420189,
0.05596381798386574,
-0.03637487068772316,
-0.012612960301339626,
0.062221359461545944,
-0.024457883089780807,
-0.008447138592600822,
-0.04021049663424492,
-0.044259313493967056,
-0.03997056931257248,
0.031379301100969315,
-0.00706522585824132,
-0.06494583934545517,
0.0018781349062919617,
0.016722435131669044,
0.032730404287576675,
0.03336094319820404,
-0.004774380009621382,
0.022865796461701393,
0.0403556264936924,
0.014604195952415466,
-0.015218214131891727,
0.07414891570806503,
0.019841980189085007,
0.01371672097593546,
0.024508358910679817,
0.002795259701088071,
-0.06819801032543182,
-0.03548109158873558,
-0.008290394209325314,
0.0037809591740369797,
0.04237338528037071,
0.0005140501307323575,
-0.03300676867365837,
-0.049642469733953476,
0.0342026948928833,
0.002516952808946371,
-0.033146388828754425,
-0.026379967108368874,
0.054633673280477524,
-0.11993689090013504,
-0.018755588680505753,
-0.027789857238531113,
-0.009424775838851929,
0.008420713245868683,
0.035964205861091614,
-0.011246646754443645,
-0.06653940677642822,
-0.03313393518328667,
0.07401798665523529,
0.002130471868440509,
0.032742392271757126,
0.029472829774022102,
0.02825874835252762,
0.017020365223288536,
0.03643493726849556,
-0.015520540997385979,
-0.0014894827036187053,
-0.008895372040569782,
-0.06350307166576385,
0.01546508353203535,
-0.016586415469646454,
-0.019642462953925133,
0.010684157721698284,
-0.04751944541931152,
0.061135195195674896,
0.04923652485013008,
-0.03165551275014877,
-0.016416579484939575,
0.1013866737484932,
-0.02338220737874508,
0.03316279500722885,
-0.04029184207320213,
0.08357225358486176,
0.028340190649032593,
-0.03543371334671974,
0.01495758444070816,
-0.02134367823600769,
-0.03514096885919571,
-0.06807783991098404,
-0.02799115516245365,
0.017128344625234604,
0.029392220079898834,
-0.002586419228464365,
0.031238337978720665,
0.023797011002898216,
0.017042577266693115,
-0.03649023920297623,
-0.047127865254879,
0.0010335380211472511,
-0.00041131870239041746,
-0.02574816159904003,
0.028666343539953232,
0.0812026858329773,
0.01274755410850048,
0.03505028784275055,
-0.039002880454063416,
0.024794980883598328,
0.0091419517993927,
0.007636308204382658,
0.021638350561261177,
0.028016477823257446,
0.006023827474564314,
0.0004785769560839981,
-0.010869285091757774,
0.05616046488285065,
0.0122538385912776,
-0.016051368787884712,
-0.04844040051102638,
0.006756430957466364,
-0.03205573558807373,
0.0012231857981532812,
-0.010267696343362331,
-0.004633713513612747,
0.026685353368520737,
0.02113027311861515,
-0.052845124155282974,
-0.04336344078183174,
-0.035096779465675354,
-0.019565274938941002,
0.005743187852203846,
-0.008075105026364326,
-0.05078332871198654,
-0.033336471766233444,
-0.01795339770615101,
0.024325169622898102,
0.005737849976867437,
-0.015592538751661777,
-0.008384752087295055,
0.03464142978191376,
0.046869002282619476,
0.03283831477165222,
0.056571852415800095,
-0.025758229196071625,
0.024287207052111626,
0.026108818128705025,
-0.011710336431860924,
0.06670160591602325,
-0.017525160685181618,
0.05371939763426781,
0.04689909145236015,
-0.038110751658678055,
-0.0028192084282636642,
-0.023986628279089928,
-0.06566014140844345,
-0.04304548352956772,
0.0029177945107221603,
0.014513222500681877,
-0.0467364676296711,
0.01056455448269844,
0.0088124368339777,
0.01275960635393858,
0.051264505833387375,
0.03254286199808121,
-0.016994524747133255,
0.021817754954099655,
0.06782952696084976,
-0.023937439545989037,
0.015933213755488396,
0.002310762880370021,
-0.009328990243375301,
0.029317237436771393,
0.04106250777840614,
0.01214631274342537,
-0.03921324759721756,
-0.001376876374706626,
-0.0017020147060975432,
-0.01924445480108261,
-0.03930904343724251,
-0.011491931974887848,
-0.05982571840286255,
-0.0475618876516819,
0.02596501260995865,
0.04058174788951874,
0.01988852769136429,
-0.015635257586836815,
0.03313307464122772,
-0.07319366186857224,
0.010373339056968689,
-0.05976551026105881,
-0.012293004430830479,
-0.009413258172571659,
-0.0011076313676312566,
0.057383399456739426,
-0.016774935647845268,
-0.011126340366899967,
-0.030777445062994957,
-0.054650384932756424,
0.014557112008333206,
0.011740169487893581,
0.04391931742429733,
0.0029793342109769583,
0.014651432633399963,
-0.030509138479828835,
-0.016576066613197327,
-0.09580341726541519,
0.06921764463186264,
-0.030957475304603577,
-0.04528401046991348,
-0.02281668409705162,
0.0317605696618557,
0.03665471822023392,
0.025453990325331688,
0.046509794890880585,
-0.0035071601159870625,
0.0010958852944895625,
-0.00837839674204588,
0.049653492867946625,
0.07503128796815872,
-0.015184561721980572,
-0.06540309637784958,
-0.04184059426188469,
-0.004633171949535608,
0.0265385452657938,
-0.016726629808545113,
0.04824812337756157,
-0.021715402603149414,
-0.023939982056617737,
-0.08225050568580627,
0.05472121015191078,
-0.011520476080477238,
-0.02806195057928562,
0.02415025420486927,
-0.07837498188018799,
0.018642915412783623,
0.010630650445818901,
-0.010926252231001854,
0.013357262127101421,
-0.011231128126382828,
-0.02624846249818802,
-0.037866923958063126,
0.03978409245610237,
-0.0389813669025898,
0.05172349512577057,
-0.02700907737016678,
-0.009242829866707325,
-0.03167889267206192,
0.020970910787582397,
-0.045732900500297546,
0.040529653429985046,
-0.009755969047546387,
0.05093948915600777,
-0.052915528416633606,
-0.03000676818192005,
-0.024421531707048416,
0.03554105758666992,
-0.034777991473674774,
-0.035020388662815094,
-0.07212907075881958,
-0.01648038998246193,
-0.06982126086950302,
0.050008323043584824,
-0.0016657451633363962,
0.003312037093564868,
-0.02896335907280445,
0.01964820735156536,
-0.01239920873194933,
-0.010936963371932507,
-0.09043146669864655,
-0.016670335084199905,
-0.041663896292448044,
-0.027437059208750725,
0.011844344437122345,
-0.016925634816288948,
0.0477108433842659,
-0.007801839150488377,
-0.00043758010724559426,
0.03569400683045387,
-0.015709133818745613,
0.004135575145483017,
0.07849932461977005,
-0.03491349518299103,
0.004014133475720882,
-0.01586676761507988,
0.0010794701520353556,
-0.004425041377544403,
-0.047416187822818756,
-0.00946394819766283,
-0.045127905905246735,
-0.05828090012073517,
-0.022718792781233788,
-0.028589149937033653,
-0.05471108853816986,
0.0020548852626234293,
0.037419162690639496,
0.0008634481928311288,
-0.037864044308662415,
-0.023668499663472176,
0.0690796971321106,
-0.02452506124973297,
-0.036856308579444885,
0.07601606845855713,
0.025408389046788216,
0.020539110526442528,
0.015028323046863079,
0.009894657880067825,
0.07456348091363907,
-0.028495462611317635,
0.057901788502931595,
-0.009054883383214474,
0.008870257064700127,
-0.03811679407954216,
-0.04240316152572632,
0.034945048391819,
0.05614664405584335,
-0.10194738954305649,
0.012910633347928524,
0.019537480548024178,
-0.03429210186004639,
-0.01836881786584854,
0.005691856611520052,
0.022139983251690865,
0.05520649626851082,
0.00016931215941440314,
-0.035759031772613525,
0.029697274789214134,
0.03438159450888634,
-0.006789784878492355,
-0.005115846171975136,
0.010320128872990608,
0.002794568659737706,
-0.007046960294246674,
-0.022223301231861115,
-0.05432576686143875,
0.02022426947951317,
0.039147477596998215,
-0.011236044578254223,
-0.03894452750682831,
0.004352514166384935,
-0.004298800136893988,
-0.007544585037976503,
0.001319719711318612,
-0.04619811847805977,
-0.036950431764125824,
-0.03119286336004734,
0.01162637397646904,
0.007191412150859833,
0.036071039736270905,
0.018913311883807182,
-0.033309049904346466,
-0.017321789637207985,
-0.02377772331237793,
-0.02351425774395466,
0.04070195183157921,
0.028566595166921616,
0.016044555231928825,
-0.012510081753134727,
-0.0870303139090538,
0.04049529880285263,
0.027670998126268387,
0.05926426500082016,
0.028997240588068962,
0.01236934494227171,
0.03108658455312252,
0.06386320292949677,
0.054749563336372375,
0.004941117484122515,
0.020039329305291176,
-0.016742581501603127,
-0.024083424359560013,
-0.0046519446186721325,
-0.00901828333735466,
0.04092694818973541,
0.03094600699841976,
-0.011324811726808548,
-0.07668819278478622,
0.0064379568211734295,
0.029371146112680435,
0.004111789166927338,
-0.039578650146722794,
0.016170309856534004,
-0.02569577656686306,
-0.0428592823445797,
-0.039369191974401474,
-0.003565703285858035,
-0.05589881166815758,
-0.0036034979857504368,
0.0074493796564638615,
-0.028380513191223145,
-0.01087975688278675,
-0.05984751135110855,
-0.01609470322728157,
0.0643431693315506,
-0.007465395610779524,
0.02306000143289566,
0.04161542281508446,
0.005072299391031265,
0.021018022671341896,
-0.0463794581592083,
-0.016581488773226738,
0.025692809373140335,
0.03869868069887161,
-0.013344972394406796,
0.0017122630961239338,
-0.03942284733057022,
0.0690351277589798,
0.041318610310554504,
-0.0646611675620079,
0.05759125202894211,
0.01659207232296467,
-0.043838489800691605,
0.026593482121825218,
0.048122700303792953,
-0.0897492840886116,
0.02703644335269928,
-0.010177412070333958,
0.004180756863206625,
0.04594571888446808,
-0.0024087419733405113,
0.04042768478393555,
-0.0013833160046488047,
0.012455443851649761,
0.027173830196261406,
-0.032058291137218475,
0.021899469196796417,
0.046035632491111755,
0.0017103679710999131,
-0.003982493653893471,
-0.04689876735210419,
0.014403737150132656,
0.02069482021033764,
-0.007137906271964312,
0.012226690538227558,
0.01188199408352375,
0.0037658866494894028,
-0.05693516135215759,
-0.04351328685879707,
0.004698802251368761,
0.028847448527812958,
-0.04361273720860481,
-0.07740281522274017,
0.0184945035725832,
0.029466843232512474,
0.016682054847478867,
-0.03737799823284149,
0.03508185222744942,
-0.051150932908058167,
-0.03572694957256317,
-0.043118130415678024,
0.0061654262244701385,
0.010778428055346012,
-0.026240728795528412,
-0.0054849376901984215,
0.01943589374423027,
-0.053229920566082,
0.0019776602275669575,
-0.023043550550937653,
0.07827852666378021,
0.019892729818820953,
-0.052233632653951645,
0.04569435492157936,
-0.06488731503486633,
-0.06206502392888069,
-0.010933098383247852,
0.008858583867549896,
0.006261278409510851,
0.008420033380389214,
-0.042590346187353134,
-0.040339671075344086,
0.0042691598646342754,
0.004720175173133612,
0.0035459045320749283,
0.017968377098441124,
0.014341822825372219,
0.012016444467008114,
0.013762421905994415,
-0.054423071444034576,
0.03818075358867645,
0.02254139631986618,
-0.05213705077767372,
-0.05223393067717552,
-0.02098086103796959,
-0.005757455714046955,
-0.02598772570490837,
-0.00430790800601244,
0.014948556199669838,
-0.008801623247563839,
-0.003463955596089363,
0.03150742128491402,
0.04671553522348404,
-0.07472014427185059,
0.006242258939892054,
-0.05466246232390404,
-0.024296628311276436,
-0.020983384922146797,
-0.04102387651801109,
-0.00103804434183985,
0.04346265643835068,
0.01519701723009348,
-0.030324561521410942,
-0.0228167325258255,
-0.010731175541877747,
-0.023199068382382393,
0.0359966866672039,
0.03060619719326496,
-0.0026320733595639467,
0.04950784891843796,
-0.059955794364213943,
0.002862136112526059,
-0.021031901240348816,
0.05083625763654709,
-0.06473765522241592,
-0.003703279187902808,
-0.036378148943185806,
-0.022079331800341606,
-0.06156568229198456,
-0.038962673395872116,
-0.024477627128362656,
-0.01902294158935547,
-0.0276960302144289,
0.018240313977003098,
0.035539381206035614,
-0.06326469779014587,
-0.010071738623082638,
-0.05907060205936432,
0.054525554180145264,
-0.000014598973393731285,
0.04650268331170082,
-0.014522613026201725,
0.05799294635653496,
-0.017938947305083275,
-0.005584560800343752,
-0.01858617179095745,
0.03922155499458313,
0.014761761762201786,
0.03753490746021271,
-0.03562450408935547,
0.020628519356250763,
-0.019799629226326942,
0.017799558117985725,
0.020829886198043823,
-0.058854855597019196,
-0.011295072734355927,
0.014465431682765484,
-0.04882464185357094,
0.10142118483781815,
0.05362234264612198,
-0.028079736977815628,
0.03735453635454178,
-0.06833179295063019,
0.0004264951276127249,
-0.05185370892286301,
0.047763239592313766,
0.016000645235180855,
0.012224835343658924,
0.0016632325714454055,
0.0049460269510746,
-0.07757031172513962,
-0.02030704915523529,
0.04870754852890968
] |
<p>Suppose there are two electrons in an atom with $s_1 = \frac{1}{2}$, $l_1 = 1$ and $s_2 = \frac{1}{2}$, $l_2 = 1$. Hence the total $S$ (of the atom) may be +1 or 0. And total $L$ is either $+2$, $+1$ or $0$.</p>
<p>Now If we consider </p>
<p>$$\begin{align}
S=1,L=2 &\to 2S+1=3; J=3,2,1\\
S=0,L=2 &\to 2S+1=1; J=2\\
S=1,L=1 &\to 2S+1=3; J=2,1,0\\
S=0,L=1 &\to 2S+1=1; J=1\\
S=1,L=0 &\to 2S+1=3; J=1\end{align}$$</p>
<p>But the last one does not show that $2S+1$ is multiplicity as it has only one $J$ value. Where am I making a mistake?</p> | g4585 | [
0.02111782692372799,
0.013196442276239395,
0.009454325772821903,
0.00005927122401772067,
0.04315032809972763,
-0.04080726206302643,
-0.019816387444734573,
0.04929106682538986,
0.006130058318376541,
0.0019077773904427886,
-0.0625562071800232,
0.055265676230192184,
0.029453841969370842,
-0.000010769768778118305,
-0.022836189717054367,
0.00528266467154026,
0.0666683167219162,
0.018843580037355423,
0.03310840204358101,
0.017243992537260056,
-0.014621592126786709,
-0.01355032715946436,
-0.015551349148154259,
-0.06661292910575867,
0.02606179751455784,
-0.0030872542411088943,
-0.02176477015018463,
-0.011488056741654873,
-0.07675101608037949,
-0.04042836278676987,
0.019775481894612312,
0.02673611417412758,
-0.005600553005933762,
-0.03305499628186226,
0.010384131222963333,
-0.031460873782634735,
0.03135720640420914,
-0.05473993718624115,
0.030021633952856064,
-0.03298284485936165,
-0.020552920177578926,
-0.052281513810157776,
0.02252025343477726,
-0.013789135962724686,
0.02297770231962204,
0.017068633809685707,
-0.05275127664208412,
0.031945083290338516,
0.02927263267338276,
-0.015447178855538368,
0.06562535464763641,
0.0805535838007927,
-0.01860780268907547,
-0.009841757826507092,
0.01935725286602974,
0.058054178953170776,
-0.03054327331483364,
-0.002539915032684803,
0.06377796828746796,
0.05103713646531105,
0.03811996802687645,
0.00369952036999166,
0.01557137444615364,
0.055328935384750366,
0.031170682981610298,
0.007341263350099325,
-0.00379287451505661,
-0.020476246252655983,
0.04716092348098755,
-0.009370136074721813,
-0.026369495317339897,
-0.046266451478004456,
0.048983603715896606,
0.004941824823617935,
-0.005736599676311016,
-0.0050734481774270535,
-0.014691643416881561,
-0.04322590306401253,
-0.020858801901340485,
0.027658000588417053,
-0.030728662386536598,
-0.02152933180332184,
0.02515215240418911,
0.03143595531582832,
0.04189440235495567,
0.02279757708311081,
-0.019612690433859825,
-0.06671588122844696,
-0.02973273955285549,
-0.04525119811296463,
-0.006322933826595545,
0.00395056651905179,
0.0022720058914273977,
-0.022938283160328865,
-0.02677036263048649,
-0.057632144540548325,
0.0006604865193367004,
0.042004987597465515,
-0.06938133388757706,
0.008407071232795715,
-0.03541073575615883,
0.05057758092880249,
0.05962761119008064,
-0.005480624735355377,
-0.009790251031517982,
-0.04863962531089783,
-0.0246969573199749,
-0.0023431472945958376,
0.006630034651607275,
-0.048586513847112656,
-0.009631003253161907,
0.010920116677880287,
-0.01654253900051117,
-0.08529390394687653,
-0.059821732342243195,
0.05391776189208031,
0.05599980056285858,
-0.02481045015156269,
-0.0004790986131411046,
0.020943066105246544,
0.06539413332939148,
-0.022899983450770378,
0.1043642982840538,
0.047498516738414764,
0.00031888243393041193,
-0.016958065330982208,
0.005642995238304138,
-0.016430562362074852,
0.0378156341612339,
-0.0156550370156765,
-0.0676392987370491,
-0.01338021457195282,
0.05649472028017044,
0.0006929766968823969,
0.021334242075681686,
-0.030485820025205612,
-0.006731984205543995,
-0.001475236495025456,
-0.04572540894150734,
-0.0032066155690699816,
0.00975620374083519,
-0.024654025211930275,
0.007144495844841003,
-0.022886747494339943,
0.009788026101887226,
-0.040466487407684326,
-0.05682205408811569,
-0.0027636196464300156,
0.0022086594253778458,
0.029966259375214577,
0.010370767675340176,
0.042500488460063934,
0.03670321777462959,
-0.022417237982153893,
-0.05709995701909065,
-0.02977611869573593,
0.03134899586439133,
0.00276525248773396,
0.019052870571613312,
-0.009152892976999283,
0.028012588620185852,
-0.02140405960381031,
0.013091480359435081,
0.030963754281401634,
-0.03535754606127739,
0.03392137214541435,
-0.004077808000147343,
-0.0558428019285202,
-0.002144445199519396,
-0.035568851977586746,
0.022784849628806114,
-0.0158894844353199,
0.021650468930602074,
-0.0003745205176528543,
0.0341280922293663,
0.05158832296729088,
0.02188786491751671,
-0.01976349577307701,
0.014529203064739704,
0.02962704934179783,
-0.032125040888786316,
-0.003958503250032663,
-0.017070377245545387,
0.006586735136806965,
-0.015424543991684914,
-0.006484696175903082,
-0.014647156931459904,
0.08134710043668747,
-0.08602099120616913,
0.009403018280863762,
0.03586408868432045,
0.06709715723991394,
0.025681674480438232,
0.028661703690886497,
0.003210783004760742,
0.028804544359445572,
-0.0028628164436668158,
-0.017287617549300194,
0.011145372875034809,
-0.014932869002223015,
0.029493503272533417,
-0.020594991743564606,
-0.01526559703052044,
0.02087574638426304,
-0.012993765994906425,
0.00040746989543549716,
-0.0248574148863554,
0.011434941552579403,
0.019531918689608574,
0.019837992265820503,
-0.06656865775585175,
-0.056458134204149246,
-0.050574544817209244,
0.013353442773222923,
-0.014647393487393856,
-0.034022461622953415,
-0.010150638408958912,
0.04019628092646599,
-0.053102802485227585,
0.004635656718164682,
-0.041151013225317,
0.0038191406056284904,
0.04465911164879799,
-0.015623346902430058,
-0.03291749954223633,
0.04861397296190262,
0.0013096746988594532,
-0.06394887715578079,
-0.037573885172605515,
0.008317227475345135,
-0.06980938464403152,
0.032512765377759933,
-0.03497583046555519,
-0.0336579866707325,
0.015493112616240978,
0.02752167172729969,
-0.035350725054740906,
0.013336488977074623,
-0.004166147205978632,
-0.009560738690197468,
0.023004457354545593,
-0.04834902286529541,
-0.0503101572394371,
-0.014840783551335335,
0.049984246492385864,
0.021181851625442505,
0.03379368409514427,
0.03489786013960838,
-0.008792674168944359,
0.06044914573431015,
-0.05478967726230621,
-0.021573731675744057,
-0.07854961603879929,
0.05576838552951813,
-0.021462952718138695,
-0.03328852355480194,
-0.05904771387577057,
0.028290115296840668,
-0.02225048840045929,
0.006484499201178551,
0.0341927595436573,
-0.00671353517100215,
-0.009938152506947517,
0.012954658828675747,
-0.019839247688651085,
-0.020872721448540688,
-0.0034567592665553093,
-0.03282135725021362,
0.03924965858459473,
0.0012283144751563668,
-0.009158442728221416,
0.031360819935798645,
-0.0024425238370895386,
0.064015693962574,
-0.039846159517765045,
-0.047496289014816284,
-0.028229737654328346,
-0.008509442210197449,
0.06812762469053268,
0.03416354954242706,
-0.029915697872638702,
0.03743746876716614,
-0.02014745958149433,
0.020635435357689857,
0.03375096619129181,
-0.031022125855088234,
-0.0015517842257395387,
0.02377910353243351,
0.03678732365369797,
0.04312906414270401,
-0.03666594624519348,
0.0139734772965312,
-0.010437491349875927,
-0.03441838175058365,
0.02882852591574192,
0.01768374629318714,
0.030253393575549126,
-0.032839905470609665,
0.0051918309181928635,
0.0754765048623085,
0.03547324240207672,
0.03159129619598389,
0.008313989266753197,
0.005738209001719952,
0.08993394672870636,
0.02179032936692238,
-0.020725317299365997,
-0.014662360772490501,
-0.04305151477456093,
-0.053741205483675,
0.01874733902513981,
0.0258638858795166,
0.011473378166556358,
-0.01837446354329586,
-0.009071948938071728,
0.008255424909293652,
0.0503416582942009,
0.027116311714053154,
0.02636615000665188,
-0.05274427682161331,
-0.00453584548085928,
-0.00010011646372731775,
0.0005894394707866013,
0.010604361072182655,
-0.0027894272934645414,
-0.012635670602321625,
-0.04165247455239296,
-0.0053126011043787,
-0.02246873825788498,
0.015616370365023613,
-0.0027056632097810507,
0.0572853684425354,
0.0024823283310979605,
-0.003239276120439172,
-0.008469258435070515,
-0.04339161887764931,
0.016353661194443703,
0.002389357192441821,
0.015625618398189545,
0.059853844344615936,
-0.05058049410581589,
-0.009057819843292236,
0.0011951993219554424,
0.024964099749922752,
-0.00517513370141387,
-0.0008643194450996816,
-0.07724687457084656,
0.039168719202280045,
0.04076749086380005,
0.0011283851927146316,
0.008107691071927547,
0.03637943044304848,
0.009723450988531113,
0.05222320556640625,
-0.06911218911409378,
0.009646864607930183,
-0.025133667513728142,
0.05338653177022934,
-0.023491334170103073,
0.049055397510528564,
0.023407043889164925,
-0.01727307215332985,
-0.0012532846303656697,
0.0073145050555467606,
-0.0020024036057293415,
-0.016565240919589996,
-0.029685460031032562,
0.03636059910058975,
0.07241011410951614,
-0.03869255632162094,
-0.05036726966500282,
-0.025748061016201973,
0.015056269243359566,
-0.0008723048376850784,
0.03826705366373062,
-0.06759444624185562,
-0.05979832634329796,
0.003274413989856839,
-0.03248116746544838,
0.07294317334890366,
0.02043887972831726,
-0.03258901834487915,
-0.010672281496226788,
0.006341348402202129,
0.0038555320352315903,
0.012639516964554787,
0.032802119851112366,
-0.05113350227475166,
-0.01527032908052206,
0.007504646200686693,
0.016959067434072495,
-0.015017679892480373,
-0.03992379084229469,
0.05421246588230133,
0.007574704010039568,
-0.018998680636286736,
0.08592500537633896,
-0.05023146793246269,
0.035451777279376984,
0.0763218104839325,
-0.005114890169352293,
-0.04820244759321213,
-0.0026989977341145277,
-0.04660380631685257,
0.031549789011478424,
0.07837769389152527,
0.06583364307880402,
0.0007300825673155487,
0.028744710609316826,
-0.03230509161949158,
-0.008071924559772015,
0.04699864611029625,
0.0561508983373642,
0.00008095270459307358,
-0.004291890654712915,
-0.005325431004166603,
0.008878523483872414,
0.01907462626695633,
0.023686476051807404,
-0.03039032220840454,
0.04037811607122421,
0.06268297135829926,
0.028064657002687454,
-0.07427588105201721,
0.03114374168217182,
0.07087498903274536,
0.026113029569387436,
-0.020751869305968285,
-0.0046949065290391445,
-0.014392999932169914,
-0.044359538704156876,
0.03432232514023781,
0.05120377615094185,
0.0329250767827034,
-0.04473921284079552,
0.010602617636322975,
-0.007736711297184229,
0.050741419196128845,
-0.03703630343079567,
0.09008877724409103,
0.041659317910671234,
0.04250021278858185,
-0.015104039572179317,
0.05750254914164543,
0.07762610167264938,
-0.027691727504134178,
-0.056738872081041336,
-0.06611844897270203,
-0.0037494353018701077,
-0.0508929118514061,
-0.052299562841653824,
0.027136899530887604,
-0.015245292335748672,
0.02247374691069126,
-0.016720114275813103,
-0.01245070155709982,
-0.08537283539772034,
-0.005456175189465284,
-0.01452560257166624,
0.004653934855014086,
-0.02805226668715477,
-0.04231129214167595,
0.0058789364993572235,
0.008608573116362095,
0.05239621922373772,
0.021367916837334633,
-0.003378281369805336,
0.002964647486805916,
-0.07069552689790726,
-0.05326499789953232,
0.02287684939801693,
-0.00712686637416482,
-0.015857061371207237,
0.0051391893066465855,
0.06677418947219849,
-0.05293542891740799,
0.006760591175407171,
0.0023124990984797478,
0.015518817119300365,
-0.017093349248170853,
-0.029470501467585564,
-0.02431570366024971,
-0.02302657812833786,
-0.033959437161684036,
-0.013981150463223457,
-0.01607508584856987,
0.016426125541329384,
-0.020531287416815758,
0.056519925594329834,
0.0007362461183220148,
0.024488119408488274,
0.026785999536514282,
0.044506486505270004,
-0.006378035992383957,
-0.0036999392323195934,
0.04772012680768967,
-0.01978011429309845,
-0.008778898976743221,
0.032643552869558334,
0.025014126673340797,
-0.051935914903879166,
0.04981441795825958,
-0.023602847009897232,
-0.012223945930600166,
-0.008416661992669106,
0.05139300972223282,
0.03348217532038689,
-0.011943085119128227,
-0.006903878878802061,
0.003556816140189767,
-0.02321568876504898,
-0.029751621186733246,
0.02247857116162777,
0.006341550033539534,
0.023938314989209175,
-0.05279740318655968,
0.003415133338421583,
0.0064562042243778706,
-0.024192646145820618,
-0.057490501552820206,
0.046285875141620636,
0.046103354543447495,
-0.002220445778220892,
-0.005752194207161665,
0.0605899803340435,
-0.03117252327501774,
-0.041951313614845276,
-0.0694744735956192,
0.022171415388584137,
0.0258705522865057,
0.007700800430029631,
-0.006686810869723558,
0.009551373310387135,
0.05558032542467117,
0.024247143417596817,
-0.006253451108932495,
-0.05983775854110718,
0.03332960978150368,
0.01934516243636608,
0.016328731551766396,
0.007306681014597416,
-0.036236632615327835,
0.003205294720828533,
0.01699869893491268,
-0.03797976300120354,
0.031462959945201874,
-0.008662339299917221,
-0.030408013612031937,
0.031209547072649002,
-0.002596502425149083,
-0.018829861655831337,
0.08604652434587479,
-0.07639981061220169,
-0.04901030659675598,
0.05124105513095856,
0.04504675045609474,
0.01928841695189476,
0.00021288736024871469,
0.02498529478907585,
0.017650829628109932,
0.01440401654690504,
-0.008453329093754292,
-0.02163887210190296,
0.012301302514970303,
0.021712765097618103,
-0.051281075924634933,
-0.05416461080312729,
-0.017937317490577698,
-0.06355659663677216,
0.04234612360596657,
-0.024799788370728493,
0.010104035958647728,
0.010566892102360725,
0.006002095993608236,
0.053695786744356155,
0.06694769114255905,
-0.04176058992743492,
-0.058792732656002045,
0.009621163830161095,
-0.08077792078256607,
-0.026853065937757492,
0.01099160686135292,
-0.029703296720981598,
-0.028347527608275414,
0.0016468666726723313,
0.03875534236431122,
-0.05961890146136284,
-0.006149479653686285,
0.10574520379304886,
-0.036841679364442825,
-0.053223706781864166,
-0.0191718228161335,
-0.04764103516936302,
0.00698504876345396,
0.005131947807967663,
-0.009955104440450668,
-0.017755169421434402,
0.012726007960736752,
-0.0017748725367709994,
0.02189166657626629,
0.06738850474357605,
0.029119795188307762,
-0.012571310624480247,
0.04245537519454956,
0.009872213006019592,
0.012577246874570847,
-0.04895477741956711,
-0.001199853839352727,
-0.01356095727533102,
0.07499897480010986,
-0.038329239934682846,
0.016565833240747452,
0.007535670883953571,
0.008138860575854778,
-0.002000183332711458,
-0.04391811788082123,
0.035941433161497116,
0.03859004005789757,
-0.029395006597042084,
-0.03859560936689377,
0.04384992644190788,
-0.027586765587329865,
-0.050365690141916275,
0.013916751369833946,
0.07504263520240784,
0.02552596665918827,
-0.0174252986907959,
0.03142521157860756,
0.01065036840736866,
-0.024519409984350204,
-0.04358820617198944,
0.02340640313923359,
0.0010555319022387266,
0.018549781292676926,
0.02819809503853321,
0.006884477566927671,
0.018205171450972557,
0.023081481456756592,
0.006782640237361193,
0.11518006026744843,
-0.062404781579971313,
0.0011054094647988677,
0.05862421914935112,
0.017366742715239525,
-0.028586125001311302,
0.01003678236156702,
0.019121799618005753,
-0.012691361829638481,
-0.1215297281742096,
-0.02507101371884346,
0.01494554989039898,
0.025677453726530075,
-0.009222443215548992,
0.037351131439208984,
-0.0028966895770281553,
-0.056517306715250015,
0.006322099361568689,
0.022344810888171196,
0.03938950598239899,
-0.04179833084344864,
0.003092709230259061,
-0.018301108852028847,
0.00980133842676878,
-0.006749735679477453,
-0.060419484972953796,
0.05209809169173241,
0.000982835772447288,
-0.05456677824258804,
-0.048628754913806915,
-0.07328750193119049,
-0.03897653892636299,
-0.02107693813741207,
0.0025730221532285213,
0.04867294430732727,
-0.020623154938220978,
-0.022272750735282898,
-0.025427522137761116,
0.02045402117073536,
-0.0082846125587821,
-0.026040922850370407,
0.02116909809410572,
0.03669058158993721,
0.00006715571362292394,
-0.00022164291294757277,
-0.017508773133158684,
0.005849268287420273,
0.0133533775806427,
-0.007712609600275755,
-0.05248108133673668,
0.019442684948444366,
0.07203719764947891,
-0.04129280522465706,
0.12575897574424744,
-0.001324373995885253,
-0.012629775330424309,
0.001771270646713674,
-0.000404062942834571,
0.04205942898988724,
0.003438787069171667,
0.041977789252996445,
0.06687047332525253,
-0.045216288417577744,
0.002262262161821127,
0.008816477842628956,
0.03050394542515278,
-0.010912684723734856,
-0.000771427876316011,
0.011820228770375252,
-0.025626225396990776,
-0.059469930827617645,
-0.010512647219002247,
0.026097925379872322,
0.0283421128988266,
0.041616640985012054,
0.020083889365196228,
-0.07811302691698074,
-0.05897600203752518,
0.0728556364774704,
-0.0072183613665401936,
-0.029673246666789055,
0.0005193412071093917,
-0.028538458049297333,
0.01607554964721203,
-0.044817596673965454,
-0.06405699998140335,
-0.018582722172141075,
0.01104405615478754,
-0.009940334595739841,
-0.0006353984936140478,
0.038828294724226,
-0.03403709828853607,
0.030570782721042633,
-0.032661888748407364,
0.04341132566332817,
-0.01890367642045021,
-0.003442775458097458,
0.04016130045056343,
-0.04898039996623993,
-0.02729661576449871,
0.00453915074467659,
-0.005767332389950752,
-0.02381836250424385,
0.01762360706925392,
-0.03520883619785309,
-0.052501074969768524,
-0.011665819212794304,
-0.0514187328517437,
0.043123237788677216,
-0.0140583710744977,
-0.057486407458782196,
-0.0734192356467247,
0.053650468587875366,
-0.021138004958629608,
0.024208281189203262,
0.0898875966668129,
0.02612292394042015,
0.041807662695646286,
-0.013659307733178139,
-0.019330013543367386,
-0.018914099782705307,
-0.07258164137601852,
-0.01330627966672182,
-0.02611199952661991,
0.011090913787484169,
-0.009585502557456493,
-0.09484144300222397,
-0.01022439543157816,
-0.0023030696902424097
] |
<p>The question I have in mind is: <strong>If we place a conductor (arbitrary shape) of total charge zero in a uniform external electric field $\textbf{E}_0$, does it experience any net force? Why (not)?</strong></p>
<p>Now I will discuss the context of the question. I am working on Griffiths <em>Introduction to Electrodynamics, Fourth Edition</em>, p.112 Problem 2.59 (<strong>not homework problem</strong>, though). it says,</p>
<blockquote>
<p>Prove or disprove (with a counterexample) the following</p>
<p>Theorem: Suppose a conductor carrying a net charge $Q$, when placed in
an external electric field $\textbf{E}_e$, experiences a force
$\textbf{F}$; if the external field is now reversed ($\textbf{E}_e \to
- \textbf{E}_e$), the force also reverses ($\textbf{F} \to -\textbf{F}$).</p>
<p>What if we stipulate that the external field is <em>uniform</em>?</p>
</blockquote>
<p>In general this is obviously not true. I will first <strong>limit myself to the case of $Q=0$</strong>.</p>
<p>One approach: when $\textbf{E}$ is reversed, the surface charged distribution $\sigma$ is also reversed (to cancel $\textbf{E}$), so the electrostatic pressure at every point, $\frac{1}{2\epsilon_0} \sigma^2\, \hat{\textbf{n}}$ stays the same. Consequently, $\textbf{F}$ stays the same rather than flips sign.</p>
<p>Another approach: there is an intuitive counterexample. A conductor is generally attracted to a point charge nearby; if the sign of the point charge is flipped, the conductor is still attracted rather than repulsed.</p>
<p>So the first question is easy, and the interesting one is "<strong>What if we stipulate that the external field is <em>uniform</em>?</strong>" I suspect that in a uniform external field the net force is zero, so that $\textbf{F} = 0 = -\textbf{F}$, but I can't think of a way to prove or disprove it.</p> | g4586 | [
0.04033021256327629,
0.029395751655101776,
0.0009373204666189849,
-0.052020687609910965,
0.08602937310934067,
0.06067676097154617,
0.022481946274638176,
0.002431908855214715,
-0.04195927828550339,
0.007341219112277031,
-0.01581696979701519,
0.029733575880527496,
-0.008709189482033253,
-0.03730020299553871,
0.00617541279643774,
0.036837853491306305,
0.06060892343521118,
-0.07869627326726913,
0.03428971767425537,
0.022349322214722633,
-0.02380727231502533,
0.017057063058018684,
0.015415843576192856,
-0.01393444836139679,
-0.014308444224298,
-0.021266644820570946,
0.018982378765940666,
-0.03381400927901268,
-0.01133044809103012,
-0.09494934976100922,
0.009010563604533672,
0.0438273549079895,
0.04455069079995155,
-0.029898419976234436,
-0.09262731671333313,
-0.0031845495104789734,
0.03395942598581314,
0.03622608631849289,
-0.033225324004888535,
0.013132947497069836,
0.04245304688811302,
-0.006144154351204634,
0.034424442797899246,
-0.0005939746042713523,
0.007942208088934422,
-0.028657125309109688,
-0.04267013072967529,
0.02647578902542591,
0.008612927049398422,
-0.007902032695710659,
-0.030078338459134102,
-0.016694337129592896,
0.015089278109371662,
-0.05986355245113373,
-0.0023426737170666456,
-0.019569747149944305,
0.03339027985930443,
0.002139895223081112,
-0.03234648331999779,
0.03973332792520523,
-0.04727604240179062,
0.014014841988682747,
0.0024469003546983004,
-0.0016978104831650853,
-0.008976282551884651,
0.016968371346592903,
-0.09860040992498398,
0.01803511194884777,
0.03662882000207901,
0.007268610876053572,
-0.057145144790410995,
-0.019127923995256424,
-0.021004261448979378,
0.0024223076179623604,
0.0010773540707305074,
0.0359666608273983,
0.007079272530972958,
-0.006605825386941433,
0.0059126513078808784,
-0.010688677430152893,
-0.05800487846136093,
-0.02057257853448391,
0.012704871594905853,
0.06942936778068542,
0.06518388539552689,
-0.02200208231806755,
0.032225556671619415,
-0.001515373820438981,
-0.009233513846993446,
0.013983430340886116,
0.024489831179380417,
0.00045709902769885957,
0.04507819935679436,
0.011819899082183838,
-0.036787401884794235,
-0.029914023354649544,
0.056794095784425735,
0.026010802015662193,
-0.051948755979537964,
-0.04815881326794624,
-0.04259798675775528,
0.006935137324035168,
-0.035799335688352585,
0.05100565031170845,
-0.0013691950589418411,
-0.014512820169329643,
0.047100745141506195,
0.028889361768960953,
-0.012074204161763191,
-0.009425908327102661,
-0.0025733804795891047,
-0.01165840495377779,
-0.037993211299180984,
-0.01588541455566883,
-0.03823316469788551,
-0.021418292075395584,
0.029261166229844093,
-0.04436973109841347,
-0.04577037692070007,
0.09235791862010956,
-0.013039284385740757,
-0.019810548052191734,
0.027065232396125793,
0.017331738024950027,
0.02117242105305195,
-0.015239004977047443,
0.02200211025774479,
0.023364318534731865,
0.02985760010778904,
-0.036601368337869644,
-0.013154396787285805,
0.03411697968840599,
-0.023432444781064987,
-0.03745337948203087,
0.024477358907461166,
0.002289474243298173,
-0.042396895587444305,
-0.022219883278012276,
0.04758641496300697,
-0.019128616899251938,
0.0020892287138849497,
-0.02762824296951294,
-0.00012182846694486216,
-0.002229412319138646,
0.0430847592651844,
-0.004342150408774614,
-0.009606539271771908,
0.015972193330526352,
0.06361319124698639,
0.02444492094218731,
-0.00012548112135846168,
0.08937039971351624,
-0.025745319202542305,
-0.0012137555750086904,
-0.017509832978248596,
-0.039975013583898544,
0.06872550398111343,
0.001146557740867138,
0.026769109070301056,
0.003844887251034379,
0.0795605406165123,
0.028826218098402023,
-0.0011935605434700847,
0.0337904691696167,
0.001065518124960363,
-0.056591954082250595,
-0.0264733899384737,
0.014751453883945942,
-0.006411513779312372,
-0.07904975116252899,
-0.052937768399715424,
0.03699277341365814,
0.016488032415509224,
0.08625325560569763,
0.008190607652068138,
-0.05262671038508415,
-0.05617472156882286,
-0.000571433745790273,
0.03591007739305496,
-0.015504480339586735,
-0.06701403111219406,
0.009438259527087212,
0.034953683614730835,
0.02251167967915535,
0.004909839481115341,
0.03609964996576309,
-0.05395537614822388,
0.09502144902944565,
-0.022928960621356964,
-0.001051391358487308,
-0.02306395024061203,
0.018855711445212364,
-0.06155361235141754,
0.009878002107143402,
0.007948344573378563,
-0.017500294372439384,
0.020755454897880554,
-0.04512637108564377,
0.014831413514912128,
-0.04035217687487602,
0.028670499101281166,
0.030623111873865128,
0.06809008866548538,
-0.022910723462700844,
-0.02378658391535282,
0.015965484082698822,
-0.036385081708431244,
-0.05251437425613403,
0.08097460120916367,
-0.009007015265524387,
0.015615541487932205,
-0.03474689647555351,
-0.016853926703333855,
0.021374907344579697,
-0.030347231775522232,
0.01208017859607935,
-0.05121223255991936,
-0.003628362901508808,
-0.08360457420349121,
-0.004619114566594362,
-0.03672095015645027,
0.0075802914798259735,
-0.0070120180025696754,
0.00817453395575285,
-0.09949453920125961,
-0.014937822706997395,
0.013911187648773193,
-0.012826002202928066,
-0.0243288055062294,
0.010454309172928333,
-0.052507106214761734,
-0.023821966722607613,
0.013160871341824532,
-0.030456839129328728,
0.05163415148854256,
0.037244148552417755,
0.005861713085323572,
-0.01002265140414238,
0.046730805188417435,
-0.05826747044920921,
0.016188498586416245,
-0.0518888495862484,
-0.009896478615701199,
0.006307339761406183,
-0.0012130890972912312,
-0.06270448863506317,
0.01935122348368168,
-0.0003280047094449401,
0.030129870399832726,
0.00883432012051344,
0.03296314924955368,
-0.001932950341142714,
0.0354887992143631,
0.043920453637838364,
-0.004878677427768707,
-0.004610750824213028,
-0.02853460982441902,
0.04895748943090439,
0.006693598814308643,
-0.022033609449863434,
-0.00473930686712265,
0.04063262417912483,
-0.019130799919366837,
0.061202503740787506,
-0.08254394680261612,
-0.013430168852210045,
-0.0709008052945137,
0.02030874229967594,
0.06260699778795242,
0.0366753414273262,
0.029957326129078865,
0.08336642384529114,
-0.03659036010503769,
0.0067321849055588245,
0.01787475310266018,
-0.01828489452600479,
-0.018109234049916267,
-0.02940443903207779,
0.042840030044317245,
0.04192069545388222,
0.023233309388160706,
0.017456892877817154,
-0.03578023239970207,
0.029432227835059166,
-0.0011413692263886333,
-0.0022112990263849497,
0.006140128243714571,
-0.03714834153652191,
-0.005666285753250122,
-0.028481939807534218,
-0.036895714700222015,
0.011057675816118717,
0.10241533070802689,
-0.020470714196562767,
0.015204050578176975,
0.020364727824926376,
0.006238674744963646,
-0.08034317940473557,
-0.004434042144566774,
-0.010388066992163658,
-0.010461702942848206,
-0.022193923592567444,
-0.025894511491060257,
0.009372829459607601,
0.05605756491422653,
0.018222039565443993,
-0.03640250489115715,
-0.05763804912567139,
0.003976546693593264,
0.02106301859021187,
-0.059995848685503006,
0.03951862081885338,
0.004641498439013958,
-0.05041393265128136,
-0.03774877265095711,
0.03972433879971504,
-0.003917810507118702,
-0.019162330776453018,
-0.014995923265814781,
-0.028038732707500458,
0.007789548486471176,
-0.037934429943561554,
-0.010458148084580898,
0.040825068950653076,
0.028229527175426483,
0.06309786438941956,
-0.0532173290848732,
0.06500178575515747,
-0.054677460342645645,
0.01924242451786995,
0.006967941764742136,
0.05047359690070152,
0.014579292386770248,
-0.043028801679611206,
-0.006247346289455891,
-0.0023780777119100094,
0.023763759061694145,
0.09157053381204605,
0.04810557886958122,
0.03563428297638893,
0.0031884631607681513,
-0.04731481522321701,
-0.03253185376524925,
-0.09408696740865707,
-0.009074551984667778,
0.02241254225373268,
-0.04517737403512001,
-0.03765488788485527,
0.0069986796006560326,
0.008401961997151375,
0.019242089241743088,
-0.03927885740995407,
0.06672287732362747,
0.036434706300497055,
0.02040826342999935,
-0.024972882121801376,
0.03041849099099636,
0.008070959709584713,
-0.026632139459252357,
-0.014299902133643627,
0.03483523055911064,
0.010757235810160637,
0.036971673369407654,
-0.05323537811636925,
0.028208879753947258,
0.008051816374063492,
0.003049989929422736,
0.03875069320201874,
-0.08549252897500992,
-0.045735206454992294,
0.033496905118227005,
-0.02616320364177227,
-0.0027629828546196222,
0.0312521830201149,
0.06562737375497818,
-0.06044517830014229,
0.006924252957105637,
0.023224791511893272,
0.049954853951931,
0.050580721348524094,
0.07502579689025879,
0.05157679319381714,
-0.008919383399188519,
0.0027840943075716496,
0.006464843172580004,
0.059528935700654984,
-0.0495464913547039,
0.03397742286324501,
0.039597369730472565,
-0.027352705597877502,
-0.042957693338394165,
0.00279515003785491,
0.0006538534653373063,
0.029422109946608543,
-0.021039403975009918,
0.010793812572956085,
0.04342631623148918,
-0.04436146840453148,
-0.02183295041322708,
-0.004121874459087849,
0.04648374021053314,
0.009004862047731876,
-0.038902442902326584,
0.00497707212343812,
-0.04398306459188461,
-0.03436416760087013,
-0.005699370056390762,
-0.06715589761734009,
-0.006420104298740625,
-0.03968041017651558,
-0.012012229301035404,
-0.030059736222028732,
-0.01496037282049656,
-0.07913385331630707,
0.0264971274882555,
0.01129052322357893,
0.033195916563272476,
0.05628303810954094,
0.029634274542331696,
-0.06032674387097359,
0.04822191596031189,
0.02191007509827614,
0.009202771820127964,
-0.025380857288837433,
0.0374494269490242,
0.060685452073812485,
0.053599387407302856,
0.045243993401527405,
-0.011767338030040264,
-0.002221778966486454,
-0.020933695137500763,
0.031790200620889664,
-0.05360369384288788,
-0.0013571650488302112,
-0.08470167964696884,
0.05066683888435364,
-0.026125848293304443,
0.06881904602050781,
0.0009099586168304086,
0.03636356443166733,
0.08120769262313843,
-0.01268058642745018,
0.005197255406528711,
-0.016532164067029953,
-0.0629827082157135,
0.012613603845238686,
-0.05185782536864281,
0.009036654606461525,
0.01707320474088192,
-0.02264699712395668,
-0.049280211329460144,
0.0035484489053487778,
-0.004160779062658548,
-0.03591519221663475,
-0.03366321697831154,
-0.03970614820718765,
-0.003009588923305273,
-0.007790376897901297,
-0.04668862745165825,
-0.0055985357612371445,
0.007225026376545429,
-0.02688768319785595,
-0.012124130502343178,
0.07109737396240234,
0.03491777181625366,
0.05474288761615753,
-0.028827283531427383,
0.0068236361257731915,
0.02473990060389042,
-0.014148704707622528,
0.028163405135273933,
0.0747186541557312,
0.07372787594795227,
0.006972523406147957,
0.025446927174925804,
0.030460931360721588,
0.03099459409713745,
-0.0367506667971611,
-0.04815303161740303,
-0.054469816386699677,
-0.03402938321232796,
0.031001806259155273,
0.015746060758829117,
-0.00850677490234375,
-0.017492877319455147,
-0.012048831209540367,
-0.023833617568016052,
0.013027203269302845,
-0.020841291174292564,
-0.06667592376470566,
-0.013331462629139423,
-0.009793541394174099,
0.01165070477873087,
-0.0070925368927419186,
-0.04479527473449707,
0.03385290130972862,
-0.020124923437833786,
0.02292347326874733,
-0.046785175800323486,
0.006341843865811825,
-0.048079755157232285,
0.007242722902446985,
-0.029418442398309708,
0.05132770165801048,
0.021277982741594315,
0.05169949680566788,
-0.03227204829454422,
-0.01761360466480255,
0.0027345330454409122,
0.02277361787855625,
-0.05878446623682976,
0.03463044390082359,
0.034650757908821106,
0.004275399260222912,
0.02759704552590847,
-0.0009642512304708362,
-0.08422031253576279,
-0.04053974896669388,
-0.05088592320680618,
-0.031312137842178345,
0.04213978722691536,
0.013157772831618786,
0.017577039077878,
-0.054763514548540115,
-0.013222213834524155,
-0.006419910583645105,
-0.01960412599146366,
-0.004453389439731836,
-0.018032481893897057,
0.009903955273330212,
-0.014373840764164925,
0.04715009778738022,
-0.04716421291232109,
-0.035849735140800476,
-0.03682318702340126,
-0.029014984145760536,
0.049431901425123215,
0.008159640245139599,
-0.00811308715492487,
-0.026659438386559486,
0.05627676099538803,
-0.044889897108078,
0.041050709784030914,
0.005586876068264246,
-0.0741286501288414,
0.030367081984877586,
-0.05530601739883423,
-0.01901692897081375,
0.02044394426047802,
-0.02334047481417656,
0.045590437948703766,
0.026544343680143356,
-0.08429834246635437,
0.015899881720542908,
0.03672219067811966,
0.036810409277677536,
0.006808931473642588,
-0.014770623296499252,
-0.012284008786082268,
-0.044641830027103424,
0.03808140009641647,
0.009385626763105392,
-0.0037400091532617807,
-0.00946117378771305,
0.044005386531353,
0.024822989478707314,
-0.02610831707715988,
0.035439927130937576,
0.027360808104276657,
0.036840371787548065,
0.03712177276611328,
0.005694585852324963,
0.037532489746809006,
-0.000005310439973982284,
0.053283676505088806,
-0.03162599354982376,
-0.004911679308861494,
-0.01661432534456253,
-0.034754738211631775,
0.008117800578474998,
-0.01757236197590828,
0.029495321214199066,
0.019509969279170036,
-0.07440689951181412,
-0.04735155776143074,
0.0006504348129965365,
-0.06199531629681587,
-0.013976050540804863,
0.04952038824558258,
-0.054849229753017426,
0.040154505521059036,
-0.029705142602324486,
0.007002672180533409,
0.000490780861582607,
-0.033740751445293427,
0.020587677136063576,
-0.002777941059321165,
0.013613537885248661,
-0.010698255151510239,
0.06206825003027916,
-0.010675951838493347,
0.029073022305965424,
0.07334702461957932,
-0.01601392589509487,
0.04912970960140228,
0.06399468332529068,
0.05128480866551399,
-0.0005336608155630529,
-0.01627863384783268,
-0.022684333845973015,
0.03140230104327202,
-0.002324372064322233,
-0.0111638642847538,
-0.034959014505147934,
0.03065703622996807,
-0.04415096715092659,
0.0016318514244630933,
0.0048507582396268845,
-0.026655735448002815,
0.0061188009567558765,
-0.012861267663538456,
-0.07117193192243576,
0.03302668407559395,
0.03275865688920021,
0.013993059284985065,
0.02400573529303074,
0.00823652371764183,
0.005260607227683067,
0.07309635728597641,
0.00146073242649436,
-0.015202351845800877,
0.009083910845220089,
-0.060551732778549194,
0.041800063103437424,
0.007671216037124395,
0.023257620632648468,
0.046388860791921616,
-0.00022677377273794264,
0.019833093509078026,
-0.024524563923478127,
-0.05515284091234207,
0.050434790551662445,
0.009207870811223984,
-0.026344507932662964,
-0.049947790801525116,
0.01054839976131916,
0.0015856954269111156,
0.004651625175029039,
-0.02716873772442341,
0.054669562727212906,
0.06879454851150513,
0.0005656441790051758,
-0.04752533137798309,
-0.014546406455338001,
-0.02127305418252945,
0.027872078120708466,
0.05748637765645981,
0.019335435703396797,
-0.02737385220825672,
0.01514680776745081,
-0.022551516070961952,
-0.008074643090367317,
0.005411663558334112,
0.016404973343014717,
-0.0261805709451437,
0.013859438709914684,
-0.003229327267035842,
-0.058701448142528534,
-0.0400269590318203,
-0.003386134747415781,
0.037586383521556854,
-0.07282714545726776,
-0.0033059767447412014,
-0.016213087365031242,
0.05587833374738693,
-0.01138010248541832,
0.0015929501969367266,
0.06637183576822281,
0.05687073618173599,
0.011536573991179466,
0.03954584524035454,
0.05101342871785164,
-0.04498457536101341,
0.036406148225069046,
-0.05137002095580101,
-0.010513466782867908,
-0.07210388779640198,
0.028720350936055183,
-0.0026326028164476156,
-0.025059698149561882,
0.046437058597803116,
0.023553302511572838,
0.006286391988396645,
0.01417718455195427,
-0.015869367867708206,
-0.017148125916719437,
0.0012240299256518483,
0.0597885325551033,
0.03321473300457001,
0.0038362951017916203,
-0.014030922204256058,
-0.011697482317686081,
-0.05189816281199455,
-0.008899238891899586,
-0.0025194541085511446,
0.013490614481270313,
-0.04335546866059303,
-0.038083504885435104,
-0.041888728737831116,
0.006194231100380421,
0.052628666162490845,
0.014635155908763409,
0.03150094673037529,
-0.015578522346913815,
0.06498789042234421,
0.0034245257265865803,
-0.07881953567266464,
-0.0006976780714467168,
0.029030276462435722,
-0.014480656944215298,
0.008845703676342964,
0.04056210815906525,
-0.005471380893141031,
0.0042127822525799274,
-0.05482263118028641,
0.01997171714901924,
-0.007916142232716084,
0.028127126395702362,
0.04587138444185257,
-0.0013433321146294475,
-0.0015441227005794644,
-0.0525597408413887,
-0.0400066040456295,
-0.00518908491358161,
-0.007141411770135164,
-0.04020821675658226,
-0.0019507169490680099,
-0.02472641132771969,
0.018513040617108345,
-0.038290709257125854,
-0.009653594344854355,
0.0200570747256279,
-0.07950831204652786,
-0.012096613645553589,
-0.035316381603479385,
0.027174877002835274,
-0.024308551102876663,
0.060836683958768845,
0.014178693294525146,
0.007712425198405981,
0.024280766025185585,
0.011846061795949936,
-0.06376854330301285,
0.018570246174931526,
0.019492167979478836,
-0.05490964278578758,
-0.039143454283475876,
-0.00037051920662634075,
0.05547379329800606,
0.04643934592604637,
-0.05046852305531502,
-0.014369150623679161,
0.021314043551683426,
-0.014442387968301773,
-0.04711698368191719,
-0.012526034377515316,
-0.026257578283548355,
-0.001853836583904922
] |
<p><a href="http://physics.stackexchange.com/q/27939/2451">Here</a> and <a href="http://physics.stackexchange.com/q/28181/2451">here</a> it states that water is at its highest density around $4^\circ$ Celsius. I know very little physics and a Google search has left me without an answer. I am teaching an <a href="http://en.wikipedia.org/wiki/Ordinary_differential_equation" rel="nofollow">ODE</a> class in the math department. I have a student that heard the above stated in a physics course. She is wondering whether this is an appropriate project for my class. So, does this fact come from some differential equations? </p> | g4587 | [
0.05550437048077583,
0.01402217335999012,
-0.007283695507794619,
-0.02404937334358692,
0.018566329032182693,
0.04559871926903725,
0.023205282166600227,
0.008490871638059616,
-0.046553418040275574,
0.012291702441871166,
-0.009204278700053692,
-0.010830824263393879,
0.06739059090614319,
-0.015922341495752335,
-0.011202303692698479,
0.015261171385645866,
0.019602922722697258,
-0.048861563205718994,
0.00441211462020874,
0.012690586969256401,
-0.03055727854371071,
-0.0483894944190979,
0.03754797950387001,
-0.02213943749666214,
0.03680305555462837,
0.044210709631443024,
0.007547224406152964,
-0.03506217524409294,
-0.05963148549199104,
-0.030134979635477066,
-0.011372999288141727,
0.04319433495402336,
0.010556615889072418,
-0.02578631602227688,
-0.08812662214040756,
-0.027294982224702835,
0.02340906485915184,
-0.007559919264167547,
0.01141238771378994,
-0.04764701426029205,
0.010622288100421429,
-0.019443687051534653,
0.03663501515984535,
0.010249718092381954,
-0.0015826052986085415,
0.001756142359226942,
-0.04315923899412155,
-0.013847419992089272,
-0.033884476870298386,
-0.02260189689695835,
0.013399520888924599,
0.03267183154821396,
0.008511170744895935,
0.010879549197852612,
-0.03668787330389023,
0.039400167763233185,
0.02494218572974205,
0.01614953577518463,
0.03002452291548252,
0.024626964703202248,
0.036708611994981766,
0.02276534214615822,
-0.012346209958195686,
-0.003945955540984869,
0.07352358102798462,
-0.02258889749646187,
-0.0457698255777359,
-0.033150628209114075,
-0.017306650057435036,
-0.01613936573266983,
0.052721451967954636,
-0.08374673128128052,
-0.05609888955950737,
-0.04397323355078697,
-0.004904006142169237,
0.02306348644196987,
0.019576286897063255,
-0.036942362785339355,
0.0058046807534992695,
-0.006751792039722204,
-0.03327740728855133,
0.015674158930778503,
0.029602844268083572,
-0.031454380601644516,
0.09155556559562683,
-0.021829137578606606,
0.030349718406796455,
0.014847534708678722,
0.0017881500534713268,
-0.016759473830461502,
-0.03173372149467468,
-0.010702330619096756,
0.070664182305336,
-0.0251894723623991,
0.03239260986447334,
-0.018371064215898514,
0.0024231821298599243,
0.024899812415242195,
0.018566831946372986,
0.02335641346871853,
-0.05420564487576485,
-0.0062096756882965565,
0.019876165315508842,
-0.01369647216051817,
-0.0151930907741189,
0.04347347095608711,
0.018846897408366203,
-0.01979033835232258,
-0.0695125088095665,
-0.0014464661944657564,
-0.009047601372003555,
-0.023148121312260628,
-0.013621481135487556,
0.026448417454957962,
-0.04983927309513092,
0.006960009224712849,
0.024947678670287132,
-0.02209268882870674,
-0.007349545136094093,
0.06390419602394104,
-0.010183651000261307,
0.09676036983728409,
0.03879963979125023,
0.0855981856584549,
0.018486568704247475,
0.022450609132647514,
0.03134751319885254,
0.03288041800260544,
0.016150498762726784,
-0.018060747534036636,
-0.0015983019256964326,
0.014318008907139301,
-0.02178533747792244,
-0.019785819575190544,
0.03628163039684296,
0.000716955226380378,
-0.009540855884552002,
0.01545277051627636,
-0.008990100584924221,
0.05476269870996475,
0.042251791805028915,
0.06650551408529282,
0.021973349153995514,
-0.01318842452019453,
-0.002706802450120449,
-0.041790325194597244,
-0.060672469437122345,
0.009212839417159557,
-0.03263049200177193,
-0.008042748086154461,
0.02645159140229225,
-0.022282006219029427,
0.02884395606815815,
-0.03935028240084648,
0.009853054769337177,
0.0031221022363752127,
-0.024651605635881424,
0.031938452273607254,
-0.00018247339176014066,
-0.015234562568366528,
-0.01233688835054636,
0.035189222544431686,
-0.0003739162639249116,
0.04525468125939369,
-0.021462690085172653,
-0.03678463026881218,
0.03504151850938797,
-0.002020155545324087,
-0.0492854081094265,
0.004706813022494316,
-0.04447215795516968,
-0.021505866199731827,
-0.05072331428527832,
-0.0037839016877114773,
-0.03052995540201664,
-0.025339389219880104,
0.03640484809875488,
-0.042840082198381424,
0.033593546599149704,
-0.03632131591439247,
-0.007360230199992657,
0.036835767328739166,
0.059479814022779465,
-0.017234662547707558,
-0.005966445431113243,
0.007898475043475628,
0.028657617047429085,
0.0029080742970108986,
-0.026246268302202225,
0.016179943457245827,
-0.0630301833152771,
-0.022559959441423416,
0.002516363048925996,
0.024327637627720833,
0.0742914006114006,
-0.02281869389116764,
0.01611437276005745,
-0.027347495779395103,
-0.023252902552485466,
0.05295957624912262,
0.00800333172082901,
0.018061282113194466,
0.018963053822517395,
-0.018649810925126076,
-0.014444052241742611,
0.048728954046964645,
-0.032371778041124344,
-0.015462223440408707,
0.03613194823265076,
-0.03404894471168518,
-0.0014175208052620292,
-0.04084508493542671,
-0.008923791348934174,
0.06273382902145386,
0.011951037682592869,
-0.01354053895920515,
-0.02840878628194332,
0.03629061579704285,
-0.033697620034217834,
0.02150268293917179,
-0.0642814189195633,
-0.00010829434904735535,
-0.0170042272657156,
0.04436175152659416,
-0.0594228059053421,
0.006819928530603647,
-0.07900420576334,
-0.035660259425640106,
0.028900498524308205,
0.025577805936336517,
-0.02326158806681633,
0.013077172450721264,
-0.014606648124754429,
0.025545690208673477,
0.05458154156804085,
0.08943987637758255,
-0.062479715794324875,
-0.016900889575481415,
0.035204850137233734,
0.009158937260508537,
0.017128732055425644,
0.0326455719769001,
-0.04845350980758667,
-0.039507947862148285,
0.03096245415508747,
-0.012720515951514244,
-0.0024163995403796434,
0.01979294791817665,
0.058811914175748825,
0.019025804474949837,
0.0055071283131837845,
-0.060504864901304245,
0.022518692538142204,
0.0632128044962883,
0.04528898000717163,
-0.0035942289978265762,
-0.04725176468491554,
0.0069273775443434715,
-0.03496308997273445,
-0.04914139583706856,
0.019479770213365555,
-0.049158141016960144,
-0.003358073066920042,
-0.03702302277088165,
-0.09793658554553986,
0.006807207595556974,
-0.06739044189453125,
-0.00543823279440403,
0.01543976366519928,
0.0021244753152132034,
0.0393669418990612,
0.06948517262935638,
-0.04056162014603615,
0.04850723594427109,
-0.0609174408018589,
-0.03928912803530693,
0.010003569535911083,
-0.0024761769454926252,
0.013560261577367783,
-0.007122568320482969,
0.02852296456694603,
0.009281223639845848,
-0.022263409569859505,
0.014603904448449612,
0.07277333736419678,
-0.021108046174049377,
-0.011294691823422909,
0.008635863661766052,
-0.018637916073203087,
0.028804536908864975,
0.01609904132783413,
0.010737672448158264,
0.004299024119973183,
0.04405227676033974,
0.018490560352802277,
0.02389632724225521,
0.02130524255335331,
-0.042553532868623734,
-0.020575813949108124,
0.010140946134924889,
-0.03775555267930031,
-0.012092117220163345,
0.01440915372222662,
-0.00454477546736598,
0.0004056868201587349,
0.042999785393476486,
-0.04396286606788635,
-0.007545096334069967,
-0.0038807038217782974,
-0.01026943139731884,
-0.027943627908825874,
-0.03404225409030914,
-0.0105664087459445,
0.031189916655421257,
-0.032890427857637405,
-0.04401205852627754,
0.0314207561314106,
-0.03215489536523819,
0.06133203208446503,
-0.05489450693130493,
0.019353197887539864,
-0.032471444457769394,
0.013191328383982182,
0.0011969569604843855,
0.026949673891067505,
0.03901077061891556,
-0.016712499782443047,
-0.026506515219807625,
-0.04534976929426193,
-0.02154277078807354,
0.01933402195572853,
-0.018047137185931206,
0.017857449129223824,
0.015082495287060738,
-0.0419684536755085,
-0.04811515659093857,
0.011820298619568348,
0.037164073437452316,
0.03130071610212326,
0.029927100986242294,
-0.0802149698138237,
-0.014210686087608337,
-0.005022734869271517,
-0.029104083776474,
-0.019396889954805374,
0.01086663082242012,
0.005622547585517168,
0.028664493933320045,
0.02972228080034256,
0.01574237085878849,
0.05624467134475708,
0.018591061234474182,
0.007561584003269672,
-0.05033939704298973,
0.021455254405736923,
-0.026138225570321083,
0.005555341951549053,
0.018214372918009758,
-0.02776547521352768,
-0.025497280061244965,
0.031628675758838654,
-0.02844713069498539,
0.06836162507534027,
0.013487217016518116,
-0.007959053851664066,
-0.0048124841414391994,
-0.056721992790699005,
0.0527430959045887,
-0.055858220905065536,
-0.015667585656046867,
-0.03447950631380081,
-0.04822865501046181,
-0.0011669090017676353,
0.08204998821020126,
0.07016734778881073,
-0.059747062623500824,
0.014524606056511402,
-0.013032469898462296,
-0.03077588602900505,
0.0383845716714859,
0.04364227503538132,
0.011013081297278404,
0.04718800634145737,
-0.006685590371489525,
-0.029445169493556023,
-0.04017573222517967,
-0.0463072843849659,
-0.04548453167080879,
0.03566879779100418,
-0.08608277887105942,
0.06934555619955063,
-0.011756335385143757,
0.007569870445877314,
0.06429284065961838,
-0.01746702380478382,
-0.022720636799931526,
0.03061954490840435,
0.04148836061358452,
-0.08434271812438965,
-0.00912483874708414,
-0.04630131646990776,
-0.023208945989608765,
0.030773386359214783,
-0.014729445800185204,
0.004439325071871281,
0.02856425568461418,
0.06381680816411972,
-0.049912042915821075,
-0.02081187628209591,
-0.056298356503248215,
0.052686236798763275,
0.04668254032731056,
-0.020991478115320206,
-0.022872064262628555,
-0.019482994452118874,
0.027737556025385857,
-0.01791154220700264,
-0.027442017570137978,
0.010174649767577648,
0.016934864223003387,
0.02027244120836258,
0.001384855480864644,
-0.05104997009038925,
0.006810849066823721,
0.02695467509329319,
0.06445258855819702,
0.0955980196595192,
-0.0090582724660635,
-0.0362420529127121,
-0.02853410504758358,
-0.025671832263469696,
-0.0050864084623754025,
-0.010042810812592506,
0.04856344312429428,
0.029274892061948776,
0.041993554681539536,
0.019843997433781624,
0.015877459198236465,
-0.03218744695186615,
0.034268904477357864,
-0.01796799525618553,
0.011629099026322365,
0.022952236235141754,
-0.00677168183028698,
0.023065559566020966,
0.042527683079242706,
0.020817911252379417,
-0.000741704658139497,
-0.0309113971889019,
-0.013585446402430534,
0.005021695047616959,
-0.00659352820366621,
-0.006742030847817659,
0.018544426187872887,
-0.009181348606944084,
-0.05556076392531395,
-0.02910999208688736,
0.026221102103590965,
-0.05696636065840721,
0.05976489931344986,
-0.010460319928824902,
-0.008645955473184586,
0.022882286459207535,
0.054672397673130035,
0.05737918242812157,
-0.08718441426753998,
0.0507546029984951,
-0.05643991380929947,
-0.044807277619838715,
-0.024431465193629265,
0.018842624500393867,
0.07622241973876953,
0.06479641050100327,
0.005571090616285801,
-0.009229980409145355,
0.01833506114780903,
0.008379993960261345,
0.01727774180471897,
0.011972264386713505,
-0.021793654188513756,
0.025946639478206635,
0.027803711593151093,
-0.051450345665216446,
0.07994053512811661,
0.011133435182273388,
0.06745170801877975,
-0.05162551626563072,
0.03660435974597931,
0.014870306476950645,
-0.016618365421891212,
-0.02372109889984131,
-0.014493484050035477,
0.03376176208257675,
0.01454909611493349,
-0.07039307057857513,
-0.06949925422668457,
0.01739327609539032,
-0.07693198323249817,
0.025212742388248444,
0.011720231734216213,
-0.029387077316641808,
-0.007978374138474464,
-0.010405694134533405,
-0.034010980278253555,
-0.012205024249851704,
0.04591251164674759,
0.05001556873321533,
0.03479127585887909,
-0.006075050216168165,
0.08237822353839874,
0.017169971019029617,
0.007524028420448303,
0.05865076929330826,
-0.001096123829483986,
0.0007081126677803695,
-0.05794626101851463,
-0.05297871306538582,
0.04345418140292168,
0.044089771807193756,
-0.01597888581454754,
0.0759652853012085,
-0.04995030537247658,
0.01264398917555809,
0.044805217534303665,
-0.014029443264007568,
-0.03437238931655884,
-0.0258380938321352,
0.01608438603579998,
0.024361956864595413,
0.022623810917139053,
0.02525441162288189,
0.020587274804711342,
0.07000963389873505,
-0.045015204697847366,
-0.023761359974741936,
-0.02425830438733101,
-0.013639544136822224,
-0.004010059405118227,
0.0545954629778862,
0.060117777436971664,
0.039315611124038696,
-0.0010043639922514558,
0.004857161547988653,
0.07136043161153793,
-0.01550000999122858,
-0.022316856309771538,
-0.04867701604962349,
-0.041752640157938004,
0.06479889154434204,
0.003935534972697496,
-0.035476554185152054,
0.014644329436123371,
-0.03998619318008423,
0.021299511194229126,
0.005390523001551628,
-0.0359002910554409,
0.013997097499668598,
-0.022857651114463806,
-0.06491570919752121,
0.017230108380317688,
0.024229269474744797,
0.061245396733284,
0.051691025495529175,
0.02138277143239975,
-0.07707546651363373,
-0.06464836001396179,
-0.019145695492625237,
-0.017930367961525917,
0.0686066523194313,
0.08323578536510468,
-0.013262465596199036,
-0.010313364677131176,
0.030830612406134605,
-0.0435958094894886,
0.06623020768165588,
-0.022835418581962585,
-0.022984040901064873,
0.022297436371445656,
-0.016853464767336845,
-0.038755495101213455,
0.0007805085042491555,
-0.01622358150780201,
-0.02190525457262993,
-0.00267901923507452,
0.0021237994078546762,
-0.011849511414766312,
-0.016716986894607544,
0.01661018095910549,
-0.02669692412018776,
-0.025731999427080154,
0.037334851920604706,
0.011670990847051144,
-0.011097335256636143,
0.008252912200987339,
0.0355098731815815,
-0.050761591643095016,
0.0018689249409362674,
0.04397242143750191,
-0.03894556686282158,
-0.003861762583255768,
0.03649193048477173,
0.005583904683589935,
-0.010094567202031612,
0.04798775911331177,
0.03294102102518082,
-0.006726753432303667,
0.056756969541311264,
0.027787650004029274,
-0.06578286737203598,
0.005692141596227884,
-0.0467170812189579,
0.04452391713857651,
0.023516714572906494,
-0.011747497133910656,
-0.0645115002989769,
-0.019385090097784996,
0.07639844715595245,
0.03348730504512787,
-0.012655136175453663,
0.022680114954710007,
-0.0024614923167973757,
-0.012271995656192303,
-0.003421778790652752,
-0.010080664418637753,
0.00744986766949296,
0.06991595029830933,
-0.05378522351384163,
0.011710068210959435,
0.07235430926084518,
-0.01987844705581665,
0.06977707892656326,
-0.03947748243808746,
-0.005378429312258959,
0.04268278181552887,
-0.01021270640194416,
0.022908996790647507,
-0.05720693618059158,
0.012418339028954506,
0.10811474174261093,
0.03868010267615318,
0.0004326209891587496,
-0.007382885552942753,
0.02030223235487938,
-0.017128482460975647,
0.012150613591074944,
-0.011040717363357544,
0.02165166474878788,
-0.041547104716300964,
-0.07614286988973618,
-0.049127355217933655,
0.0584767647087574,
-0.07058440893888474,
-0.015227971598505974,
-0.017698494717478752,
-0.016591724008321762,
0.005323539953678846,
0.031495776027441025,
0.01113999355584383,
0.0015675012255087495,
-0.004466064274311066,
-0.012062197551131248,
-0.012309429235756397,
0.027443017810583115,
0.04118090122938156,
-0.050567399710416794,
0.0195110272616148,
0.0176578126847744,
-0.012444253079593182,
-0.056762199848890305,
-0.0055363853462040424,
-0.003318110480904579,
0.03281274810433388,
-0.016903536394238472,
-0.03900017589330673,
0.011551318690180779,
0.04724018648266792,
0.00894130952656269,
-0.008164279162883759,
0.025845248252153397,
-0.00023506545403506607,
0.054316941648721695,
0.027875909581780434,
0.02224813774228096,
-0.043683011084795,
-0.06392137706279755,
-0.01182251051068306,
-0.0255103949457407,
-0.053010761737823486,
0.07578955590724945,
0.045063506811857224,
-0.0584062822163105,
0.003248174674808979,
-0.005976337939500809,
-0.03790909796953201,
-0.009240349754691124,
0.07179215550422668,
0.02343798242509365,
-0.013577776961028576,
0.019825419411063194,
0.026189003139734268,
-0.039055004715919495,
-0.008393361233174801,
-0.03083401545882225,
-0.029311245307326317,
-0.0043746656738221645,
0.022956544533371925,
0.029495105147361755,
0.037691082805395126,
-0.04606565088033676,
-0.03279843181371689,
-0.005185615736991167,
-0.04328589886426926,
0.01640038937330246,
-0.07062358409166336,
0.06873591244220734,
0.0017954816576093435,
-0.0336216539144516,
-0.04911133274435997,
-0.03073493018746376,
-0.012337405234575272,
0.007878466509282589,
0.019984452053904533,
-0.031705740839242935,
-0.04375944286584854,
-0.03554484620690346,
-0.033892348408699036,
-0.035993944853544235,
0.002941336017102003,
-0.002751857042312622,
0.01915411278605461,
-0.06946469843387604,
-0.0013767110649496317,
-0.004119690041989088,
-0.051444560289382935,
-0.01234132144600153,
-0.0034811394289135933,
0.015632668510079384,
0.038086388260126114,
0.026907822117209435,
0.06228958070278168,
-0.0015204574447125196,
-0.030084950849413872,
-0.006807828322052956,
-0.08062941581010818,
-0.0017408740241080523,
-0.06737329810857773,
-0.035842135548591614,
0.03268347308039665,
-0.005167173221707344,
-0.05603594332933426,
-0.024543356150388718,
-0.02105036936700344,
-0.03805460035800934,
0.032979972660541534,
0.002729967702180147,
-0.07189292460680008,
0.05278914049267769,
0.015825683251023293,
-0.0026789591647684574,
-0.011484996415674686,
-0.043288640677928925,
-0.04620412364602089,
0.08731438219547272,
0.01675882190465927,
0.005863857921212912,
-0.05154551938176155,
-0.029440606012940407,
-0.0606313981115818
] |
<blockquote>
<p>I have a pot with water of mass $m$ and it is heated by a stove
element of temperature $T_E$ and with a surface area of $A$. The
water starts at temperature $T_W > 0^\circ\, C$.</p>
<p>How long would it take to heat up this water to a final temperature of
$T_F$ ($T_W<T_F < 100^\circ \, C$)? Metal of the pot is negligible.</p>
</blockquote>
<p>The heat travels with convection in the water, presumably. I was trying to figure out a solution to this problem, but I am unsure as to what formula to use. </p>
<p>Would the answer change if someone is constantly stirring?</p> | g4588 | [
0.02159165032207966,
0.021041879430413246,
0.011279025115072727,
-0.026252323761582375,
-0.009109944105148315,
-0.019540030509233475,
0.04758678004145622,
0.025528881698846817,
-0.06876759231090546,
0.004419701173901558,
-0.01490488275885582,
0.06908559054136276,
0.06561274081468582,
0.04246627166867256,
0.04170006141066551,
0.03231746330857277,
0.02177419699728489,
-0.015798166394233704,
-0.02150823175907135,
0.07362940162420273,
0.0396232008934021,
-0.022142352536320686,
0.002421316225081682,
-0.0357375368475914,
-0.06876963376998901,
-0.03792024031281471,
0.0005039566312916577,
0.026920903474092484,
0.014271889813244343,
-0.041979528963565826,
-0.037230782210826874,
0.04487914964556694,
-0.039530523121356964,
-0.00523164588958025,
-0.08944699913263321,
-0.07149107754230499,
0.0048384093679487705,
0.04061231389641762,
-0.009533013217151165,
-0.0592685304582119,
0.011578679084777832,
0.0017814973834902048,
0.04093801602721214,
0.05157744139432907,
0.020840240642428398,
0.035688720643520355,
-0.021624818444252014,
0.04158177599310875,
-0.08035390079021454,
0.04423131048679352,
-0.0006224006065167487,
-0.02568398043513298,
-0.021343478932976723,
-0.04613253101706505,
-0.0896354541182518,
0.02312527224421501,
0.016676684841513634,
-0.018270496279001236,
0.008811873383820057,
0.09422618895769119,
0.008735371753573418,
-0.025028536096215248,
-0.02811211533844471,
-0.04817885160446167,
0.03387778624892235,
0.04501241818070412,
-0.027321968227624893,
0.023501213639974594,
0.0025298127438873053,
0.010746663436293602,
0.012892444618046284,
-0.017964623868465424,
0.021894432604312897,
-0.039771661162376404,
-0.05338006094098091,
-0.020492490381002426,
-0.03769960626959801,
-0.0021210787817835808,
0.010978084988892078,
-0.01882866956293583,
-0.050311896950006485,
-0.0072015197947621346,
0.013762429356575012,
-0.012816750444471836,
-0.06022163853049278,
0.007039989344775677,
-0.03150049224495888,
0.036880649626255035,
-0.032818812876939774,
0.008623757399618626,
-0.03621905669569969,
0.005479450337588787,
0.09018901735544205,
0.0014004547847434878,
-0.0010292923543602228,
-0.04403592646121979,
-0.020363572984933853,
0.030971501022577286,
-0.0623743012547493,
0.0032932108733803034,
0.03782512620091438,
-0.03268807753920555,
0.022405413910746574,
-0.010113107971847057,
-0.04788505658507347,
0.03252270445227623,
0.029671519994735718,
0.022060463204979897,
0.010800013318657875,
0.013346009887754917,
0.0009316659416072071,
-0.0654086098074913,
-0.03804614767432213,
0.009846090339124203,
-0.04615556448698044,
-0.03139492869377136,
0.010706632398068905,
0.025999993085861206,
0.024325715377926826,
-0.007449041586369276,
-0.011236052960157394,
-0.01087474450469017,
0.017657537013292313,
0.058744870126247406,
0.05741889402270317,
-0.03756040707230568,
0.06376611441373825,
0.03427873179316521,
0.03807176277041435,
0.06377717107534409,
-0.02424730733036995,
0.06186463311314583,
-0.017719263210892677,
0.023155072703957558,
0.059430427849292755,
0.012763417325913906,
-0.008284670300781727,
0.0498095266520977,
-0.0025496063753962517,
0.012079179286956787,
0.025155389681458473,
-0.04203132167458534,
0.025103935971856117,
-0.053349535912275314,
-0.04372918978333473,
0.03433046489953995,
0.017460376024246216,
-0.073799267411232,
0.041017159819602966,
-0.024252798408269882,
0.0016188517911359668,
0.03884829208254814,
0.027324043214321136,
-0.012346380390226841,
0.03520240634679794,
-0.0076871151104569435,
-0.0004295468097552657,
-0.04167479649186134,
0.13534018397331238,
-0.07211446762084961,
0.009350944310426712,
-0.00020394951570779085,
-0.021443691104650497,
-0.010197393596172333,
-0.039173830300569534,
0.025465771555900574,
-0.0322241485118866,
-0.025804506614804268,
-0.058823924511671066,
-0.03089534118771553,
-0.022067232057452202,
0.013826715759932995,
-0.07045233994722366,
0.027014674618840218,
-0.0023963216226547956,
-0.00808504968881607,
0.03409178927540779,
0.029392803087830544,
0.0078094336204230785,
-0.024427887052297592,
-0.03362661972641945,
-0.01766759715974331,
0.0666888877749443,
0.03918429836630821,
0.019260141998529434,
0.021500347182154655,
0.007955175824463367,
-0.03525867313146591,
-0.07975040376186371,
-0.015704050660133362,
0.005731303244829178,
0.005388038698583841,
0.020588381215929985,
0.08870987594127655,
-0.0007171120378188789,
-0.030403371900320053,
0.018349748104810715,
-0.019498106092214584,
-0.047536805272102356,
-0.054980117827653885,
0.022705741226673126,
0.01070201676338911,
0.03034137561917305,
-0.0041291420347988605,
0.001642372808419168,
-0.022412901744246483,
0.03213581070303917,
0.03125086799263954,
-0.017811691388487816,
-0.018008550629019737,
-0.023768052458763123,
0.025311194360256195,
-0.031967248767614365,
0.03956109657883644,
-0.025049522519111633,
0.025444578379392624,
-0.07781470566987991,
0.06262580305337906,
-0.0015332377515733242,
0.02246735617518425,
0.028597304597496986,
-0.0377110056579113,
-0.04759598523378372,
-0.03645837679505348,
-0.0465860441327095,
-0.01789313741028309,
0.029656149446964264,
-0.03186295926570892,
-0.03285374492406845,
0.07308663427829742,
-0.007750436197966337,
-0.0016314288368448615,
-0.0047227321192622185,
-0.05116339772939682,
0.027032645419239998,
0.02224751189351082,
-0.0052297902293503284,
0.026783525943756104,
0.02420281060039997,
0.019853919744491577,
0.00459156883880496,
0.016178052872419357,
-0.00944496039301157,
-0.009927871637046337,
0.006029278039932251,
-0.006926314439624548,
0.05074019730091095,
-0.006826317869126797,
0.004406739491969347,
0.057154566049575806,
0.015352155081927776,
-0.02338428981602192,
-0.026251697912812233,
0.04114783927798271,
-0.0632871612906456,
-0.05472983047366142,
-0.020952120423316956,
0.005875578615814447,
-0.02218780666589737,
0.008682501502335072,
0.0038593653589487076,
-0.02263210527598858,
0.051644254475831985,
-0.025097427889704704,
-0.023454738780856133,
-0.02817750722169876,
-0.08586407452821732,
-0.022791048511862755,
0.0026599622797220945,
0.04206334799528122,
-0.010549343191087246,
-0.023543337360024452,
0.05095314234495163,
0.0760384276509285,
-0.04734339192509651,
-0.018134186044335365,
0.04956163838505745,
-0.024776427075266838,
0.04317888617515564,
0.036871325224637985,
0.01011041458696127,
-0.05116238445043564,
-0.034260571002960205,
0.0348740853369236,
-0.013928527012467384,
-0.04483231157064438,
-0.010369503870606422,
0.0271715447306633,
0.017054997384548187,
-0.021128704771399498,
0.004699737764894962,
0.013825933448970318,
0.011231966316699982,
0.04258666932582855,
0.06704293191432953,
0.05816665664315224,
0.03190214931964874,
-0.0361250601708889,
0.011213761754333973,
-0.026273146271705627,
0.013909095898270607,
-0.00807536207139492,
-0.030015377327799797,
-0.029919402673840523,
0.04804828390479088,
-0.003976272884756327,
-0.02767568826675415,
-0.019956760108470917,
0.015568648464977741,
-0.06212472543120384,
0.006121976301074028,
0.04327996075153351,
-0.0654100701212883,
-0.00019315913959871978,
-0.0048229387030005455,
0.0253390371799469,
-0.017860623076558113,
0.013863209635019302,
0.0545445941388607,
0.012129222974181175,
-0.03788289800286293,
-0.01305445097386837,
0.028122415766119957,
0.00409278878942132,
0.011113066226243973,
0.024793047457933426,
-0.04028654098510742,
0.007097176276147366,
-0.028945067897439003,
-0.029545055702328682,
-0.022575652226805687,
0.024584682658314705,
-0.07633894681930542,
-0.05584648996591568,
-0.007883311249315739,
0.016012519598007202,
0.026593798771500587,
0.029480544850230217,
-0.04497303068637848,
0.08015573024749756,
-0.041639141738414764,
-0.055924441665410995,
-0.029495844617486,
0.018763383850455284,
0.004413631744682789,
-0.020778676494956017,
-0.009026648476719856,
-0.010781286284327507,
-0.03626146540045738,
0.04774687811732292,
0.01704208180308342,
-0.0120089091360569,
0.01767859235405922,
-0.011531505733728409,
-0.014393619261682034,
0.01906869001686573,
0.029128065332770348,
-0.0016363273607566953,
-0.032694995403289795,
-0.008603481575846672,
0.0057212794199585915,
0.009400395676493645,
0.044038064777851105,
0.00251327664591372,
-0.044910624623298645,
0.04094035550951958,
0.03245396912097931,
0.03493143990635872,
-0.0071131144650280476,
-0.0038300715386867523,
-0.0023430550936609507,
-0.040230248123407364,
-0.031060434877872467,
0.008983248844742775,
0.07046747952699661,
0.011105338111519814,
0.024013066664338112,
-0.016230104491114616,
-0.004688888788223267,
0.05155408754944801,
-0.05975181609392166,
0.020174743607640266,
-0.01007844228297472,
-0.016773967072367668,
0.009586579166352749,
0.02521650306880474,
-0.018791241571307182,
0.011086025275290012,
0.04626896232366562,
-0.09641370177268982,
0.030464330688118935,
0.002896801568567753,
0.03136833757162094,
0.037762098014354706,
0.013321835547685623,
0.005809806752949953,
0.013152679428458214,
0.031801074743270874,
-0.005896432790905237,
-0.019898822531104088,
0.04117625951766968,
-0.049238551408052444,
0.022820835933089256,
0.031177731230854988,
-0.018858570605516434,
0.030855178833007812,
0.04576311260461807,
-0.03104231134057045,
-0.007098615635186434,
-0.04112006351351738,
-0.020585214719176292,
0.021266648545861244,
-0.0011889206944033504,
0.00017001402738969773,
0.01761970855295658,
-0.0848371684551239,
0.03125828877091408,
0.0044965012930333614,
-0.021095866337418556,
-0.05801394209265709,
-0.04563259705901146,
0.013509097509086132,
-0.014886693097651005,
0.022033624351024628,
0.036198802292346954,
0.0033442990388721228,
-0.021247340366244316,
-0.028734568506479263,
0.0029214650858193636,
-0.032221727073192596,
-0.025581182911992073,
0.05975787714123726,
-0.06308595091104507,
0.025309881195425987,
-0.04685405269265175,
0.02575187012553215,
0.010555261746048927,
0.027973230928182602,
0.019456123933196068,
0.02199713885784149,
-0.0003924034826923162,
0.04188799485564232,
-0.03282734751701355,
0.03422466665506363,
0.010790521278977394,
0.04031667485833168,
0.001745960908010602,
-0.08837909251451492,
0.010425368323922157,
-0.024763375520706177,
0.01079587358981371,
0.0835409089922905,
-0.0035333482082933187,
-0.0006889746291562915,
-0.01540242787450552,
-0.019988037645816803,
-0.02192329801619053,
0.03987269848585129,
0.008391715586185455,
0.04503842443227768,
0.002827511401847005,
-0.010124732740223408,
-0.060818057507276535,
0.03597600758075714,
-0.03371879458427429,
-0.06138680502772331,
0.08317811787128448,
-0.004407084081321955,
-0.003532060422003269,
0.05726751312613487,
0.028664926066994667,
0.07617717981338501,
0.07785136252641678,
0.05732531473040581,
0.03916626796126366,
0.012800774537026882,
0.03103683888912201,
-0.009544702246785164,
0.01702130399644375,
0.03352680802345276,
-0.015760725364089012,
-0.023166850209236145,
-0.005543048959225416,
0.08858285844326019,
0.05267896130681038,
0.03253769874572754,
-0.05573100969195366,
0.004722727928310633,
0.051071662455797195,
-0.03998854011297226,
0.0069855512119829655,
0.03307074308395386,
0.01920342445373535,
-0.0015230218414217234,
0.02076190896332264,
-0.029406078159809113,
-0.020684130489826202,
-0.03935883566737175,
0.05279938876628876,
0.008199268952012062,
0.03871872276067734,
0.04885457083582878,
-0.016773957759141922,
0.019796231761574745,
-0.05119280517101288,
0.04830364137887955,
-0.016338739544153214,
0.03651402145624161,
0.021622195839881897,
0.04749102145433426,
0.021889496594667435,
0.061043255031108856,
-0.020096484571695328,
0.007049486506730318,
0.04516506567597389,
-0.03921664506196976,
-0.0011430595768615603,
-0.024103518575429916,
-0.016377752646803856,
0.02928946167230606,
0.07279374450445175,
0.005420367699116468,
-0.030012544244527817,
0.011039910838007927,
0.04258090630173683,
0.006704379804432392,
-0.0720803439617157,
-0.038221027702093124,
0.023354677483439445,
0.03482551500201225,
0.04156553000211716,
0.02370687574148178,
-0.03253564611077309,
-0.015845177695155144,
-0.05761813744902611,
0.02430536225438118,
0.032155245542526245,
-0.025630900636315346,
-0.01237417384982109,
-0.00008714447903912514,
-0.00747631024569273,
0.026342308148741722,
0.07154171913862228,
0.002542665461078286,
0.03677572309970856,
-0.0478811077773571,
-0.0016683607827872038,
-0.03857525810599327,
0.014363205060362816,
0.044188082218170166,
-0.04688354581594467,
0.05882694199681282,
0.04533744230866432,
0.03581076115369797,
0.0756228044629097,
-0.009078022092580795,
-0.022116662934422493,
-0.02881363034248352,
0.026739783585071564,
-0.05696414038538933,
0.07703831791877747,
0.028236009180545807,
0.012795763090252876,
-0.008366221562027931,
-0.04357815161347389,
-0.0533316433429718,
-0.08130710572004318,
0.006636518985033035,
0.040397949516773224,
-0.0001833540154621005,
0.03179927170276642,
-0.046192921698093414,
0.05747278034687042,
-0.040436092764139175,
-0.03162367641925812,
0.00015803641872480512,
-0.04125608503818512,
-0.008911498822271824,
-0.012293325737118721,
0.019125061109662056,
-0.027488943189382553,
0.006737044546753168,
-0.05588948726654053,
-0.0004257391847204417,
0.03668183460831642,
-0.04414613917469978,
-0.02698638290166855,
0.025997567921876907,
0.008826902136206627,
0.024636324495077133,
-0.02982618473470211,
0.013533761724829674,
0.02280391752719879,
0.04498136788606644,
0.04994087666273117,
-0.029810385778546333,
-0.03793436288833618,
0.0015498712891712785,
-0.00888113584369421,
0.038254186511039734,
0.03850098326802254,
0.01874813623726368,
0.017931856215000153,
-0.01229867897927761,
-0.04309481009840965,
0.04246306046843529,
0.02396312542259693,
0.00725594675168395,
0.039697300642728806,
-0.04954736679792404,
0.05411268025636673,
0.03557145223021507,
0.08464665710926056,
-0.021325834095478058,
-0.012869380414485931,
-0.0270541999489069,
0.04568727687001228,
0.003995096310973167,
-0.008541947230696678,
-0.04171619564294815,
0.0208352729678154,
0.012908780947327614,
0.009767323732376099,
-0.06524979323148727,
0.04679028317332268,
-0.016057221218943596,
-0.04229016974568367,
0.02584143541753292,
0.04857545346021652,
-0.05129636451601982,
0.025971470400691032,
-0.03241393715143204,
-0.0292315986007452,
-0.005609297659248114,
-0.004495719447731972,
-0.046520449221134186,
-0.025913843885064125,
0.013421487994492054,
0.0038102404214441776,
0.08634437620639801,
-0.05803071707487106,
0.022760959342122078,
0.022815775126218796,
-0.004969292785972357,
-0.02009822055697441,
-0.028085598722100258,
0.04473678395152092,
-0.05748117342591286,
-0.07293065637350082,
-0.039409853518009186,
0.01087140291929245,
-0.07391101866960526,
-0.030405811965465546,
0.005358001217246056,
-0.03676457703113556,
-0.013629340566694736,
0.007914490066468716,
-0.0638691857457161,
-0.011570028960704803,
0.04098450765013695,
-0.022998947650194168,
-0.04183182120323181,
-0.021762913092970848,
0.008116004057228565,
0.012884242460131645,
0.06380964070558548,
0.01128971204161644,
-0.021843422204256058,
-0.006913510616868734,
-0.06603959947824478,
0.00689342524856329,
-0.002331983530893922,
-0.01614258624613285,
-0.009955348446965218,
0.050016067922115326,
-0.009005478583276272,
0.008897446095943451,
0.03540714457631111,
0.025554470717906952,
-0.01064805407077074,
0.0037663185503333807,
-0.0886794924736023,
-0.020674560219049454,
-0.0359203927218914,
0.02553699165582657,
-0.04038894921541214,
-0.04131556302309036,
0.015144677832722664,
0.016564128920435905,
0.03375627100467682,
0.005872734822332859,
0.0037351413629949093,
-0.009283737279474735,
0.02111550234258175,
0.0584426075220108,
0.049621161073446274,
-0.003737527411431074,
-0.02795572765171528,
0.06981723755598068,
0.023918895050883293,
0.01759812980890274,
0.008918442763388157,
0.0289632435888052,
-0.039851509034633636,
-0.04406619071960449,
-0.022744901478290558,
-0.05852636322379112,
0.0038465610705316067,
-0.009925776161253452,
-0.0269501693546772,
-0.011842120438814163,
0.04537387937307358,
-0.04488445073366165,
-0.036526650190353394,
0.04145195707678795,
-0.01671587862074375,
-0.10808736830949783,
-0.07736034691333771,
-0.0010978413047268987,
-0.03418594226241112,
-0.044731054455041885,
-0.003773037577047944,
-0.03277700021862984,
-0.04966922104358673,
-0.004344369750469923,
-0.019091280177235603,
-0.04769020155072212,
-0.021916434168815613,
0.010239262133836746,
0.024376560002565384,
0.014845818281173706,
-0.008293169550597668,
-0.03147469833493233,
-0.015128389932215214,
0.009396090172231197,
-0.0051286183297634125,
0.036821093410253525,
-0.009297686628997326,
0.0333460308611393,
-0.010052460245788097,
-0.012415549717843533,
0.009807738475501537,
0.030559975653886795,
-0.038015216588974,
0.03252817690372467,
0.042456623166799545,
-0.06040873005986214,
0.008075926452875137,
0.06905414164066315,
-0.009248770773410797,
0.045148927718400955,
-0.01883017271757126,
-0.06437017768621445,
-0.02005830407142639,
-0.03491663932800293,
0.012875145301222801,
-0.05009977146983147,
0.012279883958399296,
-0.04019010066986084,
-0.015843790024518967,
-0.0649583712220192,
0.020680004730820656,
-0.00810729805380106,
0.05525725707411766,
-0.0013036810560151935,
-0.01252407394349575,
-0.03125426545739174,
-0.012108268216252327
] |
<p>$$E_{\mathrm{ms}} = \frac{1}{2}\mu_0 \int_V \mathbf{M} \cdot \mathbf{H}_{\mathrm{ms}} d^3 r$$</p>
<p>I can't understand this formula, what is the magnetostatic stored potential energy?! What does it show?
Does it explain anything relative to magnetization?</p> | g4589 | [
0.027369629591703415,
0.05749546363949776,
-0.04089046269655228,
-0.04147617891430855,
-0.013749003410339355,
0.03563889488577843,
0.01146033313125372,
0.04741028696298599,
-0.031391795724630356,
0.0006337345694191754,
-0.05143297091126442,
0.050510287284851074,
-0.0013999927323311567,
-0.022451993077993393,
-0.03385690227150917,
0.05768303945660591,
0.03416185453534126,
0.03823385760188103,
-0.018245354294776917,
-0.027559563517570496,
-0.009887468069791794,
-0.006185262463986874,
-0.03634221851825714,
-0.04301981255412102,
0.11070220917463303,
0.026085851714015007,
0.009193322621285915,
0.03119112364947796,
-0.037271227687597275,
-0.011102315038442612,
0.0016145919216796756,
0.0423080176115036,
0.0713876262307167,
-0.010698188096284866,
-0.042013682425022125,
0.01972971297800541,
0.02969694882631302,
0.04367109760642052,
0.03978154808282852,
-0.04453466832637787,
-0.013101283460855484,
-0.04583439230918884,
0.08314710855484009,
0.0073676020838320255,
-0.03402257338166237,
0.009570603258907795,
-0.03934366628527641,
-0.04404149949550629,
-0.05164499208331108,
0.011185267940163612,
0.0028307719621807337,
0.030849620699882507,
0.1315539926290512,
-0.009459993802011013,
0.024849824607372284,
-0.019146982580423355,
0.015952549874782562,
-0.03037341497838497,
0.014519535936415195,
0.040714114904403687,
0.03322372958064079,
-0.03112298808991909,
-0.02382221259176731,
0.03522401675581932,
0.015072938054800034,
-0.016017869114875793,
-0.022878430783748627,
-0.033189889043569565,
-0.006055890582501888,
0.002560953376814723,
-0.025883303955197334,
-0.02970944344997406,
-0.02783992886543274,
-0.03798187896609306,
-0.02910691127181053,
0.008847620338201523,
0.04715757817029953,
-0.0012495191767811775,
0.011129296384751797,
-0.0033209214452654123,
0.01676924340426922,
0.002894763369113207,
0.01324167288839817,
0.02091825194656849,
0.024675153195858,
-0.017594680190086365,
0.005752702243626118,
0.06316976994276047,
-0.038486309349536896,
0.035115208476781845,
-0.01874440908432007,
-0.044589437544345856,
-0.00312054599635303,
-0.008934448473155499,
0.024774691089987755,
0.018274154514074326,
0.07390601933002472,
-0.009558272548019886,
-0.0656018927693367,
-0.017206287011504173,
0.009942109696567059,
-0.06845171749591827,
-0.0024140882305800915,
0.01399826817214489,
0.03347567468881607,
0.033946845680475235,
0.005267775151878595,
-0.03174759820103645,
0.03146592155098915,
-0.0018069162033498287,
-0.03290027007460594,
-0.0072913989424705505,
-0.054293349385261536,
0.003704025875777006,
-0.060828354209661484,
0.02749478444457054,
0.026633111760020256,
-0.027794871479272842,
-0.038320500403642654,
0.02702934667468071,
0.07552053034305573,
0.06348329037427902,
0.001897888956591487,
0.06483300030231476,
-0.036625541746616364,
0.028196999803185463,
-0.01861305721104145,
0.03205082565546036,
0.03147468343377113,
-0.018748875707387924,
0.013489020988345146,
-0.014944183640182018,
0.01774720661342144,
-0.025867441669106483,
0.016214363276958466,
0.020782243460416794,
-0.01756197214126587,
0.03622792661190033,
-0.015271234326064587,
0.04847455024719238,
-0.013384896330535412,
-0.05880022421479225,
0.00129206373821944,
-0.05464613810181618,
-0.06727462261915207,
0.06406260281801224,
-0.014895551837980747,
-0.024810677394270897,
0.03710184246301651,
0.008607986383140087,
0.00402611680328846,
0.06660576909780502,
-0.022955507040023804,
-0.04476398602128029,
0.05669284984469414,
-0.03166121989488602,
0.010788359679281712,
-0.05900944396853447,
-0.021232448518276215,
0.07809936255216599,
0.07095471024513245,
0.02408708445727825,
0.007642828859388828,
0.028705772012472153,
-0.03884950280189514,
-0.0049600969068706036,
0.07025966793298721,
-0.02013925462961197,
-0.01208839938044548,
-0.03131168335676193,
-0.03014044091105461,
0.05781729519367218,
0.03188423812389374,
0.03013763576745987,
-0.02037891373038292,
0.009465102106332779,
-0.031084606423974037,
-0.04519174247980118,
0.04576454684138298,
0.044017430394887924,
0.07040204852819443,
0.05870708078145981,
0.061436161398887634,
-0.009878582321107388,
-0.026957526803016663,
-0.0050176396034657955,
0.0036876718513667583,
0.04730425775051117,
-0.028531119227409363,
0.006269713863730431,
-0.005551210138946772,
0.06480583548545837,
0.023340456187725067,
0.027954906225204468,
0.02378004603087902,
0.008237900212407112,
-0.004785626661032438,
-0.013233639299869537,
-0.040746625512838364,
-0.006053187418729067,
-0.0434175468981266,
0.00016808515647426248,
0.04948242008686066,
-0.013298844918608665,
-0.014689769595861435,
-0.013621417805552483,
0.09777790307998657,
0.00873544905334711,
0.025425786152482033,
0.02848447859287262,
-0.015606561675667763,
-0.014858213253319263,
-0.03899480402469635,
-0.013395083136856556,
-0.010847428813576698,
-0.03405824303627014,
0.021496668457984924,
0.01980515755712986,
-0.033409666270017624,
0.03541948273777962,
-0.023541079834103584,
-0.037001948803663254,
0.03966037556529045,
-0.0030210651457309723,
-0.08884105086326599,
0.021238844841718674,
-0.05189887434244156,
-0.002894028089940548,
0.0028912483248859644,
0.009623830206692219,
-0.02358662523329258,
0.05069173127412796,
0.0012389032635837793,
0.02823999710381031,
-0.028955746442079544,
0.030409380793571472,
-0.042567841708660126,
-0.037252046167850494,
0.001615085988305509,
0.029597941786050797,
-0.0007215614896267653,
0.025503650307655334,
0.037519995123147964,
0.011299379169940948,
0.026340076699852943,
0.016938986256718636,
0.08420521765947342,
0.051389824599027634,
0.01352422870695591,
0.04286220297217369,
0.03159848973155022,
-0.020489761605858803,
0.015113476663827896,
0.00670026196166873,
0.0007150184828788042,
-0.03299177065491676,
-0.05705951526761055,
-0.015931257978081703,
-0.09212314337491989,
-0.026644522324204445,
-0.002547099022194743,
-0.0076776957139372826,
0.016866400837898254,
-0.03796250373125076,
-0.024154191836714745,
-0.025506895035505295,
-0.04473487660288811,
0.021263545379042625,
0.02788928709924221,
-0.05351876839995384,
0.006489268504083157,
0.05530046299099922,
-0.003055398818105459,
0.06005222350358963,
-0.01742430403828621,
-0.04770567640662193,
0.07244853675365448,
-0.02640371024608612,
0.05196531489491463,
-0.07450131326913834,
-0.08485334366559982,
-0.009225089102983475,
-0.011694779619574547,
-0.008575194515287876,
-0.036044858396053314,
-0.05764996260404587,
-0.00026165659073740244,
-0.0021238112822175026,
-0.04061682149767876,
0.009963837452232838,
-0.031075024977326393,
-0.018747737631201744,
0.025989586487412453,
0.0024963829200714827,
-0.028431354090571404,
-0.03498293459415436,
0.06077071651816368,
-0.012694532051682472,
-0.015326949767768383,
0.06790348142385483,
0.03308122977614403,
0.009141037240624428,
-0.027561038732528687,
-0.02237810008227825,
-0.013985127210617065,
0.0067258961498737335,
0.01320877205580473,
-0.04871577024459839,
0.018740620464086533,
0.009102901443839073,
-0.003068513935431838,
0.05916042998433113,
0.005426952149719,
-0.05351725220680237,
-0.04384232684969902,
0.02299543283879757,
-0.0071843587793409824,
-0.040761880576610565,
0.016180796548724174,
-0.07753538340330124,
-0.013691348023712635,
-0.0429881289601326,
0.017822761088609695,
-0.04977944493293762,
0.04716503620147705,
-0.000023603333829669282,
-0.04097018763422966,
-0.007044767029583454,
-0.021639376878738403,
0.03587361425161362,
0.00892945472151041,
0.0448397658765316,
-0.016592146828770638,
-0.017692560330033302,
-0.02278265543282032,
-0.026141034439206123,
-0.04403115063905716,
0.01267686951905489,
0.00885176844894886,
-0.029896391555666924,
-0.0012028607307001948,
-0.009131829254329205,
-0.06393419206142426,
0.01409245003014803,
0.03132981061935425,
0.022043248638510704,
-0.0032216727267950773,
-0.004569814074784517,
0.05460478365421295,
0.007233354263007641,
-0.07124108076095581,
-0.015392467379570007,
0.02622256614267826,
-0.018179934471845627,
-0.008416779339313507,
-0.02334844321012497,
0.0010965483961626887,
-0.02076124958693981,
0.009941287338733673,
0.06313300877809525,
-0.012524140067398548,
-0.014397998340427876,
0.014963032677769661,
-0.01733856089413166,
-0.027476370334625244,
0.009737065061926842,
-0.027940642088651657,
-0.023523148149251938,
0.010037696920335293,
-0.034736268222332,
-0.00013067804684396833,
-0.024109695106744766,
-0.009381826035678387,
0.024725312367081642,
0.034108735620975494,
-0.0778077244758606,
-0.0613357275724411,
-0.05297761783003807,
-0.032702237367630005,
0.01548224501311779,
0.039466142654418945,
-0.017757171764969826,
0.004495795350521803,
0.009780590422451496,
-0.012955679558217525,
-0.032517168670892715,
-0.01701190322637558,
0.07356885075569153,
0.03878339007496834,
-0.04592052102088928,
0.00682022562250495,
0.02163505367934704,
-0.018867185339331627,
0.04209046810865402,
0.0417911559343338,
-0.0011206691851839423,
0.003609181148931384,
0.01766301319003105,
0.01899167150259018,
-0.011287768371403217,
0.008935142308473587,
0.020006276667118073,
-0.013989325612783432,
-0.06725908070802689,
0.0032033994793891907,
0.005769066046923399,
0.04882911592721939,
-0.03156033158302307,
0.07624545693397522,
-0.06253072619438171,
-0.014730806462466717,
-0.03380194678902626,
0.02792663499712944,
-0.023206006735563278,
0.008597094565629959,
-0.002930600196123123,
0.02980561926960945,
-0.035423628985881805,
-0.006575588136911392,
-0.04847896471619606,
0.03743293508887291,
-0.0167810320854187,
0.03568277135491371,
-0.03221799433231354,
-0.00670162308961153,
0.02070470340549946,
0.10060204565525055,
0.00047918420750647783,
-0.025262951850891113,
-0.003963348921388388,
0.03464013710618019,
0.0453074611723423,
-0.03249946981668472,
0.01133769378066063,
-0.06686191260814667,
0.04474712163209915,
-0.019332164898514748,
-0.029577791690826416,
-0.04907774180173874,
0.05684754624962807,
0.054888926446437836,
0.009632565081119537,
0.03592321649193764,
0.025749219581484795,
-0.039296019822359085,
0.03808117285370827,
-0.020404186099767685,
-0.027413973584771156,
-0.0098361074924469,
-0.04256084933876991,
0.01013981830328703,
-0.0351325199007988,
0.009634047746658325,
-0.012331396341323853,
0.04702203348278999,
0.008672517724335194,
-0.006440487690269947,
-0.01161352638155222,
0.06093508377671242,
0.053645044565200806,
-0.04646711051464081,
0.0174969881772995,
-0.05271121859550476,
0.006851624697446823,
0.030774984508752823,
-0.0093863969668746,
0.009585690684616566,
-0.011525312438607216,
0.00916407909244299,
0.049210138618946075,
0.07172806560993195,
-0.0009645344689488411,
-0.006934059783816338,
-0.04905274137854576,
0.10368777066469193,
0.01729506254196167,
0.030952606350183487,
-0.03442967310547829,
0.013296352699398994,
-0.030480023473501205,
0.005638390313833952,
0.05905236303806305,
0.006208151113241911,
0.043725594878196716,
0.03283890709280968,
0.011313808150589466,
-0.010786331258714199,
0.028001580387353897,
-0.04921767860651016,
-0.02207663096487522,
-0.012078219093382359,
0.05985981971025467,
0.042904533445835114,
-0.06535471975803375,
0.02024717628955841,
0.03581438213586807,
-0.020596174523234367,
-0.0024803478736430407,
-0.06854134052991867,
-0.06221538037061691,
0.02014857344329357,
-0.034802187234163284,
-0.05018272623419762,
0.03304153308272362,
0.007038989569991827,
0.028156766667962074,
0.06966955214738846,
-0.035986073315143585,
0.04457995295524597,
0.012171000242233276,
-0.05315389856696129,
0.006375535391271114,
0.03297022730112076,
0.024825498461723328,
0.038850799202919006,
-0.03664752095937729,
-0.029910987243056297,
0.008908907882869244,
0.015756789594888687,
-0.04617695510387421,
0.003957994747906923,
0.06557609140872955,
0.04777543619275093,
-0.053916044533252716,
0.018672075122594833,
0.012761457823216915,
-0.01622808165848255,
-0.07531744241714478,
0.02885291539132595,
0.055009324103593826,
-0.029268385842442513,
-0.016414770856499672,
0.023248914629220963,
-0.011706260032951832,
0.02347184345126152,
0.012318674474954605,
-0.017413336783647537,
-0.030012907460331917,
0.05154399201273918,
0.022391000762581825,
-0.009519971907138824,
-0.06445309519767761,
-0.01933690346777439,
0.06811127066612244,
-0.0586162768304348,
0.02861303836107254,
-0.041810765862464905,
-0.04524800553917885,
0.04245365038514137,
-0.012095672078430653,
-0.007220790255814791,
-0.018357116729021072,
0.006451180204749107,
-0.032945990562438965,
0.021427465602755547,
0.023634331300854683,
0.05640455707907677,
-0.010320629924535751,
-0.026306908577680588,
-0.04528702422976494,
0.006117943674325943,
0.03102531097829342,
-0.01808829791843891,
0.043338432908058167,
-0.011071338318288326,
-0.025728028267621994,
0.02697352133691311,
0.020868761464953423,
0.03583977371454239,
-0.0112302266061306,
0.019657649099826813,
0.0498465932905674,
0.016782358288764954,
0.025391779839992523,
-0.014116646721959114,
0.02169964835047722,
-0.0021154540590941906,
-0.00607101246714592,
-0.03310093656182289,
-0.07053745537996292,
0.002772769657894969,
0.015354274772107601,
0.05973730608820915,
0.008323479443788528,
-0.002153930487111211,
0.013733812607824802,
-0.030945681035518646,
-0.03529542312026024,
0.04539705440402031,
0.01366058737039566,
-0.004685351625084877,
0.041675351560115814,
0.007901511155068874,
-0.01959345117211342,
0.008536816574633121,
-0.009784857742488384,
-0.006276783533394337,
0.01263716071844101,
0.03490189090371132,
-0.01345440186560154,
0.004201381467282772,
0.04420469328761101,
-0.016849573701620102,
-0.044868193566799164,
0.009715915657579899,
-0.0004553864127956331,
0.0034030110109597445,
-0.0625896081328392,
-0.13158558309078217,
0.004670752678066492,
0.014981447719037533,
0.021318208426237106,
-0.041067831218242645,
0.0071087367832660675,
0.02915240451693535,
0.04249837249517441,
0.005683109164237976,
0.06206735968589783,
-0.012772800400853157,
0.016452498733997345,
-0.055424246937036514,
-0.03294910117983818,
0.03501272201538086,
-0.05779870226979256,
0.06941848993301392,
0.0051940311677753925,
-0.008288231678307056,
-0.021454153582453728,
0.003659808775410056,
-0.04412369802594185,
0.006023884750902653,
0.013395311310887337,
-0.02101913094520569,
0.04245594143867493,
0.011693382635712624,
-0.019620133563876152,
-0.0017141117714345455,
-0.0004706669133156538,
0.021484021097421646,
0.03967883437871933,
-0.06217740476131439,
0.025671660900115967,
0.0062376633286476135,
-0.019137272611260414,
-0.045184534043073654,
-0.01903088390827179,
0.008106052875518799,
0.024767979979515076,
-0.0138257946819067,
-0.008334660902619362,
0.029632680118083954,
-0.0030430727638304234,
0.016417840495705605,
0.02173578552901745,
-0.02154194936156273,
-0.025731194764375687,
0.011173042468726635,
0.007319370750337839,
0.04579762741923332,
-0.053496330976486206,
-0.013734955340623856,
0.010913344100117683,
-0.023825477808713913,
0.01817917451262474,
0.04082856327295303,
0.012983224354684353,
0.014545846730470657,
-0.06294446438550949,
0.006788716651499271,
-0.09940141439437866,
0.00720185274258256,
-0.002206140197813511,
0.0033740110229700804,
0.021844984963536263,
-0.02045285701751709,
0.03893366828560829,
0.02083437703549862,
-0.039569441229104996,
-0.013124589808285236,
-0.01068482268601656,
-0.03316840901970863,
0.008384080603718758,
0.003549478715285659,
-0.055831123143434525,
-0.02729976736009121,
0.058967676013708115,
-0.09773630648851395,
-0.025137074291706085,
0.026992665603756905,
0.08393402397632599,
0.03882770985364914,
-0.02623090147972107,
0.06227526068687439,
0.025807689875364304,
-0.01040205080062151,
-0.0029917049687355757,
0.017908157780766487,
-0.012051677331328392,
0.057901933789253235,
-0.00045871787006035447,
0.026097869500517845,
-0.051428936421871185,
0.022981401532888412,
0.0013653342612087727,
-0.011622264049947262,
-0.023738419637084007,
-0.026749886572360992,
0.024833519011735916,
-0.08726109564304352,
0.016213752329349518,
0.02801085077226162,
-0.059916313737630844,
0.02561301179230213,
-0.04225901886820793,
0.0050454167649149895,
0.028215324506163597,
-0.03177497908473015,
0.0563611201941967,
-0.029828092083334923,
-0.009238033555448055,
0.004078129306435585,
0.03411496803164482,
-0.017945563420653343,
-0.05125634744763374,
-0.033038847148418427,
-0.009295180439949036,
-0.03197820112109184,
0.000630982976872474,
0.03710062801837921,
0.02968847006559372,
-0.04595756530761719,
0.021236583590507507,
-0.0035992241464555264,
-0.03249543160200119,
-0.03678673133254051,
0.0032073776237666607,
0.010558618232607841,
-0.008478944189846516,
0.01706630364060402,
0.019001081585884094,
0.0004441026831045747,
-0.08132758736610413,
-0.005982864648103714,
-0.05744205042719841,
-0.019654836505651474,
-0.013224977999925613,
-0.11628704518079758,
-0.0039442372508347034,
0.07823582738637924,
-0.0613442026078701,
0.04171997681260109,
-0.09060601145029068,
-0.056221842765808105,
0.009440900757908821,
0.07132644951343536,
-0.02319042757153511,
0.02732684463262558,
0.03226905316114426,
0.04136938229203224,
0.0014390804572030902,
-0.01754559390246868,
-0.005379235837608576,
-0.08166324347257614,
0.024416543543338776,
0.010074693709611893,
-0.015139812603592873,
0.005184204783290625,
0.05873742327094078
] |
<p>I try to understand constructing of Hamiltonian mechanics with constraints. I decided to start with the simple case: free relativistic particle. I've constructed hamiltonian with constraint:</p>
<p>$$S=-m\int d\tau \sqrt{\dot x_{\nu}\dot x^{\nu}}$$</p>
<p>$\phi=p_{\mu}p^{\mu}-m^2=0$ $-$ <a href="http://en.wikipedia.org/wiki/First_class_constraint" rel="nofollow">first class constraint</a>.</p>
<p>Then $$H=H_{0}+\lambda \phi=\lambda \phi.$$ </p>
<p><strong>So, I want to show that I can obtain from this Hamiltonian the same equation of motion, as obtained from Lagrangian.</strong></p>
<p>But the problem is that I'm not sure what to do with $\lambda=\lambda(q,p)$. I tried the following thing:</p>
<p>$\dot x_{\mu}=\{x_{\mu},\lambda \phi\}=\{x_{\mu},\lambda p^2\}-m^2\{x_{\mu},\lambda\}=\lambda\{x_{\mu},p^2\}+p^2\{x_{\mu},\lambda\}-m^2\{x_{\mu},\lambda\}=2\lambda \eta_{\mu b} p^b+p^2\{x_{\mu},\lambda\}-m^2\{x_{\mu},\lambda\}=2\lambda \eta_{\mu b} p^b+p^2\frac{\partial \lambda}{\partial p^{\mu}}-m^2\frac{\partial \lambda}{\partial p^{\mu}}$</p>
<p>$\dot \lambda=\{\lambda, \lambda \phi \}=\{\lambda,\lambda p^2\}-m^2\{\lambda,\lambda\}=\lambda\{\lambda,p^2\}+p^2\{\lambda,p^2\}=2\lambda\eta_{ak}p^{a}\frac{\partial \lambda}{\partial x^{k}}$</p>
<p>$\dot p_{\mu}=\{p_{\mu},\lambda p^{2}-m^2\lambda \}=p^{2}\{p_{\mu},\lambda\}-m^2\{p_{\mu},\lambda\}=-p^{2}\frac{\partial \lambda}{\partial x^{\mu}}+m^2\frac{\partial \lambda}{\partial x^{\mu}}$</p>
<p>If we recall that $p^2-m^2=0$, then we get from the third equation: $\dot p=0$, and from the first: $\dot x_{\mu}=2\lambda\eta_{ak}p^{a}$.</p>
<p>So we have </p>
<p>1) $\dot x_{\mu}=2\lambda\eta_{\mu b}p^{b}$</p>
<p>2) $\dot \lambda=2\lambda\eta_{ak}p^{a}\frac{\partial \lambda}{\partial x^{k}}$</p>
<p>3) $\dot p=0$</p>
<p><em>But I dont know what to do next.</em> Can you help me?</p> | g4590 | [
0.04163326695561409,
0.009192011319100857,
0.0008696134318597615,
-0.034487035125494,
0.01535838283598423,
-0.030394164845347404,
0.024873623624444008,
-0.039129167795181274,
-0.025842202827334404,
-0.0013618964003399014,
-0.03609900921583176,
0.03701598942279816,
0.01522227842360735,
0.009939175099134445,
0.001083551556803286,
0.06584949046373367,
0.050294723361730576,
-0.0077527789399027824,
0.0012541892938315868,
0.027347858995199203,
0.01460222713649273,
0.010927467606961727,
0.034250304102897644,
-0.03382769972085953,
0.03405231237411499,
0.011476773768663406,
0.035312071442604065,
-0.04017987102270126,
-0.04169037193059921,
0.007623503915965557,
-0.019132621586322784,
-0.011707896366715431,
0.07777819037437439,
-0.04353302717208862,
0.00015308690490201116,
0.0171078871935606,
0.08189790695905685,
-0.01634116657078266,
0.014977093786001205,
0.005115203093737364,
-0.002569886390119791,
-0.03280838578939438,
0.003201524494215846,
-0.0017702513141557574,
-0.02205105870962143,
-0.03477979823946953,
0.0002072149800369516,
-0.00929796602576971,
-0.031790316104888916,
0.04046206921339035,
0.041890501976013184,
0.04363524541258812,
0.008998564444482327,
-0.08471526205539703,
-0.03677913919091225,
0.034922610968351364,
0.023229334503412247,
-0.030422091484069824,
0.025407718494534492,
0.007024016231298447,
-0.0027507483027875423,
0.011384805664420128,
0.01714642532169819,
-0.002849305747076869,
0.022213919088244438,
0.020762143656611443,
-0.033089105039834976,
-0.017742592841386795,
-0.04649527743458748,
0.04980185627937317,
-0.020219722762703896,
-0.06127118691802025,
0.04352572560310364,
-0.039082709699869156,
0.009541929699480534,
-0.004776469431817532,
-0.01767175830900669,
0.023211563006043434,
0.041426416486501694,
-0.00645465450361371,
-0.014850021339952946,
-0.04690468683838844,
0.0329570434987545,
0.004379452671855688,
0.04093444347381592,
-0.015055698342621326,
-0.023360496386885643,
-0.019259534776210785,
-0.00554946344345808,
0.0005485367146320641,
0.019254857674241066,
-0.003293488407507539,
0.024720769375562668,
-0.009232224896550179,
0.037654679268598557,
-0.01159656047821045,
-0.02349773421883583,
0.04178816080093384,
0.013648890890181065,
0.01210888009518385,
-0.031611938029527664,
0.009856277145445347,
0.024028794839978218,
-0.033754780888557434,
-0.0002388424618402496,
-0.02226921357214451,
0.007090664003044367,
0.06690685451030731,
0.036859072744846344,
-0.017855243757367134,
0.01271909661591053,
0.03704648092389107,
0.035671256482601166,
-0.028833070769906044,
-0.05934229865670204,
-0.03718327358365059,
0.05482897162437439,
-0.0018537717405706644,
0.024934416636824608,
0.06905046850442886,
-0.030093489214777946,
0.0009738815715536475,
0.052155524492263794,
0.09011686593294144,
0.0057050921022892,
-0.035213351249694824,
0.006997556425631046,
0.010261047631502151,
-0.007459803018718958,
-0.004736004862934351,
0.02152080275118351,
-0.027987156063318253,
-0.018087726086378098,
0.03680137172341347,
0.018871158361434937,
0.03899966552853584,
-0.014187505468726158,
-0.00567623833194375,
0.0056109800934791565,
0.009049181826412678,
-0.008587256073951721,
0.03242893144488335,
0.008828616701066494,
-0.013038640841841698,
-0.03735167905688286,
0.019867638126015663,
0.06644181162118912,
-0.03199297934770584,
-0.0033299310598522425,
0.03395513445138931,
-0.03383590281009674,
0.04334220290184021,
-0.002324275206774473,
0.07505802810192108,
0.024051722139120102,
-0.030616501346230507,
0.05875005945563316,
-0.016692955046892166,
-0.0023044694680720568,
-0.05492968112230301,
0.06419292092323303,
0.0024206996895372868,
0.05855312570929527,
-0.011327830143272877,
-0.017169293016195297,
0.0983612909913063,
0.0006093299016356468,
-0.016911281272768974,
-0.00691599166020751,
-0.055293355137109756,
-0.02966969832777977,
-0.028587419539690018,
0.000007313544756470947,
0.06545379757881165,
0.00019825443450827152,
0.029660765081644058,
-0.015589766204357147,
0.007096807938069105,
0.022208161652088165,
-0.024099374189972878,
0.016367845237255096,
-0.044662732630968094,
0.026393037289381027,
0.02603699080646038,
-0.05189966410398483,
0.030048010870814323,
0.012321566231548786,
0.08712947368621826,
-0.053902316838502884,
-0.005718795116990805,
-0.042400576174259186,
0.012658492662012577,
0.04927447438240051,
0.0273741502314806,
-0.029218219220638275,
0.033180125057697296,
0.01847807690501213,
-0.06800118088722229,
0.03996874764561653,
0.014265894889831543,
-0.025852859020233154,
0.057669855654239655,
0.02876405045390129,
-0.002183994511142373,
0.03393479809165001,
-0.04117807745933533,
-0.008467295207083225,
0.024736247956752777,
0.03136935457587242,
0.05383036285638809,
0.055525537580251694,
-0.04205385968089104,
-0.018841801211237907,
0.009547976776957512,
-0.023747360333800316,
-0.05729253590106964,
0.040556684136390686,
-0.01922025717794895,
-0.0124208377674222,
0.04054956138134003,
0.00222865235991776,
-0.040158264338970184,
0.027422534301877022,
-0.05413536727428436,
-0.007063057739287615,
0.0120787862688303,
-0.018937626853585243,
0.012992453761398792,
-0.003230141242966056,
0.008957487531006336,
-0.02041461504995823,
-0.013855964876711369,
-0.013743053190410137,
-0.0000022150281893118517,
0.07386043667793274,
0.0063977618701756,
-0.03407154604792595,
0.023337343707680702,
-0.006926813628524542,
0.02922709658741951,
-0.038163553923368454,
0.050283826887607574,
-0.0027316559571772814,
-0.04577019438147545,
0.04868825525045395,
-0.04139278456568718,
0.022104401141405106,
0.04809702932834625,
-0.0009266347042284906,
0.027494503185153008,
0.04049690067768097,
-0.027703871950507164,
-0.015737952664494514,
-0.06845008581876755,
0.010058213956654072,
-0.0458456389605999,
0.06759674847126007,
0.08421684056520462,
-0.005116389133036137,
-0.05473809689283371,
0.025012491270899773,
0.008732112124562263,
-0.02858552150428295,
0.08248122036457062,
-0.0019210897153243423,
0.0037268390879034996,
-0.026258554309606552,
-0.014813940972089767,
0.009431394748389721,
-0.031580615788698196,
-0.041242800652980804,
0.06937681138515472,
-0.012544864788651466,
0.04167624190449715,
0.0043650902807712555,
-0.030214430764317513,
0.019726861268281937,
-0.04780902713537216,
0.00899975560605526,
-0.015311598777770996,
0.0003610617422964424,
0.026556815952062607,
0.0014732907293364406,
0.015568279661238194,
0.02378612756729126,
-0.09200452268123627,
0.0031789594795554876,
-0.02568848617374897,
0.0009909385116770864,
0.0034236807841807604,
0.07094990462064743,
0.0602128691971302,
-0.023259779438376427,
0.0013104805257171392,
-0.05795241892337799,
-0.00023130061163101345,
-0.01918751932680607,
-0.027364926412701607,
0.009132723324000835,
0.0035558254458010197,
-0.010652915574610233,
0.010845966637134552,
-0.014669661410152912,
0.05017491802573204,
0.014602473005652428,
-0.010556264780461788,
0.010523702017962933,
-0.01825294829905033,
0.02015850506722927,
-0.010355621576309204,
0.00629677576944232,
0.014419536106288433,
0.07662064582109451,
-0.04426827281713486,
-0.014376983977854252,
-0.014527645893394947,
-0.049327552318573,
-0.049005672335624695,
0.03050149418413639,
-0.042668286710977554,
-0.01086454838514328,
-0.1136183887720108,
0.00359858269803226,
0.011715847067534924,
0.039551880210638046,
0.006010494660586119,
-0.023153996095061302,
-0.03694400191307068,
-0.07312031835317612,
-0.04409560561180115,
-0.00443112850189209,
0.026195330545306206,
0.03186172991991043,
0.0054230596870183945,
-0.007131947670131922,
-0.027144666761159897,
-0.03816063702106476,
-0.009247008711099625,
0.04117325320839882,
-0.05943235754966736,
0.0049211508594453335,
-0.0065443250350654125,
-0.043827734887599945,
0.06732583791017532,
-0.041638944298028946,
-0.052898041903972626,
0.0014440747909247875,
0.0035152302589267492,
0.03406604751944542,
-0.03353950381278992,
-0.051422711461782455,
0.004199110437184572,
0.0414857380092144,
0.014508766122162342,
-0.00557081401348114,
0.0023408408742398024,
0.018611624836921692,
0.007477188017219305,
0.06062038987874985,
-0.007964085787534714,
0.009873817674815655,
-0.06770743429660797,
-0.05494815856218338,
0.043363094329833984,
0.02566533535718918,
-0.02958250604569912,
0.035442054271698,
-0.02693074941635132,
0.019367640838027,
-0.06510072201490402,
0.08508933335542679,
-0.005427738185971975,
0.02614068053662777,
0.015614522621035576,
0.018231097608804703,
-0.009486012160778046,
0.029636291787028313,
-0.012518143281340599,
-0.015977604314684868,
0.0016240875702351332,
0.02953190915286541,
0.004028896801173687,
-0.029910268262028694,
0.06541705131530762,
0.04901880398392677,
0.0109014343470335,
0.0058472310192883015,
0.026871366426348686,
-0.018584249541163445,
-0.014556001871824265,
0.003691901220008731,
-0.045692045241594315,
-0.029012829065322876,
0.013498658314347267,
0.011281877756118774,
-0.02587772347033024,
0.08051850646734238,
-0.01371805276721716,
-0.040558844804763794,
-0.004058229736983776,
-0.09169872105121613,
0.005413831677287817,
0.02967008575797081,
0.014239436946809292,
-0.04176532104611397,
-0.07251044362783432,
0.00041003699880093336,
-0.02035863697528839,
0.007646882440894842,
-0.03900447487831116,
-0.048465218394994736,
-0.0667431652545929,
0.020180461928248405,
-0.02456103451550007,
-0.07248719781637192,
-0.025184152647852898,
0.017533747479319572,
-0.00810847245156765,
-0.051130007952451706,
-0.04623900726437569,
-0.00871853344142437,
0.017718007788062096,
0.0893726721405983,
-0.02175923064351082,
0.06350459903478622,
0.034211788326501846,
0.01745659112930298,
-0.03351471945643425,
-0.012707904912531376,
-0.05357774347066879,
-0.03261175379157066,
-0.04275340959429741,
0.0017652385868132114,
-0.021046312525868416,
-0.05850747600197792,
-0.00046102586202323437,
-0.05166490003466606,
0.034582868218421936,
-0.03358030319213867,
0.061411354690790176,
0.018926948308944702,
0.012005030177533627,
0.037055741995573044,
-0.01206937525421381,
-0.009633866138756275,
0.04046907275915146,
-0.05292670428752899,
-0.05526871606707573,
-0.06792379170656204,
-0.02730577252805233,
0.014478626661002636,
0.004813279025256634,
0.02262895368039608,
0.038618020713329315,
-0.0254843607544899,
-0.04236729443073273,
-0.04173069819808006,
0.040761034935712814,
0.017317241057753563,
0.03870149329304695,
-0.07454344630241394,
-0.07099584490060806,
0.050188273191452026,
0.010891440324485302,
0.06460339576005936,
-0.018723931163549423,
-0.0812845453619957,
0.03976527228951454,
-0.03723936527967453,
-0.04178536310791969,
0.01784694753587246,
0.023804008960723877,
0.036175698041915894,
-0.01560739241540432,
-0.028491415083408356,
0.04925745725631714,
-0.00898892804980278,
-0.001385315554216504,
0.01319093257188797,
-0.07952914386987686,
0.022364825010299683,
-0.005780230276286602,
-0.006766441278159618,
0.010419385507702827,
0.011418581940233707,
0.008110051043331623,
-0.0055604600347578526,
0.0008162279846146703,
-0.013085908256471157,
-0.03494616225361824,
-0.030796345323324203,
0.014582423493266106,
-0.020030824467539787,
0.0605672150850296,
0.024767903611063957,
0.0011886287247762084,
-0.04388326033949852,
0.008932105265557766,
0.04457031935453415,
-0.00853188056498766,
-0.07451819628477097,
0.019161827862262726,
0.028581814840435982,
0.03524959087371826,
-0.006156580056995153,
0.04423123598098755,
0.04789983853697777,
0.02909415028989315,
-0.00391329824924469,
0.022841935977339745,
-0.008408109657466412,
-0.055507443845272064,
0.011590033769607544,
-0.011187541298568249,
0.0085629653185606,
0.07417444884777069,
0.03378360718488693,
0.04350590333342552,
-0.0425911545753479,
-0.04833643138408661,
0.07876985520124435,
-0.02058909833431244,
0.04401069134473801,
-0.04358179122209549,
0.02715456672012806,
-0.027792638167738914,
-0.034774065017700195,
-0.029611069709062576,
-0.005202907603234053,
0.05605350434780121,
0.013746516779065132,
-0.024777943268418312,
0.033155687153339386,
-0.027946820482611656,
0.007604723330587149,
-0.001249610329978168,
-0.024078108370304108,
-0.029853085055947304,
-0.018716663122177124,
-0.008925379253923893,
0.019650401547551155,
-0.08963228762149811,
0.028896747156977654,
0.020582877099514008,
-0.04677940160036087,
0.010726713575422764,
-0.02781016379594803,
0.0015639129560440779,
0.029630813747644424,
-0.00002475595465512015,
-0.052488215267658234,
-0.03266467526555061,
-0.06593666970729828,
-0.04447097331285477,
0.004252237733453512,
0.028356477618217468,
0.01812027581036091,
-0.023151041939854622,
-0.002317614620551467,
0.0034411787055432796,
0.020092254504561424,
-0.046467412263154984,
-0.003080561524257064,
-0.010729186236858368,
-0.020855508744716644,
0.030886666849255562,
0.028946708887815475,
-0.018933216109871864,
0.022755196318030357,
0.03850637748837471,
-0.01399711612612009,
0.056797973811626434,
0.0011015066411346197,
0.02107533998787403,
0.03422088548541069,
0.03050297312438488,
-0.0036674020811915398,
0.006812278646975756,
-0.028675053268671036,
0.014504260383546352,
-0.051202040165662766,
0.06960653513669968,
0.026208609342575073,
-0.07946496456861496,
-0.06728588044643402,
0.06034855172038078,
0.004277877509593964,
-0.02002844400703907,
0.016353661194443703,
0.030542738735675812,
0.003854361828416586,
0.013968365266919136,
-0.06533321738243103,
-0.07504726946353912,
0.03252875432372093,
0.04529562592506409,
0.07586149871349335,
-0.0759868323802948,
-0.00790204107761383,
0.0511319637298584,
0.05604198947548866,
-0.0023340382613241673,
-0.018807940185070038,
-0.02749563381075859,
0.005344714969396591,
0.03174671530723572,
-0.032178740948438644,
0.010327802039682865,
0.010174433700740337,
-0.008622328750789165,
-0.020349282771348953,
-0.007789149880409241,
-0.02851463109254837,
0.03745928779244423,
0.025756314396858215,
-0.019361888989806175,
0.02789563499391079,
0.0809021145105362,
0.018659526482224464,
-0.005925766192376614,
0.02985650859773159,
0.010368041694164276,
-0.07263286411762238,
-0.0587238110601902,
0.006706325802952051,
0.017621595412492752,
-0.025228487327694893,
0.02250504307448864,
0.023290682584047318,
-0.013326632790267467,
0.05463181063532829,
-0.009158613160252571,
-0.014516646973788738,
0.0356760174036026,
-0.0240449421107769,
-0.0018615880981087685,
-0.09575928002595901,
0.045660946518182755,
0.035972874611616135,
0.02653297409415245,
0.03363560512661934,
-0.00297176418825984,
0.02300959825515747,
-0.028845811262726784,
-0.07660618424415588,
0.011517657898366451,
0.023384273052215576,
-0.012863476760685444,
-0.09642013162374496,
0.019386835396289825,
0.02132231742143631,
0.004039175808429718,
-0.03526803106069565,
0.007924109697341919,
0.017686767503619194,
-0.029259750619530678,
0.026186896488070488,
-0.029807893559336662,
-0.002009961288422346,
0.014706823974847794,
-0.021555010229349136,
-0.010675321333110332,
0.02461634762585163,
-0.003659107256680727,
0.035750992596149445,
0.054745208472013474,
-0.002484904835000634,
0.01645706221461296,
0.007633162662386894,
-0.0002659214660525322,
0.013491244986653328,
-0.04886946827173233,
-0.043144285678863525,
0.026019902899861336,
-0.035915225744247437,
-0.00009402563591720536,
0.036349132657051086,
0.08009476959705353,
-0.03200049325823784,
-0.04135427623987198,
-0.025519851595163345,
0.009413974359631538,
-0.0333821102976799,
-0.015811916440725327,
-0.03142721951007843,
-0.015985725447535515,
-0.01634906232357025,
-0.010602889582514763,
0.00046958684106357396,
0.061057332903146744,
-0.011437393724918365,
0.040504954755306244,
0.00814678892493248,
0.0014888991136103868,
-0.009395776316523552,
0.01085241325199604,
0.03938540071249008,
0.010592987760901451,
0.04579132795333862,
0.010447919368743896,
-0.06839853525161743,
-0.10608123987913132,
-0.01807825267314911,
0.006905332673341036,
-0.04739335924386978,
0.03154689446091652,
-0.025348639115691185,
-0.05547485500574112,
-0.07236073166131973,
0.057524364441633224,
-0.009458549320697784,
-0.006399620324373245,
-0.04296676442027092,
-0.006491242442280054,
0.1133170947432518,
0.03091232106089592,
-0.030372731387615204,
0.06572247296571732,
0.07088842242956161,
-0.04891028255224228,
-0.009273849427700043,
-0.026758549734950066,
-0.0315014123916626,
-0.07387229055166245,
0.04586014896631241,
-0.031176654621958733,
-0.03664366155862808,
-0.03305335342884064,
-0.0034346855245530605,
-0.017814304679632187,
-0.018228765577077866,
-0.045400116592645645,
-0.030131343752145767,
0.05309302359819412,
0.016032366082072258,
-0.020155539736151695,
0.0017152121290564537,
-0.044150952249765396,
0.06341062486171722,
0.04464217275381088,
-0.01882549375295639,
-0.07605451345443726,
-0.0530238039791584,
-0.011373912915587425,
0.029344454407691956,
-0.008759845048189163,
-0.021684952080249786,
0.07742805033922195,
0.043704450130462646,
-0.033323951065540314,
0.02403271198272705,
0.06064389646053314,
-0.04142836853861809,
0.00033388356678187847,
0.016277821734547615,
-0.06491632759571075,
0.0001010887062875554,
0.012958236038684845,
0.00956578180193901,
-0.007116645108908415,
-0.019393330439925194,
0.0035378988832235336,
-0.0046764579601585865,
0.008760498836636543,
0.0056171598844230175,
-0.036007415503263474,
0.026014138013124466,
0.04391981288790703
] |
<p>Let's have potential
$$
U(r) = -U_{0}e^{-\frac{r}{a}}.
$$
I need to find energy levels for particles moving in this field (for an arbitrary values of orbital number $l$). This task isn't exactly solvable, so I need some method which can help to find approximate energy levels.</p>
<p>What to do?</p>
<p>I reduced the Schrodinger equation to the form (with normalized $r \to \frac{r}{a}$ and $\Psi (r, \varphi , \theta ) = \kappa e^{-\beta r}r^{l}\kappa (r) Y_{lm}(\theta , \varphi )$)
$$
r\kappa '' + \kappa {'}(2l + 2 - 2\beta r) + \kappa (\alpha^{2}r e^{-r} - 2\beta (l + 1)) = 0,
$$
where
$$
\alpha^{2} = \frac{2mU_{0}a^{2}}{\hbar^{2}}, \quad \beta^{2} = \frac{2m |E|a^{2}}{\hbar^{2}}.
$$
It would be tempting to use the approximation
$$
r \approx \frac{1 - e^{-r}}{e^{-r}},
$$
but $r e^{-r}$ didn't reduce to the normal form.</p>
<p>The exact solution for $l = 0$ is existed.</p> | g4591 | [
-0.01407611183822155,
0.008838871493935585,
-0.015323047526180744,
-0.018708260729908943,
0.04168788716197014,
0.007094060070812702,
0.00835536140948534,
0.0230027474462986,
-0.038856301456689835,
0.0071349972859025,
-0.005601873155683279,
-0.015288658440113068,
0.005181003827601671,
0.05934159830212593,
0.0028774470556527376,
-0.0028511283453553915,
0.05828734487295151,
-0.02441689558327198,
-0.039782244712114334,
-0.011667733080685139,
0.00040891242679208517,
0.0010924863163381815,
0.05270153284072876,
0.04518882557749748,
0.04580802470445633,
-0.021137135103344917,
-0.011339678429067135,
0.04906199499964714,
-0.03209923207759857,
-0.03563055768609047,
-0.02482347935438156,
0.035032518208026886,
0.060190021991729736,
-0.038239311426877975,
0.01683999039232731,
-0.009253841824829578,
0.07724366337060928,
0.07731205970048904,
0.012718992307782173,
0.000040845272451406345,
-0.029890967532992363,
-0.04535359516739845,
0.03178539127111435,
0.02742534875869751,
0.022839626297354698,
0.003709652926772833,
0.03048524633049965,
0.004682464525103569,
0.03592917323112488,
0.008524618111550808,
0.023032577708363533,
0.07193178683519363,
0.0295556727796793,
0.010706298984587193,
0.017740905284881592,
-0.007299343124032021,
-0.037027060985565186,
-0.07553493976593018,
0.03866690397262573,
0.05868200957775116,
0.07009570300579071,
-0.05288081243634224,
-0.00611928990110755,
-0.03409811854362488,
-0.014178695157170296,
0.026138944551348686,
-0.038705695420503616,
-0.010978628881275654,
-0.02848012000322342,
-0.056216467171907425,
0.0037964140065014362,
-0.01917070895433426,
-0.06379242241382599,
-0.01708427257835865,
-0.08049339056015015,
-0.0072801983915269375,
-0.006751008331775665,
-0.03028547391295433,
0.010198308154940605,
-0.011914302594959736,
-0.0395992286503315,
-0.03138791769742966,
0.04094407707452774,
0.033551301807165146,
0.009902301244437695,
0.003420945256948471,
-0.002496578497812152,
0.03046623431146145,
0.028854114934802055,
-0.04686829075217247,
-0.05056010186672211,
-0.0446341335773468,
0.05103982612490654,
-0.08673162013292313,
0.05454615131020546,
-0.012458361685276031,
0.005777302663773298,
0.06888589262962341,
-0.05258426442742348,
-0.05187321826815605,
-0.015546766109764576,
-0.00406760023906827,
0.04559136927127838,
-0.008276556618511677,
0.01524591725319624,
-0.011243689805269241,
0.01740175671875477,
-0.03573080524802208,
0.1069517433643341,
0.010439625009894371,
-0.014475710690021515,
-0.0053374022245407104,
-0.011219941079616547,
-0.05638714134693146,
-0.020557783544063568,
-0.009369206614792347,
0.02886374481022358,
0.038675639778375626,
-0.030589928850531578,
0.013543893583118916,
-0.004976082593202591,
0.019449688494205475,
0.001566737424582243,
0.03584950417280197,
0.0002788695855997503,
0.025234030559659004,
-0.05578579753637314,
-0.027557535097002983,
-0.014132875017821789,
-0.019830815494060516,
0.028818482533097267,
-0.08157297968864441,
0.029635608196258545,
0.022097935900092125,
-0.04935631528496742,
0.05552447587251663,
-0.07933343201875687,
0.005646579433232546,
0.024668673053383827,
-0.020715394988656044,
-0.020330091938376427,
-0.03087840974330902,
0.0010922159999608994,
0.022813908755779266,
-0.06589065492153168,
0.02340083196759224,
-0.017995744943618774,
-0.023059675469994545,
0.05657327547669411,
0.03534013405442238,
-0.03310713917016983,
0.0171055868268013,
-0.009462135843932629,
0.00724382558837533,
0.030863983556628227,
-0.04316446930170059,
-0.029984155669808388,
0.018208127468824387,
-0.05262003839015961,
0.04029499739408493,
0.05792095512151718,
-0.02717416174709797,
0.024365287274122238,
-0.018031803891062737,
0.0000752705818740651,
0.11668294668197632,
-0.022563932463526726,
-0.0046593123115599155,
0.009070473723113537,
-0.045711539685726166,
-0.02804742380976677,
-0.017994273453950882,
0.03035467490553856,
0.01920662447810173,
-0.061030659824609756,
0.0808229148387909,
0.0023722515907138586,
-0.02537587471306324,
-0.029566342011094093,
0.027751704677939415,
0.06269747018814087,
-0.0580454021692276,
0.05962883308529854,
-0.0024619423784315586,
0.027853677049279213,
-0.04334690421819687,
-0.021236542612314224,
0.060348883271217346,
0.03576893359422684,
0.0063223824836313725,
0.047988008707761765,
-0.0068503255024552345,
0.032933346927165985,
-0.027294501662254333,
-0.01844685710966587,
0.04763457924127579,
0.040938008576631546,
-0.08745390176773071,
-0.02470330335199833,
-0.018439993262290955,
0.003622119314968586,
-0.01347782090306282,
0.009648535400629044,
-0.02450708858668804,
0.0693499967455864,
-0.01592813991010189,
0.04056452214717865,
-0.005389319267123938,
0.01243370771408081,
0.00994971301406622,
-0.04906154051423073,
-0.04798225685954094,
-0.026478176936507225,
0.037075430154800415,
-0.0019795435946434736,
-0.038508325815200806,
0.024912366643548012,
0.02836647443473339,
-0.05190669372677803,
0.03209926187992096,
-0.01631316728889942,
0.032219450920820236,
0.015455902554094791,
0.021504029631614685,
0.06213420629501343,
-0.007930649444460869,
-0.033442672342061996,
0.02232375182211399,
-0.008539460599422455,
0.04137038439512253,
-0.044398874044418335,
0.03932170569896698,
-0.0348086953163147,
-0.031740229576826096,
0.039606817066669464,
0.004315055441111326,
-0.034644920378923416,
-0.016877954825758934,
0.03905598446726799,
-0.030133843421936035,
0.026421070098876953,
0.0033923645969480276,
-0.01793135330080986,
0.00027403104468248785,
0.047572508454322815,
0.03029567375779152,
0.012099290266633034,
0.021240564063191414,
-0.06951924413442612,
0.032543499022722244,
0.0005535303498618305,
0.014324557036161423,
-0.03846147283911705,
0.028189534321427345,
-0.01664767600595951,
0.011807626113295555,
-0.019847096875309944,
0.05552847310900688,
0.050066303461790085,
0.014074618928134441,
-0.053712837398052216,
-0.033332426100969315,
-0.012584269978106022,
0.01466179545968771,
0.051747895777225494,
0.003618220565840602,
-0.01753827929496765,
-0.002072682837024331,
0.03305734694004059,
-0.008303438313305378,
-0.005678957793861628,
0.03608650714159012,
-0.02474105730652809,
0.03187400475144386,
-0.005672123283147812,
-0.0341082364320755,
0.028837064281105995,
0.031737376004457474,
0.03761492297053337,
0.0019094106974080205,
0.008169904351234436,
-0.06932365894317627,
0.0324602834880352,
0.060664836317300797,
-0.013275832869112492,
-0.06783045828342438,
0.01566685363650322,
0.027431391179561615,
-0.0025157176423817873,
-0.016796836629509926,
0.01143021509051323,
-0.01668825000524521,
0.025802353397011757,
0.022986551746726036,
-0.007868435233831406,
-0.002261218149214983,
0.057418111711740494,
-0.033679794520139694,
-0.006673240568488836,
0.09909941256046295,
0.02301955781877041,
-0.0033059772104024887,
-0.03950082138180733,
-0.037526506930589676,
-0.00951425638049841,
-0.022658251225948334,
-0.052973728626966476,
-0.013796747662127018,
-0.002936031436547637,
0.043416138738393784,
-0.032193489372730255,
-0.0005677014123648405,
0.01031527016311884,
0.0304863341152668,
0.007757641840726137,
0.015528146177530289,
-0.001323145697824657,
-0.007348330691456795,
0.01760816015303135,
0.0017947128508239985,
0.0027560635935515165,
-0.03365135192871094,
0.04364905506372452,
0.00682778051123023,
-0.029702838510274887,
0.07910674810409546,
-0.03926388546824455,
-0.012436737306416035,
-0.06377808749675751,
-0.040636833757162094,
0.048407409340143204,
-0.0284015741199255,
0.05552256852388382,
-0.018939606845378876,
-0.07095570862293243,
-0.0027433165814727545,
-0.046007461845874786,
0.013014554977416992,
0.0033058668486773968,
-0.00033422192791476846,
-0.05155086889863014,
0.014632114209234715,
-0.035607267171144485,
0.011395277455449104,
0.03416182100772858,
-0.05196637660264969,
-0.085729219019413,
0.002162907039746642,
-0.015519869513809681,
-0.035773370414972305,
0.004856412298977375,
-0.024514051154255867,
0.024295749142766,
0.0030213743448257446,
-0.026058189570903778,
-0.032385360449552536,
-0.0030989486258476973,
0.012450949288904667,
0.016609907150268555,
0.027132296934723854,
-0.008102199994027615,
-0.02276366576552391,
0.040732335299253464,
0.07294613122940063,
0.004291116259992123,
-0.020725617185235023,
-0.028419481590390205,
-0.008686969988048077,
0.023936590179800987,
-0.030608028173446655,
0.03395809978246689,
-0.024022074416279793,
0.07246467471122742,
0.020899880677461624,
-0.028107479214668274,
-0.007249234244227409,
-0.005387050565332174,
-0.03346886485815048,
-0.0601164735853672,
0.0067756143398582935,
0.007179668173193932,
-0.026324130594730377,
0.02282419428229332,
0.03330448642373085,
0.04035995155572891,
-0.001136173726990819,
-0.02429618313908577,
0.0008896709769032896,
0.030891790986061096,
0.023539530113339424,
-0.03755196928977966,
-0.07871150225400925,
-0.03806089609861374,
0.05148985981941223,
-0.0387880839407444,
-0.03812512755393982,
0.0444490909576416,
-0.007283343002200127,
-0.050527215003967285,
0.09182813763618469,
0.013706273399293423,
0.005019523669034243,
-0.009941854514181614,
0.03126188740134239,
-0.033682309091091156,
-0.03204270079731941,
0.03966112434864044,
-0.027382396161556244,
-0.005858899559825659,
-0.026547333225607872,
-0.03305330127477646,
0.00780715886503458,
0.02599410153925419,
-0.00209443480707705,
-0.01598975993692875,
-0.05540906637907028,
-0.017598703503608704,
-0.04004347324371338,
0.009829292073845863,
0.029016289860010147,
-0.0005681797047145665,
0.03479580953717232,
-0.03208638355135918,
-0.028617415577173233,
-0.01658136397600174,
0.07231589406728745,
-0.006577988155186176,
0.0729265883564949,
-0.02309277281165123,
-0.018973693251609802,
0.043795838952064514,
0.03683961182832718,
-0.05117325857281685,
0.0072707319632172585,
-0.05831477791070938,
0.025695104151964188,
0.0033316859044134617,
-0.030969256535172462,
-0.012700487859547138,
0.01720229908823967,
0.011178183369338512,
0.028143825009465218,
0.012648336589336395,
0.002893385710194707,
-0.03070688806474209,
0.04103685915470123,
-0.07547370344400406,
-0.06047684699296951,
-0.009205191396176815,
0.0034724902361631393,
0.003163048531860113,
0.0010655681835487485,
0.02987590804696083,
0.028164805844426155,
0.0013674356741830707,
-0.09434012323617935,
-0.051975153386592865,
0.029300738126039505,
0.030865129083395004,
0.04994288086891174,
-0.03507290035486221,
-0.0016921607311815023,
-0.007370915729552507,
-0.047731105238199234,
0.02223942242562771,
0.02355939894914627,
-0.03614474833011627,
0.05072367936372757,
-0.0060394988395273685,
-0.09109150618314743,
0.018633024767041206,
-0.02147066779434681,
0.07597095519304276,
-0.06490715593099594,
-0.027743274345993996,
-0.03574724122881889,
-0.016329113394021988,
-0.0024289891589432955,
-0.01303896401077509,
-0.006996974814683199,
-0.05142970383167267,
-0.014568839222192764,
-0.009334882721304893,
0.01855015940964222,
-0.0431625097990036,
0.042961567640304565,
-0.04516990855336189,
0.03947004675865173,
0.049468401819467545,
0.026476357132196426,
-0.01139229629188776,
0.06471990793943405,
-0.014607008546590805,
-0.06952197104692459,
0.0389736145734787,
0.015709931030869484,
-0.0023069975432008505,
0.00720213633030653,
0.047610294073820114,
0.0887514278292656,
-0.04618251323699951,
0.010498357936739922,
-0.04199916869401932,
-0.0000425004109274596,
0.019088484346866608,
0.027914084494113922,
0.044680651277303696,
0.04563751444220543,
0.017171813175082207,
-0.032911770045757294,
-0.0190420001745224,
-0.05276797339320183,
0.035231396555900574,
-0.009354344569146633,
-0.028821684420108795,
0.00440581189468503,
-0.042381636798381805,
0.06762748956680298,
-0.03400878608226776,
-0.051836688071489334,
0.06013643369078636,
-0.009528214111924171,
0.02199692465364933,
-0.019812673330307007,
-0.0218314491212368,
0.010455725714564323,
-0.0230777058750391,
-0.023994794115424156,
-0.07097351551055908,
0.026013478636741638,
-0.01966013014316559,
-0.04542851448059082,
-0.02428991161286831,
-0.0014074379578232765,
0.0012877777917310596,
0.00869560893625021,
-0.005774243269115686,
0.002405760111287236,
-0.004759631585329771,
0.023411327973008156,
-0.00415327912196517,
0.015422346070408821,
0.016518160700798035,
0.004554665181785822,
-0.03965790942311287,
0.013200925663113594,
-0.07835818827152252,
0.0027418839745223522,
0.009492136538028717,
-0.04232242703437805,
-0.022701578214764595,
-0.007397135253995657,
-0.009721788577735424,
-0.0212312750518322,
0.009021593257784843,
0.0069618821144104,
0.010222029872238636,
-0.016811205074191093,
-0.05820966884493828,
0.04666217043995857,
-0.00227932445704937,
-0.06853590905666351,
0.09273848682641983,
0.056636933237314224,
0.03982817009091377,
-0.008361337706446648,
-0.02008974924683571,
-0.05832495912909508,
0.01987515389919281,
0.015832936391234398,
-0.0508219338953495,
0.015502222813665867,
0.000869325886014849,
0.008059347979724407,
0.03786236047744751,
-0.006139990407973528,
0.005532128736376762,
-0.029799018055200577,
-0.030613182112574577,
0.058278754353523254,
-0.04707855358719826,
0.013508586212992668,
-0.012782694771885872,
0.03680111840367317,
-0.010618987493216991,
0.05479980260133743,
-0.012336866930127144,
-0.05080490931868553,
0.019434699788689613,
-0.027859458699822426,
0.014382174238562584,
-0.0017794540617614985,
0.005040391348302364,
0.019067464396357536,
0.0060074590146541595,
-0.025699350982904434,
0.015560951083898544,
-0.017881693318486214,
-0.00327246799133718,
0.06504379212856293,
0.0440710224211216,
-0.06624127179384232,
-0.0012512868270277977,
-0.010659069754183292,
0.008326934650540352,
0.031244298443198204,
-0.0892627015709877,
0.023583846166729927,
-0.04188043996691704,
0.032203804701566696,
-0.01908976584672928,
-0.036087628453969955,
-0.0030982212629169226,
-0.000972436333540827,
-0.009298480115830898,
-0.02543143555521965,
0.04822598770260811,
0.08918511122465134,
0.004393922630697489,
-0.023707235231995583,
0.030858289450407028,
-0.008861829526722431,
0.06435342133045197,
0.01912008225917816,
0.055723126977682114,
0.020616797730326653,
0.003948830999433994,
-0.023578248918056488,
0.06114199757575989,
-0.043298427015542984,
0.04726813733577728,
0.0011331994319334626,
0.03901620954275131,
0.06610818952322006,
0.0066229491494596004,
0.042414821684360504,
-0.0007446624804288149,
0.06179986894130707,
-0.04331469535827637,
0.04056836664676666,
-0.0005570760113187134,
0.008133428171277046,
0.06771710515022278,
0.02574801631271839,
-0.05398905649781227,
-0.05663865804672241,
0.0013312631053850055,
0.06759839504957199,
-0.056461695581674576,
0.008547216653823853,
0.04369828477501869,
-0.000830164470244199,
-0.062173712998628616,
0.002835508668795228,
-0.02874070592224598,
0.01590139791369438,
-0.0012666485272347927,
0.06120847165584564,
0.013093347661197186,
-0.04176986590027809,
0.021603835746645927,
-0.04051864519715309,
0.02262292616069317,
0.03382816165685654,
-0.018694503232836723,
0.050869546830654144,
-0.041525885462760925,
-0.017664479091763496,
0.009912303648889065,
-0.07169710844755173,
0.035744138062000275,
-0.048512473702430725,
-0.09036169946193695,
0.0166008323431015,
-0.05274965241551399,
0.01960848644375801,
0.03682401776313782,
0.033490441739559174,
-0.0316605307161808,
-0.04004979133605957,
-0.006758109200745821,
-0.0004939463105984032,
-0.025984473526477814,
-0.009185574017465115,
-0.002833042060956359,
0.03595197573304176,
-0.052027128636837006,
-0.011593407019972801,
0.005038504488766193,
0.024793121963739395,
-0.010037367232143879,
0.08075883984565735,
0.020591547712683678,
-0.010974213480949402,
-0.01341019757091999,
-0.021501103416085243,
-0.027070218697190285,
-0.027310701087117195,
0.05219616740942001,
0.003909231163561344,
0.021088337525725365,
-0.011779027990996838,
0.037122782319784164,
-0.01432725414633751,
-0.06472533196210861,
-0.03007587231695652,
-0.006355351768434048,
-0.03552078828215599,
-0.008360075764358044,
-0.03268134593963623,
-0.020181670784950256,
0.015632476657629013,
0.0031485911458730698,
0.02961425855755806,
0.06548333168029785,
0.022510502487421036,
0.0016830883687362075,
0.06487666070461273,
-0.004880951251834631,
-0.0014723894419148564,
-0.013162522576749325,
0.003042077412828803,
0.019283557310700417,
-0.005397056695073843,
0.01551163662225008,
-0.010065780952572823,
-0.04776326194405556,
-0.01782400906085968,
0.05312143266201019,
-0.03007500432431698,
0.007644537836313248,
-0.00047429921687580645,
-0.060608480125665665,
0.028478719294071198,
-0.0417180135846138,
-0.04123562574386597,
-0.08872871845960617,
-0.02336425706744194,
0.012916282750666142,
0.0004721144796349108,
-0.04411456733942032,
-0.07910610735416412,
0.026790035888552666,
0.021831538528203964,
0.02351531945168972,
0.000055242191592697054,
-0.006693619769066572,
0.011033864691853523,
0.03390970826148987,
0.029630672186613083,
0.02626771293580532,
0.03503770753741264,
-0.06384158879518509,
0.07261601090431213,
0.08985637873411179,
-0.05612407997250557,
0.04517098143696785,
-0.028964579105377197,
-0.03529621660709381,
0.02590027078986168,
-0.009953916072845459,
0.019797494634985924,
-0.015520758926868439,
0.04887252673506737,
0.008314481005072594,
-0.053806107491254807,
0.03793332353234291,
0.006021731533110142
] |
<p>With relativistic aberration, a sky full of stars gets concentrated in the direction of motion. As a rough measure of the degree of concentration, one could use the radius of a small circle, centered on the direction of motion, which contains the objects which, when you are at rest, are in half the sky (if you take my meaning).</p>
<p>Using the formula for relativistic aberration:</p>
<p>beta=0: half-sky radius=90 deg</p>
<p>beta=0.8: half-sky radius= 36.87 deg (this is just arcos(beta))</p>
<p>When I compare this calculation with diagrams created both by others and myself, there seems to be a difference of a few degrees, and I can't figure out why. I seem to be missing something.</p>
<p>For the case of beta=0.80, I measure the half-sky radius as 39 degrees. The difference is small, but it's large enough that I'm pretty sure it's not a measurement error.</p>
<p>You can measure this for yourself, using this diagram (created by someone else), with the 90 deg lines:
<a href="http://erkdemon.blogspot.ca/2009/11/relativistic-ellipse.html" rel="nofollow">http://erkdemon.blogspot.ca/2009/11/relativistic-ellipse.html</a></p> | g4592 | [
0.01955089531838894,
0.0052632796578109264,
-0.003846515202894807,
-0.028416428714990616,
0.04674481973052025,
0.018560729920864105,
0.06453177332878113,
-0.03414156287908554,
0.002698922296985984,
-0.021773677319288254,
-0.04909031093120575,
0.04837138578295708,
0.03972706198692322,
-0.0005209281807765365,
0.026379600167274475,
-0.002064117696136236,
0.008157321251928806,
-0.03320211544632912,
0.007837316952645779,
0.009066369384527206,
0.02469777688384056,
-0.03943005949258804,
0.0071687172167003155,
-0.030340738594532013,
0.02235245518386364,
0.07088681310415268,
0.033029284328222275,
0.033549677580595016,
-0.10138168185949326,
-0.006138607859611511,
-0.03538691997528076,
0.02599533274769783,
0.005773169454187155,
-0.030340243130922318,
0.02576025016605854,
-0.027864757925271988,
-0.01638943701982498,
0.01524273119866848,
0.007520272396504879,
-0.036806464195251465,
-0.007895679213106632,
-0.027106408029794693,
0.013293948955833912,
0.0027649742551147938,
0.0031171697191894054,
-0.07492000609636307,
-0.03008464351296425,
-0.0025820883456617594,
0.039961520582437515,
0.008863297291100025,
-0.00011134718079119921,
0.012578614987432957,
0.013396092690527439,
-0.026156537234783173,
0.04036654531955719,
0.015625111758708954,
-0.01490919291973114,
-0.009272702969610691,
0.012034752406179905,
0.0021114032715559006,
0.014037126675248146,
0.014047529548406601,
0.0024729382712394,
0.0011590714566409588,
0.015559850260615349,
0.01477398257702589,
-0.021553613245487213,
-0.027298221364617348,
0.003244534833356738,
-0.01778268814086914,
-0.030151937156915665,
-0.0314871110022068,
-0.01752110943198204,
-0.004068754147738218,
-0.09415467828512192,
-0.013082312420010567,
-0.030231229960918427,
-0.004693824797868729,
0.0010751864174380898,
0.010354751721024513,
-0.025693319737911224,
-0.08262000977993011,
-0.02488245815038681,
0.04138946533203125,
0.069058857858181,
0.05809884890913963,
-0.03033745475113392,
-0.013409602455794811,
-0.020957956090569496,
-0.011983426287770271,
0.024551020935177803,
-0.0488327220082283,
0.06999646127223969,
0.045808710157871246,
0.05927354097366333,
-0.04691111296415329,
-0.041031017899513245,
0.027484562247991562,
-0.044727690517902374,
0.04660385474562645,
-0.027371756732463837,
-0.015879888087511063,
-0.0253234151750803,
0.021379385143518448,
-0.017239723354578018,
0.01588626392185688,
0.009936138987541199,
-0.04320688918232918,
-0.016507446765899658,
-0.028402721509337425,
-0.04947532340884209,
-0.08077026158571243,
0.010317360050976276,
-0.049680717289447784,
-0.04938355088233948,
-0.04175521805882454,
0.11062270402908325,
-0.03619212657213211,
0.04512306675314903,
0.032058026641607285,
0.048139628022909164,
0.04609479382634163,
0.01830962672829628,
0.034757521003484726,
-0.039698753505945206,
0.03930055350065231,
-0.040961138904094696,
0.0037331965286284685,
0.030799509957432747,
-0.0036026884336024523,
-0.0035982460249215364,
-0.037709105759859085,
-0.00326718227006495,
0.0053352839313447475,
0.003103695809841156,
0.01027626357972622,
-0.012014908716082573,
-0.038300517946481705,
-0.06360597163438797,
0.00043694075429812074,
0.0326550267636776,
0.028096526861190796,
0.030376991257071495,
-0.028524816036224365,
-0.024166347458958626,
-0.0042326743714511395,
-0.015088556334376335,
0.056640420109033585,
0.04117211326956749,
-0.030890485271811485,
-0.016769591718912125,
0.01837342046201229,
-0.011721348389983177,
-0.025508005172014236,
-0.029271280393004417,
-0.016585635021328926,
0.023033592849969864,
0.029238330200314522,
-0.015470903366804123,
0.040334660559892654,
0.07855900377035141,
0.056426361203193665,
0.024461468681693077,
-0.03802450746297836,
-0.01775652915239334,
0.06554336100816727,
0.009260788559913635,
-0.0248662531375885,
-0.00428687734529376,
-0.016666658222675323,
-0.09246236830949783,
-0.04110199585556984,
0.008861612528562546,
-0.0021857512183487415,
-0.027092479169368744,
0.12686190009117126,
0.07507909834384918,
0.022156301885843277,
-0.043384142220020294,
0.012982983142137527,
-0.036392007023096085,
-0.0010874085128307343,
0.0015402205754071474,
0.03584320470690727,
0.018925253301858902,
-0.06261295825242996,
0.031015031039714813,
-0.0007235879311338067,
-0.027358433231711388,
-0.04400892183184624,
0.03660375624895096,
-0.048373036086559296,
-0.07436618208885193,
-0.010064758360385895,
-0.00508902920410037,
-0.004180739168077707,
0.06790038198232651,
-0.01585530675947666,
-0.030884096398949623,
0.054278358817100525,
-0.016837790608406067,
0.023644518107175827,
0.06106221675872803,
0.015314383432269096,
0.02157888188958168,
0.03043273650109768,
-0.02676173485815525,
0.000453196931630373,
0.0418078675866127,
0.04432198777794838,
-0.022676359862089157,
-0.0038648785557597876,
0.007773653604090214,
0.009925552643835545,
-0.004132379312068224,
-0.01322467066347599,
0.03432411327958107,
-0.02035118080675602,
-0.03003055974841118,
0.04414307326078415,
-0.007377122063189745,
-0.00428159162402153,
0.02747270278632641,
-0.023603646084666252,
0.04653741419315338,
0.03207774460315704,
-0.07569616287946701,
0.028591735288500786,
0.04665860906243324,
0.01192895695567131,
-0.008722797967493534,
0.016575857996940613,
-0.014557631686329842,
0.00914819911122322,
-0.0058267381973564625,
0.0035186968743801117,
0.009868733584880829,
0.00899653322994709,
0.008620386011898518,
0.00019310037896502763,
0.054102879017591476,
0.013335591182112694,
-0.03978448733687401,
-0.016466541215777397,
0.02818531170487404,
0.060146089643239975,
0.08957362920045853,
0.011117958463728428,
-0.07113094627857208,
0.0489446222782135,
-0.019024578854441643,
0.0435696542263031,
0.01497782114893198,
-0.011810862459242344,
0.04890495166182518,
0.050879281014204025,
0.0033423888962715864,
0.0031870948150753975,
-0.04438609257340431,
-0.03555388003587723,
-0.06972979009151459,
-0.04643508791923523,
0.027158357203006744,
0.0005062022828496993,
-0.022318309172987938,
0.02693823166191578,
-0.022017711773514748,
0.008312692865729332,
0.03575915843248367,
-0.022084033116698265,
-0.011611104011535645,
0.06111462414264679,
-0.0068473732098937035,
0.07394353300333023,
0.008561997674405575,
-0.01968981884419918,
0.011499633081257343,
-0.016789300367236137,
0.04995149374008179,
0.025228526443243027,
-0.01698174886405468,
0.029425768181681633,
-0.0316089391708374,
0.018121158704161644,
0.01901538483798504,
-0.0005544143496081233,
0.019039977341890335,
0.0431726798415184,
-0.05136542767286301,
0.0080926064401865,
0.018164170905947685,
0.01404154859483242,
0.005356263369321823,
-0.026005202904343605,
0.04882458224892616,
0.014459499157965183,
0.024280648678541183,
0.021964682266116142,
-0.035894714295864105,
0.0032848503906279802,
0.0015712609747424722,
0.0072003500536084175,
0.045729510486125946,
-0.024587372317910194,
-0.008555510081350803,
0.024706976488232613,
-0.00528685562312603,
-0.06657668948173523,
-0.03005264699459076,
-0.020440317690372467,
-0.04513382539153099,
-0.03739781677722931,
0.01659264974296093,
0.0027011604979634285,
0.01698797196149826,
-0.007337799295783043,
-0.0038351297844201326,
0.02631266415119171,
0.06561487168073654,
0.018837332725524902,
0.008141282945871353,
-0.06858287751674652,
0.0302603580057621,
0.010165465995669365,
0.041918493807315826,
-0.04235050827264786,
0.03070494532585144,
0.018587011843919754,
-0.054102573543787,
-0.05235157907009125,
0.005100748036056757,
-0.03510364145040512,
0.01575898751616478,
0.018647847697138786,
-0.059872761368751526,
0.029997076839208603,
-0.06200060248374939,
-0.017569493502378464,
0.00744272768497467,
0.004789669066667557,
-0.07196804136037827,
0.0021811374463140965,
-0.01494548749178648,
-0.044102974236011505,
0.05487023666501045,
0.022509636357426643,
-0.011116335168480873,
0.009302446618676186,
0.01357655692845583,
-0.02481880597770214,
0.012448059394955635,
-0.029817719012498856,
-0.02147062122821808,
-0.07281883805990219,
-0.0318940244615078,
-0.047368887811899185,
0.00045356585178524256,
0.010921617969870567,
0.028548840433359146,
0.011435498483479023,
0.02989400550723076,
-0.026405172422528267,
-0.045342687517404556,
-0.023096561431884766,
0.00417328393086791,
-0.027003895491361618,
0.014510197564959526,
0.00007001608173595741,
-0.010592903941869736,
0.03031807392835617,
-0.023750238120555878,
-0.021221844479441643,
-0.035894278436899185,
0.011685649864375591,
0.026743141934275627,
0.005859704688191414,
0.03038802370429039,
-0.008065996691584587,
0.0037596405018121004,
0.03238140046596527,
0.028960485011339188,
0.016299741342663765,
-0.025411201640963554,
0.03122524544596672,
-0.04040674492716789,
-0.024552414193749428,
-0.008089879527688026,
-0.04723507910966873,
0.008973818272352219,
-0.016690872609615326,
-0.011751196347177029,
-0.08428169041872025,
-0.026326632127165794,
-0.028922848403453827,
0.042942605912685394,
-0.030250055715441704,
0.04708985611796379,
-0.008060029707849026,
0.012384871952235699,
0.06687585264444351,
-0.031911224126815796,
0.015113072469830513,
0.01941908337175846,
-0.0021683131344616413,
-0.013212020508944988,
-0.03568089380860329,
0.006079038605093956,
0.012894133105874062,
-0.0028167946729809046,
0.014552230946719646,
-0.006797706242650747,
0.03814009577035904,
-0.0121110575273633,
-0.10659831762313843,
0.08187999576330185,
0.05959543585777283,
-0.033961690962314606,
-0.005222144071012735,
0.013641680590808392,
0.024436920881271362,
-0.04116576910018921,
0.07125389575958252,
0.00773884542286396,
-0.017153330147266388,
0.03723255917429924,
0.07716964930295944,
0.000275647355010733,
0.041120581328868866,
0.0392041951417923,
-0.0017785292584449053,
0.006137812975794077,
0.012999226339161396,
-0.036815717816352844,
0.010178749449551105,
-0.07892220467329025,
0.038645047694444656,
-0.059245143085718155,
0.07407990097999573,
0.06292752921581268,
0.02564889006316662,
0.015448340214788914,
0.026665132492780685,
0.009574061259627342,
-0.02947435900568962,
-0.015392315573990345,
0.011911248788237572,
-0.04819915443658829,
-0.06170954927802086,
-0.003122019814327359,
-0.011953195556998253,
-0.004054284654557705,
0.01743254065513611,
0.014676355756819248,
0.03797163441777229,
-0.05675113573670387,
0.006848319433629513,
-0.017729660496115685,
0.07730728387832642,
0.05753783881664276,
-0.0005888694431632757,
-0.07540863752365112,
-0.013659299351274967,
0.038048405200242996,
0.01077699288725853,
0.027597719803452492,
-0.01563575677573681,
0.0033751241862773895,
-0.00333530199714005,
-0.04792722314596176,
0.0014422787353396416,
-0.022002505138516426,
0.03492620959877968,
0.05701833218336105,
-0.00949096865952015,
-0.026351800188422203,
0.04934525862336159,
0.009896664880216122,
-0.012095264159142971,
-0.0066341678611934185,
-0.031356338411569595,
-0.06138066202402115,
-0.0309126153588295,
0.007400942500680685,
-0.005498223006725311,
-0.012271860614418983,
0.07071030139923096,
-0.02780761756002903,
-0.0012178196338936687,
0.014555134810507298,
-0.00765946414321661,
0.027426481246948242,
0.009000006131827831,
-0.020231204107403755,
-0.05562644079327583,
0.04867319017648697,
-0.05363870784640312,
0.03614862635731697,
-0.042573198676109314,
0.0277959406375885,
-0.028325919061899185,
-0.054873254150152206,
0.06400289386510849,
-0.005216276738792658,
-0.00648890994489193,
-0.04500610753893852,
0.038432955741882324,
0.007737296633422375,
-0.006435200572013855,
0.0052674864418804646,
0.024731682613492012,
-0.016226598992943764,
0.0008568895282223821,
0.013214251957833767,
0.0005413952167145908,
-0.02604103274643421,
-0.0349423922598362,
-0.01710018329322338,
0.04645618796348572,
0.010934188961982727,
-0.04056861624121666,
0.0245671346783638,
0.002105979947373271,
-0.023915370926260948,
-0.033970996737480164,
0.04191877692937851,
-0.020940324291586876,
-0.0040438235737383366,
-0.009939109906554222,
0.021413378417491913,
-0.0058804890140891075,
-0.023755749687552452,
0.039231255650520325,
0.03398152068257332,
0.020289601758122444,
0.009583146311342716,
-0.009103573858737946,
0.02266784943640232,
-0.01413201168179512,
0.06866469979286194,
0.015955062583088875,
-0.005641418509185314,
0.06168343126773834,
-0.030230984091758728,
0.08144178986549377,
-0.026880668476223946,
-0.02789679542183876,
-0.029418671503663063,
-0.0008702633786015213,
0.04954298958182335,
0.04957590997219086,
-0.023441672325134277,
0.01137787289917469,
-0.004041277337819338,
0.016536619514226913,
-0.09042072296142578,
0.022985218092799187,
-0.047716788947582245,
-0.01273187156766653,
0.0034381048753857613,
-0.04068076238036156,
0.031994257122278214,
0.013291807845234871,
0.02719961106777191,
0.024948282167315483,
0.012398074381053448,
-0.07283824682235718,
0.03140219673514366,
-0.03120204620063305,
0.085394486784935,
0.03736349195241928,
-0.03137034922838211,
-0.023809943348169327,
0.00614451989531517,
0.036232996731996536,
0.06839004158973694,
0.03624521568417549,
-0.027529871091246605,
-0.026241900399327278,
0.04895344376564026,
0.017330076545476913,
0.022301241755485535,
-0.0037531896959990263,
0.009515495039522648,
-0.07097326964139938,
0.022738799452781677,
-0.016007430851459503,
0.009096414782106876,
-0.0026238393038511276,
0.009672379121184349,
-0.010354114696383476,
0.0035171378403902054,
0.009357555769383907,
0.01951829344034195,
-0.0038884261157363653,
-0.05514762923121452,
-0.008165559731423855,
0.03040381520986557,
0.00365436146967113,
-0.0688047781586647,
0.022053303197026253,
-0.0011446818243712187,
-0.00576878571882844,
0.06903721392154694,
0.006635178811848164,
0.05744265019893646,
-0.0186814833432436,
-0.0330878309905529,
0.018445681780576706,
-0.008049936965107918,
0.0037377162370830774,
-0.004114419687539339,
0.010304566472768784,
-0.03072294406592846,
0.05181947350502014,
-0.03518281504511833,
-0.03629913181066513,
0.0026021895464509726,
0.05375202000141144,
-0.05368005484342575,
-0.03733615577220917,
-0.006628581788390875,
-0.0294241514056921,
-0.04524502530694008,
0.019218288362026215,
0.03063838742673397,
0.028212998062372208,
-0.05001991614699364,
-0.009838332422077656,
0.011488846503198147,
-0.019378580152988434,
0.03863721713423729,
0.01349671371281147,
0.011683444492518902,
0.04079429805278778,
0.10394175350666046,
0.02608153223991394,
-0.07480451464653015,
-0.0034024957567453384,
0.0163786131888628,
0.11037953197956085,
-0.040654074400663376,
0.008205884136259556,
-0.012478531338274479,
0.001778247649781406,
-0.07521738111972809,
-0.03413645550608635,
-0.022019676864147186,
0.0014681071043014526,
-0.11241357028484344,
-0.00279987882822752,
0.03049079142510891,
0.02253861539065838,
-0.052986059337854385,
-0.015343589708209038,
-0.0513424389064312,
0.019046954810619354,
0.00022592558525502682,
0.04382603242993355,
0.0016400658059865236,
-0.0871303603053093,
-0.05729127302765846,
-0.021793944761157036,
-0.04821516200900078,
-0.0001280786527786404,
0.009491085074841976,
0.0027837171219289303,
0.01699855737388134,
0.0056203934364020824,
-0.06761869788169861,
-0.07868939638137817,
-0.018235867843031883,
0.031781572848558426,
-0.02797733247280121,
-0.016639459878206253,
-0.00025413729599677026,
0.00003400081550353207,
0.029103605076670647,
-0.04658165201544762,
-0.03815174102783203,
0.02547570876777172,
-0.014753244817256927,
0.04968641325831413,
0.013943502679467201,
0.004865326918661594,
-0.08993852138519287,
0.006141994148492813,
-0.04198845475912094,
-0.003917789552360773,
0.05392232909798622,
-0.06129467859864235,
0.005236080382019281,
0.0989985242486,
-0.04942411184310913,
0.02526329644024372,
-0.018665356561541557,
-0.014915929175913334,
0.10038048774003983,
0.027017641812562943,
0.038282979279756546,
-0.03494320064783096,
0.01859571598470211,
-0.02110031060874462,
0.0018469281494617462,
0.03664788976311684,
0.07899998873472214,
0.033641524612903595,
-0.009550679475069046,
0.05650493875145912,
-0.03534752503037453,
-0.014713514596223831,
0.005195733159780502,
0.03157709166407585,
0.014538499526679516,
0.028169576078653336,
-0.056432176381349564,
0.009252582676708698,
-0.0047208042815327644,
0.03014986589550972,
-0.019173139706254005,
-0.017879171296954155,
-0.017957286909222603,
-0.020420152693986893,
0.03391945734620094,
-0.09102468192577362,
-0.037243109196424484,
-0.06731092184782028,
0.022917501628398895,
-0.044866226613521576,
0.053334880620241165,
-0.07199353724718094,
0.02479824796319008,
0.03300633281469345,
-0.08722172677516937,
0.016435515135526657,
-0.005218890495598316,
0.0177287757396698,
-0.032705746591091156,
-0.041244592517614365,
-0.028167851269245148,
-0.0049982634373009205,
-0.014294967986643314,
-0.03233242407441139,
0.057505588978528976,
-0.031800590455532074,
0.007001074496656656,
-0.03160686790943146,
-0.00933039840310812,
0.028346581384539604,
0.08825156092643738,
-0.01550225168466568,
-0.019919339567422867,
0.024908121675252914,
0.007594042457640171,
-0.02492603100836277,
0.009469697251915932,
-0.0016016645822674036,
0.025587361305952072,
-0.08324283361434937,
-0.005358423106372356,
-0.005796114914119244,
-0.014577258378267288,
-0.02111915685236454,
0.004903559107333422,
0.07824363559484482,
0.0037424389738589525,
-0.01755911484360695,
-0.009078992530703545,
0.025830935686826706
] |
<p>I would like to buy a good book on Variational Calculus. Most of the books that I find seem to be rather formal in a mathematical sense, which is not necessarily bad, but makes the studying a bit cumbersome.</p>
<p>Could you provide me with advice on a good variational calculus books which focuses on physics problems and has plenty of examples, preferably in the field of mechanics.</p> | g150 | [
0.08299820870161057,
0.035247042775154114,
0.02704652026295662,
0.0295071043074131,
0.0017771725542843342,
0.0029986489098519087,
0.003462625201791525,
-0.048472411930561066,
-0.0035841187927871943,
0.01884719543159008,
0.011321326717734337,
-0.05388066917657852,
-0.030729932710528374,
0.007048300001770258,
-0.002061726525425911,
-0.008119340054690838,
0.03242391720414162,
0.0179995596408844,
0.016731495037674904,
0.03442749008536339,
0.06202524155378342,
0.04977509379386902,
0.01916516199707985,
0.01781107299029827,
-0.010678235441446304,
-0.022988690063357353,
-0.061701320111751556,
-0.03557940945029259,
-0.05846214294433594,
0.003010103013366461,
-0.019682085141539574,
-0.08085805177688599,
-0.03404868766665459,
-0.028745105490088463,
-0.02299693413078785,
-0.009505515918135643,
0.020266186445951462,
-0.038360629230737686,
0.03856136277318001,
0.030830100178718567,
0.021762454882264137,
-0.008403007872402668,
-0.018361318856477737,
-0.01991814374923706,
-0.01594497635960579,
-0.06268960982561111,
-0.038102809339761734,
-0.022017166018486023,
-0.045010872185230255,
0.020108545199036598,
0.04115169867873192,
-0.05563438683748245,
0.013009726069867611,
-0.022918494418263435,
0.04670180752873421,
0.04357943311333656,
-0.003974395338445902,
0.05208795890212059,
-0.03719336539506912,
-0.017330508679151535,
0.0547613762319088,
0.034093864262104034,
-0.015143357217311859,
-0.061077896505594254,
0.009304155595600605,
-0.038257598876953125,
0.00330807245336473,
0.018686458468437195,
0.04800715297460556,
0.005041934549808502,
0.009423194453120232,
0.02887539565563202,
0.016133025288581848,
-0.0025555044412612915,
-0.01819426566362381,
-0.06807741522789001,
0.0025610572192817926,
-0.0005551750655286014,
0.031345903873443604,
-0.03300785645842552,
-0.05885503068566322,
0.03691760450601578,
0.04207928478717804,
0.0033529121428728104,
0.04632848501205444,
0.0007978125941008329,
-0.014284711331129074,
0.001737634651362896,
-0.058560945093631744,
-0.041853297501802444,
0.006599209737032652,
-0.024684719741344452,
0.07632617652416229,
0.01937977597117424,
-0.018589764833450317,
-0.04648995399475098,
-0.03548632934689522,
0.009286214597523212,
0.034155022352933884,
0.0437917560338974,
0.0014030544552952051,
-0.017162378877401352,
0.03991929069161415,
0.034305259585380554,
-0.04249788820743561,
0.025809915736317635,
-0.007224518805742264,
-0.006113357841968536,
0.04815150052309036,
0.015937088057398796,
-0.010293420404195786,
-0.02988947555422783,
-0.004554390907287598,
-0.054435260593891144,
-0.0368763767182827,
0.03606301546096802,
0.005632306449115276,
0.02173464559018612,
0.042389050126075745,
0.033449433743953705,
0.01752341352403164,
0.05510493367910385,
0.031018121168017387,
0.017751134932041168,
-0.0043426984921097755,
-0.01088462769985199,
-0.03017878532409668,
-0.06327890604734421,
0.060955919325351715,
-0.03459805250167847,
0.02961372584104538,
-0.018198490142822266,
-0.05430639535188675,
-0.027766641229391098,
-0.03303235024213791,
0.052613403648138046,
0.04862479865550995,
-0.019153451547026634,
0.05925312638282776,
-0.056651387363672256,
0.0008179946453310549,
0.048222824931144714,
0.02113087847828865,
-0.006777219008654356,
-0.010225988924503326,
0.04257339984178543,
-0.005459480453282595,
0.03126534819602966,
-0.010926218703389168,
-0.02755831927061081,
-0.02812645211815834,
0.016988467425107956,
0.03872914984822273,
-0.06276388466358185,
0.027737576514482498,
0.03417341783642769,
0.041861481964588165,
0.05513158068060875,
0.025169122964143753,
-0.04644482582807541,
0.020941881462931633,
-0.010687082074582577,
-0.002681923098862171,
0.012770621106028557,
-0.06187036260962486,
0.04369504377245903,
-0.06768448650836945,
-0.009841402061283588,
-0.026583025231957436,
0.025800392031669617,
-0.02253849245607853,
0.045886535197496414,
0.020927084609866142,
0.06505463272333145,
-0.0057668378576636314,
-0.016332248225808144,
0.02204102650284767,
-0.036880012601614,
-0.03180764615535736,
0.011511165648698807,
-0.05743233487010002,
-0.0532241091132164,
-0.0156191885471344,
0.0021410477347671986,
-0.04160916060209274,
0.028011556714773178,
0.007907160557806492,
-0.010245663113892078,
-0.06257935613393784,
-0.07262317836284637,
-0.04421456158161163,
-0.026116272434592247,
-0.011004183441400528,
0.013552726246416569,
0.016952557489275932,
0.04605989530682564,
0.027708541601896286,
0.0176067017018795,
-0.0247413981705904,
0.021461600437760353,
0.033103134483098984,
0.03184134140610695,
0.0738934725522995,
0.03488670289516449,
0.01774461194872856,
0.006948574911803007,
-0.007961549796164036,
-0.03472615033388138,
-0.013757145032286644,
0.008347311057150364,
0.0239988025277853,
0.029588360339403152,
0.00038919743383303285,
-0.024899039417505264,
0.022759277373552322,
-0.018502850085496902,
0.01694723404943943,
0.015950677916407585,
-0.011678681708872318,
-0.002178025897592306,
-0.015073955059051514,
0.03550507873296738,
-0.05493302270770073,
-0.009043671190738678,
0.028035078197717667,
0.02531156688928604,
-0.03459477424621582,
0.026447223499417305,
0.023691024631261826,
-0.04735996574163437,
-0.09724119305610657,
0.03590207174420357,
0.02205752581357956,
-0.05188924819231033,
-0.013750726357102394,
0.004709209315478802,
0.020977523177862167,
-0.00859557930380106,
0.03968145325779915,
0.0077892448753118515,
0.0240047387778759,
-0.007603248115628958,
0.07422268390655518,
-0.04408587887883186,
-0.03286568820476532,
-0.08606657385826111,
0.0043823872692883015,
0.03378399834036827,
-0.007278619799762964,
-0.05303933843970299,
0.04332299157977104,
-0.06774814426898956,
-0.05101244896650314,
-0.046224549412727356,
-0.011033403687179089,
-0.005216016434133053,
0.0007478776969946921,
0.030873358249664307,
0.026509420946240425,
-0.023195568472146988,
0.009342840872704983,
-0.0381556861102581,
0.039787501096725464,
0.06102048233151436,
-0.022797277197241783,
0.054181817919015884,
0.028894556686282158,
0.01907856948673725,
0.015862395986914635,
0.015617202036082745,
0.010125736705958843,
0.04727338254451752,
0.014920773915946484,
-0.02701481059193611,
-0.0009500101441517472,
-0.02002161182463169,
0.02239648438990116,
-0.0025939338374882936,
-0.011108086444437504,
-0.03862914815545082,
0.05200990289449692,
-0.04149261489510536,
0.03300865367054939,
-0.0037800606805831194,
0.012219490483403206,
0.02129139006137848,
-0.04833533987402916,
-0.06369056552648544,
-0.08387459069490433,
0.020910535007715225,
-0.01070468034595251,
0.02095314860343933,
0.031051458790898323,
-0.041485048830509186,
-0.03772252798080444,
0.030908219516277313,
-0.014337519183754921,
0.028743315488100052,
-0.0852474719285965,
0.021050002425909042,
-0.022093484178185463,
0.03407765179872513,
0.008060287684202194,
0.09649472683668137,
0.04218442738056183,
0.029337653890252113,
0.059093400835990906,
-0.05014286935329437,
0.042458098381757736,
-0.011625455692410469,
-0.00041433682781644166,
0.015196319669485092,
0.08007366955280304,
-0.0013666909653693438,
-0.05076385289430618,
0.0318182148039341,
-0.024730177596211433,
0.026242362335324287,
0.001290934276767075,
0.0032212366349995136,
0.0009264303953386843,
-0.0034940396435558796,
0.05080166831612587,
-0.02610114775598049,
0.05007612332701683,
0.03780284523963928,
0.0037988286931067705,
-0.010799722746014595,
-0.023689450696110725,
-0.017576539888978004,
-0.024531709030270576,
-0.04062950983643532,
-0.022055940702557564,
-0.04832930490374565,
-0.0720551386475563,
-0.08453181385993958,
-0.06450013816356659,
-0.016674581915140152,
0.013059637509286404,
-0.005042361561208963,
0.009272568859159946,
-0.04677481949329376,
0.022647835314273834,
-0.05388706922531128,
-0.0817141905426979,
0.011650178581476212,
-0.05949206277728081,
0.0010778374271467328,
0.02150863967835903,
-0.06775467097759247,
0.0296756811439991,
-0.04245659336447716,
0.04080279916524887,
0.013437196612358093,
-0.013031345792114735,
-0.001984626753255725,
0.009731185622513294,
-0.02702886238694191,
-0.04448467120528221,
0.009132415056228638,
-0.028373437002301216,
0.025448132306337357,
-0.049990709871053696,
0.051821019500494,
0.007157058455049992,
0.0550554059445858,
0.003433498088270426,
0.019626224413514137,
-0.007815523073077202,
0.02048180066049099,
0.024804318323731422,
0.056457214057445526,
0.04931522160768509,
0.00988003984093666,
-0.009731268510222435,
-0.0073686218820512295,
0.041017428040504456,
0.03236820921301842,
-0.04919654130935669,
-0.06851678341627121,
-0.028664054349064827,
-0.04265860468149185,
0.0541367381811142,
0.019227465614676476,
0.024061160162091255,
0.027354013174772263,
0.0015604558866471052,
0.043301913887262344,
-0.004858840256929398,
0.048946019262075424,
-0.007706334814429283,
-0.06061995029449463,
-0.05284549295902252,
0.031275901943445206,
0.04970228299498558,
-0.018355892971158028,
0.06942985951900482,
0.05039056017994881,
-0.0076109375804662704,
0.013608764857053757,
-0.026116950437426567,
0.01096564531326294,
0.026241956278681755,
0.035161152482032776,
-0.02784101851284504,
-0.019412416964769363,
0.028651956468820572,
0.018667468801140785,
0.013339177705347538,
-0.06474670767784119,
-0.005785678513348103,
-0.09210873395204544,
-0.024529609829187393,
0.01033813040703535,
-0.01584225334227085,
0.024367930367588997,
-0.009338749572634697,
-0.025604119524359703,
0.07550182193517685,
0.06516066938638687,
-0.03319966793060303,
0.03699149936437607,
-0.02798779308795929,
-0.05138646066188812,
0.003026354592293501,
-0.00961779523640871,
0.0446566566824913,
-0.033658187836408615,
-0.020718704909086227,
0.00048714090371504426,
-0.02897787280380726,
-0.042522359639406204,
0.008328508585691452,
0.010579477995634079,
-0.023941978812217712,
-0.00602682726457715,
-0.005308836232870817,
-0.0028221462853252888,
-0.0418376587331295,
0.050556544214487076,
0.023398151621222496,
0.010889568366110325,
0.01292141992598772,
0.01995653659105301,
-0.039249569177627563,
0.0977388247847557,
-0.03921665996313095,
-0.0013393227709457278,
0.005400598980486393,
0.004164198413491249,
0.0005371527513489127,
0.02571076713502407,
0.017335327342152596,
0.06163303181529045,
-0.08717972040176392,
-0.015372642315924168,
0.00374320219270885,
-0.020433049649000168,
0.07710445672273636,
0.022853191941976547,
0.027235718443989754,
0.03567506745457649,
-0.03818975016474724,
0.032813843339681625,
-0.03941933438181877,
-0.023078998550772667,
-0.04225170239806175,
0.023354368284344673,
-0.03852009028196335,
-0.059868160635232925,
0.03588505834341049,
0.05383509397506714,
0.0067190732806921005,
-0.014781498350203037,
0.005567409563809633,
-0.009882363490760326,
-0.01133873499929905,
0.0034776043612509966,
0.0034559324849396944,
0.02091641165316105,
-0.0417913943529129,
-0.005582364276051521,
-0.004829913377761841,
-0.0032680470030754805,
-0.033582523465156555,
-0.05450188368558884,
0.037945706397295,
-0.003020552219823003,
0.017261408269405365,
-0.05311641842126846,
0.03685672953724861,
-0.0009677259949967265,
0.07022718340158463,
-0.015139604918658733,
-0.05712829530239105,
-0.02816835045814514,
0.020955650135874748,
0.02352023497223854,
0.02015000209212303,
-0.03042563982307911,
-0.04356292262673378,
0.02196759171783924,
-0.04570586234331131,
-0.026242701336741447,
-0.02333480678498745,
0.00003320191535749473,
-0.012365177273750305,
-0.007766401395201683,
-0.0033913739025592804,
0.005310106556862593,
0.002107050269842148,
-0.01809358038008213,
-0.023204175755381584,
0.04415719583630562,
-0.013945951126515865,
0.03688052296638489,
0.034150850027799606,
0.00047361524775624275,
0.0069302767515182495,
-0.03868034482002258,
-0.005322445183992386,
-0.03951190784573555,
0.044396404176950455,
0.007625669240951538,
0.07648646086454391,
-0.05983776971697807,
-0.08109709620475769,
-0.030155621469020844,
-0.07859395444393158,
-0.020708801224827766,
0.026404211297631264,
0.05208790674805641,
0.039322663098573685,
0.04683004692196846,
-0.05581539124250412,
0.019234549254179,
-0.01502127293497324,
0.01638716086745262,
0.002780443523079157,
0.026658475399017334,
-0.030148549005389214,
-0.021135639399290085,
0.044144272804260254,
0.006818818859755993,
0.018632063642144203,
0.050369780510663986,
0.021380901336669922,
0.03207094222307205,
0.08012940734624863,
-0.0041183000430464745,
-0.06113739684224129,
0.014377553015947342,
-0.021358655765652657,
-0.11756136268377304,
0.028488870710134506,
-0.0035247320774942636,
-0.04827943816781044,
0.002065442968159914,
0.0015936592826619744,
0.030324360355734825,
0.02037232182919979,
-0.060013823211193085,
-0.04613535851240158,
-0.008008410222828388,
0.01661936193704605,
-0.00681077828630805,
-0.008157283067703247,
-0.03323880210518837,
0.06103987991809845,
0.07698757946491241,
-0.04086177051067352,
0.08166218549013138,
-0.017317917197942734,
-0.01186356507241726,
0.046419549733400345,
0.021513910964131355,
-0.014903091825544834,
-0.09488610178232193,
-0.0035551891196519136,
-0.014539668336510658,
0.004401154816150665,
0.04915836825966835,
0.0456610843539238,
-0.093568354845047,
0.007772693410515785,
-0.008194642141461372,
0.020310550928115845,
0.0467253141105175,
-0.03709870204329491,
-0.01382426731288433,
-0.019344862550497055,
0.03680352121591568,
0.03192142769694328,
0.00854718778282404,
0.037603773176670074,
-0.04244627058506012,
0.010268053039908409,
-0.003951908554881811,
0.06715439260005951,
0.01330854743719101,
0.018309853971004486,
0.006040751002728939,
0.005794220604002476,
-0.005830780602991581,
-0.021609775722026825,
0.044823091477155685,
0.022392472252249718,
0.025186460465192795,
-0.00612404802814126,
0.04487670585513115,
-0.012170164845883846,
0.019579647108912468,
0.004710045643150806,
0.04023446515202522,
-0.03183310106396675,
-0.0018124317284673452,
0.011220678687095642,
0.004724307917058468,
-0.013418145477771759,
-0.051803700625896454,
0.026156743988394737,
0.01362964790314436,
0.034336671233177185,
-0.02716130018234253,
-0.06836537271738052,
-0.012973600998520851,
-0.025786571204662323,
0.0674462765455246,
0.07459099590778351,
-0.057755887508392334,
0.029529236257076263,
0.03610758110880852,
0.03460916876792908,
0.07368819415569305,
0.0015048370696604252,
0.07611694186925888,
-0.016738969832658768,
0.0250850822776556,
-0.011238104663789272,
-0.018198130652308464,
-0.06113334372639656,
0.013761374168097973,
0.05597580969333649,
-0.01104684080928564,
-0.029656892642378807,
-0.06621989607810974,
-0.04908626899123192,
-0.04739152267575264,
-0.0746753066778183,
0.03477063402533531,
0.079619862139225,
0.020195210352540016,
0.015883225947618484,
0.012792159803211689,
0.003936735447496176,
0.02400985173881054,
0.07931031286716461,
-0.009317847900092602,
0.03690135106444359,
-0.012657197192311287,
-0.013676730915904045,
-0.02607601322233677,
-0.007348482497036457,
0.03437618166208267,
0.026614664122462273,
0.07798721641302109,
-0.04147392138838768,
0.02416190877556801,
0.021766670048236847,
-0.027068620547652245,
-0.02062445506453514,
0.03397463634610176,
-0.036509983241558075,
0.048456769436597824,
0.004942484200000763,
-0.02685021422803402,
-0.028271442279219627,
-0.022454883903265,
0.019164707511663437,
-0.07013741135597229,
0.025715524330735207,
0.03326285630464554,
-0.030910992994904518,
-0.006277158390730619,
-0.02925107814371586,
-0.007289978675544262,
-0.039217736572027206,
-0.02892947383224964,
0.019050773233175278,
-0.023632453754544258,
0.002068628091365099,
-0.026841184124350548,
0.0031851883977651596,
-0.050350215286016464,
0.006725803483277559,
-0.0674378052353859,
0.10214577615261078,
0.01799524948000908,
0.025457287207245827,
-0.019146034494042397,
-0.023624982684850693,
0.058988168835639954,
0.0018840174889191985,
-0.0015545006608590484,
0.004237700719386339,
-0.04049528017640114,
-0.024989739060401917,
-0.02642063796520233,
0.004923560190945864,
-0.007540744263678789,
-0.018181143328547478,
0.006832060869783163,
0.007445447146892548,
0.012366564013063908,
0.0030983234755694866,
-0.012483087368309498,
-0.0012904468458145857,
0.037163347005844116,
-0.057330258190631866,
-0.0072149611078202724,
0.00785729382187128,
-0.03083781898021698,
0.025245506316423416,
-0.06660716235637665,
0.0025496194139122963,
-0.05068730190396309,
-0.032536014914512634,
-0.02585439197719097,
-0.03191458433866501,
0.03216877952218056,
0.01860303431749344,
0.05649017542600632,
-0.026148894801735878,
0.03990781679749489,
-0.0064046005718410015,
-0.02924921363592148,
0.0035005188547074795,
-0.0031150714494287968,
-0.0039542317390441895,
-0.01136187557131052,
0.04679137095808983,
-0.06438402086496353,
-0.023404503241181374,
0.006477829534560442,
-0.014718839898705482,
-0.02477947063744068,
-0.03494137525558472,
0.02478659525513649,
-0.005385721102356911,
0.004173753783106804,
-0.052346307784318924,
0.06664347648620605,
0.003229073714464903,
-0.018153194338083267,
-0.009450392797589302,
-0.035139039158821106,
-0.002954536583274603,
0.05028205364942551,
0.027008943259716034,
0.014677133411169052,
0.005897092632949352,
-0.00953592173755169,
0.03643418475985527,
-0.03920774534344673,
-0.046767622232437134,
0.018658457323908806,
0.019171319901943207,
-0.00479171285405755
] |
<p>The equation of motion for the harmonic oscillator (mass on spring model)</p>
<p>$$\frac{d^2x}{dt^2} + \omega_0^2 x = 0$$</p>
<p>with $\omega_0^2 = D/m$, $D$ and $m$ being the force constant of the spring and the mass, has the solution</p>
<p>$$x=ce^{\lambda t}$$</p>
<p>where $c$ and $\lambda$ are a constant and a parameter.
Inserting $x$ leads to</p>
<p>$$\lambda_1 = +i\omega_0$$</p>
<p>and</p>
<p>$$\lambda_2 = -i\omega_0$$</p>
<p>and so the solutions are</p>
<p>$$x_1(t) = c_1 e^{i \omega_0 t}$$</p>
<p>and</p>
<p>$$x_2(t) = c_2 e^{-i \omega_0 t}.$$</p>
<p>In my book, I now read "...these solutions are linearly independent for $\omega_0 \neq 0$."</p>
<p>What does this mean (i.e. how can I see this) and why is it important?</p> | g4593 | [
0.03232378140091896,
0.012877320870757103,
-0.0035788954701274633,
0.00609372416511178,
0.07897055149078369,
0.008449876680970192,
0.04383041337132454,
0.0568995401263237,
-0.038594719022512436,
-0.004143875557929277,
-0.09896977990865707,
-0.009517131373286247,
0.04410117492079735,
0.023584071546792984,
0.012577447108924389,
-0.02190406061708927,
0.08691740781068802,
0.0003843580198008567,
0.003048242535442114,
-0.009896361269056797,
0.006545410957187414,
0.017622927203774452,
0.004041764419525862,
-0.020070279017090797,
0.09374967962503433,
0.028066083788871765,
0.01271999254822731,
0.010377715341746807,
-0.015399282798171043,
-0.013682110235095024,
0.01589505933225155,
-0.006398660130798817,
0.06765977293252945,
-0.016334107145667076,
-0.08822386711835861,
-0.027727091684937477,
0.07838591188192368,
-0.02598952129483223,
0.03367302194237709,
-0.03123764507472515,
-0.001919205766171217,
-0.016633691266179085,
-0.017829792574048042,
0.04233003780245781,
0.0012890984071418643,
-0.0035450535360723734,
-0.03567442670464516,
0.012297861278057098,
-0.04140545800328255,
0.026795074343681335,
0.026294734328985214,
0.0003480637969914824,
0.07001292705535889,
-0.04488958418369293,
-0.022405631840229034,
0.026920434087514877,
0.01694517582654953,
-0.007823068648576736,
0.0320877768099308,
0.03956804424524307,
-0.022035473957657814,
0.010020511224865913,
0.0015440760180354118,
-0.008251164108514786,
-0.0038152129855006933,
0.003427621442824602,
0.02476612478494644,
-0.03188552334904671,
0.01028456911444664,
-0.031590018421411514,
-0.010310279205441475,
-0.004499322269111872,
-0.010005056858062744,
-0.06506769359111786,
-0.03240188583731651,
0.020116150379180908,
0.06607481837272644,
0.025925813242793083,
-0.02400866523385048,
-0.056273773312568665,
0.051467470824718475,
0.017468135803937912,
-0.00846770592033863,
-0.006836494896560907,
0.045593805611133575,
-0.0035594420041888952,
-0.006317335646599531,
0.04159553349018097,
-0.013589692302048206,
0.06133558228611946,
-0.000021809035388287157,
-0.06388973444700241,
-0.02087434008717537,
0.031582310795784,
-0.008499333634972572,
-0.06013856828212738,
-0.01715829409658909,
0.06461180001497269,
0.018759451806545258,
-0.02407987229526043,
-0.026530783623456955,
0.019728796556591988,
-0.035794686526060104,
0.036725450307130814,
-0.004132412374019623,
0.011126184836030006,
0.019681189209222794,
0.05087368190288544,
-0.010522762313485146,
-0.03929220885038376,
-0.02997455559670925,
0.05653032660484314,
-0.01354573480784893,
-0.02328929491341114,
-0.05444519221782684,
-0.08926133066415787,
0.057936664670705795,
-0.0014318000758066773,
0.0011856198543682694,
0.011230122298002243,
-0.022190896794199944,
-0.026019323617219925,
0.0720822811126709,
0.07538539916276932,
-0.034204259514808655,
-0.05489986389875412,
0.07056818902492523,
0.01512499526143074,
0.03472684696316719,
-0.03883793205022812,
-0.023713624104857445,
0.02327008917927742,
0.024551087990403175,
0.031011322513222694,
0.021512534469366074,
0.07477568089962006,
-0.001985712442547083,
-0.013682668097317219,
0.00019112168229185045,
0.018914926797151566,
0.0068872240372002125,
0.016192171722650528,
0.02483324334025383,
-0.025187205523252487,
-0.015864737331867218,
0.027269557118415833,
0.014938551001250744,
-0.061942920088768005,
0.00406474806368351,
0.03554781153798103,
-0.023629512637853622,
0.048663895577192307,
-0.01948523335158825,
-0.006421854719519615,
0.010248461738228798,
-0.02586214616894722,
0.02517927624285221,
-0.007223640568554401,
0.007402657065540552,
-0.0016045415541157126,
0.034263383597135544,
0.003028556937351823,
0.021160345524549484,
-0.017462771385908127,
-0.06215633824467659,
0.02013992890715599,
-0.02426605299115181,
-0.061743300408124924,
0.01900363340973854,
0.03154650330543518,
-0.02300937846302986,
0.021486511453986168,
0.012099218554794788,
0.05115344375371933,
0.041893281042575836,
-0.02069501020014286,
0.004100182559341192,
-0.0957891047000885,
0.06054697558283806,
-0.009898175485432148,
0.07351236045360565,
-0.013674309477210045,
0.003929853904992342,
-0.04946669936180115,
-0.064433753490448,
0.02728937938809395,
0.034986112266778946,
0.05358356609940529,
-0.016406169161200523,
0.020708587020635605,
-0.01644771359860897,
0.027881138026714325,
0.016623007133603096,
0.07830570638179779,
-0.001578108174726367,
0.05681278556585312,
-0.046127550303936005,
-0.03931901231408119,
-0.049784742295742035,
0.004851260222494602,
0.0015272467862814665,
0.049100931733846664,
0.0717848688364029,
-0.01793844811618328,
-0.01637272536754608,
0.007810390554368496,
0.014914428815245628,
0.01160060428082943,
0.032331351190805435,
0.018390420824289322,
-0.020417071878910065,
-0.042667798697948456,
0.004544612020254135,
0.00820195209234953,
-0.011343885213136673,
-0.06710647791624069,
0.012459853664040565,
-0.03734226152300835,
-0.032183267176151276,
0.030031388625502586,
-0.05806737765669823,
0.0009083106415346265,
0.020779943093657494,
-0.012253391556441784,
-0.08083067834377289,
-0.0007087182602845132,
-0.04900893568992615,
-0.04098855331540108,
0.015441060066223145,
0.02359103038907051,
-0.00559669453650713,
-0.05540813133120537,
0.02684938535094261,
0.04313206672668457,
0.02094174176454544,
0.0030376112554222345,
-0.019685057923197746,
-0.023325402289628983,
-0.03184332698583603,
0.009863894432783127,
0.05354655161499977,
-0.05440441146492958,
-0.012258440256118774,
-0.08258555829524994,
-0.016428399831056595,
0.021067701280117035,
0.05611700192093849,
0.020419679582118988,
-0.019997211173176765,
0.007419225759804249,
-0.012205618433654308,
0.022667938843369484,
-0.005944150499999523,
0.032524775713682175,
0.01485261507332325,
-0.030367812141776085,
-0.02082071080803871,
0.0054040453396737576,
-0.026306195184588432,
0.007541193161159754,
-0.025090645998716354,
-0.02796243317425251,
-0.013606182299554348,
0.02265937626361847,
-0.09081859141588211,
-0.017746059224009514,
-0.05482020229101181,
-0.004455985967069864,
0.056922443211078644,
-0.03713839501142502,
0.01935260184109211,
0.029050804674625397,
-0.033674225211143494,
0.06179039180278778,
-0.03046990931034088,
-0.0441155768930912,
0.007143703289330006,
-0.0029315620195120573,
0.03527690842747688,
-0.014781580306589603,
0.026139266788959503,
-0.009344230405986309,
-0.05602896958589554,
0.006789986044168472,
0.007968395948410034,
-0.044298939406871796,
-0.06213809922337532,
0.018694039434194565,
0.008928893133997917,
-0.02810060605406761,
-0.01728232204914093,
0.04667007178068161,
0.017710693180561066,
-0.0264881681650877,
-0.004113547969609499,
0.08665139228105545,
-0.005855313036590815,
-0.057844378054142,
-0.010679584927856922,
0.08406726270914078,
0.02282925508916378,
-0.00031872911495156586,
-0.007669662591069937,
-0.013616261072456837,
-0.030132781714200974,
-0.0107130017131567,
0.01612706109881401,
-0.015493148006498814,
-0.02473548799753189,
0.0045667351223528385,
0.023154592141509056,
0.03610280528664589,
0.046944208443164825,
-0.03811591863632202,
-0.05528303235769272,
0.02337406761944294,
-0.05532316863536835,
-0.08936154842376709,
-0.012591715902090073,
-0.05661769211292267,
-0.008856411091983318,
-0.08240976929664612,
0.022277792915701866,
-0.03009297139942646,
-0.0033653706777840853,
-0.01976783759891987,
0.016464300453662872,
-0.0038380795158445835,
-0.0695599839091301,
-0.06929337233304977,
0.030236896127462387,
0.012195286341011524,
0.054841551929712296,
0.032671499997377396,
-0.03250163048505783,
-0.056565072387456894,
-0.044783201068639755,
0.06018032133579254,
0.04818086698651314,
0.03341984003782272,
0.01922505348920822,
0.009944816119968891,
-0.04819623380899429,
0.04747062176465988,
-0.048491548746824265,
-0.026977600529789925,
-0.015619602054357529,
0.0020550594199448824,
0.05821855366230011,
-0.049123309552669525,
0.015426130034029484,
-0.010362828150391579,
-0.01931055448949337,
-0.018196800723671913,
-0.01903129369020462,
-0.0026891303714364767,
0.028789592906832695,
0.04498296231031418,
-0.06499028950929642,
0.02633107826113701,
0.049563005566596985,
-0.08052214980125427,
0.019422397017478943,
0.059110868722200394,
0.05192594230175018,
-0.015363392420113087,
-0.014907204546034336,
0.045102063566446304,
-0.03790595754981041,
-0.02132127247750759,
-0.046666860580444336,
-0.030265018343925476,
0.03435816615819931,
0.018900113180279732,
0.06445606797933578,
-0.05792475491762161,
0.00630906131118536,
0.054414600133895874,
0.002810274250805378,
0.012247507460415363,
0.05561579018831253,
-0.057950399816036224,
-0.06735836714506149,
-0.013476726599037647,
0.023383621126413345,
-0.007955915294587612,
0.03784359246492386,
-0.02186891995370388,
0.016660556197166443,
-0.055827945470809937,
0.06843273341655731,
-0.021917620673775673,
-0.027884867042303085,
0.044172145426273346,
0.017132990062236786,
0.004736191593110561,
0.04852788895368576,
-0.019592110067605972,
-0.04064066335558891,
-0.007010527886450291,
-0.045037973672151566,
-0.04834064096212387,
-0.012198958545923233,
0.008278685621917248,
-0.0061120688915252686,
0.1075003370642662,
0.013747580349445343,
-0.04219374805688858,
0.05743526667356491,
-0.017491893842816353,
0.014249751344323158,
-0.033889494836330414,
-0.02956085279583931,
-0.021441835910081863,
0.009091487154364586,
-0.004594659898430109,
0.028481926769018173,
0.008450246416032314,
-0.015098737552762032,
-0.029018564149737358,
0.03054139018058777,
-0.010105724446475506,
-0.025329886004328728,
-0.012277222238481045,
0.015566137619316578,
0.07653386890888214,
0.08980950713157654,
0.013042195700109005,
-0.03804296255111694,
-0.07126928865909576,
-0.03486088663339615,
-0.003124843118712306,
-0.011848324909806252,
0.00858069397509098,
-0.04796434938907623,
0.0911998376250267,
0.020707357674837112,
0.07768958806991577,
-0.04896068945527077,
0.009997604414820671,
0.01467177551239729,
0.038086917251348495,
0.018888819962739944,
0.018024777993559837,
-0.015583411790430546,
0.018221784383058548,
0.024901505559682846,
-0.055495575070381165,
-0.027231689542531967,
0.013624289073050022,
0.007497138809412718,
0.014122363179922104,
0.028055818751454353,
-0.02686368301510811,
0.02430717833340168,
0.011372401379048824,
-0.02233097516000271,
0.0005455134087242186,
0.0018133082194253802,
0.006244794465601444,
-0.021352116018533707,
-0.07683323323726654,
0.05345914140343666,
0.053220491856336594,
0.03875475376844406,
-0.032818738371133804,
-0.03875431418418884,
-0.014721894636750221,
-0.013494255021214485,
0.005542431492358446,
0.028735822066664696,
0.005259676370769739,
0.018439078703522682,
0.0062262555584311485,
0.017788318917155266,
-0.029694220051169395,
-0.0002836227649822831,
-0.04364866390824318,
0.027202609926462173,
-0.032747019082307816,
-0.01033515203744173,
-0.029830191284418106,
0.0026663916651159525,
0.019055193290114403,
-0.02756648324429989,
0.010417754761874676,
-0.01777270808815956,
0.0000782423812779598,
0.021202458068728447,
0.02956499718129635,
0.0481768436729908,
0.0773053988814354,
-0.007744561415165663,
0.015372421592473984,
-0.0019984638784080744,
0.035415735095739365,
0.022062579169869423,
-0.03545640408992767,
0.009503128007054329,
0.006317661609500647,
-0.04002094268798828,
-0.002135042566806078,
0.004689963534474373,
0.04158936068415642,
-0.018663417547941208,
0.059102267026901245,
0.08446355909109116,
0.023846112191677094,
0.005924718454480171,
-0.01277083344757557,
0.02556757815182209,
0.022681090980768204,
-0.032064780592918396,
0.04163544625043869,
-0.009775104001164436,
-0.036181118339300156,
0.008563509210944176,
-0.0024723829701542854,
-0.03166241943836212,
-0.03395521640777588,
0.034790754318237305,
-0.06083536893129349,
0.0339169055223465,
-0.04111906886100769,
0.04600956290960312,
-0.013135474175214767,
-0.029997125267982483,
-0.03675825893878937,
0.0031697156373411417,
0.03463473543524742,
0.003758376697078347,
0.011551138944923878,
0.0350240059196949,
-0.0028168780263513327,
0.06552475690841675,
-0.005227458197623491,
-0.025821708142757416,
-0.009386375546455383,
-0.06047553941607475,
-0.022511932998895645,
-0.055792249739170074,
-0.0671355202794075,
0.03259940817952156,
0.041764672845602036,
-0.042756225913763046,
0.022707881405949593,
0.0514795258641243,
0.01527256891131401,
0.007361294236034155,
-0.040397461503744125,
-0.02402261085808277,
0.027629327028989792,
-0.00041535988566465676,
0.008326295763254166,
-0.01133381575345993,
0.015856465324759483,
0.023619651794433594,
0.007010486908257008,
-0.06792372465133667,
-0.00005014172347728163,
0.07650117576122284,
0.03854307532310486,
-0.005651057232171297,
-0.025155017152428627,
0.034301839768886566,
-0.008578152395784855,
0.044614579528570175,
0.007568689528852701,
0.024951515719294548,
-0.016589965671300888,
-0.00391638558357954,
0.06146771460771561,
-0.027828123420476913,
0.022825144231319427,
-0.032809481024742126,
0.0742030069231987,
-0.07466673105955124,
-0.023606019094586372,
-0.02184981480240822,
0.018352437764406204,
-0.04197797551751137,
-0.010414601303637028,
0.060630980879068375,
-0.04907919093966484,
-0.021077081561088562,
0.01816033199429512,
-0.05420736223459244,
-0.047301750630140305,
0.0668206736445427,
-0.011288793757557869,
-0.023476937785744667,
0.0039940630085766315,
-0.026065627112984657,
-0.02360888384282589,
0.02950790524482727,
0.003674930427223444,
-0.01902492344379425,
-0.0043490007519721985,
0.015804212540388107,
0.0007344026234932244,
0.040436580777168274,
0.004075761418789625,
0.04076757654547691,
0.01630529761314392,
0.0005948447505943477,
-0.010399707593023777,
-0.01611015386879444,
-0.02237151563167572,
-0.026913756504654884,
0.010839900933206081,
-0.04548099637031555,
0.027174176648259163,
0.0017648821230977774,
-0.04406096413731575,
0.01982087269425392,
-0.0067467521876096725,
-0.040289681404829025,
0.02914791740477085,
-0.044897597283124924,
0.025460131466388702,
0.04048852622509003,
-0.002664555562660098,
0.04163873568177223,
-0.05396374687552452,
0.020215963944792747,
0.02228277549147606,
-0.03224506974220276,
-0.002817670116201043,
0.007757269311696291,
-0.0020314077846705914,
-0.0016927350079640746,
0.03387176990509033,
-0.04273112490773201,
-0.007744743954390287,
-0.011624370701611042,
0.001687288167886436,
-0.013450386002659798,
-0.0034451675601303577,
0.007248260546475649,
0.03521718084812164,
-0.016272490844130516,
0.10283106565475464,
0.03105953522026539,
-0.026328859850764275,
-0.09293483197689056,
0.07850506901741028,
0.07772523164749146,
-0.011602530255913734,
-0.09650956839323044,
-0.006609001196920872,
-0.01843666099011898,
-0.006812650710344315,
-0.0004355515993665904,
-0.012652198784053326,
0.03240639343857765,
-0.035722848027944565,
-0.025893716141581535,
0.00854052696377039,
0.020881379023194313,
-0.04546765610575676,
-0.053022485226392746,
-0.04225829988718033,
0.009820859879255295,
0.010737700387835503,
0.009295253083109856,
0.051597077399492264,
0.042454566806554794,
0.0060860575176775455,
0.02769356593489647,
-0.01616141013801098,
-0.012556914240121841,
0.010859394446015358,
-0.03505935147404671,
-0.026878349483013153,
0.008497404865920544,
-0.018475836142897606,
-0.016736412420868874,
0.022858478128910065,
0.018091414123773575,
-0.019619522616267204,
0.015387768857181072,
0.015824871137738228,
-0.03974640741944313,
-0.0037935569416731596,
-0.02772984839975834,
0.03758302330970764,
0.010718435980379581,
-0.017179669812321663,
-0.01722610928118229,
0.030966775491833687,
-0.005438631400465965,
0.060486190021038055,
0.043165747076272964,
-0.023794302716851234,
-0.046875569969415665,
-0.03715825453400612,
-0.06519325077533722,
0.05418076366186142,
0.03024096041917801,
0.014200231060385704,
0.009490704163908958,
-0.02774566039443016,
-0.0025417739525437355,
0.045371755957603455,
0.02489740587770939,
0.007707678247243166,
-0.01951567642390728,
-0.04658256471157074,
0.02504248358309269,
0.015383725054562092,
-0.005477129481732845,
-0.03866606578230858,
0.009496882557868958,
0.019137471914291382,
0.00502568855881691,
0.004634763579815626,
-0.03186989948153496,
0.08632190525531769,
0.030442869290709496,
-0.03413095325231552,
-0.03848809748888016,
-0.011507331393659115,
0.026123272255063057,
-0.0797528475522995,
-0.02640477567911148,
-0.019652564078569412,
-0.018478846177458763,
0.052293505519628525,
-0.010062147863209248,
-0.023292014375329018,
-0.07790467143058777,
-0.038228992372751236,
-0.007021280936896801,
0.029362007975578308,
-0.03426472097635269,
-0.009541363455355167,
0.03239072859287262,
-0.03010072372853756,
-0.02690812572836876,
0.03063734993338585,
0.0310991071164608,
-0.12275226414203644,
-0.0003149599360767752,
0.02551925554871559,
-0.013929886743426323,
-0.04650405794382095,
-0.050115957856178284,
0.04583254083991051,
0.07275364547967911,
-0.05039719119668007,
0.03225613385438919,
0.017858387902379036,
-0.008386976085603237,
-0.00022555959003511816,
0.012931572273373604,
-0.0625929906964302,
0.000525541661772877,
-0.021427731961011887,
0.05404333025217056,
0.028071776032447815,
-0.0021138268057256937,
-0.01461374294012785,
-0.008329077623784542,
0.01169461291283369,
0.0027053586672991514,
-0.04603840783238411,
0.019287701696157455,
0.04604809358716011
] |
<p>We know that in an isolated system, the density matrix is the microcanonical distribution matrix. That this the possibility for all the states with energy in a certain interval is a constant?
But how can I deduce this from the postulate of equal probability? </p> | g4594 | [
0.0015952660469338298,
0.03201396390795708,
-0.012510146014392376,
0.0037632642779499292,
-0.0124638881534338,
-0.012399168685078621,
-0.020992854610085487,
0.05237601697444916,
-0.024066422134637833,
-0.01709500513970852,
-0.039914630353450775,
-0.005849211476743221,
0.03576182946562767,
0.011726724915206432,
-0.013016742654144764,
0.0464753657579422,
0.005571963731199503,
0.0056313141249120235,
-0.00529717979952693,
0.004981890320777893,
-0.07794871926307678,
-0.044404130429029465,
-0.008416197262704372,
0.002796334680169821,
0.07641158998012543,
-0.01968243531882763,
0.02649390883743763,
-0.02412390522658825,
-0.02163347229361534,
-0.05070403590798378,
0.02686440385878086,
-0.027276745066046715,
0.043720558285713196,
-0.05376308038830757,
-0.002630238188430667,
0.033614955842494965,
0.06623196601867676,
-0.02369610406458378,
0.010988805443048477,
-0.015080164186656475,
-0.03307151049375534,
0.014565791934728622,
-0.027660155668854713,
-0.007398329209536314,
-0.012972651980817318,
0.010761844925582409,
0.02247609943151474,
0.03803924843668938,
-0.03932341933250427,
-0.020892314612865448,
0.050455980002880096,
0.06401900947093964,
0.03643564134836197,
0.017232395708560944,
-0.038956958800554276,
0.036256093531847,
0.03508380427956581,
-0.0008656634017825127,
0.04525690898299217,
0.04277109354734421,
0.03366352245211601,
-0.05768278241157532,
-0.00413171760737896,
-0.009389390237629414,
0.06771817803382874,
-0.0017277454026043415,
-0.04733291640877724,
0.011482888832688332,
-0.0533309206366539,
-0.005627586506307125,
0.04629208892583847,
-0.0816887766122818,
0.00033095813705585897,
-0.037326402962207794,
-0.01896335743367672,
-0.012438111938536167,
0.04570244625210762,
0.026047684252262115,
0.040154263377189636,
0.02279980480670929,
-0.030121807008981705,
0.01860899291932583,
0.0460539348423481,
-0.0407210998237133,
0.015070178546011448,
-0.022728003561496735,
0.06509421020746231,
-0.019992783665657043,
0.005093580577522516,
0.027332250028848648,
0.012817628681659698,
-0.015852123498916626,
0.07124971598386765,
0.03239022195339203,
-0.01034557819366455,
-0.020582985132932663,
-0.05422757938504219,
0.04483179375529289,
-0.046247389167547226,
-0.025327691808342934,
0.015076869167387486,
0.013088319450616837,
0.02961784601211548,
-0.05825035274028778,
0.009849322959780693,
-0.009009161964058876,
-0.04590809345245361,
-0.035606905817985535,
0.00451096473261714,
-0.009235905483365059,
-0.028528625145554543,
0.02310303784906864,
-0.06776237487792969,
-0.00591344153508544,
-0.01923234947025776,
-0.06532789021730423,
0.09083238244056702,
-0.044008802622556686,
0.008288281969726086,
0.03492572158575058,
-0.047474414110183716,
0.04080977290868759,
0.015983950346708298,
0.07800980657339096,
-0.04519912227988243,
0.01058551948517561,
0.00114461372140795,
0.015605446882545948,
-0.07640901207923889,
-0.0516524463891983,
0.06380687654018402,
-0.005954107269644737,
-0.0014484883286058903,
-0.011053930036723614,
0.0365263894200325,
-0.021139737218618393,
-0.02203049510717392,
-0.0017810678109526634,
-0.005112380255013704,
0.01857987605035305,
-0.02007538639008999,
0.05426580458879471,
-0.0078488914296031,
-0.010494349524378777,
-0.012981590814888477,
-0.0323668047785759,
-0.010217143222689629,
-0.027033470571041107,
0.05302700027823448,
0.03393860161304474,
0.012843300588428974,
0.026088768616318703,
-0.0315476693212986,
-0.03625350445508957,
0.025449402630329132,
0.06388697028160095,
-0.0017470051534473896,
-0.00036935522803105414,
-0.037470296025276184,
-0.04246889799833298,
0.022273540496826172,
-0.028707675635814667,
0.022476404905319214,
-0.009675796143710613,
-0.036002740263938904,
-0.0188478734344244,
0.048480257391929626,
-0.02811286970973015,
0.017898086458444595,
-0.02269895188510418,
-0.007092377636581659,
0.0026208169292658567,
-0.0547771155834198,
0.02506103739142418,
0.009373991750180721,
0.02324717491865158,
-0.02827637270092964,
-0.08244779706001282,
0.045831967145204544,
0.015400161035358906,
0.04298749193549156,
0.03116406314074993,
0.041779711842536926,
-0.04518923535943031,
-0.010947882197797298,
-0.030776018276810646,
0.024125218391418457,
0.060118451714515686,
-0.02110469713807106,
0.006556978914886713,
0.01158622745424509,
0.05449141934514046,
-0.019739137962460518,
-0.021394478157162666,
0.06573597341775894,
-0.02448292449116707,
0.005838803946971893,
0.01811533421278,
0.016866037622094154,
-0.03550341725349426,
0.020353298634290695,
0.049982886761426926,
0.046502117067575455,
0.03344692662358284,
0.04141132906079292,
0.04568004980683327,
0.020360112190246582,
-0.001444233930669725,
0.01234582718461752,
-0.018707383424043655,
-0.002873091958463192,
-0.048384614288806915,
-0.021930526942014694,
0.06713764369487762,
-0.029672937467694283,
-0.0017246671486645937,
0.0352511890232563,
-0.024156957864761353,
0.0015843972796574235,
-0.03636713698506355,
-0.09256171435117722,
0.01905297115445137,
0.011514286510646343,
0.012655760161578655,
0.004763026721775532,
0.050842128694057465,
-0.07469524443149567,
0.0034956252202391624,
-0.006288039963692427,
0.04282580316066742,
-0.02235664799809456,
-0.04570215567946434,
-0.01840633898973465,
0.006722339894622564,
0.01799028366804123,
0.0736774206161499,
0.011012832634150982,
-0.03030451387166977,
0.015698565170168877,
0.040408939123153687,
0.010048400610685349,
-0.06985420733690262,
-0.0005660320748575032,
0.0448201522231102,
-0.016659826040267944,
-0.021336903795599937,
0.008757226169109344,
-0.00444690091535449,
0.04926447197794914,
0.030464282259345055,
-0.023127345368266106,
0.050989896059036255,
-0.015379974618554115,
0.024432722479104996,
-0.012700424529612064,
-0.041193339973688126,
0.0058254944160580635,
-0.012985436245799065,
0.02273816242814064,
-0.08374108374118805,
0.008757990784943104,
-0.01763465441763401,
0.0017740324838086963,
-0.04237791523337364,
-0.0313381589949131,
-0.00779033824801445,
-0.03625193610787392,
-0.005153471603989601,
-0.03230758383870125,
0.009553050622344017,
0.019248951226472855,
0.07237432152032852,
0.020887533202767372,
0.08982758224010468,
0.011273753829300404,
0.06546028703451157,
0.006773531902581453,
-0.06419701874256134,
-0.015286549925804138,
0.0009920409647747874,
-0.07045882940292358,
0.009421337395906448,
-0.004597227554768324,
0.005886733997613192,
0.03933418542146683,
-0.05905115604400635,
0.02721736766397953,
0.008224917575716972,
0.01489632111042738,
-0.014943757094442844,
0.014819728210568428,
0.05352828651666641,
-0.006743591278791428,
0.049217622727155685,
-0.05096299946308136,
0.01826484128832817,
0.029987599700689316,
-0.015881281346082687,
-0.012077086605131626,
0.07055230438709259,
-0.01849021203815937,
-0.008037572726607323,
0.02662629261612892,
-0.047183889895677567,
0.023936154320836067,
0.013873592019081116,
-0.028378427028656006,
0.027904652059078217,
-0.0030472762882709503,
-0.03151717782020569,
-0.04775078222155571,
-0.028215039521455765,
0.004579298198223114,
-0.012241318821907043,
-0.04019884765148163,
0.08350633084774017,
0.014934197999536991,
-0.017279120162129402,
0.06034059077501297,
-0.09688835591077805,
-0.005752728786319494,
0.004015106242150068,
-0.00981306005269289,
0.026174873113632202,
-0.008252258412539959,
-0.018819373100996017,
-0.08521607518196106,
-0.0013329369248822331,
-0.06221868470311165,
0.0271376371383667,
0.012482322752475739,
-0.02343723177909851,
0.010157130658626556,
0.021754952147603035,
-0.05766528844833374,
-0.05152969807386398,
-0.06327936053276062,
-0.012216480448842049,
0.027424979954957962,
0.03988885134458542,
-0.02380291000008583,
0.021917611360549927,
-0.055795520544052124,
0.006494459230452776,
-0.03198837488889694,
0.011878341436386108,
-0.04453074932098389,
0.015058535151183605,
0.057657744735479355,
0.008210934698581696,
-0.008737093769013882,
-0.047751907259225845,
0.06445887684822083,
0.005370814353227615,
0.003155616344884038,
0.026497971266508102,
-0.017729392275214195,
-0.007366251200437546,
0.030624164268374443,
0.009794938378036022,
0.006817829795181751,
-0.08826345950365067,
0.08074969053268433,
-0.019537223502993584,
0.02356072887778282,
-0.020067384466528893,
-0.07802728563547134,
0.03533709794282913,
0.06249881163239479,
0.025205079466104507,
-0.010633849538862705,
-0.008580013178288937,
0.0367145799100399,
0.0022922642529010773,
0.03413846343755722,
-0.043772079050540924,
0.04220743477344513,
-0.0059170047752559185,
-0.036433134227991104,
0.03778695687651634,
0.0741288959980011,
0.003616473637521267,
0.01397235319018364,
-0.001147194649092853,
0.03662342578172684,
0.013337398879230022,
-0.039526842534542084,
0.032735053449869156,
-0.004142535850405693,
-0.028242366388440132,
0.012961956672370434,
-0.07390724867582321,
-0.04254438728094101,
0.04704802855849266,
-0.02907579392194748,
0.03213409706950188,
0.016280172392725945,
-0.0239485502243042,
-0.017463358119130135,
0.07563619315624237,
0.0034805284813046455,
-0.04459555074572563,
-0.005974714644253254,
-0.0235445573925972,
0.027643445879220963,
0.02664017304778099,
0.0402882844209671,
0.015425934456288815,
0.02757457084953785,
-0.02778530865907669,
0.00760653056204319,
-0.004745262209326029,
0.08690746128559113,
-0.05392276123166084,
-0.03387078642845154,
-0.004743907600641251,
0.09508271515369415,
-0.03467566892504692,
0.02974206767976284,
0.02628374472260475,
-0.027954453602433205,
0.040861841291189194,
-0.071906678378582,
-0.003885336220264435,
0.02684820629656315,
0.037142496556043625,
0.05383399873971939,
0.03155556321144104,
-0.054909322410821915,
-0.03403515741229057,
0.027658311650156975,
-0.00850099977105856,
0.009902939200401306,
-0.005067037884145975,
-0.04805637151002884,
-0.04901810735464096,
-0.09798946231603622,
0.009606404229998589,
-0.006921859923750162,
-0.0006165536469779909,
0.00041326432256028056,
0.0106046162545681,
0.025999119505286217,
0.04677758365869522,
0.06333057582378387,
0.027625637128949165,
0.02702266164124012,
-0.027483360841870308,
-0.013339648023247719,
-0.04511803388595581,
0.03925447538495064,
-0.025464892387390137,
-0.005970473401248455,
-0.03858685865998268,
0.0141163170337677,
-0.034641627222299576,
-0.04115024209022522,
0.019748788326978683,
0.04286561533808708,
0.056000590324401855,
0.0017579803243279457,
0.029044371098279953,
-0.002590864198282361,
-0.002995346672832966,
0.04954838007688522,
0.014291581697762012,
-0.06265228986740112,
0.0655411034822464,
-0.041529178619384766,
0.03827532008290291,
0.026564957574009895,
0.033384449779987335,
0.03762517496943474,
-0.03390610218048096,
-0.01984732411801815,
-0.018290335312485695,
-0.034847553819417953,
-0.008383268490433693,
0.055432748049497604,
0.029988383874297142,
-0.01566634699702263,
0.034879762679338455,
-0.03208943456411362,
0.022567791864275932,
0.059629857540130615,
0.022559599950909615,
-0.02936544083058834,
-0.01895892061293125,
-0.03476177901029587,
-0.05287745222449303,
0.023760158568620682,
0.03219159319996834,
-0.009937919676303864,
0.0732145830988884,
0.059655070304870605,
-0.06365408003330231,
0.016663743183016777,
-0.06470509618520737,
0.013558859936892986,
0.01993156410753727,
-0.028904154896736145,
0.010109431110322475,
-0.004282030276954174,
0.02275143936276436,
0.005387411452829838,
0.01888735219836235,
0.03768128156661987,
-0.028071414679288864,
0.018569214269518852,
0.026640037074685097,
-0.01712869480252266,
0.018825730308890343,
-0.01515241339802742,
0.05329107865691185,
0.013415398076176643,
-0.048840828239917755,
-0.017970727756619453,
0.0019708157051354647,
-0.0482809841632843,
-0.02147095277905464,
0.06462188065052032,
-0.014195413328707218,
0.03702981770038605,
-0.05491238087415695,
0.010449811816215515,
-0.05745479837059975,
-0.07495104521512985,
-0.0286466795951128,
-0.026547949761152267,
0.005568339489400387,
-0.03146662190556526,
0.032776255160570145,
-0.016560900956392288,
-0.00907024648040533,
0.024378377944231033,
-0.04525577649474144,
-0.03940384089946747,
0.03625648096203804,
0.04351753368973732,
0.033333130180835724,
-0.005565250758081675,
-0.10765385627746582,
-0.027583343908190727,
-0.028133071959018707,
-0.005533692426979542,
-0.005596152041107416,
-0.07239463925361633,
0.013069908134639263,
0.020532608032226562,
-0.040064964443445206,
-0.043428607285022736,
0.035462796688079834,
-0.03576770797371864,
-0.04580572247505188,
-0.008745419792830944,
0.026399211958050728,
-0.00737000722438097,
0.06334598362445831,
-0.013102059252560139,
0.08216702938079834,
0.05677260085940361,
0.05935632437467575,
0.005106572061777115,
-0.0020411270670592785,
-0.008719257079064846,
-0.06656766682863235,
-0.008101644925773144,
0.006879478693008423,
-0.018244542181491852,
0.009321148507297039,
0.05748768523335457,
-0.04103551432490349,
0.04378277063369751,
0.010210102424025536,
0.04957333207130432,
-0.0522984080016613,
-0.010409926995635033,
0.01769520901143551,
-0.010506569407880306,
0.01600908860564232,
-0.0595015250146389,
-0.03507426008582115,
0.00788206048309803,
0.008164359256625175,
-0.040693506598472595,
0.06637214124202728,
-0.02573711983859539,
-0.08951690793037415,
-0.002088116016238928,
-0.02284749038517475,
-0.015664344653487206,
-0.04699285328388214,
-0.04093519598245621,
0.030548211187124252,
-0.037944164127111435,
0.024356966838240623,
-0.03217701613903046,
0.02200920693576336,
-0.028628287836909294,
0.005083419382572174,
0.01850629597902298,
-0.04424026980996132,
-0.013141199015080929,
-0.06897050142288208,
-0.011947895400226116,
0.0359102226793766,
-0.03816155344247818,
0.030457105487585068,
-0.020696625113487244,
0.0005454971105791628,
-0.05224992334842682,
0.05160955712199211,
0.017979465425014496,
-0.03450620919466019,
-0.0030858663376420736,
-0.022216880694031715,
-0.05383187532424927,
0.041825320571660995,
-0.06498492509126663,
0.0278102308511734,
0.0371595062315464,
0.01588241383433342,
-0.04351646080613136,
-0.1063435897231102,
0.07148408144712448,
0.02673325315117836,
-0.0347941629588604,
-0.0422392264008522,
0.03911799564957619,
0.053341761231422424,
0.0010934085585176945,
0.011305860243737698,
0.026692112907767296,
0.027511416003108025,
-0.025100892409682274,
0.030542705208063126,
-0.07034889608621597,
0.005326340906322002,
0.0739530622959137,
-0.03650326281785965,
-0.016696615144610405,
0.056314971297979355,
-0.015134812332689762,
0.023318065330386162,
0.03626883402466774,
0.051426827907562256,
0.035023678094148636,
-0.029476750642061234,
0.044884707778692245,
-0.0014599463902413845,
0.0496860146522522,
0.008683586493134499,
-0.01242621336132288,
-0.005814781412482262,
-0.014050018042325974,
0.06850894540548325,
0.01814059168100357,
-0.042975395917892456,
0.044549793004989624,
-0.04067465290427208,
-0.005415130406618118,
-0.01499317679554224,
-0.00012240977957844734,
-0.0174977146089077,
0.0032118659000843763,
0.0490167997777462,
0.02517041750252247,
-0.041506193578243256,
-0.03918800130486488,
-0.0410810224711895,
0.030217455700039864,
-0.01530204713344574,
-0.03601856902241707,
-0.007026149891316891,
-0.02306872420012951,
-0.0021349710877984762,
-0.005231039132922888,
0.02052570879459381,
0.018840115517377853,
-0.006661695893853903,
-0.026151102036237717,
0.003967650234699249,
0.014151880517601967,
0.014520124532282352,
0.028371434658765793,
0.025424117222428322,
-0.052674971520900726,
-0.04798600822687149,
-0.017493003979325294,
0.01775657758116722,
-0.014915408566594124,
-0.021946679800748825,
0.03073541820049286,
0.007843676954507828,
0.009031737223267555,
0.012165568768978119,
0.010328635573387146,
0.02025098167359829,
0.022141674533486366,
-0.009867295622825623,
-0.036825139075517654,
0.010663452558219433,
-0.0046344175934791565,
0.022538715973496437,
-0.005196999758481979,
-0.03831354156136513,
-0.037587691098451614,
0.028247255831956863,
-0.0168770644813776,
-0.015514093451201916,
0.04886001721024513,
-0.02629680000245571,
-0.06493216753005981,
-0.005722634959965944,
0.018331965431571007,
-0.028151048347353935,
-0.06956320255994797,
0.016995204612612724,
0.015033192932605743,
-0.00991485919803381,
-0.026698391884565353,
-0.023667041212320328,
0.0033881182316690683,
-0.027061806991696358,
-0.004808838479220867,
-0.05192071944475174,
-0.026284627616405487,
0.04756073281168938,
0.01104906015098095,
-0.0016272006323561072,
-0.022977981716394424,
-0.018914617598056793,
0.010394643992185593,
-0.0140791404992342,
-0.02925601229071617,
0.021050214767456055,
0.06142009422183037,
0.0028795551043003798,
-0.0010249126935377717,
0.01398546900600195,
-0.07902316004037857,
-0.0017797015607357025,
0.06514889001846313,
0.0039839185774326324,
0.06386817991733551,
0.011751490645110607,
-0.05567144975066185,
-0.006615293677896261,
0.04732174798846245,
-0.008657506667077541,
-0.05822652205824852,
-0.07437878847122192,
0.0019211783073842525,
0.033950116485357285,
0.03144529461860657,
-0.05311952158808708,
0.05575237050652504,
-0.01794438809156418,
0.003988863900303841,
0.005179914180189371,
-0.012650116346776485,
-0.013569600880146027,
0.004762905649840832,
-0.0032556706573814154,
-0.004203252028673887,
0.020722972229123116,
0.022674789652228355,
0.01435853447765112
] |
<p>I am trying to the calculate the link budget for link between a ground station on Earth (with a particular latitude and longitude) and a rover at a particular location on the surface of Mars, either directly or through a satellite on Mars. Now, if I need to determine the link availability between the rover and the ground station, the first step is to determine weather I have a line of sight between the ground station and the rover.</p>
<p>For this, the first step is to determine whether Mars is above our horizon or not and if so, for how long. This can be easily done using packages such as PyEphem or Novas.</p>
<p>The next step would be to determine if the rover is actually facing Earth or is on the other side of Mars. It is this second step that I need to determine with reasonable accuracy, but have not been able to figure out how to so far.</p>
<p>Later on I would need to include the satellites in the link path as well, but for now, I need to determine if I can get a straight line of sight communication between the rover on Mars and ground station on Earth.</p>
<p>Any sort of help will be appreciated.</p> | g4595 | [
0.013423926196992397,
0.0003315807553008199,
-0.004781728144735098,
-0.027358848601579666,
-0.022759700194001198,
0.00011296835145913064,
-0.02474738098680973,
-0.020915554836392403,
-0.013107760809361935,
-0.03895753249526024,
0.03671178221702576,
0.02150682546198368,
0.009607621468603611,
0.019922953099012375,
-0.007940148003399372,
0.04795507341623306,
0.03696727007627487,
-0.015993310138583183,
0.023809397593140602,
0.011695495806634426,
0.0694003477692604,
0.06675981730222702,
-0.0032758305314928293,
0.0021222317591309547,
-0.05352192372083664,
-0.06686010956764221,
-0.015787070617079735,
0.020963067188858986,
-0.0728711187839508,
0.012968277558684349,
-0.05414693430066109,
-0.010775801725685596,
0.05851464346051216,
-0.019785182550549507,
-0.03441770374774933,
0.029219862073659897,
0.013958223164081573,
0.008442377671599388,
-0.04343516752123833,
-0.015291805379092693,
0.008730855770409107,
-0.04185283184051514,
-0.04636185243725777,
0.046737223863601685,
0.04366098716855049,
-0.012296504341065884,
-0.03166557475924492,
-0.023038458079099655,
0.04995524510741234,
-0.027277402579784393,
-0.05404236167669296,
0.08081772178411484,
-0.03999733552336693,
0.04721350595355034,
-0.030119510367512703,
0.007078142836689949,
0.04856047034263611,
-0.015193900093436241,
0.08852376788854599,
-0.03687248378992081,
0.03161938115954399,
-0.019619982689619064,
0.007960524410009384,
-0.06519507616758347,
0.059817273169755936,
0.024876216426491737,
-0.008375059813261032,
-0.04406215250492096,
-0.026005007326602936,
-0.020963849499821663,
-0.01584434136748314,
0.00502378772944212,
-0.014072434045374393,
-0.025520669296383858,
-0.01956065557897091,
0.0038916333578526974,
0.010610670782625675,
0.012986932881176472,
0.021030202507972717,
0.0512055903673172,
0.07149335741996765,
0.0018370378529652953,
-0.013189130462706089,
0.061354100704193115,
0.09915236383676529,
-0.00018097431166097522,
-0.012151631526648998,
-0.011008457280695438,
-0.01894952915608883,
0.019733022898435593,
-0.05878959596157074,
0.03765840083360672,
-0.0061826929450035095,
0.06463229656219482,
-0.029832854866981506,
-0.01989484578371048,
-0.03726116940379143,
0.0015860761050134897,
0.050113245844841,
-0.0319383479654789,
-0.03193383291363716,
0.017627589404582977,
0.0007642710697837174,
0.006222868338227272,
-0.025127185508608818,
0.02098817564547062,
-0.04575246945023537,
0.022398531436920166,
-0.03810524567961693,
-0.05885271728038788,
0.008345527574419975,
-0.038218557834625244,
-0.017798878252506256,
0.004382311832159758,
0.02468922734260559,
-0.06215156242251396,
0.03496994078159332,
0.0045259445905685425,
0.08243916183710098,
-0.03698272630572319,
-0.0511845126748085,
0.028337905183434486,
-0.019061051309108734,
0.031246811151504517,
0.009728832170367241,
-0.025033416226506233,
-0.010531395673751831,
0.007220908999443054,
0.05284624174237251,
0.05793488398194313,
-0.019500570371747017,
-0.016169393435120583,
0.03995933756232262,
-0.023433512076735497,
-0.007716816384345293,
-0.025095194578170776,
0.031470417976379395,
-0.020459258928894997,
-0.03246412053704262,
0.024071799591183662,
-0.0380842424929142,
-0.037612225860357285,
0.023000281304121017,
-0.031235001981258392,
-0.05567776411771774,
0.039475638419389725,
0.05415729060769081,
-0.028424052521586418,
0.0038944382686167955,
0.016515040770173073,
0.022539230063557625,
0.0250654648989439,
-0.0013184811687096953,
0.06655018776655197,
0.03865472972393036,
-0.03245030716061592,
-0.013476633466780186,
-0.007070817053318024,
0.02123279869556427,
0.02479005791246891,
0.006868279073387384,
-0.017113177105784416,
-0.04686938226222992,
0.012802218087017536,
-0.0074725039303302765,
-0.016090964898467064,
-0.02361593209207058,
-0.05672689899802208,
-0.02950054034590721,
-0.013283847831189632,
0.014714736491441727,
-0.0023099719546735287,
0.061013251543045044,
0.06632798165082932,
0.012222557328641415,
0.02410978265106678,
0.05225240811705589,
-0.011697445996105671,
0.014744496904313564,
0.04576892778277397,
0.08894380182027817,
-0.031068451702594757,
0.008596089668571949,
0.06857439875602722,
-0.03943300619721413,
0.01306129153817892,
0.03954330459237099,
-0.04954680800437927,
-0.06346672028303146,
0.00906753446906805,
-0.071181520819664,
-0.016034556552767754,
-0.018600396811962128,
-0.03845537453889847,
-0.009313207119703293,
-0.026429014280438423,
0.08013094216585159,
-0.006632170174270868,
0.000368227600120008,
0.015421333722770214,
0.017537280917167664,
0.06042029336094856,
-0.024017253890633583,
0.0617598295211792,
0.008113792166113853,
-0.014824737794697285,
0.02174762263894081,
-0.01807469129562378,
0.004843234550207853,
0.0055180503986775875,
-0.024316323921084404,
-0.05307925119996071,
-0.001083353185094893,
0.02830028161406517,
0.016853151842951775,
-0.0038877567276358604,
0.00831480324268341,
-0.01385528314858675,
-0.0342998243868351,
-0.028311964124441147,
-0.00034349170164205134,
-0.0061029852367937565,
0.03630779683589935,
-0.004002207424491644,
-0.013055531308054924,
0.00870970357209444,
0.025551848113536835,
0.02832634560763836,
0.04743745177984238,
0.008872659876942635,
0.04535524174571037,
-0.010231287218630314,
-0.052461955696344376,
-0.019639965146780014,
0.016624702140688896,
0.01920272409915924,
0.028491472825407982,
-0.03622753918170929,
0.028638554736971855,
0.040988653898239136,
0.012471875175833702,
-0.0199994295835495,
-0.0005189134390093386,
0.01916402578353882,
0.05059116333723068,
-0.0009683441603556275,
0.07037938386201859,
0.006197638344019651,
0.007654523942619562,
0.03355229273438454,
0.04000139608979225,
0.03288070112466812,
0.017159128561615944,
0.019752642139792442,
-0.011697884649038315,
0.010051537305116653,
0.017555944621562958,
0.013325050473213196,
-0.035398174077272415,
-0.03556186705827713,
-0.050820618867874146,
-0.05244176462292671,
0.030966931954026222,
0.0070955147966742516,
-0.013225175440311432,
0.03827029839158058,
-0.020609276369214058,
0.025260740891098976,
-0.007986418902873993,
-0.03737033158540726,
-0.014005080796778202,
0.03628290444612503,
0.028463484719395638,
0.0047822557389736176,
-0.02841988019645214,
-0.03162107989192009,
0.03894006833434105,
0.011713540181517601,
-0.010931944474577904,
0.059882428497076035,
0.03930804878473282,
-0.04242897778749466,
0.022579995915293694,
0.06498449295759201,
0.018337290734052658,
0.03782767802476883,
0.014892888255417347,
0.0614297017455101,
0.00856194831430912,
-0.0012424503220245242,
-0.009895898401737213,
-0.009459135122597218,
-0.011929627507925034,
-0.01631719060242176,
-0.020759467035531998,
-0.02793458104133606,
0.028990747407078743,
0.032430365681648254,
0.02272498607635498,
-0.026452917605638504,
0.0373213067650795,
0.024464618414640427,
0.047350890934467316,
-0.010033528320491314,
0.013398943468928337,
-0.05571458488702774,
0.026637814939022064,
-0.0125082116574049,
-0.002943300409242511,
-0.031711261719465256,
-0.031629111617803574,
0.012549188919365406,
0.030836189165711403,
-0.07240262627601624,
0.029411382973194122,
-0.017257193103432655,
-0.014845948666334152,
-0.015335933305323124,
-0.05992396920919418,
0.06405489891767502,
-0.0038351474795490503,
-0.03597645089030266,
-0.039551593363285065,
-0.019950546324253082,
-0.004209400620311499,
0.042800601571798325,
-0.074536994099617,
-0.013243050314486027,
-0.045229438692331314,
0.022751282900571823,
-0.009087377227842808,
0.049752648919820786,
0.0017047022702172399,
-0.050514720380306244,
-0.003214985830709338,
0.038049016147851944,
0.0008217808790504932,
0.017412588000297546,
-0.01699071377515793,
0.07193874567747116,
0.000521540641784668,
0.03379176929593086,
-0.059230029582977295,
-0.009803321212530136,
0.005715150386095047,
0.003851839806884527,
-0.05205297842621803,
0.013721417635679245,
-0.05014993995428085,
-0.010933949612081051,
0.03157132863998413,
0.010633879341185093,
-0.01918184757232666,
-0.03350270166993141,
0.021714424714446068,
0.06898025423288345,
-0.03514419123530388,
-0.0011211569653823972,
-0.043391790241003036,
0.02527497708797455,
0.032887592911720276,
0.02318098023533821,
-0.005251411814242601,
-0.016241975128650665,
0.009750258177518845,
-0.04284125193953514,
0.027058515697717667,
-0.005142254754900932,
0.009938925504684448,
-0.051878735423088074,
0.10881374776363373,
0.018385980278253555,
-0.03106553480029106,
-0.008326365612447262,
-0.01156193483620882,
-0.00040786960744298995,
0.046124618500471115,
-0.06548848003149033,
-0.011570155620574951,
0.09503264725208282,
-0.031627241522073746,
0.05237853154540062,
0.014962754212319851,
0.06865774840116501,
0.05537573620676994,
-0.07015476375818253,
-0.02950727939605713,
0.007062962278723717,
0.05198323354125023,
0.01614682748913765,
-0.013106297701597214,
-0.10893391072750092,
-0.02862151898443699,
0.019076043739914894,
0.0008616195991635323,
0.03435204550623894,
-0.0033499393612146378,
0.01120261661708355,
0.0371895506978035,
0.075616754591465,
0.02197032794356346,
0.01563933864235878,
0.04163757711648941,
0.009365306235849857,
-0.06361215561628342,
-0.013909165747463703,
-0.042261045426130295,
-0.01109868660569191,
-0.017051568254828453,
0.04250209406018257,
0.04895393177866936,
0.04739655554294586,
-0.007330924738198519,
0.005558548495173454,
0.05006397143006325,
0.00756303733214736,
-0.010517057031393051,
-0.0711609274148941,
0.043432723730802536,
-0.02947990410029888,
-0.08629642426967621,
0.01460486650466919,
-0.020197659730911255,
-0.07231827825307846,
0.00766175240278244,
0.07544799894094467,
-0.016212474554777145,
-0.02162146382033825,
0.00018660363275557756,
0.06745629012584686,
-0.027647491544485092,
0.06518823653459549,
-0.030109256505966187,
-0.01812044344842434,
-0.06133899837732315,
0.0605800524353981,
-0.014421389438211918,
-0.04406214505434036,
-0.018612714484333992,
-0.0032584485597908497,
-0.0425630584359169,
-0.0023866118863224983,
-0.003302179044112563,
-0.006746896542608738,
-0.027147941291332245,
0.04105628654360771,
-0.027253402397036552,
-0.02768811769783497,
-0.022129934281110764,
-0.05072515457868576,
0.0022201980464160442,
-0.01611725054681301,
-0.0009996048174798489,
0.014474050141870975,
-0.035022154450416565,
0.009962859563529491,
-0.039508119225502014,
0.011095020920038223,
0.036386001855134964,
0.008296690881252289,
0.016998961567878723,
0.02597305178642273,
-0.01556321419775486,
0.018280059099197388,
0.0065903495997190475,
-0.023651449009776115,
-0.013204153627157211,
-0.023532021790742874,
0.004691019654273987,
0.03554968535900116,
0.0007271064096130431,
-0.003371897619217634,
0.013564426451921463,
0.028168166056275368,
-0.0539800263941288,
0.0036210007965564728,
-0.04345129430294037,
-0.015625907108187675,
0.025557801127433777,
-0.009928328916430473,
-0.040403399616479874,
0.06162143126130104,
-0.0058798519894480705,
0.015765585005283356,
-0.03794446960091591,
0.035368748009204865,
-0.018462758511304855,
-0.019388090819120407,
-0.008064433000981808,
-0.022046301513910294,
0.04318416118621826,
-0.08084467798471451,
-0.04195920377969742,
-0.029252145439386368,
-0.03458843007683754,
-0.02032821998000145,
0.01239765714854002,
-0.025618743151426315,
0.04122156277298927,
0.024139411747455597,
0.037819184362888336,
-0.031113581731915474,
-0.017641382291913033,
0.052476122975349426,
0.03011956252157688,
0.002315840218216181,
-0.004444061312824488,
-0.013833719305694103,
0.03806105628609657,
-0.0016035476000979543,
0.035375673323869705,
0.015043548308312893,
-0.022444652393460274,
-0.02069992758333683,
-0.048667244613170624,
-0.04486462473869324,
0.030727338045835495,
0.021727722138166428,
-0.05229777470231056,
0.039579834789037704,
0.013012738898396492,
0.009590765461325645,
0.02733641490340233,
0.0004009240074083209,
-0.05802043899893761,
-0.08293585479259491,
-0.02676420658826828,
0.03479550778865814,
-0.03719459846615791,
-0.019573530182242393,
0.013102744705975056,
0.011938551440834999,
-0.00868749339133501,
0.02236897312104702,
0.047960393130779266,
-0.04468059539794922,
0.009034601971507072,
-0.021319322288036346,
-0.0009398245601914823,
-0.06764539331197739,
-0.03374502807855606,
0.019438400864601135,
0.08084895461797714,
0.0516875758767128,
0.00038593538920395076,
-0.005556057207286358,
0.005631219130009413,
0.02188597060739994,
0.025336911901831627,
-0.041402481496334076,
0.029264304786920547,
0.0006034125690348446,
-0.029476700350642204,
0.025478292256593704,
0.0033939885906875134,
-0.051816411316394806,
-0.049421850591897964,
0.005745787173509598,
-0.027148867025971413,
0.01558621320873499,
0.06995034962892532,
-0.04993928596377373,
-0.04787065461277962,
0.026409806683659554,
-0.03678148239850998,
0.041609130799770355,
-0.03924427181482315,
0.0013025766238570213,
0.008020520210266113,
-0.00460636243224144,
-0.0063545433804392815,
-0.10016293823719025,
-0.08939765393733978,
-0.035031452775001526,
0.035485681146383286,
0.026810118928551674,
-0.02993040531873703,
0.02296929992735386,
-0.006670620758086443,
0.04139339178800583,
0.00463111512362957,
0.025101928040385246,
0.0006304378039203584,
-0.031786587089300156,
0.000050905080570373684,
0.03490113839507103,
-0.09237387776374817,
-0.031927790492773056,
-0.029223289340734482,
-0.022420590743422508,
-0.01651631109416485,
-0.015833288431167603,
-0.009415135718882084,
-0.07035912573337555,
-0.044261056929826736,
-0.08887390047311783,
-0.026789383962750435,
0.0043153236620128155,
0.04086080566048622,
0.04831080511212349,
-0.001639254274778068,
-0.04381071776151657,
0.11182866990566254,
-0.0038066550623625517,
0.03412877395749092,
-0.005228171590715647,
0.04496091604232788,
0.04882979393005371,
0.013605152256786823,
-0.05163620784878731,
0.031047118827700615,
0.015744535252451897,
0.03792962804436684,
0.07759850472211838,
0.01502854935824871,
0.02235013246536255,
0.009661673568189144,
0.0523800402879715,
-0.057123709470033646,
-0.04514060914516449,
0.009098675101995468,
0.012036026455461979,
-0.013478647917509079,
-0.006716910284012556,
0.01676817052066326,
0.02999153360724449,
0.04332886263728142,
0.00039429491152986884,
0.05358434095978737,
-0.031200457364320755,
0.044288281351327896,
-0.05255245789885521,
0.0012452627997845411,
-0.03026147559285164,
0.014549030922353268,
0.03300648182630539,
-0.013296536169946194,
0.0028239269740879536,
-0.031807590276002884,
0.13053639233112335,
0.022350437939167023,
-0.04045240581035614,
-0.021891864016652107,
0.03520820662379265,
-0.0037162615917623043,
-0.09976249933242798,
-0.04005882143974304,
-0.031329959630966187,
-0.07442282140254974,
0.034891173243522644,
0.04634875804185867,
-0.016599873080849648,
0.03564270958304405,
-0.005940225441008806,
0.023151200264692307,
0.07856451719999313,
-0.003742536297068,
-0.007525252178311348,
0.026365365833044052,
-0.056431788951158524,
0.013033437542617321,
-0.0026766462251544,
-0.04749961197376251,
0.007799617014825344,
0.01590047776699066,
0.0262036994099617,
-0.016663219779729843,
-0.0024980397429317236,
-0.013395136222243309,
-0.030122991651296616,
-0.005274306982755661,
-0.0146021144464612,
-0.003133960533887148,
0.020819811150431633,
-0.03451690822839737,
0.007534288335591555,
0.018813999369740486,
-0.0016637934604659677,
-0.048753805458545685,
-0.014130470342934132,
-0.008415129035711288,
-0.03570599481463432,
-0.010513699613511562,
0.021644262596964836,
0.0009726318530738354,
0.018313108012080193,
0.026409240439534187,
-0.037286918610334396,
-0.02658878266811371,
-0.010246426798403263,
-0.017243986949324608,
0.04835629463195801,
-0.0073414938524365425,
-0.053997866809368134,
-0.020859716460108757,
-0.008687403053045273,
0.033692993223667145,
-0.014026830904185772,
0.06410112231969833,
0.033190637826919556,
0.023343294858932495,
0.021224092692136765,
0.010975739918649197,
0.012840904295444489,
0.027395524084568024,
-0.016390817239880562,
0.020428672432899475,
-0.004505333490669727,
-0.03829701989889145,
-0.03331245109438896,
0.06648418307304382,
0.010389000177383423,
-0.04486075043678284,
0.06283371895551682,
-0.08873813599348068,
0.00868110079318285,
0.06639263778924942,
0.03585400432348251,
-0.009853356517851353,
-0.003277083160355687,
-0.000734237371943891,
-0.03706074878573418,
0.0249576848000288,
-0.05332706868648529,
-0.09648916870355606,
0.00026119602262042463,
-0.026265770196914673,
-0.01788407377898693,
0.03502562642097473,
-0.037161510437726974,
0.03937283158302307,
0.00916100200265646,
0.017541779205203056,
-0.0305656548589468,
0.01534451823681593,
-0.006260592024773359,
-0.015148470178246498,
-0.061674341559410095,
-0.06637938320636749,
0.009365183301270008,
-0.03792383894324303,
-0.07206720113754272,
-0.019462568685412407,
-0.016064461320638657,
0.005672869738191366,
-0.0009065284393727779,
0.05794002115726471,
0.033752888441085815,
0.05217480659484863,
0.011258190497756004,
-0.0067348601296544075,
0.07395768165588379,
0.04017873853445053,
-0.01695639081299305,
-0.03914470970630646,
-0.030628109350800514,
-0.0854199007153511,
-0.03587205708026886,
-0.06267301738262177,
0.0057131401263177395,
0.010660861618816853,
-0.020317036658525467,
0.003914427012205124,
-0.013859323225915432,
0.008147832937538624,
0.04225769639015198,
-0.038032613694667816,
0.007918166927993298
] |
<p>When working with Bose-Einstein condensates trapped in potentials, how can one tell what the density of state of a system of identical bosons given the Hamiltonian, $H$? (I have been told that it is possible.)</p>
<p>Suppose the Hamiltonian is some 2D harmonic oscillator -- so $$H=p^2/2m+(1/2)(a^2x^2+b^2y^2) \quad ?$$</p>
<p>I think there is some general formula, something like $$\rho(E)=[gV_dS_dp^{d-1}/(2\pi\hbar)^{d}] (dp/dE) \quad ,$$ where $d$ is the dimension of the space we are working in, $g=2s+1$ where $s$ is the spin of the particles and $V_d$ is the $d-$dimensional "volume", so for a fixed volume box, this is the volume of the box.</p>
<p>But what is $V_d$ in this case? And is $p$ simply $$p^2=2m[E-(1/2)(a^2x^2+b^2y^2)] \quad ?$$</p> | g4596 | [
-0.017150189727544785,
0.02793254889547825,
-0.0023576109670102596,
-0.048598188906908035,
0.028109045699238777,
-0.030583612620830536,
0.046835124492645264,
-0.030170761048793793,
-0.031633082777261734,
0.017691772431135178,
-0.007699829526245594,
0.03813423588871956,
-0.004564010538160801,
-0.0021991112735122442,
0.047207556664943695,
0.02308519184589386,
0.015059106983244419,
-0.011212462559342384,
-0.022265620529651642,
-0.07645966857671738,
-0.031692489981651306,
-0.028364496305584908,
0.006139103323221207,
0.012953815050423145,
0.01643734984099865,
-0.016458449885249138,
-0.019077053293585777,
-0.008831286802887917,
-0.02657717652618885,
-0.01092053484171629,
-0.06464230269193649,
0.005682791583240032,
0.054365068674087524,
-0.035479240119457245,
-0.010229098610579967,
0.011184902861714363,
0.07495377957820892,
-0.034832634031772614,
0.032552409917116165,
-0.0015144129283726215,
0.0031896710861474276,
-0.06347908079624176,
0.006744085811078548,
-0.010507894679903984,
-0.042463719844818115,
0.003600764088332653,
0.0032356788869947195,
0.016836348921060562,
-0.03566471114754677,
-0.0022872244007885456,
0.01879514753818512,
0.05532417446374893,
0.01502257026731968,
0.03261534497141838,
0.014272940345108509,
0.022033605724573135,
-0.00931193120777607,
-0.031294915825128555,
0.034635767340660095,
0.031951192766427994,
-0.0071811615489423275,
0.005660222843289375,
-0.001296922448091209,
0.04903149604797363,
0.07051876932382584,
0.019202696159482002,
-0.07218699157238007,
0.009948192164301872,
-0.030344460159540176,
-0.056420620530843735,
0.01232726126909256,
-0.031048957258462906,
0.0068985396064817905,
0.02324148826301098,
-0.017744336277246475,
-0.011720516718924046,
0.002485111588612199,
0.05511358007788658,
0.0019850940443575382,
-0.004340967629104853,
-0.002674241317436099,
-0.06544734537601471,
0.03297385945916176,
-0.025188429281115532,
0.11674589663743973,
-0.029927676543593407,
0.048703812062740326,
0.013099230825901031,
-0.060573846101760864,
0.05512983724474907,
-0.022613191977143288,
-0.004353041760623455,
0.10399006307125092,
0.04481092840433121,
-0.0013683312572538853,
0.006068035028874874,
-0.004657975398004055,
0.006668235640972853,
-0.04368317127227783,
0.027157319709658623,
-0.031589727848768234,
0.0030708631966263056,
-0.013737235218286514,
-0.0711606964468956,
0.002674781484529376,
0.017169278115034103,
0.04600311815738678,
-0.008979939855635166,
0.00696383835747838,
-0.026780426502227783,
-0.04684825986623764,
0.011937052011489868,
-0.004682271741330624,
0.029199164360761642,
-0.06464903056621552,
-0.016277853399515152,
0.049624573439359665,
-0.002354684052988887,
-0.019307971000671387,
0.022513331845402718,
0.011846940964460373,
0.04435301199555397,
0.04369514435529709,
0.035732515156269073,
0.01600310020148754,
-0.006940202321857214,
-0.02753501757979393,
0.035271599888801575,
0.031154334545135498,
0.052873216569423676,
-0.004722260404378176,
-0.01156382355839014,
-0.01410392951220274,
0.013655760325491428,
0.006605527363717556,
0.02767825685441494,
0.01514519564807415,
-0.020135967060923576,
0.004296834580600262,
-0.018708661198616028,
-0.04413424804806709,
-0.005865755490958691,
-0.022474925965070724,
-0.013512872159481049,
-0.0068933735601603985,
0.021829240024089813,
0.00004964363688486628,
-0.07185646146535873,
-0.0248434916138649,
0.030446333810687065,
0.043188419193029404,
0.0505521334707737,
0.05480559915304184,
-0.03357184678316116,
-0.02891054004430771,
0.007335050497204065,
0.018277859315276146,
0.049086496233940125,
-0.004922762513160706,
0.0166094321757555,
0.0355776771903038,
0.0339590385556221,
0.0017559382831677794,
-0.02801067754626274,
-0.02979002334177494,
0.016483696177601814,
-0.00021747562277596444,
-0.03171446919441223,
0.034738484770059586,
-0.029691629111766815,
0.016732197254896164,
0.03088260442018509,
-0.03854833170771599,
0.05189798027276993,
0.07617027312517166,
0.014001044444739819,
-0.04582209512591362,
-0.028459571301937103,
0.09852883219718933,
0.015905244275927544,
0.046384524554014206,
0.015036477707326412,
0.04794367402791977,
0.009996132925152779,
-0.03183158487081528,
0.013311630114912987,
0.02790001407265663,
-0.05197799950838089,
0.012513482011854649,
0.011545735411345959,
-0.02196641080081463,
-0.016853997483849525,
0.03731544315814972,
0.002723654033616185,
0.027986226603388786,
0.029660966247320175,
0.03636356070637703,
-0.06260523945093155,
-0.019646145403385162,
0.007775405887514353,
-0.08956938236951828,
0.04973891004920006,
0.05917546898126602,
-0.025513505563139915,
0.06284769624471664,
-0.0031947228126227856,
0.026698416098952293,
-0.009564601816236973,
0.027843911200761795,
0.03851611539721489,
-0.011062500067055225,
-0.06187809258699417,
-0.012742163613438606,
0.05040515959262848,
-0.011457588523626328,
0.02631894126534462,
-0.011411028914153576,
0.022677863016724586,
-0.023546086624264717,
0.002530180150642991,
-0.06872139871120453,
0.013225371018052101,
0.012757576070725918,
0.015569211915135384,
0.004107329528778791,
-0.008020395413041115,
-0.02377411723136902,
0.0016620939131826162,
0.02337995171546936,
0.03258094936609268,
-0.030563022941350937,
-0.0449194498360157,
-0.011945357546210289,
-0.024707064032554626,
-0.037506990134716034,
0.0450301393866539,
-0.07434750348329544,
-0.035788822919130325,
0.051685478538274765,
0.03168491646647453,
0.04915706813335419,
-0.02000580169260502,
-0.05410316213965416,
0.05271755903959274,
0.05650116875767708,
0.0325126051902771,
0.01727263443171978,
0.00928422436118126,
0.03639238700270653,
0.04973467066884041,
-0.04311654716730118,
-0.01770319789648056,
-0.005164775997400284,
-0.0017955248476937413,
-0.024071533232927322,
0.018051713705062866,
-0.015242532826960087,
0.010083054192364216,
0.0016750587383285165,
-0.08121737837791443,
0.00731941033154726,
-0.019663944840431213,
0.015691068023443222,
0.051663272082805634,
-0.028884893283247948,
-0.0456678606569767,
0.022582028061151505,
0.002311744261533022,
-0.013546489179134369,
0.032915543764829636,
0.05129920318722725,
0.0632997527718544,
-0.024372786283493042,
0.021688254550099373,
-0.004161956254392862,
0.001922370633110404,
-0.005024312529712915,
-0.05293310061097145,
0.04362161457538605,
-0.042157307267189026,
-0.03627707436680794,
0.04000856727361679,
-0.02444569766521454,
0.04687860235571861,
0.038194820284843445,
-0.0790528729557991,
-0.03056075982749462,
0.007348017767071724,
0.05210355296730995,
-0.018157536163926125,
0.0326518714427948,
0.04273043945431709,
-0.001884952769614756,
0.03413724526762962,
-0.033178068697452545,
0.04096737876534462,
0.0032782205380499363,
-0.03475812450051308,
-0.0012513661058619618,
0.07411554455757141,
-0.0003688693977892399,
-0.02761422097682953,
0.04139074310660362,
-0.046939365565776825,
0.011885905638337135,
0.02292073890566826,
-0.08149673789739609,
0.039192959666252136,
-0.04249872267246246,
-0.020224614068865776,
-0.018085716292262077,
-0.004149904940277338,
0.0294930562376976,
-0.05568918213248253,
-0.046285707503557205,
-0.02807978354394436,
0.011420747265219688,
-0.0549931563436985,
0.03294743597507477,
-0.03632555902004242,
0.0020224531181156635,
-0.02383369579911232,
0.03257988393306732,
-0.002956901676952839,
0.039341628551483154,
-0.0005649476079270244,
-0.06592036783695221,
-0.04369673877954483,
-0.09018919616937637,
-0.000915626878850162,
0.029664039611816406,
-0.055437806993722916,
-0.026713194325566292,
0.020759807899594307,
-0.03505352884531021,
-0.053205475211143494,
-0.02597740851342678,
-0.008063435554504395,
0.039387695491313934,
0.026724256575107574,
-0.04849787801504135,
-0.00851968489587307,
-0.026337258517742157,
0.02506696619093418,
-0.04805336520075798,
-0.038037337362766266,
0.013821037486195564,
-0.01223843265324831,
0.003768650349229574,
-0.037106286734342575,
-0.03012922778725624,
-0.04348956421017647,
0.0388670340180397,
-0.0048140608705580235,
0.007011156063526869,
0.019132262095808983,
0.06234224513173103,
-0.0076485928148031235,
0.04302374646067619,
0.005734462756663561,
0.024837713688611984,
-0.09381721168756485,
0.04475405439734459,
0.029078252613544464,
0.025152206420898438,
-0.09208621084690094,
-0.028309879824519157,
-0.04217912629246712,
-0.0055459714494645596,
-0.048525404185056686,
-0.010847784578800201,
0.008045054040849209,
0.04119155928492546,
0.0373929925262928,
0.0919254943728447,
-0.09370516240596771,
-0.03886650502681732,
-0.0527782179415226,
-0.022697990760207176,
-0.0044049108400940895,
0.027000224217772484,
-0.0008611879893578589,
0.016750827431678772,
-0.02539004758000374,
-0.0009956392459571362,
-0.07067889720201492,
0.022089408710598946,
0.0073663401417434216,
0.024064676836133003,
-0.053051456809043884,
-0.017364878207445145,
-0.026596127077937126,
-0.014896096661686897,
0.007403870113193989,
0.00804115179926157,
0.04123438522219658,
-0.0021435911767184734,
0.02993544563651085,
-0.06302449107170105,
0.03014715388417244,
-0.039660196751356125,
-0.05519845336675644,
-0.01820960082113743,
-0.049427323043346405,
0.025417612865567207,
0.028047485277056694,
0.04900897294282913,
-0.00935647077858448,
0.044723112136125565,
-0.01606985554099083,
0.000248373718932271,
0.011851558461785316,
0.03985830768942833,
-0.032682232558727264,
-0.041182950139045715,
-0.010587717406451702,
0.028546223416924477,
-0.024964027106761932,
-0.000024658284019096754,
0.03417620435357094,
0.018792811781167984,
0.010054855607450008,
0.004749005194753408,
-0.0026617047842592,
-0.03914932161569595,
-0.004922948312014341,
0.08303202688694,
-0.01127972174435854,
-0.014673767611384392,
-0.031071092933416367,
0.021544205024838448,
-0.013200070708990097,
0.025687329471111298,
0.05164505913853645,
-0.0863516554236412,
-0.02421165071427822,
-0.06318417936563492,
-0.005530673079192638,
0.007888141088187695,
0.06371203809976578,
-0.00715058296918869,
0.0062880003824830055,
-0.013564527034759521,
-0.0011334330774843693,
0.006430419161915779,
0.03819020092487335,
-0.0016077108448371291,
-0.04803716391324997,
-0.017044663429260254,
-0.035869747400283813,
0.0046317377127707005,
-0.010240166448056698,
-0.01998344250023365,
-0.049968522042036057,
0.01128633413463831,
0.022941872477531433,
-0.043423205614089966,
0.033626738935709,
0.000963452912401408,
0.03377522528171539,
-0.029159188270568848,
-0.05252762883901596,
-0.012262562289834023,
0.0019901245832443237,
-0.0039035154040902853,
-0.04577483981847763,
-0.07860077172517776,
0.021403903141617775,
-0.02965942583978176,
-0.021900709718465805,
-0.0028037785086780787,
-0.03012337163090706,
0.07979913055896759,
0.020910799503326416,
0.03555024415254593,
0.021355165168642998,
-0.036789897829294205,
0.01799701899290085,
-0.009443702176213264,
-0.009384444914758205,
0.0074050938710570335,
-0.0023159782867878675,
0.02135872095823288,
0.052366290241479874,
-0.009812292642891407,
0.03210381418466568,
-0.02265760861337185,
0.034531913697719574,
-0.03992846980690956,
0.009881577454507351,
-0.008485889993607998,
0.03409222885966301,
0.03499772027134895,
0.038131482899188995,
0.04294445738196373,
-0.046253085136413574,
-0.02592102438211441,
-0.04606246575713158,
-0.05472170189023018,
0.053530704230070114,
-0.06816946715116501,
0.03324892371892929,
0.07799586653709412,
-0.02066497690975666,
0.001110282028093934,
0.060537319630384445,
0.08732349425554276,
0.009356452152132988,
0.010116632096469402,
0.010887070558965206,
-0.03507501631975174,
0.006318085826933384,
0.009276906959712505,
0.10984170436859131,
0.009433426894247532,
-0.008783893659710884,
-0.025874866172671318,
0.07363675534725189,
-0.0001789713860489428,
-0.03921055793762207,
0.03198608383536339,
-0.006989177316427231,
0.03418448194861412,
0.01198936440050602,
-0.004963727202266455,
0.032123927026987076,
0.001895478810183704,
-0.027689319103956223,
0.04555574804544449,
0.04455672577023506,
-0.01765439100563526,
0.004035349003970623,
0.03651386871933937,
-0.0459267795085907,
-0.017537863925099373,
-0.011357713490724564,
-0.03079410269856453,
-0.005537729244679213,
0.017354322597384453,
0.06849521398544312,
-0.013076811097562313,
-0.09439680725336075,
-0.023556312546133995,
0.007023530546575785,
-0.02538350038230419,
0.010803899727761745,
-0.053923677653074265,
-0.003369844751432538,
0.032742589712142944,
0.00036236451705917716,
-0.05542309954762459,
-0.008514855057001114,
-0.03130747377872467,
-0.030642317607998848,
0.00237359874881804,
0.043766189366579056,
0.05344865098595619,
0.018543940037488937,
0.03020341694355011,
0.051925018429756165,
-0.001717099454253912,
0.02664179913699627,
0.00785916019231081,
-0.028568550944328308,
-0.03897828608751297,
0.017333107069134712,
0.01900777779519558,
-0.001002294011414051,
0.028758089989423752,
0.02331782504916191,
-0.05913512408733368,
-0.007565340958535671,
0.08821594715118408,
-0.03646518290042877,
0.0442739762365818,
0.0021767187863588333,
-0.03408054634928703,
0.007747766096144915,
-0.0032982451375573874,
0.037554897367954254,
-0.03238976374268532,
0.056694116443395615,
0.03523547574877739,
-0.01979561150074005,
-0.0045073325745761395,
0.0788501426577568,
-0.003806399879977107,
-0.046818483620882034,
0.004654036369174719,
0.0212465338408947,
-0.024839796125888824,
0.011235157027840614,
-0.015780001878738403,
-0.07352996617555618,
0.016623349860310555,
-0.02337254211306572,
-0.015608904883265495,
-0.0013873099815100431,
-0.04312906041741371,
0.012388492003083229,
0.0540449395775795,
-0.0073214005678892136,
-0.03035462461411953,
0.004544639494270086,
-0.04066167399287224,
0.02535572648048401,
-0.038345713168382645,
-0.07904155552387238,
-0.0809558555483818,
0.02250385470688343,
-0.04678728058934212,
-0.06124117225408554,
-0.013939217664301395,
-0.021472394466400146,
0.05704440921545029,
-0.041374459862709045,
0.10190213471651077,
0.047426607459783554,
-0.01947418600320816,
0.04111148416996002,
0.0376211553812027,
-0.01908440887928009,
0.0036808575969189405,
-0.05727437883615494,
0.1013166755437851,
0.01608663983643055,
-0.0028810796793550253,
-0.02652828022837639,
0.08009261637926102,
0.013604114763438702,
0.038807328790426254,
0.020056791603565216,
0.04115989804267883,
0.0270998552441597,
-0.02254962921142578,
-0.007386308163404465,
-0.010214224457740784,
0.027268528938293457,
-0.013693854212760925,
-0.01819581538438797,
-0.05570550262928009,
0.011053023859858513,
0.03157258406281471,
0.00405384786427021,
-0.08256607502698898,
0.02493991144001484,
-0.003071684157475829,
0.022095847874879837,
-0.10371269285678864,
0.03145322576165199,
-0.006835531909018755,
-0.0190015509724617,
-0.0032901489175856113,
-0.014633139595389366,
-0.02067754790186882,
-0.026201555505394936,
0.03037468157708645,
0.03421918675303459,
-0.017161687836050987,
-0.035409387201070786,
-0.030726054683327675,
-0.010348508134484291,
0.023588422685861588,
0.024397337809205055,
-0.025533944368362427,
0.033358145505189896,
0.021193042397499084,
-0.0023768246173858643,
0.009095374494791031,
-0.05290298908948898,
0.05582273006439209,
-0.016601208597421646,
-0.04329131543636322,
-0.001885314006358385,
-0.0017480263486504555,
0.001121405977755785,
0.009708420373499393,
0.04494321346282959,
0.011302024126052856,
-0.05811852216720581,
-0.02348349615931511,
0.03211444243788719,
-0.011796653270721436,
0.022142207249999046,
0.002485982608050108,
0.045611802488565445,
-0.05721253156661987,
-0.012856795452535152,
-0.006264777388423681,
0.0407535545527935,
-0.002052587689831853,
0.004764280281960964,
-0.018381530418992043,
-0.008956566452980042,
-0.006988846696913242,
0.012010171078145504,
0.03827741742134094,
0.05371284857392311,
0.0032910634763538837,
0.006458369083702564,
0.017449112609028816,
-0.0006288805161602795,
-0.0010688427137210965,
-0.002512337639927864,
-0.03940696269273758,
-0.0587238185107708,
0.017856622114777565,
-0.006117152515798807,
-0.02446487918496132,
0.010340302251279354,
0.05727085471153259,
0.04076491296291351,
0.027160359546542168,
0.018283233046531677,
0.037432048469781876,
-0.0381309948861599,
-0.05405152589082718,
0.011448174715042114,
0.011694399639964104,
-0.0572645477950573,
-0.06316501647233963,
0.016412287950515747,
-0.007692634593695402,
0.015436463989317417,
0.054331813007593155,
-0.07644437998533249,
-0.013660681433975697,
0.023034635931253433,
-0.003019475843757391,
0.023608870804309845,
-0.029489779844880104,
0.008035239763557911,
0.02855064906179905,
-0.010479659773409367,
-0.017893347889184952,
0.012524249032139778,
0.015738608315587044,
0.01361668948084116,
0.0037441663444042206,
-0.002373394090682268,
-0.050186850130558014,
-0.07560129463672638,
0.04824377968907356,
-0.036307595670223236,
0.012788789346814156,
-0.0029898961074650288,
-0.09724470227956772,
0.0105623509734869,
0.07153422385454178,
-0.04294101148843765,
-0.006046713795512915,
0.009763834998011589,
0.012634258717298508,
0.039194256067276,
0.01822664588689804,
-0.07880015671253204,
0.032408930361270905,
-0.013431881554424763,
-0.02463630586862564,
0.026562733575701714,
-0.02576810121536255,
0.012307233177125454,
-0.05271706357598305,
0.005652172025293112,
-0.03724909946322441,
-0.024057481437921524,
0.030359603464603424,
0.07448528707027435
] |
<p>I've been wondering exactly why the elements are distributed the way they are on Earth. The heavier elements have their origins in the centers of stars, or in supernovae. After the death of the stars, you end up with a dust cloud containing the heavier elements. Later, planets form out of these along with new stars.</p>
<p>If the heavier elements were randomly distributed in these explosions, how do we end up with special deposits of minerals on Earth? We have mines and special areas where the concentrations of different materials are higher. For example, we have iron, gold, nickel and uranium mines. Why aren't these materials uniformly distributed? Why isn't the Earth composed of a substance which is a uniform mixture of all the heavy elements? Why does it seem there is sometimes a preference for like materials to clump together?</p>
<p>The nickel and iron mostly make up the Earth's core, which I guess makes sense in terms of them being fairly heavy while comparatively abundant relative to heavier elements, but what about everything near the surface that we observe?</p> | g4597 | [
0.06428364664316177,
0.038174327462911606,
-0.0035249944776296616,
0.012709885835647583,
0.02283824421465397,
0.07175468653440475,
0.015163828618824482,
0.00588616356253624,
0.01315213181078434,
-0.06172424182295799,
0.007101352792233229,
0.028351934626698494,
0.0758092850446701,
0.011784711852669716,
0.0039862398989498615,
-0.020108096301555634,
0.011080248281359673,
-0.012598083354532719,
0.018703551962971687,
0.04055074602365494,
-0.011836646124720573,
-0.03523681312799454,
0.049151744693517685,
-0.007243998348712921,
-0.014407791197299957,
0.024559015408158302,
0.021039029583334923,
-0.03335610032081604,
0.05940866097807884,
-0.05132027342915535,
-0.033804554492235184,
-0.010830491781234741,
0.043877892196178436,
-0.01335916854441166,
0.00854166503995657,
-0.03128037601709366,
-0.03216208145022392,
0.004915017168968916,
0.01103428564965725,
-0.011669500730931759,
-0.013613726943731308,
-0.052204620093107224,
0.02597382292151451,
-0.06164927035570145,
-0.021127119660377502,
-0.024023285135626793,
-0.07548089325428009,
-0.02267504669725895,
0.02025906927883625,
0.0029824923258274794,
-0.027581239119172096,
0.019596941769123077,
0.01614859327673912,
0.031234880909323692,
0.06506409496068954,
-0.0013283290900290012,
0.019739700481295586,
-0.016929687932133675,
0.03869527205824852,
-0.05264347419142723,
0.04608090594410896,
0.03267235681414604,
0.04134923592209816,
-0.004264218732714653,
0.07776429504156113,
0.02420654147863388,
-0.05663786083459854,
0.0734160989522934,
0.06747900694608688,
0.026897374540567398,
0.008565920405089855,
-0.007383332587778568,
-0.046932339668273926,
-0.03790394961833954,
-0.04825478792190552,
-0.010650016367435455,
0.012963934801518917,
0.034660376608371735,
-0.0022045632358640432,
0.050987593829631805,
0.01429878082126379,
-0.00008593289385316893,
0.03733927756547928,
-0.014911978505551815,
-0.011638366617262363,
0.012105480767786503,
0.010019459761679173,
0.004719925113022327,
0.0032915726769715548,
-0.006533343810588121,
0.05175327882170677,
0.0315907783806324,
0.04343360289931297,
-0.008180951699614525,
-0.07604897022247314,
-0.03415396437048912,
-0.03396955132484436,
0.050627440214157104,
-0.05058085918426514,
-0.01199613232165575,
-0.008767827413976192,
0.02313070371747017,
0.05839699134230614,
0.016708701848983765,
0.025581905618309975,
-0.022633828222751617,
-0.05223174765706062,
0.03493364527821541,
-0.021126072853803635,
0.02060595154762268,
-0.018820544704794884,
-0.004485864657908678,
-0.013436073437333107,
0.025566333904862404,
-0.0005000477540306747,
0.042269639670848846,
0.08337482064962387,
0.014978129416704178,
0.03580322116613388,
0.049279309809207916,
0.007783464156091213,
0.027137191966176033,
-0.013617424294352531,
-0.0013400568859651685,
-0.037434808909893036,
0.006291835568845272,
0.06177105754613876,
-0.026474662125110626,
0.007357229478657246,
-0.042729929089546204,
0.007300454191863537,
0.012357681058347225,
-0.0547664575278759,
-0.026702309027314186,
0.004732212983071804,
-0.030092349275946617,
-0.05060238763689995,
0.038609378039836884,
0.031230436637997627,
0.03622568026185036,
-0.01903851516544819,
0.07380080223083496,
0.026775917038321495,
-0.06036170572042465,
-0.05330809950828552,
0.002503522438928485,
-0.07580506801605225,
0.008834906853735447,
-0.012937529012560844,
-0.03790414705872536,
0.01737317070364952,
0.00924042146652937,
0.029263779520988464,
-0.10531003028154373,
-0.032464951276779175,
0.0023652638774365187,
-0.007616805378347635,
-0.05928891524672508,
-0.010704862885177135,
-0.02299073338508606,
0.025075925514101982,
-0.01659158058464527,
-0.023641595616936684,
0.012333064340054989,
0.008893745951354504,
0.04824545234441757,
-0.02881045453250408,
-0.00938214547932148,
0.043089449405670166,
0.022334996610879898,
0.02277539111673832,
-0.02801208756864071,
-0.001555047812871635,
0.07071579992771149,
-0.030052296817302704,
0.008285224437713623,
0.11291888356208801,
-0.030418984591960907,
0.006759138312190771,
-0.0120021291077137,
-0.033335573971271515,
-0.01680489256978035,
-0.026924612000584602,
-0.04262925311923027,
0.04394887760281563,
-0.06421592831611633,
0.007216752506792545,
-0.01009936723858118,
0.016747446730732918,
0.021833203732967377,
0.023446286097168922,
-0.05810198560357094,
-0.0061614662408828735,
0.031067045405507088,
0.032533712685108185,
-0.017626913264393806,
-0.04067371040582657,
-0.028181221336126328,
-0.03982469439506531,
-0.03678983077406883,
0.003539309836924076,
-0.01568504050374031,
-0.06614307314157486,
0.0023728501982986927,
0.012320312671363354,
0.0401390939950943,
-0.04967179521918297,
0.057611409574747086,
-0.005512993782758713,
-0.01796567626297474,
0.007367536425590515,
-0.03311990946531296,
-0.0096121309325099,
-0.014333300292491913,
-0.02057548798620701,
0.00008436303323833272,
-0.027401292696595192,
-0.007577673532068729,
0.028475381433963776,
-0.000192276609595865,
-0.03817538917064667,
-0.05021350085735321,
-0.03623827174305916,
-0.03814266622066498,
0.0015869565540924668,
0.03262550011277199,
0.03193381801247597,
0.009943366050720215,
0.035096731036901474,
-0.010804197750985622,
-0.009857230819761753,
0.013100073672831059,
0.005806407425552607,
0.005986656527966261,
0.004361419007182121,
0.01985032670199871,
-0.04382012411952019,
-0.04966552183032036,
-0.03384900838136673,
-0.005116836167871952,
-0.03412514925003052,
-0.01771576516330242,
0.01750309206545353,
-0.01047112699598074,
0.07348573207855225,
-0.05782167613506317,
0.029796365648508072,
-0.020833801478147507,
-0.032409366220235825,
0.03853150084614754,
-0.0010125060798600316,
-0.03476053848862648,
-0.04572957009077072,
-0.020531203597784042,
0.008339614607393742,
-0.07445555925369263,
-0.0024416528176516294,
0.09361429512500763,
-0.01910172589123249,
-0.04949899762868881,
-0.02672831527888775,
-0.03672347217798233,
0.014083144254982471,
-0.004966252483427525,
-0.08010383695363998,
0.04207133129239082,
0.009829469956457615,
-0.026833562180399895,
0.03377106785774231,
-0.019870221614837646,
-0.017986446619033813,
-0.022827574983239174,
0.01004920993000269,
0.07408804446458817,
-0.051979318261146545,
-0.011792147532105446,
-0.014256391674280167,
0.021029824391007423,
0.011529539711773396,
0.023934852331876755,
0.06966204196214676,
0.052578236907720566,
0.005686494056135416,
-0.05654053017497063,
0.051885489374399185,
0.01144089549779892,
-0.0035329912789165974,
-0.03412344679236412,
0.017373405396938324,
-0.02443350851535797,
0.03610330447554588,
-0.07197732478380203,
0.023800784721970558,
0.021637141704559326,
0.011369148269295692,
0.0256176944822073,
0.024711227044463158,
0.000890648050699383,
-0.0647139772772789,
0.06296855956315994,
-0.02154405415058136,
-0.02877373993396759,
0.049606453627347946,
0.018106138333678246,
-0.04776834696531296,
0.05340812727808952,
0.036079879850149155,
-0.024080537259578705,
-0.06194337084889412,
-0.07245735079050064,
0.012505076825618744,
0.07250132411718369,
0.017404325306415558,
0.05565226823091507,
-0.052002955228090286,
0.01465246919542551,
-0.013673878274857998,
-0.0016264984151348472,
0.08928914368152618,
-0.09027575701475143,
-0.04807594418525696,
-0.00490779522806406,
0.028619244694709778,
-0.03992856666445732,
0.015513197518885136,
-0.030726375058293343,
-0.04195350036025047,
-0.0060417624190449715,
-0.028255101293325424,
-0.027477608993649483,
-0.022785721346735954,
0.013223700225353241,
-0.06876736879348755,
0.031021710485219955,
-0.12310782819986343,
0.02406093291938305,
-0.02350573055446148,
0.027867473661899567,
0.0659882053732872,
-0.005361315328627825,
0.028872067108750343,
0.005280559416860342,
-0.052074771374464035,
-0.008851519785821438,
-0.05254705250263214,
-0.005997528787702322,
0.021030845120549202,
-0.012979965656995773,
-0.014922164380550385,
0.047297410666942596,
0.0013268353650346398,
0.0011051244800910354,
0.03530941531062126,
-0.032311297953128815,
-0.02522885799407959,
0.014878285117447376,
0.014929174445569515,
-0.033190540969371796,
0.015997935086488724,
-0.04114152118563652,
0.04109291359782219,
-0.019626149907708168,
-0.017402706667780876,
-0.05111119523644447,
-0.03355054557323456,
0.016582705080509186,
0.04566905274987221,
-0.033133119344711304,
0.03820441663265228,
0.0378701351583004,
0.06091757491230965,
0.061954792588949203,
-0.009347056038677692,
-0.0022530308924615383,
0.05843786150217056,
0.001633971813134849,
0.04302826523780823,
0.016830813139677048,
0.0018110953969880939,
-0.07794845849275589,
-0.017595350742340088,
-0.014309700578451157,
0.020078515633940697,
-0.005824678111821413,
0.05856606364250183,
-0.019261039793491364,
-0.010337414219975471,
-0.045912034809589386,
-0.03708995506167412,
-0.024850040674209595,
0.01878993585705757,
-0.10072363168001175,
-0.027151281014084816,
0.014203094877302647,
0.017966624349355698,
-0.013455360196530819,
-0.008661195635795593,
0.011020028032362461,
0.05480869486927986,
0.04992133751511574,
-0.004285816103219986,
0.006565974559634924,
-0.007763615343719721,
-0.03808262199163437,
0.008483669720590115,
0.05663244053721428,
-0.026610558852553368,
-0.07385195791721344,
-0.01837810128927231,
-0.04876064136624336,
0.053403209894895554,
0.04865361005067825,
-0.042220745235681534,
0.0068830642849206924,
0.013879834674298763,
-0.010510609485208988,
0.003605247475206852,
0.016892094165086746,
-0.015082192607223988,
-0.04934243485331535,
-0.0019308753544464707,
0.03256642818450928,
0.04201720654964447,
-0.025278078392148018,
0.02595341205596924,
0.03243559971451759,
-0.007384888362139463,
-0.07257915288209915,
-0.0019758373964577913,
0.02749900333583355,
-0.01590869575738907,
0.013430248945951462,
0.03359576314687729,
0.021068355068564415,
-0.059637509286403656,
-0.022890053689479828,
-0.03826700896024704,
0.030959036201238632,
0.008606585673987865,
0.043819740414619446,
0.06556738168001175,
0.006597061641514301,
-0.035570964217185974,
0.08461125940084457,
0.0006409899215213954,
0.02979469485580921,
-0.01948387362062931,
0.01979600079357624,
-0.05117359384894371,
-0.004960071761161089,
0.0023480949457734823,
-0.012417247518897057,
0.0050824484787881374,
-0.027101987972855568,
-0.006992469076067209,
-0.01945083774626255,
0.01560265477746725,
0.0468328520655632,
0.04416108503937721,
0.05719892308115959,
-0.03345504403114319,
-0.037720996886491776,
-0.0033337657805532217,
0.05144232511520386,
-0.025171086192131042,
-0.003520675003528595,
-0.04266298562288284,
-0.009009456261992455,
-0.03820991516113281,
0.01830815151333809,
-0.0036098812706768513,
-0.009818259626626968,
0.0487639419734478,
0.03372268006205559,
0.043642833828926086,
0.016465263441205025,
0.0033299769274890423,
-0.07646692544221878,
0.03571965545415878,
-0.05342859402298927,
-0.0509115606546402,
0.014304065145552158,
-0.002715486101806164,
0.045579083263874054,
-0.013375342823565006,
0.007790793664753437,
-0.025855259969830513,
-0.03865065053105354,
0.02107863686978817,
-0.03287537768483162,
-0.005877567920833826,
-0.03800622746348381,
0.07352116703987122,
-0.036109358072280884,
0.05051484331488609,
-0.07130949199199677,
0.025780675932765007,
-0.011297957971692085,
-0.028274573385715485,
-0.028865879401564598,
0.00821282435208559,
0.036998894065618515,
-0.09774749726057053,
-0.0004616726946551353,
0.058802634477615356,
0.03417603671550751,
0.04809851571917534,
-0.03637681156396866,
0.07669542729854584,
-0.032131221145391464,
0.03842543810606003,
0.02824334241449833,
-0.016878444701433182,
0.018530448898673058,
-0.0017157216789200902,
0.014454311691224575,
-0.02103603444993496,
0.020839888602495193,
0.029523858800530434,
0.02863212674856186,
-0.06426011025905609,
0.01222000177949667,
0.05016427859663963,
0.004183984827250242,
0.03918062150478363,
-0.028932902961969376,
-0.03977242484688759,
-0.021788829937577248,
0.022788850590586662,
0.029508693143725395,
0.010594227351248264,
0.03358807414770126,
0.04667062684893608,
-0.029335077852010727,
-0.01759868487715721,
0.019979972392320633,
0.026453906670212746,
0.01202051155269146,
0.04623618349432945,
0.03914058580994606,
-0.0009034340619109571,
-0.04757056012749672,
0.019569460302591324,
0.04289569333195686,
0.039094991981983185,
-0.004280031658709049,
0.021227316930890083,
0.04996424540877342,
0.06361706554889679,
-0.011095521971583366,
0.004960951395332813,
0.08042560517787933,
0.041398659348487854,
0.026064535602927208,
-0.04027789458632469,
0.022092461585998535,
-0.0041053034365177155,
0.019028697162866592,
-0.011669299565255642,
-0.03630823642015457,
-0.0026227261405438185,
0.010712833143770695,
-0.02096732333302498,
-0.02915864624083042,
0.012240069918334484,
-0.049593236297369,
0.0036921037826687098,
-0.0394921638071537,
0.041909631341695786,
0.02881183661520481,
0.02528195269405842,
0.012742665596306324,
0.012950102798640728,
0.026056351140141487,
0.002104849321767688,
-0.01664869114756584,
-0.078179270029068,
-0.026498720049858093,
-0.040093209594488144,
0.007262341678142548,
0.06468089669942856,
0.022648105397820473,
0.012574863620102406,
0.0300934836268425,
-0.0038341088220477104,
0.008034797385334969,
-0.0038146988954395056,
0.010959207080304623,
-0.006224214099347591,
-0.0933525487780571,
0.07869008183479309,
0.022593442350625992,
0.036620620638132095,
0.023769818246364594,
-0.05919859930872917,
-0.017993111163377762,
-0.005976302549242973,
0.01908932626247406,
-0.044615648686885834,
-0.041689302772283554,
0.0021105811465531588,
0.023624341934919357,
0.073190838098526,
0.0350659154355526,
0.05653496831655502,
-0.05661578103899956,
0.029256179928779602,
-0.0021444505546242,
0.0161973275244236,
0.030407877638936043,
0.04404741898179054,
0.009054861962795258,
-0.04024553671479225,
0.0058068884536623955,
-0.03564075380563736,
-0.05568912997841835,
-0.05949137732386589,
0.0006439817952923477,
0.010229038074612617,
0.03515417501330376,
-0.015345821157097816,
0.008439898490905762,
-0.006512957625091076,
-0.010359779931604862,
0.010231303051114082,
0.019725145772099495,
-0.03249672055244446,
0.05729679763317108,
0.058752335608005524,
-0.00044928037095814943,
-0.026158543303608894,
0.049310650676488876,
-0.0022554623428732157,
0.03597312420606613,
-0.010458743199706078,
0.03455514460802078,
-0.006213643122464418,
-0.0022381313610821962,
0.03299793601036072,
0.009915424510836601,
-0.017083212733268738,
-0.030383996665477753,
0.02540549449622631,
0.027916869148612022,
0.001990651013329625,
0.020833700895309448,
0.015858648344874382,
-0.003703937865793705,
0.0015336504438892007,
0.012617974542081356,
0.013043501414358616,
-0.03456927835941315,
0.010608809068799019,
-0.03045605681836605,
0.01565057598054409,
0.023454822599887848,
0.01785219833254814,
-0.04543900117278099,
0.015038101002573967,
-0.08249154686927795,
-0.09184811264276505,
0.010208751074969769,
-0.015999704599380493,
0.012661628425121307,
-0.026365438476204872,
0.05067618563771248,
0.0542425662279129,
-0.01946345716714859,
-0.05751737579703331,
0.06277260184288025,
0.0006389411864802241,
0.041704874485731125,
0.001952307648025453,
0.008278479799628258,
0.0032663121819496155,
0.03949214518070221,
-0.048136357218027115,
-0.04587026312947273,
0.07177751511335373,
-0.004501710180193186,
0.04888550937175751,
0.02298308163881302,
-0.017062442377209663,
-0.024333734065294266,
-0.02308504469692707,
0.015265428461134434,
-0.013746334239840508,
0.026749495416879654,
-0.036674048751592636,
0.0003640643262770027,
0.021342985332012177,
0.012908379547297955,
0.033961594104766846,
-0.024720992892980576,
-0.014010845683515072,
-0.03379988670349121,
0.0441153347492218,
-0.029837938025593758,
0.03226592391729355,
0.016406826674938202,
-0.03736289590597153,
-0.04641597718000412,
-0.005508233327418566,
-0.0705779641866684,
0.03461270034313202,
-0.027614856138825417,
-0.01429154071956873,
0.07517164200544357,
-0.04278991371393204,
-0.02012949436903,
0.03348297253251076,
0.0393221490085125,
0.06738517433404922,
-0.01989654451608658,
-0.012318337336182594,
0.00432664854452014,
-0.006796028930693865,
-0.0049423580057919025,
-0.01981484517455101,
0.00828101858496666,
-0.0518464595079422,
0.008497917093336582,
0.0323309525847435,
-0.05612199380993843,
0.01686481200158596,
0.043917521834373474,
0.06493625789880753,
-0.035864003002643585,
0.01581217348575592,
0.021916426718235016,
-0.03592834621667862,
0.02695281431078911,
-0.020420875400304794,
-0.0064489999786019325,
0.011752708815038204,
-0.03873584792017937,
0.051191020756959915,
-0.051404207944869995,
-0.08918223530054092,
-0.0409822091460228,
0.005870594177395105,
-0.04973019286990166,
-0.01539183035492897,
-0.015196616761386395,
-0.048680681735277176,
-0.017011061310768127,
-0.045735716819763184,
0.02424965612590313,
-0.049361325800418854,
-0.059398163110017776,
-0.05057024955749512,
0.004695519804954529,
-0.04045796021819115,
0.03233747184276581,
-0.000884753477293998,
-0.0032150691840797663,
0.045795951038599014,
0.03586065396666527,
0.0002505692536942661,
-0.023120541125535965,
-0.025850508362054825,
-0.011408322490751743,
-0.04765057936310768,
0.0024632075801491737,
-0.0557962991297245,
0.008001274429261684,
-0.010536141693592072,
-0.0033600497990846634
] |
<blockquote>
<p><em>A) Explain how Kepler's $2^{nd}$ law - "The radius vector from the Sun to a planet sweeps out equal areas in equal time intervals" - can be understood in terms of angular momentum conservation.</em></p>
</blockquote>
<p>I know that:</p>
<p>Angular momentum is conserved and therefore $\vec{L}=\vec{r} \times \vec{p}=\vec{r} \times m\vec{v}=constant$ and $L=mrv\sin\theta$.</p>
<p>Kepler's $2^{nd}$ law means $\frac{dA}{dt}=constant$</p>
<p>Somehow this comes out to be $dA=(\frac{1}{2})(\frac{L}{m})dt$ but I'm having a hard time getting there.</p>
<blockquote>
<p><em>B) Explain how circular motion can be described as simple harmonic motion.</em></p>
</blockquote>
<p>I know that:</p>
<p>For circular motion
$m\vec{a}=\vec{F}_{c}=-m\frac{v^2}{R}\vec{r}=-m\omega^2R\vec{r}$</p>
<p>However, I'm fairly lost on this equation. Where does the negative sign come from, and where does the $\vec{r}$ come from?</p> | g4598 | [
0.0480785071849823,
-0.0035921589005738497,
-0.011702898889780045,
0.0248876865953207,
0.029638109728693962,
0.020336663350462914,
0.08018840104341507,
-0.030387915670871735,
0.008263610303401947,
0.015389754436910152,
-0.026141280308365822,
0.029811453074216843,
0.044029951095581055,
0.006461209151893854,
0.04405250400304794,
-0.029629748314619064,
-0.001031499239616096,
0.035520389676094055,
0.0649178996682167,
0.043722964823246,
-0.028903815895318985,
-0.00955246388912201,
0.007184379268437624,
-0.03302803263068199,
0.020185742527246475,
0.024153824895620346,
0.030312566086649895,
-0.010392539203166962,
-0.04580726847052574,
-0.025470422580838203,
0.025630760937929153,
-0.016878480091691017,
0.007078064139932394,
-0.09557310491800308,
-0.026233863085508347,
0.020311830565333366,
0.028028147295117378,
-0.0284873154014349,
0.03363807871937752,
-0.006659565027803183,
0.041482094675302505,
-0.020196203142404556,
0.0013404205674305558,
0.006544562987983227,
0.04194464534521103,
-0.016512522473931313,
-0.058453578501939774,
-0.004332518205046654,
-0.02895573154091835,
0.032789185643196106,
-0.04183618724346161,
0.058709003031253815,
0.07409612834453583,
-0.003876719158142805,
0.007213192526251078,
0.06724072992801666,
-0.0015714542241767049,
-0.06938081979751587,
0.010423601604998112,
0.015971222892403603,
-0.011295209638774395,
-0.020118312910199165,
-0.010401859879493713,
0.012617119587957859,
0.0667046532034874,
-0.008362953551113605,
-0.018526792526245117,
0.02976134978234768,
0.041476059705019,
0.031216926872730255,
0.056011613458395004,
-0.0204100850969553,
-0.026274675503373146,
-0.04422784969210625,
-0.029255257919430733,
0.004832135513424873,
0.009353435598313808,
-0.018041864037513733,
0.03459455817937851,
0.013170485384762287,
-0.04827670380473137,
0.04462974891066551,
-0.011731650680303574,
0.0268776286393404,
0.061290442943573,
-0.011794932186603546,
0.026169102638959885,
0.00022943640942685306,
-0.022699126973748207,
-0.023935722187161446,
0.04819686338305473,
-0.05086177587509155,
0.030072828754782677,
-0.015746014192700386,
0.0035231998190283775,
-0.0036200194153934717,
-0.05685119703412056,
0.03793810307979584,
-0.024226775392889977,
-0.039764683693647385,
0.052751053124666214,
0.012052595615386963,
-0.007130161393433809,
-0.04162105545401573,
0.07125074416399002,
0.043830227106809616,
0.052278660237789154,
0.018169011920690536,
0.017717616632580757,
0.0011579504935070872,
0.002236598404124379,
-0.08079539239406586,
-0.02262032777070999,
-0.028969338163733482,
-0.01940743438899517,
-0.03677232563495636,
0.09714110195636749,
-0.02466910518705845,
0.031891658902168274,
0.10523898154497147,
0.030115261673927307,
0.07752477377653122,
0.008000103756785393,
0.0808042511343956,
-0.011969109997153282,
-0.018188687041401863,
0.019055122509598732,
-0.011328608728945255,
0.09217601269483566,
0.031727276742458344,
0.0009572308626957238,
-0.00007750387885607779,
-0.02310725674033165,
0.014585419557988644,
0.03820141404867172,
0.008211194537580013,
-0.0037483558990061283,
0.013675915077328682,
-0.03436896204948425,
-0.03480693697929382,
-0.009236259385943413,
-0.003454220946878195,
0.0702565610408783,
-0.027036616578698158,
-0.07593128085136414,
-0.006222829222679138,
0.01492718793451786,
-0.045261505991220474,
0.0678422600030899,
-0.05642097070813179,
-0.014668608084321022,
0.07241076976060867,
0.015454021282494068,
-0.030550464987754822,
0.04764436557888985,
-0.024710509926080704,
0.03322077915072441,
0.024469774216413498,
-0.02414792776107788,
0.031211011111736298,
0.08968563377857208,
-0.002761602634564042,
-0.022144151851534843,
0.03310893476009369,
-0.06691426783800125,
-0.007525110617280006,
-0.013599484227597713,
-0.04898613318800926,
-0.012728367000818253,
-0.011781914159655571,
-0.052543219178915024,
-0.009780768305063248,
0.030322542414069176,
0.025330232456326485,
-0.06603828817605972,
0.010002978146076202,
-0.03569766879081726,
-0.04395327717065811,
-0.012168214656412601,
0.013716364279389381,
-0.01418278831988573,
-0.012773225083947182,
0.0492536835372448,
0.035487569868564606,
0.042660631239414215,
0.026642363518476486,
0.03241798281669617,
-0.0025507546961307526,
-0.04683322086930275,
-0.007038685493171215,
0.002719264244660735,
-0.03097396343946457,
-0.025951411575078964,
0.02574249915778637,
-0.010413466952741146,
0.03400348871946335,
-0.05160926654934883,
-0.04778197035193443,
-0.08148276060819626,
0.07550569623708725,
0.018740881234407425,
0.011739970184862614,
0.040099576115608215,
0.026037542149424553,
0.022427905350923538,
0.018153661862015724,
0.02870284393429756,
0.024959271773695946,
0.06948456913232803,
0.05091813951730728,
0.01210173312574625,
-0.03346370905637741,
-0.059177447110414505,
0.02352134883403778,
-0.02904757857322693,
-0.028973910957574844,
0.01716526784002781,
0.03322337940335274,
-0.050779640674591064,
-0.023649156093597412,
-0.029977530241012573,
-0.050854362547397614,
0.025771748274564743,
-0.008563310839235783,
-0.00174302130471915,
0.04654662311077118,
-0.04453422129154205,
0.00011973576329182833,
0.050061993300914764,
0.06393827497959137,
-0.06049343943595886,
-0.01867380365729332,
-0.035991087555885315,
0.04643642529845238,
0.02184489369392395,
0.015577862039208412,
-0.0037008230574429035,
-0.017673034220933914,
-0.017799463123083115,
0.008350010961294174,
0.026568913832306862,
0.014270258136093616,
-0.030957765877246857,
-0.04678197577595711,
0.04685837775468826,
-0.0209629088640213,
0.07768258452415466,
0.019053896889090538,
0.005876761395484209,
0.021009832620620728,
0.004909572657197714,
0.004170127213001251,
-0.004384015686810017,
-0.02829686552286148,
0.04742303863167763,
-0.02437959611415863,
-0.00842991005629301,
0.06398969888687134,
-0.06476935744285583,
-0.021147986873984337,
-0.003023876342922449,
-0.013220020569860935,
0.030073389410972595,
0.04669239744544029,
-0.022442737594246864,
-0.0638134777545929,
-0.05064843222498894,
0.054868441075086594,
0.061940670013427734,
0.00211863755248487,
-0.02372722700238228,
0.08218187093734741,
-0.03709951788187027,
0.043533843010663986,
-0.04735482484102249,
-0.0705203264951706,
0.014034434221684933,
-0.023522205650806427,
-0.013662182725965977,
0.030284840613603592,
-0.01080128364264965,
0.03307792916893959,
-0.0009057075949385762,
0.0031023453921079636,
0.06782737374305725,
-0.021792978048324585,
-0.021213771775364876,
0.08806529641151428,
-0.0042984141036868095,
0.00002438044612063095,
-0.04045146703720093,
0.024767586961388588,
0.021160319447517395,
-0.01576005108654499,
0.015212370082736015,
0.05834720656275749,
-0.02673455700278282,
-0.03942527249455452,
-0.006776726804673672,
0.010320943780243397,
0.03308665007352829,
-0.03894754871726036,
-0.032153233885765076,
0.0004719328717328608,
-0.033335063606500626,
-0.0011173016391694546,
0.0050189602188766,
-0.0584954209625721,
-0.035758186131715775,
0.0682685524225235,
-0.05546391382813454,
0.023484036326408386,
-0.0384942851960659,
-0.009234783239662647,
-0.03489500656723976,
-0.003676054300740361,
-0.04284113273024559,
-0.015166770666837692,
0.024374008178710938,
0.03710125759243965,
-0.0776413083076477,
-0.07553771883249283,
-0.014474943280220032,
0.010871106758713722,
0.01073130127042532,
0.03586646914482117,
-0.07296240329742432,
-0.0327635258436203,
-0.035661742091178894,
-0.02974722348153591,
-0.04992438852787018,
0.026775887235999107,
-0.006949542090296745,
0.021076470613479614,
-0.05096908286213875,
-0.03860477730631828,
-0.07042714208364487,
0.04788149520754814,
0.05260966345667839,
-0.02402091771364212,
0.018831942230463028,
-0.02181330695748329,
-0.06142484396696091,
-0.020580174401402473,
-0.007979058660566807,
0.03234541416168213,
0.0032343522179871798,
0.03718819096684456,
0.05002104118466377,
-0.024394700303673744,
0.014894426800310612,
-0.01360319647938013,
0.01580837368965149,
-0.0030986182391643524,
-0.021071448922157288,
0.05772930756211281,
0.01727915368974209,
0.012322680093348026,
0.009553449228405952,
-0.0015095104463398457,
0.01075192354619503,
-0.019699066877365112,
-0.0006794782821089029,
0.03736954554915428,
0.013645194470882416,
-0.0023620445281267166,
-0.019594324752688408,
0.013523113913834095,
0.004617385566234589,
0.009235099889338017,
0.04261787235736847,
-0.01874515973031521,
-0.04047926142811775,
0.02615802176296711,
0.03617468103766441,
-0.014667337760329247,
0.003586546517908573,
0.06945357471704483,
-0.019526515156030655,
0.02894992008805275,
0.002630529459565878,
0.005550178699195385,
0.03558358922600746,
0.02831823006272316,
-0.01019275188446045,
0.014425579458475113,
-0.03140995278954506,
0.05715043097734451,
0.0044519309885799885,
-0.04805951938033104,
0.020702380686998367,
-0.03949327394366264,
0.0437997505068779,
-0.059816524386405945,
0.03037680871784687,
-0.04919803887605667,
0.011827272363007069,
0.018323371186852455,
-0.043293535709381104,
0.019737843424081802,
-0.023718373849987984,
0.0033479866106063128,
-0.010361503809690475,
-0.00048197596333920956,
-0.003975046332925558,
0.05492321029305458,
-0.022632086649537086,
0.014358466491103172,
0.005328125786036253,
0.005573660135269165,
-0.002038966165855527,
-0.009162222035229206,
0.0400066040456295,
-0.030112851411104202,
0.05823710933327675,
0.02685132808983326,
-0.0010174853960052133,
-0.03117179684340954,
0.0252796933054924,
0.027021747082471848,
-0.048815347254276276,
0.03439360111951828,
0.006354890298098326,
-0.05057738348841667,
0.027961479499936104,
0.07592923194169998,
0.038505591452121735,
-0.027920670807361603,
-0.003343702992424369,
-0.03176617622375488,
-0.0011160868452861905,
-0.004757802002131939,
0.022715900093317032,
0.0015066812047734857,
-0.10418203473091125,
0.04986915364861488,
-0.06832625716924667,
0.0729655921459198,
0.014330311678349972,
0.04236200451850891,
0.02548801153898239,
-0.004477419424802065,
0.009852461516857147,
0.0002779174246825278,
-0.03935656696557999,
0.0349293053150177,
0.06568296998739243,
-0.03034745343029499,
0.027058793231844902,
-0.044034238904714584,
-0.036795176565647125,
0.03806827589869499,
0.01961679942905903,
-0.024352462962269783,
0.00522391265258193,
-0.0013514446327462792,
-0.09283565729856491,
0.029894540086388588,
0.02677624300122261,
-0.05632230266928673,
-0.06625808030366898,
0.047087375074625015,
-0.004619675688445568,
-0.0068610431626439095,
0.07867787778377533,
-0.009272601455450058,
-0.017846068367362022,
0.021556977182626724,
0.006068696267902851,
0.029827972874045372,
0.03268413990736008,
0.008349479176104069,
-0.011943328194320202,
-0.03799961507320404,
0.007871455512940884,
-0.046752654016017914,
0.025975195690989494,
0.022936386987566948,
0.010192225687205791,
-0.03572924807667732,
-0.009278830140829086,
0.024378011003136635,
0.009513791650533676,
0.03512924164533615,
0.030191512778401375,
-0.012267820537090302,
-0.03892320767045021,
-0.03716108202934265,
0.024098727852106094,
0.0030318184290081263,
-0.02004079334437847,
0.07383386045694351,
-0.0009087664657272398,
0.022669190540909767,
0.05491436645388603,
0.03344886749982834,
-0.0009635819005779922,
-0.056407034397125244,
-0.059524182230234146,
-0.03637992963194847,
-0.07884468883275986,
-0.016254927963018417,
-0.026688046753406525,
-0.005710828583687544,
0.03584062308073044,
-0.007460187654942274,
-0.023194337263703346,
0.014906140975654125,
-0.010823697783052921,
0.018980136141180992,
0.002538067754358053,
0.03756348416209221,
-0.030482178553938866,
0.006544303148984909,
-0.005133674014359713,
-0.02982882224023342,
0.026946930214762688,
0.007790339644998312,
-0.005720864050090313,
0.009422608651220798,
0.0021317426580935717,
0.01208497490733862,
0.023124778643250465,
-0.03337542340159416,
0.045301925390958786,
-0.0037882502656430006,
-0.05376187339425087,
-0.04325796291232109,
0.06048937886953354,
0.028403080999851227,
-0.016784582287073135,
-0.03635948896408081,
0.014248869381844997,
0.014888004399836063,
-0.060006000101566315,
-0.038411956280469894,
0.0005138147389516234,
-0.0024840468540787697,
0.01034675631672144,
-0.024214016273617744,
-0.046791788190603256,
-0.04841259494423866,
0.022335724905133247,
0.05347732454538345,
-0.07545509934425354,
0.0015898201381787658,
0.028016602620482445,
-0.011515647172927856,
0.016599738970398903,
-0.018355216830968857,
-0.05282248929142952,
0.0030874910298734903,
-0.005287318956106901,
-0.017001429572701454,
-0.0259384848177433,
0.012907815165817738,
-0.006612229626625776,
0.008338295854628086,
-0.033882901072502136,
-0.04712134972214699,
-0.01624090038239956,
0.02099764533340931,
0.005885416176170111,
0.01306160632520914,
0.027314644306898117,
0.01387402880936861,
0.04990847408771515,
0.010387742891907692,
0.05746926739811897,
0.06169230118393898,
-0.005017395131289959,
0.04202224686741829,
0.008696633391082287,
0.035014353692531586,
0.07785088568925858,
0.0235885102301836,
-0.03417874500155449,
-0.0007786105270497501,
-0.0985155701637268,
-0.02482503652572632,
0.04184609279036522,
0.003948098048567772,
0.03101360984146595,
-0.014757413417100906,
-0.06825066357851028,
0.06416153907775879,
-0.026853786781430244,
-0.03653842583298683,
0.04281630739569664,
-0.002026692731305957,
-0.007829724811017513,
0.01632036827504635,
-0.02396063506603241,
0.032457347959280014,
-0.012160327285528183,
0.03404220566153526,
0.009068102575838566,
-0.010659731924533844,
-0.008344101719558239,
-0.021694177761673927,
0.003280553501099348,
-0.01827971823513508,
0.0018036316614598036,
-0.02972932904958725,
0.05363187938928604,
0.004023874644190073,
-0.035466812551021576,
-0.02328038588166237,
-0.027169300243258476,
0.0417083278298378,
-0.04704972729086876,
0.021525830030441284,
0.027691146358847618,
0.004787016659975052,
-0.02269376441836357,
-0.0012212703004479408,
-0.013354740105569363,
0.0023889795411378145,
-0.01255424227565527,
-0.0026724867057055235,
0.012421580031514168,
0.014677703380584717,
-0.030474931001663208,
-0.017252560704946518,
0.059132665395736694,
0.030205653980374336,
-0.02496442012488842,
0.0068778968416154385,
0.05414891615509987,
0.04874613136053085,
0.02071002498269081,
-0.030770331621170044,
-0.03872804343700409,
0.08816314488649368,
0.025386380031704903,
0.019244641065597534,
-0.0899900570511818,
0.05612149089574814,
0.04690413177013397,
0.014296956360340118,
-0.015730993822216988,
0.021250221878290176,
0.03534410148859024,
-0.022448629140853882,
-0.06669300049543381,
-0.029299605637788773,
0.004467133432626724,
-0.046297747641801834,
-0.06666095554828644,
-0.011709191836416721,
0.027261238545179367,
0.00408706720918417,
-0.00574100948870182,
-0.044973522424697876,
-0.008761217817664146,
-0.004143827594816685,
-0.026682034134864807,
0.04333933815360069,
0.0038178313989192247,
-0.09169019013643265,
-0.03590858727693558,
-0.04609585553407669,
0.01497782301157713,
-0.0056411586701869965,
0.040414635092020035,
-0.0037131926510483027,
-0.012875593267381191,
0.008976291865110397,
0.04387260973453522,
-0.07625236362218857,
0.01583717204630375,
0.03462253138422966,
-0.04492676630616188,
0.002115070354193449,
-0.0633351281285286,
0.02107621729373932,
0.022309908643364906,
-0.0461207777261734,
-0.02357085607945919,
-0.018422624096274376,
-0.028244316577911377,
-0.0417705662548542,
0.013910805806517601,
-0.0013066533720120788,
-0.01647132635116577,
-0.01684214174747467,
-0.07536684721708298,
0.02832397259771824,
0.01895327679812908,
-0.01939726434648037,
-0.005630725063383579,
0.08197201043367386,
-0.02068806067109108,
-0.022446423768997192,
0.05050884559750557,
-0.011789140291512012,
0.03798248991370201,
0.024533351883292198,
-0.06290484964847565,
-0.013792173005640507,
0.013664488680660725,
-0.022543223574757576,
0.0018724579131230712,
0.021845653653144836,
0.06426647305488586,
0.015053514391183853,
-0.005081239156424999,
-0.058081045746803284,
-0.043953243643045425,
0.004425822291523218,
0.007040328811854124,
-0.06376064568758011,
-0.038578178733587265,
-0.042555585503578186,
0.03966891020536423,
0.0165974460542202,
0.03049289807677269,
0.024173684418201447,
0.005833622999489307,
-0.026683393865823746,
-0.01190051157027483,
-0.04524378851056099,
0.02334507554769516,
-0.13403256237506866,
-0.03067510761320591,
-0.015129582025110722,
-0.01264325063675642,
-0.023934736847877502,
0.0077171120792627335,
-0.0017796845640987158,
-0.0339353010058403,
-0.028076522052288055,
-0.04147471487522125,
0.02001148648560047,
-0.014394506812095642,
0.014138109982013702,
-0.03690950199961662,
-0.03870777785778046,
-0.03956623747944832,
0.001049799146130681,
0.032439619302749634,
-0.043138518929481506,
0.023909224197268486,
-0.017607906833291054,
-0.0386660061776638,
-0.023491915315389633,
-0.004961692728102207,
0.014628908596932888,
0.028483839705586433,
-0.04876883700489998,
0.04585077613592148,
0.05561478063464165,
-0.016264986246824265,
0.0020805266685783863,
0.023080186918377876,
-0.02968095801770687,
-0.0055091492831707,
-0.028496917337179184,
0.010764281265437603,
-0.03984897583723068,
-0.019597524777054787,
0.019145242869853973,
0.0032687350176274776,
-0.0312526598572731,
0.007225763518363237,
-0.07384321093559265,
-0.0661688968539238,
0.05449600890278816
] |
<p>Suppose there's some satellite orbiting the earth in circular motion. Suppose there's an asteroid that hits the satellite in the same direction as the instant velocity vector of the satellite. The collision causes the satellite to move faster. And here are my 2 questions:</p>
<p>1) Why will the satellite start moving in an elliptical orbit? Is it because its speed has increased, but the centripetal acceleration hasn't? It seems intuitively right for me, because then the satellite covers larger path before the centripetal acceleration causes the change in the velocity vector direction.</p>
<p>2) However, what confuses me is the fact that the centripetal acceleration is dependent on the velocity ($v^2/r$). On the other hand, since the force of gravity exerted on the satellite by the earth, hasn't changed after the hit (if we neglect asteroid's mass or suppose it just fell down after the hit), because there was no change in the radius (i suppose) of the circular path, there was no change in the centripetal acceleration. So these two arguments contradict each other. Where am I wrong? What I miss here? </p>
<p>Thanks in advance.</p> | g4599 | [
0.07480235397815704,
0.02234725095331669,
0.018658950924873352,
0.05753518268465996,
0.047308411449193954,
0.03521713241934776,
0.010147047229111195,
-0.011483845300972462,
-0.053866907954216,
-0.009734699502587318,
0.03422366827726364,
0.012655717320740223,
0.09854979068040848,
-0.039654891937971115,
0.011584158055484295,
-0.04799798130989075,
0.05990029498934746,
-0.028953349217772484,
-0.017747901380062103,
0.08913367241621017,
-0.019378380849957466,
-0.03571236878633499,
-0.04870370402932167,
-0.03815065696835518,
0.04637265205383301,
0.0458575114607811,
0.027135195210576057,
-0.012309749610722065,
-0.022714534774422646,
0.035194214433431625,
0.02097468078136444,
-0.027528127655386925,
0.02357563190162182,
-0.07705748826265335,
-0.02478800155222416,
-0.004081440158188343,
0.031295593827962875,
-0.008629629388451576,
-0.006878355052322149,
-0.01568600721657276,
0.02478165179491043,
-0.07313522696495056,
0.014028742909431458,
0.01176546048372984,
0.009990215301513672,
-0.02950395457446575,
0.014370182529091835,
-0.005360222887247801,
0.0036863815039396286,
0.017028266564011574,
-0.05770699307322502,
0.028327923268079758,
0.06356842815876007,
-0.023480774834752083,
-0.006135860923677683,
0.04142230376601219,
0.07090408354997635,
-0.01732797361910343,
0.040531791746616364,
0.008846007287502289,
-0.06712348014116287,
0.011603123508393764,
-0.007221721578389406,
-0.058415185660123825,
0.050142206251621246,
-0.08051495254039764,
0.008113997057080269,
0.011965179815888405,
0.0017033866606652737,
-0.016619684174656868,
0.000039443511923309416,
-0.005155039485543966,
-0.04900938272476196,
-0.05696874484419823,
-0.03303355351090431,
-0.01847993955016136,
0.015594612807035446,
-0.03308551385998726,
0.01645391806960106,
-0.024809731170535088,
-0.017118830233812332,
0.07234126329421997,
0.00581715814769268,
-0.01721443049609661,
0.049182869493961334,
-0.023103967308998108,
-0.014303906820714474,
0.02373393252491951,
-0.015114843845367432,
-0.03194259852170944,
0.030968356877565384,
-0.06944312155246735,
0.013146772049367428,
0.035515088587999344,
-0.032177578657865524,
-0.05608585476875305,
-0.05953250452876091,
0.0838293582201004,
0.042251601815223694,
0.057600237429142,
-0.028824029490351677,
-0.03767598792910576,
0.029192043468356133,
-0.01924765855073929,
0.02138732746243477,
-0.010855363681912422,
0.00705188000574708,
0.01985826902091503,
0.020169764757156372,
-0.03487949073314667,
-0.013056614436209202,
-0.08891300112009048,
0.03326280415058136,
-0.009281737729907036,
-0.018153635784983635,
-0.03418254479765892,
0.015459386631846428,
0.022942252457141876,
-0.005709387362003326,
0.0542251318693161,
-0.034871529787778854,
0.03318334370851517,
-0.017758918926119804,
0.04908598214387894,
-0.020677397027611732,
0.01393095776438713,
0.017023522406816483,
0.004720499739050865,
0.042199064046144485,
0.011681784875690937,
-0.055398471653461456,
0.015285006724298,
0.03251483291387558,
0.028402229771018028,
0.024885891005396843,
0.02259666845202446,
-0.03743012994527817,
-0.01570139266550541,
-0.03219868242740631,
-0.0011354744201526046,
-0.039650801569223404,
0.016516728326678276,
0.01903100684285164,
-0.023661892861127853,
-0.08064939826726913,
0.05565759167075157,
0.021238407120108604,
-0.02559339813888073,
0.06215377897024155,
0.019811859354376793,
-0.008988618850708008,
0.05411713197827339,
-0.010212749242782593,
-0.05227123573422432,
0.0348421148955822,
0.025405993685126305,
0.031229523941874504,
0.04405798017978668,
0.00797390565276146,
-0.025278396904468536,
0.10357924550771713,
0.02821427769958973,
-0.003199235536158085,
0.010140757076442242,
-0.048367150127887726,
0.060170240700244904,
0.0320243164896965,
-0.08307933807373047,
-0.014142450876533985,
0.009753688238561153,
-0.021606208756566048,
-0.07288835942745209,
0.04228552058339119,
0.08578215539455414,
-0.0814904123544693,
0.056094683706760406,
0.0096833985298872,
-0.052851539105176926,
-0.007523700594902039,
-0.029199954122304916,
-0.010687778703868389,
-0.0076374998316168785,
0.0458318255841732,
0.026296034455299377,
0.02704286389052868,
-0.05531895160675049,
0.00048609304940328,
0.006638821214437485,
-0.06996066123247147,
0.0354827456176281,
-0.006788823753595352,
-0.051682863384485245,
-0.010608676820993423,
0.050427619367837906,
-0.02554388903081417,
0.013637457974255085,
0.02480013482272625,
0.01741729862987995,
-0.09093283861875534,
0.013103856705129147,
0.04450754448771477,
0.019260788336396217,
0.046381011605262756,
0.04125049337744713,
0.025188911706209183,
-0.01020252425223589,
-0.025997500866651535,
-0.012606635689735413,
0.013751343823969364,
0.049972858279943466,
0.05956149846315384,
0.031218895688652992,
-0.03821228817105293,
0.03639199957251549,
-0.018476763740181923,
0.04710134491324425,
0.0015546065988019109,
-0.00328789628110826,
0.03477824106812477,
0.002136943396180868,
-0.029776494950056076,
-0.06688542664051056,
0.027218008413910866,
-0.036742523312568665,
-0.034221451729536057,
-0.00860030110925436,
-0.030060987919569016,
-0.020279934629797935,
0.06258972734212875,
0.028961120173335075,
-0.01822735369205475,
0.02344450168311596,
0.024847466498613358,
-0.05232314020395279,
0.043737418949604034,
0.0013852774864062667,
-0.005294899921864271,
-0.013373331166803837,
0.04397474601864815,
-0.007862710393965244,
0.056416500359773636,
-0.04713818430900574,
0.00801072083413601,
-0.010115711018443108,
0.056282564997673035,
-0.0902571976184845,
0.0665053278207779,
-0.009848595596849918,
-0.00887911207973957,
0.01621326431632042,
0.023638486862182617,
-0.03809157386422157,
-0.04622446000576019,
0.012820403091609478,
0.0419200174510479,
-0.009587399661540985,
-0.08529219776391983,
0.06700484454631805,
-0.007392464205622673,
0.04156443849205971,
-0.038217078894376755,
0.016712481155991554,
0.025613103061914444,
0.054053641855716705,
-0.03176223486661911,
0.03254464641213417,
-0.013674432411789894,
-0.03238855302333832,
-0.02343294955790043,
-0.013657434843480587,
-0.049541328102350235,
0.035642098635435104,
-0.009691194631159306,
0.061421528458595276,
0.03507872298359871,
0.005623328499495983,
-0.01831469126045704,
-0.001284891040995717,
-0.0046777669340372086,
0.011940359137952328,
-0.03326654061675072,
-0.009255344048142433,
-0.0013271392090246081,
-0.032015103846788406,
0.028635580092668533,
0.002387440064921975,
-0.009033559821546078,
0.045166224241256714,
-0.03861499950289726,
-0.05373172089457512,
-0.012017220258712769,
-0.022956958040595055,
0.03915902227163315,
0.033663246780633926,
0.00409423653036356,
0.022493289783596992,
-0.013638557866215706,
-0.027731969952583313,
-0.029964584857225418,
-0.0071560535579919815,
0.03693073242902756,
0.009736722335219383,
-0.018148520961403847,
0.00588589534163475,
0.007922614924609661,
0.04647592827677727,
-0.04461453855037689,
-0.08334726840257645,
-0.07708346098661423,
-0.011280463077127934,
-0.020501988008618355,
0.02317461371421814,
-0.02843172289431095,
-0.01539049856364727,
-0.024970781058073044,
-0.03920095041394234,
-0.04056244716048241,
0.04673810675740242,
0.032663989812135696,
0.06113481894135475,
-0.05277309939265251,
-0.06876125186681747,
-0.052470266819000244,
0.0305903609842062,
-0.004435339476913214,
0.03173968568444252,
-0.05103860795497894,
-0.04664763808250427,
0.020772520452737808,
-0.03188608959317207,
-0.01714470237493515,
0.0703849047422409,
-0.04905025288462639,
-0.011276171542704105,
-0.02285079099237919,
-0.00014534042566083372,
0.004302633460611105,
0.05444230139255524,
0.01854054257273674,
0.07500568777322769,
-0.003597811097279191,
-0.005985787604004145,
-0.021642228588461876,
-0.025007499381899834,
-0.05243765562772751,
0.04819617047905922,
0.08934063464403152,
-0.009960134513676167,
-0.028326574712991714,
-0.0005684720235876739,
0.07449957728385925,
-0.03976045176386833,
0.004496202804148197,
-0.02233107015490532,
-0.02065945789217949,
0.08348104357719421,
0.03056282177567482,
-0.0003116413427051157,
-0.05788153409957886,
0.016672540456056595,
0.04102732241153717,
0.0027367782313376665,
-0.03643053025007248,
0.027964413166046143,
-0.019964640960097313,
0.04896674305200577,
-0.046074431389570236,
-0.021528108045458794,
-0.010131919756531715,
-0.0023633770179003477,
0.004360899794846773,
-0.005170167423784733,
-0.01912613771855831,
-0.04358464851975441,
0.09504658728837967,
-0.0170519407838583,
0.01329098455607891,
0.05339967831969261,
0.011791401542723179,
-0.026986975222826004,
0.01543364580720663,
-0.017414899542927742,
0.02650298736989498,
0.02090049535036087,
0.03181605413556099,
0.004259179346263409,
-0.030568281188607216,
0.02713111601769924,
-0.03866821527481079,
-0.04600171372294426,
0.06710652261972427,
-0.012861805967986584,
0.00258631375618279,
-0.01566462405025959,
0.04865499213337898,
0.03534485399723053,
0.012372780591249466,
-0.02866748347878456,
0.019832104444503784,
-0.0068839904852211475,
-0.0042577097192406654,
0.04580079764127731,
-0.03758068010210991,
-0.042477212846279144,
-0.03252429887652397,
0.04262740537524223,
0.0049485391937196255,
-0.0011392557062208652,
-0.005023903213441372,
-0.022635001689195633,
0.014445205219089985,
0.0479426234960556,
-0.04409850388765335,
-0.024130206555128098,
0.010347412899136543,
0.028210241347551346,
-0.031517911702394485,
0.04342668876051903,
0.033308081328868866,
-0.014289634302258492,
-0.039331838488578796,
0.027189306914806366,
0.02085578441619873,
-0.022260569036006927,
-0.022196296602487564,
0.06860308349132538,
0.06363575160503387,
-0.03593287244439125,
0.027437830343842506,
0.006729328539222479,
-0.01364439632743597,
0.05582301318645477,
0.03890303149819374,
0.06559671461582184,
-0.04312935099005699,
0.05043953284621239,
0.0006405371241271496,
0.06772056221961975,
0.04398564249277115,
-0.0094721969217062,
0.01849612034857273,
0.06780467182397842,
0.0032029515132308006,
0.003904602024704218,
0.03491365537047386,
0.06189505383372307,
0.00023663791944272816,
0.003755768993869424,
0.018166346475481987,
-0.02949390560388565,
-0.015431399457156658,
0.007835195399820805,
0.037399496883153915,
-0.008416139520704746,
0.010909441858530045,
-0.01068919524550438,
-0.019213443621993065,
0.005045175086706877,
0.054709967225790024,
0.05418534576892853,
-0.005833005532622337,
0.0255417600274086,
0.001428939518518746,
0.03407740592956543,
0.03086847811937332,
-0.022886527702212334,
0.00006495359411928803,
-0.024802515283226967,
-0.03642059490084648,
0.04076099768280983,
0.012163758277893066,
-0.01894870214164257,
-0.027612436562776566,
0.03496381267905235,
-0.018608156591653824,
-0.00684965867549181,
-0.01982087641954422,
-0.0007891263230703771,
0.034661971032619476,
-0.03794633969664574,
-0.011960887350142002,
-0.07634621113538742,
0.009382408112287521,
-0.03262193128466606,
0.021482346579432487,
0.01628725603222847,
-0.007885299623012543,
-0.025429867208003998,
0.05782610923051834,
-0.03234975412487984,
0.018901623785495758,
-0.03235211595892906,
-0.03229127079248428,
-0.07080169767141342,
-0.028530575335025787,
-0.010080611333251,
0.016308041289448738,
-0.03154117241501808,
0.007083796430379152,
0.00833850633352995,
-0.04618249461054802,
-0.015127772465348244,
-0.028889313340187073,
0.0024786959402263165,
-0.012084666639566422,
0.035624563694000244,
0.07864592969417572,
-0.02739657275378704,
-0.0031496447045356035,
-0.005682275630533695,
-0.0037128611002117395,
0.08242560923099518,
0.0272381454706192,
-0.011466944590210915,
-0.01927461475133896,
-0.023020757362246513,
-0.006897872779518366,
0.005634563975036144,
0.024324608966708183,
0.010633128695189953,
0.0074363090097904205,
0.005319065414369106,
-0.02674052305519581,
-0.018838712945580482,
0.053462035953998566,
-0.028005890548229218,
0.011022471822798252,
0.026512758806347847,
-0.014174219220876694,
0.06513569504022598,
0.005471926648169756,
-0.007340318523347378,
-0.016175592318177223,
0.008612208999693394,
-0.04149237275123596,
-0.055047716945409775,
0.006977585610002279,
-0.0021306101698428392,
0.05707046389579773,
-0.05385475605726242,
-0.08065518736839294,
-0.0018077688291668892,
0.037687964737415314,
0.05915193632245064,
-0.09277566522359848,
0.024778397753834724,
0.003176264464855194,
-0.019178804010152817,
0.013298401609063148,
-0.02348790504038334,
-0.052774038165807724,
0.035071127116680145,
0.01707276701927185,
-0.009747618809342384,
-0.07791594415903091,
0.05099014192819595,
-0.01667269878089428,
0.05360369756817818,
-0.01425006240606308,
-0.08320608735084534,
0.028948523104190826,
-0.01527307741343975,
0.011402389034628868,
0.017013711854815483,
0.04371127858757973,
-0.033128079026937485,
0.007087726145982742,
-0.01834234781563282,
0.07029476016759872,
-0.03236367553472519,
-0.021727031096816063,
-0.004997436422854662,
0.011212155222892761,
0.008882592432200909,
0.054435569792985916,
0.019511990249156952,
-0.039598725736141205,
0.03396960720419884,
-0.07754246890544891,
0.042808324098587036,
0.02350461855530739,
-0.03530897945165634,
0.029299529269337654,
-0.0073039899580180645,
-0.00440733227878809,
0.04086911678314209,
-0.037279803305864334,
-0.0402071513235569,
0.06559956073760986,
-0.027655158191919327,
-0.04403211548924446,
-0.004706571809947491,
0.003645175602287054,
0.022316599264740944,
-0.09437111765146255,
-0.018210016191005707,
-0.07778678089380264,
0.051073167473077774,
0.027243241667747498,
0.04516829177737236,
0.00890758354216814,
-0.02447141520678997,
0.10679081082344055,
-0.014157949946820736,
-0.02697059139609337,
-0.015425522811710835,
-0.0029154163785278797,
-0.049856942147016525,
0.059609826654195786,
-0.03143969550728798,
0.011123799718916416,
-0.010664171539247036,
0.0025804899632930756,
0.04346797242760658,
-0.03689523786306381,
-0.02092180959880352,
-0.04168058931827545,
-0.04118497669696808,
-0.01907568983733654,
-0.04018273949623108,
-0.012627054005861282,
-0.011052793823182583,
0.028843464329838753,
-0.03204019367694855,
0.034493785351514816,
0.023284805938601494,
-0.06907040625810623,
0.014313514344394207,
0.06045380234718323,
-0.010265356861054897,
0.024648208171129227,
-0.01541869156062603,
-0.037945084273815155,
0.04729408398270607,
0.028261687606573105,
0.02963029406964779,
0.04759380593895912,
0.04784286767244339,
-0.01642969436943531,
0.023831946775317192,
0.01365602482110262,
-0.001366108888760209,
-0.04471219703555107,
-0.007521603722125292,
-0.05799155682325363,
-0.012135801836848259,
-0.01718010939657688,
-0.020665330812335014,
-0.029629364609718323,
0.002809014869853854,
-0.043679557740688324,
-0.042016953229904175,
-0.007549437694251537,
-0.010503673925995827,
0.004678188823163509,
0.00995146669447422,
-0.00825596135109663,
-0.0066432342864573,
0.05035785213112831,
-0.01879798248410225,
-0.026144592091441154,
0.01991070806980133,
-0.050687164068222046,
0.04552975669503212,
-0.008071906864643097,
-0.030785836279392242,
0.000926840293686837,
-0.015931889414787292,
0.009754843078553677,
-0.001941259135492146,
0.0018037970876321197,
0.014246209524571896,
-0.0372978039085865,
0.01667606830596924,
0.008989404886960983,
0.035585250705480576,
-0.03392452001571655,
-0.0642373338341713,
-0.014389270916581154,
0.029007423669099808,
-0.0010399597231298685,
-0.034771062433719635,
0.08150222152471542,
-0.012386824004352093,
-0.0428130216896534,
0.0392126627266407,
-0.023636002093553543,
-0.005606775637716055,
0.011049527674913406,
-0.06391242891550064,
-0.006334432866424322,
0.03949864208698273,
0.027470208704471588,
0.01997346617281437,
-0.011924522928893566,
-0.020465083420276642,
-0.010432669892907143,
0.05040470510721207,
-0.03025789186358452,
0.0077890618704259396,
-0.0006061764433979988,
-0.022640643641352654,
-0.003829570487141609,
-0.008565764874219894,
0.033451784402132034,
0.008683387190103531,
0.008713506162166595,
0.00920133851468563,
-0.054434482008218765,
0.0030317725613713264,
0.0030946943443268538,
-0.01909882016479969,
-0.0067252181470394135,
-0.04363653063774109,
-0.030666781589388847,
-0.0115581676363945,
0.023461533710360527,
0.01953023672103882,
-0.00327472435310483,
-0.02454901486635208,
-0.034581445157527924,
0.008390845730900764,
-0.0059141963720321655,
-0.07652826607227325,
-0.008770152926445007,
-0.0007036937749944627,
-0.0013383470941334963,
-0.06096426025032997,
0.013945803977549076,
-0.026226114481687546,
-0.003726242110133171,
-0.013423321768641472,
-0.017919519916176796,
-0.04298597201704979,
-0.016612494364380836,
0.02791805937886238,
-0.005463046953082085,
-0.05099497735500336,
-0.022014040499925613,
-0.004040402360260487,
-0.05690383538603783,
-0.007259699981659651,
-0.026437241584062576,
0.026752661913633347,
-0.021891245618462563,
-0.02119322121143341,
0.05240431800484657,
0.0376468263566494,
0.014563452452421188,
-0.006858132313936949,
0.021827498450875282,
0.03468472883105278,
-0.07122553884983063,
0.0317387580871582,
-0.05967351049184799,
0.04654666408896446,
0.00007395449938485399,
-0.01686199940741062,
0.004451652057468891,
-0.052180200815200806,
0.009289713576436043,
0.0196800846606493,
0.03186141699552536,
-0.07058911770582199,
-0.0022391213569790125,
-0.010713585652410984,
-0.04112408310174942,
0.02571571059525013
] |
<p>This question is about cosmology and general relativity.</p>
<p>I understand the difference between the universe and the observable universe. What I am not really clear about is what is meant when I read that the universe is infinite.</p>
<ul>
<li>Does it have infinite mass or is it
dishomogeneous? </li>
<li>How can the universe
transition from being finite near the
big bang and infinite 14 billion
years later? Or would an infinite
universe not necessarily have a big
bang at all?</li>
</ul> | g922 | [
-0.016692567616701126,
0.030940508469939232,
0.021968048065900803,
-0.062469083815813065,
0.014148588292300701,
0.07628313452005386,
-0.008392931893467903,
0.08219341188669205,
-0.019810808822512627,
-0.04872306436300278,
-0.003982292488217354,
-0.05606761574745178,
0.025251837447285652,
0.027634715661406517,
0.047964684665203094,
-0.04077516868710518,
0.040491655468940735,
-0.036785583943128586,
0.015186445787549019,
0.00249121873639524,
0.008741246536374092,
0.05531052500009537,
0.01586977392435074,
-0.03775176405906677,
-0.04605395719408989,
-0.002277577295899391,
0.021069971844553947,
0.016277264803647995,
-0.010162590071558952,
-0.032812729477882385,
0.016480905935168266,
-0.06132575869560242,
0.035836704075336456,
-0.0010022600181400776,
0.07746152579784393,
-0.027252186089754105,
0.016718465834856033,
0.01036004163324833,
0.041939474642276764,
-0.012391715310513973,
0.02717641554772854,
0.07521779835224152,
0.024918900802731514,
-0.04410092532634735,
-0.041843026876449585,
0.022237354889512062,
-0.03164835274219513,
0.0015101179014891386,
0.060838114470243454,
-0.02506253868341446,
-0.024104110896587372,
0.04183366894721985,
0.00070830003824085,
0.02381918579339981,
0.016266079619526863,
0.021853487938642502,
-0.001746277092024684,
-0.021880773827433586,
0.012214357033371925,
-0.009612989611923695,
0.012933713383972645,
-0.03737998008728027,
0.06026969850063324,
0.018288251012563705,
-0.013866745866835117,
-0.008270509541034698,
-0.03965882956981659,
0.0018096863059327006,
0.029506715014576912,
-0.004682653583586216,
0.0217752568423748,
-0.04526268690824509,
0.012882761657238007,
-0.05978798493742943,
0.0046884180046617985,
0.06340781599283218,
-0.016564184799790382,
0.014081040397286415,
-0.02642764523625374,
0.0014597069239243865,
-0.05164815112948418,
0.03242010250687599,
0.011814232915639877,
0.01617429219186306,
0.017187513411045074,
-0.010946408845484257,
-0.05247964709997177,
0.004117706790566444,
0.006238268688321114,
-0.01938285119831562,
0.05117378383874893,
-0.009183415211737156,
0.019564203917980194,
0.01245587132871151,
-0.033046409487724304,
-0.043136630207300186,
-0.019779251888394356,
0.03613780438899994,
-0.008219660259783268,
-0.005257836543023586,
-0.04827874153852463,
0.033818382769823074,
0.024897150695323944,
-0.0013385211350396276,
0.03579612076282501,
0.010202229954302311,
-0.022126713767647743,
-0.006321850698441267,
0.018039671704173088,
0.0030992927495390177,
-0.04093855619430542,
-0.06149794161319733,
-0.045182593166828156,
0.031887900084257126,
-0.03503042086958885,
0.006039850413799286,
0.06501401960849762,
0.04570918530225754,
0.04928315430879593,
0.010731002315878868,
0.01711021177470684,
0.04052627459168434,
-0.07867349684238434,
0.03500800579786301,
-0.05737173184752464,
-0.028470490127801895,
0.025839913636446,
-0.04712889716029167,
0.012236000970005989,
-0.002694112481549382,
0.03194442018866539,
0.03990297392010689,
-0.01668184995651245,
-0.027827270328998566,
-0.006823535077273846,
-0.010039622895419598,
0.029744694009423256,
-0.0023268242366611958,
-0.0030482790898531675,
0.05363193526864052,
0.002542294329032302,
-0.07016567885875702,
0.03153860941529274,
-0.0235955361276865,
0.015151879750192165,
0.04364009201526642,
-0.011023234575986862,
0.025302041321992874,
0.02816016785800457,
-0.008544321171939373,
-0.022395554929971695,
0.10385763645172119,
0.05225871130824089,
0.004137876909226179,
-0.024976087734103203,
-0.03012600727379322,
-0.0639164000749588,
0.0001656083477428183,
0.02931266278028488,
-0.034977056086063385,
0.01722051575779915,
-0.01785450428724289,
0.028091367334127426,
-0.007185204420238733,
-0.05897792428731918,
0.060540471225976944,
-0.03853658586740494,
0.0027845019940286875,
-0.010285713709890842,
0.015687882900238037,
-0.032838791608810425,
0.02240920253098011,
0.010113836266100407,
0.062195293605327606,
0.042540065944194794,
0.018481861799955368,
0.026631325483322144,
0.05672908201813698,
-0.0317324623465538,
-0.002267619129270315,
-0.01993882842361927,
-0.06039861962199211,
-0.005938272457569838,
0.05396570637822151,
0.029096797108650208,
0.01383484061807394,
-0.04315699636936188,
-0.004640355706214905,
0.01968102902173996,
-0.0039939479902386665,
-0.03873704373836517,
-0.05085720866918564,
0.04951753467321396,
0.03150913864374161,
0.02128751203417778,
0.04770047217607498,
0.030880659818649292,
-0.03317069262266159,
-0.04932475835084915,
-0.06972528249025345,
0.04542579874396324,
0.010460097342729568,
-0.004050332121551037,
0.0059257992543280125,
-0.024231117218732834,
0.0032610613852739334,
0.009155132807791233,
0.02828715182840824,
-0.04862052947282791,
-0.012017947621643543,
0.09901713579893112,
-0.06851030886173248,
0.03343987464904785,
-0.012843377888202667,
-0.0026366347447037697,
0.04283544048666954,
-0.05078013986349106,
0.03321703523397446,
-0.011144635267555714,
0.04888413846492767,
0.01761026307940483,
0.030533460900187492,
0.06730227172374725,
0.03183850273489952,
0.040826212614774704,
-0.014188874512910843,
-0.0012447352055460215,
0.011857687495648861,
0.06237662956118584,
0.06033117324113846,
-0.04623150825500488,
-0.005847619846463203,
0.06187460198998451,
-0.0031444213818758726,
-0.03522960841655731,
0.0008441407699137926,
0.0000064216569626296405,
0.015137217938899994,
-0.07072606682777405,
0.0171003807336092,
-0.01927828975021839,
0.014944268390536308,
-0.03268159180879593,
-0.005549788475036621,
-0.008518640883266926,
-0.10153241455554962,
0.07162769138813019,
-0.0416574627161026,
-0.0008466141880489886,
0.012354242615401745,
0.01898486539721489,
-0.007471059449017048,
0.024470197036862373,
0.00037940804031677544,
0.0017210246296599507,
-0.03798993304371834,
-0.005407079588621855,
0.042302921414375305,
-0.05541910603642464,
-0.011296556331217289,
0.061562441289424896,
-0.06554939597845078,
0.0453658364713192,
0.00576771330088377,
-0.04104755446314812,
0.01682809554040432,
-0.025432920083403587,
0.007384866010397673,
-0.03141891583800316,
-0.0240776464343071,
0.0305206049233675,
-0.0023995041847229004,
0.015493941493332386,
0.031668808311223984,
-0.029235156252980232,
0.00365566392429173,
-0.02474852465093136,
-0.08958463370800018,
0.03318013623356819,
-0.039870135486125946,
0.013918189331889153,
0.017654942348599434,
-0.044922538101673126,
0.006815135013312101,
0.028699129819869995,
-0.006890404503792524,
-0.05861782655119896,
0.010178851895034313,
0.04933509975671768,
-0.049661196768283844,
0.0017207926139235497,
0.005979536101222038,
0.05701940506696701,
0.02657257579267025,
0.013632937334477901,
0.05473640561103821,
-0.051704779267311096,
0.02295096591114998,
-0.06495010107755661,
-0.03455837070941925,
0.025793537497520447,
-0.0673382505774498,
0.018783818930387497,
-0.07333201915025711,
-0.04147595539689064,
0.03200250864028931,
0.047998230904340744,
0.0039625708013772964,
-0.04507657513022423,
-0.018567154183983803,
-0.02504056878387928,
0.04717177525162697,
0.04581969976425171,
-0.007037912495434284,
0.02839258499443531,
0.031183088198304176,
-0.004708555061370134,
0.024595923721790314,
0.03346047177910805,
-0.0018095828127115965,
-0.04306848719716072,
0.0011729768011718988,
-0.028335075825452805,
-0.0059136985801160336,
0.007339963689446449,
-0.01162815559655428,
-0.08685313165187836,
-0.005521532613784075,
-0.051570482552051544,
0.003225966589525342,
-0.0596342608332634,
-0.03305036574602127,
-0.08027783781290054,
-0.03289217874407768,
0.01234523206949234,
-0.001515297102741897,
-0.050416212528944016,
-0.02520015649497509,
0.0629487931728363,
0.010554742999374866,
0.008302165195345879,
-0.03143133223056793,
0.0181865394115448,
0.0331982783973217,
-0.015104956924915314,
0.05000075697898865,
0.04459955170750618,
-0.0727292001247406,
0.007400009781122208,
0.017862245440483093,
0.04393010959029198,
0.007445645984262228,
0.022273026406764984,
-0.0016612665494903922,
-0.035780999809503555,
0.008333681151270866,
-0.008487461134791374,
0.07265561074018478,
0.04852365702390671,
-0.04546361416578293,
0.04016454517841339,
-0.07769167423248291,
0.04551803320646286,
0.012189378030598164,
-0.008534584194421768,
0.03249722346663475,
-0.01650206744670868,
-0.07963649183511734,
0.0025386852212250233,
0.031230846419930458,
-0.03424357622861862,
-0.04729283228516579,
-0.022271841764450073,
-0.0059304069727659225,
0.0514492429792881,
-0.0189059991389513,
0.0553104504942894,
0.015896230936050415,
0.010838708840310574,
0.027271751314401627,
0.0447230227291584,
0.004309565760195255,
0.05448631942272186,
0.006109030917286873,
0.00463205436244607,
0.0021846340969204903,
0.010831426829099655,
-0.0754777044057846,
-0.007742197252810001,
-0.013865242712199688,
0.08827121555805206,
-0.037101566791534424,
0.030104579403996468,
-0.016732361167669296,
0.045577287673950195,
-0.04092850536108017,
-0.03596687316894531,
0.03476199135184288,
0.037012979388237,
0.018703343346714973,
-0.0022580870427191257,
0.033750809729099274,
-0.028206828981637955,
-0.006053898949176073,
0.010536524467170238,
-0.005226673558354378,
0.014398928731679916,
-0.01722545549273491,
-0.007455918472260237,
-0.054433248937129974,
0.007580568548291922,
0.005739739630371332,
0.007363436743617058,
0.0033142443280667067,
0.03303390368819237,
-0.024157393723726273,
0.002976628951728344,
-0.050960153341293335,
0.007540123071521521,
0.04580700770020485,
-0.008934363722801208,
0.05331770330667496,
-0.02596149779856205,
-0.02883431874215603,
-0.0007159010856412351,
0.05206098034977913,
0.0031790887005627155,
-0.009676653891801834,
-0.04202398657798767,
0.02128695510327816,
0.0025312616489827633,
0.04310299828648567,
0.025235330685973167,
0.10303723812103271,
-0.09404439479112625,
0.08003047853708267,
0.0030046156607568264,
-0.006069038528949022,
-0.029933204874396324,
-0.03507544845342636,
0.08088216930627823,
-0.037722423672676086,
-0.02586946450173855,
0.03941721469163895,
-0.012078761123120785,
0.07052769511938095,
0.027289841324090958,
-0.04786347597837448,
0.0013734347885474563,
-0.0660858228802681,
-0.008573895320296288,
0.030105557292699814,
-0.031954970210790634,
-0.021310336887836456,
-0.001025678007863462,
-0.044746991246938705,
0.048561941832304,
0.030049247667193413,
-0.0546506829559803,
0.0224087405949831,
-0.0355440191924572,
-0.003591409884393215,
0.0037969821132719517,
0.04390735924243927,
0.026052219793200493,
-0.049275681376457214,
-0.03681300953030586,
-0.023042820394039154,
-0.008377422578632832,
-0.005442945286631584,
-0.01614958792924881,
0.03765960410237312,
0.03349854424595833,
0.01920190081000328,
-0.03772377967834473,
0.013109450228512287,
-0.028638705611228943,
-0.049431536346673965,
0.0044784159399569035,
-0.032826151698827744,
-0.0306575745344162,
-0.01851745694875717,
0.03140328451991081,
0.019028332084417343,
0.04569773003458977,
0.048120927065610886,
-0.04779825359582901,
-0.032087355852127075,
-0.003619380993768573,
-0.014840624295175076,
-0.005408302880823612,
-0.00314585049636662,
0.08040566742420197,
0.019304173067212105,
-0.001313893124461174,
-0.029376104474067688,
-0.010968849062919617,
-0.023976990953087807,
-0.024267591536045074,
0.023357996717095375,
-0.0023392606526613235,
0.03147263079881668,
0.024149570614099503,
0.0005085467710159719,
-0.06156472489237785,
0.026982396841049194,
0.01640533283352852,
-0.003865632461383939,
0.0016775858821347356,
0.048122063279151917,
0.012353753671050072,
-0.012599210254848003,
-0.002310254843905568,
0.05682186782360077,
0.03195635601878166,
0.0015416466630995274,
-0.01386721059679985,
-0.0606599822640419,
-0.016968613490462303,
0.004344533663243055,
-0.11645921319723129,
0.05007552355527878,
0.06389611959457397,
0.019896933808922768,
0.012421289458870888,
-0.007526698987931013,
-0.008761455304920673,
-0.05379718542098999,
0.004309842362999916,
-0.025494061410427094,
0.07558342069387436,
-0.0058365873992443085,
0.02307724766433239,
-0.0268538985401392,
-0.034420277923345566,
0.0518181137740612,
0.0067493971437215805,
0.002960818586871028,
-0.005174554884433746,
-0.018456703051924706,
0.013567700982093811,
-0.01606770232319832,
0.005180026404559612,
0.06007786840200424,
0.02513348124921322,
-0.004521373193711042,
-0.041235532611608505,
0.03687285631895065,
0.07294517010450363,
-0.046090323477983475,
-0.07614800333976746,
0.02459634840488434,
0.053626395761966705,
0.04395830258727074,
-0.014264175668358803,
0.0788484588265419,
0.020221685990691185,
-0.006047883071005344,
-0.032926108688116074,
-0.027516376227140427,
-0.022217268124222755,
0.011705811135470867,
-0.013751323334872723,
-0.037677399814128876,
-0.004466744139790535,
-0.08261237293481827,
-0.021212050691246986,
-0.06304538995027542,
0.09543335437774658,
-0.0008553710649721324,
0.03525269031524658,
0.027585167437791824,
0.015127466060221195,
0.00029604442534036934,
0.009373308159410954,
0.005251227878034115,
-0.018434839323163033,
-0.03683791309595108,
-0.011490801349282265,
-0.006411190610378981,
0.018592026084661484,
-0.005129626952111721,
0.040375713258981705,
-0.024598674848675728,
0.0191209614276886,
0.011408046819269657,
-0.018290996551513672,
-0.03508878871798515,
0.016964977607131004,
-0.05123988538980484,
-0.023769671097397804,
-0.04630270227789879,
0.025128638371825218,
-0.03348759561777115,
-0.027554407715797424,
0.04944251477718353,
-0.01458186749368906,
-0.06915277987718582,
-0.01145875547081232,
-0.008518706075847149,
-0.034114763140678406,
-0.005238925572484732,
0.03364952653646469,
0.051572494208812714,
0.061601780354976654,
0.00497552240267396,
-0.053149718791246414,
-0.0009795743972063065,
0.06808700412511826,
-0.013656971976161003,
0.04144429415464401,
0.009995285421609879,
0.0005607533967122436,
-0.010264979675412178,
0.015037639066576958,
-0.010598398745059967,
-0.05656865984201431,
-0.015941917896270752,
-0.007676520850509405,
-0.03296180069446564,
0.008075974881649017,
-0.02123795449733734,
0.013576912693679333,
0.06610452383756638,
-0.056234028190374374,
0.027472738176584244,
-0.028437500819563866,
0.04864535853266716,
0.036033373326063156,
0.022579165175557137,
-0.0066016120836138725,
-0.04145986959338188,
0.015138393267989159,
0.011039931327104568,
0.027251286432147026,
0.05210760235786438,
-0.05433310940861702,
0.0247036125510931,
0.015737442299723625,
-0.019062969833612442,
0.006852279882878065,
0.042731497436761856,
0.028741607442498207,
0.05033324658870697,
-0.016069402918219566,
0.030195903033018112,
-0.025161055848002434,
-0.05703289434313774,
-0.045444048941135406,
-0.04774819687008858,
-0.028288932517170906,
-0.02167893946170807,
-0.03217457979917526,
0.06090467423200607,
-0.05587197095155716,
0.031830739229917526,
-0.04879353567957878,
-0.03096145950257778,
0.00709714088588953,
-0.09483668208122253,
-0.027575617656111717,
0.023992320522665977,
-0.01680067740380764,
0.0008640968007966876,
-0.0011793790617957711,
0.0006169337430037558,
0.020296061411499977,
-0.07037218660116196,
-0.002067764289677143,
-0.03838745877146721,
-0.01293998397886753,
-0.01889129914343357,
-0.008202063851058483,
-0.015155723318457603,
0.04989031329751015,
-0.03178807348012924,
-0.07191143929958344,
0.008550629019737244,
0.04633913189172745,
-0.005661015398800373,
-0.03957495465874672,
0.07596762478351593,
-0.002345263957977295,
0.024200493469834328,
-0.025307297706604004,
0.025132302194833755,
0.02806488238275051,
-0.0047065396793186665,
-0.007789358496665955,
-0.05545070022344589,
-0.035770121961832047,
-0.018593421205878258,
-0.021329334005713463,
-0.02160445600748062,
0.02617376483976841,
-0.017653197050094604,
-0.0017232656246051192,
-0.0018028417835012078,
0.06770061701536179,
-0.025905337184667587,
0.011263475753366947,
-0.008024103008210659,
-0.06376787275075912,
-0.01187216117978096,
0.022044135257601738,
0.034778375178575516,
-0.06994140148162842,
-0.0034220560919493437,
-0.019357673823833466,
0.02014090120792389,
0.007765547372400761,
0.030349791049957275,
0.005771303083747625,
-0.000113543079351075,
-0.025081198662519455,
0.03333218768239021,
0.026760250329971313,
-0.024441063404083252,
-0.019121753051877022,
-0.04932800680398941,
-0.009616910479962826,
-0.005696187727153301,
0.05862027406692505,
-0.03807774558663368,
-0.06308237463235855,
-0.00028494160505943,
-0.035902634263038635,
-0.02704632468521595,
-0.07692272961139679,
-0.019120946526527405,
-0.014555270783603191,
0.01497842837125063,
-0.024418672546744347,
-0.028458289802074432,
-0.09109266102313995,
0.08013742417097092,
0.005576572380959988,
-0.01772458478808403,
-0.0049172015860676765,
-0.011865787208080292,
0.000875170691870153,
0.02360432781279087,
0.01738910749554634,
0.05502898991107941,
0.0627313032746315,
-0.0008038015803322196,
-0.025231776759028435,
0.018684377893805504,
0.04527776688337326,
-0.029667576774954796,
-0.020435497164726257,
0.06861915439367294,
-0.008990508504211903,
0.03190015256404877,
-0.0289933942258358,
-0.018420934677124023,
0.034237004816532135,
-0.008075104095041752,
-0.022242972627282143,
-0.015482679009437561,
0.009314614348113537,
0.06022549793124199,
-0.001720456057228148,
-0.006055223289877176,
-0.04251526668667793,
-0.0011733409482985735,
0.006558836903423071,
-0.024281879886984825
] |
<p>Here's something that I've found difficult to wrap my head around. The relationship between the Schwarzschild radius and mass is linear. It's generally known that if you take an object in the universe and squeeze it down to it's Schwarzschild radius, that radius will always be smaller than smaller than the original object's radius. E.x, the sun has 1 solar radius, which is much larger than it's Schwarzschild radius of 3 km.</p>
<p>But if you started calculating Schwarzschild radius for an object with really high mass, things seem to get a bit funky. Take an object that has a mass of $10^{100}$ kilograms. The corresponding Schwarzschild radius for that is $1.48513 \times 10^{73}$ meters. But if we took an object that has the density of the Sun (1410 $kg/m^{-3}$) and tried to find it's radius normally, we end up with a radius of $1.19244 \times 10^{32}$ meters which is smaller than the Schwarzchild radius. How is this possible? I understand that you won't be able to have an object that large enough to even consider this to be "possible", but this still is confusing to me. Are my calculations off?</p> | g4600 | [
0.03426491841673851,
0.02907630428671837,
0.018872151151299477,
0.04129352048039436,
-0.01486556138843298,
0.021350286900997162,
-0.011611162684857845,
0.0021648637484759092,
-0.07448110729455948,
-0.02699141390621662,
-0.016676275059580803,
-0.024065399542450905,
0.003380622947588563,
0.010774435475468636,
0.03455400839447975,
0.012655729427933693,
0.01256051566451788,
-0.017436111345887184,
0.05155250430107117,
0.006881698500365019,
0.03301612287759781,
-0.050737619400024414,
0.05227071791887283,
-0.018043015152215958,
-0.06318391859531403,
0.05616213008761406,
0.03276605159044266,
0.04035741835832596,
-0.02257860265672207,
-0.026765072718262672,
-0.012159363366663456,
0.052547771483659744,
0.011143463663756847,
-0.011053998954594135,
0.03058462217450142,
-0.01071619987487793,
0.014472992159426212,
0.02006876841187477,
0.005390634294599295,
0.01661103405058384,
0.005833174102008343,
-0.041590481996536255,
0.024194858968257904,
0.037727128714323044,
0.02990736812353134,
0.02026655524969101,
-0.007401606533676386,
0.03205064684152603,
0.06505425274372101,
-0.036292944103479385,
-0.0490567609667778,
0.03677841275930405,
0.01690646819770336,
-0.009452701546251774,
0.023746242746710777,
0.020112568512558937,
0.04205362871289253,
-0.0034990659914910793,
0.030175145715475082,
0.023016195744276047,
0.0313277393579483,
-0.0032113089691847563,
0.019992943853139877,
-0.0007289756904356182,
0.057428017258644104,
0.030848221853375435,
-0.029373183846473694,
-0.0361935980618,
-0.011765403673052788,
-0.038294702768325806,
0.011019472032785416,
-0.025368966162204742,
-0.007950848899781704,
-0.07089635729789734,
-0.037666529417037964,
-0.018618352711200714,
0.029468756169080734,
0.024752918630838394,
0.003980098757892847,
0.016702722758054733,
-0.005102958530187607,
0.0018349994206801057,
0.027251651510596275,
0.01790367253124714,
0.039183590561151505,
-0.007627612445503473,
-0.009195741266012192,
0.029489299282431602,
-0.0643482655286789,
0.031075967475771904,
-0.0004912851727567613,
-0.03507619723677635,
0.03843473270535469,
0.034315075725317,
0.0023673204705119133,
-0.0020727284718304873,
-0.028596045449376106,
0.053691308945417404,
-0.032190099358558655,
-0.02221795544028282,
0.019154803827404976,
0.008899834007024765,
0.015023842453956604,
0.022992001846432686,
-0.05275730416178703,
0.013024561107158661,
-0.010447603650391102,
0.02200973592698574,
-0.0098942331969738,
-0.027396541088819504,
-0.03449411690235138,
-0.10247890651226044,
-0.014515557326376438,
-0.02224143221974373,
-0.07799769937992096,
-0.05708123743534088,
0.058339208364486694,
-0.003812206443399191,
0.013638774864375591,
0.036673806607723236,
-0.026074904948472977,
0.022580834105610847,
0.022438781335949898,
0.04522552713751793,
-0.03183158487081528,
-0.035647038370370865,
0.0068330285139381886,
-0.00830887258052826,
0.046604275703430176,
-0.010730300098657608,
-0.016071295365691185,
-0.011672157794237137,
0.02607733942568302,
-0.02660546265542507,
0.010925465263426304,
0.027060555294156075,
-0.03472062200307846,
0.028027743101119995,
-0.035690780729055405,
-0.006146661937236786,
0.01521832775324583,
-0.0155302993953228,
-0.003957643639296293,
-0.0235481858253479,
-0.06940033286809921,
0.04462721198797226,
-0.02060217596590519,
-0.001981633249670267,
-0.008213954977691174,
0.01858612336218357,
0.028547292575240135,
0.00987235177308321,
0.011938579380512238,
-0.03431310877203941,
-0.010534889996051788,
0.03923724591732025,
-0.04096841439604759,
0.022525500506162643,
0.006654774770140648,
-0.0015115143032744527,
0.067102812230587,
-0.0650525763630867,
-0.01860734634101391,
0.0015954329865053296,
-0.02276933565735817,
0.023524511605501175,
0.011853866279125214,
-0.0571385957300663,
-0.05295487865805626,
-0.0363679863512516,
-0.0475609265267849,
0.0032345603685826063,
-0.014303315430879593,
0.008425663225352764,
-0.0453198179602623,
0.013801551423966885,
0.009937450289726257,
0.0020310075487941504,
0.005356993526220322,
0.05650392919778824,
-0.017901083454489708,
-0.03107490949332714,
-0.0024632064159959555,
-0.018852053210139275,
0.048995714634656906,
-0.0021530722733587027,
0.11572351306676865,
0.04231240600347519,
0.06641366332769394,
0.011677242815494537,
-0.059293851256370544,
-0.022654255852103233,
0.0430108867585659,
0.026327885687351227,
0.015330051071941853,
0.0030742594972252846,
0.009314986877143383,
0.027191031724214554,
-0.04947909340262413,
0.006867383141070604,
-0.002874835394322872,
0.014205975458025932,
0.029941527172923088,
0.022506091743707657,
0.06080058962106705,
-0.027072910219430923,
-0.023914683610200882,
0.03448072448372841,
0.033857330679893494,
-0.017628123983740807,
0.0297906082123518,
-0.04561729356646538,
0.021022072061896324,
0.001934638014063239,
-0.0026187875773757696,
-0.013918972574174404,
-0.03334565833210945,
-0.014866416342556477,
-0.010050449520349503,
0.02013245038688183,
-0.04853721708059311,
-0.027706177905201912,
0.05694159120321274,
-0.03274039179086685,
-0.003874600864946842,
0.07161197066307068,
-0.048519864678382874,
0.03996725007891655,
0.03575603663921356,
-0.00027936010155826807,
-0.016993163153529167,
0.02793022058904171,
-0.012460380792617798,
0.028395522385835648,
-0.018010756000876427,
0.033978208899497986,
-0.010743247345089912,
-0.060505542904138565,
-0.02751624770462513,
0.03733297437429428,
0.040576983243227005,
0.0033873231150209904,
-0.03258557990193367,
-0.011384597048163414,
0.05819303169846535,
-0.028464920818805695,
0.0542616993188858,
0.008408060297369957,
-0.039012376219034195,
0.019450288265943527,
-0.028959663584828377,
0.022913599386811256,
-0.01363936997950077,
-0.03262743353843689,
0.017261208966374397,
0.010378911159932613,
-0.018942801281809807,
0.02962648682296276,
-0.016382401809096336,
-0.060440607368946075,
-0.0034723374992609024,
0.028574055060744286,
0.05742918699979782,
-0.007950164377689362,
-0.07900763303041458,
-0.025463365018367767,
-0.07745248079299927,
-0.04280418902635574,
-0.008500603027641773,
0.011959750205278397,
-0.036959223449230194,
0.04144946485757828,
0.031078211963176727,
0.04061853513121605,
0.018855756148695946,
-0.0015549672534689307,
-0.02805377170443535,
0.03418593108654022,
0.08808907866477966,
0.00006944956840015948,
0.004193296656012535,
0.05569084733724594,
-0.07047929614782333,
0.013778981752693653,
0.028331086039543152,
-0.07615774869918823,
-0.01856941729784012,
0.023200662806630135,
-0.00656951405107975,
-0.05257491394877434,
-0.011313964612782001,
0.05758111923933029,
0.032237958163022995,
0.04345565661787987,
0.013276604004204273,
0.06549093127250671,
-0.029635362327098846,
0.007167312316596508,
-0.04297083988785744,
0.016797203570604324,
0.014946007169783115,
0.0038880284409970045,
0.02369958907365799,
-0.028138544410467148,
-0.02393615059554577,
0.052993252873420715,
-0.0305629875510931,
-0.027226459234952927,
-0.05128776654601097,
-0.041918881237506866,
0.03786871209740639,
0.030812423676252365,
0.017355527728796005,
-0.004973392002284527,
-0.04694908484816551,
-0.07107479125261307,
0.023103486746549606,
-0.024771977216005325,
0.02731144428253174,
-0.015981212258338928,
0.0023760104086250067,
-0.01963764801621437,
0.0021660509519279003,
-0.01165250688791275,
0.00969527568668127,
0.007111663930118084,
-0.10894539207220078,
-0.050755441188812256,
-0.025898154824972153,
-0.03688040003180504,
-0.01284621562808752,
0.02066466026008129,
-0.022739682346582413,
-0.0005845496780239046,
-0.05382459983229637,
0.025606846436858177,
-0.030380025506019592,
-0.010717860423028469,
0.10923133790493011,
-0.007109927479177713,
0.013044639490544796,
-0.006006391253322363,
-0.016179578378796577,
-0.003633021842688322,
-0.051424674689769745,
0.1248081624507904,
-0.02479693479835987,
-0.04137081652879715,
0.023896055296063423,
-0.04194522649049759,
0.014785579405725002,
0.049958158284425735,
0.02008720673620701,
-0.008489384315907955,
0.032964594662189484,
0.05772506073117256,
0.007852211594581604,
0.03726145625114441,
0.03245694562792778,
-0.021110517904162407,
0.03965326026082039,
-0.045752014964818954,
-0.03640701249241829,
-0.01549946516752243,
-0.017835205420851707,
-0.024906501173973083,
0.03953838348388672,
-0.007173757068812847,
0.014714844524860382,
-0.0036174599081277847,
-0.04966447502374649,
-0.020538879558444023,
-0.02592557668685913,
0.02584991417825222,
0.06821411848068237,
-0.02742745541036129,
0.039140600711107254,
0.03537578508257866,
0.01691102795302868,
0.00012529616651590914,
0.06198343262076378,
0.03235730156302452,
0.015425889752805233,
-0.03387236222624779,
0.009187333285808563,
-0.03185885399580002,
-0.041967879980802536,
-0.03759370744228363,
0.04793551564216614,
0.01109404768794775,
-0.020323563367128372,
-0.0985727459192276,
-0.02057349495589733,
-0.03351485729217529,
0.05397740378975868,
-0.028077535331249237,
0.018542632460594177,
-0.044706664979457855,
-0.03991551697254181,
0.01268878672271967,
0.011300308629870415,
0.02040022239089012,
0.022692471742630005,
-0.01764957420527935,
-0.025554968044161797,
0.03213910385966301,
0.07024732977151871,
0.02587997540831566,
0.0065558901987969875,
-0.015107483603060246,
0.061234235763549805,
-0.0045288847759366035,
0.020846419036388397,
-0.09026643633842468,
0.002383619314059615,
-0.00738181546330452,
-0.04453742131590843,
0.009977957233786583,
0.015007439069449902,
0.025148671120405197,
-0.031368810683488846,
-0.005462318658828735,
-0.02656296081840992,
0.037441596388816833,
0.010906362906098366,
0.023454319685697556,
-0.006400972604751587,
-0.04192239046096802,
0.016455434262752533,
0.03490425646305084,
0.015530677512288094,
0.021762020885944366,
0.05890385061502457,
-0.019900688901543617,
-0.0534781888127327,
0.031005997210741043,
-0.026903832331299782,
0.0522334910929203,
-0.04399287700653076,
-0.009221109561622143,
-0.02214953303337097,
0.033646177500486374,
0.012499610893428326,
0.0021680661011487246,
0.04652279615402222,
-0.00657504890114069,
-0.013243632391095161,
-0.006083858665078878,
-0.03738036006689072,
-0.0070197428576648235,
-0.03596992418169975,
-0.01732678711414337,
0.01112724095582962,
-0.0067990669049322605,
-0.014511430636048317,
0.01460542157292366,
0.014294371008872986,
0.044400956481695175,
0.042761705815792084,
0.0033906863536685705,
-0.03604182228446007,
0.021776430308818817,
0.03296248987317085,
0.05763207748532295,
0.013174871914088726,
-0.07662457227706909,
-0.04232707992196083,
0.01151178777217865,
-0.013938607648015022,
0.06061204895377159,
-0.049643147736787796,
0.07003328204154968,
0.016195982694625854,
0.004816914442926645,
-0.04327463358640671,
-0.010653735138475895,
-0.04779495671391487,
-0.0586785152554512,
-0.022683074697852135,
-0.07258791476488113,
-0.044114045798778534,
0.062388163059949875,
-0.022764025256037712,
0.006659041158854961,
-0.014421414583921432,
0.05120713263750076,
-0.032827600836753845,
0.03699793666601181,
-0.00006773813220206648,
0.03232785686850548,
0.04906731843948364,
0.008256617933511734,
0.01848232001066208,
0.02024194970726967,
-0.013272887095808983,
0.01504508312791586,
0.04583903029561043,
-0.05013592913746834,
-0.0004549402219709009,
0.008591979742050171,
-0.013084626756608486,
-0.0239153653383255,
-0.03158285468816757,
0.000399493525037542,
-0.041204992681741714,
0.021610591560602188,
0.08384544402360916,
0.01885942555963993,
0.043750226497650146,
0.05004559084773064,
0.08340001851320267,
0.06176939606666565,
0.0011892671464011073,
0.007997230626642704,
-0.045377183705568314,
-0.07451973855495453,
-0.019185390323400497,
0.04443110525608063,
0.02477676421403885,
-0.008436978794634342,
0.024814656004309654,
0.006496569607406855,
0.044272687286138535,
-0.05093810334801674,
0.006987948436290026,
0.004699962679296732,
-0.016374940052628517,
0.005348692182451487,
0.0066640484146773815,
0.0549127459526062,
-0.02567213773727417,
-0.018282311037182808,
0.0020061898976564407,
0.007062884978950024,
0.011200716719031334,
-0.003792047966271639,
0.03011091612279415,
0.024777019396424294,
0.0540597178041935,
0.031257860362529755,
0.06645188480615616,
-0.03571140021085739,
-0.030081484466791153,
0.035759858787059784,
-0.004064677283167839,
0.005051750224083662,
0.023882901296019554,
0.054641369730234146,
0.043155696243047714,
-0.01979379914700985,
-0.06136728823184967,
-0.02306404709815979,
-0.06353731453418732,
0.034832946956157684,
0.014606066048145294,
0.01234881766140461,
0.041605908423662186,
-0.000782723305746913,
-0.032637257128953934,
-0.01654568873345852,
0.04847242310643196,
-0.014115878380835056,
-0.009388751350343227,
-0.07250356674194336,
-0.033742696046829224,
-0.10980156809091568,
0.02091560885310173,
-0.056651871651411057,
0.05108548328280449,
0.026354681700468063,
-0.021638335660099983,
-0.020683711394667625,
0.011516680009663105,
-0.02493741177022457,
0.047413527965545654,
0.03321518748998642,
-0.04518410935997963,
0.013118925504386425,
0.032963111996650696,
-0.024137673899531364,
0.03441571816802025,
0.011789529584348202,
0.010823879390954971,
-0.08818580955266953,
-0.01991971582174301,
0.013509421609342098,
-0.06544600427150726,
0.009968382306396961,
0.015813257545232773,
-0.05545343458652496,
-0.011154326610267162,
-0.002512815175577998,
-0.062073297798633575,
-0.03390654921531677,
-0.043599240481853485,
-0.04547462984919548,
0.02653311751782894,
0.016862384974956512,
-0.04117482900619507,
-0.01918640360236168,
-0.002716488903388381,
0.0840400904417038,
0.07777782529592514,
0.03441445529460907,
0.061462584882974625,
-0.00711065111681819,
0.00011411735613364726,
0.03555483743548393,
0.025458354502916336,
-0.0377030111849308,
-0.04696306213736534,
0.08122557401657104,
-0.003990226425230503,
0.04926599562168121,
0.02421904355287552,
-0.035884447395801544,
0.017433637753129005,
-0.0028891521506011486,
-0.07769542932510376,
-0.10454097390174866,
0.024599874392151833,
0.010466943494975567,
-0.04456140473484993,
-0.10064257681369781,
0.04631398618221283,
0.03177912160754204,
0.012258106842637062,
-0.0025657406076788902,
0.03873959928750992,
0.017590008676052094,
0.025568446144461632,
0.000007222711701615481,
0.014708520844578743,
0.04439670592546463,
0.040431100875139236,
0.07460765540599823,
-0.055261049419641495,
0.05175896733999252,
-0.0036229463294148445,
0.062152836471796036,
0.0015427502803504467,
-0.06529062986373901,
-0.011010461486876011,
0.058628518134355545,
-0.08327674865722656,
-0.029212310910224915,
-0.011016872711479664,
0.02051909640431404,
-0.06750298291444778,
-0.04387145861983299,
0.001305782119743526,
0.04239409416913986,
-0.06838516145944595,
-0.006604433059692383,
-0.01651950366795063,
-0.019448796287178993,
-0.04672649875283241,
0.05036594346165657,
-0.009389638900756836,
-0.08316339552402496,
-0.04051327705383301,
-0.006542172748595476,
0.022860931232571602,
-0.0149686299264431,
0.0072235167026519775,
0.01225710567086935,
0.0027826617006212473,
-0.020161425694823265,
-0.0022456373553723097,
0.009467191062867641,
-0.029080495238304138,
0.023776652291417122,
-0.054607972502708435,
-0.03049333579838276,
-0.0036467653699219227,
0.04733012989163399,
0.029644383117556572,
-0.024842707440257072,
0.01953449845314026,
0.02388097532093525,
-0.037143316119909286,
0.0319039411842823,
-0.047726258635520935,
0.01578160934150219,
-0.018787167966365814,
0.03631577268242836,
-0.059986669570207596,
0.0028283679857850075,
0.031245406717061996,
0.04159398376941681,
-0.03109000436961651,
0.0430227555334568,
-0.032037101686000824,
0.015367148444056511,
0.008110768161714077,
0.01551960501819849,
-0.005428009200841188,
0.044513482600450516,
0.04139545559883118,
0.03801097348332405,
-0.05590261518955231,
-0.031432949006557465,
-0.020891666412353516,
0.022216850891709328,
0.043199826031923294,
0.024800771847367287,
-0.05924130231142044,
0.024608086794614792,
-0.002866613445803523,
0.03680507466197014,
0.016610335558652878,
-0.002512932289391756,
-0.04001276195049286,
-0.020379308611154556,
0.008905874565243721,
-0.0015456464607268572,
0.02173512801527977,
0.019741768017411232,
-0.05576975643634796,
-0.07259195297956467,
-0.008181772194802761,
0.026893749833106995,
0.04640981927514076,
-0.038996558636426926,
-0.029674287885427475,
-0.05317022651433945,
0.024237265810370445,
-0.024784669280052185,
-0.032963648438453674,
-0.00020968612807337195,
-0.01762424036860466,
0.01767192967236042,
-0.014069336466491222,
-0.07043078541755676,
-0.009507359005510807,
-0.0031450847163796425,
-0.03384759649634361,
-0.000663548766169697,
-0.02346600405871868,
-0.017599375918507576,
0.0307005662471056,
-0.039566636085510254,
0.017153732478618622,
0.00992544461041689,
0.002098809229210019,
-0.054353803396224976,
-0.054190464317798615,
0.04076714068651199,
0.031088290736079216,
-0.05008698254823685,
-0.06089496985077858,
0.011889370158314705,
0.01297121774405241,
-0.0022498872131109238,
0.027853045612573624,
-0.029580403119325638,
-0.03920880705118179,
-0.06364861875772476,
-0.02691737562417984,
-0.02389201708137989,
0.03759600967168808,
0.008478429168462753,
-0.046100977808237076,
0.029086535796523094,
0.03344011306762695,
-0.016257399693131447,
-0.03587567061185837,
0.04151352867484093
] |
<p>I think we all heard general statements like "once big enough star burns out there is nothing to prevent the gravitational collapse ending in a black hole". But I can't remember even seeing the process described precisely.</p>
<p>Here's the deal: at first there is a nice object, a star. Stars can be nicely modeled by general relativity, nuclear physics and statistical physics combined and very much is known about these models and it can be observed whether they agree with things like light and neutrino fluxes, surface temperature and probably also lot of other stuff I know nothing about.</p>
<p>After the collapse we are left with another nice object, a black hole. We know that <a href="http://en.wikipedia.org/wiki/No-hair_theorem">black holes have no hair</a>.</p>
<p>The question is: what happens in-between? More precisely, between the time when all of the nuclear material has been burned out (and if possible ignore effects like reheating of the star after big enough compression) and the time where there is nothing more than just a black hole.</p>
<blockquote>
<ul>
<li><p>Give a description of what happens during the collapse?</p></li>
<li><p>How does the star "lose its hair"?</p></li>
<li><p>Can the actual collapse be solved analytically?</p></li>
<li><p>At what point is singularity created?</p></li>
</ul>
</blockquote>
<p><strong>Update:</strong> <em>I don't want to know what an outside observer will see. Instead, I'd like to find out what an individual part of the dead star will "feel" when a black hole is about to form near it. In other words, I want a complete solution (ideally analytical, but numerical would be also completely fine)</em></p>
<p>Feel free to assume anything that makes your life easier. Spherical symmetry is definitely fine. Also, if for any reason the questions don't make sense (like Cauchy problem is ill-defined in the presence of the singularity) feel free to interpret them in a way that make them sensible (e.g. assume that black hole is built from D-branes).</p>
<hr>
<p>Also, I have a feeling that what I intended as a simple question at first ended up being pretty complex. If you think it should be split into smaller (and therefore more manageable and answerable) parts, let me know.</p> | g4601 | [
-0.009369539096951485,
-0.003798488061875105,
0.026557305827736855,
-0.020953692495822906,
-0.0260359775274992,
0.03231159597635269,
0.010568037629127502,
0.05601414293050766,
-0.03948964551091194,
-0.028792090713977814,
-0.04896833002567291,
0.013923523016273975,
0.04869973659515381,
-0.002658575540408492,
0.0682152509689331,
0.005220507737249136,
0.03070598840713501,
-0.06014768034219742,
0.002105121035128832,
-0.0050585390999913216,
-0.008909483440220356,
0.03440218046307564,
0.06622176617383957,
-0.044484131038188934,
-0.08786141127347946,
-0.01344195008277893,
0.016867375001311302,
0.05723428353667259,
-0.03752628341317177,
-0.054020028561353683,
0.03311895579099655,
0.018212508410215378,
0.013703275471925735,
-0.02146586775779724,
0.029410216957330704,
-0.04614408686757088,
-0.0374431274831295,
-0.01837952993810177,
-0.03602946177124977,
0.014181086793541908,
0.025702960789203644,
-0.05176178738474846,
0.017462313175201416,
-0.06895306706428528,
-0.025287365540862083,
-0.05371719226241112,
0.03282729908823967,
-0.0465192012488842,
0.07172901928424835,
-0.008064006455242634,
0.03274643048644066,
0.05877426266670227,
0.02894308790564537,
-0.041361406445503235,
0.007380723021924496,
0.03934251889586449,
0.011611353605985641,
0.004059577360749245,
0.018134720623493195,
-0.015198769979178905,
-0.044428493827581406,
0.005525888875126839,
-0.024148762226104736,
-0.032920945435762405,
0.031024208292365074,
-0.052623018622398376,
-0.043289992958307266,
-0.011400191113352776,
-0.0014316907618194818,
0.009363883174955845,
0.0023273893166333437,
0.025235820561647415,
0.039528798311948776,
-0.005384160205721855,
-0.07292091846466064,
0.03670824319124222,
-0.05381125584244728,
0.025125863030552864,
-0.030796730890870094,
0.01336554903537035,
-0.06582527607679367,
0.04913777485489845,
0.01663673296570778,
0.0590156726539135,
0.023633025586605072,
0.015620608814060688,
-0.03273974731564522,
0.006243223324418068,
-0.011707337573170662,
0.019503094255924225,
0.008872457779943943,
0.008444405160844326,
0.04414629191160202,
-0.04461243376135826,
0.07130110263824463,
-0.007153592072427273,
0.003205907763913274,
0.045188967138528824,
0.002431744011119008,
0.019833575934171677,
0.0025539665948599577,
-0.0121693080291152,
-0.058867279440164566,
-0.020960265770554543,
-0.007023740094155073,
0.006605179514735937,
-0.007945756427943707,
0.05875129625201225,
-0.03410923108458519,
0.05102993920445442,
-0.07643325626850128,
-0.04672416299581528,
-0.01836913637816906,
0.011848528869450092,
-0.014031556434929371,
0.0019409542437642813,
0.07464738935232162,
-0.03664546087384224,
0.02762153185904026,
0.03978408873081207,
-0.02711465023458004,
0.009123015217483044,
0.0165416169911623,
-0.011452745646238327,
-0.015082667581737041,
-0.040590595453977585,
-0.006571183912456036,
-0.003526444546878338,
-0.002473242813721299,
0.03958272188901901,
0.05448726937174797,
0.0015719932271167636,
-0.006805322133004665,
0.08033046126365662,
-0.004304942674934864,
0.04661788418889046,
0.0017418167553842068,
0.025904132053256035,
0.01827891916036606,
-0.03134872019290924,
0.021380629390478134,
-0.03876955434679985,
-0.057386524975299835,
0.035844702273607254,
0.016534879803657532,
0.017981208860874176,
0.033782560378313065,
0.013129517436027527,
0.0026417342014610767,
0.018865711987018585,
0.0067322938703000546,
0.07741474360227585,
-0.013864520005881786,
-0.053067442029714584,
0.024296870455145836,
0.04009806737303734,
0.04026619344949722,
-0.002000124892219901,
-0.012922036461532116,
-0.04260268434882164,
0.07898369431495667,
-0.030737631022930145,
-0.0016214356292039156,
0.08490968495607376,
-0.05042257532477379,
0.04070088267326355,
-0.017169352620840073,
-0.09052018076181412,
0.03766286000609398,
-0.029238060116767883,
-0.017676377668976784,
-0.03519238904118538,
0.02002684585750103,
0.0751754567027092,
0.0317133292555809,
-0.0066001093946397305,
0.019709423184394836,
-0.014591998420655727,
0.0021821092814207077,
-0.012956984341144562,
0.02636147104203701,
0.018101604655385017,
0.025421028956770897,
-0.011771387420594692,
0.02355809137225151,
-0.01709901914000511,
0.05464330315589905,
0.06779255717992783,
-0.010211415588855743,
0.04126662015914917,
-0.02551041729748249,
-0.02602207288146019,
0.06266502290964127,
0.046057842671871185,
0.016892166808247566,
0.017060916870832443,
0.0661684200167656,
-0.04186999797821045,
-0.012720621190965176,
0.03520137071609497,
-0.005745306611061096,
-0.002384511288255453,
-0.011616112664341927,
0.05539742484688759,
-0.01861186884343624,
0.04248272627592087,
-0.051180656999349594,
0.020783796906471252,
-0.033477626740932465,
-0.010584804229438305,
0.047659024596214294,
-0.06498564034700394,
0.034450314939022064,
-0.031157294288277626,
-0.05141925439238548,
-0.011206709779798985,
-0.06959722191095352,
0.02510453201830387,
-0.0441603846848011,
0.016854489222168922,
-0.020022980868816376,
-0.02303285524249077,
0.02366022951900959,
-0.03674973174929619,
0.03383057937026024,
0.052628934383392334,
-0.036284711211919785,
-0.0544755719602108,
0.038663238286972046,
-0.059370968490839005,
-0.08776332437992096,
0.023742489516735077,
0.0010916886385530233,
-0.03938384726643562,
0.021134579554200172,
0.05441786348819733,
0.03331054374575615,
-0.05270983278751373,
0.005620084702968597,
0.05974773317575455,
-0.00239727389998734,
-0.01611240953207016,
-0.03955128416419029,
-0.0726873055100441,
0.06483574956655502,
-0.03086880035698414,
0.0417625866830349,
-0.0304921492934227,
-0.0049982257187366486,
0.004056648351252079,
0.02307611145079136,
-0.011957211419939995,
0.016981221735477448,
-0.021147575229406357,
0.0000035499988371157087,
-0.03223848715424538,
0.0044555761851370335,
0.06882014870643616,
-0.031697724014520645,
-0.03868423402309418,
0.028375644236803055,
0.00042983057210221887,
-0.03301166370511055,
0.0005783027154393494,
-0.07372257113456726,
-0.004655168391764164,
-0.0462227426469326,
-0.0441635437309742,
0.013582173734903336,
0.04325868934392929,
-0.0024457129184156656,
-0.00850551389157772,
0.032471247017383575,
0.034611549228429794,
-0.003253413364291191,
0.04360494017601013,
-0.07747185975313187,
0.04827026650309563,
0.0629839301109314,
-0.019012268632650375,
0.015359606593847275,
0.03802374377846718,
-0.09432021528482437,
-0.013061576522886753,
-0.01523479912430048,
-0.022784268483519554,
0.045238692313432693,
0.03507837653160095,
-0.005834219977259636,
-0.01950019784271717,
0.0047036586329340935,
-0.008454871363937855,
-0.00013445485092233866,
0.04545707255601883,
-0.01854829117655754,
0.02513539232313633,
-0.032440684735774994,
0.03296487033367157,
-0.025310086086392403,
0.02184729091823101,
0.02700495906174183,
-0.04919811338186264,
0.005094943568110466,
0.0008423895924352109,
0.010392865166068077,
0.046668630093336105,
-0.05296149477362633,
-0.03335009515285492,
0.00024025983293540776,
-0.06262259930372238,
0.0063757156021893024,
-0.024451442062854767,
0.02288222871720791,
-0.0034889564849436283,
0.012962188571691513,
-0.030910398811101913,
-0.019648484885692596,
0.03261654078960419,
-0.00701051764190197,
-0.039581138640642166,
-0.013875079341232777,
0.002789214951917529,
-0.014958580024540424,
-0.012770211324095726,
0.015316899865865707,
-0.022580338642001152,
-0.004298811312764883,
-0.009099416434764862,
-0.042574863880872726,
0.004790574312210083,
-0.07366852462291718,
-0.05177667737007141,
0.0025643554981797934,
-0.01796228252351284,
-0.009967604652047157,
-0.02283819019794464,
-0.04189600050449371,
-0.044450122863054276,
0.042513564229011536,
0.0266436655074358,
0.020541148260235786,
-0.011179434135556221,
0.03764159232378006,
0.024563034996390343,
0.04008535295724869,
-0.007136188913136721,
-0.0012135048164054751,
-0.020324477925896645,
0.02122803032398224,
-0.03185096010565758,
0.007916072383522987,
-0.059833139181137085,
0.04607803001999855,
-0.042510949075222015,
-0.041453711688518524,
0.05051140487194061,
0.014736628159880638,
-0.03340741619467735,
0.03438010811805725,
-0.00020630461222026497,
0.026797974482178688,
-0.07226402312517166,
0.025286316871643066,
0.017968516796827316,
-0.0012725807027891278,
-0.021591907367110252,
0.0942373052239418,
-0.05464906245470047,
-0.010689839720726013,
0.04686393588781357,
0.06194155290722847,
0.0695282444357872,
-0.031570665538311005,
-0.013131233863532543,
0.010946471244096756,
-0.03920483961701393,
0.040333375334739685,
0.017805734649300575,
-0.0007729033823125064,
0.04592662304639816,
0.03664594143629074,
0.014697841368615627,
0.00026829360285773873,
-0.021051818504929543,
0.004226294811815023,
0.007406211923807859,
-0.014654607512056828,
-0.0797576755285263,
0.031780995428562164,
-0.031929805874824524,
-0.004062671214342117,
-0.043451350182294846,
-0.006490288767963648,
-0.0778355672955513,
0.0472545400261879,
0.00045234127901494503,
0.008413094095885754,
-0.037363309413194656,
-0.04359014704823494,
-0.04793226718902588,
0.04818487539887428,
0.0288835596293211,
0.013364501297473907,
0.011352102272212505,
0.051297593861818314,
-0.0483439564704895,
-0.010396866127848625,
-0.014457421377301216,
-0.001478995312936604,
-0.015152102336287498,
0.020241184160113335,
0.03805350139737129,
-0.013737702742218971,
0.01219742652028799,
0.03976515680551529,
-0.07706835865974426,
0.04781254008412361,
0.0030392755288630724,
-0.014728124253451824,
-0.02732264995574951,
0.023557111620903015,
-0.004051059950143099,
-0.03540812432765961,
0.0006994379800744355,
-0.04085545241832733,
-0.027515612542629242,
0.014240807853639126,
0.027943264693021774,
0.02031693048775196,
0.04638943448662758,
0.036621566861867905,
-0.003440030850470066,
0.016359418630599976,
0.01525045745074749,
-0.05476447939872742,
0.05670168250799179,
-0.04121369123458862,
0.02863241173326969,
-0.059846192598342896,
0.062248650938272476,
0.02909504435956478,
-0.04194207862019539,
0.016653643921017647,
0.0010653105564415455,
-0.002634666860103607,
0.019757788628339767,
-0.0009165295050479472,
-0.03348642587661743,
-0.03879019618034363,
-0.03470133990049362,
-0.02208663709461689,
0.038531310856342316,
-0.017279185354709625,
-0.07481195032596588,
-0.040631089359521866,
0.021716954186558723,
0.004988339263945818,
0.07726797461509705,
0.01654747501015663,
0.0496298186480999,
-0.0195802953094244,
-0.05737859383225441,
-0.00809855293482542,
0.04128830507397652,
0.008827880956232548,
-0.0586087591946125,
-0.03685848042368889,
-0.03804325312376022,
0.009509327821433544,
-0.0036320374347269535,
-0.08257889747619629,
0.042741913348436356,
0.027768651023507118,
-0.043333202600479126,
-0.012132070027291775,
0.047897014766931534,
-0.0026725882198661566,
-0.022501900792121887,
0.054369404911994934,
-0.002838675631210208,
0.017383165657520294,
0.014820724725723267,
0.03098391368985176,
0.022577237337827682,
0.0906171053647995,
0.013920043595135212,
-0.016389552503824234,
0.006712745409458876,
-0.01025825459510088,
0.016007130965590477,
-0.03740939497947693,
0.008282053284347057,
0.010996667668223381,
0.02790839783847332,
-0.003067467361688614,
-0.07068118453025818,
-0.0036644181236624718,
-0.01527863834053278,
-0.017458826303482056,
0.0005988167249597609,
-0.03497283533215523,
0.001824933453463018,
-0.010503043420612812,
0.05826637148857117,
0.000596804020460695,
0.020238885655999184,
0.000989978201687336,
-0.008405845612287521,
0.08792178332805634,
0.06128891184926033,
-0.013068274594843388,
0.04344281554222107,
0.009535357356071472,
0.019548971205949783,
-0.02424931526184082,
-0.04877064749598503,
0.006947334855794907,
-0.01315405871719122,
0.0004141374956816435,
-0.031493011862039566,
-0.04162105545401573,
-0.028976375237107277,
0.010212247259914875,
0.06868228316307068,
0.06672997772693634,
0.0077822827734053135,
-0.08932503312826157,
0.009183675050735474,
0.025158990174531937,
-0.008583130314946175,
0.018743880093097687,
-0.03145469352602959,
-0.0070508853532373905,
-0.011024360544979572,
-0.003121286630630493,
0.06281670182943344,
-0.017743190750479698,
-0.007895675487816334,
0.05105655640363693,
-0.014283833093941212,
-0.029429573565721512,
0.04894493892788887,
-0.005973470397293568,
0.05188983306288719,
0.0060224877670407295,
-0.015744192525744438,
-0.05699751153588295,
0.0656566247344017,
0.011166354641318321,
-0.046253472566604614,
-0.05512016639113426,
-0.011115219444036484,
-0.006948219146579504,
0.05536790192127228,
0.001386226387694478,
-0.015222818590700626,
0.07017282396554947,
-0.064186692237854,
0.003982937894761562,
-0.06600300222635269,
-0.026309989392757416,
-0.01318206824362278,
0.0032753683626651764,
0.007530213799327612,
0.034470222890377045,
-0.026071887463331223,
-0.03686089068651199,
-0.005501339677721262,
0.08497123420238495,
-0.00945519283413887,
-0.03799896314740181,
-0.0030674058943986893,
0.036229319870471954,
0.03380674868822098,
-0.0013624909333884716,
0.009656156413257122,
-0.003213751595467329,
0.03561338037252426,
-0.004120462574064732,
-0.03277589753270149,
0.029221490025520325,
-0.01070555578917265,
0.07018624246120453,
-0.03249238803982735,
-0.0013918060576543212,
0.0006944962660782039,
-0.02331177145242691,
0.007497371174395084,
-0.006077398546040058,
0.04523072764277458,
0.023681441321969032,
0.050122082233428955,
0.041227810084819794,
0.022573202848434448,
-0.06189039349555969,
0.028963498771190643,
-0.0011328679975122213,
-0.06884707510471344,
-0.008213161490857601,
-0.07919879257678986,
-0.07081948220729828,
0.06412062048912048,
0.059927549213171005,
0.014764292165637016,
-0.006807269062846899,
0.029958130791783333,
-0.046557266265153885,
-0.04839234799146652,
0.03495243191719055,
-0.015300068072974682,
0.02356027066707611,
0.04269210994243622,
-0.002860361011698842,
0.026223214343190193,
0.035161565989255905,
-0.015200529247522354,
-0.0006664494285359979,
0.0342111811041832,
0.006893247831612825,
0.033458955585956573,
-0.019527534022927284,
-0.05012530833482742,
0.04246767610311508,
-0.02402910403907299,
0.02241280861198902,
0.04985126480460167,
-0.006628546863794327,
0.020885121077299118,
-0.011100297793745995,
0.01469380408525467,
0.002912457101047039,
0.02661055140197277,
-0.021781492978334427,
0.04328334704041481,
0.01029515266418457,
0.04578394442796707,
-0.014865447767078876,
-0.008638152852654457,
0.026431987062096596,
0.013099904172122478,
0.02690683677792549,
-0.020976988598704338,
0.020331256091594696,
0.03236011415719986,
-0.045833323150873184,
0.051490940153598785,
0.0031223397236317396,
-0.026033686473965645,
-0.07488187402486801,
-0.026220958679914474,
0.020302722230553627,
-0.018538614735007286,
-0.017512379214167595,
-0.021617989987134933,
-0.04965280741453171,
0.023519428446888924,
0.024839838966727257,
-0.010585132986307144,
-0.021507391706109047,
-0.057127565145492554,
0.01980840042233467,
-0.0433177575469017,
-0.014217519201338291,
-0.03559328615665436,
-0.010990161448717117,
0.01832139492034912,
0.10052567720413208,
-0.05049830675125122,
0.01808156445622444,
-0.06100540608167648,
0.019104676321148872,
0.0007307499763555825,
-0.0822424590587616,
-0.040781013667583466,
-0.01627444289624691,
-0.046009425073862076,
-0.015467703342437744,
0.028420845046639442,
0.006379298400133848,
0.011502617970108986,
0.02923385426402092,
0.027741214260458946,
-0.013519754633307457,
-0.00231588794849813,
-0.0009297149372287095,
0.03564722090959549,
-0.013390478678047657,
0.07356760650873184,
0.012738002464175224,
0.07069040089845657,
-0.026918422430753708,
0.06294737011194229,
0.0049870871007442474,
-0.012077736668288708,
0.03231862932443619,
-0.039884053170681,
0.003195982426404953,
0.015728624537587166,
-0.012348444201052189,
-0.03253425285220146,
-0.025460487231612206,
0.051363907754421234,
-0.011607221327722073,
-0.08916576951742172,
-0.018405387178063393,
0.015132163651287556,
-0.041440196335315704,
-0.004100375808775425,
-0.03506762906908989,
0.006929574068635702,
0.07849741727113724,
0.0545426569879055,
-0.027422934770584106,
-0.035662658512592316,
0.001084133516997099,
-0.052970558404922485,
-0.012748531065881252,
-0.023944443091750145,
0.010464026592671871,
-0.007980029098689556,
-0.06500539183616638,
-0.03487721458077431,
-0.0067121791653335094,
0.022811289876699448,
0.018502946943044662,
-0.013642730191349983,
-0.046947479248046875,
0.030014358460903168,
0.0016916317399591208,
-0.01939895562827587,
-0.045213453471660614,
-0.01923215389251709,
-0.007677364628762007,
0.008961737155914307,
0.026452766731381416,
0.0003844306047540158,
-0.031024331226944923,
-0.03275911137461662,
-0.04571530222892761,
0.02538962848484516,
-0.04736052453517914,
-0.04908601939678192,
0.019151225686073303,
-0.020286887884140015,
-0.010972940362989902,
-0.04820096492767334,
0.008166422136127949,
0.0637110248208046,
0.08796903491020203,
0.012127486988902092,
0.015515822917222977,
0.015433721244335175,
0.02399025671184063,
0.029713904485106468,
0.018296582624316216,
-0.01877066120505333,
-0.057329606264829636,
0.015184469521045685,
-0.045509930700063705,
0.016166621819138527,
-0.03623688593506813,
0.011599286459386349,
-0.021164657548069954,
-0.017726043239235878,
0.02182859554886818,
-0.0335012823343277,
0.0644853413105011,
-0.041153158992528915
] |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/14074/what-are-the-prerequisites-to-studying-general-relativity">What are the prerequisites to studying general relativity?</a> </p>
</blockquote>
<p>I'am 27 now and i have a burning desire to study math and physics from the ground up and I strongly prefer doing a self study.I want to be a self tutor till i reach certain level.</p>
<p>My question is what is the minimum knowledge needed to read and completely understand the General and Special Theory of Relativity.</p>
<p>As of now my level of math knowledge is basic differential calculus.I also have a basic understanding of Kinematics {One dimensional motion with constant acceleration}</p>
<p>I welcome all possible sugessions,advices and recomendations.</p>
<p>Thank's in Advance</p> | g108 | [
-0.004057388752698898,
0.07549303770065308,
0.006089627277106047,
0.02836623042821884,
-0.028454730287194252,
0.055457208305597305,
0.043472081422805786,
0.03024524822831154,
-0.006436637602746487,
0.003256617346778512,
0.011279664002358913,
0.00343916448764503,
0.026704177260398865,
0.012676677666604519,
-0.008775748312473297,
-0.0353766568005085,
0.04477754980325699,
-0.008193368092179298,
0.018438370898365974,
0.005163202993571758,
0.05482889339327812,
0.020117808133363724,
0.03493179380893707,
-0.03802615776658058,
-0.0631508156657219,
-0.028916368260979652,
-0.04245039075613022,
0.03192606940865517,
-0.0834149494767189,
-0.01479080319404602,
0.004042539279907942,
-0.028209274634718895,
0.035015515983104706,
-0.0524720624089241,
0.008154512383043766,
-0.033046603202819824,
0.03616863489151001,
0.028689557686448097,
-0.03145487233996391,
0.03540119156241417,
0.014020407572388649,
0.007394132204353809,
0.0002776094770524651,
-0.014583883807063103,
0.0754241794347763,
0.0014745172811672091,
-0.03636445105075836,
-0.04205304756760597,
0.04093964025378227,
0.002626162488013506,
-0.011526904068887234,
0.018883563578128815,
0.05646355822682381,
-0.010698264464735985,
-0.04216969758272171,
0.05347287282347679,
-0.05506567656993866,
-0.008478078059852123,
0.03503856807947159,
-0.06266359984874725,
0.02686569094657898,
-0.011121861636638641,
0.004970153793692589,
0.004524885211139917,
-0.03178127482533455,
0.01146810594946146,
-0.03809426724910736,
-0.06417427957057953,
0.06835758686065674,
-0.03787832707166672,
0.03617188334465027,
-0.011534254066646099,
0.015922868624329567,
0.03278287127614021,
0.020570674911141396,
-0.0011393793392926455,
0.03696846216917038,
0.003669368103146553,
0.031721826642751694,
0.0017732902197167277,
-0.03786743804812431,
-0.026966748759150505,
0.037647075951099396,
-0.02523987926542759,
0.07718741148710251,
-0.031039385125041008,
-0.04900490865111351,
-0.03789597377181053,
0.010421845130622387,
0.017558135092258453,
0.006614604499191046,
-0.005453687626868486,
0.050851862877607346,
0.05236312747001648,
0.04419584199786186,
0.003445382695645094,
-0.028998134657740593,
0.05689161270856857,
0.05859172344207764,
0.01761702634394169,
-0.0622573122382164,
-0.018045460805296898,
-0.003069442231208086,
-0.014859641902148724,
-0.001186863286420703,
-0.018160859122872353,
-0.008604330010712147,
0.016816802322864532,
0.04969702661037445,
-0.010258247144520283,
-0.09371738135814667,
0.010342447087168694,
-0.024968260899186134,
-0.05187288671731949,
-0.05246526747941971,
-0.010945440270006657,
0.02443188987672329,
0.029411453753709793,
-0.020618578419089317,
0.025004256516695023,
-0.037128422409296036,
0.0585382804274559,
0.06996136903762817,
0.06584333628416061,
-0.04487378150224686,
-0.030230481177568436,
0.002519075060263276,
-0.05129010230302811,
-0.023285076022148132,
0.04796706140041351,
0.0168862733989954,
-0.02795630879700184,
-0.011098174378275871,
0.030960600823163986,
-0.047030288726091385,
0.03809691220521927,
0.02047698386013508,
0.010928653180599213,
0.0017869614530354738,
-0.006203186698257923,
0.02269386686384678,
0.008196947164833546,
0.025089751929044724,
-0.007847176864743233,
-0.017597801983356476,
0.013352484442293644,
-0.01569082960486412,
0.0392036959528923,
-0.04631794989109039,
0.022769745439291,
-0.03396422788500786,
0.06701618432998657,
0.028727175667881966,
-0.035936951637268066,
0.100577212870121,
0.0028193900361657143,
-0.04107045382261276,
-0.028335530310869217,
0.07567752152681351,
0.030264895409345627,
0.061653729528188705,
0.016470205038785934,
-0.013641138561069965,
0.05693208798766136,
-0.060064896941185,
0.035250745713710785,
-0.02889528125524521,
-0.06247738376259804,
0.05371522158384323,
-0.015761464834213257,
-0.03850770741701126,
-0.029029062017798424,
0.019296184182167053,
0.020714158192276955,
-0.03514378145337105,
-0.024281248450279236,
0.012159989215433598,
-0.01986304111778736,
-0.017745109274983406,
0.013164093717932701,
0.03200457990169525,
-0.08342176675796509,
-0.010164851322770119,
-0.012458479963243008,
-0.011610923334956169,
0.015953639522194862,
-0.07029557228088379,
0.029501231387257576,
-0.03604097664356232,
0.04097835719585419,
0.00275411200709641,
-0.01614636741578579,
0.0252767875790596,
0.04726097360253334,
0.00954304076731205,
0.009808417409658432,
0.01570230722427368,
0.055269643664360046,
-0.021913500502705574,
0.03193410485982895,
-0.03703216463327408,
0.018690234050154686,
0.0728473961353302,
0.04870119318366051,
0.026387017220258713,
-0.015736905857920647,
-0.020216142758727074,
-0.024263447150588036,
0.0834924727678299,
-0.011913328431546688,
0.03849450871348381,
-0.05547008663415909,
0.041052184998989105,
-0.01499151811003685,
-0.009650075808167458,
-0.0775444358587265,
-0.025026151910424232,
-0.0031625747215002775,
0.011580815538764,
0.027708545327186584,
-0.03717561066150665,
0.006213564891368151,
0.01745125651359558,
0.01064989808946848,
-0.03666011616587639,
0.045851945877075195,
-0.00159210164565593,
-0.035321664065122604,
0.06453032046556473,
0.007112120743840933,
-0.043534841388463974,
0.021879667416214943,
0.04972440376877785,
-0.03309468924999237,
0.051603734493255615,
0.03053516335785389,
-0.01315205730497837,
-0.04679957404732704,
0.007518686354160309,
0.025060933083295822,
0.004640635102987289,
0.05067360773682594,
0.025911973789334297,
-0.04255475476384163,
-0.013527204282581806,
-0.058450497686862946,
0.06388575583696365,
0.00256130238994956,
-0.03617270290851593,
-0.039005082100629807,
-0.01929895579814911,
-0.013756443746387959,
-0.08089151978492737,
0.05379475653171539,
-0.01032600924372673,
0.0076250480487942696,
-0.02642136998474598,
-0.020432867109775543,
-0.01835515908896923,
-0.04602743685245514,
0.030618513002991676,
-0.0319085530936718,
-0.025310777127742767,
0.050706785172224045,
-0.045905906707048416,
0.029658975079655647,
-0.0727260410785675,
0.04304170981049538,
-0.0010987441055476665,
-0.004344519227743149,
0.03273307532072067,
0.005098247900605202,
-0.0394747368991375,
-0.02105393446981907,
-0.06173441559076309,
-0.021627429872751236,
-0.04157228022813797,
-0.008860384114086628,
-0.01850561797618866,
0.007591504603624344,
-0.011810778640210629,
-0.014310501515865326,
-0.0053898049518466,
-0.029894400388002396,
0.07953184843063354,
0.01179482415318489,
0.007890013977885246,
0.0233323872089386,
-0.0069031124003231525,
0.0501135028898716,
0.0055497149005532265,
0.05470655858516693,
0.015469303354620934,
-0.015429682098329067,
-0.001737874699756503,
0.05146709457039833,
-0.037804171442985535,
-0.001942039467394352,
-0.09558714926242828,
0.029315274208784103,
-0.022359533235430717,
-0.019025443121790886,
-0.0012287002755329013,
-0.02740899659693241,
-0.0642680823802948,
-0.011731921695172787,
-0.01318503636866808,
-0.025975126773118973,
-0.02993515133857727,
-0.01503930427134037,
0.0017350579146295786,
0.007971652783453465,
0.04392244666814804,
-0.015414613299071789,
0.010247502475976944,
0.01960054598748684,
-0.01830212213099003,
-0.008045989088714123,
-0.006581130437552929,
0.010204094462096691,
0.016754912212491035,
-0.007308353204280138,
-0.04980691894888878,
-0.022085916250944138,
0.03306040167808533,
0.020486891269683838,
0.03920130431652069,
-0.0243732538074255,
-0.018582617864012718,
0.02095172554254532,
0.02013823762536049,
0.0009947895305231214,
-0.06598956882953644,
0.026210883632302284,
0.01736334338784218,
-0.012425207532942295,
-0.010681341402232647,
-0.012098540551960468,
0.02248908020555973,
-0.01797541044652462,
0.08720297366380692,
0.005822692532092333,
-0.04031608998775482,
-0.01023080013692379,
0.01963847503066063,
0.03434811905026436,
0.046806998550891876,
0.033656563609838486,
-0.006055245641618967,
-0.01801344007253647,
0.00667031854391098,
-0.023800041526556015,
0.019853228703141212,
0.002246144460514188,
-0.03590426966547966,
0.05104845389723778,
0.07890733331441879,
0.11704879999160767,
0.02154170162975788,
-0.004804485011845827,
-0.04440433531999588,
-0.041894569993019104,
0.004055295139551163,
0.03834239020943642,
-0.019127871841192245,
0.02076897956430912,
-0.03283417224884033,
-0.04953043907880783,
0.0019349876092746854,
0.01946144737303257,
0.0015546820359304547,
-0.010183172300457954,
-0.0038026985712349415,
-0.026633841916918755,
-0.009405495598912239,
-0.04264130815863609,
0.06277207285165787,
0.0002858720254153013,
-0.03003508970141411,
0.003452017903327942,
0.030962172895669937,
0.017704276368021965,
0.009385792538523674,
-0.019044505432248116,
0.04615674912929535,
0.005733275320380926,
-0.0012681582011282444,
-0.01854057051241398,
0.009137986227869987,
0.0013772910460829735,
0.06995517015457153,
-0.04255784675478935,
0.010411233641207218,
-0.014933391474187374,
0.010824275203049183,
-0.01581479050219059,
0.02552160993218422,
0.058309029787778854,
-0.0004562268150039017,
0.042355090379714966,
-0.030337834730744362,
0.024425223469734192,
0.03741752728819847,
0.01204371266067028,
-0.025569003075361252,
0.018212707713246346,
-0.007147772237658501,
-0.029402071610093117,
0.022396232932806015,
0.036879222840070724,
0.036156702786684036,
0.017232757061719894,
0.01625184714794159,
0.010807698592543602,
0.0501287616789341,
-0.02077428251504898,
-0.02657283842563629,
-0.02149587869644165,
0.017524251714348793,
-0.015358828008174896,
0.025126364082098007,
0.06768445670604706,
0.016154784709215164,
-0.10405121743679047,
-0.004255728796124458,
0.07482730597257614,
0.021793505176901817,
0.03293847665190697,
0.00507977744564414,
0.04383697360754013,
0.0476534366607666,
-0.010388954542577267,
-0.070460744202137,
-0.022818392142653465,
-0.10453217476606369,
0.014396912418305874,
0.06856813281774521,
0.058097515255212784,
-0.020845631137490273,
-0.007004455663263798,
0.032975293695926666,
0.06678047776222229,
-0.01114299613982439,
0.004728967323899269,
-0.032604433596134186,
0.02533242292702198,
-0.018035931512713432,
0.022593719884753227,
-0.01585444249212742,
-0.011635622009634972,
0.011733204126358032,
0.012946917675435543,
0.01646503433585167,
-0.020059658214449883,
-0.04884163662791252,
0.006004950497299433,
-0.024629276245832443,
0.019343990832567215,
0.011417125351727009,
0.021712804213166237,
0.04799586161971092,
0.030103636905550957,
0.04548519477248192,
0.036829084157943726,
0.02199072390794754,
-0.024695543572306633,
-0.023034345358610153,
-0.009756322018802166,
-0.022702906280755997,
-0.034272417426109314,
-0.04059286415576935,
-0.03851049393415451,
-0.007386284880340099,
-0.06502672284841537,
-0.022532310336828232,
-0.011501350440084934,
-0.054079558700323105,
0.00005163296009413898,
-0.037007108330726624,
-0.011171516962349415,
-0.010565812699496746,
-0.021623874083161354,
-0.017305102199316025,
0.031315408647060394,
0.046893130987882614,
0.03404228761792183,
-0.046333495527505875,
-0.006727155763655901,
0.010808072052896023,
-0.041469696909189224,
-0.05169730260968208,
-0.0358567088842392,
0.03813342750072479,
-0.024162475019693375,
-0.11903518438339233,
-0.02622106671333313,
-0.007666918449103832,
-0.03211528807878494,
0.05362766236066818,
-0.017163937911391258,
-0.04672253504395485,
-0.00017233466496691108,
0.03935719653964043,
-0.041583701968193054,
-0.025423090904951096,
-0.05307904630899429,
-0.03918556123971939,
-0.005713580176234245,
-0.050601281225681305,
0.05134177207946777,
-0.03798608109354973,
0.01819799467921257,
0.0401516892015934,
-0.0029929615557193756,
-0.005971877835690975,
0.013894456438720226,
0.03434182330965996,
0.0325031615793705,
-0.02672463096678257,
-0.051170818507671356,
-0.04344020411372185,
-0.008379853330552578,
-0.0036000870168209076,
-0.011666347272694111,
0.009368409402668476,
0.010778657160699368,
-0.06402559578418732,
0.014844718389213085,
0.03987938538193703,
0.0020717212464660406,
0.03161086142063141,
-0.04301581159234047,
-0.0038069828879088163,
-0.012503665871918201,
-0.011442157439887524,
-0.019388215616345406,
0.010274037718772888,
-0.06119031831622124,
0.011921240016818047,
-0.06468329578638077,
-0.05126788839697838,
0.04913105443120003,
0.004852313548326492,
0.03896086663007736,
-0.023648247122764587,
-0.03138645365834236,
-0.012292589992284775,
0.016826525330543518,
0.10522216558456421,
-0.08316700905561447,
-0.08738112449645996,
-0.002708245301619172,
-0.00587444519624114,
-0.02790629118680954,
-0.0053310575895011425,
0.042826466262340546,
-0.024065211415290833,
-0.036549247801303864,
0.010457688942551613,
-0.030981209129095078,
-0.004290760029107332,
-0.0038749652449041605,
-0.00871235691010952,
0.005972289480268955,
-0.02182008884847164,
-0.05195620283484459,
0.015182159841060638,
-0.05117517337203026,
0.12367434054613113,
0.01745772548019886,
-0.058400001376867294,
-0.008021974004805088,
-0.05828193575143814,
-0.01994597725570202,
0.012478386051952839,
-0.021565567702054977,
-0.02779848873615265,
-0.015217149630188942,
-0.021737605333328247,
0.00923954788595438,
0.017214804887771606,
0.03510328009724617,
0.008152085356414318,
-0.08236192911863327,
-0.05387793481349945,
0.005106951575726271,
-0.024238748475909233,
0.025852978229522705,
-0.03877276927232742,
-0.010908091440796852,
-0.034334298223257065,
0.018036777153611183,
0.007271031383424997,
-0.044109415262937546,
-0.008870508521795273,
-0.000624649808742106,
0.08581070601940155,
-0.0019832078833132982,
0.027613377198576927,
0.01834944821894169,
-0.05443976819515228,
-0.023520147427916527,
0.04222914204001427,
0.0035659342538565397,
0.0316573865711689,
0.044373542070388794,
-0.007421381305903196,
-0.014223149977624416,
0.005796069744974375,
0.030567681416869164,
0.006245243828743696,
0.016419749706983566,
0.01886831223964691,
0.048548877239227295,
-0.0348525196313858,
-0.0021471804939210415,
-0.051684822887182236,
0.01011723093688488,
0.007988331839442253,
-0.10664226114749908,
0.07220245897769928,
0.04646662250161171,
0.03318985924124718,
0.032510727643966675,
0.004982474260032177,
-0.008681196719408035,
-0.015498565509915352,
0.005343467462807894,
0.04360610991716385,
-0.046051912009716034,
-0.00022303650621324778,
-0.018679220229387283,
-0.03585796803236008,
-0.026781121268868446,
0.04738341271877289,
0.0753287747502327,
0.0016487656394019723,
0.05001009628176689,
0.028483867645263672,
0.03842518851161003,
-0.024760697036981583,
-0.019342860206961632,
-0.014155007898807526,
-0.035436082631349564,
-0.04084903746843338,
-0.05444108322262764,
0.044708140194416046,
-0.04894471541047096,
-0.02507827617228031,
0.06099504977464676,
0.015107644721865654,
-0.030512675642967224,
-0.021636800840497017,
0.03962201997637749,
-0.09200219064950943,
0.017294876277446747,
-0.0008541260031051934,
-0.05196571722626686,
0.050869375467300415,
-0.029135871678590775,
0.03332199528813362,
-0.0026809528935700655,
-0.013045858591794968,
-0.010381641797721386,
-0.042262956500053406,
0.053636714816093445,
0.021399127319455147,
-0.044246360659599304,
-0.009297151118516922,
0.01066634338349104,
-0.018980782479047775,
0.012124737724661827,
0.01855066604912281,
-0.027903666719794273,
-0.01724443957209587,
0.006549298297613859,
-0.08304672688245773,
-0.03001604974269867,
0.01301878783851862,
-0.04392820596694946,
-0.06605163961648941,
0.05902640148997307,
0.006403262261301279,
0.050039030611515045,
-0.04301159828901291,
-0.004678558558225632,
0.05800802633166313,
-0.024212468415498734,
-0.007129998411983252,
-0.006767766550183296,
-0.039705947041511536,
-0.02356274612247944,
0.005413501523435116,
-0.007955127395689487,
0.05381321907043457,
-0.004636249039322138,
0.03569280728697777,
0.04251168295741081,
0.043773021548986435,
0.0049811480566859245,
-0.018670622259378433,
0.007130105514079332,
-0.03291211649775505,
0.01476751733571291,
-0.04093041270971298,
0.02789783477783203,
-0.04689205810427666,
0.005378550384193659,
-0.053123001009225845,
0.027995405718684196,
0.008126785978674889,
-0.002254449063912034,
0.02600352093577385,
0.023704763501882553,
0.0039454130455851555,
0.033599548041820526,
-0.00010669864423107356,
0.011843969114124775,
0.012661733664572239,
-0.008977584540843964,
0.045276809483766556,
0.03115754947066307,
0.04097624495625496,
-0.040796633809804916,
-0.055466264486312866,
-0.04557584226131439,
-0.004198977258056402,
-0.014151106588542461,
0.023869363591074944,
-0.011469129472970963,
0.045793384313583374,
-0.029308371245861053,
-0.06523213535547256,
0.07546751946210861,
0.003768192371353507,
0.04732156917452812,
0.04415939375758171,
-0.05366664007306099,
0.005949802231043577,
0.06290654838085175,
0.042326536029577255,
0.0663183182477951,
-0.015888340771198273,
0.04509834200143814,
0.008811569772660732,
-0.004458812531083822,
0.003785919863730669,
0.04372645169496536,
0.013597285374999046,
-0.050207700580358505,
-0.05357775837182999,
0.01562083512544632,
0.03875207528471947,
0.008850154466927052,
0.003938782960176468,
-0.07205454260110855,
0.02859591133892536,
0.000841526547446847,
-0.013008223846554756,
-0.02132749930024147,
-0.003437385195866227,
0.01029891986399889,
0.043042827397584915,
0.004088497720658779,
-0.04139094427227974,
-0.012798343785107136,
0.005557876080274582,
0.004275801125913858
] |
<p>Consider an point particle moving on a frictionless semicircular hill (curve). The particle's initial kinetic energy is equal to the potential energy on the top of the hill, i.e it has the necessary energy to climb the hill. </p>
<p>Will it reach the top of the hill in infinite or finite time? </p>
<p>In my proof it needs infinite time and this is quite non-intuitive because, though the particle has the necessary energy to climb the hill, it needs an infinite time. Also if we reverse the time, when the particle is in equilibrium on the top of the hill, it will never go down, therefore this process is time irreversible.</p> | g4602 | [
0.05720782279968262,
0.07023967802524567,
0.006697195582091808,
0.01738499291241169,
0.07713942229747772,
0.013521278277039528,
0.030310150235891342,
0.04891509562730789,
-0.030750969424843788,
0.050825003534555435,
-0.05482626333832741,
0.01764422282576561,
-0.020558923482894897,
-0.028047621250152588,
-0.021151775494217873,
0.01979471743106842,
0.07932409644126892,
-0.03876417875289917,
0.01815146766602993,
0.04147834703326225,
-0.013584643602371216,
0.02652767114341259,
0.03547932207584381,
-0.030054429545998573,
0.00018803704006131738,
-0.04314219206571579,
0.0353357158601284,
-0.015288788825273514,
-0.01800890639424324,
0.011527772061526775,
0.06583388149738312,
-0.03569532930850983,
0.009012921713292599,
0.025716161355376244,
-0.042013343423604965,
-0.07254773378372192,
0.06857964396476746,
-0.027075521647930145,
0.032796528190374374,
-0.02237301506102085,
0.020313996821641922,
-0.00497870147228241,
0.02776203863322735,
-0.010721900500357151,
0.032701097428798676,
0.039470694959163666,
0.01301746629178524,
0.05397132411599159,
-0.037160150706768036,
-0.02221178449690342,
-0.023893067613244057,
0.03640533983707428,
-0.029312673956155777,
0.017725450918078423,
-0.08090263605117798,
0.013333305716514587,
0.07345137745141983,
-0.02530018985271454,
0.029776787385344505,
0.05186352878808975,
0.0336725078523159,
-0.034540507942438126,
0.005162394139915705,
-0.007411832455545664,
0.0335061177611351,
-0.05665356665849686,
-0.036827366799116135,
0.014853297732770443,
0.006441156379878521,
0.012226052582263947,
-0.0011879622470587492,
-0.07885252684354782,
-0.05353228747844696,
-0.01808449998497963,
-0.01914435625076294,
0.03251045569777489,
-0.006680990569293499,
-0.0447981096804142,
0.03874388709664345,
-0.008722489699721336,
-0.08237802237272263,
0.014198966324329376,
-0.007010061293840408,
-0.023869771510362625,
0.048022519797086716,
0.005203760229051113,
0.031651079654693604,
0.015360691584646702,
-0.07093455642461777,
0.049549296498298645,
-0.018029456958174706,
-0.02140875533223152,
0.05963755398988724,
0.0005551393260248005,
0.0021799069363623857,
-0.05257544666528702,
-0.03163934499025345,
0.09078360348939896,
-0.06082959845662117,
0.011535580269992352,
-0.04145408421754837,
-0.047859497368335724,
0.05053918436169624,
-0.0014809463173151016,
0.01821991801261902,
-0.06357458233833313,
-0.0022059869952499866,
-0.010075004771351814,
0.022343795746564865,
-0.006464874371886253,
-0.000697753974236548,
-0.023729829117655754,
0.008160551078617573,
-0.05960899963974953,
-0.06089254841208458,
-0.004987654276192188,
0.030821921303868294,
0.05504753440618515,
0.010346760973334312,
0.058101825416088104,
-0.009961308911442757,
0.047954756766557693,
-0.027695845812559128,
0.07519154250621796,
-0.0765981525182724,
0.03516009449958801,
0.00374800362624228,
0.0004182907869108021,
-0.019206389784812927,
-0.014745852909982204,
-0.037224482744932175,
0.03782951459288597,
-0.009336537681519985,
0.035463884472846985,
-0.023857133463025093,
0.022450141608715057,
-0.0144846485927701,
0.006826822645962238,
0.022219879552721977,
0.06314332783222198,
0.020542889833450317,
-0.0539047047495842,
0.04131476581096649,
0.017354246228933334,
-0.04856134206056595,
0.01721036620438099,
-0.024777350947260857,
-0.013520237058401108,
0.006428987253457308,
-0.0025750226341187954,
-0.04187779873609543,
0.0024052781518548727,
0.053028207272291183,
-0.02099052630364895,
0.044358059763908386,
-0.007217489182949066,
0.0024164014030247927,
0.028692757710814476,
0.01633182168006897,
0.0002743091608863324,
0.05029932036995888,
-0.030654357746243477,
0.08943835645914078,
-0.008119777776300907,
-0.026519356295466423,
0.03840554133057594,
-0.04813848435878754,
-0.0019756434485316277,
0.017399361357092857,
-0.04622539505362511,
-0.04664452746510506,
0.04029335081577301,
0.04303193837404251,
0.02099861390888691,
-0.03514499217271805,
-0.03424270823597908,
-0.012050448916852474,
0.014444228261709213,
-0.04050783812999725,
-0.02566567063331604,
0.017866726964712143,
-0.00788440927863121,
0.024392692372202873,
0.02298835664987564,
0.0019424158381298184,
0.020733101293444633,
-0.0034831222146749496,
0.04436887428164482,
-0.03447211906313896,
-0.005466790869832039,
-0.009301930665969849,
-0.03727728873491287,
0.014006772078573704,
0.062095124274492264,
-0.008924305438995361,
-0.023941654711961746,
0.0315186083316803,
-0.046320363879203796,
0.01114004198461771,
-0.05083734914660454,
0.042378492653369904,
0.005278661847114563,
0.03617456927895546,
-0.007063676603138447,
-0.0018766855355352163,
0.03087541274726391,
-0.022405659779906273,
0.018057100474834442,
-0.04504586383700371,
-0.01441198866814375,
0.04671031981706619,
0.006103042978793383,
-0.008268266916275024,
0.022358233109116554,
-0.027152610942721367,
-0.07181090861558914,
-0.057158660143613815,
-0.025028957054018974,
0.030258413404226303,
-0.006627906113862991,
-0.030724795535206795,
-0.014195036143064499,
0.007060878910124302,
-0.03413757309317589,
-0.025643453001976013,
-0.005394426174461842,
-0.0615483857691288,
-0.1179782971739769,
-0.010709415189921856,
0.007739594206213951,
-0.02915946952998638,
-0.004635258577764034,
-0.010780472308397293,
-0.013380971737205982,
0.05514974519610405,
0.0028317896649241447,
0.029279401525855064,
0.020317601040005684,
0.04865727201104164,
-0.030527234077453613,
0.032036732882261276,
-0.08820048719644547,
0.004988204222172499,
-0.02555348351597786,
0.0351971872150898,
-0.008833058178424835,
0.01523652020841837,
0.00510646216571331,
-0.009259982034564018,
0.011591016314923763,
0.05678592249751091,
-0.0012938096188008785,
-0.021408921107649803,
0.03369702398777008,
0.04039899259805679,
-0.024873238056898117,
-0.01690100133419037,
0.0016200831159949303,
-0.031876422464847565,
-0.03933814913034439,
0.02333824895322323,
0.00732863275334239,
-0.04800711199641228,
-0.016820505261421204,
-0.029100453481078148,
0.036493103951215744,
-0.036642562597990036,
-0.002864783862605691,
-0.019797280430793762,
0.036148801445961,
-0.014789232984185219,
0.02099609561264515,
0.05859561264514923,
0.08050024509429932,
-0.0457654744386673,
-0.003967076074331999,
-0.003299910109490156,
-0.04505418986082077,
-0.018472714349627495,
-0.030377663671970367,
-0.00006896999548189342,
-0.026585005223751068,
-0.029068732634186745,
0.12117192149162292,
0.027900852262973785,
-0.01095141377300024,
0.05368607118725777,
0.03972059115767479,
-0.04066397622227669,
0.0088042626157403,
-0.001240665907971561,
0.03821286931633949,
0.10781408101320267,
0.029498640447854996,
-0.005152982659637928,
0.06578588485717773,
0.014834580011665821,
-0.06616862118244171,
-0.03254564851522446,
-0.02724340744316578,
-0.03041827492415905,
-0.04928741976618767,
-0.03912447392940521,
-0.028367986902594566,
0.06890681385993958,
0.05028311908245087,
0.008444469422101974,
-0.010655699297785759,
-0.0006202824297361076,
-0.0010868581011891365,
0.0014054083731025457,
0.09100517630577087,
-0.020025813952088356,
-0.04160286858677864,
-0.0012068782234564424,
0.03872749209403992,
-0.01470134872943163,
-0.002221896778792143,
0.032695263624191284,
0.05134028196334839,
-0.041543539613485336,
-0.007477817591279745,
-0.03203228488564491,
0.0009386513847857714,
0.03917662426829338,
-0.02614155039191246,
-0.04099041223526001,
-0.015675855800509453,
-0.05763785541057587,
-0.007613594178110361,
0.03383771330118179,
0.07102980464696884,
0.02350100502371788,
-0.02739766612648964,
0.019667571410536766,
-0.06238497793674469,
-0.0167414341121912,
-0.009888524189591408,
0.03958616405725479,
0.017719702795147896,
-0.04015682265162468,
0.0012619484914466739,
-0.03137785568833351,
0.02710908278822899,
0.01972142793238163,
0.03258174657821655,
0.01485964935272932,
0.02129467949271202,
-0.031907886266708374,
0.010954736731946468,
0.06763661652803421,
-0.05894636735320091,
0.02548854425549507,
-0.011060219258069992,
-0.015393601730465889,
0.06284935772418976,
-0.01152378972619772,
0.05982300639152527,
-0.022278662770986557,
0.0038868968840688467,
0.004012181889265776,
-0.02478729747235775,
0.06188831105828285,
0.04559069499373436,
0.036446463316679,
0.0025488524697721004,
-0.04179883748292923,
-0.02389252558350563,
0.03535600006580353,
0.02498185634613037,
-0.01007006410509348,
-0.05086126923561096,
0.044570282101631165,
0.022754404693841934,
0.026086319237947464,
-0.011617779731750488,
0.009481716901063919,
-0.03178444132208824,
-0.032689645886421204,
0.053928129374980927,
-0.016743915155529976,
-0.0300114918500185,
-0.029048927128314972,
0.012376425787806511,
-0.01719684712588787,
0.08495358377695084,
-0.06900938600301743,
-0.03438706696033478,
0.07659647613763809,
0.008503075689077377,
0.061991505324840546,
-0.007587504107505083,
0.03588450700044632,
-0.0049635739997029305,
0.022254999727010727,
0.014863615855574608,
-0.00809338316321373,
-0.033095914870500565,
-0.0013734579551964998,
-0.010279044508934021,
0.027907028794288635,
0.00983759667724371,
-0.056789930909872055,
0.004782560281455517,
0.023014836013317108,
0.01643265224993229,
0.06407348066568375,
-0.05555320903658867,
0.0036400777753442526,
-0.06732605397701263,
-0.009017715230584145,
-0.036739449948072433,
-0.0074323490262031555,
0.010957476682960987,
-0.005959615111351013,
-0.025969184935092926,
-0.0012085636844858527,
-0.054294005036354065,
-0.0025907764211297035,
0.028762945905327797,
-0.02169434353709221,
0.025300007313489914,
-0.0017797687323763967,
-0.08289834856987,
0.005390159785747528,
0.036420028656721115,
0.03683679178357124,
0.03228725120425224,
-0.10204274952411652,
-0.019974444061517715,
0.01355563011020422,
0.03579594939947128,
-0.011565609835088253,
-0.06805647164583206,
-0.04838457703590393,
0.07845882326364517,
0.03159213811159134,
0.0060630617663264275,
-0.03224819153547287,
-0.01082292478531599,
0.038233451545238495,
0.04439905658364296,
0.019236376509070396,
0.014110506512224674,
-0.010596219450235367,
0.035638559609651566,
-0.021852577105164528,
-0.06771872937679291,
-0.009738561697304249,
-0.04760804399847984,
0.04176224395632744,
0.06561361998319626,
-0.0327800028026104,
-0.049084123224020004,
-0.014413847588002682,
-0.05441846698522568,
-0.007121949922293425,
0.011527650989592075,
-0.04953502491116524,
0.031607359647750854,
-0.022464845329523087,
-0.005986747797578573,
0.03482498973608017,
0.02392943762242794,
-0.016969868913292885,
-0.01876811683177948,
-0.017158253118395805,
-0.025838017463684082,
0.005132853519171476,
0.0216364786028862,
-0.02466665767133236,
0.016197578981518745,
0.04035793989896774,
0.07519327849149704,
-0.01994854211807251,
-0.03193684667348862,
0.02959657832980156,
0.007025570143014193,
0.06962956488132477,
-0.013575257733464241,
-0.05018005520105362,
-0.011667653918266296,
-0.03665652498602867,
0.013435570523142815,
-0.04267093166708946,
0.02506556734442711,
-0.0714171752333641,
0.0037401989102363586,
0.014553386718034744,
0.01580616645514965,
0.01095322985202074,
0.012832731939852238,
0.020942093804478645,
0.023412074893712997,
0.03475116938352585,
-0.030354075133800507,
-0.0005913471686653793,
0.03146554157137871,
0.0036344528198242188,
0.04260359704494476,
-0.04704635962843895,
-0.05659995228052139,
0.026416849344968796,
-0.00810325425118208,
-0.0488906055688858,
-0.019365044310688972,
0.08039606362581253,
0.020801134407520294,
-0.024230055510997772,
0.02160363271832466,
0.004736700095236301,
-0.023196136578917503,
0.036873575299978256,
0.047987695783376694,
-0.031330253928899765,
-0.007427832577377558,
-0.026329457759857178,
-0.007668746635317802,
-0.025722026824951172,
-0.039892006665468216,
0.01569640263915062,
0.0380905419588089,
0.02235754393041134,
-0.011471036821603775,
0.044077444821596146,
0.04396812990307808,
-0.08118756115436554,
-0.05563658848404884,
-0.009434448555111885,
0.09186355769634247,
0.023578831925988197,
-0.06233398616313934,
-0.04078285023570061,
-0.025945838540792465,
-0.038923099637031555,
-0.018178243190050125,
0.016372883692383766,
-0.00014210896915756166,
0.05329957604408264,
-0.016508322209119797,
-0.04817771911621094,
-0.06609456241130829,
0.01241424772888422,
0.02290928177535534,
-0.02440466359257698,
0.0007964555989019573,
-0.10324481874704361,
-0.005420553032308817,
0.019820423796772957,
-0.05456274747848511,
0.01787683740258217,
0.032432734966278076,
0.026175793260335922,
0.012741276994347572,
-0.036265939474105835,
0.026501473039388657,
0.02713516168296337,
-0.016130749136209488,
-0.06321357935667038,
-0.042608290910720825,
0.033737558871507645,
-0.008413412608206272,
-0.010899479500949383,
0.060857225209474564,
0.048289161175489426,
0.011157133616507053,
-0.02487899921834469,
-0.0286655705422163,
0.033116210252046585,
0.010169078595936298,
0.059456221759319305,
0.019730344414711,
-0.00787742342799902,
0.05794686824083328,
0.02294781059026718,
-0.0008160942234098911,
-0.054956067353487015,
-0.06118365004658699,
-0.06405086070299149,
-0.00025758499396033585,
0.009726086631417274,
0.048821501433849335,
-0.005867393687367439,
-0.04353874549269676,
0.026248332113027573,
-0.011908953078091145,
-0.05400444194674492,
-0.011041088961064816,
0.03188418224453926,
-0.010600677691400051,
0.0003850986249744892,
-0.033432070165872574,
0.01192421279847622,
0.02993270754814148,
-0.03887849301099777,
0.018212510272860527,
-0.0420951209962368,
-0.005132708232849836,
0.02743658795952797,
0.046960216015577316,
-0.057286735624074936,
0.0070014712400734425,
-0.027047745883464813,
0.014912216924130917,
0.021490516141057014,
-0.01748383231461048,
-0.02328581176698208,
0.02721843309700489,
0.03969675302505493,
-0.027520716190338135,
0.006791119929403067,
0.041726019233465195,
0.018738189712166786,
-0.015381583012640476,
-0.04465619847178459,
-0.01934441179037094,
0.005145230330526829,
-0.002164584817364812,
-0.036096543073654175,
-0.036488015204668045,
0.03524259850382805,
0.049274545162916183,
0.0424424447119236,
0.0125975226983428,
0.024116238579154015,
-0.033658478409051895,
-0.018514402210712433,
0.054257240146398544,
0.053955234587192535,
-0.030022742226719856,
0.0028778393752872944,
-0.0015088081127032638,
-0.0690445750951767,
0.04154680669307709,
-0.02316829189658165,
-0.00472700409591198,
-0.02485642582178116,
0.03219739720225334,
-0.011807238683104515,
-0.0017361263744533062,
0.024056514725089073,
0.026350146159529686,
-0.005211416631937027,
0.044941551983356476,
-0.011950773186981678,
-0.03794912248849869,
0.03464756906032562,
-0.0018663897644728422,
-0.03349846228957176,
-0.038629673421382904,
0.035921309143304825,
0.026141682639718056,
-0.05173736438155174,
0.04724143072962761,
-0.007295719813555479,
-0.04630899056792259,
-0.037890054285526276,
-0.0008133305236697197,
0.005075071007013321,
-0.010457211174070835,
0.00820581242442131,
-0.010697303339838982,
-0.0035248608328402042,
0.0013791059609502554,
-0.0025022346526384354,
0.0163078922778368,
-0.006891902070492506,
0.002538166008889675,
0.001609985833056271,
-0.009874493815004826,
0.024487148970365524,
-0.030174994841217995,
0.0034069798421114683,
-0.03034672699868679,
-0.0015154351713135839,
0.04666179046034813,
-0.021995514631271362,
0.026839548721909523,
-0.02665870077908039,
0.021441472694277763,
0.005216609220951796,
-0.05076613277196884,
0.015094680711627007,
-0.06566081196069717,
0.004561589565128088,
-0.004668189212679863,
-0.021138250827789307,
-0.009865937754511833,
-0.0009509866358712316,
-0.00753561407327652,
-0.0122605599462986,
0.0776936486363411,
0.05399734154343605,
-0.029028434306383133,
0.06856133788824081,
0.0036367338616400957,
0.007254513446241617,
0.005649598781019449,
0.05267801880836487,
-0.025960596278309822,
0.0565011166036129,
-0.014830007217824459,
0.002548811724409461,
-0.008766449056565762,
-0.008612195961177349,
0.017096901312470436,
-0.009771487675607204,
0.01196233183145523,
-0.09572409093379974,
0.0392162911593914,
0.025036105886101723,
0.030923189595341682,
-0.0021711192093789577,
0.03650549054145813,
-0.03831326961517334,
-0.010838156566023827,
-0.06439046561717987,
0.030684828758239746,
0.005998186767101288,
-0.004947147332131863,
-0.004785967990756035,
0.01056175772100687,
-0.05306925252079964,
-0.10859385132789612,
-0.007956183515489101,
0.046688199043273926,
-0.06313403695821762,
-0.04078812524676323,
0.004724207334220409,
-0.041631221771240234,
0.029267625883221626,
-0.023064838722348213,
0.013276509009301662,
-0.011470284312963486,
-0.05381838604807854,
-0.03567614406347275,
0.0057385750114917755,
0.012950410135090351,
-0.05413056164979935,
-0.004551807884126902,
-0.07870835065841675,
-0.05331481248140335,
0.01721709594130516,
0.031555384397506714,
-0.0273272767663002,
0.008139098063111305,
0.015305637381970882,
0.01536477543413639,
0.011026717722415924,
0.02744433656334877,
0.045519500970840454,
0.07581812143325806,
-0.001454806188121438,
0.02465435490012169,
0.04572373256087303,
-0.03659239411354065,
0.008939224295318127,
0.015392843633890152,
0.010177177377045155,
0.002544752322137356,
-0.04581806808710098,
-0.007301045581698418,
0.06430193036794662,
-0.027768999338150024,
-0.013886063359677792,
-0.03545411303639412,
0.007741666864603758,
0.021672748029232025
] |
<p>I am making a comparation between the photon gas and the ideal classic gas for my Thermodynamics class. The photon gas is defined by the equations:</p>
<p>$$U=aVT^4 $$
$$P=\dfrac{1}{3}aT^4$$</p>
<p>I found this document: <a href="http://www.csupomona.edu/~hsleff/PhotonGasAJP.pdf" rel="nofollow">http://www.csupomona.edu/~hsleff/PhotonGasAJP.pdf</a> which explain how to find some basic things, like enthalpy and entropy. It says that a great exercise is to compare the Carnot cycle of the photon gas with the Carnot cycle of the ideal gas. According to it, the efficiency is $\eta=1-\frac{T_2}{T_1}$ the same as the ideal gas. I think that this is really interesting for my comparation, so I'm trying to calculate the Carnot cycle efficiency for this gas.</p>
<p>I have no problem with the isothermal process, which is solved in that document:
$$W_{ab}=-\dfrac{1}{3}aT^4\Delta V$$</p>
<p>However, I'm not sure if my result of the adiabatic process is correct. Work is $W=\int PdV$. Now, I can use the photon gas adiabatic equation (see the document) $PV^{4/3}=k$, where $k$ is a constant, to substitute $P$ in work equation, and integrate to obtain:</p>
<p>$$W_{bc} =\dfrac{3}{4}k\left( \dfrac{1}{V_b^3} - \dfrac{1}{V_c^3} \right)$$</p>
<p>I'm not sure if this result is correct. When I try to calculate the efficiency of the cycle, I have:
$$\eta=\dfrac{|W_T|}{|Q_{ab}|}=\dfrac{|W_{ab}+W_{bc}+W_{cd}+W_{da}|}{|Q_{ab}|}$$</p>
<p>where $W_{ab}$,$W_{cd}$ are isothermal and $W_{bc}$,$W_{da}$ are adiabatic. The heat is also defined in the document as:</p>
<p>$$Q_{ab}=\dfrac{4}{3}aT^4\Delta V$$</p>
<p>But with these values I can't obtain the correct expression for the efficiency, or I don't know how to reduce the efficiency expression to obtain what I want. Which is the correct way to calculate adiabatic work in a photon gas? And the Carnot cycle efficiency?</p>
<p>Thank you all for your answers :D</p> | g4603 | [
-0.03062691166996956,
-0.045590609312057495,
0.0021196245215833187,
-0.034540653228759766,
-0.0065076337195932865,
-0.033019453287124634,
0.03223361074924469,
0.005367151461541653,
-0.049540914595127106,
0.04592965170741081,
-0.0038300722371786833,
0.03277226909995079,
0.020499123260378838,
-0.014701100997626781,
0.011541816405951977,
0.050564493983983994,
0.027810536324977875,
0.01699216291308403,
0.002555709332227707,
-0.0040720864199101925,
-0.01896938681602478,
-0.012829683721065521,
-0.015469575300812721,
-0.04849880188703537,
0.029979195445775986,
-0.027815472334623337,
0.0025976805482059717,
-0.0022878232412040234,
0.001285287202335894,
-0.0380212739109993,
0.010506052523851395,
0.031104907393455505,
0.004166737664490938,
0.01594921201467514,
-0.052223287522792816,
-0.015462328679859638,
0.07836677134037018,
0.08163144439458847,
0.02709827572107315,
-0.020222580060362816,
0.02564992941915989,
-0.03350745514035225,
0.006280103232711554,
0.03207110986113548,
0.04745836555957794,
0.014717045240104198,
-0.01587670110166073,
-0.020602496340870857,
-0.05382490158081055,
0.04172557219862938,
0.027009014040231705,
0.09409665316343307,
-0.0027968231588602066,
-0.0752130001783371,
0.06754184514284134,
0.027075527235865593,
-0.019491959363222122,
0.012775413691997528,
0.01628265716135502,
0.00941403303295374,
0.003420904977247119,
-0.03856609761714935,
0.02850371226668358,
0.01691763661801815,
0.030086420476436615,
-0.04581226035952568,
0.019842011854052544,
-0.022597426548600197,
0.013388868421316147,
-0.020187100395560265,
-0.037680547684431076,
0.014766262844204903,
0.008370735682547092,
0.02251150831580162,
0.04321493208408356,
-0.05485076829791069,
-0.0030654864385724068,
-0.052134063094854355,
-0.032662637531757355,
0.022212520241737366,
-0.04650411382317543,
-0.022840552031993866,
0.004415674135088921,
-0.05681964382529259,
-0.012780596502125263,
-0.0027562060859054327,
0.04659396782517433,
-0.06469375640153885,
-0.02877330780029297,
-0.00009860091813607141,
-0.0024635670706629753,
0.01707950234413147,
0.05050453171133995,
0.029071306809782982,
0.011346464045345783,
0.07200122624635696,
-0.030800484120845795,
0.06535881757736206,
-0.010216018185019493,
-0.013079369440674782,
-0.02656107395887375,
-0.04652176797389984,
0.004700446035712957,
0.031541477888822556,
-0.030485842376947403,
-0.03697779029607773,
0.022579548880457878,
-0.03297042474150658,
-0.042783625423908234,
-0.010327555239200592,
-0.06598073989152908,
-0.004215293563902378,
-0.025900740176439285,
-0.04627907648682594,
-0.028484607115387917,
-0.05020430311560631,
0.0313902385532856,
0.00816982239484787,
0.025305250659585,
0.031061237677931786,
0.05775905400514603,
0.056099869310855865,
-0.00015042946324683726,
0.013217074796557426,
0.044278908520936966,
-0.020200124010443687,
0.009277296252548695,
-0.012904026545584202,
-0.016783958300948143,
0.004942477215081453,
0.04313974827528,
0.013227105140686035,
0.00518266623839736,
0.02885078638792038,
-0.005242225248366594,
0.04984085634350777,
0.01942731998860836,
-0.01101161539554596,
-0.017936591058969498,
0.01791032776236534,
0.016771161928772926,
0.023103509098291397,
-0.03967409208416939,
0.05359300971031189,
-0.07522333413362503,
0.019614269956946373,
-0.10496696829795837,
-0.05867703631520271,
0.00545521778985858,
-0.0031608317513018847,
0.09209137409925461,
0.04648367315530777,
0.025196146219968796,
-0.0007250211201608181,
0.028834838420152664,
-0.012318442575633526,
0.0101238414645195,
0.0066878036595880985,
0.00444969953969121,
0.023892346769571304,
0.026508066803216934,
-0.044694241136312485,
0.059787262231111526,
-0.0536736398935318,
-0.011543291620910168,
0.017317090183496475,
0.036800503730773926,
-0.05653763562440872,
0.0072561330161988735,
-0.05149371176958084,
-0.054089002311229706,
-0.023857394233345985,
-0.04984010383486748,
-0.03044505976140499,
-0.0331997275352478,
0.02635938487946987,
0.02407773584127426,
0.038222361356019974,
-0.06803098320960999,
-0.031841035932302475,
0.03020932711660862,
0.017804402858018875,
0.06919457018375397,
-0.049334410578012466,
-0.047062795609235764,
-0.00675086909905076,
-0.019356343895196915,
-0.0389811247587204,
-0.07354109734296799,
-0.01712307520210743,
-0.04284999519586563,
0.047862712293863297,
0.08320797234773636,
0.03596089407801628,
-0.033836480230093,
0.0037445295602083206,
-0.023980606347322464,
-0.04003798961639404,
-0.061934538185596466,
0.010420121252536774,
-0.040338173508644104,
0.05121932178735733,
0.038735877722501755,
0.04144987091422081,
0.0035200908314436674,
0.02609185501933098,
0.006500363349914551,
0.01721234619617462,
0.054614126682281494,
0.007316046394407749,
-0.02836734987795353,
0.009867539629340172,
0.019566679373383522,
0.011053632013499737,
-0.0021186380181461573,
0.03029603511095047,
-0.01036085095256567,
0.014666817151010036,
-0.008992299437522888,
-0.024924062192440033,
0.02745935320854187,
-0.04591202735900879,
0.004517714958637953,
0.006151037290692329,
-0.05743490904569626,
0.010460817255079746,
-0.03440825641155243,
0.002836542669683695,
0.003260862547904253,
0.0550217367708683,
-0.0205537099391222,
0.04639286547899246,
0.016202162951231003,
-0.0283399298787117,
0.0007042033248580992,
0.07452357560396194,
-0.018924450501799583,
0.0634230300784111,
0.0013935044407844543,
0.0412290059030056,
0.00036836726940236986,
-0.04725176468491554,
-0.022064505144953728,
0.011761410161852837,
0.008328570052981377,
0.00862869992852211,
0.03469327837228775,
0.016123197972774506,
-0.03274712711572647,
0.010603323578834534,
0.029941460117697716,
0.025950122624635696,
0.014394923113286495,
-0.0046775732189416885,
-0.0037215598858892918,
0.017493396997451782,
0.010460170917212963,
-0.00604963256046176,
-0.012634433805942535,
0.0320412702858448,
0.011754005216062069,
-0.025827987119555473,
-0.01498441118746996,
0.0019678995013237,
-0.00874405913054943,
-0.00610341178253293,
-0.004496028646826744,
0.004903931170701981,
0.011315640062093735,
-0.027427952736616135,
0.04196074977517128,
-0.016148746013641357,
-0.060673199594020844,
-0.013466356322169304,
0.011540290899574757,
-0.03402703255414963,
0.03330416977405548,
-0.03799214959144592,
0.003772875526919961,
-0.053522270172834396,
0.023459678515791893,
0.005393621511757374,
-0.030542274937033653,
0.006072321906685829,
0.05212024971842766,
-0.06219993159174919,
0.007996680215001106,
0.05194499343633652,
0.04472195357084274,
-0.002588412258774042,
0.005507933907210827,
0.015173479914665222,
-0.046476781368255615,
0.025314729660749435,
-0.011595726944506168,
0.0012285925913602114,
0.04322293400764465,
0.005061066243797541,
0.008276027627289295,
-0.009216229431331158,
0.015310157090425491,
-0.04806637391448021,
-0.028676733374595642,
0.015771405771374702,
0.023655200377106667,
0.009672597050666809,
-0.0744740217924118,
-0.010759151540696621,
-0.027528388425707817,
0.0617205947637558,
-0.022272827103734016,
-0.03752740100026131,
0.0015332021284848452,
-0.03417418152093887,
0.006387657485902309,
-0.019596954807639122,
0.05194966867566109,
-0.09047500044107437,
0.027352090924978256,
0.012572646141052246,
-0.0002831219171639532,
-0.031389929354190826,
0.017914757132530212,
-0.0176970437169075,
-0.016649963334202766,
0.02855651266872883,
0.0003810994967352599,
-0.018420075997710228,
-0.028542477637529373,
-0.011221558786928654,
-0.050089672207832336,
0.014946059323847294,
-0.03398889675736427,
-0.02488638460636139,
-0.01746719889342785,
-0.03357144817709923,
-0.012022055685520172,
0.04017013683915138,
-0.00028934437432326376,
-0.04484868422150612,
-0.003408796852454543,
0.042430102825164795,
-0.0052054994739592075,
0.00159155810251832,
-0.009270410053431988,
-0.018182238563895226,
0.006599328480660915,
-0.042201556265354156,
-0.014066353440284729,
0.01849708892405033,
0.09142924845218658,
-0.011216254904866219,
0.018689943477511406,
0.017712347209453583,
-0.04874131828546524,
0.031268589198589325,
-0.011844784021377563,
0.04873150959610939,
0.06870810687541962,
-0.029031852260231972,
-0.008590592071413994,
0.006615982856601477,
0.023166906088590622,
0.0013029674300923944,
-0.04879438132047653,
0.010516174137592316,
-0.004214554559439421,
0.027602458372712135,
0.06698782742023468,
0.016247598454356194,
-0.0018644883530214429,
-0.014502805657684803,
0.0269106924533844,
-0.010019119828939438,
-0.026341509073972702,
-0.03306012600660324,
0.043099723756313324,
0.025295395404100418,
-0.04985193908214569,
0.007873603142797947,
-0.007198524661362171,
0.00836353749036789,
0.03609301149845123,
0.02695261314511299,
0.03488675132393837,
0.010949765332043171,
-0.013077045790851116,
0.016347035765647888,
-0.010415172204375267,
-0.05858777090907097,
0.027380816638469696,
-0.014999962411820889,
-0.09075725823640823,
0.040968071669340134,
-0.020095165818929672,
0.0028101149946451187,
0.06343744695186615,
0.0036092535592615604,
0.006268985103815794,
0.023360371589660645,
-0.04538754001259804,
-0.03831898048520088,
0.003269738983362913,
0.03321399912238121,
-0.06704742461442947,
-0.03551171347498894,
0.02059192582964897,
-0.05618531256914139,
-0.003821644466370344,
0.042841434478759766,
0.004442895296961069,
-0.006474868394434452,
0.023153705522418022,
-0.012665323913097382,
0.06272396445274353,
-0.041048314422369,
-0.03602167218923569,
-0.037512827664613724,
0.03841196000576019,
-0.003975015599280596,
-0.050092823803424835,
0.03149571642279625,
0.007048664148896933,
-0.009802086278796196,
0.04711071401834488,
0.03179758042097092,
0.07218771427869797,
0.025678712874650955,
-0.0005567625630646944,
-0.021301807835698128,
0.014141942374408245,
0.013525860384106636,
-0.059178903698921204,
0.06082712113857269,
-0.008815735578536987,
0.06218450516462326,
-0.0292372964322567,
-0.004667667206376791,
0.08034029603004456,
0.014565284363925457,
0.09466411173343658,
0.006202206015586853,
0.0037061143666505814,
-0.06865064799785614,
0.03540053591132164,
0.04409217834472656,
-0.03205517306923866,
-0.007473493926227093,
0.016764171421527863,
-0.06772082298994064,
-0.0010428258683532476,
-0.00548649812117219,
0.026999076828360558,
-0.006881223060190678,
-0.021380465477705002,
0.05715995281934738,
0.01419263519346714,
0.02799074351787567,
-0.011743851006031036,
0.042590584605932236,
-0.07332900166511536,
-0.010936267673969269,
0.029380865395069122,
-0.026072608307003975,
0.028874635696411133,
0.00012300566595513374,
-0.05212000012397766,
0.0631006509065628,
-0.07006020843982697,
-0.07155279815196991,
0.041058316826820374,
0.023712648078799248,
-0.034733474254608154,
-0.02065359428524971,
-0.04817456379532814,
0.009473097510635853,
0.005962285678833723,
-0.028229249641299248,
0.030927931889891624,
0.02255457080900669,
0.004416545387357473,
-0.0015672303270548582,
-0.009341567754745483,
0.04269522428512573,
0.01671912707388401,
-0.03721854090690613,
-0.07482863962650299,
-0.049365296959877014,
0.008470380678772926,
-0.03135170787572861,
-0.035564593970775604,
0.04807928204536438,
0.04559134319424629,
-0.0645330399274826,
0.0012376460945233703,
0.030923523008823395,
0.06756073981523514,
0.023469343781471252,
-0.000265851296717301,
0.016781454905867577,
-0.07890605181455612,
-0.004837650805711746,
-0.07519277185201645,
-0.03791319578886032,
0.0014271872350946069,
-0.029229510575532913,
-0.009428945370018482,
0.03820188716053963,
0.022704213857650757,
0.024981003254652023,
0.034772612154483795,
-0.004751947242766619,
0.02078329585492611,
0.042641784995794296,
-0.004792308434844017,
0.008675502613186836,
0.010771241039037704,
-0.06399688124656677,
0.025922561064362526,
-0.10962343961000443,
0.0858144536614418,
0.0144800478592515,
-0.00032980507239699364,
0.03631113842129707,
0.10535278916358948,
-0.026028024032711983,
-0.031056825071573257,
-0.031138775870203972,
0.018191659823060036,
0.0022578255739063025,
-0.028271738439798355,
0.004047003574669361,
-0.017428820952773094,
-0.029255462810397148,
0.006341680884361267,
-0.009870404377579689,
-0.012960952706634998,
0.0013914959272369742,
0.07616978883743286,
0.0009380600531585515,
-0.05028800666332245,
-0.048044826835393906,
-0.00897009763866663,
0.010842042043805122,
0.021020377054810524,
-0.01940770633518696,
-0.03278780356049538,
-0.016182569786906242,
-0.033057842403650284,
0.02454262226819992,
0.006241173483431339,
0.004667815752327442,
0.05128655582666397,
-0.059877876192331314,
0.011584706604480743,
0.00251095462590456,
-0.004823263268917799,
0.01715085282921791,
0.03280191868543625,
-0.010997685603797436,
0.04780283942818642,
0.09023679047822952,
0.003151153214275837,
0.022507067769765854,
-0.03845991566777229,
-0.07867150008678436,
0.02112986333668232,
-0.015398383140563965,
0.0464315339922905,
-0.029588932171463966,
-0.010949082672595978,
0.03476971387863159,
0.0007189770112745464,
-0.00897626020014286,
0.024389976635575294,
0.0020553520880639553,
0.0004680472775362432,
-0.06989672034978867,
-0.05022360011935234,
-0.035723213106393814,
-0.030604537576436996,
-0.057311832904815674,
-0.02168651483952999,
-0.06967589259147644,
-0.0007361791795119643,
0.025963876396417618,
-0.03284449502825737,
-0.014862903393805027,
-0.04156871885061264,
0.04760318994522095,
-0.02088223583996296,
0.004338879603892565,
-0.015100091695785522,
0.05525752902030945,
0.013563376851379871,
-0.0018390135373920202,
0.02846159040927887,
-0.03149181604385376,
-0.03440990671515465,
0.004201027099043131,
-0.010163890197873116,
-0.0073598334565758705,
0.009949341416358948,
-0.06677944213151932,
0.012615788727998734,
0.05059363692998886,
-0.0206411425024271,
0.06551338732242584,
-0.02312197908759117,
-0.008307084441184998,
-0.04883286729454994,
0.028265543282032013,
0.023280048742890358,
0.02516131103038788,
0.004281213972717524,
-0.024358870461583138,
-0.018036428838968277,
0.09312663227319717,
0.057980727404356,
0.017949357628822327,
-0.002631338546052575,
0.03454986959695816,
0.08762181550264359,
-0.007795583922415972,
0.08026475459337234,
0.03395889699459076,
0.0035336914006620646,
0.041342418640851974,
0.029426995664834976,
-0.013487916439771652,
0.008445393294095993,
0.00043063965858891606,
-0.034325528889894485,
0.009979700669646263,
0.011097853071987629,
0.014888463541865349,
-0.09993785619735718,
-0.013079077936708927,
0.011243827641010284,
0.06619207561016083,
-0.010498186573386192,
0.05224734544754028,
0.05389520153403282,
0.04389392212033272,
-0.014387039467692375,
0.0073756445199251175,
0.05659152567386627,
-0.0855385959148407,
-0.04904623702168465,
-0.0007463359506800771,
0.03847893700003624,
-0.028785517439246178,
0.0005206037894822657,
-0.030827779322862625,
-0.03262169286608696,
0.0699019581079483,
-0.011981986463069916,
0.04104451835155487,
-0.04318032041192055,
-0.04991732910275459,
0.0311293788254261,
-0.043495625257492065,
0.005903682205826044,
0.054679661989212036,
0.05719086527824402,
0.03533471003174782,
0.04660928621888161,
-0.022798068821430206,
-0.011534013785421848,
-0.08145967870950699,
-0.007762305438518524,
-0.023920448496937752,
-0.03782125562429428,
0.0006483877077698708,
0.04594912752509117,
0.034525543451309204,
0.023238252848386765,
0.010799198411405087,
-0.01815544068813324,
-0.028742872178554535,
-0.039786502718925476,
0.011314557865262032,
-0.06328865140676498,
-0.024297406896948814,
0.004942535422742367,
0.07985153794288635,
-0.06708227843046188,
-0.013817546889185905,
0.02498766779899597,
0.013358005322515965,
-0.016718372702598572,
-0.04045882821083069,
0.015850888565182686,
-0.01818951591849327,
-0.025761663913726807,
0.0569625198841095,
0.007314061746001244,
0.016294565051794052,
0.0023278347216546535,
-0.00344968237914145,
0.040261249989271164,
-0.024189459159970284,
-0.0239394623786211,
0.031868696212768555,
-0.03262165188789368,
0.02223784476518631,
-0.02988390251994133,
-0.030553506687283516,
0.02561161294579506,
0.0029792680870741606,
0.0384889654815197,
-0.010012669488787651,
-0.02050360105931759,
-0.093343585729599,
0.022074460983276367,
-0.019507912918925285,
-0.027684958651661873,
-0.000013124115866958164,
0.07590314745903015,
0.019794004037976265,
-0.03819591924548149,
0.006588308606296778,
-0.005250865127891302,
-0.06131632998585701,
-0.07578568160533905,
-0.04085154086351395,
0.06499101221561432,
-0.03559216111898422,
0.04470377415418625,
-0.028145289048552513,
-0.012505299411714077,
-0.022521592676639557,
-0.03903133422136307,
-0.030254602432250977,
0.014289671555161476,
0.029715893790125847,
-0.01617937907576561,
-0.006239891983568668,
0.04491906240582466,
0.065895676612854,
-0.050879716873168945,
-0.054111458361148834,
0.046368781477212906,
-0.06582017242908478,
0.03812602907419205,
-0.015122240409255028,
-0.013434527441859245,
-0.004927514120936394,
0.03667227178812027,
-0.006537833251059055,
0.026140011847019196,
-0.06274417787790298,
-0.023045117035508156,
-0.028843985870480537,
0.034295227378606796,
-0.030650151893496513,
0.042984701693058014,
-0.01237242016941309,
0.03309648111462593,
0.0031005702912807465,
-0.007680361159145832,
0.039320848882198334,
-0.03377240151166916,
0.04998241737484932,
0.04094391316175461,
-0.03869025409221649,
0.01938086748123169,
-0.02981223538517952
] |
<p>What is the molecular level reason behind the pattern (sine function) of the waves?</p>
<p><img src="http://i.stack.imgur.com/wAoQL.jpg" alt="enter image description here"></p> | g4604 | [
0.012782908976078033,
0.00153931207023561,
-0.029374664649367332,
-0.04917751997709274,
0.06419192999601364,
0.03233746439218521,
0.0425599105656147,
0.039211101830005646,
0.0258022528141737,
-0.05113808438181877,
-0.041024282574653625,
0.021757042035460472,
0.01537265069782734,
0.03163148835301399,
0.006229599937796593,
-0.07408961653709412,
0.02100859023630619,
0.048883967101573944,
0.039472758769989014,
-0.010593481361865997,
-0.0647631511092186,
-0.015688899904489517,
-0.012952068820595741,
-0.026243671774864197,
0.024953806772828102,
0.017462970688939095,
0.048830341547727585,
-0.03826344758272171,
-0.006460113916546106,
-0.004405984189361334,
0.033780720084905624,
-0.011011229828000069,
0.038250457495450974,
0.0006822239956818521,
-0.03074106015264988,
0.03247278928756714,
-0.04780745133757591,
0.05870411917567253,
0.017371471971273422,
0.03140954673290253,
-0.05528530851006508,
-0.04035171866416931,
-0.010441047139465809,
-0.03408122807741165,
-0.008002808317542076,
-0.015086309984326363,
-0.017385000362992287,
-0.007093389052897692,
-0.013133197091519833,
-0.06896550953388214,
-0.00632775854319334,
-0.024516021832823753,
0.044142961502075195,
-0.02417873591184616,
0.03494937717914581,
0.08353059738874435,
0.039826273918151855,
0.062129728496074677,
0.052298855036497116,
0.04205944389104843,
0.019045762717723846,
0.0402534119784832,
0.03196348622441292,
-0.0016511756693944335,
0.051847927272319794,
-0.04576801508665085,
-0.03933923318982124,
0.027760641649365425,
-0.003117560176178813,
0.040840644389390945,
0.0015102701727300882,
-0.06009357422590256,
-0.09742604196071625,
-0.02938014455139637,
-0.002761115087196231,
0.005830975715070963,
0.016428861767053604,
0.059214722365140915,
-0.013981332071125507,
-0.02703365497291088,
-0.013916470110416412,
0.011169569566845894,
-0.060545600950717926,
0.07073573023080826,
0.03901290148496628,
-0.04334595799446106,
0.01634162850677967,
0.0016306465258821845,
0.0011311122216284275,
0.04735462740063667,
0.025087300688028336,
-0.00817837379872799,
0.020832296460866928,
-0.01206327136605978,
-0.04544395953416824,
-0.03431352972984314,
-0.010806441307067871,
0.03798895701766014,
0.022543450817465782,
0.004333639983087778,
0.046036407351493835,
0.0012883002636954188,
0.005791904870420694,
-0.027096277102828026,
-0.01579952985048294,
0.061128489673137665,
-0.011035955511033535,
-0.014504353515803814,
0.0026758366730064154,
0.0019729011692106724,
-0.03663552924990654,
0.027011653408408165,
-0.03531857579946518,
0.05604131519794464,
-0.0020313262939453125,
-0.008260893635451794,
-0.0023946701548993587,
-0.003748160321265459,
-0.0006373772630468011,
0.03768773004412651,
-0.00008079001418082044,
-0.05544671043753624,
-0.043994974344968796,
0.008597075939178467,
-0.02051166258752346,
-0.006924396380782127,
0.04982106387615204,
0.0037991285789757967,
0.015836939215660095,
-0.03407897800207138,
0.04690505564212799,
0.02826506271958351,
-0.021888410672545433,
-0.015449988655745983,
0.002316814148798585,
-0.024887073785066605,
-0.016664182767271996,
-0.038320593535900116,
0.037072841078042984,
0.002635276410728693,
0.046451419591903687,
-0.00837035570293665,
0.04923845827579498,
-0.09177158772945404,
-0.023134315386414528,
-0.02415517531335354,
-0.005733141675591469,
0.024611061438918114,
0.04629548266530037,
-0.03865193575620651,
-0.04307275637984276,
0.04253232106566429,
0.05376902595162392,
-0.029287001118063927,
0.0292972344905138,
-0.035844847559928894,
0.010298547334969044,
0.04142852500081062,
-0.04043805971741676,
0.0400756299495697,
0.04159729927778244,
-0.033531997352838516,
-0.02906440757215023,
0.01872202381491661,
-0.09062062948942184,
-0.03519514948129654,
0.011555835604667664,
-0.053010493516922,
-0.01333940401673317,
-0.011075560003519058,
-0.00752283725887537,
0.03787674754858017,
-0.023876631632447243,
0.023996923118829727,
0.003958520479500294,
0.07501198351383209,
0.03415781259536743,
-0.04096760228276253,
0.12028916925191879,
-0.018867626786231995,
-0.0036098065320402384,
-0.02542235143482685,
0.004290633834898472,
-0.03319315239787102,
0.04001716151833534,
-0.025730589404702187,
0.024887550622224808,
0.008283627219498158,
-0.0752151682972908,
0.0220157690346241,
0.005580763798207045,
-0.0707935243844986,
-0.040803659707307816,
-0.035321712493896484,
0.005465873517096043,
0.0058366041630506516,
0.0018852009670808911,
0.020037217065691948,
-0.04596500098705292,
0.05823344737291336,
-0.02261771634221077,
0.03428318351507187,
0.027798444032669067,
-0.02928023599088192,
-0.0032288848888128996,
0.017569759860634804,
0.0009241490624845028,
0.01850317046046257,
-0.014344645664095879,
0.04864839091897011,
-0.07515140622854233,
0.00658273184671998,
-0.011870816349983215,
-0.0022250430192798376,
-0.0332370400428772,
0.0004184455319773406,
0.048852816224098206,
0.01184217631816864,
-0.0025714607909321785,
0.03572480008006096,
0.006738313008099794,
-0.0013675016816705465,
-0.01107129454612732,
0.013307644985616207,
0.02468409202992916,
0.004817036911845207,
-0.03529445081949234,
-0.019220540300011635,
-0.002773658372461796,
-0.00432794401422143,
-0.05653475970029831,
-0.04172021523118019,
0.004710040986537933,
0.02797679416835308,
0.06307407468557358,
0.05110817402601242,
0.01332668773829937,
-0.010812054388225079,
0.009364073164761066,
-0.010909533128142357,
-0.0031567669939249754,
0.015439438633620739,
0.017545241862535477,
-0.03177858889102936,
0.04540186747908592,
0.00043773194192908704,
-0.060876622796058655,
-0.038335803896188736,
-0.07199026644229889,
-0.00011528013419592753,
0.07172942906618118,
-0.036957353353500366,
-0.0375802218914032,
0.06776179373264313,
-0.014811006374657154,
-0.083188995718956,
0.010898984968662262,
0.046719592064619064,
0.03711037337779999,
-0.027204107493162155,
-0.012368831783533096,
0.04412290081381798,
0.032997358590364456,
-0.01587381400167942,
-0.02585086226463318,
-0.05906281992793083,
0.01853371039032936,
0.022116689011454582,
0.02904721535742283,
-0.07499183714389801,
0.0059913224540650845,
0.06887523829936981,
-0.02060810476541519,
-0.039870306849479675,
-0.02490105852484703,
0.02638033591210842,
0.07789415866136551,
-0.002538928994908929,
-0.0562518872320652,
-0.01919955387711525,
-0.005874386057257652,
0.03281087055802345,
-0.03656838461756706,
0.024818161502480507,
0.04166160523891449,
-0.026408419013023376,
-0.00808886718004942,
0.040426697582006454,
-0.026192912831902504,
0.08153114467859268,
0.03302106261253357,
0.015877369791269302,
0.036824148148298264,
0.023683713749051094,
0.0131537402048707,
0.0024729082360863686,
0.03145439550280571,
-0.081403948366642,
-0.00040200501098297536,
0.06711447238922119,
-0.008004618808627129,
0.02405964583158493,
0.01182403415441513,
-0.010024813935160637,
-0.03771524876356125,
-0.018174508586525917,
0.022156737744808197,
-0.004248935729265213,
-0.07555238902568817,
0.02763522043824196,
0.03965899348258972,
-0.0572676882147789,
0.00867194589227438,
0.006818590220063925,
-0.029197530820965767,
0.058757636696100235,
-0.06558150053024292,
0.02784811519086361,
0.0021698044147342443,
0.009888251312077045,
-0.06255161017179489,
-0.057710837572813034,
-0.0013065163511782885,
-0.031160002574324608,
0.03259690850973129,
0.05359673127532005,
-0.0029382952488958836,
-0.06700325012207031,
-0.00048509740736335516,
-0.07820150256156921,
-0.01319489348679781,
-0.04794174060225487,
-0.017227385193109512,
0.008194269612431526,
0.012176573276519775,
-0.022237999364733696,
-0.07069935649633408,
0.05552691966295242,
-0.003743550041690469,
0.01506284810602665,
-0.03113473951816559,
0.056630946695804596,
-0.019578073173761368,
-0.08362367004156113,
-0.0018287079874426126,
0.02952725999057293,
-0.028850790113210678,
-0.014521964825689793,
-0.017193380743265152,
-0.08119454979896545,
-0.05874602496623993,
0.03518936038017273,
-0.01679529994726181,
-0.0032849712297320366,
-0.06313841789960861,
0.020964045077562332,
0.043794699013233185,
-0.03799063339829445,
-0.033010706305503845,
-0.01701398752629757,
-0.03406298905611038,
-0.010455464012920856,
-0.00017465777636971325,
0.01734831929206848,
-0.01880153827369213,
0.004296945873647928,
0.0018905058968812227,
0.04403122887015343,
0.0226584505289793,
-0.04460352659225464,
-0.05489866062998772,
0.003966768272221088,
-0.017587997019290924,
0.030144691467285156,
-0.010668333619832993,
0.012849747203290462,
-0.014010254293680191,
0.023477669805288315,
-0.06677036732435226,
0.011904596351087093,
0.025517528876662254,
-0.049333151429891586,
0.006262509152293205,
0.014191633090376854,
0.03851010277867317,
0.009014971554279327,
-0.08387350291013718,
0.0024409352336078882,
0.009148749522864819,
-0.032527435570955276,
-0.0035539038944989443,
-0.02561212331056595,
-0.0480332151055336,
-0.01503660436719656,
0.02903106063604355,
-0.06897301971912384,
0.0012331035686656833,
0.03421095386147499,
-0.015949254855513573,
0.09837306290864944,
0.0299790408462286,
-0.05769718065857887,
-0.027739450335502625,
-0.033754218369722366,
0.01205479260534048,
0.0009134728461503983,
0.004199060145765543,
-0.0318111926317215,
-0.02788762003183365,
0.00972648337483406,
-0.002083610277622938,
-0.0002729110128711909,
0.02788822166621685,
-0.04652511328458786,
-0.039945680648088455,
0.08551780134439468,
0.06367100030183792,
-0.041460730135440826,
0.014935247600078583,
0.021899476647377014,
-0.019693493843078613,
0.09501805156469345,
-0.008468675427138805,
0.054686661809682846,
0.015520730055868626,
0.020631765946745872,
0.04700349271297455,
0.01130738016217947,
0.05376856029033661,
-0.02968919649720192,
0.02340676449239254,
0.0001356715802103281,
-0.024701019749045372,
-0.04494829103350639,
-0.10357024520635605,
-0.004096099641174078,
-0.015146716497838497,
0.00046089422539807856,
-0.03442225977778435,
0.08414638787508011,
0.0000018738402332019177,
0.001860251883044839,
-0.0044220369309186935,
0.005794813856482506,
0.02300836518406868,
0.05327964946627617,
0.015087171457707882,
-0.0340760312974453,
-0.023510396480560303,
-0.024302199482917786,
-0.051188625395298004,
0.029618415981531143,
-0.030825108289718628,
-0.05058153346180916,
0.05236007645726204,
-0.029369764029979706,
-0.06028459221124649,
0.0622725747525692,
-0.03251556307077408,
0.030622592195868492,
-0.05604243278503418,
0.05167267099022865,
-0.06802481412887573,
0.003673110157251358,
0.06259013712406158,
0.01770833320915699,
0.0008507330785505474,
-0.019251279532909393,
-0.01123161893337965,
0.013950847089290619,
0.04901190102100372,
-0.046802304685115814,
0.04449610784649849,
-0.005232266150414944,
-0.029067883267998695,
0.018939729779958725,
-0.007931116037070751,
-0.0204874686896801,
-0.024049680680036545,
-0.04746205732226372,
-0.027110490947961807,
0.04515693709254265,
0.031375933438539505,
0.04272126033902168,
-0.014262855984270573,
-0.005628779996186495,
-0.01367107592523098,
0.04931266978383064,
-0.05655589699745178,
0.0010760233271867037,
0.012032715603709221,
0.000747371232137084,
0.0043927947990596294,
-0.05365031212568283,
0.03494751825928688,
-0.04932045564055443,
0.03740324452519417,
-0.012896176427602768,
0.022592123597860336,
-0.0641244575381279,
-0.011561824940145016,
0.004492605105042458,
-0.0011022420367226005,
0.013338060118258,
-0.023888252675533295,
0.012139677070081234,
-0.01026882790029049,
-0.04083271324634552,
0.019535472616553307,
-0.01689792238175869,
0.036109618842601776,
-0.06988488882780075,
0.008413380943238735,
-0.03666924312710762,
0.01910439319908619,
-0.08514043688774109,
0.016579389572143555,
-0.005425572860985994,
-0.0012744367122650146,
0.019019950181245804,
-0.03386038541793823,
0.020459959283471107,
0.024138374254107475,
-0.03101464919745922,
0.011759143322706223,
0.024341490119695663,
0.027394043281674385,
-0.024615027010440826,
0.01950216479599476,
0.08296909183263779,
-0.02884376049041748,
0.0359916128218174,
0.05383531376719475,
0.08713386952877045,
0.037523891776800156,
-0.02296772599220276,
-0.008492894470691681,
0.028421351686120033,
-0.007248668000102043,
0.002427520230412483,
0.04533065855503082,
-0.0002858523221220821,
-0.04352607950568199,
0.06018167361617088,
0.05373980104923248,
0.0035114367492496967,
0.04304222762584686,
-0.011551524512469769,
-0.00386259937658906,
0.024666350334882736,
-0.00002294321711815428,
0.06121877208352089,
0.001133181620389223,
-0.023755354806780815,
-0.022950517013669014,
0.03520597890019417,
-0.09126867353916168,
-0.03284222632646561,
-0.02481476217508316,
0.00763729028403759,
0.044715095311403275,
0.03207207843661308,
0.016057077795267105,
-0.04199008271098137,
0.05570961534976959,
0.005511589348316193,
-0.005338562652468681,
0.07451120018959045,
0.07253166288137436,
0.001961396774277091,
-0.07481180131435394,
0.01152748428285122,
-0.023790037259459496,
0.05058245733380318,
0.012228654697537422,
0.05354725196957588,
0.013456379994750023,
-0.0022314165253192186,
-0.013700190000236034,
-0.022579416632652283,
0.0006464216276071966,
0.009688923135399818,
-0.004699666518718004,
0.021373063325881958,
0.023996783420443535,
-0.045339249074459076,
0.0061112744733691216,
-0.008946482092142105,
0.06530462950468063,
-0.01097314152866602,
-0.07243743538856506,
0.006344200111925602,
-0.013302098959684372,
0.026508519425988197,
0.0367867536842823,
-0.048983506858348846,
0.00788868311792612,
0.039934225380420685,
0.028927860781550407,
-0.04150748997926712,
0.020901279523968697,
-0.022924387827515602,
0.010267704725265503,
0.019328175112605095,
-0.011294515803456306,
0.024816017597913742,
-0.024664685130119324,
-0.009482274763286114,
-0.10353735834360123,
0.06221235543489456,
-0.024713532999157906,
0.014230678789317608,
-0.0018323012627661228,
-0.0229103434830904,
-0.042669571936130524,
-0.03416765481233597,
-0.023433294147253036,
0.06679295748472214,
-0.012440783903002739,
-0.012877725064754486,
0.025172531604766846,
-0.003635992528870702,
0.004088436719030142,
-0.001611274667084217,
0.004390082787722349,
-0.003957176581025124,
-0.024430256336927414,
-0.005758404266089201,
0.013541392982006073,
0.011741935275495052,
0.003479602048173547,
0.032160792499780655,
0.021644385531544685,
0.051770541816949844,
-0.06595908105373383,
-0.017570847645401955,
-0.038415875285863876,
-0.002973395399749279,
0.07734871655702591,
0.007176992949098349,
-0.001497269724495709,
0.03266860544681549,
0.07545886188745499,
-0.0028141902294009924,
-0.03684931993484497,
-0.00613431865349412,
0.01980583928525448,
-0.05808860436081886,
-0.013840918429195881,
-0.012821640819311142,
0.05176805332303047,
-0.035433750599622726,
0.004508987534791231,
0.023884834721684456,
0.030148236081004143,
-0.021667541936039925,
0.045359306037425995,
-0.02088748849928379,
0.004623119253665209,
-0.04326839745044708,
-0.04855338856577873,
-0.008724316954612732,
-0.013462343253195286,
0.020230473950505257,
0.040179163217544556,
0.07352423667907715,
-0.023973584175109863,
-0.05068916454911232,
0.037919651716947556,
-0.011739283800125122,
-0.013886969536542892,
-0.0301457978785038,
0.015751009806990623,
-0.019143685698509216,
0.0029111700132489204,
0.024834876880049706,
-0.006471215281635523,
-0.0429728701710701,
-0.006686368491500616,
0.0071114529855549335,
0.041456807404756546,
0.03346988558769226,
0.029160527512431145,
-0.06582869589328766,
0.03194382041692734,
0.009444940835237503,
-0.009675420820713043,
-0.008486848324537277,
0.0029342607595026493,
0.020743679255247116,
-0.0016000726027414203,
0.03905794769525528,
-0.03517347574234009,
0.0037771884817630053,
0.027687784284353256,
0.031852319836616516,
0.0063319639302790165,
-0.009760239161550999,
0.0013530653668567538,
0.03778766468167305,
-0.0034929339308291674,
0.02098417654633522,
0.013120380230247974,
-0.02612009271979332,
-0.0017614576499909163,
-0.02721989154815674,
0.014091185294091702,
-0.010474822483956814,
0.007371704559773207,
-0.05398431420326233,
0.02927416004240513,
-0.056654129177331924,
0.002616070443764329,
0.028638657182455063,
0.03740634769201279,
0.04972787946462631,
-0.04084604233503342,
0.012663811445236206,
-0.07501893490552902,
-0.012783026322722435,
-0.008269266225397587,
0.06385781615972519,
0.01726684719324112,
-0.02012387104332447,
0.000001926565801113611,
-0.01867246814072132,
0.03578920662403107,
0.007567687425762415,
0.02131478860974312,
-0.01643395610153675,
-0.06573667377233505,
0.04657341167330742,
0.013151855207979679,
-0.038078226149082184,
-0.03719766438007355,
0.0011572301154956222,
-0.03677213937044144,
-0.01604262925684452,
0.03812987357378006,
0.015505323186516762,
0.04858486354351044,
0.02193954586982727,
0.014198364689946175,
-0.023084623739123344,
-0.04496549069881439,
-0.05026770010590553,
-0.014876431785523891,
-0.028561249375343323,
0.06274820864200592,
-0.027625126764178276,
0.03505276143550873,
0.024316975846886635,
-0.006569639779627323,
0.04059986397624016,
0.051537130028009415,
-0.043748144060373306,
-0.0008907730807550251,
0.02818041667342186,
0.05000750347971916,
-0.047297898679971695,
0.017199063673615456,
-0.007812537252902985,
0.0022297678515315056,
0.00011305007501505315,
0.05508070066571236,
-0.009066087193787098,
-0.048808541148900986,
-0.05195729061961174
] |
<p>Let a wire be shaped according to some even function $y=f(x)$, with $f'(0)=0$ and $f''(0)>0$, and let a bead of negligible size slide frictionlessly on the wire. Let the bead oscillate under the influence of gravity about $x=0$ with amplitude $A$ (i.e., between $x=-A$ and $x=+A$) and frequency $\omega(A)$. Clearly $\omega$ is nearly constant for small $A$; it differs from the frequency $\omega_o$ of simple harmonic motion by at most $O(A^2)$. By choosing $f$ to be a fourth-order polynomial, we could presumably adjust the wire's shape so as to eliminate the errors of order $A^2$ and make $\omega(A)$ constant up to $O(A^4)$. Possibly we could continue this process of approximation and make all the derivatives $d^n\omega/dA^n$ vanish up to some finite $n$, or maybe for all $n$.</p>
<p>If the derivatives can be made to vanish for all $n$, then I think $\omega$ would have to be nonanalytic at $x=0$. It seems impossible that there is any $f$ such that isochrony holds for arbitrarily large $A$. No matter how steep you make the sides, the bead can't do any better than accelerating downward with acceleration $g$. Therefore I think the best $f$ you can find is probably one that blows up to infinity at $|x|$ equal to some $x_{max}$. On dimensional grounds, we would have to have $x_{max}=cL$, where $c$ is a unitless constant and $L=g/\omega_0^2$.</p>
<p>So my multipart question is: (1) Is there a function $f$ that gives $d^n\omega/dA^n=0$ for all $n$? If so, ... (2) How is $f$ characterized, and what is $c$? (3) Is $\omega(A)$ analytic at $x=0$, and if so, what is its radius of convergence to its Taylor series in units of $L$?</p> | g4605 | [
0.051748309284448624,
0.027609923854470253,
-0.0036313633900135756,
0.005099220667034388,
0.016550302505493164,
-0.009442392736673355,
0.0928991511464119,
-0.04303663223981857,
-0.03713756799697876,
-0.013692381791770458,
-0.07300300896167755,
-0.020697198808193207,
-0.0009740263922140002,
0.06409365683794022,
0.03028005175292492,
-0.001632910338230431,
0.02675769105553627,
-0.005333408713340759,
0.06248679757118225,
-0.024349698796868324,
0.01392857450991869,
-0.0040076980367302895,
-0.0035286175552755594,
-0.0007837825105525553,
0.07449100911617279,
-0.0005885688005946577,
0.060583893209695816,
-0.037193961441516876,
-0.03666374459862709,
-0.0030723486561328173,
0.004340094514191151,
-0.03405648097395897,
0.0373595729470253,
-0.025107216089963913,
-0.032484110444784164,
0.008553897961974144,
0.003188955830410123,
0.003714796155691147,
0.037825535982847214,
0.002487185411155224,
0.03737325593829155,
-0.047757335007190704,
0.03555312752723694,
0.046918805688619614,
0.022267049178481102,
-0.01359033863991499,
-0.006272403988987207,
0.028831971809267998,
0.003021989716216922,
-0.011471602134406567,
0.01104395929723978,
0.019089918583631516,
0.06349185854196548,
-0.07026297599077225,
-0.03046823851764202,
0.05997766926884651,
0.013677569106221199,
0.0248266588896513,
-0.02563192881643772,
0.10717844218015671,
-0.03194349259138107,
-0.05490749701857567,
0.008887349627912045,
0.004491742234677076,
0.042307060211896896,
-0.031982533633708954,
-0.025174742564558983,
-0.04563514515757561,
0.02087288722395897,
0.0035629915073513985,
0.026189669966697693,
-0.07793094217777252,
-0.0030922701116651297,
0.019235316663980484,
-0.06454057991504669,
0.0037519587203860283,
-0.03880360722541809,
-0.029395058751106262,
0.01772002875804901,
-0.0318937674164772,
-0.08849352598190308,
0.06336341053247452,
-0.046832021325826645,
0.026165207847952843,
-0.012880758382380009,
-0.04229672998189926,
0.06231371685862541,
-0.012825585901737213,
0.017226150259375572,
0.035275693982839584,
0.05412859097123146,
0.0031462402548640966,
0.004859092645347118,
-0.028628148138523102,
0.027817388996481895,
0.001999881351366639,
-0.01948968879878521,
0.11906224489212036,
0.02555011585354805,
-0.02339104376733303,
-0.029350848868489265,
0.01844632998108864,
0.016741998493671417,
0.04913228005170822,
0.0004738701391033828,
-0.015928002074360847,
0.08113735169172287,
-0.04353964701294899,
0.021510852500796318,
-0.0009776076767593622,
-0.008903794921934605,
-0.028253035619854927,
-0.03694245591759682,
-0.05599795654416084,
-0.0379113033413887,
-0.010305236093699932,
-0.011020057834684849,
-0.000446539546828717,
-0.04980045184493065,
0.078901007771492,
0.007876711897552013,
-0.034728165715932846,
0.053801242262125015,
0.05707535147666931,
-0.017507631331682205,
0.05255741998553276,
0.0011342881480231881,
0.07465135306119919,
0.02426348812878132,
-0.024524910375475883,
0.017158377915620804,
0.030880926176905632,
0.05977120250463486,
-0.009019174613058567,
-0.010804051533341408,
0.023149525746703148,
-0.09103455394506454,
0.012832258827984333,
-0.05076070874929428,
0.05058737471699715,
-0.018736088648438454,
-0.09176380187273026,
0.01531127281486988,
-0.015509339049458504,
-0.06442548334598541,
0.041096072643995285,
0.012801376171410084,
-0.024528715759515762,
0.03219512104988098,
0.005785277113318443,
0.03757782652974129,
0.07021094858646393,
0.019710252061486244,
-0.029775520786643028,
0.008279294706881046,
0.06365552544593811,
0.09453348815441132,
0.003840812249109149,
0.004702720791101456,
-0.013803480193018913,
0.0024810696486383677,
-0.03669729083776474,
0.01488362718373537,
-0.004330809693783522,
-0.032650914043188095,
0.06964244693517685,
-0.03898868337273598,
-0.04749350622296333,
0.049170587211847305,
-0.024887844920158386,
-0.06013784185051918,
-0.011798239313066006,
0.01793309487402439,
0.026926638558506966,
-0.029585668817162514,
0.04307146370410919,
-0.019532538950443268,
-0.0494343526661396,
0.004076479002833366,
0.039048340171575546,
0.03132924437522888,
0.00347252213396132,
0.0011956398375332355,
-0.00034916040021926165,
0.01604638062417507,
0.04943982884287834,
0.04366191104054451,
-0.028550181537866592,
-0.008970068767666817,
0.020355384796857834,
-0.02634095959365368,
-0.04526694864034653,
-0.004943158943206072,
0.05217508226633072,
-0.029944544658064842,
0.00654835207387805,
-0.01958969049155712,
-0.0366118885576725,
-0.0437929593026638,
0.04025264456868172,
0.053662002086639404,
0.08639034628868103,
0.02706928551197052,
-0.01455353107303381,
0.012044400908052921,
0.027861667796969414,
-0.020514899864792824,
0.00033111192169599235,
-0.01760256476700306,
0.008152058348059654,
0.07775777578353882,
-0.003100121393799782,
-0.002454436384141445,
0.038788802921772,
-0.008433681912720203,
-0.05329953879117966,
0.003009652951732278,
0.006971603725105524,
0.009510823525488377,
-0.002627529203891754,
0.03551014885306358,
-0.04227345064282417,
0.0023162986617535353,
0.012602293863892555,
-0.049537401646375656,
-0.009390079416334629,
-0.01990167610347271,
-0.011045956052839756,
-0.000228755539865233,
0.005747480783611536,
-0.09468752145767212,
-0.06139705330133438,
-0.021080415695905685,
-0.04341670125722885,
0.016345836222171783,
0.004374537616968155,
-0.034549955278635025,
-0.032175514847040176,
-0.01035887561738491,
0.01103645283728838,
0.025682099163532257,
-0.0156807042658329,
-0.020785560831427574,
-0.062093768268823624,
0.018162857741117477,
-0.01790311187505722,
-0.045886337757110596,
0.07450021058320999,
0.0061741117388010025,
0.05579270049929619,
0.06660563498735428,
-0.021163491532206535,
-0.011384748853743076,
0.04271819442510605,
-0.018834533169865608,
0.022628851234912872,
-0.00452551431953907,
0.007415943779051304,
-0.020841296762228012,
-0.048777613788843155,
-0.027059640735387802,
0.014422563835978508,
0.008996665477752686,
-0.004250388592481613,
-0.03996092453598976,
-0.002615523524582386,
-0.03644435852766037,
-0.017729856073856354,
-0.005579215008765459,
-0.0013714514207094908,
0.01301480457186699,
0.02120809257030487,
0.019617179408669472,
0.05245080962777138,
0.02301916852593422,
0.0334458127617836,
-0.001639694906771183,
0.002774687483906746,
-0.0023348357062786818,
0.0362180732190609,
0.0021221921779215336,
-0.018239688128232956,
-0.01871166005730629,
-0.004074167925864458,
-0.004273773171007633,
-0.03608278930187225,
0.05300150439143181,
0.021782854571938515,
-0.005751412361860275,
0.014684042893350124,
-0.048616837710142136,
0.03136776387691498,
0.05083451792597771,
-0.009994002990424633,
-0.03771113231778145,
0.06246345490217209,
-0.032874662429094315,
-0.027686094865202904,
0.0177195742726326,
0.028493018820881844,
-0.02312493696808815,
-0.04642527550458908,
-0.013189262710511684,
0.03308935835957527,
-0.016031136736273766,
0.0464576818048954,
-0.02844412811100483,
-0.07104428857564926,
0.020531777292490005,
0.01790016144514084,
0.03589829429984093,
0.005465198308229446,
0.0044096689671278,
-0.06581398844718933,
-0.006531237158924341,
-0.015484687872231007,
0.030655235052108765,
-0.01809176243841648,
0.03014298342168331,
0.03605334833264351,
-0.01585296355187893,
-0.03192051500082016,
-0.009225384332239628,
-0.02781783416867256,
-0.004073284100741148,
-0.019935470074415207,
0.008564584888517857,
0.032001446932554245,
-0.07436826080083847,
-0.006331082433462143,
0.04615062102675438,
-0.008322563953697681,
0.026674319058656693,
-0.0005284780054353178,
0.0019277981482446194,
-0.08094463497400284,
0.0014216677518561482,
0.01926152966916561,
0.06959440559148788,
0.036385662853717804,
-0.09447241574525833,
-0.031595684587955475,
0.020534588024020195,
-0.04286469891667366,
-0.015380991622805595,
0.021625753492116928,
-0.005375656299293041,
0.05031893402338028,
-0.02152087911963463,
-0.020362671464681625,
0.09733704477548599,
-0.033023640513420105,
0.02445009909570217,
-0.033963657915592194,
0.06846822053194046,
0.035191137343645096,
0.05341041088104248,
0.036890704184770584,
-0.058331768959760666,
-0.07411492615938187,
-0.014829345047473907,
-0.06731719523668289,
-0.023688901215791702,
0.024692941457033157,
0.06525442004203796,
-0.025527967140078545,
0.05180022120475769,
0.05874146148562431,
-0.06097208335995674,
-0.0048196688294410706,
-0.0653635710477829,
-0.0035331635735929012,
-0.008185600861907005,
0.00285994540899992,
-0.010845744051039219,
-0.032804835587739944,
-0.03835083171725273,
0.018281051889061928,
-0.007951419800519943,
0.026615101844072342,
-0.0015203033108264208,
0.010210814885795116,
-0.001618046429939568,
-0.012795907445251942,
0.025657493621110916,
0.016691191121935844,
-0.009785009548068047,
-0.06666843593120575,
-0.02422507107257843,
-0.021275296807289124,
0.03468706086277962,
-0.030295349657535553,
0.043085165321826935,
-0.02224878966808319,
-0.01286130677908659,
-0.05218612402677536,
0.052793774753808975,
0.010528843849897385,
-0.08679669350385666,
-0.019177241250872612,
0.046042781323194504,
-0.055920980870723724,
-0.03917565569281578,
-0.003220252227038145,
-0.012354954145848751,
0.020570266991853714,
0.02653423510491848,
-0.017592594027519226,
0.02948090434074402,
-0.020392945036292076,
0.039408128708601,
-0.05145525559782982,
0.045611973851919174,
-0.08238229900598526,
0.03319527581334114,
-0.002525175688788295,
0.027196235954761505,
0.007025254890322685,
-0.0044440608471632,
-0.0034484094940125942,
0.04837661609053612,
0.055010873824357986,
0.017091231420636177,
-0.007980828173458576,
0.008055103942751884,
0.013987611047923565,
-0.008073397912085056,
-0.008935662917792797,
0.0112915663048625,
-0.0001243794395122677,
-0.016507336869835854,
0.004400698468089104,
-0.01262163557112217,
0.010753313079476357,
-0.041761819273233414,
0.012412931770086288,
-0.0014653303660452366,
0.017169855535030365,
0.006158630363643169,
0.06553943455219269,
0.07122216373682022,
0.02230752445757389,
0.025550859048962593,
-0.01774314045906067,
0.03682200610637665,
0.031490758061409,
-0.014406207017600536,
-0.041107553988695145,
-0.008914067409932613,
0.025513986125588417,
0.009650133550167084,
-0.0036019673570990562,
-0.021144108846783638,
0.026775620877742767,
-0.03568369150161743,
-0.00830659456551075,
-0.028291817754507065,
0.0026138178072869778,
0.0018430105410516262,
0.04676247388124466,
-0.004256151616573334,
-0.0610647089779377,
-0.08093709498643875,
0.04263356328010559,
0.000967198982834816,
0.024058887735009193,
-0.060104817152023315,
-0.00958163756877184,
-0.07473944872617722,
0.04191797226667404,
-0.03980252146720886,
0.06363791227340698,
0.06036309525370598,
-0.004818274173885584,
-0.04774967581033707,
-0.027830347418785095,
-0.0348220095038414,
0.03356034308671951,
-0.044618211686611176,
-0.005443225614726543,
-0.016190312802791595,
-0.05123230442404747,
-0.010649937205016613,
0.013569171540439129,
-0.023787036538124084,
-0.00724103394895792,
0.0018225169042125344,
-0.025343967601656914,
0.008126312866806984,
0.0220700241625309,
0.019141225144267082,
0.00835139025002718,
0.02690514177083969,
0.02216833271086216,
-0.0469517782330513,
-0.014967438764870167,
0.02252582646906376,
-0.03613509237766266,
-0.0032132298219949007,
0.03600927069783211,
-0.0580093190073967,
0.018817119300365448,
-0.029800811782479286,
0.005859105382114649,
-0.03302868828177452,
0.06103665754199028,
0.03128558769822121,
-0.011273916810750961,
0.013051421381533146,
0.0636659562587738,
-0.022790951654314995,
0.08680278807878494,
-0.04736325517296791,
-0.003140312386676669,
-0.03660237416625023,
0.007243442814797163,
-0.04134461656212807,
-0.01301319245249033,
-0.054052017629146576,
-0.00215303641743958,
0.041215069591999054,
0.03186370059847832,
-0.00553471501916647,
0.026524605229496956,
0.03612498193979263,
0.04583162069320679,
0.0011535711819306016,
-0.031326811760663986,
-0.018180372193455696,
0.008173205889761448,
0.017991527915000916,
-0.02317151427268982,
-0.01759011670947075,
-0.035529498010873795,
0.02406632900238037,
0.05476721376180649,
-0.0007264205487444997,
0.005301396828144789,
-0.01624620147049427,
-0.016720114275813103,
-0.02915620245039463,
0.0060357931070029736,
0.008650551550090313,
0.04521744325757027,
-0.04484538361430168,
-0.02422100491821766,
-0.0020446833223104477,
0.052526041865348816,
0.0018460705177858472,
-0.027786698192358017,
-0.06605584174394608,
-0.02442440576851368,
-0.018362946808338165,
0.07994250953197479,
-0.05081385001540184,
0.05796702951192856,
0.02510674297809601,
-0.06932515650987625,
0.0005065936129540205,
-0.02138340473175049,
0.021327555179595947,
0.0012453494127839804,
0.0019487097160890698,
-0.006561379414051771,
-0.008902163244783878,
-0.06042879819869995,
-0.01295839436352253,
0.03122926875948906,
0.07138071954250336,
0.04034071043133736,
-0.028807366266846657,
-0.04253433272242546,
-0.04217109456658363,
0.03373866155743599,
0.06401226669549942,
0.00014930508041288704,
-0.05523093417286873,
-0.04189756140112877,
0.012408196926116943,
0.040387969464063644,
-0.04876886308193207,
0.04635804519057274,
-0.0024344001431018114,
-0.01108913216739893,
-0.028937149792909622,
-0.0024891288485378027,
-0.010939906351268291,
0.021200869232416153,
0.010397234931588173,
-0.03288814425468445,
-0.05415111035108566,
0.010578143410384655,
0.004367518704384565,
-0.011100362986326218,
0.0017778078326955438,
-0.0458897240459919,
-0.004257561173290014,
-0.004925265908241272,
-0.01882593147456646,
0.007387153804302216,
0.021637167781591415,
0.00677092419937253,
0.04996321722865105,
0.027664557099342346,
-0.002003571717068553,
0.028930729255080223,
0.017940381541848183,
-0.018680742010474205,
0.01849902607500553,
0.006987148895859718,
0.025263119488954544,
0.05127546563744545,
0.0020250999368727207,
-0.007896690629422665,
0.007143567781895399,
-0.047695521265268326,
-0.0006765265134163201,
-0.043737705796957016,
0.03525488078594208,
-0.02953598089516163,
0.02221740037202835,
0.02949942834675312,
-0.02006509341299534,
0.015782229602336884,
0.027615362778306007,
-0.03222871199250221,
-0.040442876517772675,
0.006755935028195381,
-0.027868159115314484,
-0.022314611822366714,
0.04758110269904137,
0.0591391958296299,
-0.06924629211425781,
0.06550238281488419,
-0.0034025448840111494,
0.05425771325826645,
-0.049719616770744324,
0.034258730709552765,
0.010560364462435246,
0.03914763033390045,
0.007841002196073532,
0.06591141223907471,
-0.00041510703158564866,
0.043858788907527924,
-0.01750035025179386,
-0.029132386669516563,
0.03628745302557945,
0.02638169750571251,
-0.03556802123785019,
0.024652214720845222,
0.04500189051032066,
-0.010532181710004807,
-0.05288735777139664,
0.022878920659422874,
-0.0024593123234808445,
-0.023069234564900398,
-0.018883313983678818,
0.04120167717337608,
-0.0075679440051317215,
-0.03469597175717354,
-0.008864201605319977,
-0.023734204471111298,
0.0743197351694107,
-0.028895294293761253,
-0.007878338918089867,
0.0489928312599659,
0.03154425695538521,
-0.03912346810102463,
-0.06031475216150284,
-0.0034429116640239954,
0.014110117219388485,
-0.01987440139055252,
0.007385308854281902,
0.007042135577648878,
0.06886706501245499,
0.028147101402282715,
-0.0007744496688246727,
-0.01842242106795311,
-0.027316821739077568,
0.04083326458930969,
0.032676536589860916,
-0.020349865779280663,
0.02708548866212368,
-0.03209521621465683,
-0.032870300114154816,
0.066197969019413,
-0.04687416926026344,
0.03356905281543732,
-0.049427568912506104,
-0.009674631990492344,
0.0032319296151399612,
0.10661782324314117,
-0.009778675623238087,
-0.04567905142903328,
0.0035304161719977856,
0.044576238840818405,
-0.03176344186067581,
0.010003405623137951,
-0.01718592457473278,
-0.0097370445728302,
-0.019795000553131104,
-0.03500794991850853,
-0.020707644522190094,
0.0015093849506229162,
-0.06998425722122192,
-0.004846431780606508,
-0.027516456320881844,
-0.020991157740354538,
-0.01569351740181446,
0.03880026564002037,
-0.003799326019361615,
0.08080863207578659,
-0.06604810059070587,
0.019979937002062798,
0.06785467267036438,
0.03761933743953705,
-0.030887067317962646,
-0.01599949784576893,
0.028699690476059914,
-0.038302503526210785,
-0.03397182747721672,
-0.01419826503843069,
-0.01561431773006916,
-0.07483500242233276,
-0.008113729767501354,
-0.030396901071071625,
-0.06677724421024323,
-0.014897823333740234,
-0.014728980138897896,
-0.025887809693813324,
-0.04035070911049843,
-0.030983438715338707,
0.0066456240601837635,
0.018686197698116302,
-0.03917691856622696,
-0.03647669404745102,
-0.023588720709085464,
-0.01673690229654312,
-0.03587537631392479,
0.020788300782442093,
0.032926954329013824,
-0.03306743502616882,
-0.024508798494935036,
-0.010433845221996307,
0.023328347131609917,
0.06350450962781906,
-0.017661238089203835,
0.05567231401801109,
0.027005985379219055,
-0.043062593787908554,
-0.01374885719269514,
0.012500038370490074,
-0.014196678064763546,
-0.006938657723367214,
0.0015251407166942954,
-0.01662316359579563,
0.01851441152393818,
0.05878066644072533,
0.008093871176242828,
-0.05725996568799019,
-0.058225929737091064,
-0.057376712560653687,
-0.03544389083981514,
0.0385676845908165,
0.01434430293738842,
-0.0825287476181984,
0.052333198487758636,
0.008781373500823975
] |
<p>When a ray of ordinary light is passed on the surface of the water the reflected light will be completely polarized( vibrations in one plane).</p>
<p>My question is what will be <strong>plane of vibration in the partially polarized light</strong> that undergoes refraction? <strong>How many planes of vibration</strong> will be there? Deep explanation focusing on the <strong>planes of vibration</strong> of the partially polarized light would be appreciated.</p> | g4606 | [
0.019411437213420868,
0.026014024391770363,
0.008343011140823364,
-0.006032166536897421,
0.007865514606237411,
0.012177948839962482,
0.045690570026636124,
0.0002446859434712678,
0.03994571417570114,
-0.03928226977586746,
-0.004726381506770849,
0.00695048039779067,
-0.0341162383556366,
-0.009834603406488895,
-0.01616002433001995,
0.00478839036077261,
0.03238054737448692,
0.00889312569051981,
0.04412103071808815,
0.017675306648015976,
-0.06059694662690163,
0.008016386069357395,
-0.01974058896303177,
-0.07322140783071518,
-0.027420666068792343,
0.03167414292693138,
-0.01114236656576395,
-0.04756825417280197,
0.015374197624623775,
0.003155136713758111,
-0.007673019543290138,
-0.055569715797901154,
0.013194240629673004,
-0.00011869684385601431,
-0.005741119850426912,
-0.023921430110931396,
0.023860003799200058,
0.031189538538455963,
0.033605776727199554,
-0.015014834702014923,
0.021996760740876198,
0.032395970076322556,
-0.07953653484582901,
-0.011207247152924538,
0.08664531260728836,
-0.020319130271673203,
-0.011222819797694683,
-0.008501535281538963,
-0.052777163684368134,
-0.00874699279665947,
0.017129890620708466,
-0.004750736989080906,
0.02533602900803089,
0.024088913574814796,
-0.024663878604769707,
0.08832996338605881,
-0.020904110744595528,
0.016178466379642487,
0.0038596594240516424,
0.010018612258136272,
0.008361296728253365,
0.014636492356657982,
-0.0278093870729208,
0.04862170293927193,
0.0016488900873810053,
-0.031030841171741486,
-0.04415607079863548,
-0.022721363231539726,
0.07729053497314453,
0.027608521282672882,
0.012263622134923935,
-0.022267216816544533,
-0.04835129901766777,
-0.031412798911333084,
-0.036895833909511566,
-0.041361790150403976,
0.0042263213545084,
-0.0023086662404239178,
-0.017442453652620316,
0.041805800050497055,
0.07977750152349472,
-0.01157525833696127,
-0.03904278203845024,
-0.01514840591698885,
0.09175818413496017,
-0.01038452610373497,
-0.03292042016983032,
0.003693508915603161,
-0.03566897660493851,
-0.034268490970134735,
0.025075120851397514,
-0.028801236301660538,
0.05412551760673523,
0.0017022270476445556,
0.025853155180811882,
-0.06006114184856415,
0.0059932745061814785,
0.015578247606754303,
-0.05474556237459183,
0.01157266553491354,
-0.025363117456436157,
-0.020343994721770287,
0.0006520479219034314,
0.016984064131975174,
0.08809808641672134,
0.0010330516379326582,
0.010729768313467503,
-0.023326249793171883,
0.006118322256952524,
0.054088931530714035,
-0.021101446822285652,
-0.05398466810584068,
-0.004430690314620733,
-0.058930885046720505,
-0.019208766520023346,
-0.02647463046014309,
0.09502705186605453,
0.0521184466779232,
0.0012339403619989753,
0.1101016029715538,
0.0653645247220993,
0.011726068332791328,
-0.00032091044704429805,
0.06174890697002411,
-0.028961388394236565,
0.03322813659906387,
0.027021683752536774,
0.04250861704349518,
0.052500784397125244,
0.046645477414131165,
-0.03670015186071396,
0.017579520121216774,
-0.016348568722605705,
-0.019520152360200882,
0.006959362421184778,
0.012786039151251316,
-0.003238164819777012,
-0.05158988758921623,
-0.0010075039463117719,
-0.022234147414565086,
0.013255726546049118,
0.02598601020872593,
-0.04682257026433945,
0.019175900146365166,
0.01939532347023487,
-0.015583316795527935,
0.05537140741944313,
0.0030092326924204826,
0.012747306376695633,
0.018801549449563026,
0.011675986461341381,
0.02795892208814621,
0.000921347236726433,
-0.04991433769464493,
-0.012869028374552727,
-0.03966221213340759,
0.04829603433609009,
-0.045794934034347534,
0.041259873658418655,
0.021735016256570816,
0.02197105623781681,
0.006752608809620142,
0.03166010603308678,
-0.007187558803707361,
-0.04676399379968643,
-0.015270233154296875,
-0.02767902798950672,
-0.07887022942304611,
0.0002432939800200984,
-0.03482387959957123,
-0.03890042379498482,
0.009080459363758564,
-0.0031884785275906324,
0.022638671100139618,
-0.008289899677038193,
0.09445590525865555,
0.04605536162853241,
0.0021298083011060953,
-0.021077066659927368,
0.03616117686033249,
-0.033638857305049896,
0.0008758328622207046,
-0.002064554952085018,
-0.021508216857910156,
-0.043913036584854126,
-0.05121932178735733,
-0.007004326209425926,
-0.0051923757418990135,
-0.06709079444408417,
0.029681434854865074,
-0.04111073538661003,
0.029668746516108513,
-0.01282096654176712,
-0.017262063920497894,
-0.021020110696554184,
-0.015793750062584877,
0.025972334668040276,
0.0058950018137693405,
-0.020358318462967873,
0.03274926915764809,
0.036165136843919754,
0.03295882046222687,
0.04196725785732269,
0.04458623006939888,
-0.010679000057280064,
0.056937526911497116,
-0.005063724238425493,
-0.02534569427371025,
-0.04578021541237831,
0.02268543653190136,
0.014248068444430828,
0.00013411790132522583,
-0.0053067076951265335,
-0.0267485361546278,
-0.04576960206031799,
0.08506165444850922,
-0.036183249205350876,
0.03202416002750397,
0.0025397134013473988,
0.0315704271197319,
-0.008151669055223465,
0.02758471854031086,
-0.03972383216023445,
0.06033700332045555,
0.011344263330101967,
0.04972516745328903,
-0.05808476358652115,
-0.011432527564466,
0.07209765166044235,
0.03378639742732048,
-0.05020472779870033,
-0.02199650928378105,
0.07400128990411758,
0.054442986845970154,
-0.007311999797821045,
0.04242830350995064,
-0.0706123560667038,
0.04766223952174187,
0.0074531142599880695,
-0.05068129673600197,
0.038582805544137955,
0.0333343930542469,
-0.03505870699882507,
0.006368783302605152,
-0.03255072608590126,
0.026658831164240837,
0.014318134635686874,
-0.042713895440101624,
0.06704727560281754,
0.08137800544500351,
0.036902446299791336,
-0.0037971073761582375,
0.06696183979511261,
0.06330844759941101,
-0.022966202348470688,
-0.017691386863589287,
0.0028048560488969088,
0.0280886460095644,
0.007719376124441624,
-0.043870870023965836,
-0.025461845099925995,
-0.019429925829172134,
0.01153242215514183,
-0.003785555949434638,
-0.03097887709736824,
-0.009498413652181625,
0.0736466497182846,
0.028094695881009102,
0.03769815340638161,
-0.0017478414811193943,
-0.03544921800494194,
0.09287073463201523,
0.03306710720062256,
0.026908690109848976,
-0.014649245887994766,
-0.031213605776429176,
-0.004386584274470806,
-0.03228515386581421,
-0.036911532282829285,
0.019921479746699333,
-0.00931208860129118,
0.051302868872880936,
-0.04893484711647034,
-0.013974650762975216,
-0.00474830437451601,
-0.03959036245942116,
0.06180666759610176,
0.020234473049640656,
-0.01908867061138153,
0.05143279954791069,
-0.0941050723195076,
-0.05731085315346718,
0.055511657148599625,
0.011097249574959278,
-0.0270177461206913,
-0.007234160788357258,
0.009140954352915287,
-0.022625206038355827,
0.010719609446823597,
0.07632455974817276,
0.01644703932106495,
-0.016304494813084602,
-0.007188797928392887,
0.011840477585792542,
-0.050433848053216934,
0.004533246159553528,
0.026659982278943062,
-0.06053851172327995,
0.005792528856545687,
0.045376189053058624,
-0.0025146969128400087,
-0.021513640880584717,
0.02080729603767395,
-0.003448048373684287,
-0.010494926944375038,
0.025226671248674393,
-0.050494007766246796,
0.020166469737887383,
-0.006997702177613974,
-0.0047376505099236965,
-0.048249632120132446,
-0.00908722449094057,
-0.008506535552442074,
-0.0007880218327045441,
0.017981627956032753,
-0.06301449239253998,
0.011040168814361095,
0.0656575858592987,
-0.021738355979323387,
0.009461396373808384,
0.008202650584280491,
-0.005166446324437857,
-0.05175624042749405,
-0.030522633343935013,
-0.008453592658042908,
-0.01709609478712082,
-0.040122728794813156,
0.026719313114881516,
0.05439232662320137,
0.013373593799769878,
0.0069515639916062355,
-0.03488772362470627,
-0.050721488893032074,
-0.06523662060499191,
0.04721122235059738,
-0.015218561515212059,
-0.04117342084646225,
-0.040576234459877014,
0.002657988341525197,
-0.013028008863329887,
0.04065626114606857,
-0.0022783989552408457,
-0.016663966700434685,
0.03586909919977188,
-0.06293357163667679,
0.060108449310064316,
-0.015490680001676083,
0.025222674012184143,
0.007910267449915409,
-0.02272139862179756,
0.012218577787280083,
-0.050503622740507126,
0.051278501749038696,
-0.029622424393892288,
-0.013291336596012115,
-0.004174191039055586,
0.004581643268465996,
-0.018925169482827187,
-0.013660971075296402,
0.019495291635394096,
0.016395723447203636,
-0.08229845762252808,
-0.005438837688416243,
-0.038585346192121506,
0.030970541760325432,
0.000506931624840945,
-0.028033046051859856,
-0.03711025044322014,
-0.09165555983781815,
0.04975191131234169,
0.03672492504119873,
0.008216047659516335,
0.06659527122974396,
0.004217623267322779,
0.021454690024256706,
0.043072450906038284,
-0.022951865568757057,
-0.0001628135214559734,
-0.0056395442225039005,
-0.020518619567155838,
0.0494704470038414,
-0.03993675485253334,
-0.05277860909700394,
0.012450789101421833,
0.016332823783159256,
-0.07167863845825195,
0.03507823497056961,
0.0048437281511723995,
-0.053308676928281784,
0.02085012011229992,
0.0223421361297369,
0.046897001564502716,
-0.013771885074675083,
0.000560385815333575,
0.006806402001529932,
-0.006389033515006304,
0.016217432916164398,
-0.05855078250169754,
-0.020359467715024948,
0.011867676861584187,
0.016184309497475624,
-0.03983255475759506,
-0.039319269359111786,
-0.09458927810192108,
-0.02581965923309326,
0.04848637804389,
-0.009562892839312553,
-0.0003088840749114752,
-0.01654031127691269,
0.017697541043162346,
0.03224591165781021,
0.025372859090566635,
-0.02224322222173214,
-0.010067984461784363,
0.008404359221458435,
-0.00577338133007288,
0.044933222234249115,
-0.03248422592878342,
-0.03360548987984657,
-0.12777014076709747,
-0.013479599729180336,
-0.009130879305303097,
-0.007039267104119062,
-0.0029999990947544575,
-0.044105496257543564,
0.042791225016117096,
0.002528790384531021,
0.021982917562127113,
-0.019983697682619095,
0.0383443646132946,
0.03164638951420784,
0.013829031027853489,
0.03938665986061096,
0.020786771550774574,
0.03728741779923439,
0.0018860966665670276,
-0.0070544141344726086,
-0.07058563828468323,
0.04356149211525917,
-0.049234677106142044,
-0.052775196731090546,
0.01318392064422369,
-0.05515384301543236,
-0.0019663884304463863,
-0.04369049519300461,
0.043146762996912,
-0.03701899200677872,
0.016766268759965897,
-0.03495032340288162,
0.021879415959119797,
-0.008137254044413567,
-0.013564076274633408,
0.0062617091462016106,
-0.022935913875699043,
0.027401231229305267,
-0.038796499371528625,
-0.01641133613884449,
0.01272858027368784,
-0.08083976805210114,
0.006842575967311859,
0.009531009942293167,
0.04431542009115219,
0.0034843338653445244,
0.0007490235730074346,
0.0014537334209308028,
0.029761310666799545,
-0.07071510702371597,
-0.03671756386756897,
0.01884048990905285,
-0.05107955262064934,
0.03253331407904625,
-0.0200213473290205,
-0.02661287598311901,
-0.04668917879462242,
-0.01443551480770111,
-0.0037949534598737955,
0.033521801233291626,
0.03949800133705139,
-0.09281652420759201,
-0.0453014113008976,
-0.0671376958489418,
-0.03737808018922806,
-0.052186623215675354,
0.004018694162368774,
0.004213535692542791,
-0.021630598232150078,
-0.029111094772815704,
-0.07582218199968338,
0.02577938511967659,
0.026482045650482178,
-0.01338617317378521,
-0.029605403542518616,
0.025638585910201073,
-0.013513235375285149,
-0.01831333339214325,
-0.006067377980798483,
0.030507296323776245,
-0.045175738632678986,
-0.008808310143649578,
0.06849413365125656,
0.016973329707980156,
-0.04791202023625374,
-0.03697925806045532,
0.03230678290128708,
0.008784595876932144,
-0.063480444252491,
0.011046761646866798,
0.09379936009645462,
-0.041298385709524155,
0.00984248798340559,
0.009978457354009151,
-0.0064611900597810745,
-0.018471650779247284,
-0.015714718028903008,
0.0396113358438015,
-0.026204951107501984,
-0.04186442866921425,
0.015245183371007442,
0.06537719070911407,
-0.03620849549770355,
0.06378372758626938,
0.029224688187241554,
0.03275318816304207,
0.002670901594683528,
0.02859589084982872,
-0.0735882893204689,
0.0024050220381468534,
-0.008196852169930935,
0.019678214564919472,
0.030140681192278862,
-0.044311441481113434,
0.024151287972927094,
0.04763404652476311,
0.0842069685459137,
-0.0029186327010393143,
0.015862291678786278,
0.001479085418395698,
0.021055780351161957,
-0.0007265337626449764,
0.07305718958377838,
-0.01002640649676323,
0.023772913962602615,
-0.044525146484375,
0.023686813190579414,
-0.01861623115837574,
0.029776563867926598,
-0.0003065330092795193,
-0.07600951194763184,
0.015850426629185677,
-0.03506780415773392,
0.048578668385744095,
0.056166354566812515,
-0.026270192116498947,
-0.0383349172770977,
-0.012430625036358833,
-0.02899191342294216,
-0.014248673804104328,
-0.021201161667704582,
0.03407420590519905,
-0.0156787671148777,
-0.009473597630858421,
0.037396110594272614,
-0.004197637550532818,
0.01638907380402088,
0.0106135793030262,
0.015988824889063835,
0.005358187481760979,
-0.0112988892942667,
-0.054771166294813156,
0.04526161029934883,
0.01741880364716053,
-0.0008043317357078195,
0.0022042980417609215,
0.018244629725813866,
-0.012895563617348671,
-0.028972065076231956,
-0.01643749698996544,
0.001739628380164504,
0.0312157291918993,
-0.029991915449500084,
-0.014340605586767197,
-0.043444324284791946,
-0.039573755115270615,
0.002915693214163184,
0.054951876401901245,
-0.03898795321583748,
0.06979086995124817,
0.0322403647005558,
-0.014518176205456257,
0.003019173862412572,
0.07261953502893448,
0.007250980008393526,
0.03885076940059662,
-0.022212304174900055,
0.01598573848605156,
-0.02257869392633438,
-0.022624975070357323,
-0.06585536897182465,
0.002612448064610362,
0.06406155228614807,
0.042256880551576614,
0.02193661592900753,
-0.040473345667123795,
-0.036818020045757294,
-0.05031733959913254,
-0.05292242392897606,
0.0065338644199073315,
-0.034977320581674576,
0.057713184505701065,
0.007536894176155329,
-0.001506551168859005,
-0.0650683343410492,
0.030128497630357742,
-0.0461629256606102,
0.06169653311371803,
0.00958703737705946,
-0.02353457547724247,
-0.015152307227253914,
0.012738188728690147,
0.06759299337863922,
0.04940025880932808,
0.02631421387195587,
0.003330009523779154,
0.029309943318367004,
0.029912810772657394,
0.03532897308468819,
-0.07291550934314728,
-0.004082108847796917,
0.031535953283309937,
0.02629156783223152,
0.01770414039492607,
0.027051936835050583,
0.016937019303441048,
0.019022218883037567,
-0.05815190449357033,
0.014083248563110828,
0.0120018869638443,
-0.0832076296210289,
-0.04696090146899223,
-0.028304945677518845,
-0.03924844041466713,
-0.05370514467358589,
-0.003756089136004448,
0.03783131763339043,
-0.04612395167350769,
0.018077364191412926,
-0.029574880376458168,
-0.019306158646941185,
-0.05804240703582764,
0.015741512179374695,
-0.011138856410980225,
0.0010221994016319513,
-0.02393389493227005,
-0.03319409489631653,
-0.032973334193229675,
0.05910283327102661,
-0.000002040444996964652,
-0.03360840305685997,
0.0007825165521353483,
0.024670850485563278,
0.012348944321274757,
-0.04710998013615608,
0.031228773295879364,
0.03083929419517517,
-0.0001414577418472618,
0.062270984053611755,
0.006019748281687498,
-0.03121955133974552,
0.06980614364147186,
0.014979786239564419,
-0.03541899472475052,
0.06525900959968567,
0.001775032957084477,
-0.026097524911165237,
0.01832682266831398,
-0.036447685211896896,
-0.02063201367855072,
0.023043310269713402,
0.012387944385409355,
-0.053801730275154114,
-0.0001679360429989174,
-0.025655081495642662,
-0.011426909826695919,
0.003939671441912651,
0.021388482302427292,
-0.01710359752178192,
0.03717314824461937,
0.0025153388269245625,
0.033805329352617264,
-0.007531392388045788,
-0.019114337861537933,
0.05088917911052704,
-0.0005155198159627616,
0.02275979518890381,
-0.03656410053372383,
-0.018407857045531273,
0.02250843122601509,
-0.05976353958249092,
0.03976000100374222,
-0.03416698798537254,
0.000974655500613153,
0.0661482885479927,
0.024193905293941498,
-0.02990548312664032,
-0.019904812797904015,
-0.009747925214469433,
-0.003537274431437254,
0.026262979954481125,
-0.011655734851956367,
-0.0018791619222611189,
0.012877124361693859,
0.010631248354911804,
-0.01245793979614973,
-0.04274992272257805,
0.026389257982373238,
-0.023600436747074127,
0.04878599941730499,
-0.0032808417454361916,
0.0642467588186264,
0.050860948860645294,
0.0013160401722416282,
0.025618119165301323,
-0.04998846724629402,
0.010859448462724686,
-0.003568761982023716,
0.03050845116376877,
-0.0034830577205866575,
-0.001955304993316531,
0.02724616415798664,
-0.008477703668177128,
0.07974909991025925,
-0.011203763075172901,
-0.02035018429160118,
-0.04074450954794884,
-0.024554627016186714,
0.03402142971754074,
0.023289011791348457,
-0.00304071931168437,
0.034041937440633774,
-0.022714944556355476,
-0.04999835789203644,
0.05253239721059799,
0.06292847543954849,
0.028641950339078903,
0.03322736173868179,
-0.10976195335388184,
0.039124343544244766,
0.0018091892125084996,
0.01627541519701481,
-0.04723886772990227,
0.014148185960948467,
0.016317252069711685,
-0.026334404945373535,
-0.017503464594483376,
-0.04398741200566292,
-0.04226173833012581,
-0.039383664727211,
0.028607577085494995
] |
<p>If a future astronaut travelled to Alpha Centauri at a significant percentage of light-speed?
Apart from increased blue shifted radiation from their direction of travel - how would they experience other cosmic radiation? </p>
<p>If the trip took a subject several times faster than an observer on earth. Would the astronaut get less or more time / exposure to cosmic radiation?</p> | g4607 | [
-0.0277181975543499,
0.07386880367994308,
0.03090243600308895,
0.022838251665234566,
-0.028422068804502487,
0.0336790606379509,
-0.02469857782125473,
0.03281145542860031,
0.0036921650171279907,
-0.012524036690592766,
0.0792706087231636,
0.02572774700820446,
0.02536144107580185,
0.05813110992312431,
0.046259623020887375,
-0.004891398828476667,
0.1210041269659996,
-0.05113881826400757,
0.0168744008988142,
-0.00925004668533802,
0.018651874735951424,
-0.022640584036707878,
-0.03679559752345085,
-0.02990531362593174,
-0.014524402096867561,
-0.03738243132829666,
0.002846353454515338,
-0.026712484657764435,
-0.0865979865193367,
-0.026017259806394577,
0.04014957323670387,
-0.05532826855778694,
-0.016595570370554924,
-0.022258520126342773,
0.012185133993625641,
-0.018222924321889877,
0.003119175788015127,
0.03831598162651062,
-0.04996928572654724,
0.012406679801642895,
-0.008269131183624268,
-0.0204280074685812,
0.003386163152754307,
-0.0017875992925837636,
0.015323363244533539,
0.030137229710817337,
0.012187495827674866,
-0.006248812191188335,
-0.006718950811773539,
0.02057708613574505,
-0.06718248873949051,
0.004260653629899025,
0.005138866603374481,
0.04594797268509865,
0.04645724594593048,
-0.007097255438566208,
0.014828148297965527,
-0.06328234821557999,
0.0703929141163826,
0.01642909087240696,
-0.0121178412809968,
-0.09551499038934708,
0.00853580329567194,
-0.020631924271583557,
-0.007882552221417427,
-0.02143627405166626,
0.016431277617812157,
0.05563599616289139,
0.04502623900771141,
-0.020653478801250458,
0.06142541766166687,
-0.010748976841568947,
-0.0981932207942009,
-0.03552376851439476,
0.017042549327015877,
0.003362862393260002,
0.03216525539755821,
-0.012486753053963184,
0.025134630501270294,
0.09448482096195221,
-0.06489930301904678,
-0.007048097439110279,
-0.004144439473748207,
-0.016410725191235542,
0.06334440410137177,
-0.03899122402071953,
0.0010732848895713687,
-0.028024494647979736,
0.033982157707214355,
-0.01810223050415516,
0.03458678349852562,
-0.05568228289484978,
0.029324235394597054,
0.03176102787256241,
0.046484097838401794,
-0.027492215856909752,
-0.018164271488785744,
0.04710417985916138,
-0.025489194318652153,
-0.01019009854644537,
0.017937764525413513,
-0.005822908133268356,
0.01573188230395317,
0.053471848368644714,
0.0012427176116034389,
-0.07719400525093079,
-0.010155481286346912,
-0.026554850861430168,
-0.016601605340838432,
-0.005339675582945347,
-0.015201169066131115,
-0.06461072713136673,
0.03306543827056885,
0.013507307507097721,
-0.028311675414443016,
-0.06223108619451523,
0.0075537897646427155,
-0.017058659344911575,
0.015781711786985397,
0.0328630693256855,
-0.0076986877247691154,
0.056364431977272034,
-0.039772894233465195,
-0.01932850293815136,
-0.04185279458761215,
0.029071953147649765,
-0.030032729730010033,
-0.02982781082391739,
0.030921002849936485,
0.032302457839250565,
-0.04208714887499809,
0.023607952520251274,
0.016457078978419304,
0.049813952296972275,
-0.01695271208882332,
0.009367846883833408,
0.01794126071035862,
0.012188758701086044,
-0.007492734119296074,
0.010960958898067474,
0.025735124945640564,
-0.03967534005641937,
0.021149465814232826,
0.009936503134667873,
-0.03009609691798687,
0.0251472145318985,
-0.03497016057372093,
0.02763213962316513,
0.05030817911028862,
0.03173311799764633,
0.03368888422846794,
0.05564802139997482,
0.04754152148962021,
-0.006112126167863607,
0.031500253826379776,
0.021697424352169037,
-0.0346260666847229,
-0.013557309284806252,
-0.04722423106431961,
0.05384232476353645,
0.03980882093310356,
0.01571512036025524,
0.018949704244732857,
-0.03018699400126934,
-0.008417492732405663,
0.006838735658675432,
0.013699193485081196,
-0.07059361785650253,
-0.0228891558945179,
-0.009368181228637695,
-0.010767204686999321,
-0.005677429959177971,
0.08768795430660248,
0.009175902232527733,
0.009452789090573788,
0.027096061035990715,
0.047027964144945145,
-0.03006904199719429,
-0.018358565866947174,
-0.0040222941897809505,
-0.022216450423002243,
-0.016806870698928833,
-0.032736629247665405,
0.0021890171337872744,
0.04714973270893097,
-0.05362223461270332,
-0.048968393355607986,
-0.04290857911109924,
-0.04303167760372162,
0.026219442486763,
0.008799180388450623,
-0.07547744363546371,
-0.013348974287509918,
0.007549389265477657,
-0.022763671353459358,
-0.08141428977251053,
0.026335448026657104,
0.03606019169092178,
-0.022286435589194298,
0.056680530309677124,
-0.00020561418205033988,
0.041294753551483154,
0.02840953879058361,
-0.06527016311883926,
0.06313923746347427,
0.013462965376675129,
-0.019445041194558144,
-0.02155180834233761,
0.01140730269253254,
-0.05176026001572609,
0.05505919083952904,
0.0037424725014716387,
-0.019160471856594086,
0.011994371190667152,
-0.04484596475958824,
0.035504866391420364,
0.0014432223979383707,
0.021675843745470047,
0.04460224509239197,
-0.014844999648630619,
0.007858692668378353,
0.013398024253547192,
0.03339865058660507,
-0.031425680965185165,
-0.021236585453152657,
-0.007536550518125296,
-0.048300620168447495,
-0.025105807930231094,
0.06250107288360596,
0.04178229719400406,
-0.045697860419750214,
0.0757024809718132,
-0.01950366050004959,
0.003681155387312174,
0.030224807560443878,
-0.008651500567793846,
0.008304565213620663,
0.056147925555706024,
0.04408365488052368,
-0.040945686399936676,
-0.027567241340875626,
-0.013175802305340767,
-0.037911102175712585,
-0.024916069582104683,
0.012113516218960285,
-0.04128793999552727,
0.012438816949725151,
-0.034351520240306854,
-0.029039710760116577,
-0.006897167768329382,
-0.0008060171967372298,
0.04818668216466904,
-0.04900408163666725,
0.02303885854780674,
0.011036786250770092,
0.04875926300883293,
-0.06470663100481033,
0.05517682805657387,
-0.0849544033408165,
-0.015302889980375767,
0.011389671824872494,
-0.059021614491939545,
0.02705834060907364,
-0.051682908087968826,
0.022120701149106026,
0.07619959861040115,
0.0010798890143632889,
0.007427622098475695,
-0.035119421780109406,
0.04955389350652695,
-0.029204143211245537,
0.08094621449708939,
-0.01602194271981716,
0.06147373095154762,
-0.024674972519278526,
0.00840000156313181,
-0.00610768236219883,
-0.02607935480773449,
0.009715608321130276,
-0.021195875480771065,
0.013157564215362072,
0.0015120276948437095,
-0.01659104973077774,
-0.009826273657381535,
0.010192511603236198,
-0.024455158039927483,
-0.010504292324185371,
-0.0011298756580799818,
0.005173694342374802,
0.006879693362861872,
-0.002539378125220537,
-0.01879182830452919,
0.05300585925579071,
0.050374146550893784,
0.016425086185336113,
0.022301064804196358,
0.04873521998524666,
0.047455716878175735,
-0.028603414073586464,
-0.01517105009406805,
0.03638211637735367,
-0.07478058338165283,
0.026621820405125618,
0.0406753309071064,
-0.07557149976491928,
-0.010188130661845207,
-0.04374321922659874,
-0.01271390076726675,
0.01084485836327076,
-0.0019168603466823697,
-0.03128434717655182,
0.006104495842009783,
0.006702733691781759,
0.03452158719301224,
-0.01291179284453392,
-0.05729648470878601,
-0.007266673259437084,
0.037239521741867065,
0.03515191376209259,
0.0028426130302250385,
0.08628721535205841,
-0.022003905847668648,
-0.02354086935520172,
0.05040847510099411,
0.025828950107097626,
0.01362383458763361,
0.0034443954937160015,
-0.06417033076286316,
-0.04833215847611427,
0.007374937646090984,
0.041000500321388245,
0.025390617549419403,
-0.010425614193081856,
0.01568233221769333,
-0.07057207077741623,
0.015499071218073368,
-0.051841434091329575,
0.03769674524664879,
0.005122451111674309,
0.044573284685611725,
0.007264045998454094,
-0.02577693946659565,
0.0030666571110486984,
0.014260899275541306,
0.07953038066625595,
-0.006727232597768307,
0.05349254608154297,
0.02636794000864029,
-0.013301154598593712,
0.027880989015102386,
0.08930055052042007,
-0.010301792994141579,
-0.02618504874408245,
-0.031470149755477905,
0.0007600588724017143,
0.008270211517810822,
-0.001249130116775632,
0.03893008083105087,
-0.01828916370868683,
-0.04095765948295593,
0.008571209385991096,
0.018202699720859528,
-0.024974003434181213,
0.025608928874135017,
-0.018102973699569702,
0.015705203637480736,
-0.005211022216826677,
-0.010133020579814911,
0.011510164476931095,
0.030665019527077675,
0.04299001395702362,
0.0007621496915817261,
-0.009413973428308964,
0.008738488890230656,
0.03346927836537361,
-0.03198644891381264,
0.003908917307853699,
-0.05574072524905205,
-0.0171184279024601,
0.004962025210261345,
-0.027902472764253616,
0.033620670437812805,
0.025862105190753937,
-0.015013488009572029,
0.0356413833796978,
0.01017296127974987,
-0.0014828428393229842,
-0.00680373003706336,
-0.030499372631311417,
-0.04401378333568573,
0.009488330222666264,
-0.06513364613056183,
-0.005369242746382952,
-0.006674859207123518,
-0.00255204807035625,
-0.03537096455693245,
0.044766608625650406,
-0.02213800884783268,
0.024287359789013863,
0.06292438507080078,
-0.02726740948855877,
0.06603091955184937,
0.04894697666168213,
-0.005092443432658911,
-0.043435219675302505,
-0.007937969639897346,
-0.023105451837182045,
-0.03129889443516731,
-0.05921604856848717,
0.06406457722187042,
0.007201977074146271,
-0.022125137969851494,
-0.03730323910713196,
-0.01284151803702116,
0.006926221773028374,
-0.015231052413582802,
-0.02284250035881996,
-0.008732981979846954,
0.02215886488556862,
0.03635665774345398,
-0.005804919637739658,
-0.026654748246073723,
0.03535141423344612,
0.030572984367609024,
0.05054212734103203,
0.025433054193854332,
0.02016494795680046,
0.009513797238469124,
-0.0060122343711555,
0.03081490844488144,
0.05177399143576622,
0.02233719639480114,
-0.04426267743110657,
0.035631921142339706,
-0.053203973919153214,
0.07029332220554352,
0.0320202112197876,
0.01473250612616539,
0.0915789008140564,
-0.040175728499889374,
0.014588721096515656,
0.04602062702178955,
-0.005138522945344448,
-0.03328637406229973,
0.022021953016519547,
0.08741887658834457,
-0.04525898024439812,
-0.0862889215350151,
0.025691617280244827,
-0.026923904195427895,
-0.03562050685286522,
-0.025142759084701538,
-0.039325274527072906,
0.014065711759030819,
0.008337765000760555,
-0.0563461072742939,
-0.010039259679615498,
0.009856905788183212,
0.09576667845249176,
0.042183730751276016,
-0.038183923810720444,
0.0185257475823164,
0.0530707873404026,
-0.04379840940237045,
-0.028866935521364212,
0.05749820917844772,
-0.0007748764473944902,
0.00414570327848196,
-0.04199254512786865,
0.017748385667800903,
-0.05224001035094261,
-0.06956327706575394,
0.005900469142943621,
0.0013848233502358198,
-0.08839932084083557,
0.02493242733180523,
-0.004562808200716972,
-0.021170321851968765,
-0.028204459697008133,
0.007583754137158394,
-0.002874064492061734,
0.021153012290596962,
0.02021634578704834,
-0.006064888089895248,
-0.039874207228422165,
0.0017989177722483873,
-0.055188946425914764,
-0.005263020750135183,
0.010114016011357307,
-0.03946910798549652,
-0.023325039073824883,
-0.022004351019859314,
-0.004650042857974768,
-0.03193414583802223,
-0.05727780610322952,
0.008370822295546532,
0.007841945625841618,
-0.008076456375420094,
0.023838123306632042,
0.01778671145439148,
-0.016957802698016167,
0.03533260151743889,
0.005498813930898905,
-0.08095690608024597,
-0.0353224091231823,
0.007541341707110405,
-0.004390227608382702,
0.027864202857017517,
-0.015488938428461552,
0.07295158505439758,
-0.016269512474536896,
0.04515719413757324,
0.019467124715447426,
-0.004537863191217184,
0.009085800498723984,
0.0013417827431112528,
-0.0627526342868805,
-0.014800991863012314,
0.03653101250529289,
-0.05204261839389801,
0.01166492234915495,
0.04550614580512047,
0.05406402423977852,
0.05790937319397926,
0.023437615483999252,
-0.020522957667708397,
-0.0482696071267128,
0.0717616155743599,
0.0028459893073886633,
-0.015016810037195683,
0.007158886641263962,
0.02491309866309166,
-0.03367909416556358,
0.01025795005261898,
0.010108079761266708,
-0.005922463722527027,
0.003126951167359948,
0.03624020516872406,
0.028879517689347267,
-0.014664276503026485,
-0.05935421213507652,
-0.007398229092359543,
0.03242962062358856,
0.07079855352640152,
0.026428503915667534,
-0.012787619605660439,
-0.025795141234993935,
-0.021459968760609627,
0.023458199575543404,
-0.012307156808674335,
-0.04322690889239311,
-0.03280771151185036,
0.05222615227103233,
0.07135486602783203,
-0.000181067458470352,
0.053446657955646515,
0.0029098184313625097,
-0.020309841260313988,
-0.0021581309847533703,
-0.01823602430522442,
0.012439599260687828,
-0.020485203713178635,
0.06686506420373917,
-0.03416546806693077,
-0.012755541130900383,
-0.06822959333658218,
0.019771426916122437,
-0.06266794353723526,
0.05382808297872543,
0.03280796483159065,
-0.009394903667271137,
-0.021492017433047295,
0.028100376948714256,
-0.023250609636306763,
-0.00948869064450264,
-0.00682868342846632,
-0.03367289528250694,
-0.08080915361642838,
-0.0840567797422409,
0.015434914268553257,
-0.02065495401620865,
-0.017237285152077675,
0.0010257391259074211,
-0.009979118593037128,
0.0015590364346280694,
0.057920053601264954,
-0.003025676589459181,
0.0015177035238593817,
0.0469992496073246,
-0.060424286872148514,
0.012845219112932682,
-0.0764973908662796,
0.0036154878325760365,
-0.045458145439624786,
-0.08813396841287613,
0.014589345082640648,
-0.040374599397182465,
-0.033429112285375595,
-0.044333565980196,
0.0329117476940155,
-0.003866493469104171,
-0.03992097079753876,
0.03781680762767792,
-0.00046389270573854446,
0.04831773042678833,
-0.003448986215516925,
-0.04538403078913689,
-0.038013506680727005,
0.090131014585495,
-0.009696751832962036,
0.012537687085568905,
0.013698927126824856,
0.01914902776479721,
0.04454013705253601,
-0.024618856608867645,
0.031069545075297356,
0.056564535945653915,
-0.019930951297283173,
-0.03550615906715393,
0.01895046792924404,
0.03742422163486481,
-0.017448417842388153,
0.007416557986289263,
-0.021103059872984886,
-0.003902472322806716,
0.004998842254281044,
-0.027211317792534828,
0.019784996286034584,
0.02844926156103611,
-0.004146882798522711,
-0.020742863416671753,
0.020702708512544632,
0.020128441974520683,
0.01806029863655567,
0.054813090711832047,
-0.004799560643732548,
-0.019060876220464706,
-0.04281783849000931,
-0.018918169662356377,
0.02403530851006508,
0.0040580048225820065,
0.011431816034018993,
-0.02750283293426037,
-0.05913620442152023,
-0.026335816830396652,
0.02790234424173832,
-0.0030789426527917385,
-0.010552202351391315,
0.010796898975968361,
-0.040996186435222626,
0.03139595314860344,
-0.04481317102909088,
0.007240693084895611,
-0.0385248064994812,
0.018474768847227097,
0.009016269817948341,
-0.018689459189772606,
0.04464713856577873,
0.04698778688907623,
-0.083457350730896,
0.0032898217905312777,
-0.0037939641624689102,
-0.07025720179080963,
0.06680428981781006,
-0.005853408481925726,
-0.03409199044108391,
0.02524070255458355,
-0.0610739141702652,
0.037306174635887146,
-0.018281182274222374,
-0.020807519555091858,
0.029351599514484406,
-0.06910468637943268,
0.009386621415615082,
-0.014302188530564308,
-0.03903845325112343,
-0.022221742197871208,
-0.05374838411808014,
-0.007178527768701315,
0.05379943922162056,
0.02872903272509575,
-0.008639774285256863,
0.04713181406259537,
0.04213554784655571,
0.0014869944425299764,
0.025101354345679283,
-0.01845521852374077,
-0.061376940459012985,
0.015642074868083,
-0.0461459644138813,
-0.04891584813594818,
-0.06101464107632637,
-0.004568126983940601,
-0.033593446016311646,
-0.01812092959880829,
-0.04754434525966644,
0.01558337826281786,
0.041336432099342346,
0.07012593001127243,
0.0027853676583617926,
-0.04776553437113762,
0.017494522035121918,
0.004222057294100523,
0.011118237860500813,
0.010001306422054768,
-0.0007524016546085477,
0.021173451095819473,
-0.009929230436682701,
-0.06515420228242874,
0.03277510777115822,
0.04020596295595169,
0.03868500515818596,
-0.012717628851532936,
0.03848528116941452,
-0.021803848445415497,
0.005515549797564745,
0.006973054725676775,
-0.02595181204378605,
0.00625251280143857,
0.022003088146448135,
0.0343581885099411,
-0.009780129417777061,
-0.02317218855023384,
0.0059569887816905975,
0.0836724266409874,
0.037514325231313705,
-0.04082997143268585,
-0.0634220540523529,
-0.005630719941109419,
-0.06912140548229218,
0.042366813868284225,
0.025637676939368248,
-0.02607506886124611,
-0.005917572416365147,
-0.06759167462587357,
0.0022707669995725155,
0.016754349693655968,
-0.04960145056247711,
-0.04176021367311478,
-0.0015728760045021772,
-0.017444901168346405,
0.03588854521512985,
0.006071924231946468,
0.033527642488479614,
-0.006037259940057993,
0.027160651981830597,
0.008904382586479187,
-0.00819613877683878,
0.06158873066306114,
-0.02585770934820175,
0.03523656353354454,
-0.01042769756168127,
0.0050028604455292225,
0.014973524026572704,
-0.028762200847268105,
0.032183267176151276,
0.01224674005061388,
-0.09770967811346054,
-0.09132060408592224,
0.0010014692088589072,
0.01898825913667679,
0.014085197821259499,
0.022763099521398544,
-0.025464924052357674,
-0.030238168314099312,
-0.006378977093845606,
0.02114674635231495,
-0.04043447598814964
] |
<p>Wikipedia says:</p>
<blockquote>
<p>It is believed that, due to the extraordinarily small scale of the
universe at the time, quantum effects of gravity dominated physical
interactions.</p>
</blockquote>
<p>But I wonder whether there is any indication that the dimensions of the universe were small at the time rather than being infinite?</p>
<p>Undoubtedly it was very dense but very dense does not necessary mean "small".</p>
<p>Is Wikipedia wrong on this point?</p> | g4608 | [
0.05675315856933594,
0.09724012762308121,
0.03595200553536415,
-0.05616379156708717,
-0.023494146764278412,
0.07398399710655212,
0.03930089250206947,
-0.00491973664611578,
-0.03419702500104904,
-0.05096113309264183,
0.009926906786859035,
-0.045979373157024384,
-0.00703059509396553,
0.037197306752204895,
0.03434867039322853,
0.0031513941939920187,
0.01389121264219284,
-0.011339671909809113,
0.0077200280502438545,
-0.006099746562540531,
-0.03851966932415962,
-0.026995018124580383,
-0.010119984857738018,
-0.04571739584207535,
-0.053991466760635376,
0.01947697438299656,
0.03248488903045654,
-0.053517840802669525,
-0.010032128542661667,
-0.02591715194284916,
-0.004974990151822567,
0.003597975242882967,
-0.011709995567798615,
-0.012802330777049065,
-0.029298491775989532,
-0.06086324155330658,
-0.0009056683047674596,
0.014219442382454872,
0.04014107584953308,
-0.039972979575395584,
0.005010154563933611,
-0.013428224250674248,
-0.023038029670715332,
-0.03748423978686333,
-0.03166009858250618,
0.022079017013311386,
-0.03613293915987015,
0.03472480550408363,
0.004056193400174379,
-0.04681424796581268,
-0.05881131440401077,
0.026565663516521454,
0.042347438633441925,
0.055923666805028915,
0.08766171336174011,
0.016267668455839157,
0.06177805736660957,
0.02405369281768799,
0.07383230328559875,
0.023931367322802544,
0.000981457531452179,
-0.007123648654669523,
0.05734290927648544,
0.03711002692580223,
0.026769287884235382,
0.051647037267684937,
-0.02174151875078678,
-0.03375013545155525,
0.06594434380531311,
-0.009286069311201572,
0.011311711743474007,
-0.07213988900184631,
-0.0006521962932310998,
0.008664926514029503,
0.018334874883294106,
0.06408769637346268,
0.01951056346297264,
0.016407659277319908,
-0.032664671540260315,
-0.015279925428330898,
-0.05203373357653618,
-0.062043774873018265,
0.010732083581387997,
-0.020996803417801857,
0.02459530346095562,
-0.026298176497220993,
-0.03651820123195648,
-0.03579946234822273,
-0.0006560624460689723,
0.030303465202450752,
-0.018413443118333817,
-0.001682413392700255,
0.031223392114043236,
0.03632575273513794,
0.03817232325673103,
0.0011632527457550168,
0.03206648305058479,
0.015018983744084835,
-0.029685242101550102,
0.028168201446533203,
-0.03807031363248825,
0.060914862900972366,
0.05071352422237396,
0.00899416022002697,
0.013571683317422867,
0.0010377061553299427,
-0.044113028794527054,
-0.003774454817175865,
0.028052575886249542,
-0.04143284633755684,
-0.038998205214738846,
-0.04255632683634758,
-0.053776953369379044,
-0.05060319975018501,
-0.009329626336693764,
0.01236491184681654,
0.06253424286842346,
-0.026691507548093796,
0.0019767512567341328,
-0.012490984983742237,
-0.024825217202305794,
0.004317949991673231,
-0.028069695457816124,
0.031725410372018814,
-0.05557785555720329,
-0.05615302547812462,
-0.009531697258353233,
0.006538503337651491,
-0.01020883210003376,
-0.06994164735078812,
-0.006905501242727041,
-0.00532915722578764,
-0.008089984767138958,
0.016553625464439392,
0.010459082201123238,
-0.018207892775535583,
0.031168097630143166,
-0.059734001755714417,
-0.010204659774899483,
0.05153035372495651,
0.01752934604883194,
-0.0072816647589206696,
-0.008848226629197598,
-0.0024845872540026903,
0.047561824321746826,
-0.027714325115084648,
-0.0022150787990540266,
0.00935632735490799,
-0.06149788200855255,
-0.058225907385349274,
0.016124043613672256,
0.053628284484148026,
0.02135188691318035,
-0.04795905575156212,
-0.07260096818208694,
0.05010848492383957,
-0.002262020017951727,
0.015710512176156044,
-0.0032002143561840057,
0.004169563762843609,
0.019213730469346046,
-0.000244278198806569,
0.047653503715991974,
-0.0177594181150198,
-0.008596120402216911,
0.06315439194440842,
-0.004610853735357523,
-0.08442191779613495,
0.018755825236439705,
0.025591962039470673,
-0.049972228705883026,
-0.010955266654491425,
-0.0009938228176906705,
0.02637588232755661,
0.025145793333649635,
0.05127815902233124,
0.04353088513016701,
-0.01594681106507778,
0.000023727623556624167,
0.008500533178448677,
0.026547322049736977,
-0.02408670447766781,
0.008203941397368908,
-0.02954600192606449,
0.020889107137918472,
-0.0019915204029530287,
0.042638346552848816,
0.005781770218163729,
0.030321411788463593,
-0.017817378044128418,
-0.08411359786987305,
-0.014167317189276218,
0.018441088497638702,
0.016066692769527435,
-0.003598562441766262,
-0.0024490789510309696,
0.08685247600078583,
0.009848189540207386,
-0.09082567691802979,
-0.016457073390483856,
-0.050508271902799606,
0.0459279865026474,
0.07114299386739731,
0.027840375900268555,
0.019205264747142792,
0.049508050084114075,
-0.02228228934109211,
0.02758696861565113,
-0.014549389481544495,
-0.0491381399333477,
0.04635045304894447,
-0.020161308348178864,
-0.025106126442551613,
0.024620503187179565,
-0.06728043407201767,
-0.003602322656661272,
-0.06407956779003143,
0.04457332193851471,
0.02709008939564228,
0.07703059166669846,
-0.02544585056602955,
0.0421067550778389,
0.035714659839868546,
0.001977788982912898,
0.018214968964457512,
-0.030299151316285133,
-0.003110668156296015,
-0.0236730445176363,
-0.006427426356822252,
0.014845795929431915,
-0.07599882781505585,
-0.006174774374812841,
-0.027636297047138214,
0.0052438341081142426,
-0.04982106015086174,
0.05016174539923668,
0.0021389664616435766,
-0.05420292168855667,
-0.03283170610666275,
0.02416861243546009,
0.0479903407394886,
-0.015207952819764614,
0.0124957375228405,
-0.043234702199697495,
0.027025070041418076,
-0.07818327844142914,
0.004151356406509876,
-0.0647728368639946,
-0.006542119197547436,
-0.005626731086522341,
0.038124144077301025,
-0.039883192628622055,
-0.019865520298480988,
0.013652202673256397,
0.03445674106478691,
0.014812585897743702,
0.013429233804345131,
0.02939106523990631,
-0.05185064300894737,
-0.043571021407842636,
0.03608766570687294,
-0.01639942266047001,
0.03648783266544342,
0.04484860971570015,
0.055891003459692,
-0.04325943440198898,
-0.07608351111412048,
0.0024946657940745354,
0.0023113808128982782,
0.016008669510483742,
0.015271772630512714,
0.00856012012809515,
-0.025287602096796036,
-0.0170724056661129,
0.020819034427404404,
0.00810934603214264,
-0.07346556335687637,
-0.007673946209251881,
0.07507912814617157,
-0.001808730885386467,
-0.012751111760735512,
0.0261398795992136,
-0.03611551225185394,
0.014252816326916218,
0.06255403906106949,
-0.05686696246266365,
-0.045276347547769547,
-0.003842908889055252,
-0.0074712312780320644,
-0.012575071305036545,
0.017654474824666977,
0.012287099845707417,
0.002534212777391076,
0.013348755426704884,
0.015490461140871048,
0.05887925997376442,
-0.03039168380200863,
-0.03092234395444393,
-0.08443941920995712,
0.022472696378827095,
-0.011341131292283535,
-0.029857391491532326,
0.0021965273190289736,
-0.008671469986438751,
-0.06095973774790764,
0.011610313318669796,
0.005227380432188511,
0.02664944902062416,
-0.04949108511209488,
-0.0556793138384819,
-0.05520259961485863,
0.06607311218976974,
0.03871363773941994,
0.055248431861400604,
-0.07173284888267517,
-0.006650429684668779,
0.08076032251119614,
0.05053527653217316,
0.020012065768241882,
-0.019565686583518982,
0.06306697428226471,
-0.0023254703264683485,
-0.017760181799530983,
0.0024153573904186487,
0.03077036328613758,
0.04418715834617615,
-0.036986954510211945,
-0.03311420977115631,
0.037778012454509735,
0.03235441446304321,
-0.03987272083759308,
-0.08075675368309021,
-0.015132434666156769,
0.04401879757642746,
-0.12534533441066742,
-0.0326690636575222,
-0.0343836173415184,
-0.04462859034538269,
0.04099612683057785,
0.0030505750328302383,
-0.02582133375108242,
0.008686881512403488,
-0.008973434567451477,
0.010692935436964035,
0.05260945111513138,
0.10050062835216522,
-0.003177223727107048,
0.03357451409101486,
-0.028974587097764015,
0.020812302827835083,
0.05603726580739021,
-0.022996027022600174,
-0.009729338809847832,
-0.032047491520643234,
0.013730719685554504,
0.033298637717962265,
0.015197470784187317,
0.041145287454128265,
-0.005941855255514383,
-0.026591775938868523,
0.002843867987394333,
-0.051004938781261444,
0.03159763664007187,
-0.01868191361427307,
-0.024462366476655006,
0.030000565573573112,
-0.03517087548971176,
-0.026179272681474686,
-0.020167773589491844,
0.021862657740712166,
0.005321527365595102,
-0.002480721101164818,
-0.05779490992426872,
0.03567904606461525,
0.06978675723075867,
-0.014257547445595264,
0.08082887530326843,
-0.046750541776418686,
0.00834882166236639,
0.008940556086599827,
0.05524028465151787,
0.04932178929448128,
0.04403884708881378,
0.010006836615502834,
0.013625499792397022,
-0.029480839148163795,
-0.007184658199548721,
-0.057345323264598846,
0.00001750682531564962,
-0.006101525854319334,
0.02710302174091339,
-0.02317701280117035,
0.027330193668603897,
0.037185028195381165,
0.0036723040975630283,
0.016558321192860603,
0.008588136173784733,
-0.014547527767717838,
0.0028353140223771334,
0.005603538826107979,
-0.007381991948932409,
-0.03055550903081894,
-0.015216515399515629,
0.0002839232620317489,
-0.01028356608003378,
0.02989822067320347,
0.06628116220235825,
0.031813476234674454,
-0.030410541221499443,
-0.02955692633986473,
0.0255975853651762,
0.02945583686232567,
-0.030749797821044922,
-0.035962559282779694,
0.011442936956882477,
-0.008586075156927109,
0.014712326228618622,
-0.05849682539701462,
0.04105828329920769,
0.03950491547584534,
-0.0023685793858021498,
0.05650809034705162,
-0.009210123680531979,
-0.0032894958276301622,
0.023078111931681633,
0.04053202643990517,
-0.047992296516895294,
0.004264808259904385,
-0.045021336525678635,
0.07125848531723022,
-0.008582811802625656,
0.014217055402696133,
-0.045128561556339264,
0.038931116461753845,
0.0006553136627189815,
0.012342694215476513,
0.012146685272455215,
0.02346642129123211,
-0.011364786885678768,
-0.0025237565860152245,
0.056172024458646774,
-0.04051665589213371,
-0.016061073169112206,
0.04011010378599167,
0.01728336326777935,
0.07867802679538727,
-0.009907198138535023,
0.013666822575032711,
-0.037276625633239746,
-0.045260388404130936,
-0.007444976828992367,
0.024988697841763496,
-0.017217325046658516,
-0.026439514011144638,
0.023008909076452255,
-0.002664546249434352,
-0.006677830126136541,
0.06075546145439148,
-0.0037951271515339613,
0.07529039680957794,
-0.08278007805347443,
0.023764830082654953,
-0.07979129254817963,
0.09057150781154633,
-0.011590882204473019,
-0.0315820537507534,
-0.08294801414012909,
0.00396535312756896,
-0.08216487616300583,
-0.0017214581603184342,
-0.02895388938486576,
0.02857646904885769,
0.03167170286178589,
0.025599556043744087,
0.0059638782404363155,
0.011454906314611435,
-0.009035151451826096,
-0.055602703243494034,
0.00269114482216537,
-0.018755262717604637,
-0.03169777989387512,
-0.052808139473199844,
0.0314902700483799,
0.008416485972702503,
0.013477563858032227,
0.053715724498033524,
-0.03508756309747696,
0.014779050834476948,
-0.03265853226184845,
0.03500831127166748,
0.02129250392317772,
-0.0342913493514061,
-0.006509843282401562,
0.009885379113256931,
-0.09488175064325333,
-0.06134841963648796,
-0.0007183983107097447,
-0.06886372715234756,
0.012880034744739532,
0.01156324427574873,
0.05431695282459259,
0.032204508781433105,
0.0048087239265441895,
-0.049624986946582794,
-0.08588369935750961,
-0.03151800483465195,
-0.02013094164431095,
-0.023498183116316795,
0.005500828381627798,
0.027033165097236633,
-0.045252636075019836,
-0.0011955241207033396,
0.01244032196700573,
0.04310429468750954,
0.059433985501527786,
-0.030632037669420242,
0.011875281110405922,
0.002906371373683214,
0.03644686937332153,
-0.004559879191219807,
-0.003544762497767806,
-0.011146175675094128,
0.02640330046415329,
-0.021020738407969475,
0.055288467556238174,
0.017641613259911537,
0.06496097892522812,
-0.005925663281232119,
0.04734388366341591,
0.030038008466362953,
0.06577445566654205,
0.027413660660386086,
0.02080725133419037,
0.00910593569278717,
-0.029167262837290764,
0.0019630033057183027,
0.023071428760886192,
0.03891931474208832,
0.07383870333433151,
-0.002496295142918825,
-0.02347351424396038,
0.02023693546652794,
-0.08962847292423248,
0.016561727970838547,
-0.011238986626267433,
-0.0032429450657218695,
-0.030509402975440025,
0.03623822331428528,
0.1075339987874031,
0.007243287283927202,
-0.0079136798158288,
0.001976374303922057,
0.0003499379672575742,
0.044964250177145004,
-0.032437071204185486,
0.04265518859028816,
0.03253120929002762,
0.028130516409873962,
-0.037075791507959366,
-0.03952988609671593,
-0.0031696727965027094,
0.05786307156085968,
-0.02522558905184269,
-0.05285422131419182,
-0.08158707618713379,
-0.04171912744641304,
-0.02406407706439495,
-0.0588088221848011,
0.0487075001001358,
0.013812907040119171,
0.01876290887594223,
0.05688134953379631,
0.026380809023976326,
0.008791204541921616,
0.0167556069791317,
-0.016966519877314568,
0.02855060063302517,
-0.03944937512278557,
-0.04478822275996208,
-0.03244536370038986,
-0.02009224146604538,
-0.015131709165871143,
0.03206075727939606,
-0.02705177292227745,
0.0172823928296566,
0.03016318939626217,
0.015758760273456573,
0.014664584770798683,
0.016260547563433647,
-0.016238277778029442,
-0.009613203816115856,
0.021023914217948914,
-0.03601323068141937,
-0.012856080196797848,
-0.022429415956139565,
-0.042874790728092194,
0.01216502208262682,
0.010078591294586658,
-0.05474371463060379,
-0.008618314750492573,
-0.023101655766367912,
-0.005711992736905813,
0.013461406342685223,
0.040691982954740524,
0.019920287653803825,
-0.014759756624698639,
-0.054221298545598984,
-0.0012064510956406593,
-0.0014499009121209383,
0.08376829326152802,
-0.01173827238380909,
0.045957304537296295,
-0.019422657787799835,
-0.0035280666779726744,
-0.0038175228983163834,
-0.06987817585468292,
0.01656786911189556,
-0.017419828101992607,
-0.017953652888536453,
0.0013647048035636544,
0.031116552650928497,
-0.01043660193681717,
-0.03903372958302498,
-0.023962613195180893,
-0.012605931609869003,
0.05797847732901573,
-0.0018292336026206613,
0.03614747151732445,
0.024076340720057487,
-0.03237886354327202,
0.02414199337363243,
-0.002373520052060485,
0.05530702695250511,
0.035633981227874756,
-0.06557141989469528,
-0.011732671409845352,
-0.05581362172961235,
0.0020984236616641283,
0.0006405344465747476,
0.004975212272256613,
0.025713954120874405,
-0.0540834441781044,
0.02433270402252674,
0.015169719234108925,
-0.0250440314412117,
-0.020441532135009766,
-0.006328346207737923,
0.04232214391231537,
-0.026359379291534424,
-0.03349337726831436,
0.006679538171738386,
0.027772890403866768,
-0.0006747717270627618,
-0.019012492150068283,
-0.04982663318514824,
-0.04700334370136261,
-0.040467169135808945,
0.011314881965517998,
-0.027027593925595284,
-0.07887247949838638,
-0.056792501360177994,
-0.0040956842713057995,
-0.007190970238298178,
-0.0036791979800909758,
-0.004640037659555674,
0.02166084386408329,
0.05122033879160881,
-0.014578573405742645,
0.014894585125148296,
-0.02736818604171276,
-0.016571924090385437,
-0.01665240153670311,
-0.03091960772871971,
0.02735983021557331,
0.0433899350464344,
-0.059691980481147766,
-0.02003718540072441,
-0.006193102803081274,
0.0638929158449173,
0.05399024114012718,
0.03261113166809082,
0.009388279169797897,
-0.0058983126655220985,
0.05109214782714844,
-0.03778846561908722,
0.010411872528493404,
-0.014631586149334908,
-0.05217791348695755,
-0.019129881635308266,
0.009275817312300205,
-0.021893847733736038,
-0.03368022292852402,
-0.024042557924985886,
-0.01281507033854723,
0.002747276099398732,
0.03887462243437767,
0.013817423023283482,
0.03694956377148628,
0.013075859285891056,
-0.02055365778505802,
-0.03335629776120186,
-0.0014657704159617424,
-0.06201649457216263,
-0.04674643650650978,
0.009578695520758629,
0.029516933485865593,
0.023780878633260727,
0.06356101483106613,
-0.011836089193820953,
-0.024150457233190536,
0.045233167707920074,
0.021840060129761696,
0.0298553928732872,
0.022410517558455467,
0.03391510248184204,
0.006576521322131157,
-0.010790032334625721,
-0.024684656411409378,
0.04483867064118385,
-0.01485859602689743,
-0.011401550844311714,
-0.006303874775767326,
-0.01693679951131344,
-0.04595800116658211,
-0.0438731424510479,
0.02130943536758423,
0.0072753760032355785,
-0.03191298618912697,
-0.020575733855366707,
0.01726110838353634,
0.002049629809334874,
-0.02392319031059742,
-0.02569674700498581,
-0.02434590645134449,
-0.025623280555009842,
0.024826480075716972,
-0.015112566761672497,
0.013514580205082893,
-0.03762632608413696,
0.005942830350250006,
-0.018493518233299255,
0.027330635115504265,
0.008172457106411457,
0.04503002390265465,
0.01815185137093067,
-0.03190182149410248,
-0.05968658626079559,
-0.027850719168782234,
0.024360407143831253,
-0.04118878021836281,
0.009919257834553719,
0.02480601705610752,
0.021701525896787643,
0.037130679935216904,
0.01511329784989357,
0.036792218685150146,
0.010547847487032413,
-0.014749903231859207,
-0.0096653513610363,
-0.039364878088235855,
0.005408330820500851,
0.008403534069657326,
0.07489354908466339,
-0.015526266768574715,
0.014419229701161385,
-0.06240307167172432,
0.08184568583965302,
0.03842364251613617
] |
<p>The media are reporting the commercially sold 128-bit quantum computer from D-Wave</p>
<blockquote>
<p><a href="http://news.google.com/news?ned=us&hl=us&q=d-wave+quantum&cf=all&scoring=n">http://news.google.com/news?ned=us&hl=us&q=d-wave+quantum&cf=all&scoring=n</a></p>
</blockquote>
<p>which of course sounds amazing. The gadget is described as something capable of doing quantum annealing</p>
<blockquote>
<p><a href="http://en.wikipedia.org/wiki/Quantum_annealing">http://en.wikipedia.org/wiki/Quantum_annealing</a></p>
</blockquote>
<p>which looks less convincing. I want to ask you what classes of problems the D-Wave computer can actually solve or perform. It can't run Shor's algorithm on 128 qubits, can it?</p> | g528 | [
-0.0435236431658268,
0.12949877977371216,
0.00841048639267683,
0.004408958368003368,
0.026590393856167793,
-0.009937658905982971,
0.01469673216342926,
0.02727588824927807,
0.04083765670657158,
0.021796422079205513,
-0.0219161044806242,
0.0229449775069952,
0.00019022673950530589,
0.014177806675434113,
-0.006777746602892876,
-0.013275775127112865,
0.02534288540482521,
-0.00036350591108202934,
0.011860904283821583,
0.020448923110961914,
0.05532604083418846,
0.025234704837203026,
-0.029860347509384155,
0.029759882017970085,
-0.04929966852068901,
-0.007168406154960394,
-0.04319501295685768,
-0.029171807691454887,
-0.0319276787340641,
0.024550139904022217,
0.006493963301181793,
-0.025904597714543343,
0.025956636294722557,
-0.008412332274019718,
-0.011408399790525436,
-0.0007472487632185221,
-0.022971495985984802,
-0.023553527891635895,
-0.048588164150714874,
-0.0118949506431818,
-0.03369293734431267,
-0.07372774928808212,
-0.028986157849431038,
-0.023169921711087227,
-0.016193989664316177,
0.028303412720561028,
0.023573018610477448,
0.06748795509338379,
-0.0003786589077208191,
-0.02870710752904415,
0.017172301188111305,
0.0023276209831237793,
0.1262863725423813,
0.015327942557632923,
0.019656477496027946,
0.04681476205587387,
-0.07441814988851547,
0.05860845372080803,
0.06322462856769562,
-0.016899332404136658,
-0.028337907046079636,
-0.009908470325171947,
0.05913068726658821,
0.010901154950261116,
0.0266642514616251,
-0.005518230609595776,
-0.016179583966732025,
-0.04954197257757187,
0.027398649603128433,
0.06682292371988297,
0.03316156193614006,
-0.045194365084171295,
-0.017015090212225914,
-0.033787913620471954,
0.0449800081551075,
-0.01905355229973793,
0.0027917479164898396,
0.0037262390833348036,
-0.025014599785208702,
0.014055072329938412,
-0.026254642754793167,
-0.059867922216653824,
-0.03310605511069298,
-0.034485261887311935,
-0.038142912089824677,
0.03089779242873192,
-0.06262856721878052,
0.03181416541337967,
0.03701679781079292,
0.054445747286081314,
-0.021379979327321053,
-0.011861921288073063,
0.03721728175878525,
0.055685728788375854,
0.015889842063188553,
0.03687537461519241,
-0.04758286476135254,
-0.009207143448293209,
0.02165740169584751,
-0.006002255715429783,
-0.009468131698668003,
0.012798232957720757,
0.027588827535510063,
0.00006833238148828968,
-0.006395932286977768,
-0.010678527876734734,
0.02157018333673477,
-0.01489864569157362,
-0.0019430326065048575,
0.06029363349080086,
-0.013946189545094967,
-0.037354350090026855,
-0.002605927176773548,
-0.0029385765083134174,
-0.0031476046424359083,
0.06470891833305359,
0.014470057561993599,
-0.01981997862458229,
-0.05987953767180443,
0.017711717635393143,
0.06158461794257164,
-0.011752745136618614,
0.02372710406780243,
-0.03144596517086029,
0.019034678116440773,
-0.007810716982930899,
-0.033529676496982574,
-0.00016159354709088802,
0.0197009090334177,
0.04484095796942711,
0.01525177899748087,
0.027267327532172203,
-0.001791828777641058,
0.03814123198390007,
-0.02848779410123825,
0.0746673047542572,
0.014933638274669647,
-0.03274301439523697,
0.03528763726353645,
-0.052289869636297226,
0.03896959125995636,
-0.0017927999142557383,
-0.052094411104917526,
0.0480421744287014,
0.0056142560206353664,
-0.01274605467915535,
-0.010875397361814976,
0.037316661328077316,
-0.012454553507268429,
0.03919701278209686,
-0.004689193330705166,
0.042527295649051666,
0.0023791715502738953,
-0.044786132872104645,
0.08255954831838608,
0.018184388056397438,
0.06085553765296936,
-0.028051069006323814,
-0.004569718148559332,
0.0647253468632698,
0.04684346169233322,
-0.0065246568992733955,
0.03847038373351097,
0.04285215213894844,
-0.04397262632846832,
-0.01212229672819376,
0.05916935205459595,
0.012321645393967628,
0.021253889426589012,
0.004254457075148821,
-0.018238823860883713,
0.0197980348020792,
-0.05267228186130524,
0.00761771947145462,
-0.028219642117619514,
0.06457091122865677,
-0.02447269670665264,
0.02549021877348423,
0.03154020011425018,
0.000059259622503304854,
0.02154708281159401,
0.007741693872958422,
-0.00940624438226223,
-0.008559547364711761,
0.0075551653280854225,
-0.03113246150314808,
-0.007843433879315853,
-0.02436179667711258,
0.07437566667795181,
-0.0016431153053417802,
-0.017448950558900833,
-0.0038054208271205425,
0.040602993220090866,
0.013895027339458466,
0.013051871210336685,
-0.019881997257471085,
0.014894809573888779,
-0.03462500125169754,
0.024194084107875824,
-0.012805323116481304,
-0.021334871649742126,
0.03539083153009415,
-0.0013105424586683512,
-0.021700508892536163,
0.02939188852906227,
-0.04407479986548424,
0.004538333509117365,
-0.03517676889896393,
0.04689302295446396,
0.016225386410951614,
0.08323212713003159,
-0.03652419149875641,
0.006427801679819822,
0.021554019302129745,
0.022623207420110703,
-0.043082136660814285,
-0.0032538482919335365,
-0.04685105010867119,
0.019947925582528114,
0.040204331278800964,
-0.0022662931587547064,
-0.030440310016274452,
0.012886918149888515,
0.030428310856223106,
0.004809533711522818,
0.06085050851106644,
-0.02191680669784546,
-0.03997409716248512,
-0.059455983340740204,
0.06407463550567627,
-0.02463793009519577,
-0.010710655711591244,
-0.01130836270749569,
0.0031476893927901983,
0.08141717314720154,
0.0983273908495903,
0.009924445301294327,
-0.01569974794983864,
0.06065079942345619,
0.06147627532482147,
0.04009398818016052,
0.0877140611410141,
-0.05744100362062454,
-0.05048812925815582,
0.015167737379670143,
-0.03142501041293144,
-0.02449915185570717,
0.01230216771364212,
-0.04424083232879639,
-0.006442979443818331,
0.023970214650034904,
-0.08564966917037964,
-0.009116768836975098,
-0.007992073893547058,
0.05193961784243584,
-0.039447128772735596,
0.01869424618780613,
-0.007256329990923405,
0.06084807217121124,
0.03396480903029442,
-0.019509930163621902,
-0.001419398351572454,
0.02213258296251297,
-0.0131084518507123,
0.026899684220552444,
0.00965442880988121,
0.0010846804361790419,
0.0051804701797664165,
-0.029385218396782875,
0.03260306268930435,
-0.017014848068356514,
-0.010423856787383556,
-0.00293619348667562,
0.012758039869368076,
0.01702699065208435,
-0.023732269182801247,
0.0008193934336304665,
0.0026704941410571337,
-0.0020601896103471518,
0.028606200590729713,
-0.028780486434698105,
-0.005905841011554003,
-0.021753812208771706,
0.015160047449171543,
0.06266621500253677,
-0.006722100544720888,
-0.017153339460492134,
0.07590856403112411,
-0.017310194671154022,
0.04658433049917221,
-0.06638260930776596,
-0.037264976650476456,
0.019932135939598083,
0.015504836104810238,
-0.028607796877622604,
0.07408582419157028,
-0.06088453531265259,
0.005199912004172802,
0.007580196484923363,
0.036582596600055695,
-0.04570953547954559,
-0.02214452065527439,
-0.006602834444493055,
0.05154920741915703,
-0.005688806995749474,
0.021674850955605507,
-0.026887819170951843,
0.06259462982416153,
-0.021790312603116035,
-0.034267574548721313,
0.003353880252689123,
0.0014620989095419645,
-0.023573093116283417,
-0.01422971487045288,
0.02886522375047207,
-0.00451076403260231,
0.01049155741930008,
-0.0031793771777302027,
-0.030982179567217827,
-0.015790175646543503,
0.015131247229874134,
-0.003776427824050188,
0.027578698471188545,
-0.029582878574728966,
0.07378407567739487,
0.0724698007106781,
-0.027380073443055153,
0.05799489840865135,
0.0004916521720588207,
-0.047563597559928894,
0.04313286021351814,
0.03826410695910454,
-0.06601586937904358,
-0.005005792714655399,
-0.03993193432688713,
-0.0371292345225811,
-0.03435472398996353,
0.05746413394808769,
0.05204737186431885,
-0.03358117863535881,
-0.04917266592383385,
-0.01898730732500553,
0.03549011051654816,
0.04894978553056717,
0.020995158702135086,
0.03104642778635025,
-0.014751369133591652,
-0.038850266486406326,
-0.00892647635191679,
0.016472578048706055,
0.005308795720338821,
0.001441002357751131,
-0.013511652126908302,
0.050105780363082886,
-0.010148189030587673,
0.04219519719481468,
0.006111288908869028,
0.012666825205087662,
0.045084234327077866,
-0.05274039879441261,
-0.016961101442575455,
0.024825438857078552,
0.0678851380944252,
-0.04608733952045441,
-0.06080494448542595,
-0.02399408258497715,
0.008843190968036652,
0.012599815614521503,
-0.004717836156487465,
-0.051226794719696045,
0.0030452958308160305,
-0.07002973556518555,
0.0557643324136734,
0.0034248854499310255,
0.014310554601252079,
-0.030204148963093758,
-0.036137498915195465,
-0.04921086132526398,
-0.009234496392309666,
0.01638280414044857,
-0.01756666600704193,
-0.00410414207726717,
0.027642734348773956,
-0.028004981577396393,
-0.006331468001008034,
-0.028520215302705765,
-0.030604243278503418,
-0.051204558461904526,
-0.031367119401693344,
-0.04077090695500374,
0.018037162721157074,
-0.0004272751684766263,
-0.03071863390505314,
0.02491556853055954,
-0.021306827664375305,
0.005918498616665602,
-0.00965472124516964,
-0.05964801087975502,
-0.07085371017456055,
0.009588905610144138,
0.0024869830813258886,
-0.05571237578988075,
0.020802192389965057,
0.029492676258087158,
-0.0678638368844986,
0.013215707615017891,
-0.059430770576000214,
0.012743687257170677,
-0.005339194089174271,
0.022293515503406525,
-0.03930337727069855,
0.007994969375431538,
-0.003434540471062064,
-0.03378911688923836,
-0.0010103002423420548,
0.024266237393021584,
0.014979577623307705,
0.0072257244028151035,
-0.0012228835839778185,
-0.017581431195139885,
-0.014635018073022366,
0.054288674145936966,
0.02467920444905758,
0.03122716397047043,
-0.022662347182631493,
0.030345594510436058,
0.04089459404349327,
-0.023973222821950912,
0.029179519042372704,
-0.012553892098367214,
0.037609729915857315,
-0.024820871651172638,
-0.07251643389463425,
0.050768982619047165,
-0.00022082310169935226,
0.013976183719933033,
-0.0077235815115273,
0.013553299009799957,
0.07527782022953033,
0.04812685027718544,
0.04860350489616394,
-0.04402241110801697,
0.003811874659731984,
0.01962837018072605,
0.036287881433963776,
0.04874628782272339,
-0.04326066002249718,
-0.008754100650548935,
-0.045754462480545044,
0.053848449140787125,
0.018307708203792572,
-0.0461982786655426,
-0.01871855929493904,
0.02781939134001732,
0.012453499250113964,
-0.027284255251288414,
-0.03678644075989723,
0.060782819986343384,
-0.03164844587445259,
0.07369193434715271,
-0.05046959966421127,
-0.05228343605995178,
-0.034989841282367706,
0.07995095103979111,
-0.03980081155896187,
0.02295362763106823,
-0.015191330574452877,
-0.01947873830795288,
-0.06562799215316772,
-0.026136154308915138,
0.024735089391469955,
-0.04779990017414093,
0.03800041601061821,
0.038856133818626404,
-0.011483403854072094,
-0.07441529631614685,
-0.030179666355252266,
0.018513798713684082,
-0.019716106355190277,
0.030781446024775505,
-0.0118685532361269,
0.009873833507299423,
-0.03620960935950279,
0.050672825425863266,
-0.04985088109970093,
-0.010978775098919868,
-0.04553064703941345,
0.0361720472574234,
-0.09055036306381226,
-0.016568485647439957,
-0.008017522282898426,
0.01287035085260868,
-0.012102518230676651,
-0.06705481559038162,
0.028983531519770622,
-0.021082498133182526,
-0.0006864222232252359,
0.034207139164209366,
0.022969970479607582,
0.02610294334590435,
-0.02911498211324215,
-0.05533946678042412,
0.012397746555507183,
-0.061495404690504074,
-0.006500803399831057,
0.048261865973472595,
0.03647755831480026,
0.006239393725991249,
-0.014536049216985703,
-0.006775692570954561,
-0.0477314330637455,
0.036851104348897934,
-0.021869590505957603,
0.004659287631511688,
0.010955196805298328,
-0.016248002648353577,
0.002649198053404689,
-0.032269109040498734,
0.021626802161335945,
-0.006409491412341595,
0.009372329339385033,
0.04072814807295799,
0.016881955787539482,
0.02084617130458355,
-0.02650603838264942,
0.0022645583376288414,
-0.004488559439778328,
-0.08767631649971008,
0.02625081315636635,
0.03599688783288002,
0.0915401503443718,
0.021725349128246307,
-0.08570689707994461,
0.04507211968302727,
-0.012208725325763226,
-0.028778402134776115,
-0.030457349494099617,
0.002374052768573165,
-0.026596955955028534,
0.07963056117296219,
0.04018208757042885,
-0.0013924773083999753,
0.014270778745412827,
0.08841418474912643,
-0.046938639134168625,
-0.10249563306570053,
-0.03423422574996948,
-0.014391520991921425,
-0.028851525858044624,
-0.03948099538683891,
-0.07289291173219681,
-0.04219762608408928,
0.03176094964146614,
-0.005641703959554434,
0.018170315772294998,
0.021715492010116577,
-0.027990544214844704,
-0.006914837751537561,
0.008257574401795864,
-0.004357246216386557,
0.04031390696763992,
0.017817961052060127,
0.03837503492832184,
-0.03081454522907734,
0.0046751294285058975,
-0.03840453177690506,
-0.03675876930356026,
-0.02903079427778721,
0.02816956490278244,
-0.010867288336157799,
-0.056219253689050674,
0.008845782838761806,
-0.04630203917622566,
-0.0021402346901595592,
0.026614505797624588,
-0.05024414882063866,
0.043782152235507965,
-0.03115440160036087,
-0.0420672781765461,
-0.039398085325956345,
-0.032246191054582596,
-0.0013000895269215107,
0.012913528829813004,
0.0059532723389565945,
0.025186290964484215,
0.02309860847890377,
-0.03278842568397522,
0.06776364892721176,
-0.008490832522511482,
-0.008855185471475124,
-0.10931304097175598,
0.012358526699244976,
-0.004402500577270985,
-0.046937037259340286,
0.008759604766964912,
-0.015325179323554039,
0.007172986399382353,
0.012100491672754288,
-0.03293801099061966,
-0.011829426512122154,
0.03505700081586838,
-0.033776748925447464,
0.03627373278141022,
0.01550802867859602,
-0.04081496223807335,
0.04358901455998421,
-0.06990252435207367,
0.03645654022693634,
-0.018281258642673492,
0.02880057319998741,
-0.03735116124153137,
0.04202350229024887,
0.031511951237916946,
-0.01460829097777605,
-0.02112998254597187,
-0.07019983232021332,
0.019808722659945488,
-0.010182383470237255,
-0.008731470443308353,
0.014971827156841755,
0.06694067269563675,
0.04145059734582901,
0.002371278591454029,
0.0300837941467762,
-0.01969795860350132,
0.03900303691625595,
-0.009045928716659546,
-0.009715757332742214,
0.12216318398714066,
0.00117172219324857,
0.014954074285924435,
-0.00428105378523469,
0.061096202582120895,
-0.020825760439038277,
0.03694803640246391,
0.037403691560029984,
-0.09979671239852905,
0.005864021833986044,
-0.008191319182515144,
0.031100839376449585,
0.03903886303305626,
0.007961969822645187,
-0.03087046928703785,
-0.019121121615171432,
-0.02802400477230549,
-0.0032381326891481876,
0.059030190110206604,
0.022903650999069214,
-0.04675212875008583,
-0.00012948527000844479,
0.015595853328704834,
0.03979131206870079,
-0.07511559128761292,
-0.030851198360323906,
-0.02649158611893654,
0.028935275971889496,
0.035064902156591415,
-0.02199927344918251,
-0.01135554350912571,
-0.07365470379590988,
0.022362368181347847,
-0.07265982776880264,
-0.00461065536364913,
-0.010392110794782639,
0.002618619706481695,
0.01633881777524948,
-0.02916472591459751,
0.02503778226673603,
-0.0066938214004039764,
-0.035648163408041,
-0.050138261169195175,
-0.05396733433008194,
-0.0466289184987545,
-0.03961601480841637,
0.0672185868024826,
-0.031261831521987915,
-0.021115029230713844,
0.008494958281517029,
-0.017577756196260452,
-0.03252461180090904,
-0.0023798905313014984,
0.0479833148419857,
-0.028809910640120506,
-0.04661243408918381,
0.019097572192549706,
0.0013217410305514932,
-0.05156346783041954,
0.0003215361211914569,
0.013319309800863266,
-0.031548306345939636,
0.04809659719467163,
0.0005997751140967011,
0.017260242253541946,
-0.028740109875798225,
0.015331307426095009,
0.03401695191860199,
-0.038515035063028336,
0.008718552067875862,
0.03995857760310173,
0.004198471549898386,
-0.043532878160476685,
0.037136636674404144,
-0.013911581598222256,
0.026502739638090134,
0.027967581525444984,
0.017853014171123505,
-0.03739640861749649,
0.01890997402369976,
-0.004224687349051237,
-0.017371848225593567,
0.06335526704788208,
-0.050714269280433655,
-0.041207119822502136,
-0.03233201056718826,
0.020714331418275833,
-0.00145475915633142,
-0.009181383065879345,
-0.009599579498171806,
0.0009264479158446193,
-0.0032483076211065054,
0.04477251321077347,
0.01151310931891203,
-0.03770051151514053,
0.007297424133867025,
0.012158745899796486,
-0.07777921110391617,
0.03573179244995117,
0.023279786109924316,
-0.0058954027481377125,
-0.014760704711079597,
0.01474206242710352,
-0.01256305631250143,
0.006545227020978928,
-0.04888623580336571,
-0.0557703971862793,
0.015566516667604446,
-0.048043787479400635,
0.052523352205753326,
-0.051492705941200256,
0.07289189100265503,
0.03480888903141022,
0.031472381204366684,
0.006483239587396383,
-0.05925757437944412,
0.017463937401771545,
-0.04911132901906967,
-0.02865917608141899,
-0.03981713950634003,
0.01046760007739067,
-0.026724426075816154,
0.023935044184327126,
-0.02560996636748314,
-0.07037397474050522,
-0.05587628111243248,
-0.027866708114743233,
0.007052863948047161,
-0.025482134893536568,
0.017732102423906326,
0.060246873646974564,
-0.005607752129435539,
0.04260611534118652,
-0.03452903777360916,
0.01648288033902645,
0.010121665894985199,
0.001164229353889823,
0.008512544445693493,
-0.014634035527706146,
-0.022061342373490334
] |
<p>String theory - for example - requires extra spatial dimension. Say for example in 10 dimensional string theory, what theoretically prevents clustering of the extra 6 dimensions in 2 timeless 3 dimensional (infinite) spaces? </p> | g4609 | [
0.038905151188373566,
0.036149267107248306,
0.027315491810441017,
-0.02708575315773487,
-0.04231199249625206,
0.04116887226700783,
0.029955841600894928,
0.0148843415081501,
-0.0004124149272684008,
-0.026639031246304512,
0.01903158612549305,
-0.01146702840924263,
0.042667221277952194,
0.021835029125213623,
-0.02770141139626503,
0.008596338331699371,
0.0069478414952754974,
0.016164857894182205,
0.004809245932847261,
-0.007326523307710886,
-0.045899566262960434,
-0.008680613711476326,
0.00714270630851388,
-0.052076663821935654,
-0.04704466834664345,
-0.0037275636568665504,
0.06810104101896286,
-0.02179185301065445,
0.013425900600850582,
0.0011679845629259944,
0.09444231539964676,
-0.01474936492741108,
0.0025103408843278885,
-0.027323683723807335,
-0.011772958561778069,
0.0009722289978526533,
0.015548083931207657,
-0.004983984865248203,
-0.005865008104592562,
0.013061562553048134,
-0.025626199319958687,
-0.03678787127137184,
-0.01956975646317005,
0.005954090040177107,
-0.03875788673758507,
-0.004670307971537113,
0.029707234352827072,
-0.0009030003566294909,
0.067152239382267,
-0.017396127805113792,
-0.006777304224669933,
0.006449148990213871,
-0.0031324089504778385,
-0.005276604555547237,
0.01499388087540865,
0.018148092553019524,
-0.016192294657230377,
-0.010178885422647,
0.07880020886659622,
0.020542055368423462,
0.005542899947613478,
0.04752494394779205,
-0.04045766592025757,
0.05911659821867943,
0.034320931881666183,
-0.0008743604412302375,
-0.05883167311549187,
-0.006208360195159912,
0.016861828044056892,
-0.03287574648857117,
0.03894401714205742,
-0.008569031022489071,
-0.000329600996337831,
0.007020273711532354,
-0.015391608700156212,
0.0397656187415123,
-0.0030067076440900564,
0.037515126168727875,
-0.000445883022621274,
0.04853031411767006,
-0.027468184009194374,
0.01652723178267479,
-0.03719513863325119,
-0.05567723885178566,
0.06740777939558029,
-0.0014677414437755942,
0.004654675722122192,
-0.025572150945663452,
0.011530876159667969,
0.035205937922000885,
0.04257393628358841,
0.0031134923920035362,
0.03999466076493263,
0.05983441323041916,
0.00326453591696918,
0.04598835110664368,
0.054557282477617264,
0.05809405818581581,
-0.019562317058444023,
-0.048010360449552536,
0.03058491088449955,
0.05533904209733009,
0.06414477527141571,
-0.009529194794595242,
0.008183334022760391,
-0.07173150777816772,
0.030038537457585335,
0.015790339559316635,
0.06325333565473557,
0.018354935571551323,
-0.05852801352739334,
0.0625903308391571,
-0.09058454632759094,
-0.0011792612494900823,
-0.00035709785879589617,
-0.0017707892693579197,
0.10848864167928696,
-0.022249694913625717,
0.004034692887216806,
0.031045308336615562,
0.034581124782562256,
-0.03714091703295708,
0.03219224140048027,
-0.010331621393561363,
-0.08625970035791397,
-0.0020467506255954504,
0.006846030242741108,
0.014940070919692516,
0.023963630199432373,
-0.029988575726747513,
-0.016080569475889206,
0.03307490795850754,
-0.008381537161767483,
0.052741263061761856,
0.024647628888487816,
-0.0033576295245438814,
-0.04499165341258049,
-0.01723445951938629,
0.0004449909320101142,
0.019020630046725273,
-0.05583497881889343,
-0.007709023077040911,
-0.002428664593026042,
0.01337316632270813,
-0.02372537925839424,
-0.03656110540032387,
0.005529162939637899,
0.015033042058348656,
-0.037351854145526886,
0.01992236077785492,
-0.026896612718701363,
0.02337968721985817,
0.02849622070789337,
-0.019119812175631523,
0.03149515017867088,
0.04084666818380356,
0.06383631378412247,
-0.001204854459501803,
0.044895537197589874,
0.007024907507002354,
0.024773383513092995,
0.03345357999205589,
0.026120902970433235,
0.023737290874123573,
-0.054842542856931686,
-0.050469689071178436,
0.04723772779107094,
-0.02535056881606579,
-0.039711274206638336,
0.03188549354672432,
-0.051783956587314606,
0.03837328031659126,
0.032899774610996246,
0.068083755671978,
-0.02226131036877632,
0.04932770878076553,
-0.05920208618044853,
0.021767571568489075,
0.01112549751996994,
-0.0007403144263662398,
-0.012669311836361885,
-0.01936410181224346,
-0.005428897216916084,
0.03419319540262222,
0.04117611050605774,
0.022317225113511086,
-0.022834807634353638,
0.03626376390457153,
-0.01865861751139164,
0.012239609844982624,
-0.03066876158118248,
0.0023956620134413242,
0.024944517761468887,
0.0366295762360096,
-0.00003304592610220425,
-0.04528122395277023,
0.03310609236359596,
-0.01566876471042633,
-0.036728210747241974,
-0.009682857431471348,
-0.003384968964383006,
0.03588009998202324,
0.03888404369354248,
0.025485845282673836,
0.050540320575237274,
-0.0510205514729023,
-0.045433517545461655,
-0.000245516566792503,
0.015048778615891933,
-0.007328423671424389,
0.037944868206977844,
-0.00021814275532960892,
0.009271951392292976,
0.009792020544409752,
-0.0037566376850008965,
-0.009073186665773392,
-0.002947181463241577,
0.021682510152459145,
0.038188740611076355,
0.05119577795267105,
-0.018411939963698387,
0.006459448020905256,
0.009656126610934734,
0.02719276025891304,
-0.01215366367250681,
-0.023582549765706062,
0.01765776239335537,
-0.006280298810452223,
-0.0017760059563443065,
0.013311442919075489,
-0.07319243997335434,
-0.08205684274435043,
0.02666679583489895,
-0.051646891981363297,
-0.008485158905386925,
0.052131861448287964,
-0.0260852612555027,
0.004665089771151543,
0.007499447092413902,
0.03144752234220505,
0.09109485894441605,
0.0075756339356303215,
-0.021363958716392517,
-0.060326866805553436,
0.035291336476802826,
-0.024400025606155396,
0.04646722599864006,
-0.03193315863609314,
-0.0659601092338562,
-0.012761586345732212,
-0.06529248505830765,
0.05183521658182144,
-0.005130330100655556,
-0.020559191703796387,
0.052787840366363525,
0.03951296955347061,
0.04204094409942627,
0.05736588314175606,
-0.0686008408665657,
-0.0629621148109436,
0.031364019960165024,
-0.005179042927920818,
0.03653814271092415,
-0.015946531668305397,
-0.0009072130196727812,
-0.036441102623939514,
0.01288886833935976,
-0.007403813302516937,
-0.032918237149715424,
0.008808987215161324,
-0.01329618040472269,
0.03897293284535408,
-0.02377959154546261,
0.003613631706684828,
0.02980920672416687,
0.07533159106969833,
-0.025044236332178116,
-0.018358709290623665,
0.017475198954343796,
0.03149250149726868,
-0.011600334197282791,
0.05651630833745003,
-0.06029578670859337,
0.028559822589159012,
0.039135780185461044,
0.043916381895542145,
0.04995664954185486,
0.010513348504900932,
0.025485863909125328,
-0.06632455438375473,
0.006622790824621916,
0.010312098078429699,
0.04419124126434326,
0.029591143131256104,
0.05121103301644325,
0.03465541824698448,
-0.03912412375211716,
-0.02998739667236805,
-0.021183932200074196,
0.019216161221265793,
-0.03297606110572815,
0.04689018055796623,
0.01852680929005146,
-0.0162795539945364,
-0.040332190692424774,
-0.008430602960288525,
-0.05580528825521469,
-0.0357687808573246,
-0.03282373771071434,
-0.07636698335409164,
0.033281393349170685,
0.04728580266237259,
0.001263393904082477,
0.02650805562734604,
0.005535057745873928,
0.00908590853214264,
0.03802046924829483,
0.038687024265527725,
0.005486505106091499,
-0.039079196751117706,
-0.005292066372931004,
-0.010741641744971275,
0.03823154792189598,
-0.055365607142448425,
-0.00075419747736305,
0.02104017697274685,
-0.03592885658144951,
-0.039322227239608765,
-0.09724173694849014,
0.05972971022129059,
0.002991051645949483,
-0.03199159726500511,
-0.03765220567584038,
-0.007123378571122885,
-0.08462300151586533,
-0.039578601717948914,
-0.060138676315546036,
-0.01919717714190483,
0.07387693971395493,
0.011093617416918278,
-0.02586100809276104,
-0.018869735300540924,
-0.015281684696674347,
-0.06278448551893234,
-0.0029582143761217594,
0.05857383459806442,
0.02294774353504181,
0.0008748264517635107,
0.057781148701906204,
0.008825653232634068,
-0.007028421387076378,
0.01847534440457821,
0.011433249339461327,
-0.0058035897091031075,
0.007698257453739643,
0.10273855924606323,
0.015096569433808327,
0.006545502692461014,
-0.003787463065236807,
-0.08127034455537796,
-0.016370749101042747,
-0.04999841749668121,
-0.0477500781416893,
-0.048047084361314774,
0.009211832657456398,
0.05027596652507782,
0.049056656658649445,
-0.02291204035282135,
0.022662876173853874,
0.02695409208536148,
0.035411689430475235,
0.014764733612537384,
-0.055005595088005066,
-0.02502109855413437,
0.07463759183883667,
0.025988886132836342,
0.03365239500999451,
-0.003813262563198805,
0.04356067627668381,
-0.003043457632884383,
0.06454905867576599,
-0.017222264781594276,
-0.014014624059200287,
-0.06294267624616623,
-0.04272612929344177,
0.0018011752981692553,
-0.005189836956560612,
-0.004858681000769138,
-0.07421180605888367,
0.013455791398882866,
0.010695420205593109,
-0.01350800134241581,
-0.023142648860812187,
-0.1027144342660904,
-0.016189945861697197,
0.0014137969119474292,
-0.023114867508411407,
-0.029888486489653587,
0.03726085647940636,
-0.06001618877053261,
0.016714055091142654,
0.0025869349483400583,
0.005871362052857876,
-0.032008521258831024,
0.029962733387947083,
-0.04096323251724243,
-0.005447934847325087,
0.03420104831457138,
-0.0033219263423234224,
-0.017988229170441628,
-0.006487513426691294,
-0.0276656374335289,
0.008763853460550308,
-0.056700609624385834,
0.05722222104668617,
-0.060534365475177765,
0.03041377104818821,
0.0031905153300613165,
-0.023458877578377724,
0.032424986362457275,
0.030101416632533073,
0.06079037860035896,
-0.0165080726146698,
0.00029757965239696205,
0.01954551413655281,
0.019325129687786102,
0.0069680362939834595,
-0.004606571979820728,
-0.051105797290802,
-0.007615229114890099,
0.01564209721982479,
0.005863882135599852,
-0.0602288618683815,
-0.024777395650744438,
-0.07739468663930893,
-0.04296352341771126,
-0.04411924257874489,
0.031217727810144424,
-0.039355769753456116,
-0.03621327877044678,
0.022766288369894028,
0.01492263376712799,
0.021415598690509796,
0.03109680488705635,
-0.026738466694951057,
0.05483398586511612,
0.00380514282733202,
-0.029706230387091637,
0.029885977506637573,
0.061715852469205856,
-0.02003907971084118,
0.004134484566748142,
-0.030851401388645172,
-0.030078481882810593,
0.013597222045063972,
0.029270101338624954,
-0.04793577268719673,
0.007625652011483908,
0.05006588250398636,
0.020457835868000984,
-0.08905454725027084,
-0.0035027239937335253,
-0.05735248699784279,
0.030023574829101562,
0.006502208765596151,
-0.015642937272787094,
-0.03830386698246002,
-0.033001501113176346,
-0.04006176069378853,
0.049068231135606766,
0.02775159478187561,
0.030256634578108788,
-0.013462728820741177,
-0.015790754929184914,
0.020087534561753273,
0.01337024848908186,
-0.02315521240234375,
0.017664149403572083,
-0.06665411591529846,
-0.023865021765232086,
-0.010309772565960884,
-0.01004104781895876,
0.014240325428545475,
-0.005311713088303804,
0.011800741776823997,
-0.01501579862087965,
-0.03552889823913574,
0.00965962465852499,
-0.025143640115857124,
0.0291080791503191,
-0.004648248199373484,
-0.00016835024871397763,
-0.03212606534361839,
0.01907063089311123,
-0.015446593053638935,
-0.021285654976963997,
0.031345512717962265,
-0.02067304588854313,
-0.033927977085113525,
-0.024288835003972054,
0.002937787678092718,
-0.05720736086368561,
0.028509246185421944,
-0.06303348392248154,
-0.030018756166100502,
-0.004577809013426304,
0.07300000637769699,
-0.002783827017992735,
0.000812280282843858,
0.010262598283588886,
-0.028031080961227417,
0.04448827728629112,
0.01008895318955183,
0.0027521054726094007,
0.05886321887373924,
0.0021563551854342222,
-0.00005914213033975102,
0.02710285782814026,
0.020317843183875084,
-0.031832460314035416,
0.0005262737977318466,
0.0020032564643770456,
0.018416495993733406,
-0.013326304964721203,
0.046680599451065063,
0.016324901953339577,
-0.06227528303861618,
-0.02614692598581314,
0.020270636305212975,
0.0390625,
0.05257483571767807,
-0.02899223566055298,
-0.04929209500551224,
0.0018889307975769043,
-0.023777030408382416,
-0.03287274390459061,
0.056964099407196045,
0.003351513994857669,
0.0062946355901658535,
-0.006833417806774378,
-0.038380108773708344,
-0.05592894181609154,
-0.030651099979877472,
0.012967036105692387,
-0.017514189705252647,
-0.06097714230418205,
-0.013422580435872078,
0.011940942145884037,
0.058467086404561996,
-0.042553629726171494,
-0.06338600814342499,
0.019528482109308243,
0.0011531664058566093,
-0.026369722560048103,
-0.011327109299600124,
-0.009204505011439323,
-0.005258482880890369,
-0.045150455087423325,
-0.013050735928118229,
0.012478252872824669,
-0.021651433780789375,
0.03446329012513161,
-0.039688754826784134,
-0.01704057864844799,
-0.04264989495277405,
-0.03138687461614609,
0.006806651130318642,
0.03385769948363304,
0.11063474416732788,
0.007402957417070866,
-0.013576336205005646,
0.038305897265672684,
0.023019427433609962,
0.05638975277543068,
0.0014903658302500844,
-0.04467543214559555,
-0.00476987287402153,
-0.06123955920338631,
-0.018614554777741432,
0.0021823556162416935,
-0.08674720674753189,
0.020468443632125854,
0.06676974147558212,
-0.07654289901256561,
-0.016745153814554214,
0.04161175712943077,
-0.01351265236735344,
-0.06822521984577179,
0.02165645733475685,
-0.017479894682765007,
-0.06929292529821396,
-0.030882202088832855,
-0.02457931451499462,
0.024930287152528763,
-0.02727442793548107,
0.02811443619430065,
-0.05672728270292282,
0.08254139870405197,
-0.03383418172597885,
0.0009176385356113315,
0.03310206159949303,
0.028669526800513268,
0.0916886106133461,
0.038851041346788406,
-0.03696098178625107,
0.10417929291725159,
-0.03420232608914375,
-0.04860362410545349,
0.029982276260852814,
0.05209427326917648,
-0.014907797798514366,
-0.029483500868082047,
0.041286125779151917,
0.07537379115819931,
-0.013195617124438286,
-0.025674285367131233,
0.0008773969020694494,
-0.06158260628581047,
-0.020745301619172096,
-0.004658745136111975,
0.11771345883607864,
-0.049496959894895554,
-0.010262538678944111,
0.021993014961481094,
-0.03096650168299675,
0.06912402808666229,
-0.015476840548217297,
-0.016265515238046646,
0.05407078191637993,
0.007842947728931904,
-0.033654406666755676,
0.0219211857765913,
0.01909913495182991,
0.021326269954442978,
-0.09017161279916763,
0.014051784761250019,
-0.09842648357152939,
0.02678234875202179,
-0.05423735827207565,
-0.013464604504406452,
-0.04892757162451744,
0.026468951255083084,
0.05330948159098625,
0.030536415055394173,
-0.0013930193381384015,
0.013856877572834492,
0.030055813491344452,
-0.036613352596759796,
-0.008536347188055515,
-0.029563652351498604,
0.0070149581879377365,
0.022638823837041855,
-0.02369002439081669,
-0.022509226575493813,
-0.011036518029868603,
-0.012645239941775799,
-0.04424663633108139,
-0.020192531868815422,
0.0029602455906569958,
0.01088437344878912,
-0.0196603462100029,
0.013123909011483192,
0.023126568645238876,
-0.01595635525882244,
-0.02127186581492424,
0.029679276049137115,
0.028653837740421295,
-0.04676046967506409,
0.00667961873114109,
-0.012619676068425179,
0.014033288694918156,
0.03050387278199196,
-0.01774914562702179,
-0.04634593054652214,
0.009944736026227474,
0.012263299897313118,
-0.013702044263482094,
-0.01644495315849781,
0.02869420498609543,
0.0736280009150505,
0.024732770398259163,
0.04310449957847595,
0.010423023253679276,
-0.0239708349108696,
-0.008044583722949028,
0.027163933962583542,
0.008912795223295689,
0.034842222929000854,
0.01969212479889393,
0.023425713181495667,
0.03210967034101486,
-0.03281167149543762,
-0.009724036790430546,
-0.017625052481889725,
0.0610024631023407,
0.017415154725313187,
-0.022967075929045677,
-0.006089781876653433,
-0.0026405188255012035,
0.020565442740917206,
-0.000987127423286438,
-0.013855899684131145,
-0.0004761351447086781,
-0.03247300162911415,
0.06561998277902603,
-0.054263871163129807,
-0.029913242906332016,
-0.032993897795677185,
-0.03519048914313316,
-0.022717196494340897,
-0.05236281454563141,
0.07814428955316544,
-0.03301136940717697,
0.0009964131750166416,
-0.008058981038630009,
-0.030960291624069214,
-0.03873031586408615,
-0.003685814794152975,
0.0493859127163887,
-0.035915128886699677,
-0.04325557500123978,
-0.00310727022588253,
-0.0028489644173532724,
-0.05890379101037979,
-0.05863332748413086,
-0.03481070324778557,
0.03575899451971054,
-0.08661050349473953,
0.01591222919523716,
0.042185865342617035,
-0.030809061601758003,
0.035005584359169006,
-0.000333080388372764,
0.030495446175336838,
-0.0704190582036972,
0.022888636216521263,
-0.029572324827313423,
-0.00405759597197175,
-0.00943826138973236,
-0.03287308290600777,
-0.0180355217307806,
0.0834951400756836,
-0.013812615536153316,
-0.023474890738725662,
-0.06087292730808258,
0.028124788776040077,
-0.022586248815059662,
0.006528167519718409,
0.026216570287942886,
-0.01312326081097126,
-0.023018047213554382,
-0.0016538212075829506,
0.009854036383330822,
0.019279437139630318,
0.072200708091259,
0.004135967697948217,
0.014201425015926361,
-0.008590961806476116,
0.030236637219786644,
-0.013576246798038483,
0.016103098168969154,
0.033936914056539536,
0.011796927079558372,
0.005396447144448757,
0.005289006978273392,
-0.03759430721402168,
0.02025270089507103,
-0.0004192124179098755
] |
<p>Some time far into the future, humans have made the technology breakthroughs to construct decoherence-proof reversible quantum computers with quantum fault tolerance. They have also solved the hard AI problem. They program a quantum conscious being on such a computer and also a two state quantum system. The quantum conscious being is programmed to entangle with the quantum system, measuring it. The rules of the Copenhagen interpretation tell us the state of the quantum system happened. The programmers reverse the program, undoing the measurement, with all the memory wiped clean. Did the quantum system unhappen?</p> | g4610 | [
0.025568006560206413,
0.03975898399949074,
0.008239670656621456,
-0.016399988904595375,
-0.026560215279459953,
0.011719264090061188,
0.015233101323246956,
0.05010022595524788,
0.008840074762701988,
0.0006644494133070111,
-0.05455317720770836,
0.01960904523730278,
0.025604402646422386,
-0.012561035342514515,
0.014650709927082062,
0.040901828557252884,
0.06288670748472214,
-0.006167464889585972,
0.002649080939590931,
0.021207651123404503,
0.08058300614356995,
0.0072656734846532345,
-0.04529886692762375,
-0.035431429743766785,
-0.0386284738779068,
0.005210242699831724,
-0.010202061384916306,
0.007057680282741785,
-0.04124673083424568,
-0.0005498503451235592,
-0.005270780064165592,
-0.03714381903409958,
0.016322920098900795,
-0.04870115593075752,
-0.006620691157877445,
-0.028723087161779404,
-0.0016431177500635386,
-0.04238725081086159,
0.020402340218424797,
0.01189451478421688,
-0.0422213040292263,
0.004469333216547966,
-0.03720557689666748,
-0.004866846837103367,
0.020698752254247665,
0.037295132875442505,
0.028574645519256592,
-0.025347299873828888,
-0.0038576959632337093,
-0.03182539716362953,
0.020285803824663162,
-0.01652592048048973,
0.03111886791884899,
0.010033182799816132,
0.032794032245874405,
0.029707519337534904,
-0.015778275206685066,
-0.018525104969739914,
0.04277249425649643,
-0.052311673760414124,
0.008045642636716366,
0.0011255316203460097,
0.05351855605840683,
-0.0017678156727924943,
0.020607922226190567,
0.03177075833082199,
-0.026557523757219315,
0.05396272987127304,
-0.006521748844534159,
0.006695312913507223,
-0.0011469501769170165,
-0.0600910522043705,
-0.01794574037194252,
0.053799107670784,
0.07196337729692459,
-0.005002134945243597,
-0.0006614584708586335,
0.012001502327620983,
0.005365290213376284,
0.03617767617106438,
-0.064267098903656,
-0.08486209064722061,
-0.014733592979609966,
-0.03521009162068367,
0.015495948493480682,
-0.042379483580589294,
-0.05292651802301407,
-0.03400200605392456,
-0.022491082549095154,
0.07395163923501968,
0.018702011555433273,
-0.03951847180724144,
0.03753788769245148,
0.03399301692843437,
0.012066271156072617,
0.004923349712044001,
0.02391766756772995,
-0.0334649533033371,
-0.0718282163143158,
-0.006001920439302921,
-0.04273918643593788,
-0.057469479739665985,
-0.005667664110660553,
-0.026281727477908134,
-0.022867124527692795,
0.0012815702939406037,
-0.007828006520867348,
-0.02666710503399372,
-0.030313273891806602,
0.03240213170647621,
0.03500811755657196,
-0.03268766403198242,
-0.007592345122247934,
0.020230231806635857,
0.03778392821550369,
0.002583733294159174,
0.05407264456152916,
-0.018626615405082703,
-0.054337866604328156,
0.046430375427007675,
-0.004914403427392244,
-0.05732439458370209,
0.019205816090106964,
0.012127443216741085,
0.023343101143836975,
0.044108662754297256,
-0.027635304257273674,
-0.0340065136551857,
0.053152911365032196,
0.05130680277943611,
0.016583092510700226,
0.05676517263054848,
-0.02680012583732605,
0.05728599801659584,
0.0007061737705953419,
-0.0019180935341864824,
0.08469083160161972,
0.02456728368997574,
0.004559918772429228,
-0.0071500507183372974,
0.006534615997225046,
-0.028504181653261185,
-0.021575769409537315,
0.002150392858311534,
0.05266165733337402,
-0.12167996913194656,
0.017863312736153603,
0.010165209881961346,
-0.0341251939535141,
0.02270849235355854,
0.03178604692220688,
-0.025666773319244385,
-0.009353420697152615,
-0.053485993295907974,
-0.018794303759932518,
0.015252777375280857,
0.008576796390116215,
0.00941404141485691,
0.00038165689329616725,
-0.0170445553958416,
0.04237689822912216,
0.016878534108400345,
-0.011986271478235722,
-0.010970271192491055,
0.005783225409686565,
0.059160321950912476,
-0.033571649342775345,
-0.017137005925178528,
0.015458404086530209,
0.012383931316435337,
-0.07807659357786179,
0.0167983565479517,
-0.037096694111824036,
-0.013932335190474987,
0.011179253458976746,
0.07617930322885513,
-0.020375428721308708,
0.0010028131073340774,
0.06437482684850693,
-0.059518348425626755,
-0.007294307928532362,
0.039867665618658066,
0.0005839050863869488,
0.057550378143787384,
-0.01271356176584959,
-0.01968964748084545,
-0.014610513113439083,
0.005877099931240082,
0.029054811224341393,
-0.05513196066021919,
0.04948436841368675,
-0.02272346243262291,
-0.0018916920525953174,
-0.01869586668908596,
0.014993589371442795,
-0.07390937954187393,
0.010505923070013523,
0.031028350815176964,
0.056469809263944626,
-0.006889699026942253,
0.018063152208924294,
0.004584233742207289,
0.017845874652266502,
-0.019564315676689148,
-0.0074041360057890415,
-0.04264671728014946,
0.026307374238967896,
0.011978654190897942,
-0.03168238326907158,
-0.025198690593242645,
0.03819243609905243,
0.04527941346168518,
-0.002176002599298954,
-0.0073800780810415745,
0.006473502144217491,
0.013643267564475536,
0.049881305545568466,
-0.053828757256269455,
0.02030569314956665,
-0.0409860722720623,
0.05734022706747055,
0.02068011835217476,
0.040580350905656815,
-0.002041694475337863,
0.019356196746230125,
0.024445995688438416,
-0.09032618254423141,
-0.04233460873365402,
-0.03553532809019089,
0.009044548496603966,
-0.01224668137729168,
-0.043963752686977386,
-0.03942196071147919,
-0.004590438678860664,
0.07374905794858932,
0.06249481812119484,
0.0063608246855437756,
0.02150489203631878,
0.10790892690420151,
0.019657200202345848,
-0.002611767267808318,
0.02899767830967903,
-0.052276793867349625,
0.004935136064887047,
0.011500292457640171,
-0.02743060141801834,
-0.023353807628154755,
-0.06842396408319473,
0.00009765784488990903,
0.02010120078921318,
0.02487296797335148,
-0.0673864409327507,
-0.058411527425050735,
0.012426712550222874,
-0.002665726002305746,
0.012821193784475327,
0.037134766578674316,
-0.009811877273023129,
0.0207214392721653,
0.02031967230141163,
0.054072897881269455,
-0.004054299555718899,
-0.028341416269540787,
0.03616372123360634,
0.045398760586977005,
0.006944919936358929,
0.016716426238417625,
-0.0203776266425848,
-0.019138773903250694,
0.011971903964877129,
-0.006019946187734604,
0.031127804890275,
0.00936234463006258,
0.02589537389576435,
0.038108792155981064,
-0.0017161212163046002,
-0.04894959181547165,
-0.003508770139887929,
0.015184598043560982,
-0.006337037775665522,
-0.05482219532132149,
0.012413470074534416,
0.001102725975215435,
0.0032265661284327507,
0.06558386981487274,
-0.06523507088422775,
-0.0753481462597847,
0.047791771590709686,
0.03389601409435272,
0.03371996060013771,
-0.028250377625226974,
0.0159794669598341,
0.03809279575943947,
0.04320282116532326,
-0.08871942013502121,
0.039613377302885056,
0.017732886597514153,
-0.014587923884391785,
-0.02683626301586628,
0.03584533557295799,
0.03343275189399719,
0.003407515585422516,
-0.01982426643371582,
0.006123492494225502,
-0.008007420226931572,
-0.05075746774673462,
-0.012133422307670116,
0.06254137307405472,
-0.023928280919790268,
-0.06831363588571548,
-0.05925114080309868,
-0.01830362156033516,
0.01631159707903862,
-0.09014824032783508,
0.02561134472489357,
0.05302656441926956,
0.0030192043632268906,
0.021958574652671814,
0.028489746153354645,
-0.023638227954506874,
0.011089291423559189,
0.004774661734700203,
-0.017722249031066895,
0.0065393210388720036,
0.09655702859163284,
0.03301137313246727,
-0.044856537133455276,
0.02551725134253502,
-0.035213977098464966,
-0.02765466272830963,
0.050179094076156616,
0.02746589109301567,
-0.002505874028429389,
0.0007345879566855729,
-0.005196216516196728,
-0.07170252501964569,
-0.015546558424830437,
0.011061729863286018,
-0.010317942127585411,
-0.01767306588590145,
-0.009099380113184452,
-0.010007557459175587,
0.039392516016960144,
0.024020150303840637,
0.05153404921293259,
0.012173235416412354,
-0.009570625610649586,
-0.019550330936908722,
0.03885924443602562,
-0.000531687110196799,
0.017728185281157494,
0.040778979659080505,
-0.03847934678196907,
-0.013945634476840496,
-0.017510442063212395,
0.04217205196619034,
-0.0039108190685510635,
0.0059887622483074665,
-0.01004714798182249,
-0.019255971536040306,
-0.001660526148043573,
0.018062708899378777,
0.02277008444070816,
-0.029254425317049026,
-0.05140077695250511,
-0.009639661759138107,
0.025761935859918594,
0.04226607084274292,
-0.0006577356834895909,
-0.01073236670345068,
-0.04756464436650276,
-0.004113771952688694,
0.001066755736246705,
-0.0563613586127758,
0.01998016983270645,
-0.05870308354496956,
0.0036592057440429926,
-0.01572587341070175,
-0.009367868304252625,
0.028830207884311676,
0.019396910443902016,
-0.03800289332866669,
-0.024878690019249916,
-0.04933862015604973,
0.048876289278268814,
0.03647417202591896,
0.0074303848668932915,
-0.0622054859995842,
-0.02916315756738186,
0.04432757943868637,
0.009470509365200996,
0.027876650914549828,
-0.011190041899681091,
-0.013770312070846558,
0.042695801705121994,
0.059620801359415054,
-0.06539472192525864,
-0.04024753347039223,
-0.019453806802630424,
-0.03531336411833763,
-0.01948576606810093,
-0.03260517120361328,
0.04242503643035889,
0.032658908516168594,
-0.015848468989133835,
-0.02809125930070877,
-0.0313434898853302,
-0.024893078953027725,
0.03314290940761566,
0.05238078907132149,
0.009062767960131168,
0.006423799321055412,
0.0038117989897727966,
-0.08547497540712357,
-0.05216285213828087,
-0.008157138712704182,
0.07117799669504166,
0.036791905760765076,
0.03548833727836609,
-0.008524351753294468,
-0.038970768451690674,
0.04681779816746712,
0.04261080175638199,
0.042817793786525726,
0.005019183270633221,
-0.016870226711034775,
0.002993304282426834,
0.021540697664022446,
0.02981244958937168,
-0.058016784489154816,
0.05162934213876724,
-0.024975039064884186,
-0.042386122047901154,
0.015127022750675678,
-0.04404483735561371,
-0.008895819075405598,
0.05139143392443657,
-0.010847215540707111,
-0.021682046353816986,
0.03703174740076065,
0.047497715801000595,
0.00019355048425495625,
-0.05778271332383156,
-0.0021671983413398266,
-0.012306656688451767,
0.05093739926815033,
0.06115007773041725,
0.005216807592660189,
0.02276112139225006,
-0.03105313703417778,
-0.009876585565507412,
0.05542997270822525,
-0.011383556760847569,
0.013165704905986786,
0.019457634538412094,
-0.020976560190320015,
-0.026963304728269577,
0.0320003405213356,
0.013171736150979996,
0.0386812649667263,
-0.007930546998977661,
-0.023490166291594505,
-0.027900461107492447,
0.05145272612571716,
-0.06997590512037277,
0.013938016258180141,
-0.030678292736411095,
0.012517673894762993,
-0.025615118443965912,
0.019057216122746468,
0.01712844893336296,
0.0096304165199399,
0.002071196446195245,
0.04955163598060608,
0.040371283888816833,
-0.03967321664094925,
-0.03383529558777809,
0.02313312143087387,
0.008456139825284481,
0.07242824137210846,
0.03436201810836792,
-0.029548829421401024,
-0.0033130876254290342,
-0.006399399600923061,
-0.011086958460509777,
0.021551482379436493,
0.010358410887420177,
0.027342531830072403,
-0.044596683233976364,
-0.05745074525475502,
0.04685156047344208,
0.055455051362514496,
0.02814486436545849,
-0.06332189589738846,
0.0196730587631464,
-0.06199825555086136,
-0.0526302233338356,
0.05776027962565422,
0.02473241277039051,
0.0481499545276165,
-0.014822161756455898,
0.035345446318387985,
-0.007938617840409279,
0.0034226656425744295,
-0.0643727034330368,
0.02689010091125965,
0.03290514275431633,
-0.08272600919008255,
-0.041869789361953735,
0.05493606999516487,
-0.03940661996603012,
-0.04606354236602783,
0.03958695009350777,
0.010688969865441322,
0.039665210992097855,
0.012317552231252193,
-0.04475044459104538,
0.007605853024870157,
-0.03444480523467064,
-0.053810928016901016,
-0.007359650451689959,
0.027106497436761856,
0.03072579763829708,
0.04192468896508217,
-0.04864233359694481,
0.02165551483631134,
0.02377217635512352,
-0.06268562376499176,
0.03225552663207054,
0.05576277896761894,
0.05886254459619522,
0.08947177976369858,
0.017616622149944305,
-0.053501617163419724,
-0.006899495143443346,
-0.05019884556531906,
-0.001604381832294166,
-0.0048160189762711525,
0.0306369811296463,
0.034368135035037994,
0.0830286294221878,
0.03633912280201912,
-0.00473150797188282,
0.06124835088849068,
-0.0632336437702179,
-0.04899328947067261,
-0.058563001453876495,
0.017322128638625145,
-0.026444410905241966,
-0.07804885506629944,
-0.03332871198654175,
-0.038150448352098465,
0.00525873526930809,
0.02600128948688507,
0.010281487368047237,
0.03338770195841789,
-0.03126153722405434,
0.020087851211428642,
0.01418825052678585,
0.005592671688646078,
0.026510320603847504,
0.021625852212309837,
0.019964955747127533,
-0.003164928872138262,
-0.03398924320936203,
-0.016588527709245682,
-0.028589734807610512,
-0.021332744508981705,
0.027401631698012352,
0.031736817210912704,
0.023456724360585213,
0.022603381425142288,
0.01326366700232029,
-0.01675904355943203,
-0.0013318719575181603,
-0.006806205026805401,
-0.004620365798473358,
-0.09232931584119797,
-0.04608377441763878,
-0.06921926885843277,
0.004314160905778408,
-0.01497750822454691,
0.024350715801119804,
-0.053902581334114075,
-0.0034622210077941418,
0.00249297171831131,
-0.004471300635486841,
0.04384670779109001,
0.07062652707099915,
0.058677416294813156,
-0.014416887424886227,
0.049474380910396576,
0.010804872959852219,
-0.06773076206445694,
-0.0027123161125928164,
0.003930005710572004,
-0.024377895519137383,
-0.07066141813993454,
-0.09949439018964767,
-0.01583768241107464,
-0.07856867462396622,
-0.032487206161022186,
-0.0038776006549596786,
0.013856375589966774,
-0.019015958532691002,
0.03819716349244118,
-0.05880213901400566,
0.038946811109781265,
0.024691348895430565,
-0.03119489550590515,
-0.00963625032454729,
-0.011473018676042557,
-0.011315705254673958,
0.01270530465990305,
-0.010502194985747337,
-0.03722428157925606,
0.0685945674777031,
-0.017835848033428192,
-0.07477670162916183,
0.06937738507986069,
0.033823590725660324,
0.004320070613175631,
0.0069400290958583355,
0.01083422265946865,
0.025922469794750214,
0.03347015008330345,
0.08147856593132019,
-0.005950192920863628,
0.07528775185346603,
0.10188005864620209,
-0.005820451304316521,
-0.01787468045949936,
0.04818573594093323,
0.026441697031259537,
-0.03541530668735504,
-0.0148018728941679,
-0.05497584491968155,
0.04398179054260254,
0.03315850719809532,
0.005685301963239908,
0.03831232339143753,
-0.0016542929224669933,
-0.013793808408081532,
-0.04462027922272682,
-0.059608858078718185,
0.00009344159479951486,
0.0375814214348793,
0.013947905041277409,
-0.022023048251867294,
-0.014207959175109863,
-0.020063620060682297,
0.030194677412509918,
-0.01021082978695631,
0.005398180801421404,
-0.011962004005908966,
0.02923394925892353,
-0.0021297193598002195,
-0.011124619282782078,
-0.0004430938570294529,
-0.051275283098220825,
0.0072970143519341946,
-0.0167945995926857,
0.0045721279457211494,
-0.04770581051707268,
0.005368536338210106,
-0.01688157580792904,
0.019782887771725655,
-0.0017533525824546814,
-0.019106002524495125,
0.006018319167196751,
-0.005251574795693159,
-0.0557977631688118,
-0.05878084525465965,
0.00798626895993948,
0.016889968886971474,
-0.017838070169091225,
0.048159465193748474,
0.02850254997611046,
-0.055752288550138474,
-0.02602636069059372,
-0.016413798555731773,
-0.014486937783658504,
0.026578405871987343,
-0.04127016291022301,
0.03529259189963341,
-0.006795419380068779,
0.019193334504961967,
0.06000320240855217,
-0.01856650784611702,
-0.07421740889549255,
-0.005241277161985636,
0.00657019205391407,
0.01323709636926651,
-0.05557291582226753,
0.0014763028593733907,
0.006130120251327753,
-0.01977251097559929,
0.05137472599744797,
0.06341919302940369,
-0.027124781161546707,
0.011462459340691566,
0.005047793034464121,
0.050412047654390335,
0.06803543865680695,
-0.04673749580979347,
-0.007344402372837067,
-0.033464133739471436,
0.009746654890477657,
0.01843443140387535,
-0.024023212492465973,
-0.041880227625370026,
-0.019085709005594254,
0.023515786975622177,
-0.021027453243732452,
0.0022708417382091284,
-0.030320892110466957,
-0.04437053203582764,
-0.004458269104361534,
0.031840674579143524,
-0.01198852900415659,
0.041354622691869736,
0.011815162375569344,
-0.08495049178600311,
0.023973625153303146,
-0.03644390031695366,
0.030688351020216942,
0.0324484147131443,
0.004606220405548811,
-0.04319479316473007,
-0.02910568006336689,
0.04329923912882805,
-0.009473887272179127,
-0.02322039008140564,
-0.0386800579726696,
0.016572952270507812,
0.04077877104282379,
-0.10028693825006485,
-0.0016773638781160116,
-0.05455426871776581,
-0.04022373631596565,
-0.021214153617620468,
-0.021211819723248482,
0.011540490202605724,
-0.005730759352445602,
0.011102507822215557,
-0.07120926678180695,
-0.04240931198000908,
-0.02549307607114315,
0.052970997989177704,
-0.04603602737188339,
0.03263084962964058,
-0.049657370895147324,
-0.06075502187013626,
-0.0022111316211521626,
-0.0020627127960324287,
0.01833293028175831,
0.062065862119197845,
0.017966965213418007,
0.051541175693273544,
-0.024547165259718895,
0.0043089077807962894,
-0.01891670748591423,
0.019492285326123238,
0.025301601737737656,
-0.032555028796195984,
-0.02746046893298626,
0.006825061049312353,
0.02849338948726654
] |
<p>I can find equations to give the force of an electromagnet on a piece of iron when the iron touches the electromagnet. </p>
<p>But what about when the iron is some distance from the electromagnet? Presumably the force depends on the shape/size of the iron piece as well as the location of the piece away from the magnet. </p>
<p>If anybody can tell me how to calculate this, even if I have to write a numerical calculation routine, I would appreciate any direction on this. </p> | g4611 | [
0.04048639163374901,
0.007628777530044317,
0.003780991304665804,
0.0040103113278746605,
0.008592835627496243,
0.034591201692819595,
0.002943611005321145,
0.06149031221866608,
-0.07922721654176712,
-0.004408420529216528,
-0.03598102927207947,
0.042175982147455215,
-0.01898619718849659,
-0.039418481290340424,
0.0382230281829834,
0.07315412163734436,
0.0350164920091629,
-0.010645901784300804,
0.02779225818812847,
0.045454565435647964,
0.012318349443376064,
0.020146777853369713,
-0.014738214202225208,
-0.04324772208929062,
-0.02774185687303543,
-0.012227571569383144,
0.03308415412902832,
0.00782005861401558,
-0.0011814050376415253,
-0.0099785840138793,
-0.08661938458681107,
0.0654778853058815,
0.023328406736254692,
-0.045443613082170486,
-0.04041871801018715,
0.006844078656286001,
-0.015802038833498955,
0.03881832957267761,
-0.007265778258442879,
-0.023165684193372726,
0.01716703176498413,
-0.05283620208501816,
-0.011780372820794582,
-0.0002890518226195127,
0.039414048194885254,
-0.018753180280327797,
-0.0350540466606617,
-0.02631104178726673,
-0.0037908675149083138,
-0.00032700886367820203,
-0.016628099605441093,
0.007502604741603136,
0.027845149859786034,
0.014722730964422226,
0.06420983374118805,
0.05616952106356621,
0.08444411307573318,
-0.027506617829203606,
0.009766497649252415,
0.015344002284109592,
0.0471053272485733,
0.06681585311889648,
-0.0381084568798542,
-0.030578022822737694,
0.010462101548910141,
0.016481997445225716,
-0.030643777921795845,
-0.03999701514840126,
0.025072718039155006,
0.0075418464839458466,
-0.05138518661260605,
-0.008130348287522793,
0.031588174402713776,
-0.011092406697571278,
-0.07800168544054031,
0.01345633715391159,
0.048815734684467316,
0.036348626017570496,
0.036267440766096115,
0.03994930908083916,
-0.018559688702225685,
0.0018644580850377679,
0.03679553419351578,
-0.02738788351416588,
0.026117688044905663,
0.03480535000562668,
-0.02956213988363743,
0.03882927447557449,
-0.016132574528455734,
0.011067235842347145,
0.011010349728167057,
0.04610640928149223,
0.021471304818987846,
-0.013014462776482105,
0.0025699434336274862,
-0.048222970217466354,
0.0073608700186014175,
0.02502387948334217,
0.01425777468830347,
-0.028700951486825943,
-0.05520433187484741,
-0.04216481372714043,
-0.020303498953580856,
-0.017992977052927017,
-0.0032901333179324865,
-0.012694146484136581,
0.013229858130216599,
0.09780772775411606,
-0.02063281275331974,
0.03536704182624817,
0.01066689845174551,
-0.05989697948098183,
-0.06873621046543121,
0.016138719394803047,
-0.009069448336958885,
-0.023717783391475677,
0.026340750977396965,
-0.03769257292151451,
0.01111717987805605,
0.042838674038648605,
0.03355638310313225,
-0.02264517731964588,
0.0023716622963547707,
0.0490841381251812,
-0.019450170919299126,
-0.04789205640554428,
-0.04412307217717171,
0.011041025631129742,
0.022530125454068184,
-0.015329627320170403,
0.034115806221961975,
0.008514909073710442,
0.04475218057632446,
-0.030957970768213272,
-0.028998617082834244,
0.04368463531136513,
-0.0276202205568552,
-0.020859869197010994,
-0.026861878111958504,
0.024803945794701576,
0.008923721499741077,
-0.024864813312888145,
0.03920075669884682,
-0.04993176832795143,
-0.05293094739317894,
0.018361177295446396,
-0.02351619303226471,
-0.040186990052461624,
0.038033679127693176,
-0.030448785051703453,
0.048432234674692154,
0.04151089861989021,
-0.003847995540127158,
-0.0150435296818614,
0.01845778152346611,
-0.03334104269742966,
0.008060477674007416,
0.016205420717597008,
0.038303617388010025,
-0.03636088967323303,
0.020978862419724464,
-0.030466649681329727,
0.054409172385931015,
-0.021153202280402184,
-0.0076184505596756935,
0.021232444792985916,
-0.02924741432070732,
-0.014951542019844055,
-0.003262818092480302,
-0.027545908465981483,
-0.039753515273332596,
-0.001166184083558619,
0.050345528870821,
0.007020301651209593,
0.011607425287365913,
0.03358547389507294,
0.002451035426929593,
-0.06502842903137207,
0.035833172500133514,
-0.006796267349272966,
0.04243626445531845,
-0.03474564850330353,
0.09450285881757736,
0.026646411046385765,
-0.029227687045931816,
0.0032271691597998142,
0.022339025512337685,
0.018965821713209152,
0.025499839335680008,
0.0027292692102491856,
-0.04199811816215515,
-0.003637532703578472,
0.006624381057918072,
0.025430509820580482,
-0.022198880091309547,
0.008282952941954136,
0.029528900980949402,
-0.02924250438809395,
0.002657762262970209,
-0.06957711279392242,
-0.026301786303520203,
0.11241097003221512,
0.0190991573035717,
0.03995397314429283,
-0.009419756941497326,
0.008132115006446838,
0.01760125905275345,
0.007680218666791916,
0.015314280055463314,
0.008404701948165894,
-0.03351053223013878,
-0.007614272180944681,
-0.039638176560401917,
0.0031191478483378887,
-0.03500312566757202,
0.0443795844912529,
-0.05728832632303238,
-0.004378864541649818,
-0.05386825650930405,
0.08739636838436127,
0.024930007755756378,
-0.004293003119528294,
0.04055082052946091,
-0.015112095512449741,
-0.021974917501211166,
0.013312106020748615,
0.015515970066189766,
0.020366625860333443,
-0.02614864520728588,
-0.008530772291123867,
-0.06818205863237381,
-0.0023054522462189198,
-0.005955629516392946,
-0.009813463315367699,
0.0646783784031868,
0.05228039249777794,
0.029399696737527847,
-0.01807585172355175,
-0.007050143089145422,
-0.0015899062855169177,
0.012988509610295296,
-0.0451456755399704,
0.03381320834159851,
-0.046705957502126694,
0.020267659798264503,
-0.014674334786832333,
0.05939362570643425,
0.01562647707760334,
0.005084507167339325,
-0.02295376919209957,
0.028392618522047997,
0.007732854690402746,
-0.0017988422187045217,
0.023809975013136864,
-0.02780172973871231,
-0.022590842097997665,
-0.08713919669389725,
0.025330688804388046,
-0.05269135907292366,
-0.051479607820510864,
-0.01921801082789898,
-0.0847022607922554,
0.07403808832168579,
0.05452969670295715,
-0.05628577992320061,
-0.028992729261517525,
-0.08085376769304276,
0.004405681975185871,
0.08464352786540985,
0.0227588452398777,
-0.009325145743787289,
0.08304933458566666,
0.045703258365392685,
-0.026029670611023903,
0.0013415046269074082,
-0.10181430727243423,
0.00870728399604559,
-0.045265406370162964,
0.037558987736701965,
0.04442363604903221,
-0.034335605800151825,
-0.0026614691596478224,
-0.0014870313461869955,
0.030642682686448097,
0.02263020910322666,
-0.024463394656777382,
-0.016655953601002693,
-0.004041600972414017,
0.021685656160116196,
-0.06298880279064178,
-0.010406497865915298,
-0.04963907599449158,
0.036598216742277145,
-0.0453367717564106,
-0.009627123363316059,
0.030631886795163155,
0.053003717213869095,
0.028347035869956017,
-0.020052410662174225,
0.021045779809355736,
0.00598779134452343,
0.004350632894784212,
-0.013377627357840538,
0.030324866995215416,
0.03322816267609596,
0.02548469975590706,
0.039835501462221146,
-0.05129573494195938,
0.0036464263685047626,
-0.0754653662443161,
-0.07608373463153839,
0.039927344769239426,
0.022348517552018166,
-0.0253488440066576,
-0.06767963618040085,
-0.05705771967768669,
0.024313874542713165,
-0.013837933540344238,
0.04800361022353172,
0.028108004480600357,
0.0013983846874907613,
-0.09768828749656677,
0.05447835102677345,
0.013437969610095024,
0.02305757999420166,
0.033074669539928436,
0.006133726332336664,
0.056143373250961304,
0.016237925738096237,
0.03360580652952194,
0.022491615265607834,
0.07471542805433273,
-0.05184316262602806,
-0.03470556065440178,
-0.0736953616142273,
0.000931353832129389,
0.03250059112906456,
0.03252546489238739,
0.008486706763505936,
0.02973584085702896,
0.007511379197239876,
-0.03694269061088562,
-0.0063368999399244785,
0.00400434760376811,
-0.026879088953137398,
0.040594205260276794,
-0.03538694605231285,
0.017366066575050354,
0.030738014727830887,
-0.006581873632967472,
-0.007221683859825134,
-0.02317287027835846,
0.04165125638246536,
0.004786254838109016,
0.04650529846549034,
-0.0031407333444803953,
-0.017777854576706886,
-0.02572799101471901,
-0.02342934161424637,
0.018250709399580956,
0.04889313504099846,
-0.012538859620690346,
-0.040604230016469955,
-0.052380021661520004,
-0.030182624235749245,
-0.050848133862018585,
0.03834165260195732,
0.04657352715730667,
0.009275204502046108,
-0.0037448478396981955,
0.057175930589437485,
-0.0421159453690052,
0.032510772347450256,
0.018498212099075317,
0.02045285888016224,
0.014082797802984715,
0.00938266608864069,
0.0002365033869864419,
0.013687032274901867,
0.013417367823421955,
-0.025259269401431084,
0.1077328696846962,
-0.02510543167591095,
0.0040414887480437756,
0.04843180999159813,
-0.028273265808820724,
-0.024279389530420303,
0.036140188574790955,
0.047729458659887314,
-0.020553944632411003,
-0.016734236851334572,
-0.06904765963554382,
-0.03677928447723389,
0.04783094674348831,
0.03142903372645378,
-0.003034367924556136,
0.02449697069823742,
0.03417671099305153,
0.050250083208084106,
-0.020715197548270226,
0.025203660130500793,
0.040146324783563614,
-0.005599916912615299,
0.09289022535085678,
-0.015804067254066467,
-0.022983215749263763,
0.0003848985070362687,
0.00806344673037529,
0.03236986696720123,
-0.014706525020301342,
-0.011808059178292751,
-0.03728656470775604,
-0.024267517030239105,
-0.026081332936882973,
-0.007194271311163902,
-0.019241563975811005,
0.03685277700424194,
0.0249110609292984,
-0.021266276016831398,
-0.07612423598766327,
0.010475082322955132,
0.025258321315050125,
0.012310771271586418,
-0.06130780652165413,
-0.025047389790415764,
-0.0031753992661833763,
0.018766894936561584,
-0.048354774713516235,
0.040971823036670685,
0.03346551954746246,
-0.04909185692667961,
0.016364026814699173,
-0.006033583544194698,
-0.004989105276763439,
-0.015119084157049656,
0.029601162299513817,
-0.02552289515733719,
-0.009512723423540592,
0.012644005008041859,
0.010976564139127731,
-0.0014505961444228888,
0.0972350686788559,
0.014760415069758892,
0.044459905475378036,
-0.03511599078774452,
0.01173597015440464,
-0.07745393365621567,
-0.06102973595261574,
-0.0035298129078000784,
-0.00742678577080369,
0.008060027845203876,
-0.012125607579946518,
-0.08057165890932083,
-0.005514256190508604,
-0.04710543528199196,
0.030656350776553154,
0.0023704003542661667,
-0.03782644867897034,
0.05283915624022484,
0.014099707826972008,
-0.013238354586064816,
-0.013409365899860859,
-0.09377089887857437,
0.04312755540013313,
-0.028773123398423195,
0.03134377673268318,
-0.011778625659644604,
0.0005205487832427025,
-0.057211488485336304,
0.06819402426481247,
0.017274122685194016,
0.025273282080888748,
-0.004432935733348131,
-0.010868781246244907,
0.02420789562165737,
0.06800394505262375,
0.005853105802088976,
-0.019430669024586678,
0.015397400595247746,
0.04265692085027695,
-0.02665027230978012,
0.013023209758102894,
-0.002473813481628895,
-0.02064204216003418,
0.002163342898711562,
-0.04374797269701958,
0.03713327646255493,
0.03565127030014992,
-0.0031435673590749502,
-0.014433542266488075,
0.0066699618473649025,
0.017577150836586952,
-0.011187715455889702,
0.006884167902171612,
-0.04946888983249664,
0.029950356110930443,
-0.014202821999788284,
0.02086816169321537,
0.03387376293540001,
0.0019078976474702358,
0.0011571954237297177,
0.00461826054379344,
-0.040191538631916046,
-0.031207701191306114,
-0.023803139105439186,
0.07700168341398239,
0.02853260189294815,
-0.023535067215561867,
-0.013312706723809242,
0.028737597167491913,
0.0155583331361413,
0.021053528413176537,
0.008569695055484772,
0.0041235568933188915,
-0.009855829179286957,
0.003299159463495016,
-0.014885754324495792,
0.044172707945108414,
0.0031450530514121056,
0.04946332424879074,
0.06580723077058792,
-0.024044806137681007,
0.04806670919060707,
-0.09754185378551483,
-0.0006264494732022285,
-0.014764014631509781,
-0.019926980137825012,
0.0199116263538599,
-0.048908282071352005,
-0.02081209234893322,
0.014156531542539597,
-0.0240484606474638,
-0.00908541027456522,
-0.00737967062741518,
-0.02853972278535366,
-0.012499261647462845,
0.05412859469652176,
-0.05068302899599075,
-0.0025910455733537674,
-0.025217384099960327,
0.03640996664762497,
-0.0034964464139193296,
0.026021715253591537,
0.057173170149326324,
-0.029697177931666374,
0.0026359036564826965,
0.04508944973349571,
0.008719791658222675,
0.026696955785155296,
-0.027613259851932526,
-0.019186239689588547,
0.03412148356437683,
-0.06188658997416496,
-0.01894628442823887,
0.005613712128251791,
0.015934713184833527,
0.026913536712527275,
-0.026675840839743614,
-0.004218552727252245,
-0.06035764887928963,
0.07615605741739273,
-0.040100786834955215,
-0.03734537586569786,
-0.017253702506422997,
-0.03300970047712326,
0.014794480055570602,
-0.018841560930013657,
0.04661932960152626,
0.041146643459796906,
0.03945634141564369,
0.04671235382556915,
-0.025623289868235588,
-0.09155050665140152,
0.006956749130040407,
0.05077873915433884,
0.013536887243390083,
-0.007390335202217102,
-0.000024563345505157486,
-0.009530020877718925,
0.01642788015305996,
0.009376339614391327,
0.036408763378858566,
0.0024139229208230972,
-0.02110821194946766,
-0.022176479920744896,
0.055048223584890366,
-0.03355145826935768,
-0.02541574276983738,
0.0768035426735878,
-0.027729181572794914,
0.008940803818404675,
-0.011377283371984959,
0.025042664259672165,
-0.007019687909632921,
-0.013485580682754517,
-0.05572061613202095,
0.019478656351566315,
0.04078083112835884,
0.029006367549300194,
0.06702430546283722,
-0.015410861000418663,
0.032950159162282944,
0.045327626168727875,
-0.008013366721570492,
0.013849519193172455,
-0.0022965865209698677,
0.04231554642319679,
-0.006558774039149284,
0.038465213030576706,
-0.05042082071304321,
-0.014411045238375664,
0.049243513494729996,
-0.05034790188074112,
0.028537975624203682,
0.03127838298678398,
-0.04454689100384712,
0.011545747518539429,
-0.05651688575744629,
-0.04894430190324783,
0.03188568726181984,
-0.03395738825201988,
-0.06765364855527878,
-0.03005826473236084,
-0.06543605029582977,
0.0043378532864153385,
0.03020050749182701,
-0.016765788197517395,
0.011978400871157646,
0.0009121010662056506,
-0.04746716842055321,
0.0030205182265490294,
-0.04171445965766907,
-0.03703370690345764,
0.05929034575819969,
-0.029887622222304344,
0.04453768581151962,
0.014672748744487762,
-0.036155834794044495,
0.0209639985114336,
0.10816212743520737,
-0.03197283297777176,
-0.03132355585694313,
-0.0035819627810269594,
0.017129912972450256,
-0.04009265825152397,
-0.02498365379869938,
0.022106172516942024,
0.009968427941203117,
-0.024952882900834084,
0.05341685190796852,
0.017884641885757446,
-0.0273398756980896,
-0.0018693734891712666,
0.012967521324753761,
-0.04205399379134178,
0.006445268169045448,
-0.017109008505940437,
-0.01945730671286583,
-0.027393829077482224,
-0.03331950679421425,
-0.03420497104525566,
-0.027851153165102005,
-0.03797857463359833,
-0.017973128706216812,
-0.004807374440133572,
0.02082997001707554,
-0.008636229671537876,
-0.03896438702940941,
-0.010062593966722488,
-0.065583735704422,
-0.05374773219227791,
-0.06591217964887619,
-0.01665598526597023,
-0.017271602526307106,
-0.0025082826614379883,
0.04456975311040878,
-0.00026028353022411466,
-0.03360745683312416,
-0.03334075212478638,
-0.05549260601401329,
-0.0018576011061668396,
0.06240520253777504,
-0.03794301673769951,
-0.022392885759472847,
-0.019417401403188705,
0.016118621453642845,
0.0297059528529644,
0.06699921190738678,
0.005933855660259724,
-0.01507125236093998,
0.047882381826639175,
-0.020239241421222687,
0.01512002944946289,
-0.02126438543200493,
-0.030764231458306313,
-0.0366477333009243,
0.051022689789533615,
0.02369939349591732,
0.010296646505594254,
0.008847021497786045,
0.011506408452987671,
-0.05985840782523155,
0.051738668233156204,
-0.05461617931723595,
0.01807066798210144,
-0.007901547476649284,
-0.05233146622776985,
0.010026361793279648,
-0.005341887008398771,
-0.03648076206445694,
0.061365995556116104,
0.07545024901628494,
0.003009362379088998,
-0.02597224712371826,
-0.0015687033301219344,
0.048697639256715775,
0.014730152674019337,
0.037097569555044174,
0.03613604977726936,
-0.036957308650016785,
-0.020934326574206352,
-0.02254752442240715,
0.046738576143980026,
-0.11537131667137146,
-0.02363939769566059,
0.016996268182992935,
0.022856399416923523,
-0.010481598787009716,
0.0200404841452837,
-0.003299485892057419,
0.04782942682504654,
-0.027489785104990005,
-0.006069558672606945,
0.018682990223169327,
-0.020292207598686218,
-0.022197090089321136,
0.009626159444451332,
-0.06081344187259674,
0.02654535323381424,
-0.021862102672457695,
0.009105944074690342,
-0.06092125177383423,
-0.03070111572742462,
-0.0336126871407032,
-0.018198590725660324,
0.020970435813069344,
-0.04300827160477638,
0.04533948004245758,
0.04171651974320412,
0.059134069830179214,
0.006853819824755192,
0.018390361219644547,
-0.03225165233016014,
-0.010754735209047794,
0.01799892447888851,
-0.04294336214661598,
-0.12244663387537003,
0.029458552598953247,
0.04213033989071846,
0.012554866261780262,
-0.011236203834414482,
-0.007546651642769575,
-0.04409591481089592,
0.022928671911358833,
0.019311049953103065,
-0.02350355125963688,
-0.040458645671606064,
-0.04178163781762123
] |
<p>How to estimate the amount of water condensing from air on a surface, given the air's temperature and relative humidity and how they change over time, the surface temperature, material's thermal properites, roughness and whatever else needs to be given about the air and surface?</p>
<p>For my purpose, we may assume the surface starts off dry, but the more general situation would be as interesting. If enough water condenses, it'll form drops and run off - can we account for that? </p>
<p>Are there some fairly simple formulas or rules of thumb? High accuracy is not needed; I'll be happy to get grams per sq meter per second (or whatever) to within a factor of two. (What if we wanted higher accuracy?)</p> | g4612 | [
0.02622843161225319,
-0.015240190550684929,
0.01214834488928318,
0.032107315957546234,
-0.0456993505358696,
0.012385187670588493,
0.041563134640455246,
0.04132918640971184,
-0.06725277006626129,
0.02304726652801037,
0.005894010420888662,
0.02888438291847706,
0.026671620085835457,
0.037098225206136703,
0.008269262500107288,
0.025595711544156075,
-0.03232469782233238,
-0.054796792566776276,
0.045961108058691025,
0.019206758588552475,
0.07553692907094955,
-0.08349166065454483,
0.008073236793279648,
-0.06245254725217819,
-0.12177771329879761,
-0.041571881622076035,
-0.0174085833132267,
0.010905222967267036,
0.004646132700145245,
-0.008758977055549622,
-0.06275925785303116,
0.025820178911089897,
-0.0216805599629879,
-0.007783906534314156,
-0.01891680806875229,
-0.03718758001923561,
-0.010606521740555763,
-0.019926192238926888,
0.019407110288739204,
-0.05262060463428497,
0.03851478919386864,
-0.020739780738949776,
-0.03685745969414711,
0.06621936708688736,
0.009397883899509907,
-0.02003069594502449,
-0.036395080387592316,
-0.026359671726822853,
-0.006962509360164404,
-0.01786990277469158,
-0.008022739551961422,
0.059790369123220444,
-0.020143620669841766,
0.01243967842310667,
-0.09585032612085342,
0.04298321157693863,
0.029356999322772026,
0.0060811396688222885,
0.050719600170850754,
0.014647731557488441,
0.009853211231529713,
-0.005410484038293362,
-0.02353036403656006,
0.0018534759292379022,
0.055829450488090515,
-0.016010921448469162,
-0.027721762657165527,
-0.04545479640364647,
0.04757627099752426,
0.05236227437853813,
-0.011336201801896095,
-0.014400623738765717,
0.003922986797988415,
0.026676388457417488,
-0.029043065384030342,
-0.02405739016830921,
-0.053966082632541656,
0.006031002849340439,
0.04558704420924187,
-0.026880647987127304,
0.010406563058495522,
-0.005008923355489969,
0.021480215713381767,
0.00046053199912421405,
0.04111970216035843,
0.0004300624714232981,
0.012407137081027031,
-0.0030250102281570435,
-0.0095560597255826,
-0.015618393197655678,
-0.008262298069894314,
0.026685412973165512,
0.10342656821012497,
0.0001282935991184786,
0.0621795691549778,
-0.011863389983773232,
-0.050356220453977585,
-0.03051583655178547,
-0.009526005946099758,
0.03914445638656616,
-0.034298431128263474,
-0.03436354920268059,
0.02154681086540222,
-0.03679714351892471,
-0.024613356217741966,
0.041864462196826935,
-0.018652252852916718,
-0.016641559079289436,
-0.019798828288912773,
-0.017208557575941086,
-0.009794294834136963,
0.006615872029215097,
-0.028643660247325897,
-0.0029512187466025352,
-0.008921464905142784,
-0.018570657819509506,
0.005720054265111685,
0.05308527871966362,
0.02061341516673565,
0.015193377621471882,
0.0063020638190209866,
0.04177134111523628,
-0.00026761365006677806,
0.0239567793905735,
-0.003125762101262808,
-0.024112137034535408,
0.025396088138222694,
0.010155055671930313,
0.005424517672508955,
0.00967135839164257,
0.05163022503256798,
0.040959231555461884,
-0.019565202295780182,
0.039434827864170074,
0.0012956197606399655,
0.011971457861363888,
0.0010837960289791226,
0.032300323247909546,
0.012015612795948982,
-0.04781518504023552,
0.018972711637616158,
0.004939629230648279,
-0.030063128098845482,
0.008161417208611965,
-0.032884176820516586,
0.014569615013897419,
-0.04222836717963219,
0.05232458561658859,
0.016481958329677582,
-0.032586704939603806,
-0.0038440029602497816,
0.052029382437467575,
0.0682794526219368,
-0.02089025266468525,
0.05642397329211235,
-0.02224944345653057,
-0.0326693058013916,
-0.05538749694824219,
0.023246027529239655,
0.001842882833443582,
0.06916100531816483,
-0.042520057410001755,
0.024173321202397346,
0.06072961911559105,
-0.07246310263872147,
0.017928214743733406,
-0.02502318099141121,
-0.009285666979849339,
0.0069297985173761845,
-0.033862873911857605,
-0.03995416685938835,
-0.02174396999180317,
-0.08451966941356659,
-0.027663614600896835,
0.01544476393610239,
0.011019406840205193,
0.1442069411277771,
0.023373983800411224,
0.02974509261548519,
-0.014637022279202938,
0.06626494973897934,
0.021468456834554672,
-0.013090874999761581,
-0.017487846314907074,
0.023224646225571632,
-0.00851310696452856,
0.08211222290992737,
-0.07361394166946411,
-0.027740173041820526,
0.004137493669986725,
-0.07037480175495148,
-0.013522586785256863,
0.018690980970859528,
0.0052256896160542965,
-0.00843592919409275,
0.03630606830120087,
0.056665822863578796,
-0.021948756650090218,
-0.004327310249209404,
0.016737014055252075,
-0.020898383110761642,
-0.02930709719657898,
0.01778685860335827,
0.027234142646193504,
0.032192301005125046,
0.07194974273443222,
-0.003293515183031559,
0.02987496741116047,
0.028738850727677345,
-0.002529625315219164,
0.008251025341451168,
-0.009784571826457977,
0.057179003953933716,
0.03294900059700012,
0.04630638659000397,
0.027291368693113327,
-0.01785445399582386,
-0.009172329679131508,
0.0193594079464674,
0.005452747456729412,
0.017543179914355278,
0.054229337722063065,
0.004319445230066776,
0.05042903497815132,
-0.010343239642679691,
-0.009716018103063107,
0.01708371564745903,
0.0012496440904214978,
0.008163362741470337,
0.0561111755669117,
-0.021655496209859848,
-0.0003910908999387175,
-0.009569969028234482,
0.008581026457250118,
-0.02030165120959282,
0.012845129705965519,
-0.04545949026942253,
-0.000939711753744632,
0.08564375340938568,
-0.013876328244805336,
0.01034926064312458,
-0.033232979476451874,
-0.04941769316792488,
-0.028061002492904663,
-0.022451961413025856,
-0.016534140333533287,
-0.02442103624343872,
-0.001810670830309391,
0.0006920514279045165,
0.0020254633855074644,
0.03899625316262245,
0.019187383353710175,
-0.03247253969311714,
-0.005247754044830799,
-0.03375330567359924,
-0.052283696830272675,
-0.044159047305583954,
0.0061693438328802586,
-0.0037762667052447796,
-0.02999752014875412,
0.021081162616610527,
-0.008006504736840725,
0.0446406714618206,
0.032556552439928055,
0.011928224936127663,
-0.014262695796787739,
-0.036782559007406235,
0.019436296075582504,
0.009191679768264294,
0.027584463357925415,
0.0908493623137474,
-0.02268369495868683,
-0.00612178398296237,
0.007925677113234997,
-0.025300508365035057,
-0.020510677248239517,
-0.001131089637055993,
0.029575170949101448,
0.04539577290415764,
-0.0084415627643466,
0.02597307227551937,
-0.007215631194412708,
-0.006721206475049257,
0.035541631281375885,
0.056152381002902985,
-0.07968699932098389,
0.01667187549173832,
0.03794581815600395,
0.03445149585604668,
-0.0026434853207319975,
0.043106693774461746,
-0.013062729500234127,
-0.014909043908119202,
0.03352803364396095,
-0.039615727961063385,
0.005341168958693743,
0.023721501231193542,
0.03151236101984978,
-0.004401238169521093,
0.03313709795475006,
0.012820176780223846,
-0.04379672557115555,
0.01870596967637539,
-0.016941407695412636,
-0.01848471723496914,
0.07178714871406555,
-0.0037525524385273457,
-0.023746633902192116,
0.05566331744194031,
-0.056378234177827835,
0.026258397847414017,
0.024445105344057083,
-0.03304454684257507,
-0.008980605751276016,
-0.024599991738796234,
-0.03823953494429588,
0.019437307491898537,
-0.017226500436663628,
-0.0020074343774467707,
-0.0016140990192070603,
-0.013787070289254189,
-0.04044221341609955,
0.016139671206474304,
0.04758724197745323,
-0.00433678925037384,
0.04615841433405876,
-0.05980638414621353,
0.03512970730662346,
-0.01845025271177292,
-0.03826272115111351,
0.015210168436169624,
-0.011658781208097935,
-0.03487103804945946,
-0.03418438881635666,
-0.038845255970954895,
-0.020160766318440437,
0.038655251264572144,
-0.04506991058588028,
0.0022314051166176796,
0.008060837164521217,
-0.019306978210806847,
-0.014667792245745659,
-0.03652193769812584,
-0.0035462493542581797,
-0.01618754118680954,
-0.03350922092795372,
-0.014617818407714367,
-0.015507614240050316,
-0.02915451116859913,
-0.03633582964539528,
0.0728360116481781,
-0.06289356201887131,
0.006192594766616821,
0.0064002880826592445,
-0.0025936192832887173,
0.10280413925647736,
0.029384072870016098,
0.005350983701646328,
0.03637176379561424,
0.007321604993194342,
0.004658200778067112,
-0.06473466753959656,
0.04770344868302345,
0.03236331418156624,
-0.02572772465646267,
-0.09730365127325058,
0.028675375506281853,
0.07498782128095627,
-0.03655432164669037,
-0.02560528554022312,
0.022252559661865234,
0.006135695613920689,
-0.009138458408415318,
0.036290332674980164,
0.008819918148219585,
-0.012556856498122215,
0.0274321511387825,
0.007783220615237951,
0.043558474630117416,
0.014627141878008842,
-0.03866002708673477,
0.07903394103050232,
-0.01232975348830223,
0.009567209519445896,
-0.06281759589910507,
-0.021884096786379814,
-0.03156375512480736,
0.013743653893470764,
0.03500095009803772,
-0.09537656605243683,
-0.0615774504840374,
-0.02916731685400009,
-0.007059755269438028,
0.009576091542840004,
0.03269025683403015,
-0.01925053633749485,
0.03298906609416008,
0.02477855794131756,
-0.05613766983151436,
0.02381877228617668,
0.06455381214618683,
0.006752803921699524,
0.02423831820487976,
0.03637951239943504,
0.01629660092294216,
-0.04394003748893738,
0.008018994703888893,
-0.05964198708534241,
0.0019960401114076376,
0.03445811942219734,
0.01365363784134388,
-0.006296290550380945,
0.036892909556627274,
0.0025781714357435703,
0.032174695283174515,
-0.054331593215465546,
0.005989126395434141,
-0.044761307537555695,
0.06536877155303955,
0.019945429638028145,
0.007371820043772459,
-0.018396472558379173,
-0.0030295364558696747,
-0.016224902123212814,
-0.030484642833471298,
-0.005430360324680805,
0.04457239806652069,
-0.031306639313697815,
-0.02225472405552864,
-0.04873742535710335,
0.0010557582136243582,
0.01720842719078064,
-0.04261843487620354,
0.03714822605252266,
0.00962916761636734,
0.015367782674729824,
0.028438745066523552,
-0.03005710057914257,
0.014492151327431202,
-0.016133470460772514,
-0.018727365881204605,
0.03653394430875778,
-0.024655139073729515,
0.028991352766752243,
0.010448003187775612,
0.05638313665986061,
-0.008215239271521568,
-0.05958076938986778,
0.03330688551068306,
0.002735587302595377,
-0.037798892706632614,
0.005181643180549145,
0.05566486343741417,
-0.031463466584682465,
-0.06587212532758713,
0.03664005175232887,
0.005576091818511486,
0.012353538535535336,
-0.009039637632668018,
0.0058607663959264755,
-0.05894548445940018,
0.03903612121939659,
0.01255831215530634,
-0.018739555031061172,
-0.06178974732756615,
-0.0451057031750679,
-0.04381761699914932,
0.00196694303303957,
-0.023395227268338203,
-0.04338332638144493,
-0.021688558161258698,
-0.005647566635161638,
0.05011424049735069,
0.06051439419388771,
0.009249462746083736,
0.06416173279285431,
-0.007526889909058809,
-0.02214953862130642,
-0.004253210965543985,
0.03177203983068466,
0.016150346025824547,
-0.001498350640758872,
0.024940069764852524,
0.05763137713074684,
-0.033669136464595795,
0.006960258353501558,
0.008983981795608997,
0.056467849761247635,
-0.028689755126833916,
-0.03775714710354805,
-0.009599105454981327,
0.02603926882147789,
0.028199009597301483,
-0.004000402055680752,
-0.07925287634134293,
-0.05079641938209534,
-0.046610042452812195,
-0.010448142886161804,
0.018107831478118896,
0.021564768627285957,
-0.053446151316165924,
0.08792779594659805,
-0.03639012575149536,
0.005164173431694508,
0.01667432300746441,
0.003756752470508218,
0.015167656354606152,
-0.07539671659469604,
0.039988793432712555,
0.09944085031747818,
0.011949649080634117,
0.009398008696734905,
-0.0002723616489674896,
0.021003738045692444,
0.006916859187185764,
-0.04632209613919258,
0.007407544180750847,
0.045067720115184784,
-0.06405173242092133,
0.04562360793352127,
0.0438510999083519,
-0.035881176590919495,
-0.009945360012352467,
0.042443517595529556,
-0.03294162452220917,
-0.01631997339427471,
-0.05013461783528328,
-0.06022132188081741,
0.0072144633159041405,
0.008393876254558563,
0.011434166692197323,
-0.017768941819667816,
-0.06572916358709335,
-0.027417311444878578,
-0.022644707933068275,
0.011576635763049126,
-0.022686563432216644,
-0.00420574564486742,
0.08889919519424438,
-0.021783143281936646,
-0.0566735714673996,
0.013532263226807117,
0.008084187284111977,
0.013949349522590637,
0.06655711680650711,
-0.024165308102965355,
0.01645076461136341,
-0.008179975673556328,
0.04203961044549942,
0.025664890184998512,
-0.0035789746325463057,
-0.01278605591505766,
0.038207609206438065,
0.018908919766545296,
0.004229372832924128,
0.019298825412988663,
-0.01048214454203844,
-0.0019761479925364256,
-0.023934561759233475,
0.033269912004470825,
0.05019073560833931,
0.014192449860274792,
0.05848037078976631,
0.0034180856309831142,
-0.06488144397735596,
0.005433924496173859,
-0.05264576897025108,
0.013423045165836811,
-0.0458260253071785,
-0.007015249226242304,
-0.03020983189344406,
-0.04026975855231285,
0.0032470643054693937,
-0.05246634781360626,
-0.056636013090610504,
0.07210373878479004,
-0.02437521331012249,
-0.008652394637465477,
0.010577156208455563,
-0.010447383858263493,
-0.0023231469094753265,
0.005824156105518341,
0.022180287167429924,
-0.046008311212062836,
-0.012480553239583969,
0.0010299282148480415,
-0.026397954672574997,
0.03475172445178032,
-0.017567817121744156,
0.07441072165966034,
-0.015932340174913406,
0.00824234914034605,
0.004927143454551697,
-0.053890880197286606,
-0.014628549106419086,
-0.05479729175567627,
0.0009021033183671534,
0.041867196559906006,
0.017871743068099022,
-0.005539930425584316,
0.03685532510280609,
0.053070858120918274,
0.0340016707777977,
-0.08133995532989502,
0.05793507397174835,
0.013613457791507244,
0.03306807950139046,
-0.012179332785308361,
0.06159680709242821,
-0.06328249722719193,
-0.034276511520147324,
-0.018568510189652443,
0.025777481496334076,
-0.004650618880987167,
-0.017780210822820663,
-0.061595674604177475,
0.04134194180369377,
0.08558420836925507,
0.030844083055853844,
-0.03104405291378498,
0.016923673450946808,
0.03055129386484623,
0.020590219646692276,
-0.05772620812058449,
0.0031732365023344755,
0.009222927503287792,
0.023525666445493698,
0.05628373846411705,
0.023025255650281906,
0.03188537806272507,
0.03482019901275635,
-0.007771796081215143,
-0.03251892700791359,
0.00042489025508984923,
-0.04264049977064133,
0.08633121848106384,
-0.05113044008612633,
0.027180124074220657,
0.04195203259587288,
0.033660322427749634,
-0.02173377014696598,
-0.013258135877549648,
-0.0163497906178236,
0.06325769424438477,
-0.0355113185942173,
-0.06394345313310623,
-0.012585590593516827,
-0.051379889249801636,
-0.0370209626853466,
-0.03411727026104927,
0.008876373060047626,
-0.13789008557796478,
-0.006449492182582617,
0.02813328243792057,
0.0031354643870145082,
0.04547946900129318,
0.041865408420562744,
-0.014464648440480232,
-0.020824473351240158,
0.01481556985527277,
-0.0421435721218586,
-0.06832116097211838,
0.04616817831993103,
0.01401437260210514,
0.000648729270324111,
0.06955774128437042,
0.008532609790563583,
0.012617030180990696,
0.02538680098950863,
-0.058846600353717804,
-0.004930444061756134,
-0.055886320769786835,
0.012752792797982693,
-0.025987699627876282,
0.00016310611681547016,
0.0018754495540633798,
0.024070555344223976,
0.002517544198781252,
-0.014859028160572052,
0.03672453388571739,
-0.036965545266866684,
-0.00009374718501931056,
-0.005376409739255905,
-0.022625545039772987,
0.024406665936112404,
-0.004589547403156757,
-0.011777421459555626,
0.042739082127809525,
0.04120446369051933,
-0.027888882905244827,
-0.004631403833627701,
-0.0221694428473711,
-0.00954299233853817,
-0.002590117510408163,
-0.053829044103622437,
-0.03285941109061241,
0.10809317231178284,
-0.0571274571120739,
0.028924886137247086,
-0.005315196700394154,
0.010019307024776936,
0.012018771842122078,
0.01517088059335947,
-0.04695698618888855,
-0.015187515877187252,
-0.015185891650617123,
-0.024410920217633247,
-0.029840316623449326,
0.005767987575381994,
-0.017278295010328293,
-0.008756298571825027,
0.0066875978372991085,
-0.013049254193902016,
-0.014926964417099953,
-0.045367058366537094,
-0.04085966944694519,
-0.05851458013057709,
-0.06613461673259735,
-0.025462975725531578,
-0.024126026779413223,
-0.061935700476169586,
-0.04625999927520752,
-0.013085879385471344,
-0.01779528148472309,
0.052428971976041794,
0.014351608231663704,
0.0014257984003052115,
0.017521550878882408,
0.024383021518588066,
0.03603339567780495,
-0.021098677068948746,
0.020402615889906883,
0.020235132426023483,
-0.012269754894077778,
0.020593887194991112,
0.025172637775540352,
0.07880204170942307,
-0.028698375448584557,
-0.05911599472165108,
0.0008385740802623332,
-0.018214423209428787,
0.01731889136135578,
0.04356149956583977,
-0.05363111570477486,
0.013054030016064644,
-0.061704669147729874,
0.0393594391644001,
0.03207753971219063,
0.06787343323230743,
-0.06645084917545319,
0.0022493035066872835,
0.05741493031382561,
0.05076194182038307,
-0.023162247613072395,
-0.039651136845350266,
-0.07945878803730011,
-0.00850006379187107,
-0.00799292791634798,
0.009511014446616173,
-0.01239628903567791,
-0.07111091166734695,
-0.02994966320693493,
0.01854347251355648,
-0.011995150707662106,
-0.0114296181127429,
0.00818614475429058,
-0.028264883905649185,
-0.008088620379567146
] |
<p>Also the side question is how many Joules is one photon (any between 450-660nm).
Thank you</p>
<p>P.S. I am asking because I want to estimate how much thermal energy should be dissipated by LED when part of known energy is emitted as light.</p>
<p>P.S. Got an answer from Robert. Thank you.
So those 6500 Lumen 100Watt white LED arrays emit about 9 watt of energy in photons alone and rest 91W goes into heat. Not bad.</p> | g4613 | [
-0.014813263900578022,
0.023944025859236717,
0.020711183547973633,
0.010502721183001995,
-0.003484866116195917,
-0.07602773606777191,
0.03799300268292427,
0.07479777187108994,
0.0023569536861032248,
0.002642550738528371,
0.0033562781754881144,
0.075205497443676,
-0.047197964042425156,
0.013242094777524471,
-0.0531415194272995,
-0.027679109945893288,
0.0567861944437027,
-0.020792091265320778,
0.07365147024393082,
0.10051830857992172,
-0.054579414427280426,
-0.04328054562211037,
-0.06815176457166672,
-0.04364427551627159,
-0.009565220214426517,
0.011025003157556057,
0.0022177896462380886,
0.00562104769051075,
-0.04891204833984375,
-0.05979858711361885,
0.022817283868789673,
0.01213481742888689,
0.04412491247057915,
0.006374119780957699,
-0.05252448096871376,
0.01640048436820507,
0.02577131614089012,
-0.034970127046108246,
-0.007201727479696274,
-0.021553320810198784,
-0.03288307040929794,
0.023081162944436073,
0.06461737304925919,
0.044117264449596405,
0.039857372641563416,
-0.03306609019637108,
0.023345250636339188,
-0.008541278541088104,
0.003214066382497549,
0.022204997017979622,
0.011218398809432983,
0.011375452391803265,
0.0172110702842474,
0.02185910753905773,
0.02695862390100956,
-0.01711445488035679,
-0.06396448612213135,
-0.027792129665613174,
0.023691799491643906,
0.042527392506599426,
-0.005589228589087725,
-0.02956319786608219,
-0.049008775502443314,
-0.02256045490503311,
0.033515237271785736,
0.00563634792342782,
-0.01607811078429222,
-0.01609417237341404,
-0.0015643868828192353,
-0.01393478736281395,
0.09015973657369614,
0.04419611021876335,
0.001444717519916594,
0.015527944080531597,
0.030286818742752075,
-0.02701391652226448,
0.03246314078569412,
0.0035570613108575344,
-0.01433449238538742,
0.014810029417276382,
-0.04015549272298813,
-0.0324908122420311,
0.003583412617444992,
-0.03821222111582756,
0.023851880803704262,
0.014332635328173637,
-0.05214966461062431,
-0.0018470146460458636,
-0.0046693566255271435,
0.009799723513424397,
0.06021715700626373,
0.05016699060797691,
0.1068209782242775,
0.005015199538320303,
0.050276607275009155,
-0.023016365244984627,
0.016702109947800636,
0.008159643039107323,
-0.0015750081511214375,
-0.027540940791368484,
0.046750351786613464,
0.0035579639952629805,
-0.05120103061199188,
0.023164818063378334,
0.01689489185810089,
-0.0328206829726696,
-0.004006996750831604,
-0.05593351274728775,
-0.05151160806417465,
0.06159302219748497,
-0.023007571697235107,
-0.054270416498184204,
-0.06609103828668594,
-0.001117104315198958,
-0.017940692603588104,
-0.015916548669338226,
0.07529260218143463,
-0.07746345549821854,
0.01037695910781622,
0.05968070030212402,
0.0392974354326725,
0.013515152968466282,
-0.012879244983196259,
-0.009121238254010677,
0.045558858662843704,
0.010876002721488476,
0.032871827483177185,
-0.016534501686692238,
-0.02805771864950657,
0.011790338903665543,
-0.00269603100605309,
-0.015115146525204182,
-0.07596305757761002,
0.059782955795526505,
0.03504224866628647,
0.06534083932638168,
0.0061757187359035015,
-0.0033283024094998837,
-0.01956910267472267,
0.018149513751268387,
0.043989330530166626,
-0.00028532370924949646,
0.033002905547618866,
0.002655956195667386,
0.01420523226261139,
0.014003685675561428,
-0.03674033284187317,
0.04025673121213913,
0.008780019357800484,
0.11213628947734833,
0.07724747061729431,
0.040517937391996384,
0.009064044803380966,
-0.11414165049791336,
0.028530815616250038,
-0.036409225314855576,
-0.01721704564988613,
-0.00620536832138896,
-0.0744866281747818,
0.0054439944215118885,
-0.004981948994100094,
0.0468466579914093,
0.10388636589050293,
-0.018088052049279213,
-0.010519025847315788,
-0.035381097346544266,
-0.0004513378080446273,
-0.041896119713783264,
-0.010817612521350384,
-0.01602889411151409,
-0.0034937767777591944,
0.005413215607404709,
-0.04269680753350258,
0.011562313884496689,
-0.009252136573195457,
0.0019968152046203613,
0.013467471115291119,
-0.007196118123829365,
-0.005941371433436871,
-0.002466735430061817,
0.013724235817790031,
0.00037500090547837317,
0.03822401911020279,
-0.028791336342692375,
0.002164153615012765,
-0.005288893822580576,
-0.03178806230425835,
-0.005482266191393137,
-0.009798096492886543,
0.05224807932972908,
-0.02308790199458599,
0.0003662653616629541,
0.04618800804018974,
-0.029866183176636696,
-0.036835674196481705,
-0.0008790873689576983,
0.045326001942157745,
-0.021477196365594864,
-0.007249702233821154,
0.0034793505910784006,
-0.009355904534459114,
0.02156367525458336,
-0.0659039095044136,
-0.014876584522426128,
0.04898449406027794,
0.016048161312937737,
0.019653931260108948,
0.005320818163454533,
0.008365927264094353,
-0.07189187407493591,
-0.011045466177165508,
0.0007397412555292249,
0.027442047372460365,
0.027478128671646118,
0.03375890851020813,
-0.020134547725319862,
-0.013573846779763699,
-0.014843499287962914,
-0.009691976942121983,
0.03404480218887329,
0.0031313709914684296,
0.02072509191930294,
0.051701635122299194,
-0.033720463514328,
-0.03569159284234047,
-0.005739027168601751,
-0.07549432665109634,
0.0033654365688562393,
0.010045747272670269,
0.0401604101061821,
-0.10203158855438232,
0.02759941667318344,
-0.015042086131870747,
-0.04421033337712288,
0.0514240525662899,
0.00025435391580685973,
-0.06097648665308952,
-0.024883003905415535,
-0.00539008341729641,
-0.02465927042067051,
0.03717454895377159,
0.006727027241140604,
0.0162011981010437,
0.007727202493697405,
-0.044123101979494095,
-0.044756241142749786,
0.024150878190994263,
-0.039016544818878174,
0.01897309347987175,
0.022396910935640335,
-0.04518146812915802,
-0.023811347782611847,
0.013986245729029179,
0.02941989153623581,
-0.033626098185777664,
-0.01962919719517231,
-0.037339214235544205,
0.006088774185627699,
-0.033414602279663086,
-0.027457106858491898,
-0.0053295292891561985,
-0.1252651810646057,
-0.06370573490858078,
-0.033476583659648895,
0.044607989490032196,
-0.03449489548802376,
0.017107363790273666,
-0.06670939922332764,
0.03441498428583145,
0.011029795743525028,
0.0026251170784235,
0.0260136928409338,
0.0017366032116115093,
-0.022185450419783592,
0.058759238570928574,
0.028775133192539215,
0.0026366745587438345,
0.00753271346911788,
-0.010890752077102661,
-0.034671276807785034,
0.03221782296895981,
-0.010489767417311668,
-0.061355773359537125,
-0.0015508770011365414,
0.0241807010024786,
-0.12475631386041641,
0.014354346320033073,
-0.010426645167171955,
0.008068124763667583,
0.05287637561559677,
-0.06165207549929619,
-0.01508301217108965,
-0.0018734580371528864,
-0.04205493628978729,
-0.02375197596848011,
0.008425799198448658,
0.041385333985090256,
0.00960647501051426,
-0.024888090789318085,
-0.016975833103060722,
-0.000045681903429795057,
-0.044916871935129166,
-0.034099966287612915,
-0.05571332201361656,
-0.02778063714504242,
0.019659729674458504,
-0.03551285341382027,
-0.034302856773138046,
0.015008619986474514,
-0.023559575900435448,
-0.009679851122200489,
0.01798665151000023,
0.009149924851953983,
0.045857738703489304,
-0.054833441972732544,
-0.025249268859624863,
0.012250478379428387,
-0.05385478585958481,
-0.015801353380084038,
0.04169148951768875,
0.008593038655817509,
0.03301174193620682,
0.030650537461042404,
-0.012799450196325779,
-0.02899664081633091,
-0.010284356772899628,
0.043901026248931885,
-0.030878039076924324,
0.044225726276636124,
0.03135085478425026,
-0.022842224687337875,
0.01211582776159048,
-0.05999878793954849,
0.023533809930086136,
0.03723637014627457,
0.012953292578458786,
-0.062391940504312515,
0.02121061272919178,
0.05187911167740822,
0.018867993727326393,
-0.07023069262504578,
-0.007921158336102962,
-0.04170850291848183,
-0.016702663153409958,
0.05808883532881737,
0.03221691772341728,
-0.03720413148403168,
-0.01933326944708824,
0.01644650474190712,
-0.04907923564314842,
0.043854858726263046,
-0.04440811648964882,
-0.029750457033514977,
-0.05585769936442375,
-0.06820115447044373,
0.06013021990656853,
-0.04489734396338463,
0.09815206378698349,
0.03533751145005226,
0.0031354068778455257,
0.019013727083802223,
0.0025803467724472284,
0.06199871376156807,
-0.05091222748160362,
-0.022636808454990387,
0.013472940772771835,
-0.011004290543496609,
0.0331198051571846,
0.014234254136681557,
0.004426027648150921,
-0.058977652341127396,
0.02295825071632862,
-0.03479507938027382,
-0.028990285471081734,
-0.013876835815608501,
0.013062357902526855,
0.009983627125620842,
0.014380757696926594,
-0.036570459604263306,
0.050465404987335205,
-0.02937249280512333,
-0.028747232630848885,
-0.01734393648803234,
-0.002355169504880905,
-0.030399486422538757,
0.010784744285047054,
-0.017734216526150703,
-0.011921092867851257,
0.017757892608642578,
-0.03766482695937157,
0.0006965154316276312,
-0.029986189678311348,
-0.0076548028737306595,
-0.009014461189508438,
-0.00032916179043240845,
-0.04691698029637337,
0.024819716811180115,
0.0042035807855427265,
0.0043993680737912655,
0.03573281690478325,
0.04255111515522003,
0.0637919157743454,
0.08648300915956497,
-0.019314821809530258,
0.009909942746162415,
0.04628380015492439,
0.04739682003855705,
-0.03248106688261032,
-0.007750530261546373,
0.0034293506760150194,
-0.035877127200365067,
0.00982970092445612,
0.027027491480112076,
-0.016508735716342926,
0.019512470811605453,
0.0022275580558925867,
0.03697776421904564,
-0.01064209546893835,
0.07346800714731216,
0.008309006690979004,
0.009952887892723083,
-0.016195403411984444,
-0.05479364097118378,
-0.027851184830069542,
0.0023140059784054756,
0.11069202423095703,
0.016094978898763657,
-0.019895171746611595,
0.00649854214861989,
-0.01762581057846546,
0.09436223655939102,
-0.01382338535040617,
-0.03160427510738373,
0.0033058193512260914,
-0.04219795763492584,
0.02239341475069523,
0.033524323254823685,
0.02258194051682949,
0.008834385313093662,
0.006669160444289446,
0.010614623315632343,
-0.04614169895648956,
0.016723932698369026,
-0.026877863332629204,
0.023208094760775566,
0.018479835242033005,
0.007967568002641201,
-0.01372344046831131,
-0.06088526174426079,
-0.0558338426053524,
-0.0003857470874208957,
-0.0028338308911770582,
-0.060260675847530365,
-0.0340297594666481,
0.00103376479819417,
-0.0055328733287751675,
0.004139110445976257,
-0.02502444013953209,
0.06619463115930557,
0.08220067620277405,
-0.04510210081934929,
-0.019816718995571136,
0.026332780718803406,
-0.02271142229437828,
0.02970695309340954,
0.0016938084736466408,
-0.049005694687366486,
0.01773485355079174,
0.017744479700922966,
-0.04205753654241562,
-0.007173494435846806,
-0.017550164833664894,
-0.0272253155708313,
0.04008615016937256,
-0.03968952223658562,
-0.042991116642951965,
-0.030071362853050232,
-0.062457747757434845,
0.023184748366475105,
0.04702761769294739,
-0.0022093630395829678,
-0.01192481815814972,
-0.014932560734450817,
0.016289664432406425,
0.018844405189156532,
0.0009679611539468169,
-0.03342723101377487,
0.01589891128242016,
0.05922401323914528,
-0.01023192796856165,
-0.06897351890802383,
0.018664581701159477,
-0.018119435757398605,
-0.020860813558101654,
-0.03936312720179558,
0.03199462592601776,
-0.010009069927036762,
-0.02093259058892727,
-0.030094673857092857,
0.09310097247362137,
-0.02319095842540264,
-0.014995765872299671,
-0.053577620536088943,
-0.04375256225466728,
-0.03240049257874489,
0.017968052998185158,
0.0003494325210340321,
-0.03214854747056961,
-0.009171049110591412,
0.046679913997650146,
-0.014634199440479279,
0.014256863854825497,
0.027737213298678398,
-0.011642232537269592,
-0.01152798067778349,
-0.06778797507286072,
-0.008035075850784779,
0.01506046298891306,
0.03506792336702347,
0.01653115265071392,
0.022642696276307106,
0.03400009498000145,
0.020160943269729614,
0.07013960182666779,
0.018999166786670685,
-0.022485433146357536,
-0.043819814920425415,
-0.009222133085131645,
0.02295198105275631,
-0.021178731694817543,
0.022518545389175415,
-0.013930976390838623,
-0.05342542752623558,
0.012795943766832352,
-0.008586600422859192,
-0.02399905025959015,
0.023053618147969246,
0.0014082090929150581,
0.005046512931585312,
0.000060623329773079604,
-0.04417034238576889,
0.026992904022336006,
0.006775565445423126,
0.0614648312330246,
0.04550939053297043,
-0.03356083109974861,
-0.003320513293147087,
-0.04648713022470474,
0.010337893851101398,
0.03077235445380211,
0.08234526962041855,
0.04522695019841194,
0.05707208439707756,
-0.01193324662744999,
0.0288525577634573,
-0.0042124055325984955,
0.024995915591716766,
0.012080738320946693,
0.04625760391354561,
0.002663287566974759,
0.017826654016971588,
0.07311254739761353,
-0.03738310560584068,
0.00904657319188118,
0.027776066213846207,
-0.03323183208703995,
-0.043256111443042755,
-0.09539058059453964,
-0.020880326628684998,
0.047072913497686386,
0.08588208258152008,
-0.00949926022440195,
-0.019914641976356506,
-0.02513357810676098,
0.002065107924863696,
0.055714063346385956,
0.012908737175166607,
-0.048337068408727646,
-0.05041058361530304,
-0.013379133306443691,
0.018009718507528305,
0.0171316210180521,
0.025539444759488106,
-0.015531552024185658,
0.02701905183494091,
0.015795603394508362,
0.0032466594129800797,
0.0445864200592041,
0.012486662715673447,
-0.020770128816366196,
0.011402765288949013,
-0.018755894154310226,
0.04287121817469597,
0.02030990831553936,
-0.02098771743476391,
-0.02942860871553421,
-0.0021948935464024544,
0.014215592294931412,
0.007589529734104872,
-0.008163091726601124,
-0.02356862649321556,
0.015688369050621986,
-0.05307237431406975,
-0.0003364193835295737,
0.06478986889123917,
-0.006677074357867241,
-0.04472135007381439,
-0.002952154027298093,
-0.004519452806562185,
0.017591413110494614,
-0.0016839600866660476,
0.02279440127313137,
0.008423841558396816,
0.03957648575305939,
0.02613096311688423,
-0.039996374398469925,
0.0042332978919148445,
0.01794634759426117,
-0.020922407507896423,
0.04328085109591484,
-0.01952417567372322,
-0.0851806104183197,
0.012164315208792686,
0.0298551544547081,
-0.004577476531267166,
0.11185508966445923,
-0.004441497381776571,
0.07705637812614441,
0.03223690390586853,
0.022062385454773903,
-0.02186516672372818,
0.008351335301995277,
0.033216796815395355,
0.03353435546159744,
0.06463392823934555,
-0.017373783513903618,
-0.04534301534295082,
-0.010814235545694828,
0.00040644092950969934,
0.0076575325801968575,
-0.008965427055954933,
-0.0027662503998726606,
0.04451526701450348,
0.04330826178193092,
-0.04042753577232361,
0.09972857683897018,
-0.015729956328868866,
0.04129580408334732,
0.04839865118265152,
0.04705051705241203,
-0.004578317515552044,
-0.039451032876968384,
-0.032812148332595825,
0.016661755740642548,
-0.02690821699798107,
0.04022382199764252,
-0.03658479452133179,
0.01202757004648447,
-0.04592500999569893,
-0.021902987733483315,
0.04409891739487648,
0.047004103660583496,
0.010282705537974834,
0.024235643446445465,
0.016712041571736336,
-0.006267823278903961,
0.07424596697092056,
-0.0018086114432662725,
-0.03339175134897232,
-0.03719320520758629,
-0.028229255229234695,
-0.013055793009698391,
-0.029345951974391937,
-0.05284528806805611,
-0.046649180352687836,
-0.018127430230379105,
-0.023730235174298286,
0.023380201309919357,
-0.004699584562331438,
-0.040172502398490906,
-0.05116784945130348,
0.03282802179455757,
-0.028522690758109093,
0.008627213537693024,
0.008666257373988628,
0.026141582056879997,
0.00893118791282177,
-0.03561145439743996,
0.042442984879016876,
0.02931675873696804,
-0.07276542484760284,
-0.04075273498892784,
0.030913636088371277,
-0.03169934079051018,
-0.019402973353862762,
0.03413030877709389,
-0.0068444497883319855,
-0.02170058712363243,
0.0341130867600441,
0.06743090599775314,
-0.00340714817866683,
0.01618805155158043,
0.02051570452749729,
-0.05026204138994217,
-0.05292806029319763,
0.03577969968318939,
0.00551220728084445,
0.0035829150583595037,
0.010839427821338177,
-0.024547383189201355,
0.005290151108056307,
-0.0058987755328416824,
0.0495794415473938,
0.06328760087490082,
0.008921394124627113,
-0.004261076916009188,
-0.08299132436513901,
0.01263471320271492,
0.045347169041633606,
0.0005083606229163706,
0.01182992197573185,
0.01484000589698553,
-0.029674742370843887,
0.007141507230699062,
0.03274151310324669,
-0.037179797887802124,
0.023502802476286888,
0.022901002317667007,
0.010565255768597126,
-0.012909573502838612,
-0.01789596863090992,
-0.008170921355485916,
-0.027317969128489494,
-0.040941715240478516,
-0.029785608872771263,
0.03941360116004944,
0.058275140821933746,
0.006718209944665432,
0.0009277043864130974,
0.03464680537581444,
0.032738957554101944,
-0.023708799853920937,
-0.025791918858885765,
-0.043903425335884094,
0.016369836404919624,
-0.07688350230455399,
-0.05377864092588425,
0.04244300723075867,
0.0315193347632885,
-0.017607932910323143,
0.003565246006473899,
0.0267617329955101,
-0.04338107258081436,
0.049456339329481125,
0.04333384707570076,
-0.05627797544002533,
-0.022315645590424538,
-0.010531469248235226,
-0.01793246902525425,
-0.00968426838517189,
-0.0009210944990627468,
-0.017780577763915062,
0.010137955658137798,
0.00805611815303564,
0.0458279512822628,
-0.018923915922641754,
-0.019665654748678207,
-0.06313057988882065
] |
<p>Cellular automata provide interesting models of physics: Google Scholar gives more than 25,000 results when searching for <a href="http://scholar.google.com/scholar?q=%22cellular+automata%22+physics&hl=en&btnG=Search&as_sdt=2001&as_sdtp=on">"cellular automata" physics</a>.</p>
<p>Google Scholar still gives more than 2.000 results when searching for <a href="http://scholar.google.com/scholar?hl=en&q=%22quantum+cellular+automata%22&btnG=Search&as_sdt=2000&as_ylo=&as_vis=0">"quantum cellular automata"</a>.</p>
<p>But it gives only <a href="http://books.google.com/books?hl=en&lr=&id=sab-9fGPCEcC&oi=fnd&pg=PA1&dq=%22relativistic+cellular+automata%22&ots=rG9eoNgPYh&sig=ZNQpI-0B-0S2358zX9To-h4NtdI#v=onepage&q=%22relativistic%20cellular%20automata%22&f=false">1</a> (one!) result when searching for <a href="http://scholar.google.com/scholar?hl=en&q=%22relativistic+cellular+automata%22&btnG=Search&as_sdt=2000&as_ylo=&as_vis=0">"relativistic cellular automata"</a>, i.e. cellular automata with a (discrete) Minkoswki space-time instead of an Euclidean one.</p>
<blockquote>
<p>How can this be understood? </p>
<p>Why does the concept of QCA seem more
promising than that of RCA?</p>
<p>Are there conceptual or technical barriers for a thorough treatment of RCA?</p>
</blockquote> | g4614 | [
-0.00560096837580204,
0.022750265896320343,
0.004251816309988499,
-0.047713518142700195,
0.06947464495897293,
-0.05224385857582092,
0.02196384221315384,
-0.02370816469192505,
-0.035243310034275055,
0.005273652728646994,
0.05246619135141373,
0.009044625796377659,
0.03936032950878143,
0.0013982641976326704,
-0.02358228713274002,
-0.02391347661614418,
0.02371012233197689,
0.028507383540272713,
-0.002469623228535056,
0.05013492330908775,
-0.025307418778538704,
-0.028874514624476433,
0.026969963684678078,
-0.046150125563144684,
-0.04564748331904411,
-0.01941247656941414,
0.007539977319538593,
-0.032426003366708755,
-0.057396259158849716,
0.0169457346200943,
0.003040221519768238,
-0.07424483448266983,
0.04632556810975075,
-0.1145433783531189,
-0.023829219862818718,
-0.025884512811899185,
0.03616409748792648,
-0.026190288364887238,
0.010288095101714134,
0.03393854573369026,
0.03489319607615471,
0.021436244249343872,
-0.024891531094908714,
0.01850978285074234,
0.011040321551263332,
0.00089818867854774,
-0.044428206980228424,
-0.0016419925959780812,
-0.026188338175415993,
-0.02656375803053379,
-0.007002014666795731,
0.051712896674871445,
0.037118736654520035,
0.04420354217290878,
0.05723026767373085,
0.03177672624588013,
-0.017055729404091835,
-0.0005076378001831472,
0.0371004156768322,
-0.009332043118774891,
-0.015963546931743622,
0.07815206050872803,
-0.01538372877985239,
-0.000057763532822718844,
0.06812749803066254,
-0.027860581874847412,
-0.018997522071003914,
-0.008241741918027401,
-0.009615445509552956,
0.005634194239974022,
0.025018639862537384,
-0.10639891773462296,
-0.01185491681098938,
0.016489656642079353,
-0.010245498269796371,
0.007722347974777222,
-0.04638202488422394,
0.01777876913547516,
0.027239913120865822,
0.03253554552793503,
-0.07353462278842926,
-0.00916528981178999,
0.002314420649781823,
0.02567242830991745,
0.010092138312757015,
-0.001728427829220891,
-0.014056870713829994,
-0.007323085330426693,
0.04812724515795708,
0.02736623026430607,
0.009475133381783962,
-0.03627656772732735,
0.09319666773080826,
-0.012059112079441547,
-0.03203887492418289,
0.016162220388650894,
-0.042215991765260696,
0.0006016173283569515,
-0.033697113394737244,
0.05029073357582092,
-0.02135111205279827,
0.018694113940000534,
0.04637320712208748,
0.006581345573067665,
-0.05082758888602257,
0.007245271932333708,
0.007847270928323269,
-0.00075726822251454,
-0.03419538214802742,
0.01562800258398056,
-0.03887702524662018,
0.00795376393944025,
-0.028144679963588715,
0.022695105522871017,
-0.05389634892344475,
-0.022109532728791237,
0.08954375237226486,
-0.009725767187774181,
0.0058707064017653465,
-0.01055893488228321,
-0.009280632250010967,
0.041289154440164566,
0.03241414204239845,
0.030916322022676468,
-0.023413460701704025,
0.01975233294069767,
0.015456371940672398,
0.03699224442243576,
0.005694814026355743,
-0.0024738458450883627,
0.01739242859184742,
-0.021898599341511726,
-0.02478095144033432,
0.03376871347427368,
-0.013896982185542583,
0.04060522839426994,
-0.06470556557178497,
0.004139457363635302,
-0.007280758116394281,
0.03323201835155487,
0.018123343586921692,
-0.022788861766457558,
0.007817670702934265,
-0.014978736639022827,
-0.018286151811480522,
-0.07159620523452759,
-0.05138538405299187,
0.030094578862190247,
-0.01243015006184578,
-0.025770949199795723,
0.00023318429884966463,
0.04138210415840149,
0.010811364278197289,
-0.012541691772639751,
0.011514871381223202,
0.07389688491821289,
0.037162624299526215,
-0.002567645628005266,
-0.02001488022506237,
-0.011325634084641933,
0.025774938985705376,
-0.027065865695476532,
-0.05932816118001938,
-0.011561406776309013,
-0.04573653265833855,
0.034852832555770874,
0.023929651826620102,
-0.09521051496267319,
0.031408146023750305,
-0.03751327842473984,
0.0007394324638880789,
-0.014346137642860413,
0.04213162884116173,
0.08310963213443756,
0.041087228804826736,
0.08236908912658691,
-0.010572769679129124,
-0.047527387738227844,
0.0016499453922733665,
-0.016262205317616463,
0.015400005504488945,
-0.050659578293561935,
0.007272806018590927,
0.016977688297629356,
-0.023055579513311386,
0.011611835099756718,
-0.06585802137851715,
0.027691872790455818,
-0.027923274785280228,
-0.03596144914627075,
0.01232033222913742,
-0.03547271341085434,
-0.008520991541445255,
0.023622142150998116,
-0.002468588063493371,
0.03272482752799988,
-0.026988724246621132,
-0.03938470408320427,
-0.012234484776854515,
-0.03575490042567253,
0.034363601356744766,
-0.027616102248430252,
0.07193315774202347,
0.01879175938665867,
0.058873310685157776,
-0.029340479522943497,
0.015936732292175293,
-0.015266385860741138,
0.017687028273940086,
-0.03569868579506874,
0.026032838970422745,
-0.030693067237734795,
-0.013330785557627678,
0.06811665743589401,
0.018780356273055077,
-0.07421892881393433,
0.039354320615530014,
-0.025405054911971092,
-0.010947706177830696,
0.05067398399114609,
-0.011348790489137173,
-0.047908965498209,
-0.01284304354339838,
0.03262581303715706,
-0.06592292338609695,
-0.021414561197161674,
-0.008715547621250153,
-0.004468191880732775,
-0.00011021416139556095,
0.006211495958268642,
-0.07613667100667953,
0.017283359542489052,
-0.04309439659118652,
-0.054311223328113556,
0.03312477469444275,
0.0482383631169796,
-0.000516780826728791,
0.018091652542352676,
0.007993128150701523,
-0.02008739486336708,
-0.016928253695368767,
-0.009250392206013203,
-0.03096800483763218,
0.01088668592274189,
0.009880869649350643,
-0.12374234199523926,
0.014474157243967056,
0.00276841945014894,
0.008938192389905453,
0.009496647864580154,
0.021891247481107712,
0.0059717632830142975,
-0.0979357361793518,
-0.019662003964185715,
0.03790507838129997,
-0.029261555522680283,
0.06114036589860916,
0.04663732647895813,
-0.007302905898541212,
0.06869814544916153,
0.05017001926898956,
0.016227472573518753,
-0.0629650205373764,
-0.012081647291779518,
0.019649788737297058,
-0.02429262176156044,
-0.01103366632014513,
-0.016023745760321617,
-0.05175364390015602,
-0.0029314018320292234,
-0.0508771687746048,
0.050235942006111145,
0.06861194223165512,
-0.03660646453499794,
0.013478291220963001,
0.013311595655977726,
-0.02582463249564171,
-0.01615983061492443,
0.02973111905157566,
-0.05231262370944023,
-0.011882470920681953,
-0.045502398163080215,
-0.05067449063062668,
-0.016902917996048927,
-0.01370263658463955,
-0.006443781778216362,
-0.005484499968588352,
0.009209086187183857,
0.02238190546631813,
0.030791940167546272,
0.010485990904271603,
0.032040055841207504,
0.04114373400807381,
-0.01362480130046606,
-0.05955500528216362,
0.06203095242381096,
-0.01767711713910103,
-0.02904883399605751,
-0.009624450467526913,
0.05842333287000656,
0.0010620896937325597,
0.007868081331253052,
0.015048585832118988,
0.034952521324157715,
-0.01916007697582245,
-0.013585951179265976,
-0.005569325760006905,
0.005037934985011816,
0.03110797330737114,
0.0025589701253920794,
0.05609655752778053,
0.02996215596795082,
-0.01324284914880991,
-0.055337052792310715,
-0.02265949174761772,
-0.011291305534541607,
-0.01240906398743391,
0.025633512064814568,
0.03325003385543823,
0.0101175457239151,
0.016719847917556763,
-0.01562124490737915,
-0.018001973628997803,
-0.026518022641539574,
0.06761245429515839,
0.03260981664061546,
-0.05634849891066551,
0.02773832343518734,
0.003245463827624917,
-0.06653871387243271,
0.06414756178855896,
0.028921429067850113,
0.03515593335032463,
-0.05291687324643135,
-0.12428224086761475,
-0.08614924550056458,
-0.08127307891845703,
0.003541001118719578,
0.0029209901113063097,
-0.0627836063504219,
-0.05403560400009155,
-0.005927504040300846,
-0.003932246472686529,
-0.003818040480837226,
0.009258506819605827,
0.04352802038192749,
0.027898771688342094,
0.012197115458548069,
0.015146753750741482,
-0.007278413977473974,
0.012491513043642044,
-0.011105002835392952,
-0.018341150134801865,
-0.019572829827666283,
-0.028065742924809456,
0.06865858286619186,
-0.020969156175851822,
0.024671899154782295,
0.054936639964580536,
-0.0034962156787514687,
0.015354680828750134,
-0.023673424497246742,
0.036417052149772644,
-0.019859444350004196,
-0.020015999674797058,
0.06355296075344086,
0.03217600658535957,
0.07300429791212082,
-0.005064822267740965,
-0.0044041783548891544,
0.020400360226631165,
-0.00047484561218880117,
-0.022241011261940002,
-0.004922233987599611,
0.04149061068892479,
-0.0014033172046765685,
-0.0034067234955728054,
-0.02369370311498642,
-0.037795089185237885,
0.013990278355777264,
-0.013239901512861252,
-0.020190494135022163,
-0.006762553937733173,
-0.02356352098286152,
0.03638310730457306,
0.014296907931566238,
-0.009263874031603336,
-0.03386393189430237,
-0.08999867737293243,
-0.01526482030749321,
-0.040958259254693985,
0.058716241270303726,
-0.04103456065058708,
0.03917471319437027,
-0.017667163163423538,
-0.017672477290034294,
0.022350415587425232,
0.055104851722717285,
0.0014533654320985079,
0.006491443607956171,
0.01102443877607584,
-0.03800976648926735,
-0.015714196488261223,
0.010010634548962116,
0.02956356294453144,
-0.019220560789108276,
-0.019939452409744263,
0.009604967199265957,
-0.026442021131515503,
-0.020929567515850067,
-0.07405441254377365,
0.035950105637311935,
0.030299408361315727,
-0.08683595061302185,
0.047226451337337494,
0.04502738267183304,
0.009987118653953075,
-0.00594270508736372,
-0.009685393422842026,
0.009807947091758251,
-0.021446261554956436,
0.0042387014254927635,
0.043062347918748856,
-0.006721465382725,
0.01556876115500927,
0.04746289178729057,
0.003042367286980152,
0.02789517305791378,
0.03563173860311508,
-0.03775675222277641,
0.07236941158771515,
-0.013363722711801529,
0.0008311293204315007,
0.04670529067516327,
-0.026112493127584457,
0.051846735179424286,
-0.004284359980374575,
0.08371304720640182,
0.03864981234073639,
-0.004584646318107843,
0.049074672162532806,
-0.012705926783382893,
0.030642693862318993,
0.006498250178992748,
0.002470768289640546,
0.03039451129734516,
-0.0331793949007988,
0.03636321425437927,
-0.06862738728523254,
0.0053443582728505135,
0.037639517337083817,
-0.001326670404523611,
-0.0030401444528251886,
-0.01013636402785778,
-0.006532734259963036,
-0.022506259381771088,
-0.03349160775542259,
0.03092481568455696,
0.0506717823445797,
0.04137676954269409,
-0.03361138701438904,
-0.011391595005989075,
-0.033180780708789825,
0.030064979568123817,
0.03745539113879204,
0.012754455208778381,
-0.020188361406326294,
0.022221500054001808,
-0.05012105777859688,
-0.03883260488510132,
0.009609312750399113,
0.01869083195924759,
-0.015458258800208569,
0.0066510760225355625,
-0.020777320489287376,
-0.005702969152480364,
-0.007669203449040651,
0.0005467692972160876,
-0.026259247213602066,
0.014582445845007896,
-0.009270353242754936,
-0.00006139759352663532,
-0.0609750971198082,
0.049031756818294525,
0.018021732568740845,
0.037531156092882156,
0.020952148362994194,
0.012166102416813374,
-0.004232452251017094,
-0.032234739512205124,
0.013594853691756725,
-0.01990641839802265,
0.031425006687641144,
-0.016875801607966423,
-0.0693952664732933,
-0.05744615197181702,
0.0032975892536342144,
0.0019056082237511873,
0.00846169888973236,
0.02556442655622959,
-0.027650082483887672,
0.015107395127415657,
-0.012617930769920349,
-0.012084820307791233,
-0.029949942603707314,
0.10810508579015732,
0.057200297713279724,
-0.0003002787125296891,
-0.014278212562203407,
-0.007473423145711422,
-0.009470753371715546,
0.035688694566488266,
0.019282305613160133,
0.07709917426109314,
0.05667448416352272,
0.03491136431694031,
-0.01939529925584793,
0.04138827323913574,
-0.05174519866704941,
-0.06616511195898056,
0.008370094932615757,
-0.01507107075303793,
-0.0042709182016551495,
-0.028998907655477524,
-0.004535718820989132,
0.018698591738939285,
-0.0391807034611702,
-0.05962400510907173,
0.0091607216745615,
-0.007007317617535591,
-0.011289040558040142,
0.05381327494978905,
-0.0009336606017313898,
0.017374476417899132,
-0.022733941674232483,
0.006733003072440624,
-0.008725754916667938,
-0.014507380314171314,
0.053350429981946945,
-0.03757975995540619,
-0.021041519939899445,
0.03220987319946289,
0.028662826865911484,
0.02354408986866474,
0.025357576087117195,
-0.049457281827926636,
-0.03883777931332588,
0.007065199315547943,
0.062868632376194,
-0.07102610915899277,
-0.045594412833452225,
-0.05867687985301018,
-0.0351870022714138,
-0.010178168304264545,
0.04617617651820183,
-0.016862910240888596,
-0.0028627226129174232,
-0.024751178920269012,
-0.021677032113075256,
0.08512720465660095,
0.004330173134803772,
0.0842999592423439,
0.08304435759782791,
-0.018596582114696503,
0.09043779224157333,
0.022453397512435913,
-0.004787766840308905,
-0.02707144431769848,
0.0852314829826355,
0.04467180371284485,
0.04252782464027405,
-0.007756598759442568,
0.02965005859732628,
0.03665482625365257,
-0.006379520986229181,
0.008808155544102192,
0.0041940524242818356,
-0.02149837277829647,
0.002125589642673731,
0.009329459629952908,
0.054808665066957474,
-0.039813701063394547,
0.01637997291982174,
-0.007876832969486713,
0.056039828807115555,
0.04255091771483421,
-0.014873743988573551,
0.03692992776632309,
-0.0170330461114645,
-0.0027296950574964285,
-0.018236683681607246,
-0.00391531502828002,
0.029989495873451233,
-0.041561007499694824,
-0.055085424333810806,
-0.010403978638350964,
-0.01949533075094223,
-0.009595372714102268,
-0.033456072211265564,
0.02429630607366562,
0.032418400049209595,
-0.007146194577217102,
0.01221187599003315,
-0.00619145855307579,
0.024835024029016495,
0.011600933037698269,
-0.04478304088115692,
0.014597571454942226,
0.006060030777007341,
0.010913366451859474,
-0.011163506656885147,
0.029434463009238243,
-0.02119763009250164,
0.02426532842218876,
-0.03654477000236511,
-0.08952995389699936,
-0.006946458015590906,
-0.01638990454375744,
-0.057543545961380005,
-0.028765911236405373,
0.03774015232920647,
0.030827270820736885,
0.010252272710204124,
-0.05606985464692116,
-0.0031626953277736902,
0.024149494245648384,
-0.026770461350679398,
0.0514383465051651,
0.11433140933513641,
0.0278010293841362,
0.008007451891899109,
-0.052557848393917084,
-0.00022111069120001048,
0.027052756398916245,
0.014520448632538319,
0.028956150636076927,
-0.07089409977197647,
-0.007222524378448725,
0.04868537560105324,
-0.030000947415828705,
0.002908562310039997,
0.019086135551333427,
0.031464703381061554,
-0.04080658033490181,
0.046956535428762436,
-0.049583908170461655,
0.007667034398764372,
0.06095324456691742,
-0.024195626378059387,
0.01720290631055832,
0.07168174535036087,
-0.01617751456797123,
-0.058475252240896225,
-0.07368189841508865,
-0.02266322821378708,
0.004478872288018465,
-0.01083299983292818,
0.015543516725301743,
0.056669048964977264,
-0.06528398394584656,
-0.0008111528004519641,
-0.003394401865079999,
0.008782602846622467,
0.09584955126047134,
0.03223494440317154,
-0.00550327030941844,
-0.007463876623660326,
-0.014084587804973125,
0.026746755465865135,
-0.037788573652505875,
-0.0029109963215887547,
-0.03479188308119774,
-0.034685153514146805,
-0.010941950604319572,
0.017085416242480278,
-0.027056725695729256,
-0.04340088739991188,
-0.003934443462640047,
0.012251615524291992,
-0.025651751086115837,
0.036119069904088974,
-0.010629761964082718,
-0.007081992458552122,
0.0005441611865535378,
0.025103377178311348,
0.011160173453390598,
0.010841762647032738,
-0.02842833660542965,
0.01693691685795784,
-0.033284980803728104,
-0.023223532363772392,
0.005353670101612806,
0.008803002536296844,
-0.03452729806303978,
0.048407554626464844,
0.004350380040705204,
0.03320525959134102,
0.007457476109266281,
0.010790254920721054,
0.01734279654920101,
-0.006638783495873213,
-0.0034985695965588093,
0.03456366807222366,
-0.0007229304756037891,
0.02912966161966324,
-0.029806746169924736,
0.02510327473282814,
-0.037734635174274445,
-0.030059879645705223,
-0.020059291273355484,
-0.07309984415769577,
0.04403959587216377,
-0.004988052416592836,
-0.031944964081048965,
0.05344025790691376,
-0.022077936679124832,
-0.06272508203983307,
0.04596759378910065,
-0.007092638872563839,
-0.033766742795705795,
-0.011922242119908333,
-0.08702762424945831,
-0.04917394369840622,
0.0062796371057629585,
0.021644024178385735,
-0.017758216708898544,
0.034139715135097504,
-0.022296950221061707,
-0.07716056704521179,
-0.010533240623772144,
-0.0027486076578497887,
-0.003642073832452297,
-0.052989304065704346,
-0.03921973705291748,
-0.05512535199522972,
0.033140629529953,
0.03327391669154167,
-0.04657771810889244,
0.02462431788444519,
0.02724619023501873,
-0.08382906019687653,
0.0009423168958164752,
-0.003210453549399972,
0.05635920539498329,
0.02253144420683384,
-0.055278584361076355,
-0.07581645250320435,
0.04631552845239639,
0.03640293702483177,
-0.037904344499111176,
-0.0333656370639801,
0.020890776067972183,
-0.038970258086919785,
-0.011481338180601597,
0.05807269364595413,
0.03430020809173584,
0.06080416589975357,
0.007274926640093327,
0.03521118685603142,
0.0028943652287125587,
0.042063500732183456,
-0.01370252389460802,
0.04774092137813568,
-0.005313710309565067,
-0.029441308230161667,
-0.010593673214316368,
0.004386240150779486,
-0.06529265642166138
] |
<blockquote>
<p><strong>Possible Duplicates:</strong><br>
<a href="http://physics.stackexchange.com/questions/14973/what-would-be-the-immediate-effects-if-light-does-not-go-at-the-maximum-speed-pos">What would be the immediate effects if light does not go at the maximum speed possible?</a><br>
<a href="http://physics.stackexchange.com/questions/14968/superluminal-neutrinos">Superluminal neutrinos</a></p>
</blockquote>
<p>I was reading this <a href="http://hosted.ap.org/dynamic/stories/E/EU_BREAKING_LIGHT_SPEED?SITE=AP&SECTION=HOME&TEMPLATE=DEFAULT" rel="nofollow">article</a> about a group of scientist thinking that they might have surpassed the speed of light with neutrinos, and are wanting other groups to check their work.</p>
<p>If their research is proven true, what impact would this finding have on the world of physics?</p> | g83 | [
0.012070880271494389,
0.07378534972667694,
0.018557606264948845,
0.030734986066818237,
0.0412164144217968,
-0.03279080241918564,
-0.025446046143770218,
0.01928512565791607,
-0.015904366970062256,
-0.016857681795954704,
0.022585563361644745,
-0.01568085141479969,
-0.004324173554778099,
0.03360443189740181,
-0.018872994929552078,
-0.026231441646814346,
0.0775613784790039,
-0.04398961737751961,
0.049420613795518875,
-0.00046009503421373665,
0.03236904740333557,
0.00390610727481544,
-0.04667693376541138,
-0.05916930362582207,
-0.06569574773311615,
0.012038766406476498,
-0.0000715717687853612,
-0.05164039507508278,
-0.0665377527475357,
-0.038053542375564575,
0.01313040778040886,
-0.05206918716430664,
-0.012973902747035027,
-0.07707971334457397,
-0.003272673347964883,
-0.020107366144657135,
0.0237136073410511,
0.04213991016149521,
-0.004547402262687683,
0.013067378662526608,
-0.029359564185142517,
-0.01776575669646263,
0.023706264793872833,
-0.026608217507600784,
-0.006811404600739479,
-0.010848762467503548,
0.037425775080919266,
0.0065989308059215546,
-0.003974590450525284,
-0.07648780941963196,
0.00610317150130868,
-0.018383270129561424,
0.02869066409766674,
0.06122057884931564,
0.02912207506597042,
-0.00391619885340333,
0.018002161756157875,
-0.031015243381261826,
0.09011336416006088,
0.003171616932377219,
0.011918345466256142,
-0.0314444862306118,
-0.0005663660704158247,
-0.06439772993326187,
0.040861427783966064,
-0.024312186986207962,
0.0004012115823570639,
-0.014218556694686413,
0.027839241549372673,
-0.0303831547498703,
0.020109310746192932,
0.009148817509412766,
-0.03089304082095623,
-0.02867649868130684,
0.010723058134317398,
0.0686681941151619,
0.04839268699288368,
0.020448392257094383,
0.025427797809243202,
0.006075709592550993,
0.011593068949878216,
-0.04402485117316246,
-0.015606029890477657,
0.01680191420018673,
0.033498432487249374,
-0.05592954903841019,
-0.0007143240072764456,
0.04470809921622276,
0.009238003753125668,
0.017950065433979034,
0.04834826663136482,
-0.07342293113470078,
0.014967482537031174,
-0.03178873285651207,
-0.00928020291030407,
0.0034379304852336645,
0.09469502419233322,
0.002584966830909252,
-0.004622375592589378,
-0.003146740607917309,
-0.05221041664481163,
-0.03480932116508484,
-0.0042137205600738525,
0.03778328001499176,
-0.037816084921360016,
0.015388228930532932,
0.04912058264017105,
0.0257637407630682,
-0.06136036291718483,
-0.0056932298466563225,
0.011383346281945705,
-0.07317149639129639,
-0.012782122008502483,
-0.019618645310401917,
-0.03656361624598503,
-0.03180735558271408,
0.018197230994701385,
-0.013500637374818325,
-0.03532988578081131,
0.02377241477370262,
0.029989982023835182,
0.01808687299489975,
-0.015068162232637405,
0.051949866116046906,
-0.027222177013754845,
-0.03930429369211197,
0.037162382155656815,
-0.0034332030918449163,
0.031122799962759018,
-0.03325149044394493,
-0.055752579122781754,
0.00702163390815258,
-0.015097555704414845,
0.07886022329330444,
-0.01291620172560215,
0.023832270875573158,
0.0595623217523098,
0.027123359963297844,
0.018614506348967552,
-0.046096280217170715,
-0.017537040635943413,
0.0011453288607299328,
0.008172508329153061,
0.0418802909553051,
0.0025107760448008776,
-0.024542413651943207,
0.014123297296464443,
0.06651578098535538,
0.004500333685427904,
0.036478396505117416,
0.03281354904174805,
0.009321935474872589,
-0.014920110814273357,
-0.03498460724949837,
-0.00813730712980032,
0.014526238664984703,
-0.020814670249819756,
0.027957912534475327,
0.006644528359174728,
0.029137900099158287,
0.014551345258951187,
-0.0012093274854123592,
-0.059819839894771576,
-0.013764150440692902,
-0.031992148607969284,
0.0447431355714798,
0.09946054220199585,
-0.0028547942638397217,
-0.018285995349287987,
-0.032273877412080765,
-0.12856221199035645,
0.019265852868556976,
-0.0010506199905648828,
0.02304619550704956,
0.03867614269256592,
0.03655388951301575,
0.024956021457910538,
-0.06086588650941849,
-0.028514528647065163,
0.015308037400245667,
-0.061774563044309616,
-0.055268872529268265,
-0.01615036092698574,
-0.022266799584031105,
0.017076535150408745,
-0.001355690648779273,
-0.03076860122382641,
0.03105291724205017,
-0.014385136775672436,
0.02353391796350479,
-0.019364165142178535,
-0.013108977116644382,
-0.004822423681616783,
-0.005994586739689112,
-0.06631360948085785,
0.010468611493706703,
0.014050934463739395,
-0.053642090409994125,
0.005515402648597956,
-0.00218712049536407,
-0.018901390954852104,
0.05490651726722717,
-0.00881419237703085,
-0.04184384644031525,
0.05208790302276611,
-0.009047901257872581,
-0.014142968691885471,
-0.004477390553802252,
0.022969432175159454,
-0.01631557196378708,
0.03047892451286316,
-0.009438416920602322,
0.012149497866630554,
0.03906802088022232,
0.0006528066005557775,
-0.023350223898887634,
-0.041546136140823364,
0.01638338901102543,
0.005050068721175194,
0.05302157998085022,
-0.015637891367077827,
0.02128899283707142,
-0.014059294946491718,
-0.028097666800022125,
-0.01653418131172657,
-0.029084907844662666,
-0.03869308903813362,
-0.08299065381288528,
-0.0024289251305162907,
0.0065256329253315926,
-0.05425108224153519,
0.05348893254995346,
-0.043119750916957855,
-0.04419726878404617,
0.014120862819254398,
0.015639929100871086,
-0.0011088537285104394,
-0.018421370536088943,
0.05329645797610283,
0.02574806474149227,
0.01164085604250431,
0.003628513775765896,
-0.04233936220407486,
0.019143719226121902,
-0.023935116827487946,
-0.04837702587246895,
0.01864495314657688,
-0.059646714478731155,
-0.002239919500425458,
0.06651534140110016,
0.0006976124714128673,
-0.00903561431914568,
-0.003292874898761511,
0.023403087630867958,
0.03447214514017105,
-0.007330300286412239,
-0.009095648303627968,
0.058685462921857834,
-0.06428570300340652,
0.020510073751211166,
0.02604098618030548,
0.0692359134554863,
-0.008314766921103,
-0.028170254081487656,
0.00420658104121685,
0.034489624202251434,
0.00264568324200809,
0.003973003476858139,
-0.035606931895017624,
0.021771231666207314,
-0.05541202053427696,
0.01693863794207573,
0.00759356003254652,
-0.005921925418078899,
-0.002647274173796177,
0.0024056772235780954,
0.03292121738195419,
-0.0029115360230207443,
0.046202562749385834,
-0.016152869910001755,
-0.01773853413760662,
0.000820079876575619,
-0.019632743671536446,
-0.006622674409300089,
-0.0034760504495352507,
-0.10703188180923462,
0.005104318726807833,
-0.028269881382584572,
-0.01435448881238699,
0.041372403502464294,
-0.027767501771450043,
0.022113490849733353,
0.04998613893985748,
0.007114745210856199,
0.00650234567001462,
0.0557369738817215,
0.014589358121156693,
0.027438392862677574,
-0.015569359995424747,
0.009580603800714016,
0.038404129445552826,
-0.037992991507053375,
-0.001187558053061366,
0.06599250435829163,
0.03380195423960686,
-0.042262833565473557,
-0.05549183860421181,
-0.00004776311470777728,
0.03949201479554176,
0.013524646870791912,
0.000008936559424910229,
0.06865838170051575,
0.018207110464572906,
0.04387465491890907,
-0.0027273078449070454,
0.0009207396651618183,
0.036789845675230026,
0.046475980430841446,
0.0204814150929451,
-0.07750502228736877,
0.036658890545368195,
-0.03685503080487251,
-0.03311646729707718,
0.003663795767351985,
0.023843081668019295,
0.011507243849337101,
0.01685275323688984,
0.008752034045755863,
-0.04170134663581848,
0.04403996840119362,
0.02019873633980751,
0.02781308814883232,
0.006851505022495985,
-0.003709091804921627,
-0.04583794251084328,
-0.008660722523927689,
0.0016952004516497254,
0.06365258991718292,
0.057569243013858795,
0.024259105324745178,
-0.012815000489354134,
0.0000937541262828745,
-0.046332113444805145,
0.0202302448451519,
0.04725463688373566,
0.03786996379494667,
-0.05023280903697014,
-0.0035694479010999203,
-0.013864327222108841,
0.04354957491159439,
0.07872428745031357,
0.045045871287584305,
-0.04265123978257179,
-0.016993533819913864,
0.05472664535045624,
0.0008483111741952598,
0.045489270240068436,
0.006160583812743425,
0.03968655318021774,
-0.04462162405252457,
-0.02180463820695877,
0.01725282520055771,
0.03818845376372337,
-0.003397346241399646,
-0.040875956416130066,
0.036152433604002,
0.0016548087587580085,
0.04370300844311714,
0.028657102957367897,
0.0033183260820806026,
-0.002750217216089368,
-0.034757860004901886,
-0.002568584168329835,
-0.012628613039851189,
0.03885185718536377,
0.03502257540822029,
0.017754575237631798,
0.006766926497220993,
-0.04996613785624504,
0.0529421791434288,
0.05472579225897789,
0.04196019843220711,
0.05042753368616104,
-0.05589668080210686,
-0.012965992093086243,
-0.001547337044030428,
-0.06276634335517883,
-0.029628049582242966,
-0.04856984689831734,
-0.06461818516254425,
-0.04990008473396301,
0.019372494891285896,
-0.03897406533360481,
0.0019254990620538592,
-0.058033086359500885,
-0.017595157027244568,
-0.03598818928003311,
-0.019809138029813766,
-0.008905911818146706,
0.024112150073051453,
-0.030944237485527992,
-0.0077904388308525085,
-0.011880702339112759,
0.027806904166936874,
-0.07593873143196106,
-0.06563293188810349,
0.02644451893866062,
0.008831878192722797,
0.023995906114578247,
0.030779726803302765,
-0.0023754609283059835,
0.0069811781868338585,
-0.041687045246362686,
-0.06367699801921844,
0.01555020920932293,
0.05667565390467644,
0.014630376361310482,
-0.07665953785181046,
-0.014662720263004303,
0.026555687189102173,
0.04870351031422615,
-0.026082724332809448,
0.007119291927665472,
0.017412491142749786,
0.03884867578744888,
-0.0022241927217692137,
0.026518138125538826,
-0.03149266541004181,
-0.0007968364516273141,
-0.01661408692598343,
0.040356531739234924,
0.042343560606241226,
-0.008544114418327808,
0.03301161527633667,
0.03156066685914993,
0.07694410532712936,
0.03396493196487427,
0.039109792560338974,
0.006976090371608734,
0.08481492102146149,
0.013721903786063194,
-0.0022300691343843937,
0.06479699909687042,
0.019790248945355415,
0.012469915673136711,
0.09366153180599213,
-0.12402699887752533,
-0.0019095141906291246,
0.014998020604252815,
-0.03738948330283165,
-0.022909555584192276,
-0.005452791694551706,
-0.006540781352669001,
0.006710475776344538,
-0.04648757725954056,
-0.06306689977645874,
-0.026544393971562386,
0.024768806993961334,
0.04657268896698952,
0.05440640076994896,
-0.05405210703611374,
0.03643114119768143,
0.0789702758193016,
0.006048169452697039,
0.07050767540931702,
0.03025021031498909,
-0.015191419050097466,
-0.030359812080860138,
-0.10023356974124908,
-0.051707688719034195,
-0.07875023782253265,
-0.021660665050148964,
0.015427068807184696,
0.016074461862444878,
0.007271099369972944,
-0.02993267960846424,
-0.025438236072659492,
0.061777692288160324,
-0.027859864756464958,
-0.011089980602264404,
-0.04311781004071236,
-0.029552677646279335,
0.01094385702162981,
-0.0677839145064354,
-0.04424702748656273,
0.008259022608399391,
-0.09846805781126022,
0.001663977513089776,
-0.0014911782927811146,
-0.045266494154930115,
-0.013210000470280647,
-0.01213760208338499,
-0.0010860678739845753,
-0.024330615997314453,
-0.023686373606324196,
-0.01018583495169878,
0.06090334430336952,
0.029770735651254654,
-0.03234856575727463,
-0.02857850305736065,
-0.03835572302341461,
0.06391499936580658,
0.04379601776599884,
-0.033458780497312546,
-0.05362623929977417,
0.07309849560260773,
0.037529561668634415,
0.034617625176906586,
-0.025583961978554726,
-0.045678310096263885,
-0.023815641179680824,
0.033460166305303574,
-0.0016381572932004929,
-0.014543076045811176,
0.01742544397711754,
-0.01961522176861763,
-0.029640918597579002,
-0.0051970090717077255,
-0.014000819064676762,
-0.0500316396355629,
0.01035880297422409,
-0.015493418090045452,
0.0650133565068245,
-0.006584238260984421,
0.03667660430073738,
-0.002307441085577011,
-0.04734460636973381,
0.021269556134939194,
0.020886849611997604,
0.016589637845754623,
0.03755570948123932,
-0.028397591784596443,
0.05122000351548195,
0.01902513951063156,
0.008396157994866371,
-0.02165503054857254,
0.008198685012757778,
-0.03848941996693611,
-0.06916612386703491,
0.009426579810678959,
-0.03821822255849838,
-0.013176175765693188,
0.016632338985800743,
0.05587238445878029,
-0.007261820137500763,
-0.013569864444434643,
-0.0358097068965435,
0.03416896611452103,
0.01834874600172043,
-0.027775850147008896,
-0.011604538187384605,
0.0145928505808115,
0.02611129730939865,
0.03550659492611885,
0.022415582090616226,
-0.010238789021968842,
-0.031120453029870987,
-0.019500814378261566,
-0.056380514055490494,
-0.020939810201525688,
0.0307583250105381,
0.026802580803632736,
0.02535777911543846,
-0.026505401358008385,
0.005233205389231443,
-0.0301328357309103,
-0.016398919746279716,
-0.03469744697213173,
0.04216727614402771,
0.01886218786239624,
0.043758735060691833,
0.046701300889253616,
-0.00035579752875491977,
-0.050117623060941696,
-0.021763263270258904,
-0.02472522109746933,
0.04578613117337227,
0.02069568820297718,
-0.056171730160713196,
-0.029688537120819092,
-0.019912075251340866,
-0.02446231245994568,
0.0302575770765543,
-0.014351132325828075,
-0.022881876677274704,
0.01923486217856407,
-0.004565947223454714,
0.12046597898006439,
0.010110508650541306,
-0.06323537975549698,
0.01143859513103962,
-0.021179240196943283,
-0.010946515016257763,
-0.023056119680404663,
-0.0693853572010994,
-0.06296497583389282,
-0.019661258906126022,
-0.029951682314276695,
-0.0736008808016777,
0.05203166976571083,
0.003791143884882331,
-0.03337293490767479,
0.013863706029951572,
0.02874942496418953,
0.03314846754074097,
0.03939644619822502,
-0.008314820006489754,
0.00601463345810771,
-0.011714443564414978,
-0.0024861893616616726,
-0.017437446862459183,
0.006308803800493479,
-0.025812696665525436,
0.02417142316699028,
-0.02973008342087269,
-0.02495523728430271,
0.030702317133545876,
-0.07429881393909454,
0.019888224080204964,
0.007250573020428419,
0.020803820341825485,
-0.041724756360054016,
0.011233322322368622,
-0.044832903891801834,
-0.06622905284166336,
0.06156833469867706,
-0.016187679022550583,
-0.04913919046521187,
0.018838591873645782,
0.03561525419354439,
0.06846927851438522,
-0.011574272066354752,
0.029892444610595703,
0.05484839901328087,
0.009870669804513454,
-0.0006236750050447881,
0.018890555948019028,
0.010658496990799904,
-0.032343268394470215,
-0.001317485119216144,
0.031153617426753044,
-0.013564693741500378,
-0.01436406560242176,
-0.03721114993095398,
0.02877749130129814,
-0.024824561551213264,
0.021399928256869316,
0.031020279973745346,
0.03083731420338154,
-0.06181741878390312,
-0.03338058292865753,
-0.04700719937682152,
0.00849717017263174,
0.026835286989808083,
0.0017025928245857358,
-0.02218448743224144,
-0.012921751476824284,
0.016735928133130074,
-0.03329971060156822,
-0.06038806959986687,
-0.05262867733836174,
-0.01206001453101635,
0.002337065292522311,
0.008809101767838001,
-0.02248033694922924,
0.023083511739969254,
-0.00796270277351141,
-0.07881641387939453,
0.014300335198640823,
-0.01719205267727375,
0.024712521582841873,
-0.03863956779241562,
-0.01318962313234806,
-0.05216320976614952,
0.018447449430823326,
-0.025543056428432465,
-0.03005760721862316,
-0.007017473690211773,
0.008744182996451855,
-0.014524895697832108,
0.0276136826723814,
0.019907420501112938,
0.004211795516312122,
0.005759501829743385,
-0.019428517669439316,
0.07313729077577591,
-0.0705198124051094,
0.025066502392292023,
0.022207429632544518,
-0.01567254215478897,
-0.0020711543038487434,
-0.002027178183197975,
0.011609748005867004,
-0.009532132185995579,
-0.013909608125686646,
0.0124360928311944,
-0.05585436895489693,
0.020778397098183632,
0.06742778420448303,
0.0443316213786602,
-0.062440503388643265,
0.019863972440361977,
-0.01831655390560627,
0.012185126543045044,
0.03493582457304001,
0.034946296364068985,
0.04144308716058731,
0.01808503083884716,
-0.020058035850524902,
-0.01602708362042904,
-0.004006387200206518,
0.10095275193452835,
-0.01027487963438034,
0.010176843032240868,
0.03432988375425339,
0.011366141960024834,
0.0030329611618071795,
-0.03326619789004326,
0.05813820660114288,
0.06593278050422668,
0.009339980781078339,
0.02875179797410965,
-0.04783380776643753,
-0.009193350560963154,
-0.020110588520765305,
0.004090039525181055,
0.005100142676383257,
0.051338959485292435,
-0.020654236897826195,
-0.009489425458014011,
0.02761884778738022,
-0.0060485354624688625,
-0.034222617745399475,
-0.01968306675553322,
-0.09025838971138,
0.05699406564235687,
0.034224070608615875,
0.08967068046331406,
-0.03750615566968918,
0.023810088634490967,
-0.0487716943025589,
-0.04844742268323898,
-0.03330891951918602,
0.002013105433434248,
-0.021329175680875778,
-0.016422631219029427,
-0.023685146123170853,
0.03213223069906235,
0.0045905387960374355,
-0.049062907695770264,
0.037988562136888504,
0.045221202075481415,
-0.008376809768378735,
0.09468517452478409,
0.05787140130996704,
-0.04920738562941551,
0.002704123966395855,
-0.01766281947493553,
-0.01285499706864357,
0.01685902290046215,
-0.0071908263489604,
-0.021767161786556244,
0.023772871121764183,
-0.006024536676704884,
0.0413840152323246,
-0.01902405545115471,
-0.019258517771959305,
0.02825949713587761
] |
<p>How does it make sense to vary the position and the velocity independently?</p>
<p><strong>Edit:</strong></p>
<p>Velocity is the derivative of position, so how can you treat them as independent variables? Doesn't every physics student ask this question when he learns calculus of variations? Does anybody ever answer this question? Ever? If so, please educate me.</p> | g505 | [
0.024659311398863792,
0.004115596879273653,
-0.012113736942410469,
0.04999552294611931,
0.022449437528848648,
0.011389690451323986,
0.031968820840120316,
0.00642617791891098,
-0.020905034616589546,
-0.04915634170174599,
-0.04326329380273819,
-0.005329238250851631,
-0.013892733491957188,
0.021534450352191925,
-0.008815816603600979,
-0.022910624742507935,
0.06485592573881149,
-0.005185047164559364,
0.07035805284976959,
0.022681739181280136,
-0.03898131474852562,
0.001067272387444973,
0.019197674468159676,
-0.012659906409680843,
0.04116028547286987,
-0.08018950372934341,
0.00038057478377595544,
-0.09293236583471298,
-0.05031372234225273,
0.02544601447880268,
0.015460296534001827,
0.01783086732029915,
0.055958524346351624,
-0.0112497853115201,
-0.02584102936089039,
-0.00950772687792778,
0.02933436818420887,
-0.013316137716174126,
0.01025196723639965,
0.02694282867014408,
-0.013174555264413357,
-0.018561270087957382,
0.01453479751944542,
-0.018331995233893394,
-0.04315910115838051,
-0.012441636994481087,
-0.013595488853752613,
-0.04940785840153694,
-0.045699216425418854,
0.010098644532263279,
-0.020153051242232323,
0.02027459442615509,
0.038059450685977936,
-0.0011035839561372995,
0.04078967869281769,
0.039846744388341904,
0.003470098599791527,
0.03179704397916794,
-0.022933369502425194,
0.019716914743185043,
0.032186683267354965,
-0.014307175762951374,
-0.0005442736437544227,
-0.019867753610014915,
0.04779163748025894,
-0.006880195811390877,
-0.07543051987886429,
-0.002761660609394312,
-0.01702452078461647,
-0.006468770559877157,
-0.00926450826227665,
-0.02619343437254429,
-0.02492567151784897,
-0.02015942521393299,
-0.03866060823202133,
-0.031856026500463486,
0.011582862585783005,
-0.028976203873753548,
0.030755650252103806,
-0.025873206555843353,
-0.00868245866149664,
0.008827360346913338,
0.023398857563734055,
-0.045159418135881424,
0.025190649554133415,
-0.01137902494519949,
0.0491553470492363,
0.06361450254917145,
0.01186305284500122,
0.040409885346889496,
0.00438985088840127,
0.0021011950448155403,
0.051128678023815155,
0.06261619925498962,
-0.03459467366337776,
-0.09422195702791214,
-0.060668811202049255,
0.09075960516929626,
0.04891778901219368,
0.024370601400732994,
-0.026866180822253227,
0.06928543001413345,
-0.03545990586280823,
0.0364026241004467,
-0.04663371294736862,
-0.01365858968347311,
0.06878478080034256,
0.024593466892838478,
0.03834832087159157,
-0.04579693451523781,
-0.000516112195327878,
-0.05066397786140442,
-0.0049802944995462894,
0.008294072933495045,
-0.01780661754310131,
-0.013048539869487286,
0.022189682349562645,
0.020837459713220596,
0.0005094498628750443,
0.03221357241272926,
-0.019580921158194542,
0.04379868507385254,
0.010217535309493542,
0.04984414577484131,
-0.019127845764160156,
0.007127671502530575,
0.0309824887663126,
-0.030095983296632767,
0.0000058829573390539736,
-0.03414909541606903,
0.06770768016576767,
-0.032760173082351685,
0.018574023619294167,
0.014377693645656109,
-0.012358237989246845,
0.040584202855825424,
-0.0050064753741025925,
0.03733518719673157,
-0.006556789390742779,
0.042719874531030655,
0.04892507195472717,
0.025953669100999832,
-0.022271182388067245,
-0.011678826995193958,
-0.002611001953482628,
-0.00988474115729332,
0.007311903405934572,
-0.053914763033390045,
0.0243007130920887,
-0.0245966874063015,
0.02777358703315258,
0.08338606357574463,
-0.051864247769117355,
-0.018343016505241394,
0.0037340319249778986,
-0.02077152021229267,
0.07161955535411835,
0.04573918133974075,
0.030781684443354607,
-0.012382633984088898,
0.10293575376272202,
-0.0494520477950573,
0.016396524384617805,
-0.002623893553391099,
-0.05792475491762161,
0.038604576140642166,
0.000010494866728549823,
0.0068697272799909115,
0.0010784054175019264,
-0.015835190191864967,
-0.06106884032487869,
-0.040717992931604385,
-0.004477526992559433,
0.020819690078496933,
0.01790819875895977,
-0.0017744451761245728,
-0.042333099991083145,
-0.0953739807009697,
0.013176380656659603,
0.03674033656716347,
-0.05044671893119812,
0.0019439497264102101,
0.00915501732379198,
-0.06693306565284729,
0.009661535732448101,
0.025910884141921997,
-0.027455102652311325,
-0.07332327961921692,
-0.07059353590011597,
-0.012688067741692066,
-0.034076496958732605,
-0.05194777622818947,
0.004345113877207041,
0.04151970148086548,
-0.004331854172050953,
-0.006314048543572426,
-0.02546675130724907,
0.0007019416079856455,
-0.0854741632938385,
0.09874730557203293,
-0.03565093129873276,
0.04854169860482216,
0.08788207173347473,
0.01583167538046837,
-0.030905552208423615,
0.017318131402134895,
-0.005169819574803114,
0.0025011261459439993,
0.011762761510908604,
0.008863134309649467,
0.0925188660621643,
0.046107612550258636,
-0.004270298406481743,
0.00514998659491539,
0.006309221964329481,
-0.043172311037778854,
0.019369954243302345,
-0.028423698619008064,
-0.006050002761185169,
0.013075217604637146,
-0.03989400714635849,
-0.028592465445399284,
0.00036221128539182246,
0.025049589574337006,
-0.06063801795244217,
0.0255324337631464,
-0.05532962083816528,
-0.003922357689589262,
0.018843837082386017,
0.02857862412929535,
-0.04072096198797226,
0.015044358558952808,
-0.009583435021340847,
0.011345546692609787,
0.06856159120798111,
0.021316731348633766,
0.00020368924015201628,
0.07469017058610916,
0.012263447977602482,
0.04714313521981239,
0.03361813724040985,
-0.09871961921453476,
0.06798522919416428,
-0.033789198845624924,
-0.020548786967992783,
-0.02134166657924652,
0.061894286423921585,
0.008154829032719135,
-0.04909319803118706,
-0.031166084110736847,
0.0007946061086840928,
-0.083265520632267,
-0.0568109005689621,
-0.01741781458258629,
0.0009233317687176168,
0.02873031422495842,
-0.022184137254953384,
0.02632952108979225,
-0.06365782767534256,
-0.04523681104183197,
-0.0031769373454153538,
0.016187625005841255,
0.03785502910614014,
0.07117308676242828,
-0.005349014885723591,
0.01004001684486866,
0.049740441143512726,
0.00727463886141777,
0.015405474230647087,
-0.02655804716050625,
0.025463180616497993,
0.04282210394740105,
-0.015283162705600262,
0.08202492445707321,
-0.03143784776329994,
0.010130726732313633,
0.0010055305901914835,
-0.02535940892994404,
-0.01607835851609707,
0.044578105211257935,
0.01334166619926691,
0.0124300392344594,
-0.03125167265534401,
-0.022160794585943222,
0.07501285523176193,
-0.01729867421090603,
0.05141061916947365,
0.01659739762544632,
-0.037804074585437775,
0.014642010442912579,
0.024965105578303337,
0.033885031938552856,
-0.0032190533820539713,
-0.046038538217544556,
-0.0006303595728240907,
0.04194237291812897,
-0.023119399324059486,
-0.04578913748264313,
-0.030735181644558907,
0.014949352480471134,
0.03147488459944725,
0.026847537606954575,
0.016678640618920326,
0.07986477017402649,
0.05630296841263771,
0.034830931574106216,
-0.030895547941327095,
-0.016312113031744957,
-0.013871907256543636,
-0.03054097294807434,
0.023708365857601166,
0.026253968477249146,
-0.0020193178206682205,
-0.0212550088763237,
-0.06886669248342514,
-0.028152484446763992,
-0.055866748094558716,
-0.036509282886981964,
0.03897405415773392,
-0.002715981798246503,
-0.048549897968769073,
-0.06212722137570381,
0.026847971603274345,
-0.0018536323914304376,
0.04425610601902008,
0.012547444552183151,
0.013307870365679264,
0.0071594566106796265,
-0.04054877161979675,
-0.04744468629360199,
-0.021625928580760956,
0.061167944222688675,
0.0035704157780855894,
-0.03698377683758736,
-0.03951890394091606,
-0.06562098115682602,
0.03298542648553848,
-0.017893048003315926,
0.03890377655625343,
-0.014174973592162132,
0.009430915117263794,
-0.05365706607699394,
-0.045838817954063416,
0.027549851685762405,
-0.036666348576545715,
0.010557042434811592,
0.09077952802181244,
-0.02356705442070961,
0.02281281352043152,
0.018968841060996056,
0.0478038489818573,
-0.016006501391530037,
0.012911234982311726,
-0.015230715274810791,
0.015365428291261196,
-0.022872701287269592,
0.030494162812829018,
0.03256616368889809,
-0.060193102806806564,
0.033581092953681946,
0.006308358162641525,
-0.04287588223814964,
-0.05501808971166611,
0.06150181218981743,
-0.03597884625196457,
0.019294973462820053,
0.020973026752471924,
0.0010775162372738123,
-0.045018669217824936,
0.017829813063144684,
0.02114383690059185,
0.02475106716156006,
-0.022443782538175583,
-0.023364873602986336,
-0.0006617921171709895,
-0.03433958813548088,
0.038212668150663376,
0.0023796421010047197,
-0.019767291843891144,
-0.05980614200234413,
0.03783854469656944,
-0.008698535151779652,
0.006584509275853634,
0.03891520947217941,
0.0021270897705107927,
0.024728264659643173,
-0.04886326938867569,
0.005677003413438797,
-0.011789582669734955,
-0.03966200351715088,
0.01843472383916378,
0.006607940886169672,
-0.003648083657026291,
-0.023570502176880836,
0.010072395205497742,
-0.008054367266595364,
0.07209917157888412,
-0.00461636483669281,
-0.01687535271048546,
0.015429318882524967,
-0.058088935911655426,
-0.009775511920452118,
-0.027676185593008995,
-0.007803574204444885,
-0.03421357274055481,
0.018936917185783386,
0.02377859130501747,
-0.06621023267507553,
0.006628114264458418,
0.008960644714534283,
-0.04793984815478325,
-0.042426612228155136,
0.004129407927393913,
-0.03895314782857895,
-0.01570977084338665,
0.021404709666967392,
0.03377918154001236,
0.013887554407119751,
-0.006621412467211485,
-0.002982873935252428,
0.09103867411613464,
0.013909906148910522,
0.06311993300914764,
0.013119353912770748,
0.035554807633161545,
0.03233958035707474,
0.06564824283123016,
0.011401659809052944,
0.03854123502969742,
-0.025474192574620247,
-0.024293845519423485,
0.02726241946220398,
0.06621728837490082,
-0.008313044905662537,
-0.042137354612350464,
0.006333048455417156,
0.037129759788513184,
0.03671780228614807,
-0.00487143499776721,
0.05569477006793022,
0.01677645742893219,
0.01578948274254799,
-0.00021445534366648644,
-0.05708027258515358,
-0.022636162117123604,
0.023545201867818832,
-0.029565950855612755,
-0.030531365424394608,
0.03835970163345337,
-0.053593795746564865,
-0.04638174548745155,
0.06865575909614563,
-0.028509119525551796,
0.029041530564427376,
-0.002956625074148178,
0.003178250975906849,
0.005834720563143492,
-0.02519826404750347,
0.04546213150024414,
-0.03247401490807533,
-0.016295602545142174,
0.02532164752483368,
-0.015184430405497551,
0.028729252517223358,
-0.027326855808496475,
0.02342587150633335,
-0.0319737084209919,
0.018963802605867386,
-0.0318039245903492,
0.016215404495596886,
0.016145961359143257,
0.04073737934231758,
0.012224972248077393,
0.029114924371242523,
0.04478859528899193,
-0.014098308980464935,
0.039763983339071274,
-0.009940115734934807,
0.0005261930637061596,
-0.02570842020213604,
-0.027742702513933182,
-0.009134520776569843,
0.05260525271296501,
-0.024390600621700287,
-0.021256817504763603,
-0.09435422718524933,
-0.08660107851028442,
-0.0728520080447197,
-0.039453525096178055,
-0.05140497907996178,
0.005531899631023407,
0.05103901028633118,
0.039467524737119675,
0.039885856211185455,
-0.039987582713365555,
-0.05756216496229172,
0.005365519784390926,
-0.007216234225779772,
0.012582002207636833,
-0.050125978887081146,
-0.0699043795466423,
0.0023618906270712614,
0.013797853142023087,
0.002615789184346795,
-0.03709346801042557,
0.03996336832642555,
0.05701237916946411,
0.008214354515075684,
-0.05148126557469368,
0.0017420037183910608,
0.04101737588644028,
0.0462237112224102,
-0.014125121757388115,
-0.002288754330947995,
-0.020182061940431595,
-0.024998726323246956,
0.021730506792664528,
-0.0218551866710186,
-0.018823523074388504,
-0.03236206993460655,
0.05789753794670105,
0.02236824668943882,
0.049251705408096313,
-0.006714001297950745,
0.04210514947772026,
-0.026563948020339012,
-0.14768458902835846,
-0.023396091535687447,
-0.022469716146588326,
0.009145455434918404,
-0.020322291180491447,
0.024351969361305237,
0.005615916568785906,
0.03509949892759323,
-0.03424342721700668,
-0.007212670054286718,
-0.003307028440758586,
-0.05131138116121292,
-0.02702958695590496,
0.01839623413980007,
-0.06893153488636017,
-0.011708315461874008,
-0.001894765766337514,
0.036654576659202576,
-0.040708716958761215,
-0.0004376873839646578,
0.027958393096923828,
-0.006054806523025036,
0.0664263665676117,
-0.03948580101132393,
-0.08657737076282501,
0.03215629234910011,
-0.007380032446235418,
-0.05151020362973213,
-0.042008791118860245,
0.017698101699352264,
-0.018001755699515343,
-0.04732269048690796,
-0.0026873217429965734,
-0.012982633896172047,
0.030528776347637177,
-0.032838985323905945,
0.0031376273836940527,
0.008261261507868767,
0.010380743071436882,
-0.04488510638475418,
0.05656064301729202,
0.03470100089907646,
0.046983204782009125,
0.06773530691862106,
-0.07445989549160004,
0.036931730806827545,
-0.021699408069252968,
-0.04770422726869583,
0.010446762666106224,
0.006858091801404953,
-0.0138601865619421,
0.02797473594546318,
-0.034030597656965256,
-0.03205736353993416,
-0.0027455142699182034,
-0.010770831257104874,
-0.002403770573437214,
-0.05780787020921707,
-0.07598668336868286,
0.011883844621479511,
-0.03795505315065384,
0.0283636674284935,
0.025656115263700485,
0.01978042535483837,
-0.012619628570973873,
-0.024923022836446762,
-0.04984573647379875,
0.014683534391224384,
-0.03988136723637581,
-0.00683657918125391,
0.02151801995933056,
-0.00037347342004068196,
-0.02376083843410015,
-0.025762001052498817,
0.025918155908584595,
-0.010841903276741505,
0.04200208932161331,
0.009641248732805252,
-0.019070865586400032,
-0.016007687896490097,
0.008824434131383896,
0.012765525840222836,
-0.014063511043787003,
0.00016667466843500733,
-0.03382468223571777,
0.044094257056713104,
0.053086306899785995,
0.01938122697174549,
-0.03895176574587822,
0.007048712577670813,
-0.04207732155919075,
0.014008283615112305,
-0.0026878935750573874,
-0.06441681832075119,
0.03565796837210655,
-0.005450613796710968,
0.045245107263326645,
-0.0012803818099200726,
0.028125206008553505,
0.02229117602109909,
-0.04749935865402222,
0.013700326904654503,
0.004227554425597191,
-0.019895516335964203,
0.09272933751344681,
0.06316372007131577,
0.03494653105735779,
0.003616065252572298,
-0.049680858850479126,
0.0893009677529335,
-0.07458589971065521,
0.04937656968832016,
0.01300717331469059,
0.015235303901135921,
-0.001485072891227901,
0.06409569829702377,
0.005488169379532337,
0.013869247399270535,
-0.021400315687060356,
0.019603034481406212,
0.035530880093574524,
-0.03224308788776398,
-0.05178704112768173,
0.004711139015853405,
-0.020505916327238083,
-0.003333284752443433,
-0.06524281948804855,
0.011347312480211258,
0.04287907853722572,
0.04207015410065651,
0.017552491277456284,
-0.005443355068564415,
-0.010179225355386734,
-0.021443618461489677,
-0.04919124394655228,
-0.0411008857190609,
-0.013681778684258461,
0.02189583331346512,
-0.0011465511051937938,
0.060054052621126175,
-0.009514178149402142,
-0.03318031504750252,
-0.03662059083580971,
0.047588616609573364,
-0.018950320780277252,
-0.020399218425154686,
-0.027423197403550148,
0.029352424666285515,
0.04236845299601555,
-0.0323493555188179,
-0.05281816050410271,
0.004926878027617931,
-0.0049146320670843124,
0.03561222925782204,
0.017223941162228584,
0.06516963988542557,
-0.005888659972697496,
-0.016865551471710205,
-0.04407862573862076,
0.027827588841319084,
0.0020024196710437536,
0.01312344241887331,
0.02020995318889618,
-0.06638824194669724,
-0.010133340954780579,
-0.03415565565228462,
-0.000671122339554131,
0.01324378326535225,
-0.045513879507780075,
0.01976991817355156,
0.03001430444419384,
0.03493453562259674,
0.0049698371440172195,
0.026108361780643463,
0.02264045923948288,
-0.0447273775935173,
-0.006766402628272772,
0.05402744561433792,
0.0684274360537529,
-0.030462130904197693,
-0.014773030765354633,
-0.005509101320058107,
-0.036428727209568024,
-0.02936662547290325,
0.00669870525598526,
0.009544126689434052,
0.0641726478934288,
-0.014795507304370403,
-0.018884550780057907,
0.01620321534574032,
-0.0016672357451170683,
0.005340337287634611,
-0.024389808997511864,
0.04195946082472801,
0.0033944256138056517,
-0.027633853256702423,
0.03647753968834877,
-0.051948707550764084,
-0.0006275528576225042,
-0.05192466452717781,
0.020948832854628563,
-0.0650101751089096,
-0.012479734607040882,
-0.0030098797287791967,
0.006241266615688801,
-0.007788014132529497,
-0.0023187855258584023,
0.05490493401885033,
-0.009939111769199371,
0.009336988441646099,
0.014146885834634304,
0.005490184295922518,
-0.019788602367043495,
0.0010242045391350985,
0.0070765516720712185,
-0.021057041361927986,
-0.024244647473096848,
0.021300533786416054,
-0.04172096773982048,
-0.010937351733446121,
0.04911905899643898,
0.06181549280881882,
0.032343991100788116,
-0.03623920679092407,
0.02316911146044731,
0.07572685182094574,
-0.02513057366013527,
0.013823376968502998,
0.025221239775419235,
-0.01609020307660103,
-0.053916942328214645,
0.041342027485370636,
0.0014354492304846644,
0.03656463697552681,
-0.010336634702980518,
0.01248070877045393,
-0.028513843193650246,
-0.0326903760433197,
0.03251854330301285,
-0.02241501957178116,
-0.018796829506754875,
0.03929286077618599
] |
<p>Inspired by <a href="http://physics.stackexchange.com/questions/234/how-should-a-physics-student-study-mathematics">How should a physics student study mathematics?</a> and in the same vein as <a href="http://physics.stackexchange.com/questions/193/best-books-for-mathematical-background">Best books for mathematical background?</a>, although in a more general fashion, I'd like to know if anyone is interested in doing a list of the books 'par excellence' for a physicist.</p>
<p>In spite of the frivolous nature of this post, I think it can be a valuable resource.</p>
<p>For example:</p>
<hr>
<p><a href="http://rads.stackoverflow.com/amzn/click/0750628960">Course of Theoretical Physics</a> - <strong>L.D. Landau, E.M. Lifshitz.</strong></p>
<p><a href="http://rads.stackoverflow.com/amzn/click/0805370021">Mathematical Methods of Physics</a> - <strong>Mathews, Walker</strong>. Very nice chapter on complex variables and evaluation of integrals, presenting must-know tricks to solve non-trivial problems. Also contains an introduction to groups and group representations with physical applications.</p>
<p><a href="http://rads.stackoverflow.com/amzn/click/048667164X">Mathematics of Classical and Quantum Physics</a> - <strong>Byron and Fuller.</strong></p>
<p><a href="http://rads.stackoverflow.com/amzn/click/0471010901">Topics in Algebra</a> - <strong>I. N. Herstein</strong>. Extremely well written, introduce basic concepts in groups, rings, vector spaces, fields and linear transformations. Concepts are motivated and a nice set of problems accompany each chapter (some of them quite challenging).</p>
<p><a href="http://rads.stackoverflow.com/amzn/click/0126546568">Partial Differential Equations in Physics</a> - <strong>Arnold Sommerfeld</strong>. Although a bit dated, very clear explanations. First chapter on Fourier Series is enlightening. The ratio interesting information/page is extremely large. Contains discussions on types of differential equations, integral equations, boundary value problems, special functions and eigenfunctions.</p>
<hr> | g4615 | [
0.012592311948537827,
0.027816811576485634,
0.002151122549548745,
-0.026445463299751282,
0.029721273109316826,
0.014543475583195686,
0.0332585945725441,
0.03937111794948578,
-0.013705856166779995,
-0.006215591449290514,
0.012802579440176487,
0.01893724501132965,
0.0027372250333428383,
-0.024848809465765953,
-0.02325940690934658,
-0.02596662938594818,
0.0440245158970356,
0.03907192125916481,
0.021390939131379128,
-0.017494607716798782,
0.0018895440734922886,
0.05490865558385849,
0.046237651258707047,
-0.059323813766241074,
-0.012940231710672379,
-0.0018218725454062223,
0.009480131790041924,
-0.08520324528217316,
-0.04330316185951233,
-0.016278544440865517,
-0.04971333593130112,
0.003094122977927327,
0.02751605026423931,
0.0023440003860741854,
-0.0014354903250932693,
-0.037157442420721054,
0.026491299271583557,
0.017194319516420364,
0.0679827556014061,
-0.002433300716802478,
0.042530715465545654,
-0.04710725322365761,
-0.002539990236982703,
-0.021883921697735786,
0.02196653187274933,
-0.016810880973935127,
-0.017150666564702988,
-0.042435336858034134,
-0.021323762834072113,
0.07694069296121597,
-0.0013458490138873458,
0.05357638746500015,
0.043350428342819214,
-0.0016197951044887304,
0.0550806038081646,
0.015889590606093407,
-0.0026341648772358894,
0.01829652115702629,
0.087961845099926,
-0.023893995210528374,
0.024670280516147614,
0.010311080142855644,
-0.036979544907808304,
-0.033850476145744324,
-0.02193916216492653,
-0.007179937791079283,
0.014829481020569801,
-0.01012998167425394,
-0.010637413710355759,
0.017954714596271515,
0.03005027398467064,
-0.026813898235559464,
0.04651001840829849,
0.008210287429392338,
0.02901221625506878,
0.004786576144397259,
0.05606217309832573,
-0.023669708520174026,
0.019721349701285362,
0.007205524947494268,
-0.04412957280874252,
-0.03903649002313614,
0.017953604459762573,
-0.04535401985049248,
-0.008596113882958889,
-0.0442582331597805,
-0.006333026569336653,
0.01392536610364914,
-0.003997266758233309,
-0.0017727183876559138,
0.0010324903996661305,
0.03793318197131157,
0.03687571361660957,
0.034118976444005966,
-0.03046398237347603,
-0.0005823562387377024,
-0.007671800442039967,
0.0007080974755808711,
-0.015779690816998482,
0.01093070488423109,
-0.022381391376256943,
0.05724802240729332,
0.03590518236160278,
0.02365206740796566,
-0.0057541984133422375,
0.016349758952856064,
0.03659256175160408,
0.052153706550598145,
0.010175120085477829,
0.03389762341976166,
-0.06669304519891739,
-0.01165811438113451,
-0.004021911881864071,
-0.02767367660999298,
-0.02445775642991066,
0.04773646593093872,
0.050635699182748795,
-0.027011333033442497,
-0.0182782094925642,
0.11079874634742737,
0.014982462860643864,
0.04162469506263733,
0.07637128978967667,
0.002916522789746523,
-0.004615867510437965,
-0.03755337744951248,
0.017808930948376656,
-0.06494501978158951,
0.024912048131227493,
-0.026275869458913803,
0.04101761057972908,
-0.05012110620737076,
-0.047374773770570755,
0.015998637303709984,
-0.02298750728368759,
0.049504354596138,
0.006922753527760506,
0.045075852423906326,
0.0010772169334813952,
-0.030065327882766724,
0.004351841751486063,
-0.00813361443579197,
-0.016558200120925903,
-0.031077487394213676,
-0.010591886937618256,
0.02035660482943058,
-0.04769987612962723,
-0.06297367066144943,
-0.011883004568517208,
0.019061684608459473,
0.018273960798978806,
0.050235990434885025,
0.008728663437068462,
-0.0202524121850729,
0.013854623772203922,
-0.0018535410054028034,
0.03917602077126503,
0.017027733847498894,
0.02222559042274952,
-0.02248637191951275,
0.03277682512998581,
0.00942674558609724,
-0.10454786568880081,
0.07928528636693954,
0.0018850123742595315,
0.04806555435061455,
-0.005726265255361795,
-0.08231515437364578,
0.03863470256328583,
0.017202109098434448,
-0.016654403880238533,
-0.006234738044440746,
0.03920850530266762,
0.016382994130253792,
-0.03575843200087547,
0.00044976413482800126,
-0.0006485290359705687,
-0.024961018934845924,
0.03227898105978966,
0.035598959773778915,
-0.015667639672756195,
-0.08007366210222244,
0.06249073147773743,
-0.03271651640534401,
-0.05083385854959488,
0.05192093923687935,
-0.0050185988657176495,
0.06713611632585526,
-0.11800786852836609,
0.0357193797826767,
-0.0658959299325943,
0.02408289723098278,
-0.01374453492462635,
-0.0023311583790928125,
0.018388153985142708,
-0.02143089845776558,
-0.034904416650533676,
-0.016185389831662178,
-0.049584031105041504,
0.03684943541884422,
-0.00864145066589117,
0.029163269326090813,
0.08365577459335327,
0.030657565221190453,
0.0044355206191539764,
0.09286409616470337,
-0.020634297281503677,
-0.06529229134321213,
0.03865305706858635,
-0.045542679727077484,
0.03109460137784481,
0.0012584896758198738,
0.06522075831890106,
0.06253828853368759,
-0.007975502870976925,
-0.02859998121857643,
-0.04406043887138367,
-0.0337897427380085,
-0.02232964336872101,
0.08770963549613953,
-0.006802248302847147,
-0.021361980587244034,
-0.031139614060521126,
-0.013611190021038055,
-0.03600228205323219,
0.013607988134026527,
-0.07783897966146469,
-0.033720068633556366,
-0.032717201858758926,
-0.008667746558785439,
-0.06268417835235596,
0.03750991448760033,
-0.03285324200987816,
-0.02656449005007744,
0.06541081517934799,
-0.012865487486124039,
0.008366699330508709,
-0.04984457045793533,
0.03694413974881172,
0.036506056785583496,
-0.03480292111635208,
-0.0075582535937428474,
0.03684608265757561,
-0.048432569950819016,
-0.01990581303834915,
-0.07829683274030685,
0.024898415431380272,
-0.016872141510248184,
-0.039665624499320984,
-0.030306104570627213,
0.041091062128543854,
-0.07113522291183472,
-0.009091158397495747,
0.014563489705324173,
-0.00508051598444581,
0.0092874551191926,
-0.029870878905057907,
0.03942735120654106,
0.056056950241327286,
-0.003627716563642025,
0.027203507721424103,
-0.03557579219341278,
-0.05232207104563713,
0.05008138716220856,
-0.07201698422431946,
-0.0054358248598873615,
-0.08286050707101822,
0.015406344085931778,
-0.01515193935483694,
-0.027302665635943413,
0.038017019629478455,
0.07516174763441086,
0.004360048100352287,
0.0023042140528559685,
-0.03768983483314514,
-0.0024230913259088993,
0.026553338393568993,
0.021384647116065025,
0.008997256867587566,
-0.011592600494623184,
0.061652667820453644,
-0.0617775097489357,
-0.0362909771502018,
-0.009418699890375137,
0.05660298839211464,
-0.03600216284394264,
0.03081502765417099,
0.003002260811626911,
-0.021222546696662903,
-0.02453913725912571,
-0.01076546125113964,
0.04972899332642555,
0.006858368404209614,
-0.022005625069141388,
-0.02690800279378891,
-0.004410451743751764,
0.011406498029828072,
-0.04553376883268356,
-0.05523037537932396,
0.0226972047239542,
-0.04121633246541023,
-0.004821510054171085,
0.023028196766972542,
0.004480371251702309,
-0.01591188833117485,
-0.00508623942732811,
-0.04797505959868431,
-0.024196522310376167,
-0.002645698841661215,
0.044817302376031876,
-0.005037323106080294,
0.0013050622073933482,
0.009299080818891525,
0.0016182197723537683,
-0.023824281990528107,
-0.0035637454129755497,
0.02287958562374115,
-0.018603134900331497,
0.029394855722784996,
-0.06689203530550003,
-0.04298808053135872,
-0.009042192250490189,
0.0912829041481018,
-0.08662252128124237,
0.08359354734420776,
0.016610579565167427,
0.02113901451230049,
-0.047227147966623306,
-0.020151907578110695,
-0.03337669000029564,
0.028130052611231804,
-0.028595788404345512,
-0.0016752483788877726,
-0.034227125346660614,
-0.07635948061943054,
-0.04068071395158768,
0.028669919818639755,
-0.015143832191824913,
0.01296885497868061,
-0.015482663176953793,
-0.01948097161948681,
-0.04119396209716797,
-0.019045136868953705,
0.02636575512588024,
-0.023074693977832794,
-0.049083609133958817,
0.002414482180029154,
0.0364842489361763,
0.04335206374526024,
-0.047538068145513535,
0.003318510251119733,
0.05408770591020584,
0.07388168573379517,
0.001604215009137988,
-0.023475106805562973,
0.025785228237509727,
0.04432414844632149,
0.019272183999419212,
0.024591650813817978,
0.0010546266566962004,
-0.044730234891176224,
-0.012658181600272655,
-0.02044791541993618,
-0.016832927241921425,
-0.06113826483488083,
0.023595241829752922,
-0.012037583626806736,
0.020413001999258995,
-0.03226575255393982,
-0.018160458654165268,
0.051968082785606384,
-0.003447340102866292,
0.009256970137357712,
-0.015233931131660938,
-0.009527851827442646,
-0.05291341245174408,
0.011612567119300365,
0.006977557670325041,
-0.03518016263842583,
-0.03930485248565674,
-0.0001276486727874726,
0.016626132652163506,
0.07538244128227234,
0.02428065799176693,
0.006734115537256002,
0.024176830425858498,
0.01920175552368164,
0.01469421200454235,
0.04091921076178551,
0.014025022275745869,
0.056723929941654205,
-0.0012834827648475766,
-0.010481247678399086,
0.050992581993341446,
-0.012629253789782524,
-0.023359006270766258,
-0.004304883535951376,
0.012881702743470669,
-0.0312928631901741,
0.05685760825872421,
-0.040318433195352554,
-0.060076747089624405,
-0.02856370061635971,
0.03750528395175934,
-0.026586029678583145,
-0.008281455375254154,
0.008017978630959988,
-0.06657424569129944,
-0.0018289064755663276,
-0.026918329298496246,
-0.02116956003010273,
-0.011957339942455292,
0.02420751191675663,
-0.024256203323602676,
0.016716716811060905,
0.0063661192543804646,
-0.025667227804660797,
-0.0711064487695694,
0.01467911433428526,
-0.031246474012732506,
0.014255154877901077,
0.029361825436353683,
-0.02523197792470455,
-0.04340309277176857,
0.041822727769613266,
0.05896374583244324,
0.08478064090013504,
-0.001713037840090692,
0.013689515180885792,
0.005246021319180727,
-0.020662739872932434,
0.0012291744351387024,
-0.016384616494178772,
0.004261736758053303,
-0.05938958376646042,
-0.022827662527561188,
-0.056425634771585464,
0.027110576629638672,
0.01850656233727932,
0.052760712802410126,
0.06230573356151581,
0.02437090314924717,
-0.04495817795395851,
-0.038750339299440384,
-0.02386450208723545,
0.04868931695818901,
-0.04274695739150047,
0.005085103679448366,
0.02525193989276886,
-0.02483373135328293,
-0.010174375958740711,
0.02747523784637451,
-0.005213058087974787,
0.037505827844142914,
-0.059161193668842316,
-0.011552728712558746,
-0.0162903293967247,
-0.02821117453277111,
0.035823553800582886,
0.0007740959990769625,
-0.03452927619218826,
0.007126939482986927,
-0.004797554109245539,
-0.0049366457387804985,
-0.024011626839637756,
-0.007957551628351212,
-0.02703082747757435,
-0.006328603718429804,
-0.028893359005451202,
-0.045722752809524536,
-0.00863721128553152,
0.010945143178105354,
0.03421634063124657,
-0.09639659523963928,
0.049832217395305634,
-0.04194340854883194,
-0.018751827999949455,
-0.01552700623869896,
-0.055958185344934464,
-0.02634233608841896,
0.027873963117599487,
0.03212127834558487,
0.005652266554534435,
-0.012502554804086685,
0.010277444496750832,
0.010501429438591003,
-0.039505816996097565,
-0.022162966430187225,
-0.05785834416747093,
-0.06886027008295059,
-0.0373179130256176,
0.004676513839513063,
0.06797292083501816,
-0.003534998744726181,
-0.046792250126600266,
-0.06131144240498543,
0.04123317077755928,
0.026430508121848106,
0.0029124808497726917,
-0.023551728576421738,
-0.022014115005731583,
0.0249189380556345,
-0.05472896248102188,
-0.02547760121524334,
0.007092224434018135,
0.004840242210775614,
0.05692264810204506,
-0.0071873972192406654,
-0.023511581122875214,
-0.007528738118708134,
0.01137155294418335,
0.005937196314334869,
0.04004722088575363,
-0.03365255147218704,
0.0013367453357204795,
0.08694352954626083,
0.02299945056438446,
0.02310079336166382,
-0.036377839744091034,
-0.024389388039708138,
-0.0028090868145227432,
-0.030429651960730553,
0.02852609194815159,
-0.015033925883471966,
0.0677429735660553,
-0.014138438738882542,
-0.11232281476259232,
-0.023767884820699692,
-0.02827649749815464,
0.0781094878911972,
-0.004311316646635532,
-0.015257053077220917,
-0.023329226300120354,
-0.010756281204521656,
-0.01212979480624199,
-0.011642402037978172,
-0.026872118934988976,
-0.00643160380423069,
-0.025436315685510635,
0.01213054358959198,
-0.050482187420129776,
0.005358160939067602,
0.006962044630199671,
0.037329282611608505,
-0.014694076031446457,
-0.00928422063589096,
0.0492144376039505,
0.07095914334058762,
0.09629566967487335,
-0.06028024107217789,
-0.05456579104065895,
-0.026313073933124542,
-0.017002318054437637,
-0.0687028020620346,
0.07106050848960876,
0.010582092218101025,
-0.03525923565030098,
-0.022981753572821617,
0.02960725873708725,
0.037302304059267044,
0.019401319324970245,
-0.034619685262441635,
-0.02341642789542675,
0.031478915363550186,
0.006362473592162132,
-0.00015480376896448433,
-0.0009258964564651251,
-0.05192689597606659,
0.024075394496321678,
0.004185955040156841,
0.0030322859529405832,
0.0010828101076185703,
0.006687862798571587,
-0.011420471593737602,
0.040686897933483124,
0.008032355457544327,
-0.000544336624443531,
-0.050867583602666855,
0.02060648612678051,
-0.05530091002583504,
0.017589101567864418,
0.025351805612444878,
0.07006713002920151,
-0.06694524735212326,
-0.01974594220519066,
0.02667243406176567,
0.007823753170669079,
0.010920468717813492,
-0.003288805717602372,
0.01309377420693636,
-0.030340367928147316,
0.0010336004197597504,
0.0009845213498920202,
-0.0019373525865375996,
0.026354655623435974,
-0.006451265420764685,
0.08803801238536835,
0.021940656006336212,
0.0010230053449049592,
0.01154944859445095,
0.0166440699249506,
-0.022611631080508232,
0.008323337882757187,
0.08510343730449677,
0.038952238857746124,
0.01949995569884777,
0.0027154753915965557,
-0.032625775784254074,
-0.03270381689071655,
0.02818448096513748,
-0.0038716846611350775,
0.03491532802581787,
-0.040818262845277786,
0.03633740544319153,
-0.029806382954120636,
-0.05611761659383774,
0.03155161067843437,
0.03697049990296364,
0.033893708139657974,
-0.09268949180841446,
0.05657944455742836,
0.028620213270187378,
0.04236208274960518,
-0.0019677469972521067,
-0.011547540314495564,
0.05598222091794014,
0.0030109179206192493,
0.07408909499645233,
0.0657132938504219,
-0.020701278001070023,
0.06264837086200714,
0.013981057330965996,
0.03691724315285683,
0.02812959998846054,
-0.004236495587974787,
0.07674972712993622,
-0.011754574254155159,
0.03247440978884697,
-0.006259005516767502,
0.04797537252306938,
-0.017343362793326378,
0.031013179570436478,
0.05664128065109253,
-0.01967211812734604,
-0.024869950488209724,
-0.06630650162696838,
-0.012059311382472515,
-0.08051978051662445,
-0.07763249427080154,
-0.006725297775119543,
0.07567296177148819,
0.008285382762551308,
-0.05146626755595207,
0.020411064848303795,
-0.009121120907366276,
-0.0007191390031948686,
0.047898050397634506,
-0.003751743584871292,
0.0543568879365921,
-0.024835100397467613,
-0.057161666452884674,
0.02350742183625698,
0.04061487689614296,
0.011917764320969582,
-0.021547166630625725,
0.06298220902681351,
0.02060089446604252,
-0.005340700037777424,
0.03627399727702141,
0.03555572032928467,
0.022962583228945732,
0.009296787902712822,
-0.00876067578792572,
0.012357259169220924,
0.021054707467556,
-0.004738734569400549,
0.030639169737696648,
-0.022793134674429893,
-0.008870272897183895,
-0.03768924996256828,
-0.0014267725637182593,
0.03627021983265877,
-0.005071474704891443,
-0.01007635798305273,
-0.01668262667953968,
0.010154432617127895,
-0.045952215790748596,
0.009576268494129181,
0.04109017550945282,
-0.012208322063088417,
-0.0340244434773922,
-0.027500491589307785,
0.02147851139307022,
-0.01731168106198311,
0.004419772420078516,
0.018992358818650246,
0.053507249802351,
-0.01278594695031643,
0.04748755320906639,
0.00374148809351027,
-0.012488874606788158,
0.011958724819123745,
-0.041078075766563416,
-0.05148729309439659,
0.013740208931267262,
0.019335083663463593,
-0.007523463573306799,
0.004149780608713627,
0.006338205654174089,
0.010639495216310024,
-0.019479237496852875,
0.034499142318964005,
0.005271757487207651,
-0.014746195636689663,
0.04581298679113388,
0.010656660422682762,
-0.010869013145565987,
0.00012883596355095506,
-0.02074887417256832,
0.007262450642883778,
0.035791411995887756,
-0.0006830974016338587,
-0.027517225593328476,
-0.027304718270897865,
-0.017994100227952003,
-0.04560017213225365,
-0.008099652826786041,
-0.021727124229073524,
-0.0009146552765741944,
-0.018618298694491386,
-0.0013636485673487186,
-0.01975114829838276,
-0.037235110998153687,
0.021237919107079506,
-0.024061687290668488,
-0.020627791061997414,
0.04811139777302742,
-0.0002727361279539764,
0.03634656220674515,
-0.00557282567024231,
0.06387125700712204,
-0.05584557726979256,
-0.03164653480052948,
0.01481042429804802,
-0.023771727457642555,
-0.00822956021875143,
-0.05204791575670242,
-0.011626500636339188,
-0.0012052853126078844,
-0.03369522839784622,
-0.06074073910713196,
0.0386304035782814,
0.0186319537460804,
0.11255709081888199,
0.009949921630322933,
-0.026382911950349808,
0.05085550248622894,
0.043480440974235535,
0.04699654132127762,
0.002377032535150647,
-0.0021621077321469784,
0.01208622194826603,
0.013006075285375118,
0.023232830688357353,
-0.07536033540964127,
-0.045912548899650574,
-0.015152443200349808,
-0.01028144359588623
] |
<p>If a rectangular pan has a constant and uniform temperature $T$ first, then put it in a vacuum. Considering the effect of thermal radiation, the temperature distribution of the rectangular blackbody will change. My question is, will the temperature of the corner be higher than the edge?</p> | g4616 | [
0.07356446236371994,
-0.010556928813457489,
0.013333816081285477,
-0.013632851652801037,
0.010766800493001938,
-0.008569221012294292,
-0.05571748688817024,
0.06013466790318489,
-0.037708353251218796,
0.0023889471776783466,
-0.026405317708849907,
0.07721584290266037,
-0.0020464095287024975,
-0.01330648548901081,
0.020985588431358337,
-0.0036248487886041403,
-0.009993718937039375,
-0.030909081920981407,
0.017295051366090775,
0.018924806267023087,
-0.03187550604343414,
-0.020592348650097847,
0.02670826017856598,
-0.08186966180801392,
0.005245247855782509,
-0.017747700214385986,
0.006073263939470053,
0.036219507455825806,
-0.03251160681247711,
-0.06067163497209549,
-0.006770828273147345,
0.03394738584756851,
-0.014515765011310577,
-0.02191380225121975,
-0.03233234956860542,
0.029918093234300613,
0.0316627137362957,
0.03915299102663994,
0.003690856508910656,
-0.014492613263428211,
-0.010230882093310356,
0.008675355464220047,
0.04514238238334656,
0.0149823147803545,
0.019416622817516327,
0.039756618440151215,
-0.0017550484044477344,
0.02349812351167202,
0.001768573303706944,
0.04319535940885544,
-0.01359532866626978,
-0.036787088960409164,
0.031330861151218414,
-0.0723404660820961,
0.005185894668102264,
-0.014683928340673447,
-0.03037918172776699,
-0.022925902158021927,
0.01128479652106762,
0.0205538310110569,
-0.03373200446367264,
0.02566804550588131,
-0.025385567918419838,
-0.020063161849975586,
0.03314032778143883,
0.029142772778868675,
-0.048234570771455765,
0.03469494730234146,
-0.026487136259675026,
-0.0030856288503855467,
0.002392504131421447,
0.0017492948099970818,
-0.013567745685577393,
-0.03623442351818085,
-0.02890853025019169,
0.03227486461400986,
-0.022302353754639626,
-0.0126073332503438,
-0.07655583322048187,
0.027423249557614326,
-0.0528460256755352,
0.05264495313167572,
0.0191388800740242,
0.07652885466814041,
0.06363660842180252,
-0.03880614414811134,
0.02408759482204914,
0.035450682044029236,
-0.032016657292842865,
0.024983860552310944,
0.07685180008411407,
0.02860439196228981,
0.08859500288963318,
0.0092525789514184,
0.03530919924378395,
-0.0039340537041425705,
0.011065930128097534,
0.0444781519472599,
-0.01821514032781124,
0.015592099167406559,
-0.013278745114803314,
0.014686732552945614,
0.035810891538858414,
-0.03388819471001625,
-0.027330098673701286,
-0.0004899390623904765,
-0.005635041743516922,
-0.003988577052950859,
-0.00913751870393753,
0.011991561390459538,
-0.021489342674613,
-0.06697368621826172,
-0.08745478093624115,
-0.07038188725709915,
-0.04851863533258438,
0.011996296234428883,
0.07031384855508804,
-0.044650524854660034,
0.04639694094657898,
0.053061593323946,
0.02694515883922577,
0.001685260096564889,
0.011764416471123695,
0.05489107221364975,
0.05443083867430687,
-0.02693946100771427,
-0.03482227399945259,
-0.007366381119936705,
0.014971138909459114,
-0.0023034922778606415,
-0.016981320455670357,
0.04270618408918381,
-0.038186896592378616,
0.04518589749932289,
0.03358512371778488,
0.08637414872646332,
0.014581341296434402,
0.005263167899101973,
0.016452614217996597,
-0.01628997176885605,
-0.008892404846847057,
0.016998950392007828,
-0.02075120061635971,
-0.003156015183776617,
-0.03143603727221489,
-0.0015110115054994822,
-0.009452889673411846,
-0.0009145900839939713,
-0.011125002056360245,
-0.0019521090434864163,
0.0034845906775444746,
0.08371260017156601,
-0.013314949348568916,
-0.0020616110414266586,
-0.03753188997507095,
-0.01359446533024311,
0.019919972866773605,
0.011047796346247196,
0.06771914660930634,
-0.06354919821023941,
0.029334625229239464,
0.029736507683992386,
0.034659672528505325,
0.014531866647303104,
-0.018482500687241554,
-0.07162830233573914,
-0.027216631919145584,
-0.03205946832895279,
-0.019620196893811226,
-0.04347939416766167,
0.031044267117977142,
0.017783794552087784,
-0.039305634796619415,
0.03335193917155266,
-0.054999642074108124,
-0.00801063422113657,
0.03617572411894798,
0.012804956175386906,
0.07432767748832703,
-0.04745278134942055,
-0.016286015510559082,
0.03133688494563103,
0.04139920696616173,
-0.03791196271777153,
0.024995511397719383,
-0.01196758821606636,
0.06343653798103333,
0.0160690750926733,
-0.008213345892727375,
-0.007579719182103872,
-0.04158816114068031,
-0.05470341444015503,
-0.044492412358522415,
0.019404212012887,
0.05203939601778984,
0.004696504678577185,
0.010414892807602882,
-0.02668718807399273,
-0.017348336055874825,
-0.02390194498002529,
-0.05598853528499603,
0.01571871154010296,
0.03683316335082054,
0.005183168686926365,
-0.023904234170913696,
0.02609432116150856,
0.013129603117704391,
-0.01706080511212349,
-0.018071722239255905,
-0.01340391580015421,
-0.022253768518567085,
0.021287748590111732,
0.043526291847229004,
0.06101660430431366,
0.025462772697210312,
0.09225966036319733,
-0.051925335079431534,
0.023792194202542305,
0.02330305613577366,
-0.011015526950359344,
-0.053825344890356064,
-0.003936471417546272,
-0.0383344367146492,
-0.016543082892894745,
-0.020625915378332138,
-0.0340258851647377,
-0.08276842534542084,
-0.07271748781204224,
0.015504959970712662,
0.017060989513993263,
-0.0711408406496048,
-0.03253081813454628,
0.0166836678981781,
0.004981105215847492,
0.0028710339684039354,
-0.021484004333615303,
-0.03644045814871788,
0.02526133321225643,
0.03937069699168205,
-0.012391711585223675,
0.01762699894607067,
-0.00704063568264246,
-0.0670054703950882,
-0.008051282726228237,
0.023932024836540222,
0.0017185471951961517,
0.02700267732143402,
-0.032279957085847855,
0.017881600186228752,
0.0198076032102108,
-0.031204447150230408,
-0.012887963093817234,
-0.027027389034628868,
0.027817953377962112,
-0.021305015310645103,
-0.024737820029258728,
-0.03770681470632553,
-0.006833419669419527,
-0.03809967264533043,
-0.04924275726079941,
0.0016938915941864252,
-0.07381389290094376,
0.0097969276830554,
-0.0018407925963401794,
-0.07851973176002502,
0.029332928359508514,
-0.06477311253547668,
-0.0006232817540876567,
0.011244794353842735,
0.05846606567502022,
-0.03513052687048912,
0.048300229012966156,
0.03978428617119789,
0.07507538050413132,
0.014161042869091034,
-0.04141674563288689,
0.02895820513367653,
-0.0341816246509552,
0.029480108991265297,
-0.040070995688438416,
-0.014526007696986198,
0.009263879619538784,
-0.10871471464633942,
0.021972494199872017,
0.022792408242821693,
-0.012709178030490875,
-0.0321313701570034,
-0.019745349884033203,
-0.07996056228876114,
-0.03370292857289314,
0.0011108695762231946,
0.050552841275930405,
0.00294491252861917,
0.058849725872278214,
0.01208354439586401,
0.004665570333600044,
0.022120598703622818,
0.009606913663446903,
-0.021877409890294075,
0.03249570354819298,
-0.030166439712047577,
-0.055779166519641876,
-0.042640890926122665,
-0.05962328612804413,
0.04573769122362137,
0.007398754823952913,
-0.033385951071977615,
-0.06714940071105957,
0.08580311387777328,
0.010636147111654282,
0.032234322279691696,
-0.009746376425027847,
-0.040288493037223816,
0.056304384022951126,
-0.017183713614940643,
0.02426844649016857,
-0.015008196234703064,
0.0337376743555069,
0.028736373409628868,
0.00743530597537756,
-0.015985623002052307,
0.02415977604687214,
-0.05687427893280983,
-0.018552809953689575,
0.0400206483900547,
0.06850526481866837,
0.0489053837954998,
-0.020306454971432686,
0.007333078421652317,
0.06686044484376907,
-0.0025601638481020927,
0.033789005130529404,
0.002223392017185688,
0.0003264974511694163,
0.04863399267196655,
0.03301591798663139,
-0.02467220649123192,
-0.042009152472019196,
0.02770133689045906,
0.0139019675552845,
-0.044501788914203644,
-0.0822131410241127,
0.0029768492095172405,
0.0038249148055911064,
0.09454645216464996,
-0.0023514837957918644,
-0.002660478698089719,
0.002972765825688839,
-0.016776148229837418,
0.01767842285335064,
0.028121108189225197,
-0.004836485255509615,
0.008238877169787884,
0.04035545513033867,
-0.025028903037309647,
0.028057444840669632,
-0.013839402236044407,
0.006367258727550507,
0.005412018857896328,
0.03235407546162605,
-0.008751902729272842,
-0.08123430609703064,
0.04338737949728966,
-0.06681200116872787,
0.010631966404616833,
0.006101060658693314,
0.07424210757017136,
0.026154031977057457,
0.02070254273712635,
0.02173287607729435,
-0.06565980613231659,
-0.05563722550868988,
-0.05055293068289757,
0.020551171153783798,
0.05175353214144707,
0.03940005972981453,
-0.01775791123509407,
0.006147880107164383,
-0.03309960290789604,
0.04087153077125549,
-0.00783040001988411,
0.03075103834271431,
-0.0018637811299413443,
-0.007300035562366247,
-0.008530358783900738,
0.07156691700220108,
-0.0025300062261521816,
-0.054838068783283234,
0.0455503836274147,
-0.07614502310752869,
0.02108912728726864,
-0.043333545327186584,
0.02996761165559292,
-0.012626538053154945,
0.012494061142206192,
-0.02849458158016205,
-0.010830197483301163,
-0.030543826520442963,
-0.015356275252997875,
-0.025222819298505783,
0.08606819808483124,
0.01930132880806923,
0.04467129334807396,
-0.01788157969713211,
-0.017161203548312187,
0.023987973108887672,
0.04481577128171921,
-0.007640048861503601,
-0.058133311569690704,
-0.007465267088264227,
-0.017081964761018753,
-0.018826261162757874,
0.000005748780949943466,
-0.028180750086903572,
0.06530425697565079,
-0.007670908235013485,
0.02638084627687931,
0.04988044127821922,
-0.05631512030959129,
-0.010577678680419922,
-0.030362596735358238,
-0.02089063823223114,
0.026808328926563263,
0.01624630205333233,
0.006438000127673149,
-0.007840348407626152,
0.018875930458307266,
-0.011136439628899097,
0.006592248100787401,
-0.01842707023024559,
-0.01710277982056141,
0.002474541775882244,
-0.05984910577535629,
0.026823749765753746,
-0.037455908954143524,
0.046595681458711624,
-0.05542932078242302,
0.002326004672795534,
-0.044668689370155334,
0.03363809734582901,
0.013451986946165562,
-0.005580088589340448,
-0.021095668897032738,
-0.022946935147047043,
-0.03576722368597984,
0.04266168922185898,
-0.018795989453792572,
-0.03632080927491188,
0.009160359390079975,
-0.02297838404774666,
-0.010213878005743027,
-0.025272918865084648,
-0.038223542273044586,
-0.02257385291159153,
0.014620627276599407,
-0.09363285452127457,
-0.006372322794049978,
0.0030666314996778965,
0.03605261817574501,
-0.004138158634305,
-0.057599280029535294,
0.011649206280708313,
0.010488544590771198,
0.02436532825231552,
0.03401658684015274,
-0.008194131776690483,
-0.030977880582213402,
0.06348495930433273,
0.006150231231004,
0.06098172068595886,
-0.006970718037337065,
0.08791780471801758,
-0.018420016393065453,
0.05053781718015671,
-0.013368522748351097,
0.04861493036150932,
-0.024594010785222054,
-0.005564315710216761,
0.007673295680433512,
-0.034983906894922256,
-0.03812374174594879,
-0.02691684290766716,
0.030095767229795456,
-0.01949097029864788,
-0.005930009763687849,
-0.034184589982032776,
-0.06006842106580734,
0.013921190984547138,
0.06522174924612045,
-0.0050147902220487595,
0.012288516387343407,
-0.01789742149412632,
0.019679872319102287,
0.04550705477595329,
-0.013900673016905785,
-0.01594904623925686,
0.05366523936390877,
-0.042806778103113174,
0.05494938790798187,
0.02902698889374733,
-0.03092993050813675,
-0.0007138298242352903,
0.03536200895905495,
-0.0020344939548522234,
0.037119533866643906,
0.032496996223926544,
0.0014801023062318563,
-0.01919274590909481,
0.01928558200597763,
0.030249927192926407,
0.01580279879271984,
0.07093586772680283,
0.04051084443926811,
-0.04582155868411064,
0.009603627026081085,
-0.035430070012807846,
0.0182532649487257,
-0.03610021248459816,
-0.03085046447813511,
0.00182525091804564,
0.079576775431633,
0.017944157123565674,
0.020082084462046623,
-0.024003444239497185,
-0.008382592350244522,
0.07456722855567932,
-0.009608146734535694,
0.025468308478593826,
-0.029140306636691093,
-0.0006484899786300957,
0.0544934906065464,
0.058642372488975525,
0.01157181616872549,
0.009595860727131367,
-0.06653852015733719,
0.013364944607019424,
0.02693570964038372,
0.040621764957904816,
0.07915051281452179,
0.01775486022233963,
-0.010225096717476845,
-0.007772525306791067,
0.023164978250861168,
0.006789879407733679,
-0.009931309148669243,
0.020271871238946915,
-0.07296330481767654,
0.05830666422843933,
-0.001098725711926818,
-0.022055400535464287,
-0.0016273661749437451,
0.03076423518359661,
-0.012736527249217033,
-0.020487627014517784,
-0.011453360319137573,
0.02200513891875744,
0.06034833937883377,
0.013525770045816898,
0.010393977165222168,
-0.02514086291193962,
0.028463130816817284,
-0.05774647742509842,
0.0734567642211914,
-0.008035409264266491,
-0.013983541168272495,
-0.0644693374633789,
-0.0009034168324433267,
-0.03625914454460144,
0.07602507621049881,
0.002100493060424924,
0.011387601494789124,
-0.029975509271025658,
0.017703726887702942,
-0.0125270402058959,
0.0043057529255747795,
-0.03163083270192146,
-0.03679610416293144,
0.010049731470644474,
-0.030987270176410675,
0.034163184463977814,
-0.05269068107008934,
0.018528619781136513,
-0.0014340411871671677,
-0.004695471376180649,
-0.013651447370648384,
0.09007599949836731,
-0.053210411220788956,
0.02219664305448532,
0.028026675805449486,
-0.030884819105267525,
-0.004080282058566809,
-0.04021337255835533,
0.03986898437142372,
0.03978380560874939,
-0.008785907179117203,
0.033738553524017334,
-0.06672021001577377,
-0.014882074669003487,
-0.06408655643463135,
0.048066459596157074,
0.03195922449231148,
-0.021901888772845268,
-0.04331593215465546,
-0.0011446907883509994,
0.008134884759783745,
-0.03834833577275276,
0.019985968247056007,
0.016102775931358337,
0.0197698175907135,
0.01915457472205162,
0.09383419156074524,
0.0014493425842374563,
-0.00747401500120759,
-0.01649654097855091,
-0.0007568530854769051,
-0.02251446060836315,
0.04342380166053772,
-0.00195330916903913,
-0.010476892814040184,
0.005425043869763613,
0.004658838734030724,
-0.011285225860774517,
-0.07630015164613724,
-0.006433014292269945,
0.07403416186571121,
0.03504733368754387,
-0.04850140959024429,
0.0037392943631857634,
0.05453820526599884,
-0.0051308670081198215,
0.019381752237677574,
-0.03510615974664688,
-0.07406323403120041,
0.0266699381172657,
-0.004974793642759323,
0.02782316319644451,
-0.06896574795246124,
0.0162349883466959,
-0.0014053441118448973,
0.051395196467638016,
-0.01647014543414116,
-0.016784867271780968,
0.041731689125299454,
0.008220640011131763,
-0.004822972696274519,
0.05871271342039108,
-0.026891082525253296,
0.05755054950714111,
-0.041999783366918564,
0.026987452059984207,
0.013558441773056984,
-0.013533519580960274,
-0.06469707936048508,
0.0020651728846132755,
-0.008295704610645771,
-0.025152720510959625,
-0.005660868249833584,
-0.01892148330807686,
-0.026027319952845573,
0.001150463824160397,
-0.02535979077219963,
-0.09571988135576248,
-0.05475606769323349,
-0.010345508344471455,
0.05766894668340683,
0.02326807752251625,
0.025591183453798294,
0.0063093481585383415,
-0.021923048421740532,
-0.07918395847082138,
-0.00904148630797863,
-0.07429254055023193,
-0.03274322301149368,
-0.002862862078472972,
0.0111885080114007,
0.008140308782458305,
-0.047614242881536484,
0.04391090199351311,
0.0024600434117019176,
0.021249888464808464,
0.03918839246034622,
-0.011669250205159187,
0.006681523285806179,
-0.012687308713793755,
-0.013556858524680138,
0.055590782314538956,
0.0024899663403630257,
-0.0013429473619908094,
0.09443794190883636,
-0.051756832748651505,
-0.04242749139666557,
0.0346548818051815,
-0.04108012095093727,
-0.003956568893045187,
-0.01972840167582035,
0.0003419800486881286,
-0.03646406531333923,
-0.004015729296952486,
-0.009657756425440311,
-0.012480792589485645,
0.002926996909081936,
0.013963788747787476,
-0.05501595139503479,
0.00003340281546115875,
-0.020891746506094933,
0.047004349529743195,
-0.007824688218533993,
-0.05634984374046326,
-0.021586930379271507,
-0.01836109533905983,
0.07289945334196091,
0.039765626192092896,
0.06530021876096725,
0.028216982260346413,
-0.03671951964497566,
-0.04984646663069725,
-0.050360582768917084,
-0.01498443353921175,
0.0056661455892026424,
0.022630276158452034,
-0.028828812763094902,
0.0036679832264781,
-0.034096114337444305,
-0.012440597638487816,
0.016016477718949318,
-0.016566887497901917,
-0.03435118868947029,
-0.012482346035540104,
0.01695551536977291,
0.0032566601876169443,
0.06208997964859009,
0.018905356526374817,
-0.02717333287000656,
-0.013812972232699394,
0.020559625700116158,
-0.00039972871309146285,
0.03483733907341957,
0.008285299874842167,
0.04632982984185219,
0.025252938270568848,
-0.028101947158575058,
-0.03489027917385101,
0.05803490802645683,
-0.04417017847299576,
-0.024660350754857063,
0.028017759323120117,
-0.052472904324531555,
-0.001609672443009913,
0.0187892597168684,
0.05864448472857475,
-0.03142191842198372,
-0.020020537078380585,
-0.06260338425636292,
0.009053955785930157,
0.01584813743829727,
-0.03503422066569328,
0.0031682769767940044,
-0.011219995096325874,
-0.0122342174872756,
0.04823513329029083,
-0.09158967435359955,
0.0022318826522678137,
0.013396330177783966,
-0.05120609700679779,
-0.005859028082340956,
0.01973804086446762,
0.029322274029254913,
-0.025185761973261833
] |
<p>As the air molecules are environment for carrying sound waves, could stream of photons be environment for carrying electromagnetic waves? What contradictions cause this assumption in the existing theories?</p> | g4617 | [
-0.005512877833098173,
0.022904817014932632,
0.0032240517903119326,
0.04584350436925888,
0.016931740567088127,
0.09631582349538803,
-0.014137559570372105,
-0.029625482857227325,
-0.015601576305925846,
-0.0036631557159125805,
0.01933601126074791,
-0.006582011468708515,
-0.024091234430670738,
0.055320266634225845,
-0.06192600727081299,
0.02416004240512848,
0.032016266137361526,
-0.010034932754933834,
-0.0031551255378872156,
0.002549059921875596,
-0.09075406193733215,
-0.020530205219984055,
-0.013656922616064548,
-0.07942330837249756,
-0.0728917270898819,
-0.009987954050302505,
0.065364770591259,
-0.07506775856018066,
-0.02825286239385605,
-0.05643065273761749,
0.02679293230175972,
-0.041574761271476746,
0.043244171887636185,
0.02032656967639923,
-0.04824697598814964,
-0.057940997183322906,
-0.010116380639374256,
0.06419916450977325,
0.003766677575185895,
0.01897726207971573,
0.06372876465320587,
-0.007742573507130146,
-0.05885758250951767,
0.0021890304051339626,
0.01937820389866829,
-0.020355191081762314,
0.013713624328374863,
0.04834338277578354,
-0.013015522621572018,
-0.04908156394958496,
-0.0189760010689497,
-0.019717486575245857,
0.015860745683312416,
0.08777587115764618,
0.03461683169007301,
0.05482317879796028,
-0.02053312584757805,
-0.03670449182391167,
0.031096016988158226,
0.009980089962482452,
-0.008392023853957653,
0.039091113954782486,
-0.011308522894978523,
0.005706914234906435,
0.042027465999126434,
-0.058811627328395844,
-0.03406890854239464,
-0.03303435817360878,
0.002471382264047861,
0.00048245323705486953,
0.06842238456010818,
-0.04557318240404129,
-0.042576078325510025,
0.0452803373336792,
0.034110862761735916,
0.023704232648015022,
-0.03430289402604103,
0.023226412013173103,
0.04189131036400795,
0.025994613766670227,
0.011205441318452358,
0.03988795727491379,
0.025042476132512093,
-0.023250460624694824,
0.01993374526500702,
-0.05121908709406853,
-0.0322963185608387,
-0.015934087336063385,
0.02000051736831665,
-0.005254225805401802,
-0.01310892216861248,
-0.056819893419742584,
0.06760628521442413,
0.00019600878295022994,
0.00483221560716629,
0.02390979789197445,
-0.04843248054385185,
0.050047386437654495,
0.01771671511232853,
0.018943943083286285,
-0.004708028864115477,
-0.039444029331207275,
0.009569678455591202,
0.04734073951840401,
0.01651008427143097,
0.050486523658037186,
-0.04133598506450653,
-0.013674107380211353,
-0.030647991225123405,
-0.0028980225324630737,
-0.01944214478135109,
0.018700944259762764,
-0.043466966599226,
-0.025978077203035355,
-0.02349269576370716,
-0.039902713149785995,
-0.0058672791346907616,
-0.014647532254457474,
0.042386844754219055,
0.10226405411958694,
0.011346397921442986,
0.023609669879078865,
-0.03359002247452736,
0.008251232095062733,
0.015801239758729935,
0.006619177758693695,
-0.021691102534532547,
-0.018310602754354477,
0.027382858097553253,
-0.04401753842830658,
0.011976228095591068,
0.011025014333426952,
-0.051056355237960815,
0.013658028095960617,
0.025688448920845985,
-0.06494542956352234,
0.046153608709573746,
-0.04025173559784889,
-0.01519448310136795,
-0.01579698547720909,
0.09454400837421417,
0.01068544015288353,
0.032344523817300797,
-0.05892108380794525,
-0.036329854279756546,
-0.015613192692399025,
0.014393292367458344,
-0.012677716091275215,
0.015064554288983345,
-0.00314215081743896,
0.019289612770080566,
0.06742055714130402,
0.0005111518548801541,
-0.002671897644177079,
-0.008304949849843979,
-0.02813347429037094,
0.007991381920874119,
0.028737546876072884,
-0.014815651811659336,
0.048631343990564346,
0.04581834748387337,
0.0295467097312212,
0.03575693070888519,
-0.005888808518648148,
-0.05921970307826996,
-0.007143011782318354,
-0.017435267567634583,
-0.01727885566651821,
-0.04423316568136215,
0.003849038388580084,
-0.051119640469551086,
0.011142517440021038,
0.0069036176428198814,
0.06915849447250366,
0.00010493728041183203,
0.06658056378364563,
0.048718880861997604,
0.009446273557841778,
-0.02495124377310276,
-0.004837178159505129,
0.01434892974793911,
0.024197082966566086,
-0.03446067497134209,
-0.058810945600271225,
-0.01337397564202547,
-0.0025762836448848248,
-0.07912751287221909,
-0.0204122606664896,
-0.07927429676055908,
-0.04940631240606308,
-0.03993072360754013,
0.012198420241475105,
-0.04304330796003342,
0.015613985247910023,
-0.01898050867021084,
-0.014024348929524422,
-0.014811841771006584,
-0.00162988540250808,
-0.006689758971333504,
0.039114415645599365,
-0.04710687696933746,
0.034592486917972565,
0.041685380041599274,
-0.045804839581251144,
0.03469565883278847,
0.03915907442569733,
-0.0026562984567135572,
-0.04300590604543686,
0.019565485417842865,
-0.0061337086372077465,
0.012462385930120945,
-0.00961499847471714,
0.013780811801552773,
0.005955052096396685,
0.004566015210002661,
-0.0072846501134335995,
-0.028416721150279045,
-0.021354440599679947,
-0.007741054054349661,
0.03830738738179207,
-0.018103471025824547,
0.000011617455129453447,
-0.00503395264968276,
0.015180462971329689,
0.003388234181329608,
-0.03275448456406593,
-0.03556489944458008,
-0.020081359893083572,
-0.044782787561416626,
-0.0020503741689026356,
0.006643835920840502,
0.0314953587949276,
0.004498830996453762,
-0.015657950192689896,
0.049139637500047684,
0.054821159690618515,
-0.008319441229104996,
-0.011897627264261246,
0.016541529446840286,
-0.0027011653874069452,
0.03469561040401459,
0.009221568703651428,
-0.07043460756540298,
-0.02102060429751873,
-0.03158969059586525,
-0.03208131343126297,
-0.01287694089114666,
-0.05646004155278206,
-0.0006617541657760739,
0.0340440534055233,
0.020353732630610466,
-0.029484041035175323,
0.02465251088142395,
-0.008094088174402714,
-0.02497330866754055,
-0.04476703330874443,
0.014465905725955963,
0.022437062114477158,
0.04392547532916069,
-0.010805467143654823,
-0.04871460795402527,
-0.07197248935699463,
-0.023769302293658257,
-0.04627754166722298,
-0.044800881296396255,
0.0060803247615695,
-0.0359485000371933,
0.022916464135050774,
0.0071626449935138226,
-0.04080156236886978,
0.025468386709690094,
0.04352598264813423,
-0.0010993521427735686,
0.018753953278064728,
-0.000521300476975739,
0.010563647374510765,
0.004049696493893862,
0.03082362748682499,
0.04767826199531555,
0.00685953488573432,
-0.04483794420957565,
-0.01938171312212944,
-0.035842183977365494,
-0.02925841696560383,
0.034717462956905365,
-0.07689981162548065,
-0.014134657569229603,
0.02861541509628296,
0.006615626625716686,
-0.009423269890248775,
0.03215872123837471,
0.021070335060358047,
0.04122929647564888,
0.0637158527970314,
-0.028770485892891884,
0.05182700604200363,
0.039036400616168976,
-0.004257931839674711,
0.011344199068844318,
0.044312313199043274,
0.002604337641969323,
0.025991234928369522,
0.018655218183994293,
-0.02492627687752247,
0.009324111044406891,
0.014492793940007687,
-0.043726108968257904,
-0.02125745452940464,
0.060635268688201904,
0.0001031085048452951,
0.01913939230144024,
0.04854220151901245,
0.01513211615383625,
0.039916690438985825,
0.004840606823563576,
-0.02153579331934452,
-0.0420696958899498,
-0.0003158525505568832,
0.0648709088563919,
0.0374770388007164,
-0.01052910927683115,
-0.02797226421535015,
0.018369676545262337,
-0.026144005358219147,
0.07768544554710388,
-0.0023046366404742002,
0.0110072186216712,
0.007622804492712021,
-0.04927735775709152,
0.000009328213309345301,
-0.0008558941772207618,
-0.03734533116221428,
-0.009313910268247128,
0.007214176468551159,
0.00017943719285540283,
-0.05693333223462105,
0.027355674654245377,
0.027566328644752502,
-0.016150228679180145,
-0.05854353681206703,
0.0302277822047472,
-0.014397552236914635,
-0.004284699447453022,
-0.017343780025839806,
0.003930467180907726,
0.01729540154337883,
-0.00007923709199531004,
0.015080397017300129,
0.06405999511480331,
-0.06233732029795647,
0.014899921603500843,
0.014956600032746792,
-0.0033571640960872173,
0.0587717704474926,
-0.04065435379743576,
0.0015831388300284743,
0.03826679661870003,
0.03583141043782234,
0.07951224595308304,
-0.03741561248898506,
-0.058390673249959946,
-0.016922011971473694,
0.07845636457204819,
-0.04127398505806923,
0.014030260033905506,
0.020294733345508575,
-0.02042427659034729,
0.0352117158472538,
0.03398986533284187,
0.0041837310418486595,
-0.020245525985956192,
0.000494910404086113,
-0.07413423806428909,
0.020611437037587166,
0.008295649662613869,
-0.03609438240528107,
0.016793135553598404,
-0.004128233529627323,
-0.055469729006290436,
0.028531689196825027,
0.001271683257073164,
0.014331568032503128,
0.04473157599568367,
0.05270875245332718,
0.0037859308067709208,
-0.021094925701618195,
-0.030206842347979546,
0.04415757954120636,
-0.06752262264490128,
0.033245719969272614,
-0.04128602519631386,
0.004839280620217323,
-0.07138326019048691,
-0.03831085190176964,
0.000002010424168474856,
-0.04135953634977341,
0.0000370875459339004,
-0.057919591665267944,
-0.04085483402013779,
0.0471704937517643,
0.07777738571166992,
0.0023364503867924213,
0.022560125216841698,
0.0004390259273350239,
-0.028342049568891525,
0.04763002321124077,
0.03969397768378258,
0.0018778032390400767,
-0.05615686997771263,
0.0032908152788877487,
0.02179381623864174,
0.03652099519968033,
-0.01556102093309164,
0.0027849413454532623,
0.002038263948634267,
0.009936216287314892,
-0.0076802936382591724,
-0.04999624565243721,
0.06809436529874802,
0.022620126605033875,
-0.017383933067321777,
0.03715146705508232,
-0.0039027826860547066,
-0.01753026433289051,
0.02113037183880806,
0.07710904628038406,
0.11082585155963898,
-0.02269039675593376,
-0.009414342232048512,
-0.04339092597365379,
-0.05031328648328781,
-0.014796768315136433,
-0.025083791464567184,
0.03674428164958954,
-0.006078634411096573,
0.042149752378463745,
-0.040699779987335205,
0.003644904587417841,
0.049863338470458984,
0.04799259454011917,
0.08778717368841171,
-0.03969622030854225,
0.008334468118846416,
-0.016264595091342926,
0.0073819453828036785,
0.07699484378099442,
0.007581264711916447,
-0.03912698104977608,
-0.00023491842148359865,
0.059036221355199814,
-0.033445071429014206,
0.03190826252102852,
-0.01310387346893549,
0.02691071666777134,
-0.020665699616074562,
0.04055565968155861,
-0.0344182625412941,
-0.007411124184727669,
0.03060462884604931,
-0.028377166017889977,
-0.047329872846603394,
0.022953398525714874,
0.012227095663547516,
0.018338216468691826,
0.046300008893013,
-0.003765970002859831,
-0.007764828857034445,
-0.008900715038180351,
-0.07433321326971054,
-0.04175345599651337,
0.012665915302932262,
0.006743280682712793,
0.008974390104413033,
0.07035450637340546,
0.009618865326046944,
-0.009792391210794449,
-0.05212748423218727,
-0.03384406492114067,
-0.0512942373752594,
-0.03400111198425293,
0.08956849575042725,
-0.013370474800467491,
0.015849780291318893,
0.08448875695466995,
-0.025156008079648018,
0.015060629695653915,
-0.06576722860336304,
0.0480806864798069,
-0.0417257621884346,
-0.054309599101543427,
0.028376130387187004,
-0.020077576860785484,
-0.08626934885978699,
-0.05225245654582977,
-0.018378686159849167,
0.032174427062273026,
-0.017363639548420906,
-0.00855270680040121,
-0.01944739930331707,
-0.03093024343252182,
-0.011939067393541336,
-0.023701488971710205,
0.06059351935982704,
-0.0159115232527256,
0.0469076931476593,
0.006355820689350367,
0.01929040253162384,
0.03513946011662483,
-0.007003991864621639,
0.04314866662025452,
0.025707222521305084,
-0.03637910634279251,
-0.05049874633550644,
0.0565112940967083,
0.05171484872698784,
-0.06828300654888153,
-0.05172835662961006,
0.01809224858880043,
0.002308149356395006,
-0.02089998498558998,
0.007878640666604042,
0.0020755166187882423,
-0.0038978306110948324,
-0.01902899332344532,
0.018616123124957085,
0.03423088788986206,
0.021327901631593704,
-0.05584300681948662,
0.02120082639157772,
0.03604390099644661,
0.02316266857087612,
0.002405524253845215,
0.04935115575790405,
0.00980738177895546,
0.09191830456256866,
-0.05315710976719856,
0.018263930454850197,
0.017208773642778397,
0.0037431828677654266,
0.04210609942674637,
-0.03361601382493973,
-0.02765733003616333,
-0.030699348077178,
0.07092999666929245,
0.05386191979050636,
0.05211733281612396,
0.030544355511665344,
0.04674810916185379,
0.08207407593727112,
-0.05825329199433327,
-0.005836671683937311,
0.06693687289953232,
-0.02244543842971325,
-0.017144570127129555,
0.006171640008687973,
-0.03907056152820587,
0.00837335642427206,
-0.004694563802331686,
-0.03499212488532066,
-0.0009236200130544603,
0.06963708251714706,
0.06462614983320236,
-0.01625610515475273,
-0.018763691186904907,
0.04329720139503479,
0.029401008039712906,
0.003991519566625357,
0.006960725877434015,
0.009180711582303047,
0.02285325527191162,
-0.07266904413700104,
0.03797600418329239,
0.003860675496980548,
-0.03617902845144272,
-0.02825060859322548,
-0.032897401601076126,
0.028250347822904587,
-0.05776859447360039,
-0.011971402913331985,
-0.042970169335603714,
0.029309960082173347,
0.005059188697487116,
0.009995106607675552,
-0.07371131330728531,
-0.028508057817816734,
-0.04791315272450447,
0.006152436602860689,
0.0016689016483724117,
0.06829030066728592,
-0.001324990764260292,
0.013042769394814968,
-0.0431709885597229,
-0.02138354815542698,
-0.018306272104382515,
-0.06403173506259918,
-0.056090544909238815,
0.03166733682155609,
0.010357101447880268,
0.03575257584452629,
0.005057208240032196,
0.07999500632286072,
-0.032384004443883896,
0.009015231393277645,
0.007251419126987457,
0.03291837126016617,
0.024444404989480972,
-0.061933379620313644,
0.032126329839229584,
-0.02195851504802704,
0.007883298210799694,
-0.03411688655614853,
-0.04034005105495453,
0.031162798404693604,
-0.007558648474514484,
-0.01888960413634777,
-0.04656178504228592,
-0.00997068639844656,
0.03678147494792938,
-0.041031643748283386,
0.01451687142252922,
0.021587679162621498,
0.02190028689801693,
-0.0076330662705004215,
-0.035052187740802765,
0.03628072515130043,
0.005665592849254608,
-0.026561841368675232,
0.0005765806417912245,
0.022122636437416077,
0.046501196920871735,
0.01073377300053835,
0.03921449929475784,
0.019058238714933395,
-0.006726336199790239,
-0.028705282136797905,
-0.011884704232215881,
0.0032842308282852173,
-0.05195785313844681,
0.01310184970498085,
-0.0025776783004403114,
0.0012532570399343967,
0.04462294280529022,
0.06553620100021362,
0.025025321170687675,
-0.032529495656490326,
-0.006800324190407991,
0.028925752267241478,
-0.040388837456703186,
-0.033135849982500076,
-0.04680781811475754,
-0.021610772237181664,
-0.04268840700387955,
0.033903058618307114,
-0.03241224214434624,
0.009005069732666016,
-0.013847026973962784,
-0.011937172152101994,
0.007929169572889805,
-0.03444364666938782,
-0.05923334136605263,
-0.07011854648590088,
-0.08125556260347366,
-0.013632222078740597,
0.05742526054382324,
-0.016215596348047256,
0.014484362676739693,
0.03065739944577217,
-0.08424447476863861,
-0.036276016384363174,
-0.009588138200342655,
-0.00007305580948013812,
-0.00038636161480098963,
0.014660001732409,
-0.053871821612119675,
-0.08063895255327225,
-0.03094419091939926,
-0.016745740547776222,
0.07059528678655624,
-0.021120311692357063,
0.03587131202220917,
0.025463905185461044,
0.029084959998726845,
0.03885002061724663,
-0.023042071610689163,
0.03201855346560478,
-0.017654063180088997,
0.019270125776529312,
-0.01896621845662594,
0.030964110046625137,
-0.05769090726971626,
-0.004023788496851921,
-0.005682701710611582,
0.006753616034984589,
-0.011956163682043552,
-0.03187006339430809,
-0.0020393873564898968,
0.08585358411073685,
0.029813241213560104,
0.009039975702762604,
-0.0026672077365219593,
-0.06092996522784233,
-0.017191875725984573,
-0.026930250227451324,
0.03215601667761803,
-0.00607330771163106,
-0.0062406291253864765,
0.06080230697989464,
0.02724834717810154,
-0.00878152996301651,
-0.039046142250299454,
-0.006097897887229919,
0.010385938920080662,
-0.028721779584884644,
0.06884151697158813,
0.04882087931036949,
0.00014521097182296216,
-0.01737770438194275,
0.058472972363233566,
0.02015095204114914,
-0.01564886048436165,
-0.023285401985049248,
0.011808366514742374,
-0.05976884812116623,
0.03238401189446449,
-0.011003089137375355,
0.014857486821711063,
0.03763878345489502,
-0.014517958275973797,
-0.026668686419725418,
-0.08198457956314087,
-0.0047780717723071575,
0.029025521129369736,
0.017252489924430847,
-0.06963808089494705,
-0.005347286816686392,
-0.003101624781265855,
-0.036732085049152374,
0.034702129662036896,
-0.015767931938171387,
-0.008209878578782082,
-0.0007328834035433829,
0.0009366818703711033,
-0.022307097911834717,
-0.03065519966185093,
-0.026362909004092216,
-0.06737971305847168,
-0.03337176889181137,
-0.007878094911575317,
0.025466391816735268,
-0.023356638848781586,
0.011317000724375248,
0.046704474836587906,
0.031030790880322456,
0.06728438287973404,
0.0327288843691349,
-0.05417138710618019,
0.0549309216439724,
0.049741100519895554,
0.03873547166585922,
0.020607171580195427,
-0.027052748948335648,
-0.0017962540732696652,
0.03166162595152855,
-0.04505782946944237,
-0.016462653875350952,
-0.010717106983065605,
-0.01949351094663143,
0.005591419991105795
] |
<p>All around I read that buoyancy is numerically equal to the weight of fluid <strong>displaced</strong> by a submerged object, the volume of displaced fluid being equal to that of the <strong>submerged portion</strong> <a href="https://en.wikipedia.org/wiki/Archimedes%27_principle" rel="nofollow" title="Wikipedia - Archimedes' principle">(Wikipedia)</a>. However, thinking about it brought me to believe that such wording is not very good.</p>
<p>Consider the 2D example below of a box being sunk into water.</p>
<p><img src="http://i.stack.imgur.com/gJ5MV.png" alt="Archimedes 1"></p>
<p>In this example, it is clear that the buoyancy is equal to the weight of 4 cm² of water, which is the volume of the submerged box. However, closer inspection reveals that this does not match the displaced volume.</p>
<p><img src="http://i.stack.imgur.com/pBWhx.png" alt="Archimedes 2"></p>
<p>I concluded that the common definition works well when the body of fluid is large compared to the object, such that its surface level does not change significantly upon submersion. In this case, <em>displaced volume</em> matches <em>volume of submerged portion</em>. However, for the more general case (including example above), it would be more accurate to forgo <em>displaced volume</em> and hang on to <em>volume of submerged portion</em> only.</p>
<p>Am I missing something here? Is the original, ubiquitous wording indeed accurate?</p> | g151 | [
0.031834445893764496,
0.013753318227827549,
-0.013151077553629875,
-0.03644106164574623,
0.02140161767601967,
0.07787910103797913,
0.024864383041858673,
0.021960575133562088,
-0.022412771359086037,
-0.024222616106271744,
0.037931255996227264,
-0.022426096722483635,
0.04511435329914093,
-0.018975989893078804,
-0.024210916832089424,
0.0019714334048330784,
0.046326763927936554,
-0.013135516084730625,
-0.02748926728963852,
-0.001145913265645504,
-0.033147506415843964,
0.0208720900118351,
-0.0388154499232769,
0.015932327136397362,
-0.09369124472141266,
-0.0041156308725476265,
0.009028133004903793,
-0.0013425397919490933,
-0.024662362411618233,
-0.02051398530602455,
-0.06061544269323349,
0.006644182838499546,
0.004518560133874416,
-0.05041620507836342,
-0.019548768177628517,
-0.009274309501051903,
-0.034740377217531204,
-0.023543979972600937,
0.03666294738650322,
-0.0035326573997735977,
0.0174180306494236,
0.028764428570866585,
-0.03382328897714615,
0.0377865731716156,
-0.07739243656396866,
-0.00534830242395401,
-0.022879360243678093,
-0.025308256968855858,
-0.030233150348067284,
-0.099057137966156,
0.03128466755151749,
-0.008950725197792053,
-0.004428323358297348,
0.017872938886284828,
0.020724859088659286,
0.00848280731588602,
-0.020475836470723152,
0.027716048061847687,
-0.05242111161351204,
-0.023656463250517845,
0.004088184796273708,
0.0009694318869151175,
-0.02288985624909401,
0.004844584967941046,
0.06774340569972992,
0.045343853533267975,
-0.09884536266326904,
-0.02001277543604374,
-0.013399777002632618,
0.0027723137754946947,
0.03917316347360611,
0.0057560475543141365,
-0.041403040289878845,
-0.06531195342540741,
-0.07464868575334549,
0.01598828099668026,
-0.002803416922688484,
0.0055036540143191814,
0.03462549299001694,
-0.026595599949359894,
-0.015061700716614723,
0.06781626492738724,
0.025124959647655487,
0.02702396549284458,
0.10837489366531372,
0.006876339204609394,
-0.03247523307800293,
0.046354349702596664,
0.029976297169923782,
0.0008023534319363534,
-0.022834504023194313,
-0.02508367970585823,
0.08272513747215271,
0.056894537061452866,
0.0037052640691399574,
-0.0574929416179657,
0.00033140479354187846,
0.004487289115786552,
-0.05841907113790512,
0.01815599761903286,
-0.031411439180374146,
0.018555091693997383,
-0.03394566476345062,
0.020964056253433228,
-0.04295669123530388,
0.08622005581855774,
0.0627618059515953,
0.019165877252817154,
0.01910668984055519,
-0.0029914374463260174,
-0.01127877738326788,
-0.026932507753372192,
-0.005640690214931965,
-0.0411863811314106,
-0.029125835746526718,
-0.04859182611107826,
0.0414627343416214,
0.04212464019656181,
-0.03129875659942627,
0.018199777230620384,
-0.05996598303318024,
0.05129758268594742,
0.06683829426765442,
0.0633782148361206,
0.057854752987623215,
-0.033266469836235046,
-0.02872161567211151,
0.04578965902328491,
-0.006256973836570978,
0.002574272220954299,
0.004700693767517805,
-0.02173589915037155,
-0.0373358316719532,
0.006944241933524609,
0.02324095368385315,
-0.003950035199522972,
-0.03455075994133949,
0.0065565514378249645,
-0.02160589024424553,
0.001962091540917754,
0.037218064069747925,
-0.03908282518386841,
-0.0049224477261304855,
-0.014726485125720501,
0.01211275439709425,
-0.0345555804669857,
0.016234930604696274,
0.026249190792441368,
0.028820302337408066,
0.0072521427646279335,
0.024673277512192726,
0.10224907100200653,
-0.013732995837926865,
-0.030425559729337692,
0.051297642290592194,
0.001876557245850563,
0.051130566745996475,
-0.00962707120925188,
-0.006424503866583109,
0.00797862745821476,
-0.007755879778414965,
0.05762229859828949,
0.011738629080355167,
-0.005540323909372091,
0.0262213833630085,
0.031440865248441696,
-0.0213926974684,
-0.04414789378643036,
-0.02176583558320999,
-0.029117388650774956,
-0.07863941043615341,
-0.03574110195040703,
-0.03879810497164726,
0.07530380040407181,
-0.031206300482153893,
-0.004351500421762466,
0.08090055733919144,
-0.011610397137701511,
-0.012862914241850376,
0.039640750735998154,
-0.014438759535551071,
0.05513246729969978,
0.008208328858017921,
0.0036510222125798464,
-0.043932877480983734,
0.021843181923031807,
-0.0021090484224259853,
0.014374861493706703,
-0.022779680788517,
-0.012680777348577976,
-0.034129805862903595,
-0.012727165594696999,
0.01327828411012888,
0.07282016426324844,
0.01982971280813217,
0.008600483648478985,
0.08765320479869843,
-0.041371721774339676,
-0.021224748343229294,
0.02094775252044201,
0.010285870172083378,
-0.013084685429930687,
0.03602108359336853,
-0.023267650976777077,
0.01761007122695446,
0.029558785259723663,
-0.041929636150598526,
0.010214478708803654,
-0.021130500361323357,
0.0410141684114933,
0.025470567867159843,
0.000047864290536381304,
-0.01947527751326561,
-0.03584086894989014,
0.003702665911987424,
-0.01350053958594799,
-0.05162256211042404,
0.13026383519172668,
0.041267719119787216,
0.0031025782227516174,
-0.021645432338118553,
0.02999533899128437,
-0.01860588788986206,
-0.008240842260420322,
0.008044418878853321,
0.020461292937397957,
-0.03064030036330223,
-0.01035188790410757,
0.003022748278453946,
-0.010530318133533001,
-0.00693291611969471,
-0.028133634477853775,
0.016378875821828842,
-0.0464378297328949,
0.0670824646949768,
0.05155076086521149,
0.00499004079028964,
0.024356115609407425,
0.054189249873161316,
0.06206479296088219,
0.02112765610218048,
-0.01705341413617134,
-0.04433516412973404,
-0.022178445011377335,
-0.00861291028559208,
0.025490576401352882,
-0.011919891461730003,
-0.0048307087272405624,
0.010517967864871025,
0.020533191040158272,
-0.0567346066236496,
-0.03296839818358421,
0.0168528463691473,
-0.01681585982441902,
0.032993342727422714,
0.06992946565151215,
-0.0366118960082531,
-0.06322108954191208,
0.007082871161401272,
0.02478019893169403,
0.01032275427132845,
-0.05462559312582016,
-0.019918382167816162,
0.0015341424150392413,
-0.05499262735247612,
-0.06055616959929466,
-0.032802268862724304,
-0.006385978311300278,
0.06085981801152229,
0.019863223657011986,
0.019406871870160103,
0.03261597454547882,
0.037077534943819046,
0.08520270138978958,
-0.002173021202906966,
-0.004479051101952791,
-0.022884100675582886,
0.03495100885629654,
0.022964676842093468,
0.008288078010082245,
0.031231548637151718,
0.029033919796347618,
-0.05746432766318321,
0.01081325113773346,
0.03276408091187477,
-0.061229705810546875,
-0.016904132440686226,
0.02839479222893715,
0.00014444513362832367,
0.013523693196475506,
0.09887716174125671,
-0.026307206600904465,
0.009845922701060772,
-0.012244531884789467,
0.025844331830739975,
0.05136655271053314,
0.06357785314321518,
-0.06786610186100006,
-0.05290854722261429,
0.03606877848505974,
-0.019329288974404335,
0.047986045479774475,
0.0440293587744236,
-0.026013262569904327,
0.029769450426101685,
0.04016498103737831,
0.0019900172483175993,
-0.024997247382998466,
-0.004063345026224852,
-0.013716435059905052,
-0.05581613630056381,
0.008216978050768375,
0.0011053676716983318,
-0.0517512783408165,
-0.040040623396635056,
-0.02642226032912731,
-0.035402532666921616,
-0.029188605025410652,
-0.009693373925983906,
-0.019390957430005074,
-0.05031714215874672,
0.03153585270047188,
-0.006626512855291367,
0.023978617042303085,
0.028121445327997208,
-0.005290188826620579,
-0.02959137037396431,
0.060906656086444855,
-0.03212462365627289,
0.01838371716439724,
0.029777798801660538,
0.017911814153194427,
-0.017396070063114166,
-0.0236667413264513,
-0.008185201324522495,
0.017708197236061096,
0.06939127296209335,
-0.0109007703140378,
0.04358568415045738,
-0.008121341466903687,
0.020621949806809425,
-0.06192100793123245,
0.05853761360049248,
-0.03159588202834129,
0.017182854935526848,
-0.02968422695994377,
-0.00408037519082427,
0.023915816098451614,
-0.050494350492954254,
-0.014730212278664112,
0.029450323432683945,
0.022833257913589478,
0.002705034799873829,
0.003657866735011339,
0.0009212473523803055,
0.03509936481714249,
0.026521114632487297,
0.036530569195747375,
-0.061853911727666855,
0.042347606271505356,
0.02715940773487091,
-0.009900776669383049,
0.03117818385362625,
0.008654789067804813,
-0.01736678183078766,
-0.004981848876923323,
-0.025569742545485497,
0.022015787661075592,
-0.02780294045805931,
-0.014616338536143303,
0.0011672631371766329,
-0.06676369905471802,
-0.05968000367283821,
-0.00395645247772336,
0.07833891361951828,
-0.045542601495981216,
0.05681777372956276,
-0.0389086939394474,
-0.043048832565546036,
-0.06646264344453812,
0.0832146555185318,
0.008778142742812634,
-0.0007623560959473252,
-0.006499513518065214,
-0.03438790887594223,
0.03935916721820831,
-0.07498052716255188,
-0.002166055841371417,
0.030283452942967415,
-0.02050844207406044,
-0.05772244185209274,
0.026594188064336777,
-0.02782786823809147,
0.02517840638756752,
0.04957175254821777,
0.007110736798495054,
-0.010250136256217957,
-0.0033734855242073536,
-0.05473499372601509,
0.02805953100323677,
0.011856479570269585,
0.02296057902276516,
-0.014761281199753284,
0.018220506608486176,
0.013673825189471245,
-0.023243635892868042,
0.06321635097265244,
-0.07621865719556808,
-0.05386100709438324,
-0.02271323837339878,
0.03565026819705963,
-0.0027214407455176115,
-0.03649110347032547,
-0.010875589214265347,
-0.002036517485976219,
0.03181923180818558,
-0.00899242702871561,
0.005914938636124134,
0.016944358125329018,
-0.0029612763319164515,
0.03513040021061897,
0.04278683289885521,
-0.07356133311986923,
0.001981694484129548,
-0.05802922695875168,
-0.017169320955872536,
-0.01212342455983162,
0.018373915925621986,
0.05429574474692345,
-0.005886988714337349,
-0.0060189650394022465,
0.011610428802669048,
0.018771156668663025,
0.046839285641908646,
0.005803071428090334,
0.0032072782050818205,
0.05072412267327309,
0.018197735771536827,
0.03122451715171337,
0.041680701076984406,
-0.0011022081598639488,
0.004729458596557379,
-0.043182987719774246,
0.0005757379694841802,
-0.001210640068165958,
0.03098263591527939,
-0.0060624838806688786,
0.019022155553102493,
0.0476679764688015,
0.0043347906321287155,
-0.056478578597307205,
0.05171746388077736,
0.07113722711801529,
-0.0005077801179140806,
0.01232547964900732,
0.025117944926023483,
-0.03446602076292038,
-0.036892201751470566,
-0.03261585533618927,
-0.07105991244316101,
-0.017556095495820045,
-0.05108267813920975,
-0.0046903109177947044,
-0.0032145825680345297,
0.022143524140119553,
-0.009202161803841591,
-0.017411017790436745,
0.0021249696146696806,
-0.014045012183487415,
-0.0004351138777565211,
0.0038945022970438004,
0.014564202167093754,
0.008662642911076546,
0.016769248992204666,
0.02554788999259472,
0.03757152333855629,
0.029320048168301582,
-0.04582780972123146,
0.03461913764476776,
-0.09456141293048859,
-0.03070703148841858,
-0.03723444044589996,
-0.012321428395807743,
0.03911576047539711,
-0.04520595073699951,
0.024043085053563118,
0.029463818296790123,
0.04645230993628502,
-0.020796792581677437,
0.029599633067846298,
-0.000015038001038192306,
-0.037648383527994156,
-0.01931031607091427,
-0.000006329129519144772,
-0.029366739094257355,
-0.010280701331794262,
0.0023667234927415848,
0.014069031924009323,
-0.02631848305463791,
0.028291823342442513,
-0.043231695890426636,
0.02128545381128788,
0.03408969193696976,
-0.0016201313119381666,
-0.011326485313475132,
-0.0009774821810424328,
0.050335537642240524,
0.021692320704460144,
-0.024592066183686256,
0.022411607205867767,
0.051481377333402634,
-0.03700334578752518,
-0.012468449771404266,
-0.036622337996959686,
0.0031369798816740513,
-0.08347203582525253,
0.008188826963305473,
0.05871211737394333,
0.02709602378308773,
0.029795784503221512,
0.0006066536880098283,
-0.006008031312376261,
0.04447776451706886,
0.003660553600639105,
-0.049559589475393295,
-0.0012245816178619862,
-0.032130733132362366,
-0.032271381467580795,
-0.013449421152472496,
0.043757762759923935,
0.011245228350162506,
0.0471721775829792,
-0.025380749255418777,
-0.018549270927906036,
-0.06565234810113907,
-0.0564102903008461,
-0.07171905785799026,
0.012787536717951298,
0.05290074273943901,
-0.04009518772363663,
0.045678842812776566,
-0.009585944004356861,
0.01091394480317831,
0.10382179915904999,
-0.008822835981845856,
0.04420407861471176,
-0.0482824482023716,
-0.08385542780160904,
0.06577657908201218,
-0.04172587767243385,
-0.00899603869765997,
0.06488832086324692,
-0.03917214646935463,
0.06212877109646797,
-0.019168997183442116,
-0.026023808866739273,
-0.020688513293862343,
-0.04598269984126091,
-0.05368625745177269,
-0.010935456492006779,
0.010189136490225792,
-0.017569873481988907,
0.019221127033233643,
0.003853933187201619,
0.009809336625039577,
-0.013849652372300625,
-0.010571335442364216,
0.026951899752020836,
-0.05348910018801689,
0.10351427644491196,
-0.03206707164645195,
-0.0764663964509964,
0.06842312216758728,
-0.011808712966740131,
-0.0009039995493367314,
0.031325485557317734,
-0.04712678864598274,
0.010249689221382141,
-0.025394026190042496,
0.02252957783639431,
0.013698453083634377,
-0.028259597718715668,
0.03330238163471222,
-0.05883609130978584,
-0.03962972015142441,
-0.030301041901111603,
-0.038413260132074356,
-0.004552885890007019,
0.045877255499362946,
-0.02427905984222889,
0.02052835375070572,
-0.005555279552936554,
-0.038635242730379105,
-0.010350127704441547,
-0.015581022948026657,
0.007109200116246939,
0.01781749725341797,
0.026723749935626984,
-0.022037213668227196,
0.021481269970536232,
0.008539830334484577,
0.007684630341827869,
-0.03136424347758293,
-0.055120088160037994,
0.06217733398079872,
0.01454097032546997,
0.016293833032250404,
-0.05768169090151787,
-0.057853177189826965,
-0.03360208868980408,
-0.000012601937669387553,
0.036923687905073166,
-0.003853048663586378,
-0.017970355227589607,
-0.02161727473139763,
-0.07923947274684906,
-0.005332892760634422,
-0.009908104315400124,
-0.00802362710237503,
0.004821053706109524,
-0.02542276866734028,
-0.02121509611606598,
0.05068955570459366,
0.012611333280801773,
0.06311936676502228,
0.056737519800662994,
-0.07518211752176285,
0.025102945044636726,
0.02038407512009144,
-0.013095712289214134,
0.015666360035538673,
-0.018933897837996483,
0.08430495113134384,
0.01666310615837574,
0.003207169007509947,
0.048417698591947556,
-0.003626149846240878,
0.02922946959733963,
0.05257706344127655,
0.039430953562259674,
-0.033414244651794434,
0.007948258891701698,
0.02376396581530571,
-0.008733673021197319,
-0.0038991249166429043,
-0.01855107769370079,
-0.008568834513425827,
0.035919565707445145,
0.01092426385730505,
0.0005565087194554508,
0.050653014332056046,
0.01837998628616333,
-0.04969334602355957,
0.051427703350782394,
-0.018995502963662148,
0.008208874613046646,
-0.018180688843131065,
-0.05368092283606529,
0.014668310061097145,
-0.021275430917739868,
-0.03268567472696304,
0.02658892795443535,
-0.0032355976291000843,
-0.022664552554488182,
-0.062222305685281754,
0.011348826810717583,
-0.02249635010957718,
-0.04957737773656845,
-0.0097963260486722,
0.004583648405969143,
0.0518161877989769,
-0.01649777777493,
-0.024250242859125137,
0.04274793341755867,
-0.013088211417198181,
0.025682590901851654,
0.0076090674847364426,
0.003123370697721839,
-0.015966514125466347,
0.03330876678228378,
0.01810232363641262,
-0.02282419428229332,
0.024230841547250748,
0.018732450902462006,
0.00250198133289814,
-0.023528719320893288,
-0.10910863429307938,
0.03908376395702362,
-0.003491529729217291,
0.019626324996352196,
0.03561105206608772,
-0.039887890219688416,
-0.027540503069758415,
0.0029950474854558706,
0.005927609279751778,
0.04929061233997345,
0.06866718083620071,
0.006329669151455164,
0.03816425800323486,
0.02034689672291279,
-0.006292227655649185,
-0.014837602153420448,
0.03295838460326195,
-0.03591950237751007,
0.01888914406299591,
-0.03434263914823532,
-0.024066198617219925,
0.04448791965842247,
0.016539188101887703,
-0.04629351198673248,
0.04141305759549141,
0.04711268097162247,
0.03532989323139191,
-0.04382104054093361,
0.02039952203631401,
-0.028150290250778198,
-0.008123844861984253,
-0.04690556600689888,
-0.062234170734882355,
-0.022384043782949448,
-0.007649170234799385,
0.0521211251616478,
-0.009944230318069458,
-0.03508114814758301,
-0.017268260940909386,
-0.022827766835689545,
-0.022089337930083275,
-0.01701592095196247,
-0.04659730941057205,
0.015704533085227013,
-0.07516013830900192,
0.010783357545733452,
-0.021351151168346405,
0.07419334352016449,
0.05041170120239258,
0.04166358336806297,
0.024127554148435593,
0.049437426030635834,
-0.014328106306493282,
-0.05587034299969673,
0.051619257777929306,
-0.022069938480854034,
0.0066390084102749825,
0.025064636021852493,
0.039116039872169495,
-0.009543743915855885,
-0.02318742871284485,
-0.030514992773532867,
0.008057145401835442,
-0.07135656476020813,
-0.004087509587407112,
0.015694037079811096,
0.0005183557514101267,
-0.014393962919712067,
0.019078684970736504,
-0.05084850639104843,
0.008499566465616226,
-0.018948353826999664,
-0.02697661519050598,
-0.03309669718146324,
-0.015295324847102165,
-0.008651556447148323,
-0.02644786424934864,
-0.07061517238616943,
-0.03740157186985016,
-0.03110278584063053,
-0.02657550573348999,
0.049323126673698425
] |
<p>What are the physics of wind (or any gas flow really) bouncing off surfaces?</p>
<p>If a wind hits a wall directly (in a 90 degree angle) does any of it bounce back? </p>
<p>Are there any similarities with, say, light rays hitting a mirror?</p>
<p>I understand, that the other extreme case is a 0 degree angle in gas pipes, for example, where the surface guides the flow further.</p> | g4618 | [
0.07974173873662949,
0.03852401673793793,
-0.016325799748301506,
0.025080764666199684,
0.046085018664598465,
0.0463312491774559,
0.043204475194215775,
0.018295107409358025,
-0.04307794198393822,
-0.044819850474596024,
0.009506366215646267,
0.027520189061760902,
0.05013405904173851,
-0.005759485065937042,
-0.02686966024339199,
0.0006836313987150788,
0.009913899935781956,
0.013030014932155609,
0.008568108081817627,
0.02455088309943676,
-0.05059514194726944,
-0.051176585257053375,
0.028593910858035088,
-0.022120989859104156,
0.013672868721187115,
-0.0839659795165062,
-0.010166752152144909,
-0.0238180048763752,
-0.01182279922068119,
-0.018887493759393692,
-0.043053314089775085,
0.03398195281624794,
0.01544880773872137,
-0.08253349363803864,
-0.048636239022016525,
-0.034080423414707184,
-0.03935753554105759,
-0.056043993681669235,
0.0033944135066121817,
-0.017843885347247124,
0.01528137270361185,
0.010871629230678082,
0.01671924814581871,
0.06782949715852737,
0.059486474841833115,
0.05959959328174591,
-0.010734728537499905,
0.01290835626423359,
-0.0041881888173520565,
-0.026656484231352806,
-0.010217282921075821,
-0.014907876029610634,
-0.00725471880286932,
-0.03364383056759834,
-0.0011525839800015092,
0.012249944731593132,
0.06097044795751572,
0.0038500407245010138,
0.07668440043926239,
0.03028704784810543,
0.003346238285303116,
0.009611574932932854,
-0.059527210891246796,
-0.015906987711787224,
0.019076494500041008,
-0.052441202104091644,
-0.05059172958135605,
-0.012491053901612759,
0.009993492625653744,
-0.0033996826969087124,
0.0628451257944107,
0.03916233032941818,
0.01753165014088154,
-0.05565536767244339,
0.0005341489450074732,
-0.008323043584823608,
-0.020115582272410393,
-0.04568799212574959,
-0.011780657805502415,
0.02701840177178383,
0.004350495059043169,
-0.05172685161232948,
-0.07847321778535843,
0.026183966547250748,
0.02109353244304657,
-0.015209896489977837,
-0.033824775367975235,
0.07065755873918533,
-0.0013080587377771735,
-0.06488656252622604,
0.036925800144672394,
-0.005315433256328106,
0.04152596369385719,
-0.012021901085972786,
-0.03179240599274635,
0.009094132110476494,
-0.03447166457772255,
0.05343589186668396,
-0.003964285831898451,
-0.012546326965093613,
-0.03328345715999603,
0.0019438567105680704,
-0.0007692273356951773,
0.04219929128885269,
0.04097472503781319,
-0.04414911940693855,
0.007094350177794695,
0.034352242946624756,
-0.0018938197754323483,
-0.011083265766501427,
-0.05300091207027435,
-0.03537581115961075,
-0.02367497980594635,
0.015142425894737244,
-0.03553440049290657,
0.02005143277347088,
0.09605468809604645,
-0.0006588945398107171,
0.032751791179180145,
0.09591663628816605,
0.06197606399655342,
0.06714949011802673,
-0.007349551655352116,
0.009318273514509201,
0.002305877860635519,
-0.010728803463280201,
0.01282011903822422,
-0.01945982314646244,
-0.019645143300294876,
-0.006565807852894068,
0.057540081441402435,
0.004516645334661007,
-0.07340448349714279,
0.0020775452721863985,
0.05012260377407074,
-0.01378326490521431,
-0.0410185270011425,
0.015506420284509659,
0.0038146895822137594,
0.02831087075173855,
0.0748508870601654,
0.001432059914804995,
-0.002324221655726433,
-0.008825932629406452,
-0.02157159149646759,
-0.022700710222125053,
-0.0023631444200873375,
0.010239662602543831,
-0.0015078096184879541,
-0.011673366650938988,
-0.004536125343292952,
0.013864686712622643,
0.022068239748477936,
-0.06854668259620667,
0.02214675582945347,
-0.03621795400977135,
0.0015240152133628726,
0.008415119722485542,
0.06771527975797653,
0.04522553086280823,
0.06634882092475891,
0.0063058799132704735,
0.08739855140447617,
-0.017875907942652702,
-0.028950173407793045,
-0.04591134190559387,
-0.0555293932557106,
-0.007763402536511421,
0.028787530958652496,
0.04502842202782631,
-0.10703124850988388,
-0.0028941109776496887,
-0.005431205499917269,
0.02940506301820278,
-0.032131802290678024,
0.039092931896448135,
0.005206799600273371,
-0.04798971489071846,
-0.008979025296866894,
-0.01895970292389393,
0.005937608424574137,
-0.042667195200920105,
-0.023253463208675385,
0.0048737917095422745,
0.0741586983203888,
0.014884931966662407,
-0.010846356861293316,
0.014358229003846645,
-0.049886323511600494,
0.003930875100195408,
-0.024914616718888283,
-0.04919492080807686,
0.003777120728045702,
-0.04882577434182167,
0.016484083607792854,
-0.03413355350494385,
0.010421899147331715,
0.012410962022840977,
-0.06172377988696098,
0.00021479475253727287,
-0.016823817044496536,
0.06443838030099869,
0.033181916922330856,
0.018580002710223198,
-0.0475521944463253,
0.0942593440413475,
-0.022285519167780876,
-0.019736584275960922,
-0.0054190573282539845,
-0.02877012826502323,
-0.024283919483423233,
0.0216913353651762,
0.04724377766251564,
0.048574939370155334,
0.006761408876627684,
0.019298065453767776,
-0.016795288771390915,
0.008133054710924625,
0.029503552243113518,
0.008381761610507965,
0.060161590576171875,
0.025055158883333206,
0.03261887654662132,
-0.01664346642792225,
0.02596958540380001,
-0.00999045092612505,
-0.05862607806921005,
0.036982450634241104,
0.07352778315544128,
0.05108379200100899,
-0.029362503439188004,
-0.018230684101581573,
0.027286002412438393,
-0.008966394700109959,
0.03433286398649216,
0.000645089487079531,
0.028783520683646202,
0.01216580718755722,
0.002172035863623023,
-0.08457062393426895,
0.012802233919501305,
-0.06044045090675354,
-0.06919022649526596,
-0.020827412605285645,
0.03330647572875023,
0.029325682669878006,
0.015377751551568508,
0.016961634159088135,
0.049240533262491226,
0.011528483591973782,
0.05414540693163872,
0.028308987617492676,
-0.0039376020431518555,
0.03307654336094856,
-0.004155390430241823,
-0.010547115467488766,
0.02402174286544323,
-0.015173193998634815,
-0.04665989428758621,
-0.027032336220145226,
0.0019343572203069925,
0.009720939211547375,
-0.02373807318508625,
0.016247203573584557,
-0.04958394914865494,
0.018664315342903137,
-0.01153587270528078,
0.10571186244487762,
-0.02965415269136429,
0.024671951308846474,
0.02222169190645218,
0.0690721720457077,
0.007300287950783968,
0.02771061658859253,
0.01180217694491148,
0.006351984106004238,
0.022312361747026443,
-0.012282167561352253,
-0.008056789636611938,
-0.025548387318849564,
-0.023903192952275276,
-0.011804988607764244,
-0.00901155173778534,
-0.0649338960647583,
0.003977655898779631,
-0.038785725831985474,
-0.003159663872793317,
0.013587628491222858,
-0.011403833515942097,
0.046729475259780884,
0.0015306278364732862,
-0.009838410653173923,
0.009505114518105984,
-0.034400779753923416,
-0.0333179235458374,
0.03712760657072067,
0.01935327798128128,
0.005301790777593851,
-0.016994653269648552,
0.03548208251595497,
-0.05528613552451134,
-0.007394975516945124,
-0.058384813368320465,
0.025171291083097458,
-0.08155359327793121,
0.03720924258232117,
-0.006815725471824408,
-0.06851475685834885,
0.045193735510110855,
-0.02190273068845272,
-0.0395980142056942,
0.03107859194278717,
-0.012270906940102577,
0.053901199251413345,
-0.014378676190972328,
0.014290884137153625,
-0.013475493527948856,
0.007405065931379795,
-0.01642465405166149,
0.04865460842847824,
-0.057831671088933945,
0.013060520403087139,
0.021068252623081207,
-0.028112726286053658,
0.014175130054354668,
0.039853524416685104,
-0.011330521665513515,
0.03935070335865021,
-0.02562895603477955,
0.023720068857073784,
0.02685210481286049,
0.03457832708954811,
-0.012160886079072952,
-0.05002586543560028,
-0.020328206941485405,
0.071403868496418,
-0.026421034708619118,
0.04266521334648132,
0.04569420963525772,
-0.0026110303588211536,
0.004171117674559355,
-0.029095152392983437,
-0.05769144371151924,
-0.07476790994405746,
0.03468937426805496,
0.05017056688666344,
0.0006956398719921708,
-0.027477452531456947,
0.025501418858766556,
-0.033668022602796555,
0.06372681260108948,
0.008752260357141495,
-0.0049288952723145485,
0.0073071690276265144,
-0.007847086526453495,
-0.02167477458715439,
0.0472482331097126,
0.04822390526533127,
0.026353614404797554,
0.015626046806573868,
-0.037314411252737045,
-0.033445097506046295,
0.017068106681108475,
-0.05037003383040428,
-0.052681129425764084,
-0.05642196163535118,
-0.004875351674854755,
0.038845136761665344,
-0.057294733822345734,
0.0001858374453149736,
-0.0347517766058445,
-0.02735022082924843,
-0.022980308160185814,
0.011488046497106552,
-0.03468680381774902,
0.006343013606965542,
0.0016744727035984397,
-0.013757465407252312,
0.03263738751411438,
0.02958596870303154,
0.05833563581109047,
0.05378589406609535,
0.020195359364151955,
0.06163027510046959,
-0.026983851566910744,
-0.03997255489230156,
-0.007753326557576656,
-0.014903396368026733,
0.0402757003903389,
-0.08091545104980469,
0.03501324728131294,
-0.027415141463279724,
0.000477613735711202,
0.008348355069756508,
0.0549180842936039,
-0.023815317079424858,
0.0011617457494139671,
0.016889136284589767,
-0.07241044193506241,
0.03972639515995979,
0.0836833119392395,
0.0693264976143837,
0.002555061597377062,
-0.0029836930334568024,
-0.01436466071754694,
-0.011036749929189682,
0.010689177550375462,
-0.019279373809695244,
-0.024928132072091103,
0.008843510411679745,
0.003173279110342264,
-0.05718713626265526,
-0.009783496148884296,
-0.07232053577899933,
0.01988094300031662,
0.006251385435461998,
0.011047792620956898,
0.014764197170734406,
0.027491062879562378,
-0.03197925537824631,
0.023463871330022812,
0.014811834320425987,
0.02788151614367962,
0.016819866374135017,
-0.0018631764687597752,
0.014773215167224407,
0.08606211841106415,
-0.03865550085902214,
-0.04153983294963837,
-0.00746792322024703,
0.01393936574459076,
-0.011636368930339813,
-0.05060042440891266,
0.003932008054107428,
0.009856940247118473,
0.06560178101062775,
-0.002983954269438982,
0.004604702349752188,
0.03630385547876358,
0.05518316105008125,
0.048008523881435394,
-0.006791362538933754,
0.02088245004415512,
-0.008877381682395935,
0.015749726444482803,
0.06232735887169838,
0.015047149732708931,
-0.0036640968173742294,
0.011135238222777843,
0.010419122874736786,
-0.06554371863603592,
-0.04432522505521774,
0.016806604340672493,
-0.06321795284748077,
-0.06955491006374359,
-0.015955738723278046,
-0.036229848861694336,
0.023933734744787216,
-0.027359995990991592,
-0.005861426237970591,
0.006819724105298519,
0.0113206272944808,
0.06502164155244827,
0.002087582368403673,
0.001163780689239502,
-0.02553877793252468,
-0.005009994376450777,
0.0036763346288353205,
-0.12883314490318298,
-0.034843020141124725,
-0.02360798604786396,
0.04635479301214218,
0.01714371331036091,
0.06222250312566757,
-0.0033494774252176285,
-0.002976621501147747,
-0.014220154844224453,
-0.0013311723014339805,
0.014907813630998135,
-0.02239331603050232,
0.025982704013586044,
-0.007623764686286449,
-0.02020009234547615,
-0.010933184996247292,
-0.023865802213549614,
-0.04194682091474533,
-0.059398699551820755,
-0.005477594211697578,
0.004352635238319635,
-0.010456220246851444,
-0.008249329403042793,
-0.022785909473896027,
-0.0741555318236351,
-0.01251078862696886,
-0.062055472284555435,
-0.0050850315019488335,
-0.018975362181663513,
0.005325525999069214,
-0.008725195191800594,
-0.01085144653916359,
-0.014880920760333538,
-0.005931237246841192,
-0.006518916692584753,
0.01227476354688406,
0.014150920324027538,
0.02567661926150322,
0.006984934210777283,
-0.010638294741511345,
0.022851113229990005,
0.06924806535243988,
-0.019113508984446526,
-0.026659410446882248,
-0.002552599646151066,
0.019864514470100403,
0.009829392656683922,
-0.04693221673369408,
0.005923743359744549,
-0.024436602368950844,
0.022631974890828133,
-0.026631534099578857,
0.01959690824151039,
-0.030636247247457504,
-0.07547614723443985,
-0.011139169335365295,
0.009319727309048176,
0.02530016377568245,
-0.06465565413236618,
0.013341969810426235,
-0.0035092856269329786,
0.026666706427931786,
0.025396784767508507,
-0.044101644307374954,
0.04793142154812813,
0.02845807373523712,
-0.01862560398876667,
-0.057399723678827286,
0.031709592789411545,
-0.01808127388358116,
0.06120697781443596,
-0.03197376802563667,
-0.029350951313972473,
0.04593098163604736,
0.02748609334230423,
0.048979852348566055,
0.03725700452923775,
0.012445645406842232,
0.0404520221054554,
0.07787918299436569,
0.0597449466586113,
-0.02576025016605854,
-0.01845552586019039,
0.049020957201719284,
-0.03211648389697075,
0.07615307718515396,
-0.03640339896082878,
-0.01867545209825039,
-0.009499465115368366,
-0.01368086040019989,
-0.0018705212278291583,
-0.0652623102068901,
0.0445895679295063,
0.0245868768543005,
0.05096002295613289,
-0.05304829776287079,
0.027470892295241356,
0.03238237649202347,
-0.04341764748096466,
-0.026159346103668213,
0.044242069125175476,
0.02191907726228237,
0.00818348117172718,
0.00569760799407959,
-0.01586083695292473,
-0.029964134097099304,
0.0018075614934787154,
-0.032811641693115234,
-0.04585607722401619,
0.01640956476330757,
-0.0201948881149292,
0.012211383320391178,
0.004655719734728336,
-0.02496672235429287,
0.07064781337976456,
-0.06903459876775742,
0.0026169021148234606,
-0.06840541213750839,
-0.012829798273742199,
0.0287870354950428,
-0.04131779074668884,
-0.0022186031565070152,
-0.015795407816767693,
-0.06518962234258652,
0.020859960466623306,
-0.004130081739276648,
-0.05442100763320923,
-0.08747169375419617,
0.03581400215625763,
0.04412056505680084,
-0.041259780526161194,
-0.011659614741802216,
0.010304178111255169,
0.05260385572910309,
0.009380948729813099,
0.003826648462563753,
0.04177654907107353,
0.024535665288567543,
0.023139864206314087,
0.00543085066601634,
-0.034142956137657166,
0.039731547236442566,
0.042223136872053146,
0.013606595806777477,
-0.0041657742112874985,
0.02414417453110218,
-0.06303515285253525,
-0.022233113646507263,
-0.03420837223529816,
-0.05281481519341469,
-0.0209256149828434,
-0.0054352134466171265,
-0.015674224123358727,
-0.05592363700270653,
0.047159601002931595,
-0.05327842757105827,
0.028578858822584152,
0.055108893662691116,
-0.058757830411195755,
0.054413288831710815,
0.013597652316093445,
0.0236145481467247,
0.06927084177732468,
-0.018775982782244682,
0.010772552341222763,
0.014636131934821606,
-0.0006811865023337305,
0.03938578441739082,
-0.021298173815011978,
0.04371052235364914,
0.007452333811670542,
0.0865652859210968,
-0.016319645568728447,
0.08630381524562836,
-0.010538469068706036,
0.017840059474110603,
-0.024403410032391548,
-0.02954454906284809,
-0.052212320268154144,
-0.0661524310708046,
0.000615134253166616,
-0.022404015064239502,
-0.02255420573055744,
-0.06471741199493408,
0.01295666303485632,
-0.014176875352859497,
-0.025881154462695122,
0.03975199535489082,
-0.03503405675292015,
0.012024840340018272,
-0.01787315495312214,
-0.07136491686105728,
-0.04265059530735016,
0.05547332391142845,
0.0197693333029747,
-0.013557192869484425,
-0.008939639665186405,
0.02469230443239212,
0.02091405913233757,
0.01531011238694191,
0.011634674854576588,
0.0021556722931563854,
0.012344551272690296,
-0.07899153232574463,
-0.04245626553893089,
0.02560051530599594,
0.011825921013951302,
0.030885696411132812,
-0.06289195269346237,
0.014337739907205105,
0.028123144060373306,
-0.008202915079891682,
0.01824946515262127,
0.05142231285572052,
0.02898111566901207,
0.009065050631761551,
-0.010000952519476414,
0.02681281603872776,
0.010231025516986847,
0.05113580822944641,
-0.017230309545993805,
-0.10270682722330093,
-0.021846728399395943,
0.027990445494651794,
0.013211957179009914,
0.0003245268599130213,
-0.07928641885519028,
-0.004398991819471121,
0.06280061602592468,
-0.007861212827265263,
-0.02094648778438568,
0.01879279315471649,
0.0000020802506242034724,
0.0026172196958214045,
-0.0012418997939676046,
0.00013661359844263643,
0.0449281744658947,
0.019029969349503517,
0.02912081964313984,
-0.009207626804709435,
-0.00837564468383789,
-0.03132893890142441,
-0.0026046971324831247,
0.025803616270422935,
-0.00843000691384077,
-0.009066860191524029,
-0.0032471774611622095,
-0.010004160925745964,
0.0034993328154087067,
0.017866522073745728,
0.017091337591409683,
0.02765769138932228,
0.02186630666255951,
0.00005759397754445672,
-0.005641575437039137,
-0.028111528605222702,
-0.029455484822392464,
0.008187204599380493,
-0.028151312842965126,
0.0011924661230295897,
-0.015142850577831268,
0.0037987902760505676,
-0.0046474686823785305,
-0.015777409076690674,
-0.008444279432296753,
0.046558525413274765,
-0.03620944917201996,
0.00193117989692837,
0.06367950141429901,
-0.04694150388240814,
-0.05348223075270653,
-0.03295927122235298,
0.06935451924800873,
0.026874806731939316,
-0.0039227195084095,
-0.06218123808503151,
-0.050795622169971466,
-0.03239312022924423,
0.03780882805585861,
0.009313317015767097,
-0.04058878496289253,
0.014021857641637325,
0.07919392734766006,
0.03151596337556839,
0.017397664487361908,
0.008610108867287636,
-0.0003545463550835848,
-0.05783073604106903,
-0.02362571470439434,
0.02565188892185688,
0.016430459916591644,
-0.008853605017066002,
0.009248172864317894,
-0.003868909552693367,
0.02228512428700924,
-0.06079521030187607,
-0.019653841853141785,
-0.08406032621860504,
-0.07934688776731491,
0.013070317916572094
] |
<p>In a Leyden jar, I have read that a charged object is brought in contact with the conductor in contact with the metal inside the jar, thus giving the inner metal a similar charge. And the metal outside the jar then gets an opposite charge.</p>
<p>My question is simply how does the metal outside the jar get the opposite charge, given that there is an insulator in-between?</p>
<p>I hope that someone can give me a clear reply, explaining exactly what happens with the outer metal.</p> | g4619 | [
0.004568060394376516,
0.013533868826925755,
0.02656617760658264,
0.003382148453965783,
0.036980174481868744,
0.04681948199868202,
-0.02750968374311924,
-0.040018193423748016,
-0.056948430836200714,
0.004368136171251535,
-0.04532171040773392,
0.06085983291268349,
-0.04786637797951698,
-0.02214937098324299,
0.09843680262565613,
-0.026496892794966698,
-0.014365463517606258,
0.015643836930394173,
0.00880335085093975,
0.016537146642804146,
-0.04656316712498665,
0.02246570773422718,
-0.009789339266717434,
-0.024835936725139618,
-0.062433794140815735,
0.007831965573132038,
0.0026562833227217197,
0.037280529737472534,
0.04003339260816574,
-0.041615743190050125,
0.054682422429323196,
0.018470056354999542,
-0.025129208341240883,
-0.04024365171790123,
-0.07531455904245377,
-0.01441972330212593,
-0.000942014274187386,
-0.01263353880494833,
-0.05277677997946739,
0.05034998059272766,
0.007062850520014763,
-0.010765241459012032,
0.02317415550351143,
-0.036016229540109634,
0.027368923649191856,
-0.03710028529167175,
-0.031251270323991776,
-0.0034157715272158384,
-0.01245034672319889,
-0.0005907982704229653,
-0.05048542842268944,
0.013065403327345848,
0.04488705098628998,
-0.0028179846704006195,
0.029243791475892067,
0.0042852675542235374,
-0.012645774520933628,
-0.05863634869456291,
0.023406680673360825,
0.03000902757048607,
-0.017299538478255272,
0.024336788803339005,
-0.03209103271365166,
-0.006649022456258535,
0.020966876298189163,
0.008130062371492386,
-0.034828122705221176,
0.03677607327699661,
0.0035829986445605755,
0.029151281341910362,
0.006141552235931158,
0.025247205048799515,
-0.05620841309428215,
-0.0557788722217083,
-0.022152375429868698,
0.02158646658062935,
0.047899387776851654,
-0.00978216901421547,
0.08163043111562729,
-0.0000681142118992284,
0.010199368000030518,
-0.017450034618377686,
0.05287357419729233,
-0.01250141579657793,
0.04007362201809883,
0.015485652722418308,
-0.028405820950865746,
-0.06019475683569908,
-0.058411967009305954,
-0.04378039389848709,
0.038377545773983,
-0.015155840665102005,
0.02575843036174774,
0.004160336218774319,
-0.0855507105588913,
-0.05887861177325249,
-0.004955798853188753,
0.023525118827819824,
-0.008471906185150146,
-0.019840441644191742,
-0.0031352927908301353,
-0.06224209815263748,
0.04077901691198349,
0.04182625934481621,
-0.037890393286943436,
0.016836775466799736,
0.039220020174980164,
0.01863921992480755,
-0.02857876569032669,
0.035458583384752274,
-0.04383019357919693,
-0.032033707946538925,
-0.03999974578619003,
-0.03715301677584648,
0.04306058958172798,
0.024894636124372482,
0.007463543675839901,
0.015237368643283844,
0.03957969322800636,
0.03414427116513252,
-0.04309098795056343,
0.007916508242487907,
0.01869630627334118,
-0.02731325663626194,
0.0017145388992503285,
-0.045940861105918884,
0.03986264020204544,
-0.01724845916032791,
0.02131739817559719,
0.019232459366321564,
-0.01200273260474205,
0.015581861138343811,
-0.003842985024675727,
-0.02093401923775673,
0.007645478937774897,
0.03352925181388855,
-0.01635107211768627,
-0.002523592906072736,
-0.0029569617472589016,
-0.056360673159360886,
0.04923216253519058,
-0.03495253250002861,
-0.029234401881694794,
-0.013640585355460644,
0.009574665687978268,
0.030057886615395546,
-0.022438442334532738,
0.03147963434457779,
-0.017053334042429924,
-0.004613352473825216,
0.044852256774902344,
0.03703094646334648,
0.010781862773001194,
-0.001627420075237751,
-0.009532462805509567,
-0.02928289584815502,
0.07076269388198853,
-0.025617368519306183,
0.04605170339345932,
0.014156336896121502,
0.05026785656809807,
-0.016192559152841568,
0.05706110596656799,
0.036156173795461655,
-0.06236570328474045,
0.04635019227862358,
0.0651935562491417,
-0.0028963687364012003,
0.05047042295336723,
-0.06668636202812195,
0.0036010926123708487,
0.005457683932036161,
0.004417700693011284,
0.051883019506931305,
0.0683462917804718,
0.058993417769670486,
-0.004017156083136797,
0.0051303948275744915,
0.06532635539770126,
-0.0017304139910265803,
-0.05324581265449524,
0.0040925913490355015,
0.021456444635987282,
0.03322151303291321,
-0.04346812516450882,
0.011146293953061104,
-0.03494890034198761,
0.036654695868492126,
-0.00821628887206316,
-0.0024691002909094095,
-0.03434894233942032,
-0.06197039410471916,
0.013241351582109928,
-0.03333502635359764,
-0.012268592603504658,
-0.02985595539212227,
0.02565697953104973,
-0.02037203684449196,
0.006706631742417812,
-0.048107896000146866,
-0.04361052066087723,
-0.0011525453301146626,
0.018244551494717598,
0.024946795776486397,
0.036978580057621,
-0.005149869713932276,
-0.02877107635140419,
-0.01212144922465086,
0.061197344213724136,
-0.005378205329179764,
-0.01978403702378273,
0.02749190665781498,
0.06443570554256439,
-0.03621623292565346,
-0.07148412615060806,
0.02372198924422264,
-0.0015806364826858044,
0.023487640544772148,
0.007312725763767958,
0.031432364135980606,
0.002201377646997571,
-0.04327896237373352,
0.0291146133095026,
-0.051698628813028336,
-0.010231449268758297,
-0.016189472749829292,
0.05373619869351387,
0.006198388058692217,
-0.028395330533385277,
0.023097679018974304,
-0.024205364286899567,
-0.017425091937184334,
-0.01296368520706892,
0.00009636790491640568,
0.007965415716171265,
0.03812986612319946,
0.02114913798868656,
0.029979651793837547,
-0.009278660640120506,
-0.09146483987569809,
-0.036752503365278244,
0.013676092028617859,
-0.04718552529811859,
0.0539332777261734,
-0.04036660119891167,
-0.03004053235054016,
0.030392372980713844,
-0.01697106473147869,
-0.04699442908167839,
0.03586867079138756,
0.07276409864425659,
0.0002028172166319564,
-0.02054595947265625,
0.025742556899785995,
-0.02997497096657753,
-0.04365713894367218,
-0.06295322626829147,
0.023554135113954544,
-0.025597577914595604,
-0.0939004123210907,
0.011736218817532063,
-0.05204077064990997,
0.08056604862213135,
-0.021333245560526848,
-0.08506669849157333,
-0.032447077333927155,
0.011339387856423855,
-0.03279823809862137,
0.08452990651130676,
0.005283438600599766,
-0.038284651935100555,
0.07861576974391937,
-0.02580912783741951,
-0.013053102418780327,
0.034713950008153915,
-0.00287856487557292,
-0.007357764523476362,
-0.02365286834537983,
0.02050466276705265,
-0.043150369077920914,
0.016364147886633873,
0.042568933218717575,
-0.03373054042458534,
0.02936021238565445,
-0.004782258067280054,
-0.05150064080953598,
0.032408807426691055,
0.01948506012558937,
0.03518194332718849,
-0.021411867812275887,
0.006326909177005291,
-0.03784681111574173,
0.05331099033355713,
0.01830727979540825,
0.04890495911240578,
0.01892835460603237,
0.02967163734138012,
0.03208567947149277,
-0.01664409413933754,
-0.0029789924155920744,
-0.028230253607034683,
-0.03576100245118141,
0.009478973224759102,
-0.03613660857081413,
0.03542275354266167,
0.05437557026743889,
-0.0745292380452156,
-0.02173408307135105,
-0.006841843016445637,
-0.03997141867876053,
-0.005727935582399368,
0.039761025458574295,
-0.021052595227956772,
-0.05656999722123146,
-0.006855464074760675,
0.004781002644449472,
-0.04271616414189339,
0.009483405388891697,
0.003217005170881748,
0.017609640955924988,
-0.04544936493039131,
0.0337524488568306,
0.010801061056554317,
0.011323582381010056,
-0.002874016063287854,
-0.02052876725792885,
-0.02490955963730812,
-0.02441607229411602,
-0.0478416308760643,
0.01294135395437479,
-0.04382232949137688,
0.036959968507289886,
-0.031427353620529175,
-0.04722876101732254,
-0.03531535714864731,
-0.029955115169286728,
-0.026187969371676445,
0.05808444693684578,
0.05844346806406975,
0.061130233108997345,
-0.010774320922791958,
-0.05221012979745865,
-0.04234618321061134,
-0.02946370653808117,
0.028353676199913025,
0.032622843980789185,
-0.04379575327038765,
0.0493423193693161,
0.035868167877197266,
-0.011317356489598751,
0.025603778660297394,
-0.023115811869502068,
-0.0013682142598554492,
-0.004810987040400505,
-0.01549296174198389,
0.04425003007054329,
-0.02438383363187313,
0.031304698437452316,
-0.0017080646939575672,
0.004035181365907192,
0.03593797981739044,
-0.020509693771600723,
0.004653641954064369,
-0.05965806543827057,
0.022938868030905724,
-0.044385772198438644,
0.03815590217709541,
0.015161910094320774,
0.010115404613316059,
-0.05339764431118965,
0.008882636204361916,
0.033405739814043045,
-0.021885855123400688,
0.012707769870758057,
0.023850630968809128,
-0.053696922957897186,
0.023882277309894562,
0.033681854605674744,
0.018372133374214172,
0.011174635030329227,
-0.01604924164712429,
0.047789622098207474,
0.038292717188596725,
-0.0407588817179203,
0.008977020159363747,
0.0748470202088356,
0.0255318284034729,
0.030359627678990364,
-0.005964446812868118,
-0.039145685732364655,
-0.04253796860575676,
-0.005285219289362431,
0.04373699426651001,
-0.031504422426223755,
-0.0001229117187904194,
0.013986005447804928,
0.019139546900987625,
-0.039134010672569275,
-0.025006940588355064,
-0.05878964811563492,
0.008729640394449234,
0.030117709189653397,
-0.014687568880617619,
-0.05444954335689545,
-0.015174729749560356,
-0.01082042045891285,
0.006237808149307966,
-0.045462723821401596,
0.0024242440704256296,
-0.05162576958537102,
-0.010829601436853409,
0.00981665775179863,
-0.0072153108194470406,
-0.04931741580367088,
-0.003241219324991107,
-0.05540739372372627,
0.09516669064760208,
0.1023208349943161,
0.01335661206394434,
-0.012198151089251041,
0.023469306528568268,
0.003427190473303199,
0.014988900162279606,
-0.010273149237036705,
-0.0030967500060796738,
0.07031150162220001,
0.008451709523797035,
0.01386566087603569,
0.022977136075496674,
-0.016581982374191284,
-0.05009091645479202,
0.03470802307128906,
-0.012700463645160198,
0.007565539330244064,
-0.10381019860506058,
0.009152334183454514,
-0.046726077795028687,
0.03398103266954422,
-0.011731348000466824,
0.05238214507699013,
0.038448214530944824,
0.023890724405646324,
-0.017265895381569862,
-0.03412926569581032,
0.03096686117351055,
0.004332592245191336,
-0.019912652671337128,
0.03005819208920002,
0.009374852292239666,
-0.07483457028865814,
-0.04051433131098747,
0.013466807082295418,
-0.02402980625629425,
-0.09154893457889557,
0.04793217033147812,
0.024609258398413658,
0.024784334003925323,
-0.05359345301985741,
-0.03688543289899826,
-0.03190408647060394,
-0.030086491256952286,
0.017299147322773933,
-0.026663566008210182,
0.004945671651512384,
0.018526241183280945,
-0.043749697506427765,
0.011435376480221748,
-0.05567009001970291,
-0.07878650724887848,
0.0034673544578254223,
0.029854143038392067,
0.0805923193693161,
0.05564199015498161,
-0.004601418040692806,
0.14562898874282837,
-0.01819838397204876,
-0.013086863793432713,
-0.025192175060510635,
-0.01742125302553177,
-0.0305287167429924,
-0.019272124394774437,
0.05506608262658119,
0.004841238260269165,
-0.03550969809293747,
-0.01150570623576641,
-0.02134866639971733,
-0.023753197863698006,
0.018923286348581314,
-0.026848329231142998,
-0.05732168257236481,
0.03900585696101189,
-0.004386130720376968,
0.00853415485471487,
0.019642503932118416,
-0.013893005438148975,
0.08505810052156448,
0.023611821234226227,
0.0033973134122788906,
-0.030480416491627693,
0.015214716084301472,
-0.02192807011306286,
-0.00040399370482191443,
-0.018423760309815407,
0.058976441621780396,
0.037046562880277634,
0.04836537688970566,
-0.02778550423681736,
-0.03778451308608055,
-0.023923244327306747,
0.013328568078577518,
-0.01479252614080906,
0.06126917898654938,
0.03194807469844818,
0.09639713168144226,
0.00714777922257781,
0.016357233747839928,
-0.044134046882390976,
0.03995669633150101,
-0.02351774089038372,
0.05042905732989311,
-0.039996735751628876,
0.025134742259979248,
-0.00894926767796278,
-0.07357818633317947,
-0.03195105865597725,
0.008732902817428112,
0.004444711375981569,
-0.026584940031170845,
0.0331009104847908,
0.06541565805673599,
-0.01804235577583313,
0.041067905724048615,
0.03839423879981041,
-0.03360613062977791,
-0.017475198954343796,
-0.00963189359754324,
0.04304781183600426,
0.024995794519782066,
0.008080710656940937,
0.07587697356939316,
0.06375513225793839,
-0.04051825776696205,
0.003272351576015353,
0.0020971347112208605,
-0.04719454050064087,
-0.015655474737286568,
-0.025164036080241203,
0.009110125713050365,
0.0305184219032526,
0.018467139452695847,
-0.0022734638769179583,
0.006034777499735355,
0.008359577506780624,
0.001552978646941483,
0.07049534469842911,
0.050724294036626816,
0.005077689420431852,
-0.032653529196977615,
0.019084574654698372,
0.0017503007547929883,
0.05636139214038849,
0.01056419312953949,
0.018752997741103172,
0.02287856675684452,
0.01180883590131998,
-0.05127323791384697,
-0.04856616258621216,
-0.0020261965692043304,
0.08018971979618073,
-0.0031851509120315313,
0.06781120598316193,
-0.03964248299598694,
0.028307640925049782,
-0.04311634972691536,
0.04040122404694557,
0.01644880883395672,
-0.027068546041846275,
-0.006539779715240002,
-0.004780430346727371,
0.020936794579029083,
0.035202499479055405,
-0.014971522614359856,
0.018804416060447693,
-0.002133064204826951,
-0.011499383486807346,
-0.0061686234548687935,
-0.03260252997279167,
-0.036351315677165985,
0.0375945083796978,
-0.12835247814655304,
-0.03104041889309883,
0.021110668778419495,
-0.0221237875521183,
-0.07743631303310394,
0.007235663942992687,
0.04787915199995041,
0.024920662865042686,
0.06917692720890045,
-0.01147438120096922,
0.04479075223207474,
-0.00909191183745861,
-0.002181380521506071,
0.02827964350581169,
-0.025719746947288513,
0.025568801909685135,
-0.014764990657567978,
-0.007438358385115862,
0.012057299725711346,
-0.004883576184511185,
-0.014639363624155521,
0.017608128488063812,
0.0001027855250868015,
0.029346011579036713,
-0.006379977334290743,
0.000697288429364562,
0.025321539491415024,
-0.05012879893183708,
-0.0013274135999381542,
0.028395667672157288,
0.007249057292938232,
-0.03126043826341629,
-0.04961313679814339,
-0.030964862555265427,
-0.03327000141143799,
0.049917012453079224,
0.03562215343117714,
-0.021058009937405586,
0.027434751391410828,
-0.0015199710614979267,
0.04984066262841225,
-0.09630672633647919,
0.03363090753555298,
-0.015256252139806747,
0.013385552912950516,
0.022295404225587845,
-0.011712291277945042,
0.04921688139438629,
-0.0018789805471897125,
0.012806854210793972,
0.0248784851282835,
-0.03178238496184349,
-0.0240761898458004,
-0.0010642645647749305,
0.061940453946590424,
-0.04271821305155754,
0.017630964517593384,
0.05800710618495941,
-0.036471620202064514,
-0.04979541897773743,
0.009021010249853134,
-0.062083650380373,
-0.0603485181927681,
-0.032099828124046326,
0.012012440711259842,
-0.025050992146134377,
0.020845411345362663,
-0.006554237101227045,
0.04830654338002205,
0.03520209342241287,
-0.02403520792722702,
-0.05362433195114136,
-0.035737842321395874,
-0.03812268003821373,
0.00653496477752924,
0.0400802418589592,
0.008317101746797562,
-0.017865676432847977,
-0.05105716362595558,
-0.04203382134437561,
0.029407214373350143,
-0.013541948981583118,
-0.06301198154687881,
-0.0023968529421836138,
0.0025398952420800924,
0.00866516213864088,
0.03323197364807129,
-0.0010085443500429392,
0.07567749917507172,
-0.03572428598999977,
-0.03664105385541916,
-0.04609150066971779,
0.06463271379470825,
-0.007004537619650364,
0.01804814115166664,
-0.016730360686779022,
-0.02308514714241028,
-0.031449250876903534,
-0.0029095292557030916,
0.014176835305988789,
-0.023783769458532333,
0.06615908443927765,
0.015787677839398384,
0.009255305863916874,
0.010001000948250294,
-0.013289990834891796,
0.048325732350349426,
-0.014590555801987648,
0.0348924919962883,
0.015924734994769096,
0.03144902363419533,
0.00196357280947268,
0.012496251612901688,
0.025782234966754913,
-0.022568264976143837,
0.020441178232431412,
0.01776605099439621,
-0.03687718138098717,
0.02086397260427475,
-0.0010562688112258911,
-0.004636902362108231,
0.07560410350561142,
0.03648579120635986,
0.04924457520246506,
-0.010748883709311485,
0.04119173809885979,
-0.007424157112836838,
-0.055645737797021866,
0.03407694399356842,
-0.007292722351849079,
0.016260065138339996,
-0.025721320882439613,
0.048095785081386566,
0.05400591716170311,
-0.0056151519529521465,
-0.07458499073982239,
-0.024252666160464287,
0.013891714625060558,
0.057997290045022964,
-0.02504800260066986,
-0.014167234301567078,
0.017356107011437416,
0.028772225603461266,
-0.036423031240701675,
0.05366704985499382,
0.01421238761395216,
-0.03485417738556862,
0.026486951857805252,
-0.024808749556541443,
0.015475887805223465,
-0.04122481122612953,
0.04670378193259239,
0.00766022177413106,
-0.014412001706659794,
-0.010382077656686306,
-0.013022310100495815,
-0.0005213744007050991,
-0.03728092834353447,
0.060643330216407776,
0.008080849424004555,
0.008002229034900665,
-0.06443127989768982,
-0.009442736394703388,
-0.013616315089166164,
0.01750769466161728,
0.008206999860703945,
-0.0799112394452095,
-0.06568590551614761,
0.0218141358345747,
-0.01881691813468933,
0.007048241328448057,
-0.023405058309435844,
0.021292682737112045,
-0.023269983008503914,
0.005155631341040134,
-0.011042975820600986,
-0.018963869661092758,
-0.08394339680671692,
0.027751822024583817
] |
<p>Earlier today, I saw <a href="http://www.orlandosentinel.com/business/nationworld/sns-bc-eu--breakinglightspeed,0,5266439.story">this link</a> on Facebook about neutrinos going faster than the speed of light, and of course, re-posted. Since then, a couple of my friends have gotten into a discussion about what this means (mostly about time-travel), but I don't really know what this really implies. This made me wonder...</p>
<p>What are the biggest and most immediate implications of this potential discovery?</p>
<p><strong>Related:</strong> <a href="http://physics.stackexchange.com/q/14968/3454">Superluminal neutrinos</a></p> | g83 | [
0.03078417293727398,
0.1254720836877823,
-0.0011139983544126153,
0.04112826660275459,
0.022959934547543526,
-0.03014439530670643,
-0.009593326598405838,
0.0021190312691032887,
0.00932841282337904,
-0.031069280579686165,
-0.029678331688046455,
0.0033442224375903606,
0.03362809121608734,
0.025537248700857162,
-0.019049715250730515,
-0.033504415303468704,
0.06382197141647339,
-0.03298583999276161,
0.03837054222822189,
-0.014179548248648643,
0.03580240532755852,
0.019200164824724197,
-0.0550750233232975,
-0.02936830185353756,
-0.05166900157928467,
0.004675874952226877,
0.025320162996649742,
-0.05922968313097954,
-0.026987073943018913,
-0.0011113754007965326,
0.03558291494846344,
-0.06498062610626221,
-0.023280946537852287,
-0.048742398619651794,
0.012374281883239746,
-0.022677920758724213,
0.0036382139660418034,
0.030855394899845123,
0.01508247945457697,
0.0034303946886211634,
-0.0520855188369751,
0.003214780706912279,
-0.004943785723298788,
0.0002458085655234754,
0.02293224446475506,
-0.01048316527158022,
0.02718496508896351,
0.010460328310728073,
-0.02520589716732502,
-0.08505045622587204,
0.024477887898683548,
-0.013138173148036003,
0.023284627124667168,
0.07730882614850998,
0.044649384915828705,
-0.005599403753876686,
0.0683107003569603,
-0.02171322889626026,
0.04815904051065445,
0.009246235713362694,
0.008076535537838936,
-0.01142478920519352,
0.008354147896170616,
-0.04427019879221916,
0.05656326562166214,
-0.008050632663071156,
-0.005881263874471188,
-0.004965937230736017,
0.04047283157706261,
-0.001350990030914545,
0.059097569435834885,
0.010784768499433994,
-0.03798193112015724,
-0.029117459431290627,
-0.027987482026219368,
0.06974043697118759,
0.02793697640299797,
0.009778386913239956,
0.005095014348626137,
-0.015514087863266468,
-0.005067253019660711,
-0.023740321397781372,
-0.013843050226569176,
-0.015264294110238552,
0.03040795773267746,
-0.04798266664147377,
0.008434101939201355,
0.04317579045891762,
0.02083926647901535,
0.003239286597818136,
0.02303539775311947,
-0.05442877858877182,
0.002642615931108594,
-0.013780303299427032,
-0.02242111600935459,
-0.01043823454529047,
0.11321227252483368,
0.026675375178456306,
0.018575839698314667,
-0.02958015538752079,
-0.02016160637140274,
-0.013330619782209396,
-0.04552040249109268,
0.041650038212537766,
-0.021900245919823647,
-0.00018075121624860913,
0.022791743278503418,
-0.02973778359591961,
-0.02408699505031109,
-0.004203223157674074,
-0.009658086113631725,
-0.024119701236486435,
-0.0009161708876490593,
-0.003181867301464081,
-0.006444152444601059,
-0.006250909063965082,
-0.004948642570525408,
-0.011775150895118713,
-0.02898903377354145,
0.03853399679064751,
0.015938613563776016,
0.008233726024627686,
-0.03273247554898262,
0.0738101601600647,
-0.05409444123506546,
-0.017653068527579308,
0.042918913066387177,
0.005076345056295395,
-0.014377359300851822,
-0.006931515410542488,
-0.04037655144929886,
0.0015902927843853831,
0.004832788370549679,
0.07710636407136917,
0.01593155413866043,
0.028683604672551155,
0.0113845095038414,
0.012241153046488762,
0.008222222328186035,
-0.0015649909619241953,
0.011993983760476112,
-0.052830036729574203,
0.03207701817154884,
0.05854339525103569,
-0.015275553800165653,
-0.024225721135735512,
-0.030708223581314087,
0.04988551139831543,
-0.015440295450389385,
0.013995436020195484,
-0.024777540937066078,
0.03813613951206207,
-0.047202713787555695,
-0.07075456529855728,
0.012110564857721329,
0.009947583079338074,
-0.014281130395829678,
-0.026755446568131447,
-0.016557544469833374,
0.026517676189541817,
0.022104909643530846,
-0.0008627030765637755,
-0.04908531531691551,
-0.018846824765205383,
-0.04548168554902077,
0.012529951520264149,
0.0663006529211998,
-0.013918958604335785,
-0.036867085844278336,
-0.02070964127779007,
-0.0833810344338417,
0.03311966732144356,
0.004342688713222742,
0.056181736290454865,
0.013526862487196922,
-0.007698019500821829,
0.03479671850800514,
-0.06598159670829773,
-0.07099243998527527,
-0.005724424496293068,
-0.09396733343601227,
-0.06844823062419891,
0.00823384989053011,
0.01256625447422266,
0.031225550919771194,
-0.0023452031891793013,
-0.034196168184280396,
0.09541956335306168,
-0.009735329076647758,
0.029683999717235565,
-0.040148939937353134,
-0.04220758378505707,
-0.009166833944618702,
0.03040536306798458,
-0.03295092284679413,
-0.005118316039443016,
-0.017775779590010643,
-0.03561273217201233,
-0.047832898795604706,
-0.05637240782380104,
-0.008570373989641666,
0.021671470254659653,
-0.0023284852504730225,
-0.029471147805452347,
0.0579390749335289,
0.013517860323190689,
-0.028844309970736504,
0.0270017609000206,
-0.00583236338570714,
0.042370643466711044,
0.036286212503910065,
-0.023145608603954315,
0.020009759813547134,
0.0007927022525109351,
0.008897688239812851,
-0.037478938698768616,
-0.03576246276497841,
0.03321180120110512,
0.018001489341259003,
0.011438998393714428,
-0.0030402448028326035,
-0.02989242784678936,
0.016334639862179756,
-0.052173614501953125,
-0.03784550353884697,
-0.029268071055412292,
-0.009793512523174286,
-0.09713027626276016,
-0.0002666642831172794,
0.02004172094166279,
-0.06109358370304108,
0.07372399419546127,
-0.04106775298714638,
0.03719490021467209,
-0.004969346337020397,
0.02974984422326088,
0.014531043358147144,
-0.07628332823514938,
0.049276549369096756,
0.018102414906024933,
0.03674205765128136,
-0.012038810178637505,
-0.008747652173042297,
0.02589862048625946,
0.0029999816324561834,
-0.01688627153635025,
0.023448791354894638,
-0.07825171947479248,
-0.009248027577996254,
0.05640844628214836,
0.024927297607064247,
-0.013598167337477207,
0.011221807450056076,
0.033977359533309937,
0.04788782075047493,
-0.009751805104315281,
-0.007455727085471153,
0.037948522716760635,
-0.08189478516578674,
0.0052536725997924805,
0.012073967605829239,
0.0538521483540535,
-0.055485378950834274,
-0.012087440118193626,
0.07488083094358444,
0.013451118022203445,
0.011556652374565601,
0.026076573878526688,
-0.050877656787633896,
-0.02040078677237034,
-0.07256757467985153,
-0.019233347848057747,
-0.020160069689154625,
-0.03254838287830353,
0.0015878350241109729,
0.007920402102172375,
0.05650991201400757,
0.0026675178669393063,
0.05503701791167259,
-0.020220808684825897,
-0.0404139943420887,
0.00021966548229102045,
-0.029363686218857765,
-0.04074544832110405,
-0.013869358226656914,
-0.06299766898155212,
-0.010186969302594662,
0.029822373762726784,
0.006542831659317017,
0.018472284078598022,
-0.0008664911729283631,
-0.013449600897729397,
0.040799036622047424,
-0.008766891434788704,
0.04030262678861618,
0.009844810701906681,
0.030687086284160614,
0.06896205991506577,
0.02048563025891781,
-0.021949876099824905,
0.08678440749645233,
-0.04644251987338066,
0.025050798431038857,
0.05210863798856735,
-0.0000025141966943920124,
-0.0064452821388840675,
-0.07548923045396805,
0.01161680556833744,
0.006985028740018606,
-0.01560081634670496,
0.021012552082538605,
0.05659721419215202,
0.002598673105239868,
0.03382892534136772,
0.0012927488423883915,
0.013501173816621304,
0.020205868408083916,
0.0857200101017952,
0.022439364343881607,
-0.03039620630443096,
0.020700618624687195,
-0.05481003597378731,
-0.03394307568669319,
0.01086062379181385,
0.06574440747499466,
-0.021626796573400497,
-0.0029309233650565147,
0.008595851249992847,
-0.03897951543331146,
0.042554620653390884,
-0.00042703773942776024,
0.002590821823105216,
-0.013580809347331524,
0.02238270826637745,
-0.07538533210754395,
-0.009839990176260471,
0.013133412227034569,
0.06751877814531326,
0.026406079530715942,
0.0004111610760446638,
0.0008392920135520399,
-0.03794850781559944,
-0.03186870366334915,
0.026297247037291527,
0.058652378618717194,
-0.007061860524117947,
-0.013796832412481308,
-0.014243467710912228,
-0.009073377586901188,
0.021986914798617363,
0.039419881999492645,
0.010316233150660992,
-0.026474550366401672,
0.005183470901101828,
0.04155130311846733,
0.020517753437161446,
0.008964872919023037,
-0.018851395696401596,
0.04198019206523895,
-0.0414012148976326,
-0.047296710312366486,
0.02496674470603466,
0.03984839469194412,
0.028853025287389755,
-0.04068422690033913,
0.010985946282744408,
-0.05674442648887634,
0.007312539033591747,
0.003841379191726446,
-0.027180995792150497,
0.0062372419051826,
-0.020002048462629318,
0.0050692991353571415,
-0.0031027731020003557,
0.032286833971738815,
0.033812664449214935,
-0.01538783684372902,
-0.012911295518279076,
-0.0345928929746151,
0.018669214099645615,
0.04734918847680092,
0.062051646411418915,
0.05668802931904793,
-0.029866937547922134,
0.003047229489311576,
0.029394177719950676,
-0.0757218599319458,
-0.03783845901489258,
-0.06854619830846786,
-0.07609444856643677,
-0.0599883534014225,
0.03967037796974182,
-0.043803680688142776,
0.001828721142373979,
-0.036431845277547836,
0.004677176009863615,
-0.003403163980692625,
-0.010492741130292416,
0.027802927419543266,
0.0200776569545269,
-0.040955059230327606,
0.00892133079469204,
-0.012310504913330078,
0.007942801341414452,
-0.06554998457431793,
-0.007106789853423834,
0.0054012080654501915,
-0.02836437150835991,
0.006669860798865557,
-0.003365874057635665,
0.01561861764639616,
0.044148098677396774,
-0.034422896802425385,
-0.07664132118225098,
0.005701543763279915,
0.060627274215221405,
0.017499910667538643,
-0.09692728519439697,
-0.019989021122455597,
0.010031644254922867,
0.043626997619867325,
-0.05111624300479889,
0.006370393559336662,
0.005918864626437426,
-0.026636574417352676,
0.02266998402774334,
0.034473903477191925,
-0.031744204461574554,
-0.028661632910370827,
0.01836542785167694,
0.0362735278904438,
0.053079500794410706,
-0.017754314467310905,
0.027408884838223457,
0.049042217433452606,
0.043513279408216476,
0.06346270442008972,
0.03839510306715965,
0.015213808976113796,
0.08729834109544754,
0.03536684811115265,
-0.012122569605708122,
0.06458588689565659,
-0.025061435997486115,
0.007359267678111792,
0.04695917293429375,
-0.11423192173242569,
-0.03082434833049774,
-0.017710411921143532,
-0.046998366713523865,
-0.02499227412045002,
0.04300958290696144,
0.019530078396201134,
0.014045823365449905,
-0.0035803294740617275,
-0.040937479585409164,
-0.01534112449735403,
-0.0024505173787474632,
0.03177453204989433,
0.029310505837202072,
-0.05630963668227196,
0.03773048520088196,
0.07745429873466492,
-0.012887462042272091,
0.04354790970683098,
0.029639339074492455,
-0.025401338934898376,
-0.032798703759908676,
-0.0590442530810833,
-0.03160328418016434,
-0.08798625320196152,
-0.038924574851989746,
0.03895701840519905,
0.004489061422646046,
-0.02054372988641262,
-0.008122440427541733,
-0.010352243669331074,
0.0368947796523571,
0.01735280081629753,
0.012115905992686749,
-0.028527386486530304,
-0.0037039450835436583,
0.008086987771093845,
-0.03786063566803932,
-0.030065465718507767,
0.015175990760326385,
-0.06144924834370613,
0.021594757214188576,
0.004009122494608164,
-0.03519827499985695,
-0.016581349074840546,
-0.018551474437117577,
0.03806237876415253,
0.024074433371424675,
-0.032650478184223175,
-0.01053015235811472,
0.09495332092046738,
0.01804908737540245,
-0.02578078769147396,
-0.006049034651368856,
-0.05280313268303871,
0.03572232648730278,
0.06543881446123123,
-0.02654157765209675,
0.009875442832708359,
0.07316023856401443,
0.04264000430703163,
0.02207046188414097,
-0.020976806059479713,
-0.030979163944721222,
-0.03169957548379898,
0.009983481839299202,
-0.050786104053258896,
-0.030097657814621925,
0.03768599405884743,
-0.0206492580473423,
-0.015066307969391346,
-0.003298175986856222,
0.02091773971915245,
-0.00943575706332922,
-0.01324322447180748,
-0.006911850068718195,
0.04463665932416916,
-0.009819436818361282,
-0.0011046429863199592,
-0.008895186707377434,
-0.03622732311487198,
0.0016945959068834782,
0.041732292622327805,
-0.018726520240306854,
0.011482436209917068,
-0.02907039411365986,
0.07803769409656525,
0.008235118351876736,
0.023769088089466095,
0.013230914250016212,
0.04307697340846062,
-0.031214920803904533,
-0.04159488156437874,
0.010941981337964535,
-0.03514624014496803,
0.004400472156703472,
-0.06327207386493683,
0.08578311651945114,
-0.03046215884387493,
-0.05438844487071037,
0.017730163410305977,
-0.019938144832849503,
-0.011098304763436317,
-0.02337040938436985,
-0.00009195208986056969,
0.0045370981097221375,
0.033575840294361115,
-0.0015839303378015757,
0.024005170911550522,
0.03460836037993431,
0.008480400778353214,
-0.015630710870027542,
-0.07740972191095352,
-0.02002517133951187,
0.038646820932626724,
0.04257110133767128,
0.04872657731175423,
0.009437955915927887,
0.013207904994487762,
-0.0015582622727379203,
-0.04645780473947525,
-0.017316048964858055,
0.05763278901576996,
0.027582617476582527,
0.036639489233493805,
0.05273057892918587,
0.005667068064212799,
-0.04482945427298546,
-0.03983980789780617,
-0.041894011199474335,
0.042685676366090775,
0.014785793609917164,
-0.06684605777263641,
-0.014111096039414406,
-0.04682442173361778,
-0.04188563674688339,
0.0742717981338501,
0.0015707587590441108,
-0.027858048677444458,
0.01845531538128853,
-0.03084539622068405,
0.04964142292737961,
0.047114405781030655,
-0.019794046878814697,
0.03387416899204254,
-0.03752594068646431,
-0.004512634593993425,
-0.05595110356807709,
-0.08049605041742325,
-0.05696867033839226,
-0.009095398709177971,
-0.056078504770994186,
-0.08304212242364883,
0.02021237276494503,
-0.016071263700723648,
0.01061281468719244,
0.02978472039103508,
0.019700385630130768,
0.018162742257118225,
0.01987997069954872,
-0.012616544961929321,
0.011343158781528473,
0.018224099650979042,
-0.02468772791326046,
0.0076036411337554455,
0.017968924716114998,
-0.03541279211640358,
0.009449833072721958,
-0.030098285526037216,
-0.00807521678507328,
0.004942374303936958,
-0.037121955305337906,
0.009550823830068111,
0.03930147737264633,
0.01800350472331047,
-0.015593284741044044,
-0.002318547572940588,
0.04183061793446541,
-0.020389139652252197,
0.042844563722610474,
-0.03171084076166153,
-0.024979431182146072,
0.0011248126393184066,
0.0354398638010025,
0.03402014076709747,
0.030635397881269455,
0.004201162606477737,
0.05192083120346069,
0.019934220239520073,
-0.025333968922495842,
0.04317646473646164,
-0.012763194739818573,
-0.006019769702106714,
-0.002783308969810605,
0.003421458415687084,
-0.05630236119031906,
-0.022626185789704323,
-0.03539060428738594,
0.0029041075613349676,
-0.0020637980196624994,
0.011590950191020966,
0.025524361059069633,
0.02759137935936451,
-0.0661134347319603,
-0.05678287893533707,
-0.05961185321211815,
-0.004825083073228598,
0.023135434836149216,
0.016475964337587357,
-0.05460701510310173,
0.0070643252693116665,
0.011460843496024609,
-0.003844260238111019,
-0.04345205798745155,
-0.05356236547231674,
-0.032602548599243164,
0.01381892804056406,
-0.00284969131462276,
0.011470180004835129,
0.03213604539632797,
-0.026225309818983078,
-0.06451371312141418,
0.03766173496842384,
-0.035212960094213486,
0.001568854320794344,
-0.009885898791253567,
0.00023786209931131452,
-0.0759030133485794,
-0.02644449658691883,
-0.023745005950331688,
-0.0063950298354029655,
-0.017288299277424812,
-0.015752792358398438,
-0.006950145587325096,
0.042166855186223984,
0.06816745549440384,
0.01816767454147339,
0.0028211018070578575,
-0.0077371662482619286,
0.06103399023413658,
-0.07579661905765533,
0.017663944512605667,
-0.023086117580533028,
-0.011389798484742641,
0.00018951624224428087,
0.014206930994987488,
0.015521430410444736,
0.03119257651269436,
0.011967993341386318,
0.016852375119924545,
-0.03642836958169937,
0.03000112995505333,
0.07938739657402039,
0.04169438034296036,
-0.09985636174678802,
0.025835290551185608,
-0.0047090076841413975,
0.017051178961992264,
0.02194073237478733,
0.02679024636745453,
0.04125213995575905,
-0.0393461175262928,
-0.0360369049012661,
0.0443672239780426,
0.006815205793827772,
0.04790424555540085,
0.038463328033685684,
0.014272309839725494,
0.04070286452770233,
0.049152255058288574,
0.040684644132852554,
-0.01639007218182087,
0.02267025038599968,
0.05952922999858856,
0.0006103144260123372,
0.051321934908628464,
-0.021739816293120384,
0.007983043789863586,
-0.03449854999780655,
-0.02207931876182556,
0.006185317877680063,
0.04478395730257034,
-0.03178856894373894,
-0.028498170897364616,
-0.0048378026112914085,
-0.021160578355193138,
-0.016709642484784126,
-0.015202476643025875,
-0.0947122797369957,
0.049245432019233704,
0.009385719895362854,
0.08392887562513351,
-0.02205364592373371,
0.017283963039517403,
0.00030807871371507645,
-0.06740395724773407,
-0.02594798244535923,
-0.026571717113256454,
-0.05061134323477745,
-0.022656569257378578,
0.016776572912931442,
0.04416368156671524,
-0.028159985318779945,
-0.035322319716215134,
0.08148228377103806,
-0.008395794779062271,
-0.03703249245882034,
0.07448167353868484,
0.020215176045894623,
-0.010228775441646576,
-0.0070083290338516235,
-0.004525523632764816,
-0.04541410133242607,
-0.009051174856722355,
0.024516819044947624,
-0.01609726808965206,
0.008331366814672947,
0.030346378684043884,
0.040115468204021454,
-0.002378408797085285,
-0.015528763644397259,
0.027911940589547157
] |
<p>A teacher of mine told me once that there were no ninth gluon because such a one should be white and interact infinitely far, and no one has been observed. Is there also a theoretical reason?</p> | g4620 | [
0.05330589413642883,
0.0854792669415474,
0.01602836512029171,
-0.09847407788038254,
0.08104417473077774,
0.02058565802872181,
-0.008075377903878689,
0.04122663289308548,
-0.0075989654287695885,
-0.06744933873414993,
-0.011155843734741211,
-0.013203611597418785,
0.006106928922235966,
0.013308209367096424,
-0.02453896403312683,
0.01594761572778225,
0.08363974094390869,
0.012327050790190697,
0.015004917979240417,
0.015356470830738544,
0.004043552093207836,
-0.006097345147281885,
-0.023645304143428802,
0.010135001502931118,
-0.012099024839699268,
0.01386568695306778,
0.01620730198919773,
-0.0038079246878623962,
0.006602408830076456,
-0.00373915396630764,
0.029203182086348534,
-0.0014795678434893489,
0.021183757111430168,
-0.017932739108800888,
-0.017401935532689095,
-0.05028434097766876,
-0.01081960741430521,
-0.020210886374115944,
0.040540240705013275,
-0.005608635023236275,
0.016677776351571083,
0.04001517593860626,
-0.017971213907003403,
-0.03516823425889015,
-0.041883014142513275,
0.07221544533967972,
-0.02662094682455063,
0.01421249471604824,
0.00886828824877739,
-0.001058698515407741,
-0.01568480022251606,
0.008347705006599426,
0.05803341418504715,
0.016434278339147568,
-0.004712188150733709,
0.0018038840498775244,
0.049626100808382034,
0.011765803210437298,
0.018021808937191963,
0.08433632552623749,
-0.002045877045020461,
-0.01101047731935978,
-0.004987327381968498,
0.00415191613137722,
0.031092045828700066,
-0.0440533384680748,
-0.04864656925201416,
0.06075669452548027,
-0.03975553810596466,
0.028522321954369545,
0.0035872049629688263,
-0.05597130209207535,
-0.006935261655598879,
0.0391308069229126,
0.03315533325076103,
0.05666070058941841,
-0.005127443931996822,
0.060779035091400146,
0.020327236503362656,
0.008392153307795525,
-0.02825457602739334,
-0.0071827080100774765,
-0.008547879755496979,
-0.013950454071164131,
0.11913570016622543,
-0.03842102363705635,
-0.016221407800912857,
0.0013600160600617528,
-0.03062511421740055,
-0.012344030663371086,
0.009294774383306503,
0.02406117133796215,
0.029954491183161736,
-0.01912591978907585,
0.01998438872396946,
-0.06925039738416672,
0.01077368576079607,
0.05994846299290657,
-0.03424093499779701,
-0.0399564765393734,
0.012917163781821728,
0.03193916752934456,
0.019884837791323662,
-0.001211304566822946,
0.017213985323905945,
-0.08083703368902206,
-0.0006479900912381709,
-0.051504384726285934,
0.06761009246110916,
-0.02109340950846672,
0.030180368572473526,
-0.004401701502501965,
0.0042067780159413815,
-0.0449964664876461,
0.06355059891939163,
0.005690046586096287,
0.05891401693224907,
-0.02885996177792549,
0.03207416459918022,
0.018864085897803307,
-0.012705623172223568,
-0.012883154675364494,
-0.07348527014255524,
0.012196145951747894,
-0.03029162995517254,
-0.05753654986619949,
0.05370466783642769,
0.01590237021446228,
0.008774921298027039,
0.007110638543963432,
-0.041909147053956985,
0.03724592924118042,
-0.021996978670358658,
0.03664402663707733,
0.020277000963687897,
0.008972962386906147,
-0.02842765860259533,
-0.0378677174448967,
-0.00556821096688509,
0.056265417486429214,
-0.017394067719578743,
0.019343562424182892,
-0.048785071820020676,
0.007739684544503689,
0.08047284185886383,
-0.01598362624645233,
-0.040730010718107224,
-0.022252866998314857,
-0.012723413296043873,
0.0033154678530991077,
0.0055626146495342255,
-0.0027895814273506403,
0.04356081411242485,
0.008007257245481014,
-0.018810942769050598,
-0.04325225204229355,
0.055975694209337234,
0.011331193149089813,
0.003405543277040124,
0.03568888455629349,
0.03260231018066406,
-0.0009760548709891737,
-0.016621388494968414,
0.020665280520915985,
-0.0570884570479393,
-0.08184336870908737,
-0.0003655940236058086,
-0.013871151953935623,
-0.024869142100214958,
0.006851733662188053,
-0.035924479365348816,
-0.033298734575510025,
0.03163113445043564,
0.08673878014087677,
-0.012371162883937359,
0.04569999501109123,
-0.03905189409852028,
-0.002571949502453208,
-0.026284413412213326,
0.0028717834502458572,
-0.03622058406472206,
-0.02917698584496975,
0.014888782054185867,
-0.01613043062388897,
0.067461758852005,
-0.030112139880657196,
-0.03518066555261612,
0.0024737087078392506,
-0.015467364341020584,
0.01915004476904869,
-0.07988198101520538,
-0.03502647578716278,
0.02240973897278309,
0.0034722110722213984,
0.02878328040242195,
-0.028506513684988022,
0.018001588061451912,
-0.025742247700691223,
-0.03801312297582626,
0.07400085031986237,
-0.057547491043806076,
-0.010981446132063866,
-0.05566861480474472,
-0.014163373038172722,
-0.011874377727508545,
-0.04464362561702728,
-0.022982282564044,
0.005532820709049702,
0.10128983110189438,
-0.04079039394855499,
-0.013012002222239971,
-0.017518023028969765,
-0.009339040145277977,
0.04033290594816208,
-0.04091408848762512,
-0.03842977061867714,
0.011908290907740593,
0.01602126844227314,
-0.0003597194154281169,
-0.004646788816899061,
0.008771223947405815,
-0.01005141157656908,
0.013945750892162323,
-0.027370233088731766,
0.035353899002075195,
-0.012868398800492287,
-0.10293856263160706,
-0.04052785038948059,
-0.0217431727796793,
0.040494758635759354,
-0.06536255031824112,
-0.0638267993927002,
-0.011156119406223297,
-0.007832189090549946,
0.0013688966864719987,
0.038992758840322495,
-0.02077179029583931,
-0.03109775111079216,
0.017613785341382027,
0.0387948676943779,
0.01033573318272829,
-0.04600364342331886,
-0.029514532536268234,
-0.008575658313930035,
0.030981965363025665,
-0.008424818515777588,
0.0034288624301552773,
0.0181308351457119,
-0.022119272500276566,
0.05007120594382286,
0.0057906657457351685,
0.027846232056617737,
-0.025827374309301376,
0.004300679080188274,
0.019794929772615433,
0.0014525441220030189,
0.07218695431947708,
0.006632874719798565,
-0.039460595697164536,
-0.04461841285228729,
-0.022565117105841637,
-0.06450580805540085,
0.03703717514872551,
-0.047244369983673096,
-0.03117990493774414,
-0.011937798000872135,
-0.0673617422580719,
0.03117372840642929,
-0.06482541561126709,
0.030669428408145905,
-0.0011703104246407747,
0.031256332993507385,
0.019731441512703896,
-0.009766781702637672,
0.001539723132736981,
-0.0017103501595556736,
-0.02961999922990799,
0.01011683139950037,
0.012636270374059677,
-0.003829072928056121,
-0.008093075826764107,
0.021360209211707115,
0.014249834232032299,
-0.044652607291936874,
0.04278238117694855,
0.0010654873913154006,
0.005921363364905119,
0.0018747359281405807,
0.03750056400895119,
0.045707184821367264,
-0.04676308482885361,
-0.0674501359462738,
0.02449149452149868,
0.009216779842972755,
-0.015604685060679913,
0.022184353321790695,
0.008393540978431702,
-0.023304712027311325,
0.020996183156967163,
0.08462384343147278,
0.027005856856703758,
-0.027500424534082413,
0.007918721996247768,
0.007144287694245577,
0.022861165925860405,
-0.04075431823730469,
0.013434925116598606,
0.06476520001888275,
-0.017741672694683075,
0.005975726991891861,
0.02552606165409088,
0.07533260434865952,
0.02135634608566761,
0.028166113421320915,
0.016312019899487495,
0.012000205926597118,
-0.007551989052444696,
0.04237229749560356,
0.006924566812813282,
-0.01078882347792387,
-0.030171481892466545,
0.046976324170827866,
-0.007440999150276184,
-0.04025406762957573,
0.020143242552876472,
0.05493716150522232,
-0.019811637699604034,
-0.008152446709573269,
-0.017328009009361267,
-0.006326423026621342,
-0.043719127774238586,
-0.009661144576966763,
-0.051924895495176315,
-0.00006743210542481393,
-0.018450506031513214,
0.005376768764108419,
-0.02553325518965721,
0.030926300212740898,
0.05017291381955147,
0.044945381581783295,
-0.027835849672555923,
-0.0018504424951970577,
-0.05908765643835068,
0.002425889251753688,
0.024677425622940063,
-0.04617449641227722,
-0.049451135098934174,
-0.005091024097055197,
-0.014625495299696922,
0.017930153757333755,
0.04723905026912689,
-0.010630111210048199,
-0.003894590074196458,
-0.06525938212871552,
-0.014909203164279461,
0.05281638354063034,
-0.048414379358291626,
0.056141626089811325,
0.038857217878103256,
-0.02745029143989086,
0.011651057749986649,
0.05286485329270363,
0.015455988235771656,
-0.05479490011930466,
0.0034755778033286333,
0.00969984382390976,
-0.05611720308661461,
0.017447229474782944,
0.07062491029500961,
0.0031252135522663593,
-0.00943715963512659,
0.045611318200826645,
-0.06547348946332932,
-0.014190045185387135,
0.08885074406862259,
-0.016740258783102036,
0.012468035332858562,
0.07316005975008011,
-0.07109276205301285,
0.06585287302732468,
0.020616112276911736,
-0.035720232874155045,
0.005281850695610046,
-0.0009731602622196078,
0.023750267922878265,
0.02908448688685894,
-0.03513509780168533,
-0.04978259280323982,
-0.021415777504444122,
-0.04142941161990166,
-0.031826287508010864,
0.0314439982175827,
-0.01686030626296997,
-0.04022714123129845,
-0.033799368888139725,
-0.0518217496573925,
0.00747788418084383,
0.026655418798327446,
-0.003288562875241041,
0.0019646722357720137,
-0.025308355689048767,
-0.01660122163593769,
-0.016258539631962776,
-0.05403025820851326,
-0.004323531407862902,
0.004708665423095226,
0.002736723283305764,
0.02226587012410164,
-0.0000958994569373317,
0.0033576330170035362,
0.01005113497376442,
0.06643826514482498,
0.012091231532394886,
-0.08175639063119888,
-0.01418979000300169,
-0.02603059634566307,
-0.011907977983355522,
0.013781524263322353,
-0.017585724592208862,
-0.0015494542894884944,
0.06970290839672089,
-0.02325223945081234,
-0.04288092255592346,
0.01994156651198864,
-0.005399856250733137,
0.05240948498249054,
-0.042726561427116394,
-0.026034947484731674,
-0.00248327455483377,
0.008827208541333675,
0.06663742661476135,
-0.008211295120418072,
-0.009096027351915836,
-0.011952828615903854,
0.013163615018129349,
0.04803502932190895,
-0.0073529742658138275,
0.05357958748936653,
0.04916828125715256,
0.05311992019414902,
0.09193550795316696,
-0.033152468502521515,
-0.005505767650902271,
0.009910525754094124,
0.03525325283408165,
0.031605951488018036,
0.006329074501991272,
-0.056450579315423965,
-0.012103566899895668,
0.021022140979766846,
-0.03839196637272835,
-0.07506439089775085,
-0.08104745298624039,
0.028265589848160744,
-0.0025524639058858156,
-0.06445733457803726,
-0.047642916440963745,
-0.005019685719162226,
0.00779232382774353,
0.03148283809423447,
-0.06470108032226562,
0.006030615419149399,
-0.04799043759703636,
0.041815999895334244,
0.04533069208264351,
-0.0036490338388830423,
0.030446307733654976,
-0.000508094672113657,
-0.07356362789869308,
0.0017174046952277422,
-0.05883407220244408,
0.09448689222335815,
0.06584062427282333,
0.016035938635468483,
-0.005956502631306648,
-0.08257502317428589,
0.001426072558388114,
-0.046972278505563736,
0.005577329080551863,
0.02640078030526638,
-0.060449786484241486,
-0.029157262295484543,
0.03309358283877373,
-0.04060535132884979,
-0.03935553878545761,
0.06314399093389511,
-0.02878701500594616,
0.036496471613645554,
0.02461560256779194,
0.00007416228618239984,
0.060020748525857925,
-0.01988888531923294,
0.04242638871073723,
-0.01889294944703579,
0.03368881717324257,
-0.03592127561569214,
0.028668876737356186,
0.008237075991928577,
0.012099167332053185,
0.014676336199045181,
-0.05438339710235596,
-0.007556977216154337,
-0.022205578163266182,
0.021589523181319237,
-0.002530452096834779,
0.09277249872684479,
0.07474777847528458,
-0.014548483304679394,
-0.0076915062963962555,
-0.0056424858048558235,
-0.0028147660195827484,
-0.046854376792907715,
0.050727467983961105,
0.021967027336359024,
0.01967727020382881,
-0.018827559426426888,
-0.04915263503789902,
0.001544256112538278,
-0.030296998098492622,
0.0340024009346962,
0.04173377528786659,
-0.037639956921339035,
-0.05185389891266823,
-0.021299362182617188,
-0.041622620075941086,
-0.008610167540609837,
-0.005123930051922798,
-0.06233307719230652,
0.008115412667393684,
0.0024277677293866873,
0.039317939430475235,
-0.05555202066898346,
0.08016388863325119,
0.02235967293381691,
-0.004413780756294727,
-0.04839043319225311,
-0.016024643555283546,
0.032734617590904236,
-0.011541672050952911,
-0.0020965533331036568,
0.0059042987413704395,
0.011616230010986328,
0.02247854880988598,
0.07140817493200302,
0.015045451931655407,
0.026287229731678963,
0.0027698471676558256,
-0.002066347748041153,
0.05643366649746895,
0.03911013901233673,
-0.022252971306443214,
0.051543641835451126,
0.014090840704739094,
0.09597202390432358,
0.026201114058494568,
-0.02529734931886196,
-0.006114097312092781,
0.029829243198037148,
-0.030491426587104797,
0.016834333539009094,
0.008873922750353813,
0.08069895207881927,
-0.028878187760710716,
0.0056969099678099155,
0.001604827935807407,
-0.058383457362651825,
-0.0339069627225399,
-0.004768738057464361,
0.04534527659416199,
0.02044304646551609,
0.005076274275779724,
0.03069004788994789,
0.014341733418405056,
0.06312098354101181,
0.026516657322645187,
-0.02161417528986931,
0.0037135297898203135,
0.0003065417695324868,
0.05066779628396034,
-0.06450166553258896,
-0.003079100977629423,
0.029786454513669014,
-0.018641183152794838,
-0.06826969236135483,
0.03803011029958725,
0.03804567828774452,
0.00952636543661356,
-0.007821055129170418,
0.03832519054412842,
0.0031185478437691927,
-0.00409003347158432,
0.005819346755743027,
0.009260866791009903,
0.0044865976087749004,
0.036875005811452866,
-0.03261866793036461,
-0.023543382063508034,
0.012401117943227291,
-0.026590993627905846,
-0.06363358348608017,
0.045986637473106384,
-0.017097987234592438,
0.025889158248901367,
0.05008349567651749,
0.002980763791128993,
0.05966132879257202,
-0.03093917854130268,
0.03551851585507393,
-0.0173275638371706,
0.06386476755142212,
0.02525070682168007,
0.02567439153790474,
0.0007100396906025708,
-0.04780671373009682,
-0.01925167255103588,
-0.06679502874612808,
0.021262196823954582,
-0.013397032395005226,
-0.0312979631125927,
0.0013674687361344695,
0.017214063555002213,
-0.025798439979553223,
-0.09386803954839706,
-0.034044720232486725,
0.012991921976208687,
0.07439582794904709,
-0.04408877715468407,
0.04768472909927368,
0.04515615850687027,
0.04831647127866745,
-0.056554198265075684,
0.03735143318772316,
0.06950244307518005,
0.018321486189961433,
0.020490247756242752,
-0.01260883267968893,
-0.042763929814100266,
-0.052632853388786316,
-0.0020656229462474585,
0.004710229113698006,
-0.014853565953671932,
-0.06209399923682213,
0.011802050285041332,
0.013440420851111412,
0.0418698824942112,
0.04092134162783623,
0.0368783175945282,
-0.01648157648742199,
0.00439060153439641,
-0.004286957439035177,
0.0024281947407871485,
-0.074118971824646,
0.043098084628582,
-0.006333025172352791,
-0.009424555115401745,
-0.019780516624450684,
-0.04650351032614708,
-0.02495862916111946,
0.021538935601711273,
0.03429434821009636,
-0.059215664863586426,
0.03674950823187828,
-0.018510570749640465,
0.008732866495847702,
-0.0032845796085894108,
0.006557842250913382,
0.014476105570793152,
-0.07059648633003235,
-0.00712532689794898,
-0.007793005555868149,
-0.014855604618787766,
-0.018900347873568535,
0.023018773645162582,
-0.04155483841896057,
-0.007829342037439346,
-0.04645824059844017,
-0.017912324517965317,
0.01964670419692993,
0.01300529483705759,
0.032097380608320236,
0.0027817680966109037,
0.06154436618089676,
0.006175042130053043,
0.023897921666502953,
-0.03646392747759819,
0.01166413351893425,
0.019103217869997025,
-0.044133320450782776,
-0.05707879737019539,
0.049095503985881805,
-0.007590906694531441,
-0.03824228420853615,
-0.0090990224853158,
-0.09046348184347153,
0.029400747269392014,
0.050235796719789505,
-0.02162274532020092,
-0.02429862879216671,
-0.023542551323771477,
-0.008361347019672394,
-0.017203377559781075,
-0.002019356470555067,
-0.07832489907741547,
-0.03756263479590416,
0.027418265119194984,
0.046787988394498825,
0.012380030937492847,
0.025170600041747093,
0.006527781020849943,
0.036025822162628174,
-0.031242473050951958,
0.05379465967416763,
0.05158611387014389,
0.0504700168967247,
0.032999955117702484,
-0.01205909438431263,
-0.047419674694538116,
-0.026999803259968758,
0.016115723177790642,
-0.030786436051130295,
0.0020764595828950405,
-0.05064978450536728,
-0.03357510268688202,
0.043911371380090714,
-0.02420150861144066,
0.009682740084826946,
-0.0036812264006584883,
-0.004686783999204636,
-0.009326212108135223,
0.056284427642822266,
-0.03096507489681244,
-0.031180767342448235,
-0.012496983632445335,
-0.06248628348112106,
-0.07399304211139679,
-0.024536291137337685,
0.007022761274129152,
-0.022462159395217896,
-0.00991183053702116,
-0.010333959013223648,
0.037191130220890045,
-0.01633421517908573,
0.011539625003933907,
-0.02577526681125164,
-0.009234698489308357,
0.0021129280794411898,
-0.03510857746005058,
-0.035783398896455765,
0.0030382690019905567,
0.025466114282608032,
-0.02714180201292038,
0.03294868394732475,
-0.00790996104478836,
0.025712143629789352,
0.0406552292406559,
-0.019866596907377243,
0.03387175127863884,
0.01780536398291588,
-0.027025990188121796,
-0.033680081367492676,
-0.008710662834346294,
-0.030390417203307152,
-0.02887727878987789,
0.01991642452776432,
0.012842085212469101,
0.004804499447345734,
-0.01420650165528059,
-0.06791777163743973
] |
<p>The derivation for Heat Equation I am reading starts by stating </p>
<p>Net change of heat inside $[x,x+\Delta x]$ = Net flux of heat across boundaries + Total heat generated inside $[x,x+\Delta x]$ and writes the conservation equation</p>
<p>$$\textit{Total Heat Inside} [x,x+\Delta x]=
cpA \int _{ x}^{x+\Delta x}u(s,t) ds
$$</p>
<p>and later equates net flux across the boundary with</p>
<p>$u_x(x+\Delta x,t) - u_x(x,t)$,</p>
<p>so the heat flow is proportional to the spatial gradient of temperature at both ends. What I dont understand is why is net flux proportional to the spatial gradient, why cant we use the temparature variable $u$ itself to measure the difference? If the temparature difference at both ends is high, then we would expect higher flow from high temparature to low, right? What would be the physical intuition behind this? Was this model arrived at by experimentation?</p>
<p><img src="http://i.stack.imgur.com/d5On3.png" alt="enter image description here"></p> | g4621 | [
0.04308919981122017,
-0.07144547998905182,
-0.0365966334939003,
0.0028319410048425198,
0.03607326000928879,
0.041194479912519455,
0.07690085470676422,
0.06435807794332504,
-0.08644607663154602,
-0.016285141929984093,
-0.04630056768655777,
0.05490083247423172,
0.06302197277545929,
0.03121531940996647,
-0.009623263031244278,
-0.005205776542425156,
0.027909494936466217,
-0.014146536588668823,
0.05006725341081619,
0.03575362265110016,
-0.04923126846551895,
-0.0063256267458200455,
0.029919184744358063,
-0.03562142699956894,
-0.021357610821723938,
-0.020758481696248055,
-0.00955271627753973,
0.0023386843968182802,
-0.027961352840065956,
0.022955911234021187,
0.02185993455350399,
0.007809288799762726,
0.06491613388061523,
-0.04052312672138214,
-0.07109683007001877,
0.010822800919413567,
0.012066741473972797,
0.08229856193065643,
0.03403939679265022,
-0.024590786546468735,
0.02872159518301487,
0.005790126975625753,
0.027593892067670822,
-0.014476439915597439,
-0.04760975018143654,
-0.037096068263053894,
-0.06102362647652626,
-0.026115214452147484,
-0.02958553470671177,
0.04164433106780052,
-0.0035269588697701693,
0.029255496338009834,
-0.0073603978380560875,
-0.0185175072401762,
-0.013444995507597923,
-0.0008780370699241757,
0.023744232952594757,
-0.048484720289707184,
0.0034883839543908834,
0.02677857130765915,
0.05251855030655861,
0.03799654543399811,
-0.04215388372540474,
0.04060274735093117,
0.03603075444698334,
-0.028119642287492752,
-0.029795892536640167,
0.0022128114942461252,
-0.045793332159519196,
0.03364454582333565,
0.01610446721315384,
0.028511689975857735,
-0.00265056942589581,
-0.04313625395298004,
-0.024034757167100906,
-0.005565132945775986,
-0.009448282420635223,
-0.054289236664772034,
-0.002866319613531232,
-0.032858435064554214,
0.0034611502196639776,
0.031621575355529785,
0.012885788455605507,
0.053667180240154266,
0.04393523186445236,
0.015471942722797394,
-0.0031677926890552044,
0.018310416489839554,
-0.06256613880395889,
0.021174483001232147,
-0.0043923938646912575,
0.014735718257725239,
0.09971959888935089,
0.015730490908026695,
-0.006919491104781628,
-0.008536460809409618,
0.013876612298190594,
-0.005051848012953997,
0.016969213262200356,
-0.014584220014512539,
0.004199364688247442,
0.03517016023397446,
0.017276454716920853,
0.008368575014173985,
-0.029291993007063866,
0.001928232260979712,
0.0074922554194927216,
0.041175685822963715,
-0.05216240882873535,
-0.019570110365748405,
0.022112209349870682,
0.002671400085091591,
-0.11683900654315948,
0.06227589398622513,
-0.006580563262104988,
-0.0071774134412407875,
0.006309935357421637,
-0.0046720909886062145,
0.0034656624775379896,
0.009759321808815002,
0.00780480494722724,
-0.0018475198885425925,
-0.005354844965040684,
0.06582140922546387,
-0.0004574325284920633,
0.03776911273598671,
0.016025463119149208,
0.003508178982883692,
0.027822982519865036,
0.03410293906927109,
0.002177942544221878,
-0.014122635126113892,
-0.049377840012311935,
0.041524212807416916,
0.06656035780906677,
-0.006335499230772257,
-0.041480012238025665,
0.016862355172634125,
-0.017892759293317795,
0.02527450956404209,
-0.029790012165904045,
-0.01350168976932764,
-0.025393670424818993,
-0.04761310666799545,
-0.027386855334043503,
0.07068696618080139,
-0.005990660283714533,
-0.01221609115600586,
0.057476840913295746,
-0.08392160385847092,
0.04789339751005173,
0.1119731143116951,
-0.004093215800821781,
-0.014926942996680737,
-0.031941600143909454,
-0.011339780874550343,
0.03448224067687988,
-0.00886425469070673,
0.012268620543181896,
-0.06040560081601143,
0.013955737464129925,
0.0232151597738266,
0.06780482083559036,
-0.006060069426894188,
-0.06542454659938812,
-0.02146158367395401,
-0.018773570656776428,
-0.03998437896370888,
-0.005658869165927172,
-0.029199618846178055,
-0.03916899859905243,
0.014997662045061588,
0.002101555932313204,
-0.0291824322193861,
-0.007287974003702402,
0.07074413448572159,
0.038025688380002975,
0.009931190870702267,
0.03199649974703789,
-0.025302881374955177,
-0.02777455374598503,
0.01834418997168541,
0.08067715167999268,
-0.06146933138370514,
0.027860891073942184,
0.0007902473444119096,
0.0024945498444139957,
-0.017362287268042564,
-0.043655574321746826,
-0.029536770656704903,
0.01571771316230297,
-0.04925065115094185,
-0.005286738742142916,
0.0273616723716259,
0.013718925416469574,
0.018426256254315376,
0.014594240114092827,
-0.07692833989858627,
-0.04565652832388878,
0.0606413334608078,
-0.057044658809900284,
0.01826738938689232,
0.057762499898672104,
-0.020571310073137283,
-0.027395304292440414,
0.007344776298850775,
-0.007355821784585714,
-0.012229646556079388,
0.01967245526611805,
0.030129535123705864,
-0.02325204759836197,
-0.012701255269348621,
-0.0025046970695257187,
0.007356420159339905,
-0.005410155281424522,
0.009180338121950626,
0.035165175795555115,
-0.03725235536694527,
-0.035009901970624924,
-0.038029745221138,
-0.05042136833071709,
-0.031698863953351974,
0.010370480827987194,
-0.02472267486155033,
-0.11198824644088745,
0.012697909027338028,
-0.006031987722963095,
-0.00003105024734395556,
-0.035063594579696655,
0.06789232790470123,
-0.00885892752557993,
0.00014156888937577605,
0.020503466948866844,
-0.010108436457812786,
0.015881327912211418,
0.02726643718779087,
0.044994838535785675,
0.00893398467451334,
-0.02884608507156372,
0.02534172497689724,
0.029161548241972923,
-0.04736845940351486,
-0.03674115985631943,
0.0879572331905365,
0.0020388346165418625,
0.010243258439004421,
0.010859957896173,
0.025540873408317566,
-0.0275371503084898,
-0.029033944010734558,
0.019992392510175705,
0.005756635218858719,
0.049857400357723236,
-0.009565460495650768,
0.018523825332522392,
-0.03936608135700226,
-0.03321556746959686,
0.003805504646152258,
-0.02808520384132862,
-0.03388768434524536,
-0.035847920924425125,
-0.028797293081879616,
0.028966322541236877,
0.036674343049526215,
0.0009760374668985605,
-0.04039742797613144,
0.010082695633172989,
0.008976912125945091,
0.07051418721675873,
-0.007725891657173634,
0.011751171201467514,
0.03587307035923004,
-0.01107859332114458,
0.0194554403424263,
0.015567654743790627,
-0.0063386340625584126,
0.02081024833023548,
-0.028208445757627487,
0.04472044110298157,
-0.04770367592573166,
0.014721937477588654,
0.008295661769807339,
-0.011549405753612518,
0.029134541749954224,
0.0813324898481369,
-0.07803210616111755,
-0.0034101419150829315,
-0.0073801795952022076,
-0.016047801822423935,
0.005095444619655609,
-0.000507946009747684,
-0.015178448520600796,
-0.006149590015411377,
-0.029066123068332672,
0.06655065715312958,
-0.045858703553676605,
0.027406087145209312,
-0.051257580518722534,
0.019200140610337257,
-0.022316453978419304,
-0.010614327155053616,
-0.004637648351490498,
-0.0018415767699480057,
0.007277868688106537,
-0.01445695199072361,
0.039710987359285355,
-0.06664187461137772,
-0.02836596965789795,
-0.013019769452512264,
-0.009610195644199848,
0.01880732551217079,
-0.03130670264363289,
0.028975959867239,
-0.05476904660463333,
-0.011279483325779438,
-0.041386354714632034,
-0.027677107602357864,
0.0009926063939929008,
0.0011416322086006403,
0.018360665068030357,
-0.022188883274793625,
-0.031715672463178635,
-0.00847137812525034,
0.02199399471282959,
-0.00853723380714655,
-0.014812810346484184,
-0.03650150075554848,
-0.04680010303854942,
-0.0303619634360075,
-0.0362449549138546,
-0.0007217810489237309,
-0.005400225054472685,
0.00086741812992841,
-0.002178169321268797,
0.008123028092086315,
-0.020014433190226555,
-0.01800885796546936,
-0.0020585565362125635,
0.024939149618148804,
0.005354440305382013,
-0.017637990415096283,
-0.03312485292553902,
-0.06436213105916977,
0.022110717371106148,
-0.0024647703394293785,
0.001893961918540299,
0.009895511902868748,
0.018633192405104637,
-0.002778096590191126,
0.00492843659594655,
0.019008640199899673,
-0.007151584606617689,
0.010909633710980415,
-0.028522588312625885,
-0.033023651689291,
0.028962325304746628,
0.04152790457010269,
0.04550529271364212,
0.020782876759767532,
0.058343153446912766,
0.056279417127370834,
-0.0036734750028699636,
0.013776558451354504,
-0.017410440370440483,
-0.0354464165866375,
0.046884387731552124,
0.11224416643381119,
-0.04071841761469841,
-0.05233503133058548,
-0.04794800654053688,
-0.021530402824282646,
0.01934756524860859,
-0.07684485614299774,
-0.03163411095738411,
0.07083594799041748,
-0.021714217960834503,
0.05051422864198685,
0.006471801549196243,
-0.03544529899954796,
0.014324692077934742,
0.032488591969013214,
0.0076130833476781845,
0.018039660528302193,
0.02664840966463089,
0.03137640655040741,
-0.00036653230199590325,
-0.010483471676707268,
0.008767901919782162,
-0.030780471861362457,
-0.04427047818899155,
-0.017078673467040062,
-0.0024499439168721437,
-0.010296560823917389,
-0.00022841164900455624,
-0.008531270548701286,
0.041906461119651794,
-0.005305839236825705,
0.032633811235427856,
-0.02452315203845501,
-0.014412859454751015,
-0.006887094117701054,
-0.02722751721739769,
-0.009366032667458057,
-0.020245270803570747,
-0.04883016645908356,
-0.055697083473205566,
0.03635270148515701,
0.013648591935634613,
-0.046154800802469254,
-0.027447139844298363,
-0.014382423833012581,
-0.04678779095411301,
0.005275729577988386,
-0.04469049721956253,
0.0025597636122256517,
-0.042803678661584854,
0.022820444777607918,
0.010809280909597874,
0.06281928718090057,
-0.02633471041917801,
0.0514795184135437,
-0.020516930148005486,
0.006516619585454464,
0.03451460599899292,
0.045979782938957214,
0.09927835315465927,
0.04098156839609146,
0.023023420944809914,
0.022416790947318077,
-0.05709846690297127,
-0.050139881670475006,
0.04332423955202103,
-0.022167330607771873,
0.05431924760341644,
-0.0631643533706665,
0.0750940591096878,
-0.04201208055019379,
0.05527198314666748,
-0.031657177954912186,
0.004401171579957008,
0.02390473149716854,
0.041719626635313034,
0.0060946340672671795,
-0.009276090189814568,
0.031633250415325165,
0.0243127029389143,
0.03581904619932175,
-0.055135805159807205,
-0.04170568659901619,
-0.07310082763433456,
-0.03568316251039505,
0.07670146971940994,
-0.0299027431756258,
0.018136585131287575,
-0.014120672829449177,
-0.01770702190697193,
0.01954828016459942,
-0.0012541583273559809,
-0.008111181668937206,
-0.0031349388882517815,
-0.05564846843481064,
-0.006406981032341719,
-0.036443840712308884,
0.003478151746094227,
0.05375951901078224,
-0.05465565249323845,
-0.027348630130290985,
0.017926236614584923,
0.0333186499774456,
0.01526118628680706,
0.02785436436533928,
0.048308033496141434,
0.010008350946009159,
0.02417229488492012,
0.06788410991430283,
0.028316346928477287,
-0.0006048797513358295,
-0.047380514442920685,
0.03211955353617668,
-0.04888175055384636,
-0.014314649626612663,
0.041755568236112595,
0.045103300362825394,
0.059658233076334,
0.02138473652303219,
-0.024566885083913803,
-0.0983872190117836,
-0.022218404337763786,
0.08110528439283371,
-0.03150958940386772,
0.0036950428038835526,
-0.01645561307668686,
0.019156944006681442,
0.04013373330235481,
-0.029298583045601845,
-0.016006289049983025,
0.0045328885316848755,
-0.03725304454565048,
0.02641800045967102,
-0.03627411648631096,
-0.07132019847631454,
0.07231031358242035,
-0.051145248115062714,
0.02545715868473053,
0.05788597837090492,
0.06357277929782867,
0.00913558155298233,
-0.002063947031274438,
0.024851500988006592,
0.013133852742612362,
0.014245282858610153,
0.0021151460241526365,
-0.020601151511073112,
-0.03816326707601547,
0.022921845316886902,
-0.035592641681432724,
0.07034730911254883,
-0.03517778217792511,
0.008349034935235977,
-0.028590617701411247,
0.05858330801129341,
0.019186347723007202,
0.020171698182821274,
-0.0034310887567698956,
0.04871927946805954,
-0.0035660930443555117,
-0.033680252730846405,
-0.02833130955696106,
-0.0037398161366581917,
-0.016856225207448006,
-0.025445949286222458,
0.0468776561319828,
-0.021770067512989044,
0.04294880852103233,
-0.047587309032678604,
0.001131438068114221,
-0.0006855733226984739,
0.0037953227292746305,
0.025718871504068375,
-0.033909182995557785,
0.01292084064334631,
-0.06415172666311264,
-0.008201584219932556,
0.0747094675898552,
0.053870443254709244,
0.015508705750107765,
-0.043000705540180206,
-0.024645373225212097,
-0.024790113791823387,
-0.004287482239305973,
-0.006334531586617231,
0.0036971040535718203,
0.005154730752110481,
-0.03432925045490265,
0.013617899268865585,
-0.00460605276748538,
-0.0012024017050862312,
-0.027099603787064552,
0.041594669222831726,
0.005544758401811123,
0.017935888841748238,
0.020463857799768448,
0.02063835598528385,
0.025219593197107315,
0.020524276420474052,
-0.05748981609940529,
-0.025634225457906723,
0.03366154804825783,
0.05341923236846924,
-0.007496409583836794,
0.014459202066063881,
-0.02019084244966507,
-0.007925309240818024,
-0.0008028203737922013,
0.022019997239112854,
0.014897018671035767,
-0.021827489137649536,
-0.017598170787096024,
-0.044394925236701965,
-0.03209858015179634,
0.0033278632909059525,
-0.04300519824028015,
-0.020392421633005142,
-0.05029543861746788,
0.0046676709316670895,
0.003196926321834326,
-0.05788423866033554,
0.028990115970373154,
0.0503421388566494,
0.016735196113586426,
-0.024777481332421303,
-0.047950971871614456,
0.03215077519416809,
0.04489312320947647,
0.02790950983762741,
-0.00438058702275157,
0.02706574648618698,
0.021577978506684303,
-0.03508378937840462,
-0.021060597151517868,
-0.000907515175640583,
0.01307598315179348,
0.03000493347644806,
-0.06179291382431984,
-0.0062485346570611,
0.032995156943798065,
0.06461445987224579,
0.025148088112473488,
-0.016744663938879967,
0.04532921314239502,
0.023727286607027054,
0.0636015459895134,
0.07156684249639511,
0.027833381667733192,
-0.006785096600651741,
-0.021052993834018707,
-0.03112093172967434,
0.03810346499085426,
0.005066134501248598,
-0.012314110063016415,
-0.041885167360305786,
-0.015018303878605366,
0.034258998930454254,
-0.008891068398952484,
0.0877406969666481,
0.05704357102513313,
-0.047362808138132095,
0.08718585222959518,
0.013997047208249569,
0.04134407266974449,
-0.017009364441037178,
0.03433885797858238,
-0.053685929626226425,
0.0479186587035656,
-0.029941484332084656,
-0.017016470432281494,
0.010751888155937195,
0.01102881133556366,
0.05022263899445534,
0.016682295128703117,
-0.04271448403596878,
-0.01562950760126114,
0.004491074476391077,
0.004987508058547974,
-0.035154059529304504,
0.032711535692214966,
-0.04207534343004227,
-0.035728033632040024,
-0.10211419314146042,
0.033191751688718796,
0.0007824392523616552,
0.013840093277394772,
-0.08668279647827148,
-0.03759685158729553,
0.00555372005328536,
0.02277628891170025,
-0.022636007517576218,
0.014871833845973015,
-0.00291452556848526,
-0.010880808345973492,
0.006257469300180674,
-0.10346587747335434,
0.00901073683053255,
0.08167553693056107,
0.09469780325889587,
0.049049630761146545,
0.02477005124092102,
-0.05026602745056152,
0.07201513648033142,
-0.03586893528699875,
0.01976725086569786,
-0.04748648777604103,
-0.0065993559546768665,
0.052126046270132065,
-0.011927323415875435,
0.030670499429106712,
-0.0006855159299448133,
0.01722794584929943,
0.012130938470363617,
-0.0025726761668920517,
0.028360724449157715,
-0.008747522719204426,
0.03655929118394852,
-0.061154820024967194,
-0.04118739068508148,
-0.014969580806791782,
0.008200980722904205,
-0.014208823442459106,
0.008260498754680157,
-0.0141036007553339,
-0.04369227588176727,
0.033623598515987396,
0.06348428130149841,
0.01097799837589264,
-0.0004678511177189648,
0.07838309556245804,
-0.01099584810435772,
0.0258906502276659,
0.011377728544175625,
-0.011600763536989689,
0.038124021142721176,
-0.05246526375412941,
0.013369619846343994,
-0.010769596323370934,
0.0254816897213459,
0.023408500477671623,
-0.004770186729729176,
0.004382371436804533,
-0.012986690737307072,
-0.03239323943853378,
0.035749971866607666,
0.019714759662747383,
0.06942832469940186,
0.043983232229948044,
-0.0017114134971052408,
-0.03352779150009155,
-0.05931152030825615,
-0.05418403446674347,
-0.038115665316581726,
-0.06263270974159241,
-0.010237039066851139,
-0.0517866276204586,
-0.04249229654669762,
-0.09824192523956299,
-0.018031993880867958,
-0.034256499260663986,
-0.0040090931579470634,
-0.07488635927438736,
0.031155357137322426,
-0.021904727444052696,
-0.026886479929089546,
0.04017338901758194,
-0.05066043883562088,
-0.03990959748625755,
0.003530514193698764,
0.01831226795911789,
0.019757788628339767,
0.0011837980709969997,
0.06587591767311096,
-0.010374781675636768,
0.004881133791059256,
-0.0451202467083931,
0.017825346440076828,
-0.04385541006922722,
-0.041152406483888626,
0.013035831972956657,
-0.04322642832994461,
0.02870057336986065,
-0.02815399505198002,
-0.040053799748420715,
0.050523459911346436,
-0.030067024752497673,
-0.04460252821445465,
0.034291867166757584,
0.04661130532622337,
-0.06857885420322418,
-0.028001023456454277,
-0.005947710946202278,
-0.0008750986307859421,
0.00693468376994133,
-0.05329744890332222,
-0.042495980858802795,
0.0071580009534955025,
0.0062318905256688595,
0.027041925117373466,
-0.012946032918989658,
-0.004053747281432152,
-0.00957286823540926
] |
<p>I am still struggling with C being a constant and what that implies.
So can an experiment be done to find the resting state for the universe?
Take a device with an observer and a light source and two mirrors, one 10 meters in front and the other 10 meters behind the light source. Now move this through space at some speed. Can’t you determine your speed by using the red/blue shift from the light reflected by the mirrors? Will this allow you to find the resting reference for the entire universe?</p> | g4622 | [
0.01250989269465208,
-0.009523492306470871,
-0.004649917129427195,
-0.04214229807257652,
0.039993517100811005,
-0.005733252968639135,
0.06406836956739426,
0.04925325885415077,
-0.04017074406147003,
-0.04823163524270058,
0.022830620408058167,
-0.020529400557279587,
-0.009402243420481682,
0.017198074609041214,
-0.00772474892437458,
-0.021684395149350166,
0.03381262347102165,
-0.019812559708952904,
0.04829628765583038,
-0.03079473227262497,
-0.035216666758060455,
0.026576336473226547,
-0.04299138858914375,
-0.0512879379093647,
-0.013070928864181042,
0.03324351832270622,
-0.002437485149130225,
-0.017660921439528465,
-0.06146644428372383,
-0.018392855301499367,
0.03899800032377243,
-0.06338920444250107,
0.04628429561853409,
-0.019596388563513756,
0.04097902402281761,
-0.04783519357442856,
0.06706399470567703,
0.04704277217388153,
-0.00002322992258996237,
0.022664345800876617,
-0.017709869891405106,
0.02536848746240139,
-0.0035215409006923437,
-0.004410436376929283,
0.03278990089893341,
0.047971829771995544,
0.0161771010607481,
-0.0350787453353405,
0.032528385519981384,
-0.06599174439907074,
-0.06767483800649643,
0.018459578976035118,
0.011571484617888927,
0.03155573457479477,
0.02012450061738491,
0.011675924994051456,
-0.022122617810964584,
-0.03788015618920326,
0.015484092757105827,
-0.042214348912239075,
0.035657111555337906,
-0.08960002660751343,
0.04303205385804176,
-0.0051030912436544895,
0.019710378721356392,
-0.013181821443140507,
-0.025818802416324615,
0.015852630138397217,
-0.04581715911626816,
-0.05477637052536011,
0.014254731126129627,
-0.00520419143140316,
-0.005271759815514088,
-0.01655312441289425,
-0.08256597071886063,
0.0200488418340683,
0.049714431166648865,
-0.0535099096596241,
-0.016533151268959045,
0.020679442211985588,
-0.022829901427030563,
-0.04276619851589203,
0.056117746978998184,
0.0362442210316658,
0.06514887511730194,
-0.007684442680329084,
-0.042420893907547,
0.04099835455417633,
0.02539743483066559,
0.009213047102093697,
-0.005920805037021637,
-0.02989181876182556,
0.11375974863767624,
0.030262967571616173,
0.03937426954507828,
-0.008045430295169353,
0.01631452515721321,
0.08982688188552856,
-0.014515034854412079,
0.017043691128492355,
-0.05986654758453369,
0.015383186750113964,
-0.044055577367544174,
0.03659569099545479,
0.014350533485412598,
-0.01700333133339882,
-0.014937777072191238,
-0.00046968553215265274,
-0.02971622534096241,
-0.03253598138689995,
-0.010358832776546478,
-0.045217834413051605,
0.0050867595709860325,
0.01610809750854969,
-0.09145962446928024,
-0.03736409172415733,
0.05728677287697792,
0.026406098157167435,
0.019391415640711784,
0.01854437030851841,
-0.00426205899566412,
0.052733637392520905,
-0.03573574125766754,
0.015619524754583836,
-0.026680437847971916,
0.033555347472429276,
-0.037335142493247986,
-0.0255472082644701,
0.003219407284632325,
0.04356144368648529,
-0.03644772619009018,
0.05412791296839714,
-0.018956873565912247,
0.017322150990366936,
-0.035119663923978806,
-0.004311963450163603,
0.029463034123182297,
-0.057846106588840485,
-0.018831240013241768,
0.044229716062545776,
-0.021948065608739853,
-0.014155881479382515,
0.004131678491830826,
-0.03137332946062088,
-0.003772242460399866,
0.009829932823777199,
-0.01672867313027382,
-0.0023681509774178267,
0.038555413484573364,
0.027468565851449966,
0.018139023333787918,
0.07897892594337463,
-0.010276131331920624,
-0.060656409710645676,
-0.003128781681880355,
-0.03316356986761093,
0.020796723663806915,
-0.013225675560534,
-0.01545148529112339,
0.04619412496685982,
0.05372807756066322,
-0.00382617418654263,
-0.06356795132160187,
0.0007377853617072105,
0.0012614389415830374,
-0.044003862887620926,
-0.05199392884969711,
-0.0412156842648983,
0.029702791944146156,
-0.03612345829606056,
-0.09991487115621567,
0.009781215339899063,
0.02410717122256756,
0.03388458862900734,
0.012654530815780163,
0.004620889667421579,
-0.009103167802095413,
-0.003958012908697128,
0.022251131013035774,
0.027241326868534088,
0.011940421536564827,
-0.048714153468608856,
-0.011557775549590588,
-0.026996711269021034,
0.0061066471971571445,
0.035672083497047424,
-0.03494398295879364,
-0.11751812696456909,
-0.03180453181266785,
0.007077348884195089,
0.011913006193935871,
-0.070376917719841,
-0.05958869308233261,
0.037271592766046524,
0.014873936772346497,
-0.008006814867258072,
0.03360181301832199,
-0.017773276194930077,
-0.015882115811109543,
0.0499580055475235,
0.01941642537713051,
0.010443434119224548,
0.01957220584154129,
-0.005448285490274429,
0.02090897224843502,
-0.034278664737939835,
0.04994820058345795,
-0.04411482810974121,
-0.02690625749528408,
0.003454431425780058,
0.054813116788864136,
0.05534413829445839,
0.011020079255104065,
0.05279802903532982,
-0.004857179243117571,
-0.001973272068426013,
-0.010008538141846657,
0.0025402551982551813,
0.016913434490561485,
0.025143874809145927,
0.009345266036689281,
-0.00033291714498773217,
0.05927111580967903,
0.010960490442812443,
-0.014571760781109333,
-0.013276541605591774,
-0.07548084110021591,
0.03602694347500801,
0.03681640699505806,
0.04007339105010033,
-0.04780958965420723,
0.0153322983533144,
0.04147638753056526,
0.0392899252474308,
0.0632462203502655,
0.04338633269071579,
-0.004587841220200062,
0.017981380224227905,
-0.00154952856246382,
0.030177799984812737,
0.016886524856090546,
-0.01695600524544716,
-0.06750202178955078,
-0.011477623134851456,
-0.04619134962558746,
-0.00786257442086935,
0.045967113226652145,
0.001311961212195456,
0.006515994668006897,
0.011580683290958405,
0.014505879022181034,
0.00487759942188859,
0.009931201115250587,
-0.0614897683262825,
-0.04203768074512482,
-0.016651013866066933,
-0.03349931538105011,
0.022644812241196632,
-0.06039495766162872,
-0.0345647819340229,
0.05979175865650177,
-0.042491503059864044,
0.03834684565663338,
0.02442817948758602,
0.010027293115854263,
-0.024254200980067253,
-0.036650970578193665,
-0.024058083072304726,
-0.04416710138320923,
0.024387294426560402,
-0.03396598994731903,
-0.003239419311285019,
0.03980002924799919,
0.02518685720860958,
0.009978034533560276,
0.007510211318731308,
0.02298358827829361,
-0.0634278729557991,
0.018874365836381912,
0.021557781845331192,
-0.047438718378543854,
0.02433602511882782,
-0.06627733260393143,
-0.011644638143479824,
-0.04630112648010254,
-0.017054283991456032,
-0.012913997285068035,
0.025303127244114876,
-0.0064764609560370445,
0.019270436838269234,
-0.0025072041898965836,
0.011677815578877926,
-0.0008656001300550997,
0.07206469774246216,
0.025837378576397896,
0.028895137831568718,
0.032078322023153305,
-0.04208509996533394,
0.02644379995763302,
0.06217701733112335,
0.0015868882182985544,
-0.0417732335627079,
0.029943160712718964,
-0.007612820249050856,
-0.04614860191941261,
-0.027176043018698692,
-0.005307355429977179,
-0.007925604470074177,
0.03420328348875046,
0.026479797437787056,
-0.012083207257091999,
0.04052390158176422,
-0.008710040710866451,
-0.005252907518297434,
0.014945263043045998,
0.06115204840898514,
-0.002857841784134507,
-0.012743269093334675,
0.02045045793056488,
0.03720270097255707,
0.06604676693677902,
0.007775370962917805,
-0.022756807506084442,
-0.03735654056072235,
0.05685264617204666,
0.027553332969546318,
0.00029252259992063046,
-0.04104289785027504,
-0.11146073043346405,
-0.024287836626172066,
0.0011396721238270402,
-0.004513174761086702,
-0.016578970476984978,
-0.009566559456288815,
0.05006246268749237,
-0.035530682653188705,
-0.028328772634267807,
-0.041445281356573105,
0.03597439080476761,
0.02073400281369686,
-0.022234370931982994,
-0.033201444894075394,
-0.041145436465740204,
0.007794610690325499,
0.06569383293390274,
0.013496840372681618,
-0.030865678563714027,
0.013426699675619602,
-0.0032416554167866707,
-0.005218869540840387,
0.055137038230895996,
0.006438033655285835,
-0.018121622502803802,
-0.024752948433160782,
-0.0039019642863422632,
0.03725501894950867,
-0.004204404074698687,
0.031558699905872345,
0.00359596055932343,
0.009215855039656162,
-0.003093329956755042,
-0.01376508828252554,
-0.02285119518637657,
0.0210848618298769,
0.020134756341576576,
-0.030020972713828087,
-0.03521818667650223,
0.05238715931773186,
0.010061370208859444,
0.046324461698532104,
0.01949579454958439,
-0.017066339030861855,
-0.04325610771775246,
-0.017011672258377075,
0.02879589982330799,
0.02165837585926056,
0.02869667112827301,
-0.01340232603251934,
-0.05938386917114258,
0.056229617446660995,
-0.03191208839416504,
0.03780549764633179,
0.0147457430139184,
-0.021009046584367752,
0.009121905080974102,
0.044276297092437744,
-0.012508447282016277,
-0.020790280774235725,
-0.036154765635728836,
-0.018822336569428444,
0.06994104385375977,
-0.06595005095005035,
-0.06477437168359756,
-0.024688836187124252,
-0.0070475805550813675,
0.001336276764050126,
0.019437173381447792,
-0.05523887649178505,
0.03252687677741051,
-0.019933702424168587,
0.011531662195920944,
0.02916606329381466,
-0.032676491886377335,
0.005681627430021763,
-0.009092497639358044,
0.01314937137067318,
-0.01336297020316124,
0.00191438477486372,
0.007873022928833961,
0.04647158458828926,
-0.052744075655937195,
0.04431489109992981,
0.006714425981044769,
-0.14117375016212463,
0.10230211913585663,
-0.0028400032315403223,
0.02441183663904667,
-0.032581180334091187,
0.055409613996744156,
0.006114906165748835,
-0.013763368129730225,
0.03888332098722458,
0.03533926233649254,
0.01726723276078701,
-0.03897849842905998,
0.006435748189687729,
-0.034780293703079224,
0.01267528347671032,
0.020854711532592773,
-0.010533667169511318,
0.0428779236972332,
-0.03147488459944725,
0.03511741757392883,
0.06752274185419083,
-0.03813713416457176,
0.07451756298542023,
0.023399552330374718,
-0.02712441422045231,
-0.0443529412150383,
0.005869787652045488,
0.026316100731492043,
0.010508811101317406,
-0.013382704928517342,
-0.003602170618250966,
-0.09703271090984344,
0.1279798150062561,
-0.06931905448436737,
-0.07875476032495499,
0.006566556170582771,
-0.037787605077028275,
0.004409303423017263,
-0.0022086335811764,
-0.02971169725060463,
0.033916816115379333,
-0.002182179829105735,
-0.0016039983602240682,
-0.00412964029237628,
0.05897023528814316,
0.06430602073669434,
0.06070922315120697,
-0.04255582019686699,
0.030302489176392555,
0.0014634828548878431,
-0.023597173392772675,
0.06295236945152283,
-0.01990990899503231,
-0.010354246012866497,
-0.030497252941131592,
-0.04502401873469353,
0.06377333402633667,
-0.02726498804986477,
0.0347215011715889,
0.07822578400373459,
0.007890808396041393,
-0.006424540653824806,
-0.007807142101228237,
0.026913365349173546,
0.024323413148522377,
-0.03874671459197998,
0.003003983525559306,
-0.03952096402645111,
0.027053168043494225,
0.03761325404047966,
-0.026388654485344887,
-0.009939581155776978,
-0.01112586259841919,
-0.03404960781335831,
0.03889989107847214,
-0.02814687229692936,
-0.02743569016456604,
0.008678584359586239,
0.009883063845336437,
0.056451622396707535,
-0.019980812445282936,
0.025412721559405327,
0.025269944220781326,
-0.029432041570544243,
-0.07603077590465546,
-0.04388312250375748,
0.013649314641952515,
0.01743893139064312,
0.06798528879880905,
0.05165412276983261,
0.021644700318574905,
-0.06647463142871857,
0.040521424263715744,
0.020409846678376198,
0.008154002949595451,
-0.022472087293863297,
0.04909767210483551,
-0.03403292968869209,
0.014062967151403427,
0.012946803122758865,
0.05119892954826355,
0.017321081832051277,
-0.014033299870789051,
0.04192955046892166,
0.04264403134584427,
-0.018712421879172325,
-0.024072211235761642,
-0.02381310425698757,
0.052192945033311844,
0.03472977504134178,
0.027250375598669052,
0.009049429558217525,
-0.03770117461681366,
-0.021414319053292274,
0.06666578352451324,
0.02623896859586239,
-0.03600842133164406,
0.0443674698472023,
0.04632074013352394,
0.02296924591064453,
-0.0427689366042614,
-0.03809580206871033,
-0.0727546289563179,
-0.0008598914137110114,
-0.021794358268380165,
0.01182993222028017,
-0.028607474640011787,
-0.054719310253858566,
-0.02513117343187332,
0.03085726499557495,
0.02802937850356102,
0.017004236578941345,
-0.006641715299338102,
-0.05233335867524147,
0.02560816891491413,
0.07257741689682007,
-0.04660208150744438,
-0.04342641681432724,
0.06470588594675064,
0.011031130328774452,
0.07360150665044785,
-0.015529186464846134,
0.0365341491997242,
-0.03765001520514488,
0.0014239520533010364,
-0.02803940698504448,
-0.015099323354661465,
-0.03275907784700394,
-0.010889951139688492,
0.059547994285821915,
-0.011505333706736565,
-0.018835479393601418,
-0.05330343171954155,
-0.018787939101457596,
0.00820267852395773,
0.09384733438491821,
0.002149731619283557,
0.010970942676067352,
-0.035271622240543365,
-0.027657242491841316,
-0.024501802399754524,
0.004974064417183399,
-0.014901104383170605,
-0.05129002779722214,
-0.007536764722317457,
-0.05093597620725632,
0.029807252809405327,
0.0027264547534286976,
-0.003501089056953788,
0.03141588345170021,
0.0227341428399086,
-0.0054138097912073135,
0.015157915651798248,
0.004250973463058472,
-0.0025535887107253075,
-0.002412488916888833,
-0.014095100574195385,
-0.0015834264922887087,
-0.010111866518855095,
-0.025857362896203995,
-0.016733461990952492,
-0.04674653708934784,
-0.016477687284350395,
-0.005297091323882341,
-0.06682057678699493,
-0.05297303572297096,
0.02286520227789879,
0.025483867153525352,
0.0009458200074732304,
0.019863490015268326,
0.004744745325297117,
0.052225567400455475,
0.018573541194200516,
-0.038748376071453094,
-0.026219971477985382,
0.06356184929609299,
0.008191920816898346,
0.030710123479366302,
0.012239891104400158,
-0.012469843029975891,
0.02532707154750824,
-0.02205817401409149,
-0.01693137362599373,
0.021687116473913193,
-0.01994292251765728,
0.0046014804393053055,
-0.03619891405105591,
0.06080431491136551,
-0.023230120539665222,
-0.01669691875576973,
-0.011715095490217209,
0.020778242498636246,
0.06430406868457794,
-0.03556779772043228,
-0.007078069262206554,
0.0460151769220829,
0.03836340084671974,
-0.05140409246087074,
0.023429401218891144,
0.031717944890260696,
-0.038524433970451355,
0.026175789535045624,
0.007272891700267792,
-0.020834041759371758,
0.02767854556441307,
0.03609893471002579,
0.0024899968411773443,
-0.007883368991315365,
-0.014352435246109962,
0.03330782800912857,
-0.04171327129006386,
-0.04381502792239189,
0.01915576681494713,
0.05012766644358635,
-0.009850049391388893,
0.009311346337199211,
0.023181477561593056,
0.014575498178601265,
-0.0004385349457152188,
-0.019049927592277527,
0.020593097433447838,
-0.03532087057828903,
0.04125678166747093,
0.022120291367173195,
0.01612160913646221,
-0.018215537071228027,
-0.0956907644867897,
-0.030190272256731987,
-0.05671316012740135,
-0.06657716631889343,
-0.024497520178556442,
-0.04062188044190407,
-0.025017138570547104,
-0.03775043785572052,
-0.040779195725917816,
-0.005136311054229736,
-0.05343995243310928,
0.004752350505441427,
-0.007413775660097599,
-0.06659924983978271,
0.04687981680035591,
-0.012425236403942108,
-0.03305318206548691,
-0.03592472895979881,
0.020664647221565247,
0.005457686260342598,
-0.013574537821114063,
-0.020091893151402473,
0.012467969208955765,
-0.00940373819321394,
0.02409117855131626,
-0.05820426344871521,
0.05928986147046089,
-0.030633745715022087,
-0.02112661860883236,
0.02397741749882698,
-0.06615910679101944,
-0.0219526719301939,
0.02460700459778309,
-0.01743292808532715,
-0.07414191961288452,
0.010685376822948456,
0.02181065082550049,
0.03734282776713371,
0.03344276547431946,
0.06893721967935562,
-0.024886155501008034,
-0.016373127698898315,
-0.049664102494716644,
0.012471096590161324,
0.018256893381476402,
0.008121034130454063,
-0.01732257567346096,
-0.04586862400174141,
-0.027745939791202545,
0.003515974385663867,
0.049292463809251785,
-0.004255519714206457,
0.06021096557378769,
-0.04392688721418381,
-0.026269132271409035,
-0.0005692325066775084,
0.012403611093759537,
-0.03528117761015892,
0.014326193369925022,
0.03518110141158104,
0.018395371735095978,
-0.05093061551451683,
-0.013103315606713295,
0.0065643880516290665,
0.0013346519554033875,
0.021203000098466873,
-0.004096129443496466,
-0.02417110465466976,
-0.05343875288963318,
-0.04545052349567413,
0.0352916345000267,
0.019962510094046593,
0.03328103944659233,
-0.05034635215997696,
-0.03382842242717743,
0.03281750530004501,
0.02290949784219265,
-0.002217512344941497,
-0.022319672629237175,
-0.024644864723086357,
0.031139785423874855,
-0.027199257165193558,
-0.09154370427131653,
0.05360686033964157,
0.003890075720846653,
0.03792809322476387,
-0.010222758166491985,
-0.006563767325133085,
-0.0027929842472076416,
0.06081223487854004,
-0.08813419938087463,
0.05211752653121948,
0.00941590778529644,
0.004827720113098621,
0.005832810886204243,
0.04941600188612938,
-0.014687588438391685,
0.06206899881362915,
-0.027529047802090645,
0.00621304614469409,
0.05417995899915695,
-0.015004676766693592,
0.020980004221200943,
-0.006687304936349392,
0.01907360553741455,
-0.006234359461814165,
-0.018533790484070778,
0.05249388515949249,
0.01291664782911539
] |
<p>I know it is hard , but can we transfer the charge on a capacitor plate elsewhere? </p> | g4623 | [
0.07163286954164505,
0.0596429817378521,
0.0003783456631936133,
-0.02083561383187771,
0.04093484953045845,
0.02540643885731697,
-0.03431312367320061,
-0.005783340893685818,
-0.036919966340065,
0.04726441949605942,
-0.07203563302755356,
0.058387961238622665,
-0.043043795973062515,
0.0008565642056055367,
0.013558264821767807,
-0.023247208446264267,
0.11344614624977112,
-0.010039538145065308,
0.031207066029310226,
0.06614279747009277,
-0.012892408296465874,
-0.0457862913608551,
0.00047918548807501793,
-0.056224338710308075,
-0.044113606214523315,
-0.051216550171375275,
-0.022894825786352158,
-0.03213505074381828,
-0.006514193024486303,
-0.03395005688071251,
-0.023689888417720795,
-0.012001076713204384,
0.004688004031777382,
0.0052473340183496475,
-0.03958510607481003,
-0.014362693764269352,
0.023778755217790604,
-0.028433164581656456,
0.024626852944493294,
0.05240917578339577,
-0.03495488688349724,
0.055594734847545624,
0.01819618046283722,
0.04356247931718826,
0.03661898151040077,
-0.032224975526332855,
-0.017936406657099724,
-0.03468874841928482,
-0.011345705948770046,
-0.040100209414958954,
-0.05682381987571716,
0.055860236287117004,
0.017176762223243713,
0.004971184302121401,
0.029969507828354836,
-0.0034582463558763266,
0.005405150819569826,
-0.006476020906120539,
0.004844184033572674,
0.03468530625104904,
-0.019698215648531914,
0.015976347029209137,
0.030776403844356537,
0.0135654266923666,
-0.0400359220802784,
0.0037857298739254475,
-0.04481058195233345,
0.010379977524280548,
-0.010505019687116146,
0.008250594139099121,
0.026401536539196968,
-0.014908083714544773,
0.024989906698465347,
-0.017765162512660027,
0.00882064551115036,
-0.021232571452856064,
0.03589002415537834,
-0.03636297211050987,
0.030524229630827904,
-0.03131278604269028,
-0.0016618025256320834,
-0.05093981698155403,
0.0234969649463892,
-0.03923714533448219,
-0.02681550197303295,
-0.00709617231041193,
0.017603697255253792,
0.01776965521275997,
-0.06018461287021637,
-0.0495961531996727,
-0.0008047969895415008,
-0.028061723336577415,
-0.004794418811798096,
-0.0034916033037006855,
0.06205819174647331,
-0.040939196944236755,
-0.0067758806981146336,
-0.004227600526064634,
-0.02444453537464142,
-0.05101703852415085,
-0.0387117974460125,
0.012621024623513222,
0.001413515186868608,
0.06766454875469208,
0.0016433170530945063,
0.047714367508888245,
0.0461169108748436,
0.015250129625201225,
0.05109882727265358,
-0.026250071823596954,
0.024491101503372192,
-0.04231145977973938,
0.007703493814915419,
-0.005828123539686203,
-0.010434562340378761,
-0.005918205250054598,
0.01760711893439293,
-0.012343132868409157,
0.013998928479850292,
0.002385735046118498,
0.038024552166461945,
-0.01702353172004223,
-0.005690407939255238,
0.042480580508708954,
0.019782431423664093,
-0.026355627924203873,
0.036700669676065445,
0.02522960864007473,
0.015182530507445335,
0.02322027087211609,
-0.00019415492715779692,
-0.036821261048316956,
-0.02444794774055481,
-0.02027788572013378,
0.024404244497418404,
-0.002496046246960759,
0.030685845762491226,
-0.018061315640807152,
0.023809103295207024,
-0.005322571843862534,
0.052686840295791626,
0.006056154612451792,
-0.01906549371778965,
0.04292743653059006,
0.04352667182683945,
-0.0032326786313205957,
-0.0298368688672781,
-0.017767909914255142,
0.012283387593925,
-0.02121037431061268,
0.03306487202644348,
0.01065652072429657,
0.01883978210389614,
0.016742922365665436,
0.03377314656972885,
-0.04585689306259155,
0.08942055702209473,
0.010880837216973305,
0.07359880208969116,
-0.03046475537121296,
-0.02629043161869049,
0.024257877841591835,
-0.021794680505990982,
-0.021208779886364937,
0.002810809528455138,
-0.03634147346019745,
-0.02771248109638691,
0.005830218084156513,
0.010161705315113068,
-0.06496039777994156,
0.06713934987783432,
-0.09355904906988144,
0.011506562121212482,
-0.02357940934598446,
0.044742126017808914,
0.0322873555123806,
-0.059785641729831696,
0.049745697528123856,
0.008620379492640495,
-0.008497453294694424,
-0.015569665469229221,
-0.013271619565784931,
0.0013008355163037777,
-0.0668359249830246,
0.007125042844563723,
0.03462498262524605,
-0.009540224447846413,
-0.006209495011717081,
0.11032883077859879,
0.022769233211874962,
-0.008307297714054585,
-0.0068171522580087185,
0.03541739284992218,
0.016369957476854324,
-0.0027334901969879866,
-0.04184841737151146,
0.03826785087585449,
-0.03105670027434826,
0.06255580484867096,
-0.04091709479689598,
0.023324890062212944,
0.02230885811150074,
0.07029789686203003,
-0.012084108777344227,
0.05985094979405403,
-0.04103931412100792,
0.015418323688209057,
-0.05348322540521622,
-0.00043708461453206837,
-0.018239494413137436,
-0.007601544726639986,
-0.011847599409520626,
-0.02834778092801571,
0.0018459815764799714,
-0.006424717605113983,
-0.01537626888602972,
-0.015964403748512268,
-0.004038230050355196,
-0.013335910625755787,
0.03979077935218811,
-0.06406020373106003,
0.0038098322693258524,
0.04849075898528099,
0.03417447581887245,
-0.007058529648929834,
0.02139219269156456,
0.004428884945809841,
-0.0033919087145477533,
-0.07934538275003433,
-0.009283534251153469,
-0.0719015970826149,
0.016699444502592087,
0.017709000036120415,
-0.011819267645478249,
0.023691583424806595,
0.05790195241570473,
-0.05380933731794357,
-0.021397659555077553,
-0.09148389846086502,
0.030932573601603508,
-0.029398223385214806,
-0.05909649282693863,
0.00791930127888918,
0.04122861102223396,
-0.06217782571911812,
-0.022956635802984238,
-0.04904361814260483,
-0.006516235414892435,
-0.01888250932097435,
0.002809214871376753,
0.04277833551168442,
-0.00868984404951334,
0.017542164772748947,
0.01969347894191742,
0.006392286159098148,
-0.025181176140904427,
-0.015438790433108807,
-0.006067708134651184,
0.0036711690481752157,
-0.061275169253349304,
-0.009007837623357773,
-0.04271218180656433,
-0.010962607339024544,
0.011747212149202824,
-0.02334471233189106,
-0.004370641894638538,
-0.07446896284818649,
0.03393989056348801,
0.030885392799973488,
-0.0030506199691444635,
0.04020281136035919,
0.054161954671144485,
0.008372750133275986,
-0.01370676513761282,
0.021075032651424408,
-0.06620591133832932,
0.008810930885374546,
-0.0411471389234066,
0.009361925534904003,
-0.04576306417584419,
-0.027385996654629707,
-0.006527215242385864,
-0.04002204164862633,
-0.04940006881952286,
-0.025955528020858765,
-0.03055691160261631,
0.021436965093016624,
-0.014366748742759228,
-0.009776869788765907,
-0.009387138299643993,
-0.01091965101659298,
-0.03795545920729637,
0.026263460516929626,
-0.0579601414501667,
0.04136355221271515,
0.012041701003909111,
0.1234765350818634,
0.01702960953116417,
-0.011011559516191483,
0.027488958090543747,
0.04568726196885109,
0.00030016046366654336,
-0.03198070824146271,
0.016093170270323753,
0.05711262300610542,
0.07955792546272278,
0.027476293966174126,
0.015696179121732712,
0.03797426074743271,
0.04044313356280327,
0.00477337883785367,
-0.017156636342406273,
0.023105986416339874,
0.03394021838903427,
-0.019993120804429054,
-0.013057181611657143,
-0.01240448746830225,
-0.03927389159798622,
0.01693732850253582,
-0.0142322713509202,
-0.0032470503356307745,
-0.0004230971971992403,
-0.022987721487879753,
0.09652643650770187,
-0.02307782508432865,
0.030918307602405548,
-0.07370278239250183,
0.037667255848646164,
-0.0058657643385231495,
0.0033179218880832195,
0.01632089912891388,
0.0933602899312973,
-0.009855042211711407,
-0.053514264523983,
-0.013296953402459621,
-0.0013310268986970186,
0.020723756402730942,
0.053242117166519165,
0.06459221988916397,
-0.0403183251619339,
0.009473953396081924,
0.006212559062987566,
-0.030103720724582672,
-0.033089444041252136,
-0.05484478548169136,
0.010701597668230534,
0.004450769163668156,
0.016446929425001144,
-0.013515104539692402,
-0.03933289274573326,
-0.010882606729865074,
-0.0004949074937030673,
0.002304990775883198,
0.024872399866580963,
-0.027567001059651375,
-0.01693357154726982,
-0.0044874330051243305,
0.0003046946076210588,
-0.043337080627679825,
0.03081332892179489,
0.03859016299247742,
-0.030193492770195007,
0.10190766304731369,
0.019950829446315765,
0.061383605003356934,
0.002248360076919198,
-0.08402720093727112,
0.031722649931907654,
-0.024291247129440308,
-0.04497789591550827,
-0.021318474784493446,
-0.03332750126719475,
0.014564177952706814,
0.04708997905254364,
0.012321877293288708,
-0.05300355330109596,
-0.034019552171230316,
-0.010693923570215702,
-0.013855048455297947,
0.0705651268362999,
-0.04085693508386612,
-0.048007119446992874,
-0.01876462809741497,
-0.06583300232887268,
0.0007229040493257344,
0.046521443873643875,
-0.01956849731504917,
0.02089184708893299,
-0.03346746414899826,
0.017442982643842697,
-0.016980674117803574,
-0.06411214172840118,
0.00972517766058445,
-0.024027641862630844,
-0.004314383026212454,
-0.020715398713946342,
-0.03590242937207222,
-0.034378573298454285,
0.0047463043592870235,
-0.029692580923438072,
0.03654872253537178,
-0.020609041675925255,
0.01902014948427677,
-0.024107839912176132,
-0.04664873704314232,
-0.0026690559461712837,
0.08194174617528915,
-0.014165237545967102,
-0.006420334335416555,
-0.0026153726503252983,
-0.01915646530687809,
-0.08722738176584244,
0.013018516823649406,
0.019484806805849075,
-0.01283098105341196,
-0.09404191374778748,
0.0006622099899686873,
0.08430518209934235,
0.03334943577647209,
-0.004772939719259739,
-0.013648766092956066,
0.006344294175505638,
0.01744956523180008,
0.01908283866941929,
0.02781257964670658,
0.006758277770131826,
0.0036445320583879948,
-0.06040314584970474,
0.04714348167181015,
0.03824200481176376,
-0.08503296971321106,
0.04789574071764946,
-0.009374227374792099,
0.03397178277373314,
0.0033911701757460833,
0.011628500185906887,
-0.02032548561692238,
-0.019233491271734238,
-0.02171759121119976,
0.025004824623465538,
0.0921381264925003,
-0.035275887697935104,
0.0016798380529507995,
0.022480012848973274,
-0.0008622200693935156,
0.03403162583708763,
-0.013220978900790215,
0.011508862487971783,
0.05865176394581795,
-0.032708145678043365,
-0.05652342736721039,
-0.0019206537399441004,
-0.04916805773973465,
0.021117735654115677,
0.05083845183253288,
0.04454740881919861,
-0.011348020285367966,
-0.05625347048044205,
-0.033604733645915985,
0.015932153910398483,
-0.03137161582708359,
0.03530890867114067,
0.022706475108861923,
-0.007332510780543089,
0.022307071834802628,
-0.014116729609668255,
-0.0575411394238472,
-0.0670175775885582,
-0.033626243472099304,
-0.06798307597637177,
0.005301661789417267,
0.058889687061309814,
0.05418385565280914,
0.009142743423581123,
0.03514547273516655,
0.005041609052568674,
0.0006819404661655426,
-0.03582306578755379,
-0.07034934312105179,
-0.04274210333824158,
-0.02015923522412777,
0.020180676132440567,
-0.020397335290908813,
0.024444811046123505,
-0.06872370094060898,
-0.009478000923991203,
-0.04705990105867386,
0.03178657591342926,
-0.007723265327513218,
-0.0617607980966568,
-0.03356063738465309,
0.031771235167980194,
0.013502765446901321,
0.019487254321575165,
0.045717209577560425,
0.019497793167829514,
0.0023443244863301516,
0.002272386569529772,
-0.03105095773935318,
0.043678976595401764,
0.01170177198946476,
0.02650393173098564,
-0.04104126989841461,
0.052002474665641785,
-0.000030192468329914846,
0.0031613982282578945,
-0.006238438189029694,
0.05882037803530693,
-0.026815038174390793,
0.04019984230399132,
0.009791371412575245,
0.017435410991311073,
-0.01318938098847866,
0.0002304937515873462,
0.05050087347626686,
0.020785143598914146,
-0.015677299350500107,
-0.04064808785915375,
0.0005637349677272141,
0.008098682388663292,
-0.009066317230463028,
0.041268717497587204,
-0.011413819156587124,
-0.0034820239525288343,
-0.04280594736337662,
0.01921813376247883,
-0.0014736891025677323,
-0.11010274291038513,
-0.0002426290448056534,
-0.01451193355023861,
0.019448133185505867,
0.008622410707175732,
-0.04919528216123581,
0.007930731400847435,
-0.047946613281965256,
-0.03272948041558266,
-0.0697593167424202,
-0.046204205602407455,
-0.015045452862977982,
0.004462030716240406,
0.02412364073097706,
-0.07534635066986084,
0.007212013937532902,
0.040817759931087494,
0.0214329045265913,
0.05286020040512085,
-0.0342991016805172,
0.015253115445375443,
-0.007415051106363535,
-0.01868399605154991,
-0.027111005038022995,
-0.0224954541772604,
0.021722843870520592,
-0.029180925339460373,
0.04974798858165741,
-0.04534126818180084,
0.0007457927567884326,
-0.03599565848708153,
0.04655110090970993,
-0.017806753516197205,
0.019668951630592346,
0.019720379263162613,
0.003059165785089135,
-0.03819265216588974,
-0.015114372596144676,
-0.013983809389173985,
0.03925607353448868,
-0.020663052797317505,
0.054662272334098816,
-0.022573236376047134,
-0.01404210738837719,
-0.06576742231845856,
-0.03585268557071686,
-0.017488714307546616,
-0.01638605259358883,
-0.00946449488401413,
0.020327098667621613,
0.14332754909992218,
0.03675493597984314,
0.020893359556794167,
-0.04744959622621536,
0.009198689833283424,
0.00846558716148138,
0.015727449208498,
0.0011727724922820926,
0.04443943873047829,
0.07137970626354218,
-0.03065595030784607,
0.02314797416329384,
-0.006565622054040432,
0.003485881257802248,
-0.025166040286421776,
0.08270417153835297,
-0.030705725774168968,
-0.034771066159009933,
0.02018490433692932,
0.04970027506351471,
0.04838837310671806,
0.03642106056213379,
0.06425849348306656,
0.011538291350007057,
-0.014277814887464046,
0.0050297449342906475,
-0.041758760809898376,
0.0029857421759516,
-0.021118974313139915,
0.017069540917873383,
0.0012200865894556046,
0.010814270935952663,
-0.016189685091376305,
-0.06479604542255402,
-0.016757702454924583,
0.01663399301469326,
-0.03657668083906174,
0.04295272007584572,
0.030228767544031143,
0.03024250455200672,
0.021500246599316597,
-0.0020076122600585222,
0.06887520849704742,
0.07657492160797119,
0.0423668771982193,
-0.00852334126830101,
0.04797107353806496,
-0.05538874864578247,
-0.018496915698051453,
0.009554645046591759,
0.014441688545048237,
0.01767002046108246,
0.01575944758951664,
-0.030858652666211128,
0.0644342377781868,
-0.002409294480457902,
0.012140552513301373,
0.00401507830247283,
0.11249641329050064,
0.016487471759319305,
-0.04181911423802376,
-0.025089122354984283,
-0.03323421999812126,
-0.01007766742259264,
0.05920642241835594,
0.030761143192648888,
0.015153633430600166,
-0.02471337653696537,
0.027537047863006592,
0.03967636451125145,
0.014809058047831059,
-0.04235401377081871,
0.06694633513689041,
0.05567140132188797,
0.02161366119980812,
-0.05603749677538872,
-0.009906195104122162,
0.016317516565322876,
-0.0045892721973359585,
0.03050035797059536,
0.05511618033051491,
-0.061800435185432434,
0.02235734649002552,
0.0020013803150504827,
0.0007791205425746739,
0.014832938089966774,
-0.0289455596357584,
0.016577929258346558,
-0.005477113649249077,
-0.005115626845508814,
-0.019432278349995613,
-0.0024110290687531233,
-0.09099855273962021,
0.023842722177505493,
-0.028682967647910118,
-0.05689922720193863,
0.015181589871644974,
-0.029170216992497444,
-0.004219363443553448,
0.0546996109187603,
0.043683409690856934,
-0.0333026647567749,
0.00048612183309160173,
0.023828202858567238,
-0.010991531424224377,
-0.023888103663921356,
0.02265140786767006,
0.009461074136197567,
-0.044779133051633835,
-0.021262021735310555,
0.031994808465242386,
0.03459463268518448,
0.02457662858068943,
-0.007877616211771965,
-0.010014361701905727,
0.035111214965581894,
0.02766985073685646,
0.019477548077702522,
0.0038377821911126375,
-0.01145708654075861,
-0.03671499341726303,
0.028448108583688736,
0.00990350916981697,
0.025757016614079475,
-0.05201210081577301,
0.009510424919426441,
-0.03760777413845062,
-0.004241233691573143,
-0.012111261487007141,
-0.029980914667248726,
-0.017842872068285942,
-0.015710990875959396,
-0.014759204350411892,
0.05060682073235512,
0.04770169034600258,
-0.047672681510448456,
0.02205643802881241,
0.10862135887145996,
0.019783873111009598,
-0.0458323210477829,
0.04158532992005348,
-0.0023893755860626698,
0.04382353276014328,
-0.00004442162025952712,
-0.04691798612475395,
-0.013195603154599667,
0.00747380405664444,
0.01500327792018652,
0.01605784334242344,
0.07196979224681854,
0.0005011311150155962,
0.027103303000330925,
-0.06294742971658707,
-0.009741324000060558,
0.02585052326321602,
-0.013801481574773788,
-0.01968470588326454,
-0.0256295595318079,
-0.0051162755116820335,
-0.0179880503565073,
0.015302696265280247,
0.022446027025580406,
-0.015465540811419487,
0.007150608580559492,
-0.03412674367427826,
-0.013042595237493515,
-0.01262782234698534,
-0.031688712537288666,
0.013802590779960155,
-0.05317132547497749,
0.03752654790878296,
0.024553505703806877,
-0.007162770722061396,
-0.015820996835827827,
-0.02068527229130268,
-0.05404293164610863,
-0.028927283361554146,
0.013684161938726902,
-0.0555986613035202,
-0.034412551671266556,
0.04344191402196884,
0.07490361481904984,
0.0041718254797160625,
-0.06244032457470894,
0.0061174603179097176,
-0.040580831468105316,
-0.02991734817624092,
0.07975934445858002,
-0.04955710843205452,
-0.017809974029660225,
-0.02582043968141079
] |
<p>The usual "proof" entropy is a state property is like that:</p>
<p>"Consider a system which undergoes a reversible process from state 1 to state 2 along path A, and let cycle be completed along path B, which is also reversible. Since the cycle is reversible we can write: </p>
<p>$$\int_1^2 \delta Q / T + \int_2^1 \delta Q / T = 0 $$</p>
<p>Now let cycle be completed along path C, but paths B and C represent arbitrary reversible processes. So $\int_2^1 \delta Q / T $ is the same for all reversible paths between states 2 and 1."</p>
<p>My question is, isn't the equation above already assume entropy is a state property? Only if it is a state property it can go around a cycle without changes. How can it be valid to prove entropy is state property if it is already assumed from the beginning?</p> | g4624 | [
0.009015250951051712,
-0.0249553844332695,
0.019384892657399178,
-0.004227310419082642,
0.010301893576979637,
-0.03472987189888954,
0.02625679224729538,
0.04381898045539856,
-0.034119706600904465,
0.028513558208942413,
-0.0172762218862772,
0.06276868283748627,
0.008374636061489582,
-0.043007344007492065,
-0.028251096606254578,
0.0015405697049573064,
0.06621543318033218,
-0.030780192464590073,
0.0010978421196341515,
0.07219589501619339,
0.02065039984881878,
-0.02534528821706772,
0.009023541584610939,
-0.0652938112616539,
0.025421489030122757,
-0.04595763608813286,
0.019890734925866127,
-0.028038766235113144,
-0.037385374307632446,
0.0336327999830246,
0.006697135511785746,
-0.002992122434079647,
0.06316711753606796,
-0.03695157170295715,
0.01597309485077858,
-0.04824342951178551,
0.006623805500566959,
-0.03440294414758682,
0.02469669096171856,
-0.0844012200832367,
-0.006342760287225246,
0.0769878625869751,
-0.006879017222672701,
0.011746594682335854,
0.03876053914427757,
0.007380180060863495,
0.03283572569489479,
0.03453822061419487,
-0.051692042499780655,
-0.02214430831372738,
-0.0030908759217709303,
0.07726239413022995,
0.02451983094215393,
-0.03838431090116501,
-0.02546950988471508,
0.036664463579654694,
0.04445275664329529,
-0.008982541039586067,
0.04531582444906235,
-0.009286858141422272,
-0.013853753916919231,
0.006861710920929909,
0.013659664429724216,
0.05683650076389313,
-0.007659299299120903,
-0.031399548053741455,
0.013237778097391129,
0.020042628049850464,
0.013427892699837685,
0.05490967631340027,
-0.025065114721655846,
0.0012959277955815196,
-0.013597418554127216,
0.011827148497104645,
0.05896803364157677,
-0.01063647773116827,
0.01712110824882984,
-0.0073296367190778255,
0.008486231788992882,
0.012752916663885117,
-0.07579237967729568,
-0.042040858417749405,
0.0418412908911705,
0.01805090717971325,
0.035925932228565216,
0.022856878116726875,
0.029801879078149796,
-0.06463342905044556,
-0.023852042853832245,
0.037720225751399994,
-0.03698026388883591,
-0.06023538112640381,
-0.012421993538737297,
0.020020511001348495,
-0.04149014502763748,
-0.010688289068639278,
-0.05164610594511032,
-0.023777537047863007,
-0.021556716412305832,
0.03316669911146164,
-0.045531366020441055,
-0.06572940945625305,
0.029394526034593582,
-0.007527423091232777,
-0.034273095428943634,
-0.05115599185228348,
-0.005560997407883406,
-0.03486247733235359,
-0.0265386700630188,
0.023216452449560165,
0.02470299042761326,
-0.0005370874423533678,
-0.02985120192170143,
0.0323038287460804,
-0.030381426215171814,
0.05114566907286644,
0.04621715843677521,
0.021225934848189354,
0.01602199487388134,
0.01663990318775177,
-0.0030761901289224625,
0.059745095670223236,
-0.0215336624532938,
0.06859265267848969,
0.015216726809740067,
0.10318519175052643,
-0.00011067442392231897,
-0.013970093801617622,
0.0719345286488533,
-0.0077184452675282955,
0.024898240342736244,
0.024656258523464203,
0.0000749360115150921,
0.015220674686133862,
0.003131531411781907,
-0.015539076179265976,
0.03913169354200363,
0.026139140129089355,
0.00045476810191757977,
-0.0056175836361944675,
-0.009543989785015583,
-0.003376992419362068,
0.010745501145720482,
0.0032000448554754257,
0.02079567313194275,
-0.025964606553316116,
-0.019222069531679153,
-0.061605602502822876,
-0.010183103382587433,
-0.04927203059196472,
-0.0036519181448966265,
0.04138645902276039,
-0.02461930923163891,
-0.03386444225907326,
0.003098007058724761,
0.0007658838876523077,
0.05350473150610924,
-0.0010705385357141495,
0.013621383346617222,
0.01930842362344265,
0.07578331232070923,
0.003356151282787323,
0.06027974188327789,
-0.037080589681863785,
-0.013244868256151676,
0.019758692011237144,
0.006966664921492338,
-0.030909491702914238,
-0.0835026353597641,
-0.07514374703168869,
-0.040311239659786224,
0.014625477604568005,
-0.02918863482773304,
0.027340244501829147,
-0.008414152078330517,
0.0096130957826972,
0.002492661355063319,
0.0651974231004715,
0.05364161729812622,
-0.059145670384168625,
-0.019152559340000153,
0.028298674151301384,
0.0584234744310379,
-0.0012085436610504985,
0.01051859837025404,
0.02130936272442341,
0.00859738327562809,
0.0067340051755309105,
-0.10246214270591736,
-0.017434246838092804,
0.013720221817493439,
0.042907796800136566,
-0.023710554465651512,
0.02675592713057995,
0.03517243266105652,
-0.04286688193678856,
-0.0051622455939650536,
-0.02620045468211174,
-0.005698679946362972,
-0.004676028620451689,
0.04960109665989876,
0.05556093156337738,
0.010425344109535217,
-0.024755934253335,
-0.0300188846886158,
0.07281710207462311,
-0.03791235759854317,
0.04240933805704117,
0.007593201007694006,
-0.016214706003665924,
0.009332859888672829,
-0.043333426117897034,
-0.05296001210808754,
0.009337272495031357,
0.02628791518509388,
-0.001336852670647204,
-0.015520983375608921,
-0.009853465482592583,
-0.001968806842342019,
-0.01329829916357994,
-0.0028811278752982616,
-0.0005097124958410859,
0.00991302914917469,
0.05919715762138367,
-0.045647334307432175,
0.06411345303058624,
-0.08967903256416321,
-0.022526510059833527,
-0.014923863112926483,
0.09212293475866318,
0.005505365319550037,
0.002029725117608905,
-0.010570410639047623,
-0.02429806813597679,
0.02427797205746174,
0.04765265807509422,
0.0038116162177175283,
0.011168258264660835,
0.030252955853939056,
-0.02605537511408329,
0.034753553569316864,
-0.030015619471669197,
0.011238296516239643,
0.009581184014678001,
0.07982810586690903,
-0.07250716537237167,
-0.02002561278641224,
-0.026193540543317795,
0.02468782477080822,
0.012441443279385567,
0.026116030290722847,
-0.04127858951687813,
0.0045973449014127254,
0.05558180436491966,
0.03188207373023033,
-0.06295592337846756,
0.05602094158530235,
-0.02371661365032196,
0.009570486843585968,
-0.015800107270479202,
0.018805870786309242,
-0.01232434343546629,
0.050793975591659546,
0.028957657516002655,
-0.07225456833839417,
-0.03903517499566078,
-0.008149800822138786,
-0.04624856263399124,
-0.025034567341208458,
-0.026424765586853027,
0.01606152579188347,
-0.023123037070035934,
-0.016813896596431732,
0.037551216781139374,
-0.028921684250235558,
-0.04861437901854515,
0.000246916722971946,
0.004175957757979631,
0.0039567784406244755,
0.00741342268884182,
-0.03396802768111229,
-0.011142340488731861,
-0.049790043383836746,
0.014571606181561947,
0.014197858981788158,
-0.05379413440823555,
-0.016685908660292625,
0.002323393477126956,
-0.006866565439850092,
0.04164556413888931,
0.002033107914030552,
0.025282206013798714,
0.03225021809339523,
-0.010010761208832264,
-0.05475239455699921,
0.035691116005182266,
-0.01715448684990406,
-0.12422270327806473,
0.0025907757226377726,
0.0005234225536696613,
-0.02168351225554943,
0.007004953920841217,
-0.03637077659368515,
-0.005695478059351444,
0.07269151508808136,
0.058122869580984116,
-0.04626981541514397,
-0.01392439566552639,
0.004514625761657953,
0.028327079489827156,
-0.012690650299191475,
0.006713947746902704,
-0.05781334638595581,
-0.04107482358813286,
0.032977987080812454,
0.029263656586408615,
0.03578346595168114,
-0.02403370477259159,
0.04676974564790726,
0.0036386605352163315,
0.020297454670071602,
-0.01886240765452385,
0.025127580389380455,
0.08204934746026993,
0.06558685749769211,
-0.059399984776973724,
-0.03547124192118645,
0.023549379780888557,
-0.048126861453056335,
-0.003979870583862066,
0.05049905553460121,
0.043596718460321426,
0.011363313533365726,
-0.06456014513969421,
0.0027003453578799963,
-0.05478506535291672,
-0.028011947870254517,
-0.009911436587572098,
0.01066220086067915,
-0.020576605573296547,
-0.016121169552206993,
0.04166574403643608,
-0.032126378268003464,
0.04053742438554764,
-0.022846920415759087,
0.014759908430278301,
-0.020926354452967644,
0.00325285573489964,
0.0058267926797270775,
-0.010354932397603989,
0.016966741532087326,
-0.014811892993748188,
0.019995547831058502,
-0.013268062844872475,
-0.04994618892669678,
0.05718585103750229,
-0.00012492129462771118,
-0.07312782853841782,
0.033249933272600174,
0.008267647586762905,
0.024137744680047035,
-0.05495776608586311,
-0.010031076148152351,
-0.035110101103782654,
0.016278637573122978,
0.036616526544094086,
-0.0004770790401380509,
0.027665579691529274,
0.04732956737279892,
0.011701207607984543,
0.01800982654094696,
-0.07069558650255203,
0.020833652466535568,
-0.02551310323178768,
0.036356840282678604,
-0.015932973474264145,
0.03685469925403595,
0.045565228909254074,
-0.03426932543516159,
0.05982958525419235,
0.046929728239774704,
-0.023512564599514008,
0.031245188787579536,
0.0028504838701337576,
-0.017432451248168945,
0.03938223421573639,
-0.020697128027677536,
0.03892761841416359,
0.010808013379573822,
0.02726186066865921,
0.031031962484121323,
0.011416025459766388,
-0.00243394635617733,
-0.04260675609111786,
0.032278068363666534,
0.06452414393424988,
0.025198165327310562,
-0.00869598425924778,
0.03862305358052254,
-0.0019551250152289867,
-0.008216321468353271,
-0.014017458073794842,
0.003912805579602718,
0.023670105263590813,
-0.008929934352636337,
-0.048613082617521286,
-0.03992768004536629,
-0.0010776154231280088,
0.0037292626220732927,
-0.027723010629415512,
-0.010017822496592999,
0.0019767447374761105,
-0.03638537973165512,
0.004641913343220949,
-0.06968415528535843,
0.028702618554234505,
-0.002943902276456356,
-0.05756020545959473,
-0.012113931588828564,
-0.002374793868511915,
-0.03877146914601326,
0.014226710423827171,
0.01625780388712883,
0.05267562344670296,
-0.010737431235611439,
0.08056393265724182,
0.053058162331581116,
-0.038713183254003525,
-0.038411449640989304,
-0.06855598837137222,
-0.024442851543426514,
0.055671319365501404,
-0.02392699010670185,
0.05752548202872276,
-0.03608318045735359,
0.037531763315200806,
-0.03902476653456688,
0.012874445877969265,
-0.003747370559722185,
-0.04467201605439186,
0.020200833678245544,
-0.02067270316183567,
-0.0003166249953210354,
-0.011790897697210312,
-0.027584852650761604,
0.005348533857613802,
-0.007875061593949795,
-0.008237740956246853,
-0.01349714770913124,
-0.059984590858221054,
-0.05964936688542366,
0.015257582999765873,
-0.04025939106941223,
-0.05949500948190689,
-0.029730739071965218,
-0.009263841435313225,
-0.02990429289638996,
0.04841618984937668,
-0.06326714903116226,
-0.008491190150380135,
0.029805071651935577,
-0.03759351745247841,
0.0701213926076889,
-0.007427397649735212,
-0.024638395756483078,
0.006742072757333517,
-0.03295910730957985,
0.02173653617501259,
-0.007898692972958088,
0.005763384513556957,
0.06969409435987473,
-0.007937577553093433,
-0.014213797636330128,
0.06910617649555206,
0.030611690133810043,
-0.05033621937036514,
0.030404718592762947,
-0.0063478704541921616,
0.008969518356025219,
0.012632658705115318,
-0.01845134049654007,
0.02595442906022072,
0.015618596225976944,
0.08763798326253891,
0.029365649446845055,
-0.02881457842886448,
0.0021439616102725267,
-0.0023590310011059046,
-0.0011868684086948633,
-0.027574358507990837,
0.005267212633043528,
0.06954249739646912,
0.055154651403427124,
0.02215229906141758,
0.003842842299491167,
-0.04770713299512863,
-0.018976647406816483,
-0.02347738668322563,
0.005114526953548193,
0.009014387615025043,
-0.13008764386177063,
0.036320753395557404,
0.033917561173439026,
0.032148104161024094,
-0.018050745129585266,
0.02205299586057663,
-0.01994682289659977,
0.01234580297023058,
-0.04400772601366043,
-0.006461357697844505,
0.0224363561719656,
0.0022712713107466698,
-0.04354386031627655,
0.03438530117273331,
0.05057930946350098,
-0.04023642838001251,
-0.05864780396223068,
-0.05234784632921219,
-0.024778427556157112,
-0.046518027782440186,
0.017257027328014374,
0.001811650930903852,
0.06588096916675568,
-0.015467675402760506,
-0.027417289093136787,
0.023613216355443,
-0.05657753720879555,
-0.030417852103710175,
0.00881844200193882,
0.06269901245832443,
-0.006964589934796095,
-0.014171143993735313,
-0.0040285345166921616,
-0.01792733371257782,
-0.002851408440619707,
-0.029248343780636787,
-0.019727040082216263,
0.01417918037623167,
0.02547828108072281,
0.00974970031529665,
-0.014757129363715649,
-0.09828073531389236,
-0.009748187847435474,
0.05166884511709213,
-0.0855480432510376,
-0.041923440992832184,
-0.024153631180524826,
-0.08438964933156967,
-0.05235844850540161,
-0.08194838464260101,
-0.006954165641218424,
0.00921081006526947,
-0.062121130526065826,
-0.009348376654088497,
-0.022760851308703423,
0.022993747144937515,
0.013696257956326008,
0.020753949880599976,
-0.003545519430190325,
-0.025739697739481926,
0.08507373183965683,
0.001640624599531293,
0.03922566771507263,
0.005209607072174549,
0.03353681042790413,
-0.0761856734752655,
0.023581035435199738,
0.016520405188202858,
0.00969894789159298,
0.06787920743227005,
0.03446391969919205,
0.04493798315525055,
-0.003129302291199565,
0.007466545328497887,
-0.03680834546685219,
0.0005935852532275021,
-0.05255303531885147,
-0.04623318836092949,
-0.04186655208468437,
-0.038726385682821274,
-0.05294020101428032,
0.02352912351489067,
0.03496061637997627,
-0.042380690574645996,
-0.01694631017744541,
-0.0005579954013228416,
-0.008749939501285553,
0.014742536470293999,
0.03785393759608269,
0.04937108978629112,
-0.03389812633395195,
-0.027381543070077896,
-0.02398952841758728,
-0.014015667140483856,
-0.013001276180148125,
0.036347609013319016,
-0.021668000146746635,
0.02300608716905117,
0.014678596518933773,
0.0012591819977387786,
0.023535938933491707,
-0.022480247542262077,
0.022128062322735786,
-0.07688089460134506,
-0.035341739654541016,
0.043795861303806305,
0.0011786993127316236,
0.017712580040097237,
0.056972384452819824,
0.008765904232859612,
0.011332550086081028,
0.0012073236284777522,
0.06063145771622658,
-0.0043386491015553474,
-0.01980249583721161,
-0.0528634749352932,
-0.052601661533117294,
0.05077178403735161,
-0.028268516063690186,
0.04228692501783371,
-0.007321061100810766,
0.06758914887905121,
0.026084020733833313,
0.03346870467066765,
0.0648556724190712,
0.07015391439199448,
-0.03764593228697777,
0.0755663737654686,
0.030332600697875023,
0.06315677613019943,
-0.01734277419745922,
0.02993333525955677,
-0.03830641135573387,
0.0605139322578907,
0.020478006452322006,
-0.018283668905496597,
-0.03742144629359245,
0.054121989756822586,
0.05095963552594185,
0.003259959165006876,
-0.002756330417469144,
-0.007961157709360123,
-0.0036502776201814413,
0.006302190478891134,
-0.02122262492775917,
-0.03617219626903534,
0.028562767431139946,
-0.00009590190893504769,
-0.03635907173156738,
-0.05494115129113197,
0.024391472339630127,
0.023510156199336052,
-0.02709379605948925,
0.01287136785686016,
0.001315224333666265,
-0.003653367282822728,
-0.004946041852235794,
0.005523793864995241,
-0.003638673573732376,
0.0028785744216293097,
0.025384383276104927,
-0.011090860702097416,
0.04568057134747505,
0.027089985087513924,
0.011555534787476063,
0.035003967583179474,
0.060091305524110794,
-0.03690851852297783,
0.0212451983243227,
-0.010026752948760986,
0.029545024037361145,
-0.06491714715957642,
0.026371203362941742,
0.05627567321062088,
-0.04094034433364868,
0.029321888461709023,
0.0240541473031044,
0.0363679900765419,
0.04757770895957947,
0.007163854315876961,
0.016022879630327225,
0.023448701947927475,
-0.0038022149819880724,
-0.043627187609672546,
-0.07729948312044144,
0.02117156609892845,
-0.020689789205789566,
0.08573625236749649,
-0.028872182592749596,
-0.025100626051425934,
-0.02313816361129284,
0.030152611434459686,
0.037439942359924316,
-0.059001050889492035,
0.0041135577484965324,
0.021907927468419075,
0.0589173249900341,
0.02822083979845047,
-0.006190608721226454,
-0.06829710304737091,
0.02700898051261902,
-0.043517280369997025,
0.006463553290814161,
0.011951309628784657,
0.03396082669496536,
-0.028818773105740547,
-0.024936163797974586,
-0.05101267993450165,
-0.03844331577420235,
0.011756561696529388,
-0.006924486253410578,
-0.04069603607058525,
0.014760861173272133,
0.0010570090962573886,
-0.048703309148550034,
-0.06453527510166168,
-0.045626163482666016,
-0.0020324978977441788,
0.008984149433672428,
0.011255940422415733,
-0.03835116699337959,
-0.03172601759433746,
-0.06888464838266373,
-0.033743783831596375,
-0.018165992572903633,
-0.006783695425838232,
-0.005788527429103851,
-0.008650236763060093,
-0.018904240801930428,
0.0005485262954607606,
-0.0028232429176568985,
0.06618279218673706,
-0.004562287125736475,
-0.007712804712355137,
-0.04352264851331711,
0.0692937821149826,
0.013907017186284065,
-0.04768143594264984,
0.00599309429526329,
0.0046682050451636314,
-0.0007626473088748753,
-0.007876558229327202,
0.03049628436565399,
0.014787283726036549,
-0.002465122612193227,
-0.06474824994802475,
0.002101963385939598,
-0.003629809943959117,
0.030817991122603416,
-0.04901465028524399,
0.017300482839345932,
-0.054577991366386414,
-0.038962580263614655,
-0.03285001963376999,
0.015127526596188545,
0.02600715495646,
0.018842993304133415,
0.02015923522412777,
0.01647832989692688,
0.030372915789484978,
0.00861811637878418,
0.030116260051727295,
-0.030042964965105057,
0.012153241783380508,
-0.06097422167658806,
-0.05021549016237259,
-0.03539782017469406,
0.0438932366669178
] |
<p>I was doing some simple harmonic motion problems and I came across this <a href="http://i.imgur.com/W2zi40o.jpg" rel="nofollow">picture</a> describing the position, velocity and acceleration of a linear oscillator. At the moment in time when v is 0 the linear oscillator should not be moving, only changing directions. I'm having a hard time understanding why the acceleration is the greatest at that time (according to these graphs), since there is no velocity change. Is it because acceleration is only the difference in velocity at two different points in time and not one? How exactly does the change in direction affect acceleration?</p>
<p>edit: I found another <a href="http://physics.stackexchange.com/questions/34178/how-can-an-objects-instantaneous-speed-be-zero-and-its-instantaneous-accelerat?rq=1">question</a> that answered my question. haha.</p> | g152 | [
0.08397728949785233,
0.02253137156367302,
-0.007885580882430077,
0.031013213098049164,
0.0914861187338829,
-0.00920090451836586,
0.06378966569900513,
0.0681101605296135,
-0.07880687713623047,
-0.026119060814380646,
0.002364343497902155,
0.017347807064652443,
-0.008677867241203785,
0.000370562425814569,
0.0011500500841066241,
-0.056845229119062424,
0.06453541666269302,
0.014333132654428482,
0.005690967198461294,
0.0037336864043027163,
0.01654944196343422,
-0.010216619819402695,
-0.038790151476860046,
-0.04350336641073227,
0.04882710054516792,
-0.025022784247994423,
-0.015134898014366627,
-0.07068266719579697,
-0.04359230771660805,
0.0028506785165518522,
0.0008736509480513632,
-0.018383018672466278,
0.012970905750989914,
-0.03311917558312416,
-0.018360493704676628,
-0.050917770713567734,
0.035809196531772614,
-0.02360658533871174,
0.01215226948261261,
-0.009251396171748638,
0.019457809627056122,
-0.1031329557299614,
0.06570900976657867,
-0.026910217478871346,
0.04711771011352539,
-0.0023154360242187977,
0.005645835772156715,
-0.0023777030874043703,
-0.02760416828095913,
-0.028070246800780296,
-0.03762165084481239,
-0.009425409138202667,
0.02218913845717907,
0.010995556600391865,
-0.005105368793010712,
0.01825355924665928,
0.012451397255063057,
0.02794518508017063,
0.043932605534791946,
0.023121923208236694,
-0.08178222179412842,
-0.02702816016972065,
0.037513960152864456,
-0.006012077443301678,
0.0020624531898647547,
-0.01413385197520256,
-0.038732606917619705,
-0.014316887594759464,
0.009686852805316448,
-0.01684216968715191,
0.023405026644468307,
-0.03284436836838722,
-0.06284387409687042,
-0.03949343040585518,
-0.008639625273644924,
0.022755486890673637,
-0.0031017607543617487,
-0.060263827443122864,
0.017731590196490288,
0.0028104025404900312,
-0.05291052907705307,
0.013598000630736351,
0.0005289682885631919,
0.0063227703794837,
0.03298920765519142,
0.019110865890979767,
0.05666952207684517,
0.034617383033037186,
-0.010205165483057499,
-0.032662127166986465,
0.024260425940155983,
-0.015449801459908485,
0.018541598692536354,
0.06209847703576088,
-0.055752675980329514,
-0.05040748417377472,
-0.06696809083223343,
0.1019759327173233,
0.02674388699233532,
0.02261360175907612,
-0.03928869962692261,
0.009228425100445747,
0.017125440761446953,
0.030006106942892075,
0.028528545051813126,
-0.021582668647170067,
0.05367349833250046,
-0.02740464173257351,
-0.058810628950595856,
-0.05989256501197815,
-0.015110568143427372,
-0.0530766025185585,
-0.006617589388042688,
-0.06724890321493149,
-0.004420778714120388,
-0.021530862897634506,
0.06339063495397568,
0.03201213851571083,
0.023008450865745544,
0.03082938678562641,
0.010350336320698261,
0.0348113588988781,
-0.006818901281803846,
0.07013188302516937,
0.0299456138163805,
-0.01831902004778385,
-0.01860540546476841,
0.00048698074533604085,
0.003874128917232156,
-0.0038670056965202093,
0.018644027411937714,
0.03695901110768318,
0.019717922434210777,
0.04201660305261612,
-0.04068062826991081,
-0.005455381702631712,
0.01272675022482872,
0.015399373136460781,
0.04269386827945709,
-0.014906703494489193,
0.03091954067349434,
-0.04510748013854027,
0.008226979523897171,
0.0036202683113515377,
0.00452018715441227,
-0.00790261011570692,
-0.012997557409107685,
-0.002803284674882889,
0.05446145310997963,
0.010591883212327957,
0.02950149215757847,
0.037529926747083664,
0.011809906922280788,
-0.014563740231096745,
0.004355710931122303,
-0.0021464515011757612,
0.04001080244779587,
0.06355653703212738,
-0.011134005151689053,
-0.01835603266954422,
0.058628153055906296,
0.02421669475734234,
0.04563280940055847,
-0.01348764169961214,
-0.10424333810806274,
0.007581897545605898,
-0.010516561567783356,
-0.013406194746494293,
0.0014813820598646998,
0.05636902153491974,
-0.014397275634109974,
-0.03415919095277786,
-0.010820199735462666,
0.05170087516307831,
-0.007550442591309547,
0.0037840744480490685,
0.0448896586894989,
-0.02725992165505886,
0.010981820523738861,
-0.0012166419764980674,
0.012922055087983608,
-0.040393438190221786,
-0.024082627147436142,
-0.08676561713218689,
-0.009361890144646168,
-0.022605672478675842,
-0.017970271408557892,
0.05582788214087486,
-0.09915437549352646,
0.007880045101046562,
0.0017809447599574924,
-0.06628607213497162,
-0.015124212019145489,
-0.006631503347307444,
-0.09927665442228317,
0.028623096644878387,
-0.01986403577029705,
-0.055196426808834076,
-0.07099336385726929,
0.03347374498844147,
-0.005541129969060421,
0.014666776172816753,
0.03773054853081703,
0.017037440091371536,
-0.005027927923947573,
-0.025477616116404533,
-0.010631080716848373,
-0.02077299728989601,
-0.015828879550099373,
0.024712976068258286,
0.038827084004879,
0.038272738456726074,
0.02677624672651291,
0.023104991763830185,
0.028113478794693947,
-0.0014902768889442086,
0.012586724013090134,
-0.027622612193226814,
0.01989302970468998,
0.002167688449844718,
-0.00026304982020519674,
-0.044985294342041016,
0.03742699697613716,
-0.010616972111165524,
-0.04871479794383049,
-0.06024130806326866,
0.03985501453280449,
-0.09189491719007492,
-0.014556498266756535,
0.06615347415208817,
-0.07409626990556717,
0.016339953988790512,
0.0011606189655140042,
0.01210496574640274,
0.0299406535923481,
-0.01849447935819626,
-0.014420047402381897,
0.017115598544478416,
0.03290311247110367,
0.008813719265162945,
0.03759431466460228,
-0.017272915691137314,
-0.05194741114974022,
-0.021871883422136307,
0.03937888890504837,
-0.07978484034538269,
0.07768503576517105,
-0.023063909262418747,
-0.0014804044039919972,
0.0045713018625974655,
0.024020962417125702,
-0.01193268597126007,
-0.0003529029490891844,
0.01037065964192152,
-0.000845282687805593,
-0.01191727351397276,
0.00007190815085778013,
0.018013490363955498,
-0.04550888016819954,
-0.024373207241296768,
0.003688778495416045,
0.009088881313800812,
0.04388341307640076,
0.022035960108041763,
-0.018670015037059784,
-0.01843407191336155,
0.007078790105879307,
-0.0007105491240508854,
-0.021064886823296547,
-0.042165473103523254,
-0.05612734705209732,
0.06385501474142075,
-0.0038074839394539595,
0.08434338122606277,
-0.04830586537718773,
0.010251699946820736,
0.012459078803658485,
-0.006047332659363747,
0.009640710428357124,
0.010565592907369137,
-0.010438663884997368,
-0.021132513880729675,
-0.040775932371616364,
0.007734575774520636,
0.036296546459198,
-0.013814626261591911,
0.047944407910108566,
0.002326542278751731,
-0.02539505623281002,
-0.04934641718864441,
-0.09274308383464813,
0.03419683128595352,
0.06306441128253937,
-0.03915519639849663,
-0.007436561863869429,
0.025752335786819458,
0.002185339108109474,
-0.023672623559832573,
0.008759444579482079,
0.0038819056935608387,
0.04942290857434273,
0.01612965203821659,
0.008016630075871944,
0.041612446308135986,
0.04325677454471588,
0.009717844426631927,
-0.02507023513317108,
-0.04963494464755058,
-0.05998638644814491,
0.05100790038704872,
0.03543519228696823,
0.039839889854192734,
-0.023662304505705833,
-0.0195769052952528,
0.008433806709945202,
-0.019972121343016624,
-0.0664934292435646,
0.011455458588898182,
-0.007873628288507462,
0.030575517565011978,
-0.06660342961549759,
-0.09374605864286423,
-0.012547609396278858,
0.02703404426574707,
0.015345430001616478,
0.033545203506946564,
0.036983758211135864,
0.006560376845300198,
-0.026459509506821632,
0.003279157215729356,
-0.005398475099354982,
0.03819543123245239,
0.03728464990854263,
-0.014671720564365387,
-0.0022807035129517317,
-0.05679294466972351,
-0.01941322721540928,
0.004925349727272987,
0.04591193050146103,
0.029418135061860085,
-0.00769005948677659,
-0.025096647441387177,
-0.06555740535259247,
0.02625328116118908,
0.022544629871845245,
0.002085774904116988,
0.03676812723278999,
0.0003820745332632214,
-0.0022431048564612865,
-0.017739471048116684,
0.04685428366065025,
-0.018388858065009117,
-0.03175951912999153,
-0.008577938191592693,
-0.034646280109882355,
-0.01578625477850437,
0.03297321870923042,
0.04809703677892685,
-0.05621025338768959,
0.022367969155311584,
-0.030623525381088257,
-0.03371138498187065,
0.001078818691894412,
0.06475453078746796,
0.03024587221443653,
0.026127060875296593,
-0.02872025966644287,
0.041302140802145004,
-0.01827172376215458,
0.0023299935273826122,
0.013355078175663948,
-0.037352364510297775,
0.005037965718656778,
-0.031665291637182236,
0.008890069089829922,
-0.03892029449343681,
-0.01944919303059578,
0.022540824487805367,
-0.009597297757863998,
0.05031827092170715,
0.064519502222538,
-0.01297167968004942,
0.01220034435391426,
-0.012482688762247562,
0.008790708146989346,
-0.0032289791852235794,
-0.054215528070926666,
-0.017108777537941933,
0.0003418021078687161,
-0.07021640241146088,
0.09344615787267685,
0.031957581639289856,
0.01430991105735302,
-0.030650848522782326,
-0.00714647863060236,
0.01705244556069374,
-0.005913214758038521,
0.026450416073203087,
-0.043060120195150375,
0.035894908010959625,
-0.0583965964615345,
0.0032431120052933693,
-0.04036468639969826,
-0.022609170526266098,
0.003648532321676612,
0.051527660340070724,
0.050141386687755585,
0.00721321813762188,
-0.02066567726433277,
-0.028078973293304443,
-0.017083274200558662,
0.006920325104147196,
-0.03743447735905647,
-0.028970425948500633,
-0.01270981039851904,
0.024531899020075798,
0.01641903817653656,
0.031380102038383484,
-0.0039025312289595604,
0.01648876816034317,
0.04791830852627754,
0.03201492503285408,
-0.019202139228582382,
-0.04930918663740158,
0.0039691501297056675,
0.0656333938241005,
0.06929267942905426,
-0.015413749031722546,
0.0387822762131691,
-0.013157357461750507,
0.0037169400602579117,
0.019454902037978172,
0.03391474857926369,
0.02352621592581272,
0.016918331384658813,
0.07036612182855606,
0.013659816235303879,
0.08537786453962326,
0.026736192405223846,
0.01298239454627037,
0.07177482545375824,
0.04244613274931908,
0.03426261246204376,
0.012155513279139996,
-0.01744963973760605,
0.06519635766744614,
-0.00681632524356246,
-0.054985541850328445,
0.03555050492286682,
-0.06937828660011292,
-0.009447792544960976,
0.08115164190530777,
-0.0030127381905913353,
-0.004286697134375572,
-0.006047168746590614,
-0.026207180693745613,
0.0018845914164558053,
-0.025882620364427567,
-0.019690724089741707,
0.05004361271858215,
-0.043421097099781036,
-0.03837618604302406,
-0.012300984933972359,
0.011538754217326641,
0.022755147889256477,
0.009071442298591137,
-0.05979469045996666,
-0.03432909771800041,
-0.04783022776246071,
-0.016490446403622627,
0.026066185906529427,
0.010019143112003803,
-0.03563603386282921,
0.05582498386502266,
0.06806948781013489,
-0.0044454713352024555,
0.007331539876759052,
-0.0034984152298420668,
-0.013164023868739605,
-0.05616108328104019,
-0.07598525285720825,
-0.050407856702804565,
0.0812499076128006,
-0.0014261082978919148,
0.033669110387563705,
0.00773816742002964,
-0.0662437379360199,
-0.033471908420324326,
0.037576980888843536,
-0.02211545966565609,
0.009203608147799969,
-0.00016187099390663207,
-0.008273604325950146,
-0.03907400742173195,
0.04191109538078308,
-0.01397901214659214,
0.007050609216094017,
0.0002582462620921433,
-0.04444918781518936,
-0.04690771549940109,
-0.08958137035369873,
0.033197492361068726,
-0.022287368774414062,
-0.04989398270845413,
-0.038606613874435425,
0.07541940361261368,
0.047951605170965195,
-0.04282759130001068,
-0.018056834116578102,
0.017270024865865707,
-0.01070744264870882,
0.08357890695333481,
0.011093156412243843,
0.0007560835801996291,
0.02766764536499977,
-0.06850852072238922,
0.001217035809531808,
-0.03037402778863907,
0.004782917443662882,
0.006073182914406061,
0.027890237048268318,
-0.0012250789441168308,
0.015326308086514473,
-0.05391698703169823,
0.046538304537534714,
0.044954173266887665,
-0.029230425134301186,
-0.0013540565269067883,
0.0006850080681033432,
0.05246874317526817,
-0.015491914935410023,
0.005890409927815199,
0.02272672764956951,
-0.03634980320930481,
-0.03463044390082359,
0.023111069574952126,
0.028730902820825577,
-0.04492096230387688,
0.00444897823035717,
0.0008582823211327195,
-0.09204919636249542,
-0.028174690902233124,
-0.01573624275624752,
0.04449132829904556,
-0.06543496251106262,
0.0027910752687603235,
-0.0849974974989891,
0.014535467140376568,
-0.007848517037928104,
-0.03528148680925369,
-0.04393131658434868,
0.007034634239971638,
0.030225470662117004,
0.02731373719871044,
-0.05645226687192917,
0.03209760785102844,
-0.0018957307329401374,
0.007721861358731985,
-0.027591368183493614,
-0.0677768811583519,
0.1134234368801117,
0.04863610491156578,
0.03334102779626846,
-0.0019890237599611282,
0.06528423726558685,
-0.01604899950325489,
0.0512223020195961,
-0.0104768555611372,
0.08601044118404388,
0.004266188479959965,
-0.003803356783464551,
0.008418703451752663,
-0.016194121912121773,
0.056711457669734955,
-0.010470939800143242,
0.00999779999256134,
-0.03827390819787979,
-0.04485051706433296,
-0.10855484008789062,
0.024450143799185753,
-0.01006057858467102,
0.01277914084494114,
0.016670972108840942,
-0.06422404199838638,
0.0013955269241705537,
0.01588750071823597,
-0.028589816763997078,
-0.00729537894949317,
0.09707412123680115,
0.023814262822270393,
-0.06193729490041733,
0.00444424943998456,
0.027165964245796204,
-0.08224540203809738,
-0.0524202436208725,
-0.05122251808643341,
-0.02774135395884514,
-0.0029442950617522,
0.0017104946309700608,
0.023330988362431526,
-0.012211324647068977,
0.0008136138203553855,
-0.005132054444402456,
0.03678811714053154,
0.020697729662060738,
0.01782805845141411,
-0.0006954586715437472,
0.0029746275395154953,
0.05276951938867569,
-0.02735843136906624,
-0.07507983595132828,
0.031138084828853607,
0.03638308867812157,
0.03509438782930374,
0.02751413732767105,
0.01789798028767109,
0.004880037624388933,
-0.020633796229958534,
-0.002350755035877228,
-0.027923334389925003,
0.02126026339828968,
-0.00592156033962965,
-0.020304087549448013,
0.04610235244035721,
0.010983359068632126,
0.024578437209129333,
-0.05420864000916481,
-0.003623777301982045,
0.06276730448007584,
0.00014867780555505306,
0.023877248167991638,
0.008631408214569092,
-0.020005622878670692,
0.06286068260669708,
0.01776942051947117,
-0.008876364678144455,
-0.019273322075605392,
0.03076561912894249,
0.0034545192029327154,
-0.011096995323896408,
0.043579619377851486,
0.025342248380184174,
-0.020851237699389458,
-0.007774678990244865,
-0.027717815712094307,
0.04505228251218796,
0.012689645402133465,
-0.004721985664218664,
-0.08755330741405487,
-0.029295077547430992,
-0.003075050190091133,
-0.03294806554913521,
0.010711361654102802,
0.03769978508353233,
0.0035930685698986053,
0.010546771809458733,
-0.007006981410086155,
0.02152801863849163,
0.010757464915513992,
-0.022862015292048454,
-0.06077989563345909,
-0.008851900696754456,
0.01657797209918499,
0.037420108914375305,
-0.003453228622674942,
0.0031781375873833895,
0.011434542015194893,
-0.01371617242693901,
-0.0016994884936138988,
-0.006068739574402571,
0.022334381937980652,
-0.01685812510550022,
0.03412226587533951,
-0.023341087624430656,
0.047743041068315506,
0.04937373101711273,
-0.03358696401119232,
0.009066210128366947,
-0.01883595436811447,
-0.006763200741261244,
-0.011503375135362148,
0.030559640377759933,
0.016085699200630188,
-0.03136853873729706,
0.011019916273653507,
0.044291749596595764,
-0.05899953469634056,
0.025620007887482643,
-0.020531926304101944,
-0.06388915330171585,
-0.0033788022119551897,
0.019708679988980293,
-0.012266740202903748,
-0.01783326268196106,
-0.036093197762966156,
0.02358189970254898,
-0.03927406668663025,
0.050674110651016235,
-0.029549967497587204,
-0.0020567041356116533,
0.04037168622016907,
-0.055181849747896194,
0.0009067390346899629,
0.03842543438076973,
0.008530317805707455,
-0.008050845935940742,
0.03320392593741417,
-0.03645090386271477,
-0.009352600201964378,
0.04006557911634445,
-0.005091287195682526,
0.019135303795337677,
0.020092366263270378,
-0.028335772454738617,
0.03905072435736656,
0.02886461280286312,
0.008592058904469013,
0.028610214591026306,
-0.0026179805863648653,
-0.003940341528505087,
0.0015258309431374073,
0.008248280733823776,
0.04105398803949356,
-0.09247616678476334,
0.005192005541175604,
0.018015999346971512,
-0.023212576285004616,
0.009309723041951656,
0.004981315229088068,
-0.054423850029706955,
0.017795320600271225,
-0.009572964161634445,
0.01993556320667267,
0.04669366776943207,
-0.10167428106069565,
0.010112480260431767,
-0.005344534758478403,
0.026768477633595467,
-0.013417303562164307,
0.02005399949848652,
-0.03373297303915024,
-0.04289337247610092,
-0.041468296200037,
0.03628941625356674,
-0.003440050408244133,
-0.015385200269520283,
0.009062298573553562,
0.05037133768200874,
0.05696132406592369,
-0.05934491381049156,
-0.007577904965728521,
0.01545808371156454,
-0.0894852802157402,
-0.005428320728242397,
-0.0258376095443964,
-0.0007829805836081505,
-0.02213129587471485,
-0.015882667154073715,
0.026296379044651985,
-0.0019348259083926678,
0.006155814975500107,
0.04034273326396942,
0.011810561642050743,
-0.013658985495567322,
0.031136563047766685,
-0.014221775345504284,
-0.04854339733719826,
0.005670599173754454
] |
<p>Isn't speed a relative thing in space? If so, why would the speed of a propellant matter? Why can't a space ship accelerate infinitely?</p> | g4625 | [
0.04364602640271187,
0.06759954243898392,
0.008185630664229393,
0.02038424089550972,
0.03341049700975418,
0.02606971189379692,
-0.00014999430277384818,
0.05193008854985237,
-0.06758448481559753,
-0.07910588383674622,
0.06712837517261505,
0.012140163220465183,
0.047140758484601974,
0.03715848922729492,
0.032142020761966705,
-0.006137157324701548,
0.08411478996276855,
-0.03335460647940636,
0.009973517619073391,
0.052145883440971375,
0.006049807649105787,
-0.045632172375917435,
-0.011629902757704258,
-0.02884036675095558,
0.0030631942208856344,
0.02440568059682846,
-0.011529332958161831,
-0.10494481772184372,
0.000700140546541661,
-0.0017925120191648602,
-0.01880870945751667,
-0.02539151906967163,
-0.04011622071266174,
-0.06669715791940689,
-0.041733384132385254,
-0.07356403023004532,
-0.04009251296520233,
-0.009535614401102066,
0.0553402379155159,
-0.01301397755742073,
-0.019015582278370857,
-0.01621546596288681,
-0.013907077722251415,
-0.002799086272716522,
-0.012842915020883083,
0.036684799939394,
0.013767323456704617,
-0.020500482991337776,
-0.0031528729014098644,
0.006603678688406944,
-0.03654249757528305,
0.0029919331427663565,
-0.031521253287792206,
-0.007054867688566446,
-0.021697914227843285,
-0.017104003578424454,
0.0169784314930439,
-0.004265818744897842,
0.035162363201379776,
0.02157597243785858,
-0.026891818270087242,
-0.029678041115403175,
0.03862837702035904,
0.023694928735494614,
0.03686099126935005,
-0.053120434284210205,
-0.00003074104097322561,
0.018607622012495995,
0.016714846715331078,
0.04984789714217186,
0.049327436834573746,
-0.02252376638352871,
-0.07528634369373322,
-0.05251944810152054,
-0.03327326476573944,
-0.03458412364125252,
-0.024349557235836983,
0.013604188337922096,
-0.04286956414580345,
0.004272611811757088,
0.013268756680190563,
0.011633098125457764,
0.04184309020638466,
0.0029352072160691023,
-0.013771489262580872,
-0.020712973549962044,
-0.0005346337566152215,
-0.04897725582122803,
-0.012441310100257397,
0.0065960753709077835,
0.0023375386372208595,
0.030392000451683998,
0.05275353044271469,
0.050470124930143356,
-0.023505935445427895,
0.0024552601389586926,
-0.009869496338069439,
0.04162565991282463,
-0.016827493906021118,
0.0011571628274396062,
-0.047969624400138855,
-0.0186470914632082,
0.04598160460591316,
0.013605375774204731,
0.020303785800933838,
-0.024516956880688667,
0.09428740292787552,
0.024855371564626694,
0.046938180923461914,
-0.10876245051622391,
0.003620781935751438,
-0.06889815628528595,
0.0029799677431583405,
-0.03902935981750488,
0.017778944224119186,
-0.023780664429068565,
0.026310497894883156,
-0.037461262196302414,
-0.0032199614215642214,
0.04209771379828453,
0.02370922639966011,
-0.01734822243452072,
-0.057833682745695114,
0.055364806205034256,
-0.015207226388156414,
-0.0003333926433697343,
0.027679823338985443,
-0.025075793266296387,
-0.033478569239377975,
-0.01159338653087616,
-0.03424089401960373,
0.021193597465753555,
-0.021899864077568054,
-0.0009403461590409279,
-0.02636982686817646,
-0.04203279688954353,
-0.06875266134738922,
-0.007248410955071449,
-0.015500180423259735,
0.023695681244134903,
-0.03333593159914017,
-0.022515183314681053,
0.0014041848480701447,
0.03889225423336029,
-0.05230123549699783,
0.006019567139446735,
-0.029238523915410042,
0.03926162049174309,
0.02412215806543827,
-0.007337000221014023,
0.007682734169065952,
0.07251477986574173,
0.01930580846965313,
0.015702372416853905,
0.020225748419761658,
0.013816198334097862,
0.05645604431629181,
0.01574847474694252,
0.0014298268361017108,
0.013360866345465183,
0.07531393319368362,
0.06107424199581146,
-0.04510195553302765,
-0.025348160415887833,
-0.08502956479787827,
0.0518476776778698,
0.004055842757225037,
-0.0043676672503352165,
-0.03543677181005478,
-0.00000709243249730207,
-0.03945864737033844,
-0.046848345547914505,
0.015131840482354164,
0.01681152544915676,
0.007352182175964117,
-0.050342243164777756,
0.07345238327980042,
0.029810775071382523,
-0.008386989124119282,
0.0011412319727241993,
-0.037050534039735794,
-0.028058694675564766,
0.003378248307853937,
-0.03135434910655022,
-0.018297461792826653,
0.04808022826910019,
-0.02242370881140232,
0.02466033399105072,
-0.0797371044754982,
0.06593934446573257,
-0.003073335625231266,
-0.03344043344259262,
0.00915896613150835,
0.06012481451034546,
0.0035887560807168484,
-0.024131469428539276,
-0.024847744032740593,
-0.044438835233449936,
-0.05010441690683365,
0.0106638940051198,
-0.009860404767096043,
0.04003636911511421,
-0.006006993819028139,
0.015337014570832253,
0.028517495840787888,
-0.032541945576667786,
-0.054644837975502014,
-0.004940260201692581,
0.04181322827935219,
-0.0264188963919878,
0.08080822974443436,
0.006519930437207222,
0.0018505174666643143,
0.050122566521167755,
0.06984005123376846,
-0.06671874970197678,
-0.08119915425777435,
0.03296959400177002,
0.028923317790031433,
-0.024396225810050964,
-0.017032401636242867,
-0.044848911464214325,
0.053291790187358856,
-0.052391499280929565,
-0.04099484533071518,
-0.041690416634082794,
0.006379233207553625,
-0.018408862873911858,
0.03546762466430664,
0.042184703052043915,
-0.018803007900714874,
-0.009992701932787895,
-0.005132168065756559,
0.009092865511775017,
-0.004686060827225447,
-0.003393544815480709,
0.05183319374918938,
0.02798994444310665,
-0.02597370557487011,
0.07785741239786148,
0.03446299955248833,
-0.052694257348775864,
-0.03244290128350258,
0.01276607345789671,
0.05116662383079529,
-0.05826178193092346,
0.010297195054590702,
-0.04257066920399666,
-0.005765620619058609,
-0.013355940580368042,
0.0008589010103605688,
0.025525160133838654,
-0.017232904210686684,
-0.019390564411878586,
0.010702705942094326,
-0.004956752527505159,
-0.05304909124970436,
0.030309338122606277,
-0.06270336359739304,
-0.000056894779845606536,
-0.010385614819824696,
0.034427840262651443,
0.0205567367374897,
-0.0039335996843874454,
-0.0008530126651749015,
0.03591393679380417,
-0.04596492648124695,
0.00004421893390826881,
-0.007107321638613939,
-0.016175970435142517,
-0.02177407406270504,
0.006880049593746662,
-0.005472654942423105,
0.02732648327946663,
-0.04227224737405777,
0.05490602180361748,
0.01771620474755764,
-0.04415636137127876,
0.02735603228211403,
0.05683336406946182,
-0.014380200766026974,
-0.027442172169685364,
-0.014308572746813297,
0.026960385963320732,
-0.002010588999837637,
-0.0400468148291111,
0.03525840491056442,
0.021625299006700516,
0.03015172854065895,
-0.04464023560285568,
0.0008840030059218407,
-0.006118602119386196,
-0.0018122262554243207,
-0.005676147527992725,
0.06661724299192429,
0.037051159888505936,
0.020041145384311676,
0.01548520103096962,
-0.034638240933418274,
-0.05136913061141968,
0.07301478832960129,
-0.0039047161117196083,
0.03794734179973602,
0.036539673805236816,
0.00754174217581749,
0.026949001476168633,
-0.06387925148010254,
-0.011381296440958977,
-0.0442243292927742,
0.030919935554265976,
0.011379463598132133,
0.06470528244972229,
-0.020368613302707672,
0.06405366212129593,
-0.03287608548998833,
0.019107794389128685,
0.015867535024881363,
0.0003580646007321775,
-0.016731154173612595,
-0.03564169257879257,
-0.028220780193805695,
-0.0513843335211277,
-0.01254025474190712,
-0.01934758946299553,
0.0018451869254931808,
0.012956897728145123,
-0.045189738273620605,
-0.029979979619383812,
0.023946380242705345,
0.02183184213936329,
-0.008701283484697342,
0.01038957480341196,
0.008739873766899109,
-0.047174952924251556,
-0.03862227499485016,
0.017294833436608315,
0.010254612192511559,
0.08167935907840729,
-0.013853002339601517,
0.07381008565425873,
-0.015276994556188583,
0.033120449632406235,
-0.010496249422430992,
0.06644650548696518,
-0.02025197632610798,
0.07087688148021698,
0.06053757295012474,
0.01739923655986786,
-0.00898360088467598,
0.010298574343323708,
0.07577116787433624,
-0.041643209755420685,
0.013395464979112148,
0.0029321962501853704,
-0.03609570115804672,
0.035396724939346313,
0.020534636452794075,
-0.013654083013534546,
-0.009341398254036903,
-0.039044369012117386,
-0.01379635650664568,
0.06141209602355957,
-0.013428802601993084,
0.026286985725164413,
-0.0005550332716666162,
0.06054721772670746,
0.004624560009688139,
-0.016009025275707245,
-0.0003246711567044258,
-0.020422130823135376,
-0.0009464499307796359,
-0.0352117121219635,
-0.033066775649785995,
-0.015966616570949554,
0.08709778636693954,
-0.015278820879757404,
0.03363613784313202,
0.010057847015559673,
-0.017582029104232788,
-0.026179205626249313,
0.08063473552465439,
0.005665802396833897,
-0.022797510027885437,
-0.010994385927915573,
0.01597878336906433,
0.04443557187914848,
-0.052239853888750076,
-0.003969128709286451,
-0.030011354014277458,
-0.04366695508360863,
0.04759388044476509,
-0.015244293957948685,
-0.03639689460396767,
-0.01909494213759899,
0.03216322511434555,
-0.00332647911272943,
-0.0206949170678854,
-0.014064702205359936,
0.01667410135269165,
-0.0043007307685911655,
-0.044141050428152084,
0.0036285934038460255,
-0.043384093791246414,
-0.0011871937895193696,
-0.023833053186535835,
0.011330409906804562,
-0.002546790987253189,
-0.0180337093770504,
-0.05980126932263374,
-0.0010966206900775433,
0.011044153943657875,
0.0440063551068306,
-0.02895566262304783,
-0.02514711581170559,
-0.03620333969593048,
0.01759410835802555,
0.019135620445013046,
0.000559368112590164,
0.023916080594062805,
-0.0027746877167373896,
0.042215052992105484,
0.025927413254976273,
0.02182740904390812,
-0.03261592611670494,
0.0584368072450161,
0.03061593323945999,
0.04730760306119919,
0.04193180799484253,
0.028901232406497,
0.0003234066825825721,
0.006392242386937141,
0.0523664727807045,
0.05815654247999191,
0.09168542921543121,
-0.029919423162937164,
0.05063123628497124,
0.0065534100867807865,
0.08574612438678741,
0.0458066463470459,
0.04442809894680977,
0.04762912541627884,
0.0019346141489222646,
0.06832204014062881,
0.013082040473818779,
-0.017943598330020905,
0.049185480922460556,
-0.015631796792149544,
-0.04793984815478325,
-0.06149458885192871,
-0.010142560116946697,
-0.045050717890262604,
-0.04529186338186264,
-0.0409131683409214,
-0.027816956862807274,
0.0018021868309006095,
0.026007868349552155,
-0.025439469143748283,
-0.014065283350646496,
0.04801582172513008,
0.058378010988235474,
-0.052040547132492065,
0.009050046093761921,
0.03534426540136337,
0.006659310776740313,
0.018997976556420326,
0.04717501252889633,
0.001868166378699243,
-0.03708898276090622,
-0.046285200864076614,
0.022424817085266113,
0.023768693208694458,
-0.014234707690775394,
-0.008343222551047802,
0.05723792687058449,
-0.008736745454370975,
-0.024568146094679832,
0.028854187577962875,
-0.06740590929985046,
-0.04613145813345909,
-0.01422012411057949,
-0.07496379315853119,
-0.068462073802948,
0.03314812853932381,
-0.003069851081818342,
0.008185544982552528,
0.046952877193689346,
-0.0648333802819252,
0.04279732331633568,
-0.03407185524702072,
-0.043133024126291275,
0.0026322598569095135,
-0.004625158384442329,
-0.039086051285266876,
-0.02160942368209362,
-0.021618548780679703,
0.033206526190042496,
0.025910472497344017,
-0.012858239002525806,
-0.01258840598165989,
0.007286212407052517,
-0.04418720677495003,
-0.008381335064768791,
0.018601253628730774,
-0.021884145215153694,
-0.05653063952922821,
0.009555325843393803,
0.03374927490949631,
-0.004846011754125357,
-0.05349961668252945,
-0.0086453752592206,
-0.0503610298037529,
0.04452397674322128,
0.0010335756232962012,
0.03763173893094063,
0.02836478501558304,
-0.044106435030698776,
0.041356105357408524,
-0.06169363483786583,
0.03658771887421608,
-0.004359492100775242,
0.041169166564941406,
-0.032768893986940384,
0.005570678971707821,
0.05444711446762085,
0.014745067805051804,
0.06919967383146286,
-0.04534956440329552,
-0.0647948607802391,
-0.024079710245132446,
0.05749101936817169,
0.05599255859851837,
0.016022194176912308,
0.0005757072940468788,
-0.041818391531705856,
-0.06862681359052658,
0.01041367743164301,
0.022895772010087967,
0.007184709422290325,
0.010427450761198997,
-0.033654890954494476,
-0.08565659821033478,
-0.0123308589681983,
-0.008663533255457878,
0.056017715483903885,
0.009464297443628311,
0.0038908831775188446,
-0.046368230134248734,
-0.05235575512051582,
-0.027611207216978073,
-0.07224319875240326,
-0.056912779808044434,
0.0000012771813544532051,
0.0439300611615181,
-0.037240080535411835,
0.010051279328763485,
0.06451665610074997,
0.005832785740494728,
0.005107529927045107,
-0.016433903947472572,
-0.04226858913898468,
-0.029846452176570892,
0.02262314409017563,
0.03009229525923729,
0.04343383386731148,
-0.0038840181659907103,
-0.050577934831380844,
-0.01729290932416916,
-0.029421191662549973,
-0.0018417806131765246,
-0.030280930921435356,
-0.056663885712623596,
0.028142662718892097,
-0.029729854315519333,
0.03112255036830902,
0.051119476556777954,
-0.04530949518084526,
-0.06442905962467194,
-0.0172897856682539,
-0.0756583958864212,
-0.023570997640490532,
0.045282360166311264,
-0.03737408295273781,
0.005259730853140354,
-0.015107407234609127,
0.002698850352317095,
-0.017276622354984283,
0.04644743725657463,
0.0018890119390562177,
0.07640466094017029,
0.005625538993626833,
0.019950365647673607,
-0.03147970885038376,
0.0059156580828130245,
-0.0380718931555748,
-0.031840499490499496,
0.02387077920138836,
-0.0660226121544838,
0.04136580973863602,
-0.00025161527446471155,
0.02202446572482586,
0.03454876318573952,
0.025553029030561447,
0.05582817271351814,
0.03890642896294594,
-0.0033041404094547033,
-0.001780094113200903,
-0.02600649558007717,
0.010526236146688461,
0.0493716299533844,
0.05646693706512451,
0.005596074741333723,
0.03414589911699295,
-0.0063046906143426895,
-0.04484159126877785,
-0.022360417991876602,
0.000018564667698228732,
-0.03306451439857483,
-0.01990364119410515,
-0.028284037485718727,
0.01996329054236412,
0.07604409754276276,
-0.03996250778436661,
-0.032678257673978806,
-0.0030092198867350817,
0.07910527288913727,
-0.013127090409398079,
-0.03528974950313568,
0.04378369450569153,
0.02419062703847885,
-0.03385497257113457,
-0.0012504925252869725,
-0.0004437270399648696,
-0.030139798298478127,
0.04188837856054306,
0.004697284661233425,
-0.011074215173721313,
0.005771435331553221,
-0.0011322895297780633,
-0.007776009850203991,
-0.006326042581349611,
0.038792964071035385,
-0.01708928681910038,
-0.03822117671370506,
0.06849513947963715,
-0.007253897842019796,
-0.010923233814537525,
0.035243529826402664,
-0.08305154740810394,
0.009492022916674614,
-0.05295339599251747,
0.0017044480191543698,
-0.08502434939146042,
-0.048083748668432236,
0.015032695606350899,
0.010542983189225197,
0.022604316473007202,
0.007268456742167473,
0.0019017598824575543,
0.053072866052389145,
-0.020403839647769928,
-0.011604038998484612,
-0.005583254620432854,
0.023822136223316193,
0.028839459642767906,
0.020772289484739304,
0.014682894572615623,
-0.01383891049772501,
-0.015601275488734245,
0.04697804898023605,
0.04217570275068283,
0.03481864556670189,
0.011104453355073929,
0.009973155334591866,
0.012278485111892223,
0.07543980330228806,
0.03560508042573929,
-0.007120420690625906,
-0.05740811675786972,
0.07635818421840668,
0.02960434928536415,
0.03102959506213665,
0.011299296282231808,
0.0007775473641231656,
0.0775742456316948,
0.006303338799625635,
0.005765609443187714,
-0.05027476325631142,
-0.0662882998585701,
0.01975744590163231,
-0.05982835963368416,
-0.009097418747842312,
0.01767285168170929,
0.02787247858941555,
0.01445796899497509,
0.013755022548139095,
0.013676143251359463,
0.00635963398963213,
0.045545950531959534,
-0.045037198811769485,
-0.030251983553171158,
0.03125355392694473,
-0.0029604516457766294,
0.040615785866975784,
0.0003977123706135899,
-0.000565253256354481,
0.0170939601957798,
-0.013775893487036228,
0.016638651490211487,
-0.008937520906329155,
-0.03103821724653244,
-0.0028790810611099005,
-0.0000908082802197896,
0.01915273815393448,
-0.020938338711857796,
0.0046686893329024315,
-0.04942502826452255,
0.003947220277041197,
-0.03669428452849388,
-0.030070196837186813,
0.010651705786585808,
0.03526068106293678,
0.019223881885409355,
0.016173960641026497,
-0.061060428619384766,
0.0268614012748003,
-0.018675751984119415,
-0.011434638872742653,
-0.07623695582151413,
0.028257790952920914,
-0.04367617517709732,
0.004542835056781769,
-0.003309022868052125,
0.017494576051831245,
0.03471798077225685,
-0.0988881066441536,
0.0414917878806591,
0.03749340772628784,
0.0063390908762812614,
-0.031222399324178696,
0.03826018050312996,
-0.023527581244707108,
0.00362381455488503,
0.0027454975061118603,
0.05257122963666916,
0.027052663266658783,
-0.0021268706768751144,
-0.02714606560766697,
0.025090569630265236,
0.009298974648118019,
0.02472158707678318,
0.06539686024188995,
0.04484211280941963,
-0.04857379570603371,
0.005142929032444954,
0.003226714674383402,
-0.012127145193517208,
0.02240322157740593,
0.005362236872315407,
-0.055623382329940796,
-0.005104330368340015,
-0.01638781651854515,
0.01621760055422783,
-0.01937195658683777,
-0.03330901265144348,
-0.025028862059116364,
-0.09907831251621246,
-0.038030244410037994,
0.01629137434065342
] |
<p>I'm current developing cargo loader software, but i have a little challenge with calculating load for each axle when a cargo is placed on container. I know that all axles will be affected (the nearest ones are the most affected ones of course), and I want to find approximately the value of each load. Here's example scenario in pictures:</p>
<p><img src="http://i.stack.imgur.com/LCqjF.jpg" alt="enter image description here"> </p>
<p>I tried to find loads using balance rules taking each point as a pivot and calculating equation based on that position as below (EDIT: on the following figure in case 4 the 5th axle is pivot, I forgot to show it on figure):</p>
<p><img src="http://i.stack.imgur.com/3AP9g.jpg" alt="enter image description here"></p>
<p><img src="http://i.stack.imgur.com/v0D88.jpg" alt="enter image description here"></p>
<p>But I think I have problem with above solution as I could not find F3, F4, F5 in special examples (putting "d" distance values from pivot - P.S in this last picture all "d"s are different distances from pivot in that case - so d3 in the first equation is not equal to d3 in second equation as these both have different distances to different pivots) - for easy calculation you can use Cramer's rule online calculator <a href="http://matrix.reshish.com/cramer.php" rel="nofollow">here</a>.</p>
<p>I tried to solve this problem with moment but I could not done as I'm not good in physics :( I could not find relations between different forces in that case, I had only F1*d1 + F2*d2 + F3*d3 = F4*d4 + F5*d5 and F1 + F2 + F3 + F4 + F5 = mg ===> i got 5 unknowns but only 2 equations :(</p>
<p>So, i need your help! Any suggestions will be appreciated! </p> | g4626 | [
0.011663995683193207,
0.02174276113510132,
-0.021921537816524506,
-0.05978156626224518,
0.06485465168952942,
-0.05115627869963646,
0.014867483638226986,
-0.06586714833974838,
-0.09158670902252197,
0.007293128874152899,
-0.04784061014652252,
-0.048355963081121445,
-0.012952581979334354,
-0.018530378118157387,
0.07268712669610977,
0.0563461109995842,
0.06211547553539276,
-0.006338840816169977,
0.022826120257377625,
0.049464743584394455,
0.05186718702316284,
0.025104913860559464,
-0.05740224942564964,
-0.020309872925281525,
-0.07567263394594193,
0.02822614461183548,
-0.04996848851442337,
0.12343230098485947,
-0.06111094728112221,
0.04492862522602081,
-0.0355524942278862,
-0.07666346430778503,
-0.04252234473824501,
-0.04262256622314453,
-0.10003731399774551,
-0.07168974727392197,
0.04101370647549629,
0.005843512713909149,
0.0689883828163147,
0.02517557144165039,
-0.014657750725746155,
-0.06767819076776505,
0.01698981411755085,
0.03138821944594383,
-0.010447358712553978,
0.007046010345220566,
-0.026258746162056923,
0.02242465130984783,
0.036420393735170364,
0.014943627640604973,
-0.05304402485489845,
0.019461646676063538,
0.007450592238456011,
-0.04618849605321884,
0.023505840450525284,
-0.00032703261240385473,
0.02580409310758114,
-0.010189954191446304,
-0.025820991024374962,
-0.014870383776724339,
-0.02188710682094097,
0.004952902905642986,
-0.012312423437833786,
0.035850245505571365,
0.03362312912940979,
-0.011895549483597279,
-0.024144303053617477,
0.005644287448376417,
-0.022940265014767647,
0.008170321583747864,
0.039360467344522476,
0.003985743969678879,
-0.02850293181836605,
-0.04812648519873619,
-0.06555785238742828,
0.0026227161288261414,
-0.021923091262578964,
0.050525665283203125,
-0.005917062517255545,
-0.018311122432351112,
0.024597110226750374,
0.0031068758107721806,
0.057945504784584045,
0.03135598078370094,
0.029868438839912415,
0.008426644839346409,
0.011984208598732948,
0.06036008894443512,
-0.011462406255304813,
-0.0038124362472444773,
0.045095380395650864,
0.004831851460039616,
0.06891200691461563,
-0.030132394284009933,
-0.0464223213493824,
-0.02221321314573288,
-0.007999458350241184,
0.02341420017182827,
-0.007110247854143381,
0.006045802496373653,
-0.012183383107185364,
0.048221781849861145,
-0.004691822919994593,
-0.05121222883462906,
-0.03330688551068306,
-0.024836543947458267,
0.008095068857073784,
0.061537593603134155,
0.02163381688296795,
-0.05052410066127777,
-0.06931347399950027,
-0.031028911471366882,
-0.0011637444840744138,
-0.05871580168604851,
0.05078592896461487,
0.003539893077686429,
0.05308962240815163,
0.014915096573531628,
0.03785525634884834,
0.013816703110933304,
0.011161728762090206,
0.020583990961313248,
-0.030007073655724525,
0.11593564599752426,
0.027162108570337296,
-0.055036235600709915,
-0.019846100360155106,
0.05152449756860733,
0.05189816281199455,
-0.009547676891088486,
0.0021985541097819805,
-0.08141385763883591,
0.028287597000598907,
0.023416072130203247,
0.0012829158222302794,
0.034446317702531815,
-0.03426935896277428,
0.03898640349507332,
-0.004310171585530043,
-0.023539185523986816,
-0.02348223514854908,
-0.0035879507195204496,
0.0004147080471739173,
-0.008892831392586231,
-0.0019453944405540824,
0.024730617180466652,
-0.014187559485435486,
0.011328502558171749,
0.05768801271915436,
-0.04493271932005882,
-0.0011951701017096639,
0.033601924777030945,
-0.07762838900089264,
0.052806202322244644,
-0.02171638049185276,
0.007488275412470102,
0.010848306119441986,
-0.03822707384824753,
-0.022837916389107704,
0.017957031726837158,
0.0022210583556443453,
0.004143670201301575,
0.011946584098041058,
-0.03689799830317497,
-0.0026367458049207926,
0.06630994379520416,
-0.020285870879888535,
-0.007878445088863373,
0.010849233716726303,
-0.05760427936911583,
-0.12049182504415512,
-0.05098049342632294,
0.0386321023106575,
-0.01525918859988451,
0.01694679446518421,
-0.003957588691264391,
0.04000839963555336,
0.008051244542002678,
0.074394591152668,
0.05026549473404884,
0.031150484457612038,
0.02044498361647129,
0.10212432593107224,
-0.013369260355830193,
-0.06047613173723221,
-0.05321147292852402,
0.02280060015618801,
-0.01665164902806282,
-0.008197270333766937,
0.025429632514715195,
0.012834389694035053,
0.029490217566490173,
0.016713393852114677,
-0.022016340866684914,
-0.05592434108257294,
-0.011951299384236336,
0.029161980375647545,
-0.043159060180187225,
-0.03845497965812683,
-0.006259576883167028,
-0.04857475310564041,
-0.006324347574263811,
0.0035683223977684975,
0.06412937492132187,
-0.02532515674829483,
-0.019119776785373688,
-0.008617370389401913,
-0.03772270679473877,
0.022351620718836784,
-0.015701085329055786,
-0.04236282780766487,
-0.008547003380954266,
-0.024843182414770126,
0.04874022305011749,
-0.021230127662420273,
0.025772951543331146,
0.03099711239337921,
0.0436786450445652,
-0.014781204052269459,
0.006051419302821159,
0.005147705785930157,
0.004078343976289034,
0.005604627542197704,
0.0026192618533968925,
0.019969817250967026,
-0.02174193225800991,
0.03577012941241264,
-0.026119181886315346,
0.04953773692250252,
0.00907067395746708,
0.007712260819971561,
0.038649171590805054,
-0.022287579253315926,
0.017898980528116226,
0.06486924737691879,
-0.02027019113302231,
0.022593868896365166,
0.03813784569501877,
0.02486530691385269,
0.06926457583904266,
0.030637839809060097,
0.025855761021375656,
-0.030615609139204025,
-0.0041290465742349625,
0.005707590840756893,
0.008923579938709736,
0.060599375516176224,
-0.013260473497211933,
0.0496126189827919,
0.006796177010983229,
0.016273995861411095,
-0.020172452554106712,
0.0009365321020595729,
-0.019057657569646835,
0.0155593017116189,
0.005390472710132599,
-0.008574577048420906,
-0.021376855671405792,
-0.007607423234730959,
0.03340187668800354,
-0.0341813750565052,
-0.010338328778743744,
0.03324614465236664,
0.04752523824572563,
-0.03295891359448433,
-0.02701694704592228,
0.011875682510435581,
-0.020251460373401642,
0.03557193651795387,
0.01629217341542244,
-0.038374096155166626,
-0.0737675353884697,
-0.04564184322953224,
0.017264457419514656,
-0.010091184638440609,
-0.033216871321201324,
0.0055926344357430935,
-0.010837961919605732,
-0.036451034247875214,
0.06522814184427261,
-0.009099219925701618,
-0.03767580911517143,
-0.05042712762951851,
0.012796495109796524,
0.029503701254725456,
0.0029945417772978544,
0.04159683734178543,
0.05727872997522354,
0.03318598493933678,
0.046654991805553436,
0.01318748015910387,
-0.007902761921286583,
0.0015050474321469665,
-0.007006098050624132,
0.012320039793848991,
0.04658353328704834,
0.009256059303879738,
-0.005749813746660948,
-0.013537428341805935,
-0.03163379430770874,
-0.01224298682063818,
0.017767226323485374,
0.051297497004270554,
0.016947640106081963,
-0.01744762808084488,
0.04831207916140556,
-0.005416648928076029,
-0.04397552087903023,
0.052298881113529205,
0.022086070850491524,
-0.07762370258569717,
-0.004124606493860483,
0.02357521280646324,
-0.04072360321879387,
-0.04801679775118828,
-0.010494820773601532,
0.016858814284205437,
-0.02013699896633625,
-0.008212974295020103,
-0.08108025789260864,
-0.020336205139756203,
-0.03969704732298851,
-0.026051506400108337,
0.00803602859377861,
0.0539272204041481,
0.09290717542171478,
-0.053261853754520416,
0.07437339425086975,
0.01318002212792635,
0.0005094559746794403,
0.02007228136062622,
0.01153118722140789,
0.03440530598163605,
-0.01937856338918209,
-0.012921007350087166,
-0.04388827830553055,
0.02092677541077137,
-0.012217720039188862,
0.009189710021018982,
0.0039323302917182446,
-0.05169098079204559,
0.01938576065003872,
-0.015867264941334724,
-0.033286210149526596,
-0.06502102315425873,
-0.003064637305215001,
0.020743221044540405,
0.04598649591207504,
0.02681475318968296,
0.008482350036501884,
-0.05045868828892708,
0.017487574368715286,
0.07641122490167618,
0.004585305228829384,
0.03140776604413986,
-0.015103894285857677,
-0.004890564829111099,
-0.0018625984666869044,
0.0022736575920134783,
0.07627270370721817,
-0.031098050996661186,
0.02791074477136135,
-0.05585237219929695,
0.047100868076086044,
0.04900088906288147,
-0.05218992754817009,
-0.0002780027862172574,
0.026730433106422424,
0.028592528775334358,
-0.035169780254364014,
0.0478825643658638,
0.005952668376266956,
0.00865563377737999,
-0.06745325028896332,
0.024107368662953377,
-0.03584250062704086,
0.04888402298092842,
-0.004874709993600845,
-0.039824776351451874,
0.023305485025048256,
0.0009543701307848096,
0.048263248056173325,
-0.01913273334503174,
-0.01779261976480484,
0.02323792316019535,
-0.0034604810643941164,
0.058708079159259796,
0.020335258916020393,
-0.018966691568493843,
0.041923604905605316,
-0.008998324163258076,
-0.06454717367887497,
-0.026482217013835907,
-0.006976677570492029,
0.031860727816820145,
0.018035709857940674,
-0.0363127700984478,
-0.00909727718681097,
0.022907309234142303,
0.03850775957107544,
0.05669856444001198,
-0.006771205924451351,
0.05488334968686104,
0.04410693049430847,
0.0113900201395154,
-0.011497817002236843,
0.026248209178447723,
0.009740264154970646,
0.00785280205309391,
0.031066151335835457,
-0.018031692132353783,
0.018770016729831696,
0.01947294920682907,
-0.014615494757890701,
0.016935767605900764,
0.021737342700362206,
0.026150330901145935,
-0.034843336790800095,
-0.012199876829981804,
-0.03222049027681351,
0.05247713252902031,
0.05182948336005211,
-0.038926877081394196,
-0.07235745340585709,
0.005011307075619698,
-0.007916534319519997,
-0.02077268622815609,
-0.002954188035801053,
0.029722603037953377,
-0.014548546634614468,
-0.028866605833172798,
0.007081956136971712,
-0.030363649129867554,
0.018285105004906654,
-0.018348542973399162,
0.01630103960633278,
0.03325905650854111,
0.010132014751434326,
0.033659543842077255,
-0.003812068607658148,
-0.011163257993757725,
0.08495685458183289,
-0.018850740045309067,
-0.017338847741484642,
-0.03479347005486488,
0.07063325494527817,
-0.050859469920396805,
-0.047913532704114914,
0.053617529571056366,
-0.019701233133673668,
0.016602596268057823,
-0.05110558494925499,
-0.014136635698378086,
0.007431062404066324,
0.030100151896476746,
0.0049726818688213825,
-0.022523930296301842,
-0.03300430625677109,
0.06363081187009811,
0.0030660636257380247,
-0.05620148777961731,
-0.00971037708222866,
0.002446540165692568,
-0.06279737502336502,
-0.0009725562413223088,
-0.0183261651545763,
0.026748066768050194,
-0.0074938214384019375,
-0.017780596390366554,
-0.024361424148082733,
-0.021218646317720413,
-0.01961023546755314,
0.03431607037782669,
-0.018306804820895195,
0.021079372614622116,
0.0030802409164607525,
-0.030451955273747444,
0.027982527390122414,
-0.010586034506559372,
-0.03141199052333832,
-0.05378837510943413,
-0.013140377588570118,
-0.04164181649684906,
0.0001736847625579685,
-0.036676812916994095,
0.005569436587393284,
-0.0017903400585055351,
0.0008663209737278521,
0.06310753524303436,
-0.04289701208472252,
0.0030896435491740704,
0.03255462646484375,
-0.08237940818071365,
-0.004060117993503809,
0.021293438971042633,
0.006139243487268686,
0.020131999626755714,
-0.00359160965308547,
-0.051709145307540894,
-0.07771996408700943,
0.005307543091475964,
-0.0032125189900398254,
0.004017346538603306,
-0.027690883725881577,
-0.0015506629133597016,
-0.0030379649251699448,
0.07212472707033157,
-0.016539951786398888,
0.008651874028146267,
0.008831649087369442,
0.0645194947719574,
-0.022581595927476883,
0.03770073875784874,
-0.05745115876197815,
-0.04059300571680069,
-0.01751537434756756,
0.01970442570745945,
0.04679865390062332,
-0.029329145327210426,
0.03733162209391594,
0.01628236472606659,
0.02687879651784897,
0.01838977262377739,
-0.057893384248018265,
0.04172755777835846,
-0.06952772289514542,
-0.04957672581076622,
-0.022702114656567574,
-0.01976231299340725,
0.012245869264006615,
-0.051619015634059906,
0.005810462404042482,
0.04067343845963478,
-0.03810950741171837,
-0.03841456398367882,
-0.03719471022486687,
0.020323796197772026,
0.033738505095243454,
0.054569829255342484,
0.0034843229223042727,
-0.02963954396545887,
-0.01570601388812065,
0.004136424046009779,
-0.011121268384158611,
-0.031171469017863274,
-0.009241567924618721,
-0.03190084919333458,
-0.0369262620806694,
0.047170937061309814,
0.0018051501829177141,
-0.00011127534526167437,
0.09417407959699631,
-0.02298862300813198,
-0.028005750849843025,
-0.007877444848418236,
0.02446806989610195,
-0.055920518934726715,
-0.012916672974824905,
-0.021387767046689987,
-0.02475636452436447,
0.03988386318087578,
-0.03252609819173813,
0.033606696873903275,
0.007434563711285591,
0.027616824954748154,
0.08026815205812454,
-0.07582094520330429,
0.03175852820277214,
0.038117069751024246,
0.06108469516038895,
0.017414608970284462,
-0.04551619663834572,
0.0011460245586931705,
-0.02999291755259037,
0.07714278995990753,
0.01815061829984188,
-0.02756197564303875,
-0.046148184686899185,
-0.05162244290113449,
0.04489031061530113,
-0.0008176324190571904,
-0.012824144214391708,
0.022676706314086914,
0.029546689242124557,
-0.06636925041675568,
0.037048909813165665,
0.015432938002049923,
-0.05027531459927559,
0.027466654777526855,
-0.08439648151397705,
0.023602399975061417,
0.01502973958849907,
-0.04946638643741608,
-0.014698727987706661,
0.004485464654862881,
0.005960535258054733,
0.0438370406627655,
0.02665882185101509,
0.02532428316771984,
0.03677777945995331,
0.053688663989305496,
-0.019551685079932213,
0.05560901015996933,
-0.04848133400082588,
0.00015384804282803088,
-0.008497936651110649,
-0.018837563693523407,
-0.03505123034119606,
-0.0527244471013546,
-0.018831204622983932,
-0.007629711646586657,
0.05297091603279114,
-0.023805133998394012,
0.07791133224964142,
-0.02382490038871765,
-0.03322897106409073,
-0.06380032747983932,
-0.008274580352008343,
0.048899225890636444,
0.005530485883355141,
-0.02734985388815403,
-0.003584418212994933,
-0.0013328740606084466,
-0.060653023421764374,
0.04105053469538689,
0.04470588639378548,
-0.06215904280543327,
-0.019943350926041603,
0.029298778623342514,
0.009042929857969284,
0.03244524449110031,
-0.05194663256406784,
0.042751189321279526,
-0.0028260427061468363,
0.009268921799957752,
0.023267989978194237,
0.023120351135730743,
0.030919348821043968,
-0.00967271439731121,
0.045271120965480804,
0.009475352242588997,
0.016529586166143417,
-0.05399210378527641,
0.0008549609337933362,
-0.0018549220403656363,
-0.03489021211862564,
-0.02070687897503376,
-0.07196930795907974,
-0.01795121841132641,
0.05391308665275574,
0.016696758568286896,
0.007322415243834257,
0.027596255764365196,
0.05791763961315155,
-0.03316657245159149,
0.0021326406858861446,
0.04473678022623062,
-0.0018689691787585616,
0.03153884783387184,
-0.00575886107981205,
-0.0126621313393116,
-0.03340892493724823,
0.019647303968667984,
-0.03338003158569336,
-0.031559623777866364,
0.04950712248682976,
0.017804177477955818,
-0.014502516016364098,
-0.0003590518899727613,
0.05890240892767906,
-0.009638562798500061,
-0.0335967093706131,
-0.06853631138801575,
0.03372278809547424,
0.053861577063798904,
0.028589077293872833,
0.028947485610842705,
0.007231019902974367,
-0.04175248742103577,
-0.041395775973796844,
-0.0029220536816865206,
-0.011899699456989765,
-0.08063692599534988,
-0.010724538937211037,
0.034696273505687714,
0.04621223732829094,
-0.007956438697874546,
-0.03180320933461189,
0.0005758859915658832,
0.0031092199496924877,
0.08007863909006119,
0.04994184151291847,
-0.004692850634455681,
-0.02950797602534294,
-0.04005369171500206,
0.015026245266199112,
0.052556611597537994,
0.03602117300033569,
0.03292979300022125,
-0.029316814616322517,
-0.005054067354649305,
-0.020575538277626038,
0.018343370407819748,
-0.012613825500011444,
-0.03607548773288727,
0.0014489494496956468,
-0.06906459480524063,
0.013026591390371323,
-0.027430459856987,
-0.0020934257190674543,
0.07210872322320938,
0.044718459248542786,
0.007251420058310032,
-0.04044085368514061,
-0.02068539336323738,
0.02150624431669712,
0.021760841831564903,
-0.00032316017313860357,
0.03668311983346939,
0.06267795711755753,
-0.009805223904550076,
0.0008502202108502388,
-0.0011683461489155889,
-0.01120492909103632,
0.006005467846989632,
-0.019053595140576363,
-0.028284795582294464,
-0.01835377886891365,
-0.004950460512191057,
0.014462508261203766,
-0.019877102226018906,
-0.03715312108397484,
-0.023638064041733742,
0.049663443118333817,
0.03558726981282234,
0.027866553515195847,
-0.018873943015933037,
-0.03834611922502518,
-0.013403884135186672,
0.022440044209361076,
0.0017964718863368034,
-0.11852465569972992,
0.016087748110294342,
-0.009485209360718727,
0.006235731765627861,
0.027258824557065964,
-0.013253767043352127,
0.01511908695101738,
-0.0317251980304718,
-0.025040393695235252,
-0.000633668270893395,
0.024499092251062393,
-0.010532033629715443,
0.004402720369398594,
-0.05184587463736534,
-0.01335293147712946,
-0.05439410358667374,
-0.026767227798700333,
-0.02859886735677719,
-0.005906003061681986,
0.004091488663107157,
-0.014379116706550121,
-0.09023276716470718,
-0.012522623874247074,
0.008248609490692616,
-0.025672806426882744,
-0.00887592975050211,
-0.03144431486725807
] |
<p>The question I am working on is, "Two blocks are free to slide along the friction-less wooden track shown below. The block of mass $m_1 = 4.98~kg$ is released from the position shown, at height $h = 5.00~m$ above the flat part of the track. Protruding from its front end is the north pole of a strong magnet, which repels the north pole of an identical magnet embedded in the back end of the block of mass $m_2 = 9.40~kg$, initially at rest. The two blocks never touch. Calculate the maximum height to which $m_1$ rises after the elastic collision."</p>
<p><img src="http://i.stack.imgur.com/Uz4To.gif" alt="enter image description here"></p>
<p>This question comes from webassign. On webassign they have a feature called "Watch It;" this feature allows you to see a person solve a problem nearly similar to this one. I feel as though there is an error in what the person says in the video. The person says that the mechanical energy of the block-earth system is conserved, but that wouldn't be true; if we were looking at the block-block system--that is, $m_1$ and $m_2$--the mechanical energy would be conserved. By looking at just the block-earth system, there would be a loss in kinetic energy, because when the two blocks "collide," they apply a force over a distance(work), causing a change in kinetic energy of each block, because the kinetic energy of the moving block is transferred into the other block, which is why the first block doesn't return to its initial height. Is this correct? If not, what am I misunderstanding?</p>
<p>As a result of this contention with what the person said in the video, I am not very certain on how to solve this problem.
EDIT (attempt to solve): </p>
<p>Energy analysis:</p>
<p>$m_1:$ $PE_i=mgh=KE_f$, where $h$ is the height from which it drops.</p>
<p>$KE_i=0~J$; $PE_f=mgh_0$, where $h_0$ is the height is rises to after the collision</p>
<p>$m_2:$ $KE_i=PE_i=PE_f=0~j$; $KE_f=\frac{1}{2}m_2v^2_{f,2}$</p>
<p>Momentum Analysis:</p>
<p>$m_1:$ $\vec{p}_{i,1}=m_1\vec{v}_{i,1}$; $\vec{p}_{f,1}=m_1\vec{v}_{f,1}$</p>
<p>$m_2:$ $\vec{p}_{i,2}=m_2\vec{v}_{i,1}$; $\vec{p}_{f,2}=m_2\vec{v}_{f,2}$</p>
<p>When I set up an equation for change in mechanical energy, and an equation for conservation of momentum, I get two equations, with a lot of unknowns. What did I do wrong?</p> | g44 | [
0.07996620237827301,
0.010569564998149872,
0.02236894704401493,
0.047842640429735184,
0.01766118034720421,
0.011494548991322517,
0.0391642302274704,
0.031340762972831726,
-0.07318843901157379,
0.0029908849392086267,
-0.012262753210961819,
-0.006567820906639099,
0.008670279756188393,
0.01824931986629963,
-0.004934956319630146,
0.020090000703930855,
0.12376450002193451,
-0.056131087243556976,
0.013856586068868637,
0.03944815695285797,
-0.06643521785736084,
0.009078040719032288,
-0.028684863820672035,
-0.016514882445335388,
-0.016810180619359016,
-0.0042794193141162395,
0.024428049102425575,
0.017157671973109245,
-0.04695415496826172,
-0.03028402104973793,
-0.006440592929720879,
-0.01571641117334366,
0.033128466457128525,
-0.0825170949101448,
-0.08341258019208908,
0.025102129206061363,
0.08241169899702072,
-0.04258806258440018,
0.0007222268613986671,
-0.010851268656551838,
0.05913780257105827,
-0.08231747895479202,
0.022715583443641663,
-0.008197594434022903,
0.009426174685359001,
-0.017367418855428696,
-0.031426802277565,
-0.04495103657245636,
-0.005616785958409309,
0.027017340064048767,
0.010569018311798573,
0.06299728155136108,
0.051692426204681396,
0.03608875349164009,
-0.0027771168388426304,
0.03322727233171463,
0.027225442230701447,
-0.026783689856529236,
0.07708609849214554,
0.01571398228406906,
-0.02194938436150551,
-0.01111523061990738,
0.029022661969065666,
-0.03419242799282074,
0.04781970754265785,
-0.029027681797742844,
-0.05481670796871185,
0.02025694027543068,
0.03548675775527954,
-0.008367323316633701,
0.02509324811398983,
0.005289644468575716,
0.007004266604781151,
-0.011711908504366875,
-0.006952787283807993,
-0.019014516845345497,
0.018561415374279022,
0.0004271980724297464,
0.029070207849144936,
0.018313903361558914,
-0.0949748083949089,
0.10234679281711578,
0.010858090594410896,
0.019197896122932434,
0.03664484620094299,
0.048505883663892746,
-0.033310387283563614,
0.05401548743247986,
-0.05367705971002579,
0.046143561601638794,
0.02854587882757187,
-0.0068932780995965,
0.07212647050619125,
-0.0061551048420369625,
0.010179008357226849,
0.0002643930783960968,
-0.04430295154452324,
0.06058434024453163,
0.06717429310083389,
0.030606959015130997,
-0.016332922503352165,
-0.049367278814315796,
-0.011161336675286293,
-0.018954431638121605,
0.055433087050914764,
-0.039230331778526306,
0.02284841611981392,
0.046061109751462936,
-0.044302914291620255,
-0.010280054062604904,
0.03016636334359646,
-0.10706188529729843,
-0.06220391020178795,
-0.0771741271018982,
-0.02609597146511078,
-0.04371611028909683,
0.07243107259273529,
0.025454452261328697,
0.01204616203904152,
0.04168713092803955,
0.006009550765156746,
-0.012402652762830257,
0.007193609140813351,
0.06609568744897842,
-0.019574545323848724,
-0.04950894042849541,
-0.008919029496610165,
-0.03435344621539116,
0.031757403165102005,
-0.014443369582295418,
-0.0626816675066948,
-0.029623763635754585,
0.07388627529144287,
0.0009266778943128884,
0.00010755503171822056,
0.013872400857508183,
-0.0051947301253676414,
0.06855574250221252,
0.00830609630793333,
0.005936116445809603,
-0.04005769267678261,
0.008198871277272701,
-0.014271550811827183,
-0.04191242903470993,
-0.06068142503499985,
0.03774262219667435,
0.02444612607359886,
-0.02854435332119465,
0.07095574587583542,
-0.023460792377591133,
0.003916510846465826,
0.06364908069372177,
-0.03777231276035309,
-0.02596520073711872,
0.05275627225637436,
-0.010142408311367035,
0.04881885647773743,
0.018207712098956108,
0.007366526871919632,
0.015039214864373207,
0.0528714545071125,
-0.05005822330713272,
0.07804635167121887,
-0.013581319712102413,
-0.0379178449511528,
0.0013983926037326455,
0.01718708872795105,
-0.05873233079910278,
0.03187329322099686,
-0.01620071940124035,
-0.062268324196338654,
-0.05816050246357918,
0.03660256415605545,
0.07895729690790176,
-0.05508023872971535,
0.027515819296240807,
0.09937886893749237,
-0.06943608075380325,
-0.012782343663275242,
0.014521445147693157,
0.021672556176781654,
0.006669152993708849,
0.0965820923447609,
0.022561142221093178,
0.005130498204380274,
-0.011518974788486958,
0.03081754967570305,
0.08660612255334854,
-0.00971802044659853,
-0.04077773168683052,
-0.0357171967625618,
-0.022388773038983345,
0.01966053619980812,
0.003935010638087988,
-0.011708283796906471,
0.03282498940825462,
-0.012791321612894535,
-0.017219316214323044,
-0.03472145274281502,
-0.004419222008436918,
-0.013325255364179611,
0.04231851547956467,
0.006546531338244677,
0.035618070513010025,
-0.029605383053421974,
0.020012307912111282,
0.013382014818489552,
0.019442472606897354,
-0.0016542469384148717,
-0.06365998089313507,
-0.014929908327758312,
0.04388478398323059,
-0.09190648049116135,
0.04097931832075119,
0.001852836343459785,
-0.041251085698604584,
-0.0094526382163167,
-0.009170852601528168,
-0.06692126393318176,
0.002212751191109419,
-0.046040479093790054,
-0.022534048184752464,
0.020266765728592873,
-0.00765674002468586,
-0.02309277467429638,
-0.05562981218099594,
-0.015663793310523033,
-0.04813887178897858,
-0.022763051092624664,
0.0012346758740022779,
-0.03722303360700607,
0.0599491260945797,
-0.008349448442459106,
-0.020761098712682724,
0.08765378594398499,
0.037013620138168335,
-0.0060360729694366455,
0.013153601437807083,
0.013645852915942669,
-0.006100828293710947,
0.033180560916662216,
-0.06121458858251572,
-0.03559999167919159,
-0.0630866065621376,
0.07661537081003189,
-0.026840610429644585,
0.06850004941225052,
0.0014211899833753705,
0.025325654074549675,
0.019406232982873917,
0.03102092631161213,
-0.014370450749993324,
-0.0014282885240390897,
-0.016306471079587936,
0.03969196602702141,
-0.004373785108327866,
-0.03502273187041283,
-0.007926261983811855,
-0.03643117472529411,
-0.028814319521188736,
0.01764884777367115,
-0.08349421620368958,
0.005009356886148453,
0.0738721415400505,
-0.062084171921014786,
-0.009388449601829052,
-0.05047057941555977,
-0.03127044811844826,
-0.01078152284026146,
0.00918743759393692,
-0.050089359283447266,
0.026433216407895088,
0.023978808894753456,
0.09451355040073395,
-0.02764316461980343,
-0.049462057650089264,
-0.004185056313872337,
-0.00395302614197135,
0.019249269738793373,
0.020000478252768517,
-0.0116344653069973,
0.015984119847416878,
-0.019631726667284966,
-0.003977532498538494,
0.05109734833240509,
0.0005313253495842218,
-0.028758715838193893,
0.008666661567986012,
-0.002801783150061965,
-0.019946686923503876,
-0.06446728110313416,
0.023597026243805885,
0.07179152220487595,
0.043567534536123276,
-0.02590055949985981,
0.08087609708309174,
-0.015155111439526081,
-0.05705684423446655,
-0.06092303991317749,
-0.01813543029129505,
-0.015028279274702072,
0.0008934653596952558,
0.011444454081356525,
0.041502490639686584,
0.025954360142350197,
0.06289011240005493,
-0.012116419151425362,
-0.01776113174855709,
0.0012609174009412527,
0.007961167022585869,
-0.05415942519903183,
0.03195568174123764,
0.0132584935054183,
-0.02245115116238594,
-0.06547633558511734,
0.003313870867714286,
0.04831864312291145,
-0.04272777959704399,
-0.009987087920308113,
-0.0005414983606897295,
-0.05733223259449005,
-0.02118980884552002,
0.012667680159211159,
0.019262943416833878,
-0.013149459846317768,
0.024487029761075974,
-0.08060349524021149,
0.029170885682106018,
-0.028257152065634727,
0.015466944314539433,
-0.01078872475773096,
0.09317623823881149,
0.008044632151722908,
-0.04189629107713699,
-0.03189535066485405,
-0.05156822130084038,
0.017116352915763855,
-0.02612648531794548,
0.04693223536014557,
0.008610649965703487,
-0.04701213538646698,
0.010389624163508415,
-0.00048274107393808663,
-0.028548389673233032,
0.006290554068982601,
0.03706565499305725,
-0.006616091355681419,
-0.0014935011276975274,
-0.03148871660232544,
-0.05766508728265762,
0.09663397818803787,
0.008276434615254402,
0.012219136580824852,
0.03488621115684509,
-0.03607757017016411,
0.040819067507982254,
-0.016223182901740074,
-0.02025311253964901,
-0.062294505536556244,
0.044035203754901886,
0.028875576332211494,
-0.012724093161523342,
0.01589290052652359,
-0.0247514508664608,
-0.02445394918322563,
-0.017520640045404434,
-0.05905604735016823,
0.02017378807067871,
0.025700215250253677,
-0.05401761829853058,
0.04670703411102295,
-0.028282983228564262,
-0.05045771971344948,
-0.0025579766370356083,
0.03527117520570755,
-0.03671219199895859,
0.014620834961533546,
-0.009656076319515705,
-0.019565485417842865,
0.03553980961441994,
0.04342605173587799,
-0.035324469208717346,
-0.048836614936590195,
0.015509374439716339,
0.05125388875603676,
0.0463540181517601,
-0.007705011870712042,
0.01941780373454094,
0.05047096684575081,
0.020797375589609146,
0.008514595218002796,
0.04170938953757286,
-0.01821068301796913,
0.03731256350874901,
0.013818678446114063,
0.037500590085983276,
0.011954818852245808,
0.0027828284073621035,
-0.008961593732237816,
0.011035775765776634,
-0.011203344911336899,
0.012320361100137234,
-0.0737956240773201,
0.011413279920816422,
0.017763767391443253,
0.003622481133788824,
0.04170089215040207,
-0.0025836618151515722,
0.013222054578363895,
0.0338357649743557,
0.030313972383737564,
-0.041519131511449814,
-0.030492212623357773,
-0.05996936187148094,
-0.025774843990802765,
-0.034359999001026154,
-0.015225160866975784,
0.03271695598959923,
0.011859824880957603,
-0.030476752668619156,
-0.012407580390572548,
0.0460846871137619,
-0.022777479141950607,
-0.06340248137712479,
0.042362362146377563,
0.030230049043893814,
0.01955449767410755,
0.0026699246373027563,
-0.020340649411082268,
0.009451589547097683,
0.01957537792623043,
0.036663297563791275,
-0.0029797654133290052,
-0.00998010579496622,
-0.04061710089445114,
0.08555582165718079,
-0.002490539802238345,
0.023246295750141144,
0.008668262511491776,
0.05119219794869423,
0.053966742008924484,
0.019143441691994667,
-0.023349808529019356,
0.01796182245016098,
0.021019555628299713,
0.02561863884329796,
-0.006246122065931559,
-0.012888669967651367,
-0.001157882739789784,
-0.07322723418474197,
0.0033565079793334007,
-0.008324655704200268,
0.03633171319961548,
0.004667098633944988,
0.013348879292607307,
-0.03305923193693161,
0.012469781562685966,
0.027362434193491936,
0.015684477984905243,
0.023981643840670586,
0.013957029208540916,
-0.009884987957775593,
-0.01815325953066349,
0.022498225793242455,
-0.011735552921891212,
0.012705760076642036,
-0.005986700765788555,
0.0029277873691171408,
-0.03302714601159096,
0.007279957644641399,
0.04977620020508766,
-0.014758971519768238,
-0.022587938234210014,
-0.0007912578294053674,
-0.007894504815340042,
0.07109732925891876,
-0.03483933210372925,
0.03338760882616043,
0.08255288749933243,
-0.07317057251930237,
-0.011646111495792866,
0.003939306829124689,
-0.010178782977163792,
0.02394532412290573,
0.011780070140957832,
0.01267825998365879,
-0.07494541257619858,
0.012445719912648201,
0.05115705356001854,
0.011284363456070423,
0.00733810244128108,
0.022805387154221535,
-0.030534403398633003,
-0.009120834060013294,
-0.008765732869505882,
-0.0006222708616405725,
0.02867688611149788,
0.001037665526382625,
-0.01448031235486269,
-0.011842925101518631,
-0.014221468940377235,
0.00127500353846699,
-0.016542164608836174,
-0.03032573126256466,
-0.00793522410094738,
0.026796972379088402,
0.04075739532709122,
0.01354912482202053,
-0.0031556591857224703,
0.037191636860370636,
-0.05994671955704689,
0.03255370631814003,
0.036443259567022324,
0.05801350250840187,
0.009687855839729309,
-0.019808374345302582,
0.056882623583078384,
0.013218219392001629,
-0.03848588094115257,
-0.025712499395012856,
0.038286324590444565,
-0.012281777337193489,
0.07631931453943253,
0.011718318797647953,
-0.018807360902428627,
0.02696709707379341,
0.014813434332609177,
-0.041705869138240814,
-0.08035999536514282,
0.09657683968544006,
-0.005191553384065628,
-0.0391695499420166,
-0.007554220966994762,
0.019281359389424324,
-0.029419053345918655,
-0.022578764706850052,
-0.028511684387922287,
-0.030440671369433403,
0.005796036217361689,
-0.03164136782288551,
0.015534545294940472,
-0.031737107783555984,
0.028280891478061676,
0.042314331978559494,
-0.037925515323877335,
0.005955867003649473,
-0.023493120446801186,
-0.04412081837654114,
0.03306544944643974,
-0.014836047776043415,
-0.015364488586783409,
0.026994822546839714,
0.025128023698925972,
-0.02368541620671749,
0.0008034513448365033,
-0.029692107811570168,
0.011393087916076183,
-0.017204785719513893,
0.03202144801616669,
-0.019781945273280144,
0.019594751298427582,
-0.005154116079211235,
-0.05109225958585739,
0.039810407906770706,
0.044153712689876556,
-0.020452214404940605,
-0.028432270511984825,
-0.02916751056909561,
0.02649705670773983,
-0.011795931495726109,
0.009096428751945496,
0.03155804052948952,
-0.009236362762749195,
0.024311857298016548,
0.05550007522106171,
-0.005856954026967287,
-0.10220053046941757,
-0.029805278405547142,
-0.05550295487046242,
-0.041583046317100525,
-0.015925902873277664,
-0.000046861405280651525,
0.0055341278202831745,
-0.039593327790498734,
-0.003996105864644051,
-0.016917353495955467,
-0.0754471868276596,
-0.023199178278446198,
0.0005810596630908549,
-0.0034426094498485327,
-0.0017362663056701422,
0.021549368277192116,
0.000644790125079453,
0.04598316177725792,
0.007128358352929354,
-0.029167979955673218,
-0.045498643070459366,
-0.003313995897769928,
-0.03605534881353378,
0.025420935824513435,
0.01154889166355133,
-0.030267149209976196,
0.02496432512998581,
-0.0399409681558609,
0.0026908491272479296,
0.031456295400857925,
-0.03229276090860367,
0.030569277703762054,
0.011780094355344772,
-0.024682583287358284,
-0.03559455648064613,
0.06370683759450912,
-0.01531269308179617,
0.024509968236088753,
-0.03656729683279991,
-0.030809862539172173,
0.03134799376130104,
0.0007631779299117625,
-0.02602059207856655,
-0.057462580502033234,
-0.02291080541908741,
-0.0011195482220500708,
0.03064734861254692,
-0.07449086010456085,
0.0015096502611413598,
0.014021262526512146,
-0.029207710176706314,
0.011942355893552303,
0.04805544391274452,
0.013030294328927994,
-0.017946748062968254,
0.016195068135857582,
-0.05787430703639984,
0.06427203863859177,
-0.011227747425436974,
0.10520616918802261,
-0.031452007591724396,
0.044617678970098495,
0.00939500704407692,
0.025189748033881187,
-0.03703415393829346,
-0.015025441534817219,
-0.025927219539880753,
0.05695398151874542,
-0.04693048074841499,
-0.02235294133424759,
0.0289374478161335,
-0.020405374467372894,
-0.027241718024015427,
-0.007175287697464228,
-0.025017159059643745,
0.009662812575697899,
-0.016580132767558098,
-0.0012999337632209063,
-0.015789395198225975,
-0.013900219462811947,
-0.06067495048046112,
0.012558821588754654,
0.07492146641016006,
0.006639807019382715,
-0.0006215860485099256,
-0.04908357933163643,
0.014675701037049294,
-0.019985146820545197,
-0.02700827643275261,
0.025160886347293854,
-0.014117313548922539,
0.008098808117210865,
0.0074221352115273476,
0.009307900443673134,
-0.00888269953429699,
-0.030980443581938744,
-0.01411456149071455,
0.0316920131444931,
-0.023870229721069336,
0.016486473381519318,
0.011152314022183418,
-0.02463839203119278,
-0.025285160169005394,
-0.02622082270681858,
-0.006343036890029907,
0.0163335669785738,
-0.018628159537911415,
0.012266331352293491,
0.01474278699606657,
0.01721484400331974,
-0.0332719124853611,
0.044856514781713486,
0.000448787584900856,
0.01616228185594082,
-0.02335638366639614,
0.11192059516906738,
0.05713491514325142,
-0.0004968693247064948,
-0.017910191789269447,
0.008080653846263885,
0.02116767130792141,
0.011045408435165882,
0.002210552804172039,
-0.028132345527410507,
0.013872303068637848,
0.0026763039641082287,
-0.016563929617404938,
0.05062849074602127,
0.003266763873398304,
0.02656661905348301,
0.014906450174748898,
-0.05052051320672035,
-0.03280084952712059,
0.003486126195639372,
0.016636984422802925,
0.04532403498888016,
0.029554618522524834,
0.004198759328573942,
0.0030963418539613485,
0.014476819895207882,
0.012545866891741753,
0.019226951524615288,
0.009098981507122517,
0.004662743769586086,
-0.030685842037200928,
-0.000513125560246408,
-0.03731881082057953,
-0.11398746073246002,
-0.02865982986986637,
-0.007839564234018326,
0.010988003574311733,
-0.014674851670861244,
-0.026314416900277138,
0.02160263992846012,
-0.012547783553600311,
-0.06739991903305054,
-0.024089761078357697,
0.009166592732071877,
0.020273402333259583,
-0.03146013990044594,
0.012452201917767525,
-0.027296308428049088,
-0.03284108266234398,
0.008971140719950199,
-0.06108831614255905,
-0.048318471759557724,
-0.0366692841053009,
0.011713988147675991,
-0.016550874337553978,
-0.022627437487244606,
0.01370962429791689,
0.0401577353477478,
0.027311837300658226,
-0.046084921807050705,
0.05134795606136322,
0.023042064160108566,
-0.02146218717098236,
0.018759114667773247,
0.00433740857988596,
-0.01590879075229168,
-0.0009347886661998928,
-0.00351450452581048,
-0.007813690230250359,
-0.01949469745159149,
-0.012306289747357368,
-0.027869392186403275,
-0.03358619660139084,
-0.07250065356492996,
0.020721567794680595,
-0.04017263650894165,
0.003518675919622183,
0.024693626910448074
] |
<p>Ok, so I remember reading that every conservation law has a corresponding symmetry (i.e. conservation of momentum is translational symmetry, conservation of angular momentum is rotational symmetry).</p>
<p>Now conservation of energy is temporal symmetry (you can rewind the tape and it looks exactly the same, but in reverse--you don't get a different "movie" running the tape in reverse).</p>
<p>But I just saw an article here...</p>
<p><a href="http://arstechnica.com/science/2012/11/finding-a-direction-of-time-in-exotic-particle-transformations/" rel="nofollow">http://arstechnica.com/science/2012/11/finding-a-direction-of-time-in-exotic-particle-transformations/</a></p>
<p>...where researchers found violations of time-reversal symmetry.</p>
<p>Now wouldn't that therefore mean that they found processes that create or destroy energy?? Does T-Symmetry violation mean that energy is not being conserved?</p> | g4627 | [
0.034117039293050766,
-0.0065124970860779285,
0.010761146433651447,
-0.02059384435415268,
0.04798698425292969,
-0.009587157517671585,
0.029070252552628517,
0.05367876589298248,
-0.0679214745759964,
0.03740229830145836,
0.018287669867277145,
-0.02756277285516262,
-0.0012914964463561773,
-0.028668299317359924,
0.004461733624339104,
-0.0239902101457119,
0.08774442225694656,
0.01568245142698288,
0.02547488547861576,
0.0734969899058342,
-0.013405859470367432,
-0.04301151633262634,
-0.05695304274559021,
-0.005303357262164354,
-0.0009111300460062921,
0.025561822578310966,
-0.01741599105298519,
-0.023140698671340942,
-0.04164593666791916,
-0.04976293817162514,
0.11387599259614944,
-0.010563808493316174,
-0.008816939778625965,
-0.04474345222115517,
-0.02174002304673195,
-0.07453642040491104,
0.062423352152109146,
-0.026230938732624054,
0.05424109101295471,
0.01473743561655283,
0.015541418455541134,
0.03647821024060249,
-0.03643643856048584,
-0.0173789132386446,
0.03935029357671738,
0.0017864657565951347,
-0.01619051769375801,
-0.03557479381561279,
-0.057653166353702545,
-0.04680468887090683,
0.018177388235926628,
-0.007730414159595966,
0.030834732577204704,
0.01693101041018963,
0.00015162487397901714,
-0.06825809180736542,
-0.011238561011850834,
-0.045423928648233414,
0.07238615304231644,
0.022524919360876083,
-0.014859510585665703,
0.017849469557404518,
0.02791568823158741,
0.06044512987136841,
0.06515077501535416,
-0.054687805473804474,
-0.02968461997807026,
0.03458161652088165,
0.03223208338022232,
-0.00386846368201077,
0.05096088722348213,
0.023227635771036148,
-0.022491557523608208,
0.04976392164826393,
0.0056388527154922485,
0.012098991312086582,
0.03718447685241699,
0.005662357900291681,
-0.08135969191789627,
-0.023665541782975197,
-0.09708813577890396,
0.006387133616954088,
-0.039864275604486465,
0.07793022692203522,
0.09204407781362534,
-0.02409987710416317,
-0.03760969638824463,
0.05767880752682686,
-0.03744310140609741,
0.039338529109954834,
-0.002793816616758704,
-0.07350438088178635,
0.10444685816764832,
-0.012100495398044586,
-0.022919395938515663,
0.006969906389713287,
0.007955692708492279,
0.0809311494231224,
-0.05511552095413208,
0.026958778500556946,
-0.0022943574003875256,
-0.027482787147164345,
-0.012813975103199482,
-0.03386746346950531,
0.03897566348314285,
0.021397311240434647,
0.0591883510351181,
-0.042740922421216965,
-0.0319758877158165,
-0.0039596171118319035,
0.05485653504729271,
-0.00511793652549386,
-0.01828003115952015,
0.03325137123465538,
-0.013732649385929108,
-0.006037426646798849,
0.0550912544131279,
-0.04783625155687332,
0.04082879424095154,
0.04945482313632965,
0.021644826978445053,
-0.026552392169833183,
-0.025802763178944588,
0.02765713818371296,
-0.03579416871070862,
0.023602915927767754,
-0.026235204190015793,
-0.034491509199142456,
0.05609550327062607,
-0.015165379270911217,
-0.06331732124090195,
-0.004558779299259186,
-0.004709039814770222,
0.07318039983510971,
0.03983879089355469,
0.0038951756432652473,
0.011775041930377483,
0.05089898407459259,
-0.01113012246787548,
-0.06360085308551788,
0.0027221154887229204,
-0.013229777105152607,
0.008655207231640816,
0.030607372522354126,
0.005469765514135361,
-0.036628615111112595,
-0.05144293233752251,
-0.006188436411321163,
0.019010260701179504,
0.014831013977527618,
0.022292785346508026,
0.056946877390146255,
-0.017288509756326675,
-0.0346362441778183,
0.002856727223843336,
-0.015732288360595703,
-0.008868728764355183,
0.02027878724038601,
-0.015492197126150131,
0.020839788019657135,
0.032177288085222244,
-0.01829555630683899,
0.013604454696178436,
-0.0041451468132436275,
-0.03379819169640541,
-0.00981695856899023,
-0.024938898161053658,
-0.03863536939024925,
-0.0005636530695483088,
-0.03727195784449577,
-0.0704822912812233,
0.02862735278904438,
0.0031431280076503754,
0.03713402897119522,
-0.005462348461151123,
0.05704442784190178,
-0.04755610600113869,
-0.03823793679475784,
-0.006466398946940899,
-0.03512324392795563,
0.007484573405236006,
0.003425789065659046,
-0.015108087100088596,
0.01890653930604458,
0.05952920764684677,
0.028034044429659843,
0.02622245065867901,
0.013469316065311432,
-0.0475536584854126,
-0.003408353077247739,
0.03241255134344101,
0.04466896876692772,
-0.0197518952190876,
0.028132420033216476,
-0.023523660376667976,
-0.0020367351826280355,
-0.020420748740434647,
-0.033285897225141525,
-0.09660661220550537,
0.048662878572940826,
-0.005025116261094809,
-0.012164604850113392,
0.010441320948302746,
-0.013291713781654835,
-0.017337055876851082,
0.03419485315680504,
-0.05416353791952133,
0.010442717932164669,
0.027155660092830658,
-0.005784655921161175,
0.033099863678216934,
0.031401485204696655,
-0.056501299142837524,
-0.023359451442956924,
0.010169170796871185,
-0.016193997114896774,
-0.01640419103205204,
0.011457044631242752,
-0.03178928419947624,
-0.004335957579314709,
-0.06634818017482758,
0.01809876784682274,
0.029177948832511902,
0.01733360067009926,
0.020896203815937042,
0.004253976512700319,
-0.04883245751261711,
-0.09340469539165497,
-0.03042786568403244,
-0.013301918283104897,
-0.0433257520198822,
0.035307228565216064,
-0.071624755859375,
0.019896935671567917,
0.055203814059495926,
0.010780330747365952,
0.018930191174149513,
0.008353807963430882,
0.0694696381688118,
-0.009544193744659424,
-0.026156574487686157,
-0.015458580106496811,
-0.0454857163131237,
0.011506914161145687,
0.054320111870765686,
0.007451830431818962,
0.03135005757212639,
-0.03899663686752319,
0.05201099440455437,
-0.05300405994057655,
0.09000148624181747,
-0.010859671048820019,
-0.038997583091259,
-0.0066581848077476025,
0.048678554594516754,
-0.007042677141726017,
0.027740363031625748,
0.05407541245222092,
-0.020350338891148567,
0.008886188268661499,
0.05667896568775177,
0.0024532123934477568,
0.014919346198439598,
-0.0011734344298020005,
0.01103346049785614,
-0.017861967906355858,
0.0052702175453305244,
0.020123720169067383,
-0.0025555489119142294,
0.023314058780670166,
-0.04614206403493881,
0.06467213481664658,
-0.014708785340189934,
-0.0015549672534689307,
-0.018657512962818146,
-0.015102967619895935,
0.015978874638676643,
-0.03311328589916229,
0.006235559470951557,
-0.0558139830827713,
-0.0468599908053875,
-0.017894262447953224,
-0.018297571688890457,
0.04509347677230835,
0.06489776074886322,
-0.03783891350030899,
-0.0620904341340065,
-0.02174108475446701,
-0.06512382626533508,
0.040044717490673065,
-0.05647766590118408,
-0.007850698195397854,
0.011143607087433338,
-0.052447400987148285,
-0.0014437444042414427,
0.013210668228566647,
-0.025575634092092514,
-0.05003504827618599,
-0.04367418587207794,
0.05121461674571037,
-0.03164800629019737,
-0.01140617486089468,
0.014155290089547634,
0.02918205037713051,
0.05974702909588814,
0.04425593465566635,
-0.0540413036942482,
-0.029157593846321106,
0.012682461179792881,
0.0033413346391171217,
-0.04383321478962898,
0.006414841860532761,
-0.0734369084239006,
0.033089492470026016,
0.01620730385184288,
0.0005520707927644253,
-0.02899589017033577,
-0.017167460173368454,
0.04685484990477562,
0.014026649296283722,
-0.058135658502578735,
0.043707288801670074,
0.03433181345462799,
0.006948514841496944,
0.012500941753387451,
-0.0024404460564255714,
-0.036619868129491806,
-0.011094867251813412,
-0.019064245745539665,
-0.0228960569947958,
-0.010633652098476887,
-0.041766293346881866,
0.02818245068192482,
-0.04948814958333969,
-0.005744206253439188,
0.00740306731313467,
-0.04115396738052368,
0.00015409252955578268,
0.02955125831067562,
-0.009690848179161549,
-0.012624887749552727,
0.017355643212795258,
0.02867056056857109,
0.014606806449592113,
0.04845425486564636,
0.05786648392677307,
-0.05034254118800163,
0.02570548839867115,
0.0007789338123984635,
0.033129479736089706,
0.06702899932861328,
0.020340964198112488,
0.014429479837417603,
-0.02726553939282894,
-0.005065834149718285,
0.046913351863622665,
0.008803528733551502,
0.06245727092027664,
0.03631909564137459,
-0.015311081893742085,
-0.01347380131483078,
-0.02255411073565483,
0.027628397569060326,
-0.02826276235282421,
-0.020379243418574333,
0.04452650621533394,
-0.029510319232940674,
-0.05351805314421654,
0.04324775189161301,
-0.02113836631178856,
0.015766138210892677,
-0.010375448502600193,
-0.003930547274649143,
-0.03224724903702736,
-0.01477881520986557,
0.0010583101538941264,
0.009454627521336079,
0.023803509771823883,
-0.03075423091650009,
0.04138600081205368,
0.0730125904083252,
-0.06438788026571274,
-0.008550355210900307,
0.0203538965433836,
0.04709756746888161,
0.03123929724097252,
-0.025547107681632042,
-0.0007648027967661619,
-0.025769541040062904,
0.00784989446401596,
0.004638530779629946,
0.02070935256779194,
0.03326764702796936,
-0.05228639394044876,
-0.017689434811472893,
-0.013349349610507488,
-0.0059234765358269215,
-0.050164539366960526,
-0.007024425081908703,
-0.04354293271899223,
-0.0020481240935623646,
0.01955905742943287,
0.013735883869230747,
0.00037691558827646077,
0.008813244290649891,
0.013204052112996578,
0.04056194797158241,
-0.050966378301382065,
-0.033142682164907455,
-0.007739762309938669,
-0.016079558059573174,
-0.007359461858868599,
-0.009942210279405117,
-0.06274642050266266,
-0.01271571684628725,
-0.011101115494966507,
-0.04026168957352638,
-0.02696741744875908,
0.061471790075302124,
0.010042279027402401,
0.06382638216018677,
0.010975307784974575,
0.003671439364552498,
-0.007130021695047617,
-0.022519022226333618,
0.08142437040805817,
0.0012174996081739664,
-0.02101796679198742,
-0.03202643617987633,
-0.04991518333554268,
-0.0024282438680529594,
-0.016280662268400192,
0.010910222306847572,
-0.02508249506354332,
-0.05496176704764366,
-0.025201445445418358,
-0.03139789029955864,
0.03721073642373085,
0.0600985586643219,
0.03787936270236969,
0.10441558808088303,
-0.01835946924984455,
0.005957324989140034,
0.003780476050451398,
-0.031024480238556862,
0.04435509443283081,
-0.012955852784216404,
-0.01172576379030943,
0.022707900032401085,
0.008221253752708435,
-0.04283713176846504,
0.07267450541257858,
-0.021421005949378014,
0.0016607000725343823,
-0.008095042780041695,
-0.026336761191487312,
0.008038169704377651,
0.03402310982346535,
-0.03956983983516693,
0.05126866698265076,
-0.11493448168039322,
-0.010088516399264336,
0.05927683040499687,
0.009237495250999928,
0.048249561339616776,
0.05184630677103996,
0.004860736895352602,
-0.007437412161380053,
0.016334328800439835,
-0.035900622606277466,
0.012360087595880032,
-0.01374328788369894,
-0.027075765654444695,
0.04017442837357521,
0.017260972410440445,
-0.005212422460317612,
-0.011063015088438988,
0.004959470126777887,
0.0371796153485775,
-0.015126475133001804,
-0.046444203704595566,
0.011015588417649269,
0.0857580155134201,
0.006362296640872955,
0.020755071192979813,
0.02057007886469364,
-0.06269288063049316,
0.02485484816133976,
0.03676927834749222,
-0.0026107586454600096,
-0.020133590325713158,
0.0038116062059998512,
-0.0280840452760458,
-0.05386962741613388,
0.06995828449726105,
0.03452606871724129,
0.015050533227622509,
-0.02861041948199272,
-0.03727739304304123,
-0.004895683377981186,
-0.01152858231216669,
-0.004021240398287773,
-0.0031540135387331247,
-0.013482715003192425,
0.045249179005622864,
0.01747770980000496,
0.04311954230070114,
0.056297171860933304,
-0.039294254034757614,
-0.03877120092511177,
0.01321336254477501,
-0.03496100381016731,
-0.03411626070737839,
0.007588531356304884,
0.05470559746026993,
0.008992401883006096,
-0.008010941557586193,
0.022690756246447563,
-0.02686132676899433,
-0.05762796849012375,
-0.0428294837474823,
0.03753911703824997,
0.02082924358546734,
-0.011612203903496265,
-0.028820281848311424,
0.011900370009243488,
-0.04002884402871132,
-0.036967094987630844,
0.008082468062639236,
0.03376452252268791,
-0.03238832205533981,
-0.03827779367566109,
0.07438082247972488,
0.03909164294600487,
-0.022529160603880882,
-0.015229971148073673,
0.006884506903588772,
0.00120185362175107,
0.03732955828309059,
0.013224521651864052,
0.007692885119467974,
0.007980898022651672,
-0.005955924745649099,
0.04488137736916542,
-0.049873095005750656,
-0.0062249586917459965,
-0.06070219352841377,
0.0005787232657894492,
-0.004264469258487225,
-0.050506431609392166,
0.009440113790333271,
-0.019585518166422844,
0.017120275646448135,
-0.02220313437283039,
0.011578221805393696,
0.030121253803372383,
0.009248250164091587,
-0.03367986902594566,
-0.061813388019800186,
-0.03256962448358536,
-0.02658233791589737,
0.06517186015844345,
0.013796565122902393,
0.019672255963087082,
0.0341014489531517,
-0.021183378994464874,
-0.013497759588062763,
-0.05907770246267319,
-0.003785592969506979,
0.05033199489116669,
0.04717965051531792,
0.04764026030898094,
0.010530166327953339,
0.006500808987766504,
0.043145954608917236,
-0.014455078169703484,
-0.051346227526664734,
-0.030785417184233665,
-0.07943950593471527,
-0.01830483414232731,
0.03746519982814789,
-0.09241647273302078,
0.030989205464720726,
-0.06327993422746658,
0.007938839495182037,
-0.0005840682424604893,
-0.011751127429306507,
0.0014887548750266433,
0.08269937336444855,
0.0019009107491001487,
-0.027080735191702843,
-0.01873188652098179,
-0.02342144586145878,
0.018286319449543953,
0.02542153187096119,
0.05838651582598686,
-0.010005619376897812,
-0.03261749446392059,
-0.02578871324658394,
0.011267189867794514,
-0.0018336359644308686,
-0.032486457377672195,
0.011605452746152878,
-0.05526157096028328,
0.031112514436244965,
0.025032496079802513,
-0.047643035650253296,
0.0696701630949974,
0.00926187913864851,
0.004381035454571247,
-0.0275350883603096,
0.05209530517458916,
0.013991209678351879,
-0.02511046640574932,
-0.047864723950624466,
0.03873346745967865,
-0.004937493242323399,
-0.01704619824886322,
-0.047709666192531586,
0.013663828372955322,
0.030678899958729744,
-0.00945658702403307,
-0.012446047738194466,
0.03995328024029732,
0.05175933986902237,
0.03925874084234238,
-0.04325934126973152,
0.06298484653234482,
0.024446263909339905,
0.011953705921769142,
-0.000022467544113169424,
0.027057558298110962,
-0.0047149076126515865,
0.033895254135131836,
-0.0462384968996048,
-0.015450365841388702,
-0.07300668954849243,
0.006440016906708479,
0.009687789715826511,
0.003754129633307457,
-0.009357767179608345,
0.033109601587057114,
0.012588459067046642,
-0.02585771307349205,
-0.0708087906241417,
0.07007943093776703,
-0.0020934815984219313,
0.0019835305865854025,
-0.04091544449329376,
-0.04937724024057388,
-0.005065159406512976,
-0.005685911048203707,
-0.01773875206708908,
0.01298536080867052,
0.011239934712648392,
0.0020724216010421515,
0.02659549005329609,
-0.005613066256046295,
-0.01176979299634695,
-0.06730735301971436,
-0.0068039963953197,
-0.02569975145161152,
0.005530268885195255,
0.002735069952905178,
0.014526497572660446,
0.024951571598649025,
0.029558993875980377,
-0.048575691878795624,
0.040390029549598694,
-0.013012834824621677,
-0.02405688911676407,
-0.019601846113801003,
-0.028777435421943665,
0.02021849900484085,
-0.017945313826203346,
-0.0016348054632544518,
0.036010388284921646,
0.005772823933511972,
-0.0137821389362216,
0.019183550029993057,
-0.027295654639601707,
0.015393322333693504,
-0.02866472490131855,
-0.01316065900027752,
-0.009577094577252865,
-0.0013898925390094519,
-0.059899408370256424,
0.03002838045358658,
-0.057228997349739075,
-0.01983966864645481,
-0.07158146798610687,
0.07052109390497208,
0.012462828308343887,
-0.022692052647471428,
0.028934437781572342,
-0.003505899803712964,
0.10917694866657257,
0.029472200199961662,
-0.0889635682106018,
-0.030939914286136627,
0.011649558320641518,
-0.004874079022556543,
0.02025625668466091,
0.016904141753911972,
-0.00031655540806241333,
0.007285770028829575,
0.0396643728017807,
-0.03339726850390434,
-0.022333048284053802,
0.05433909595012665,
-0.05190907418727875,
-0.018060410395264626,
0.041405998170375824,
0.02719089761376381,
0.10705464333295822,
-0.026833582669496536,
-0.006884589325636625,
-0.03167298808693886,
0.03876226022839546,
-0.020420977845788002,
0.00025531777646392584,
0.000686291663441807,
-0.04318351671099663,
-0.05498563125729561,
-0.030178869143128395,
-0.028677161782979965,
0.030926838517189026,
0.0008525553857907653,
0.051947787404060364,
-0.03108016587793827,
-0.03197986260056496,
0.05235154926776886,
-0.01446523331105709,
0.020466869696974754,
0.022149527445435524,
0.01718493551015854,
0.020813994109630585,
-0.058412641286849976,
-0.02977956272661686,
-0.009395377710461617,
0.07769476622343063,
0.002861465560272336,
0.006123784929513931,
-0.01765722595155239,
-0.04702756926417351,
-0.024942360818386078,
0.02509927935898304,
0.006325527559965849,
0.019307881593704224,
-0.0582406185567379,
0.11017129570245743,
0.005929113831371069,
-0.014239141717553139,
0.006869941018521786,
0.01304866187274456,
-0.014864197932183743,
0.05643573775887489,
0.004692963790148497,
-0.00925205834209919,
0.04049210250377655,
-0.018506888300180435,
0.04057006165385246,
0.0004516553308349103,
-0.0031483895145356655,
-0.029395371675491333,
-0.041736993938684464,
-0.014633351936936378,
0.044440630823373795
] |
<p>What is the orbital motion where both foci are located at one point? I know that an ellipse orbit is motion with two distinct foci.</p> | g4628 | [
0.04543048143386841,
0.09026823192834854,
0.0016931458376348019,
0.06591144949197769,
0.051780689507722855,
-0.018900342285633087,
0.008200529031455517,
-0.0146251255646348,
0.039873700588941574,
-0.015835421159863472,
-0.012840515933930874,
0.01953439973294735,
0.0335954949259758,
-0.038180988281965256,
0.0005251186667010188,
-0.05607768893241882,
0.010753416456282139,
0.001032058848068118,
0.046695560216903687,
0.03950022533535957,
0.02688293717801571,
-0.00619130302220583,
-0.0013815711718052626,
0.04578894004225731,
0.008868665434420109,
0.04133075475692749,
0.028057461604475975,
-0.013236800208687782,
-0.07941030710935593,
0.015166115015745163,
0.06005724146962166,
-0.019381346181035042,
0.05919883772730827,
-0.0201010312885046,
0.013515396974980831,
-0.014718490652740002,
-0.0034163922537118196,
-0.014858373440802097,
0.03584412857890129,
0.01715519092977047,
0.011567856185138226,
-0.019795583561062813,
0.029914353042840958,
-0.02956543304026127,
0.0355805940926075,
-0.049512509256601334,
-0.028724171221256256,
-0.03963099420070648,
0.011995446868240833,
-0.016570396721363068,
-0.02000892348587513,
0.06822788715362549,
0.03920640051364899,
-0.01798146776854992,
-0.028634170070290565,
0.014844012446701527,
0.024532394483685493,
0.008399789221584797,
-0.013136443682014942,
0.029727093875408173,
-0.002330522984266281,
0.03674415871500969,
0.07003691047430038,
0.0017360416240990162,
0.02657119370996952,
0.02591499127447605,
-0.029052237048745155,
0.05163969099521637,
-0.002891364973038435,
0.0005797257763333619,
-0.015414229594171047,
-0.010813073255121708,
-0.009558473713696003,
-0.02807704173028469,
-0.061128102242946625,
0.00834554061293602,
0.04477393999695778,
-0.03063930757343769,
0.010836190544068813,
-0.010649239644408226,
-0.015282598324120045,
-0.023608803749084473,
0.026402397081255913,
-0.01089215837419033,
0.036581143736839294,
0.028279302641749382,
-0.020878206938505173,
-0.019434064626693726,
-0.04473339021205902,
-0.05474136397242546,
0.023125823587179184,
0.015414141118526459,
0.0362110435962677,
0.06252088397741318,
-0.0008870494202710688,
-0.03947969526052475,
0.001560625503771007,
0.07434617727994919,
-0.005416285712271929,
0.04073292389512062,
-0.03518160805106163,
0.04594928026199341,
-0.012460531666874886,
-0.004962952341884375,
0.08600932359695435,
-0.03701221942901611,
0.007608179003000259,
-0.010654921643435955,
-0.01333792693912983,
-0.010221416130661964,
0.017968231812119484,
-0.039064791053533554,
0.03205541521310806,
-0.040140796452760696,
-0.02538643404841423,
0.017337562516331673,
0.0676991418004036,
-0.013728586956858635,
0.04536566510796547,
0.008286533877253532,
0.03283572196960449,
-0.03286303952336311,
0.014478430151939392,
0.07231713831424713,
0.023439953103661537,
0.019232213497161865,
0.036025408655405045,
-0.024557730183005333,
0.029892239719629288,
0.03068985417485237,
0.054877541959285736,
0.013971906155347824,
0.014857485890388489,
-0.007804648019373417,
-0.01323394849896431,
-0.049164071679115295,
-0.004393231589347124,
0.01189988199621439,
-0.0033317937050014734,
-0.011289948597550392,
-0.00011258903396083042,
-0.023078173398971558,
0.03200601041316986,
-0.048832282423973083,
-0.029750360175967216,
-0.06163150072097778,
0.037642404437065125,
0.011483837850391865,
0.011267260648310184,
-0.01135225035250187,
-0.014880119822919369,
0.06516139954328537,
-0.012601830065250397,
-0.03389301151037216,
0.008345278911292553,
-0.03630224987864494,
0.008462936617434025,
0.011945250444114208,
0.0003814686497207731,
0.03907572105526924,
0.07806185632944107,
0.019839340820908546,
0.050211504101753235,
0.012217997573316097,
-0.03334210440516472,
0.011594436131417751,
-0.009328761138021946,
-0.04854589328169823,
0.030563727021217346,
0.0006546168006025255,
-0.0387846902012825,
-0.09362886101007462,
-0.011993239633738995,
0.07194513082504272,
0.011168014258146286,
0.04662288725376129,
-0.00044625255395658314,
-0.025720085948705673,
0.01492216344922781,
0.05122096464037895,
-0.004368024878203869,
0.02901851199567318,
-0.048326168209314346,
0.0552840456366539,
-0.0016996638150885701,
-0.030920404940843582,
-0.01489411573857069,
-0.017129793763160706,
-0.09913666546344757,
0.003919512499123812,
0.04964907839894295,
-0.04736972600221634,
-0.003933091182261705,
0.015157180838286877,
0.00769036402925849,
-0.004537730012089014,
0.03321027755737305,
-0.02201993763446808,
-0.02650497481226921,
0.02778802625834942,
0.018441859632730484,
-0.05495554208755493,
-0.0008348850533366203,
0.010159534402191639,
-0.008959018625319004,
0.018590476363897324,
0.026407821103930473,
-0.03461921960115433,
-0.0027523087337613106,
0.06835287064313889,
-0.03205541893839836,
0.03181298077106476,
-0.006235482636839151,
0.005359833128750324,
0.0016317389672622085,
0.03209959343075752,
-0.010038482956588268,
-0.025912607088685036,
-0.04013456404209137,
-0.04275800660252571,
-0.03403257578611374,
0.015345720574259758,
0.04838555306196213,
-0.012687704525887966,
0.054795652627944946,
-0.01459380891174078,
-0.011669980362057686,
-0.0314570888876915,
0.057469435036182404,
0.045307062566280365,
-0.06137849763035774,
0.022143356502056122,
-0.00035943780676461756,
-0.02279089204967022,
-0.01482896413654089,
-0.029779525473713875,
0.03711532801389694,
0.02428150549530983,
-0.02237815223634243,
0.00212847744114697,
0.019900403916835785,
-0.024529222398996353,
-0.05652078241109848,
-0.02945520170032978,
0.036194950342178345,
-0.042853549122810364,
0.08203795552253723,
0.04545337334275246,
-0.011109388433396816,
0.04984063655138016,
-0.014903574250638485,
-0.02388567291200161,
-0.07656844705343246,
0.020410161465406418,
0.002205566270276904,
-0.0010200610850006342,
-0.009080014191567898,
0.06430307775735855,
-0.09350630640983582,
-0.01993640325963497,
-0.018514690920710564,
-0.01314342487603426,
0.03072012960910797,
-0.023039160296320915,
-0.01921786740422249,
-0.03510342165827751,
0.036523643881082535,
-0.026547273620963097,
0.020894700661301613,
-0.028659719973802567,
-0.05195392668247223,
0.06455352902412415,
0.00979704037308693,
0.012173580937087536,
-0.06252310425043106,
-0.04826894775032997,
-0.00405797827988863,
-0.039083823561668396,
-0.04221857711672783,
0.038755420595407486,
0.007697541732341051,
-0.02988588996231556,
-0.046173159033060074,
0.030230257660150528,
0.04512087255716324,
0.021552929654717445,
0.0055165900848805904,
0.1260712742805481,
0.013216640800237656,
0.0015040012076497078,
-0.03002399392426014,
0.0419367253780365,
0.017489474266767502,
-0.0022365222685039043,
-0.01743478514254093,
-0.015542072243988514,
-0.04631248489022255,
-0.016395146027207375,
0.05878583714365959,
0.025265555828809738,
-0.017977768555283546,
0.016207784414291382,
0.003006962826475501,
0.05957014486193657,
0.0015121405012905598,
0.023249628022313118,
-0.021285826340317726,
-0.04109768941998482,
-0.030359482392668724,
0.0003663430397864431,
-0.016484759747982025,
0.06098802387714386,
0.006360542494803667,
0.004430441651493311,
0.013171562924981117,
0.015225042589008808,
-0.005026415456086397,
0.03812553361058235,
-0.010319149121642113,
0.009554293937981129,
-0.03744170069694519,
-0.05742926523089409,
-0.01996198482811451,
0.018102791160345078,
0.04144182428717613,
0.04594099149107933,
-0.001331328065134585,
0.0030054436065256596,
0.01811007410287857,
-0.011451175436377525,
-0.08825378865003586,
0.003502383129671216,
-0.057621780782938004,
0.007459731772542,
0.019977698102593422,
-0.0003644253592938185,
-0.03713946416974068,
0.0038789573591202497,
0.058995138853788376,
-0.01635035127401352,
-0.0009628520347177982,
0.053581010550260544,
-0.01862017810344696,
-0.05472450703382492,
0.052739545702934265,
-0.03708835691213608,
0.06686636805534363,
0.027580387890338898,
0.06309161335229874,
-0.006200836971402168,
-0.0029354786965996027,
-0.0867246687412262,
0.004616684280335903,
-0.005981992464512587,
-0.03653458133339882,
-0.06134886294603348,
0.003280032193288207,
-0.028453394770622253,
-0.014722397550940514,
0.0312671884894371,
-0.007808113005012274,
0.01344969216734171,
-0.006066808942705393,
0.01814008317887783,
0.04341400787234306,
-0.06928695738315582,
-0.04550226405262947,
0.03733077272772789,
-0.012233227491378784,
-0.01405760645866394,
-0.03361516445875168,
0.01778126135468483,
0.017611470073461533,
-0.05049288272857666,
0.07087349146604538,
-0.037420254200696945,
-0.007482714951038361,
0.006358965765684843,
-0.012558437883853912,
0.039993420243263245,
0.02082696557044983,
0.05062565580010414,
-0.036050524562597275,
0.05285672843456268,
-0.015744026750326157,
0.016885051503777504,
-0.05854902043938637,
0.004120565019547939,
0.03693075478076935,
-0.03380291163921356,
0.07633914053440094,
-0.04552863910794258,
-0.007889613509178162,
-0.005152881145477295,
0.06942787021398544,
-0.03870203346014023,
0.07801393419504166,
-0.013337154872715473,
0.001417268067598343,
0.016271252185106277,
-0.014247198589146137,
0.02330382913351059,
-0.04093172773718834,
-0.036697424948215485,
-0.05219102278351784,
-0.0018851225031539798,
-0.020985623821616173,
0.010252455249428749,
0.047100648283958435,
0.036919932812452316,
0.025454845279455185,
0.045468296855688095,
0.06196325272321701,
0.043946363031864166,
0.0028328190091997385,
0.043396495282649994,
-0.03404441475868225,
0.025470096617937088,
0.02608310617506504,
0.02939627133309841,
-0.050851061940193176,
0.14018359780311584,
0.02967252768576145,
-0.04268471151590347,
-0.003961256239563227,
0.058287810534238815,
0.021470792591571808,
-0.007689948659390211,
-0.00475718267261982,
-0.025847377255558968,
0.007594119757413864,
0.020864643156528473,
0.012368031777441502,
0.036967482417821884,
-0.04375196248292923,
0.02597860060632229,
-0.002500114729627967,
0.022790418937802315,
0.028719553723931313,
0.024947723373770714,
0.00796671211719513,
0.00986759178340435,
-0.03397918865084648,
0.007539921440184116,
0.025876395404338837,
0.018418921157717705,
0.02332756109535694,
-0.030041225254535675,
-0.0661788135766983,
-0.042435381561517715,
0.033342257142066956,
-0.016884775832295418,
-0.012363957241177559,
0.04469342529773712,
-0.08213852345943451,
0.006803080905228853,
-0.05934784561395645,
-0.011173498816788197,
-0.02773280069231987,
-0.03889009729027748,
0.041483331471681595,
-0.025793280452489853,
0.012246871367096901,
0.04388922080397606,
0.02716987580060959,
-0.021755648776888847,
-0.022499723359942436,
-0.005939234048128128,
-0.03679981082677841,
0.02717803232371807,
-0.007352306507527828,
0.03151535987854004,
-0.007578526623547077,
-0.00006035787737346254,
0.011456894688308239,
-0.04369192197918892,
0.03264038264751434,
-0.044712137430906296,
0.00042562143062241375,
-0.026279088109731674,
-0.037854645401239395,
-0.021868348121643066,
0.016347168013453484,
-0.02569105289876461,
-0.019210144877433777,
-0.014558065682649612,
0.0017761650960892439,
-0.0510234460234642,
0.06674742698669434,
0.041382670402526855,
-0.010568749159574509,
0.0027626119554042816,
0.0011115565430372953,
0.0002740478375926614,
-0.003835253417491913,
-0.049973729997873306,
0.013148762285709381,
-0.025657348334789276,
0.01769184321165085,
-0.003254811279475689,
-0.021655017510056496,
0.011263021267950535,
0.014813038520514965,
-0.00407028803601861,
0.04721376299858093,
0.028733063489198685,
0.05958263576030731,
-0.0312007125467062,
0.001130189630202949,
-0.017473889514803886,
0.0014823124511167407,
-0.018007762730121613,
-0.06919189542531967,
-0.037168968468904495,
0.01186804473400116,
0.0020421582739800215,
0.03740913048386574,
-0.017216378822922707,
-0.04750250652432442,
-0.030010582879185677,
0.03821972385048866,
0.05305594205856323,
-0.014627759344875813,
-0.012608869932591915,
0.04664290323853493,
-0.0544612742960453,
-0.0480356365442276,
0.04417701065540314,
0.029855595901608467,
0.06650490313768387,
-0.009653895162045956,
-0.0394054614007473,
-0.024135373532772064,
-0.037870973348617554,
-0.046890657395124435,
-0.03787737712264061,
0.05017394199967384,
-0.04503931477665901,
0.03741687908768654,
-0.014733349904417992,
-0.03265532851219177,
-0.028637675568461418,
-0.008497613482177258,
0.046920232474803925,
-0.10609018057584763,
0.002790615428239107,
-0.03404443711042404,
0.029031703248620033,
0.02069668471813202,
-0.02511436492204666,
0.0009709911537356675,
0.016202954575419426,
0.014122827909886837,
-0.00891000684350729,
-0.018889974802732468,
0.11130443215370178,
-0.04018944501876831,
0.013104368932545185,
-0.025346806272864342,
-0.05897616222500801,
-0.005598000250756741,
-0.015163877978920937,
0.08291638642549515,
0.02238508313894272,
0.021815279498696327,
-0.060371920466423035,
-0.04381083324551582,
-0.019254397600889206,
0.01435747928917408,
0.009945405647158623,
0.004114109091460705,
-0.016891032457351685,
-0.07262667268514633,
0.024256158620119095,
0.053353555500507355,
0.011801524087786674,
0.012216570787131786,
0.010471357963979244,
-0.0300873015075922,
-0.0003302671539131552,
0.0186654943972826,
0.057983171194791794,
0.005543798208236694,
-0.005838375072926283,
-0.06500282138586044,
0.07435546815395355,
-0.03478335216641426,
-0.03822151571512222,
-0.0292009599506855,
0.042350444942712784,
0.024085287004709244,
-0.012626158073544502,
-0.062116362154483795,
-0.0009428206249140203,
-0.03255428373813629,
0.051888998597860336,
-0.04273562133312225,
0.08251805603504181,
0.0049476963467895985,
0.033072248101234436,
-0.0014351306017488241,
0.009385459125041962,
0.06548430025577545,
-0.015452836640179157,
-0.06130673736333847,
0.06100989133119583,
-0.0014677809085696936,
-0.0199738796800375,
-0.013602811843156815,
-0.0038517809007316828,
0.011188321746885777,
-0.037760283797979355,
-0.017247747629880905,
-0.034116070717573166,
-0.05779244005680084,
0.009974691085517406,
-0.062482334673404694,
-0.02032686583697796,
-0.011374227702617645,
-0.0164923258125782,
0.003544959705322981,
-0.044432852417230606,
-0.05364902690052986,
-0.0009120878530666232,
-0.01697978936135769,
0.04492197185754776,
-0.035690873861312866,
-0.02106321230530739,
0.016065141186118126,
-0.029908081516623497,
0.007882269099354744,
-0.04721863195300102,
-0.01597878523170948,
0.02929512970149517,
0.00590720446780324,
-0.004121043719351292,
-0.09312346577644348,
0.05262037366628647,
-0.013946850784122944,
-0.00943795032799244,
0.07228212058544159,
0.010605324059724808,
-0.04243112727999687,
0.01792113296687603,
-0.049579065293073654,
0.000498100824188441,
0.017556609585881233,
0.005005725659430027,
-0.052404001355171204,
0.006519049871712923,
-0.011712891049683094,
-0.04725205525755882,
-0.033977754414081573,
0.037681449204683304,
-0.018034841865301132,
0.012216977775096893,
-0.005124002229422331,
-0.01940414309501648,
-0.013928474858403206,
-0.025831976905465126,
-0.03378094732761383,
0.001498471014201641,
-0.06566470116376877,
0.009021151810884476,
0.0036535041872411966,
-0.052172329276800156,
-0.029654081910848618,
-0.031849537044763565,
-0.06667865812778473,
-0.03597419336438179,
-0.039998751133680344,
0.029393548145890236,
-0.050210487097501755,
0.03283664211630821,
-0.042857371270656586,
-0.0175403393805027,
-0.006074446253478527,
0.004697282332926989,
-0.021127047017216682,
-0.015639277175068855,
-0.026819728314876556,
0.031650785356760025,
0.004422174300998449,
-0.0021182142663747072,
-0.031126148998737335,
0.019565347582101822,
-0.006637377664446831,
-0.046462249010801315,
-0.02143940143287182,
-0.03711189329624176,
0.003382293973118067,
0.10088380426168442,
-0.008332774043083191,
-0.042255863547325134,
-0.03819016367197037,
0.048646192997694016,
0.03719435632228851,
0.011355357244610786,
-0.025060197338461876,
0.00984276831150055,
0.009714067913591862,
0.019793203100562096,
0.005515224765986204,
0.052339449524879456,
0.010430603288114071,
-0.0352393202483654,
0.01750972680747509,
-0.014868819154798985,
0.0038132336921989918,
0.05846978724002838,
-0.011862963438034058,
0.03573155030608177,
-0.0020953344646841288,
-0.03308480978012085,
-0.015913445502519608,
-0.0249638669192791,
-0.007256877142935991,
0.061006274074316025,
0.04049965366721153,
0.07921809703111649,
0.018087051808834076,
-0.04033679887652397,
-0.013290469534695148,
-0.08325641602277756,
-0.011210986413061619,
-0.022710468620061874,
0.06053568050265312,
-0.0609021857380867,
0.10759769380092621,
-0.016044611111283302,
0.04086625948548317,
-0.0025123252999037504,
-0.015086117200553417,
0.024209272116422653,
-0.011030741035938263,
0.008613905869424343,
-0.046868663281202316,
-0.0954924151301384,
-0.023986827582120895,
0.033991944044828415,
-0.028108293190598488,
-0.0224240031093359,
-0.004295422229915857,
-0.0033479039557278156,
-0.028558118268847466,
-0.008298773318529129,
0.02029815874993801,
0.03832269087433815,
0.050317175686359406,
0.002410094253718853,
-0.01955314725637436,
-0.01009749248623848,
-0.03938198462128639,
0.039709486067295074,
0.038236457854509354,
0.006773835513740778,
-0.04376444220542908,
0.030810946598649025,
-0.06933148205280304,
-0.0035556312650442123,
-0.035680100321769714,
0.02132745459675789,
0.047767240554094315,
-0.0074991947039961815,
-0.07587296515703201,
0.017170608043670654,
-0.028177505359053612,
0.06077958643436432
] |
<p>I have this problem:</p>
<p>A 4.0 kg block is given an initial speed of 8.0 m/s at the bottom of a 20° incline. The
frictional force that retards its motion is 15.0 N. (a) If the block is directed up the
incline, how far does it move before stopping? (b)Will it slide back down the incline? </p>
<p>I've managed to get part (a) which was 4.51m but I'm not sure how to start part (b)..</p>
<p>The coefficient of Kinetic Friction was 0.407</p>
<p>Any ideas?</p> | g4629 | [
0.06765516102313995,
0.015929043292999268,
0.0071396962739527225,
0.044107306748628616,
0.05106406286358833,
0.0074964542873203754,
0.09111097455024719,
0.03048839420080185,
-0.052332695573568344,
0.01484143827110529,
-0.028035078197717667,
0.03619002550840378,
-0.017549943178892136,
-0.015040983445942402,
0.008427967317402363,
0.06108313426375389,
0.07604029774665833,
-0.03472515568137169,
0.031346458941698074,
0.04309098795056343,
-0.02961636148393154,
0.011557693593204021,
-0.06183721125125885,
-0.06579545140266418,
0.036807674914598465,
0.001158737693913281,
0.028189154341816902,
-0.03765040263533592,
-0.036596424877643585,
0.031533967703580856,
-0.029971998184919357,
-0.03676925599575043,
-0.010507602244615555,
-0.032001644372940063,
-0.03205070644617081,
0.046543318778276443,
0.09266994893550873,
-0.014487084932625294,
-0.031345441937446594,
-0.024450046941637993,
0.04975288361310959,
-0.05628492683172226,
0.027463896200060844,
0.0023436457850039005,
0.009601918049156666,
0.024424243718385696,
-0.0024341384414583445,
-0.00744158960878849,
-0.024950772523880005,
0.055000804364681244,
-0.024254200980067253,
0.05018261820077896,
0.01674901880323887,
-0.0050950790755450726,
-0.0808938667178154,
0.003892140928655863,
0.021189922466874123,
-0.022067196667194366,
-0.005455261096358299,
0.01215170044451952,
-0.0325881689786911,
-0.022615566849708557,
0.04065009579062462,
-0.07959552109241486,
0.05987923592329025,
-0.049768660217523575,
-0.055743563920259476,
0.03587248921394348,
0.006521994713693857,
0.026558110490441322,
-0.04240310564637184,
0.024836277589201927,
0.030472343787550926,
-0.026895558461546898,
-0.0696415975689888,
-0.018555983901023865,
0.05576469376683235,
-0.015914572402834892,
0.046548161655664444,
0.014487194828689098,
-0.05768662691116333,
0.0945102646946907,
0.04119729995727539,
-0.02711724117398262,
0.056390076875686646,
0.014334491454064846,
-0.0032227805349975824,
0.06201180815696716,
-0.07677340507507324,
-0.009125152602791786,
-0.007210288662463427,
-0.024127589538693428,
0.03871644660830498,
0.04662507772445679,
0.029611647129058838,
-0.059681300073862076,
-0.0637335553765297,
0.09128063172101974,
0.031991828233003616,
0.0017112947534769773,
-0.0067229922860860825,
-0.042842961847782135,
0.02829664945602417,
-0.038593173027038574,
0.007238373626023531,
-0.035967737436294556,
0.0023933411575853825,
-0.030170058831572533,
-0.008984978310763836,
-0.0010280876886099577,
0.018629388883709908,
-0.06753576546907425,
-0.06815817207098007,
-0.08659417182207108,
0.009525648318231106,
-0.049965787678956985,
-0.011732975952327251,
0.042406417429447174,
-0.03941846638917923,
0.017755810171365738,
-0.03981456905603409,
0.011980777606368065,
-0.007053948938846588,
0.03379344940185547,
-0.0013591240858659148,
-0.01519072987139225,
-0.0032210382632911205,
-0.006438146345317364,
0.0407986082136631,
0.023586707189679146,
0.0031213804613798857,
0.046109575778245926,
-0.008607485331594944,
-0.01768391951918602,
-0.027410348877310753,
0.04854881390929222,
-0.02346114069223404,
0.04934850335121155,
-0.015528966672718525,
0.0025077161844819784,
-0.011977390386164188,
-0.017668720334768295,
0.05112234130501747,
-0.013116411864757538,
-0.03593752533197403,
-0.013391365297138691,
0.015591401606798172,
0.0020713259000331163,
0.06078943610191345,
-0.026408925652503967,
0.009134238585829735,
0.027202611789107323,
-0.016781823709607124,
-0.0270392969250679,
0.06444229930639267,
-0.016190750524401665,
0.07590147107839584,
0.05720595642924309,
0.03505459427833557,
-0.03657027333974838,
0.02205510064959526,
-0.0343359038233757,
0.041682180017232895,
-0.03221867233514786,
-0.0662766695022583,
0.024906810373067856,
-0.04776739329099655,
-0.02785162441432476,
0.0438358299434185,
-0.020744848996400833,
-0.07630185782909393,
-0.012797627598047256,
0.019267041236162186,
0.036059074103832245,
-0.048838041722774506,
0.05228140950202942,
0.08108904212713242,
0.018339091911911964,
-0.029858412221074104,
0.03836201876401901,
0.051703061908483505,
-0.025275006890296936,
0.09023867547512054,
0.05780545622110367,
-0.013821398839354515,
0.018265027552843094,
0.024231554940342903,
0.03715778887271881,
-0.03751135244965553,
-0.07148134708404541,
0.05545816943049431,
-0.004952789284288883,
-0.02153148129582405,
-0.016546741127967834,
-0.02410147152841091,
0.03021100163459778,
-0.013869070447981358,
-0.05307408422231674,
0.024225184693932533,
0.004664323758333921,
0.04586515948176384,
0.02521802857518196,
0.01977444626390934,
0.03204258531332016,
-0.02530692331492901,
-0.037095945328474045,
0.0010610935278236866,
0.024945225566625595,
-0.005293224006891251,
0.002298555104061961,
0.047780074179172516,
0.031215965747833252,
-0.07248289883136749,
0.0419880710542202,
-0.003938267473131418,
-0.043997351080179214,
0.0657772421836853,
0.006604112219065428,
-0.02263111062347889,
-0.03282979875802994,
-0.06721026450395584,
-0.004290572367608547,
-0.041664768010377884,
-0.0027865448500961065,
-0.004987669177353382,
-0.04037761688232422,
-0.023847952485084534,
-0.057500481605529785,
-0.007296175695955753,
0.018342673778533936,
-0.031807344406843185,
-0.009041146375238895,
-0.025751667097210884,
-0.06415528059005737,
0.07710941135883331,
0.061463672667741776,
0.015894168987870216,
0.017616013064980507,
-0.009598808363080025,
-0.03772031143307686,
0.028422711417078972,
-0.02648945339024067,
0.010296745225787163,
-0.07212845236063004,
0.017055917531251907,
-0.033823784440755844,
0.037356600165367126,
0.008207246661186218,
0.0011624005855992436,
0.032916683703660965,
0.004081518389284611,
-0.045081764459609985,
-0.04131597280502319,
0.05402974411845207,
0.0010200196411460638,
0.027493134140968323,
-0.06299535185098648,
0.02371247671544552,
-0.0017731515690684319,
-0.05425264686346054,
-0.03529641777276993,
0.015596841461956501,
-0.02943677268922329,
0.047594476491212845,
-0.055478911846876144,
0.004235955886542797,
-0.07858922332525253,
-0.03200123831629753,
0.06426522135734558,
0.03518134355545044,
-0.012344651855528355,
-0.01469440944492817,
0.017634673044085503,
0.05928795412182808,
-0.013460062444210052,
-0.0300665944814682,
0.0039012576453387737,
-0.023354317992925644,
-0.030856570228934288,
0.027317533269524574,
0.02696741372346878,
0.0278267040848732,
-0.02395789697766304,
-0.012008140794932842,
0.024137988686561584,
-0.02567976899445057,
0.019949978217482567,
0.06216488778591156,
-0.0689295083284378,
-0.004145363811403513,
-0.0434899665415287,
0.057921115309000015,
0.08441636711359024,
0.06956200301647186,
0.0388309471309185,
0.07790829241275787,
0.019553977996110916,
-0.08712669461965561,
-0.026830554008483887,
-0.025026876479387283,
0.024516241624951363,
-0.05729766562581062,
0.0015330874593928456,
-0.02544005587697029,
-0.008212585933506489,
-0.016698351129889488,
-0.005988901015371084,
-0.014957823790609837,
0.009973336942493916,
0.013396412134170532,
0.004167700652033091,
0.01916263997554779,
-0.03170539811253548,
-0.01975814253091812,
-0.020365586504340172,
-0.03642762452363968,
0.05603555962443352,
0.01737663894891739,
0.04630750045180321,
0.013109974563121796,
-0.02432207763195038,
-0.07039041072130203,
-0.004504552576690912,
0.0472550168633461,
0.040678899735212326,
0.02174607291817665,
-0.05379295349121094,
0.012838974595069885,
0.001238285913132131,
0.0032452745363116264,
0.0029102482367306948,
0.07762207090854645,
-0.014922158792614937,
-0.010242050513625145,
0.032215818762779236,
-0.004687564913183451,
-0.0008817415800876915,
0.01056300662457943,
0.0066045853309333324,
0.00915928091853857,
-0.033300116658210754,
0.010214153677225113,
0.007558137644082308,
0.013287311419844627,
-0.0439598374068737,
0.015836229547858238,
0.01015964150428772,
-0.012251120060682297,
-0.07930480688810349,
-0.0032357284799218178,
0.04847615957260132,
-0.03418712690472603,
0.0017588549526408315,
0.006861139554530382,
0.00993379671126604,
0.008834760636091232,
0.03221508488059044,
0.012093503028154373,
-0.045062921941280365,
-0.026617946103215218,
0.004137026146054268,
-0.02106064185500145,
-0.017744800075888634,
0.06653106212615967,
0.011496749706566334,
0.02660851925611496,
-0.02829582244157791,
0.032925598323345184,
-0.03295363858342171,
-0.006707106716930866,
-0.012126433663070202,
-0.059015385806560516,
-0.006776320748031139,
-0.0271074827760458,
-0.004662077408283949,
-0.0042756046168506145,
0.02431151084601879,
-0.007770990487188101,
0.018040645867586136,
0.05465447157621384,
-0.00017944617138709873,
0.036754805594682693,
-0.024748001247644424,
-0.008885164745151997,
0.015020730905234814,
0.09225260466337204,
-0.03667234256863594,
-0.03813851252198219,
0.06651844829320908,
0.009675734676420689,
0.01717529445886612,
-0.0022411616519093513,
-0.0013034394942224026,
0.014009775593876839,
0.010105784982442856,
0.010463006794452667,
0.0480443611741066,
0.035598766058683395,
-0.010921195149421692,
-0.008699946105480194,
-0.004496324807405472,
0.025071049109101295,
-0.02459002658724785,
0.06611692160367966,
-0.03028988465666771,
0.03780459985136986,
0.03668856993317604,
-0.016204454004764557,
0.03983855992555618,
-0.015258576720952988,
-0.016793521121144295,
-0.03820757567882538,
-0.067802295088768,
0.0032355610746890306,
-0.014482864178717136,
0.00902082584798336,
0.003788172733038664,
0.07511503994464874,
0.0218467079102993,
0.007338743191212416,
-0.04179219901561737,
0.05174519866704941,
-0.004989199806004763,
-0.026698339730501175,
0.016826331615447998,
-0.02284161187708378,
0.022286852821707726,
0.013421043753623962,
-0.009161524474620819,
0.024784566834568977,
-0.030798031017184258,
0.012117891572415829,
-0.026786228641867638,
-0.028709016740322113,
-0.024491727352142334,
0.052605144679546356,
0.0443943589925766,
0.013407849706709385,
0.00008077617530943826,
0.055000510066747665,
0.0025971506256610155,
0.048790767788887024,
-0.00906255654990673,
0.005899739917367697,
0.004982132464647293,
0.02748785726726055,
-0.01755017414689064,
-0.046852096915245056,
0.02188057452440262,
-0.02344047836959362,
0.02006755769252777,
0.0179299246519804,
-0.04596811160445213,
0.003632831620052457,
-0.01869785599410534,
0.059723131358623505,
0.006050811614841223,
0.015472677536308765,
-0.04731925204396248,
0.012801882810890675,
0.07113077491521835,
-0.008278685621917248,
-0.014719481579959393,
-0.05173932760953903,
-0.07327382266521454,
-0.04395380988717079,
0.059806011617183685,
0.004573917016386986,
-0.03871586173772812,
0.02202172391116619,
0.05806262418627739,
-0.03649388626217842,
-0.004082691390067339,
0.0671456977725029,
-0.0061161271296441555,
0.060375507920980453,
0.022977381944656372,
0.062162332236766815,
0.0733368918299675,
-0.036349598318338394,
-0.022571008652448654,
0.012632093392312527,
0.02916041761636734,
-0.011062836274504662,
0.00016399839660152793,
-0.06014099717140198,
-0.04324343800544739,
-0.015972614288330078,
0.08110905438661575,
-0.030583785846829414,
0.028880633413791656,
0.05007718503475189,
-0.030388953164219856,
-0.021515166386961937,
-0.049979452043771744,
0.021358560770750046,
-0.0036726261023432016,
0.05635451897978783,
0.05918942019343376,
0.04343261569738388,
-0.00995238684117794,
0.007947335951030254,
0.016602717339992523,
0.004143455531448126,
0.01429697684943676,
0.010933979414403439,
0.03404373303055763,
-0.0386771596968174,
-0.0017125032609328628,
0.04304968938231468,
-0.025641383603215218,
0.06340669840574265,
0.03985957056283951,
-0.004662231542170048,
-0.028443792834877968,
-0.022468365728855133,
0.019562024623155594,
0.014237882569432259,
-0.056642256677150726,
-0.025134291499853134,
0.03928772732615471,
-0.038668859750032425,
-0.0033254812005907297,
-0.00644152145832777,
-0.04875798523426056,
-0.02721872180700302,
-0.04722133278846741,
0.004644641652703285,
-0.09174084663391113,
0.005709851626306772,
0.01013198308646679,
-0.03310316056013107,
0.059419918805360794,
-0.0062268637120723724,
-0.006560876965522766,
-0.04412166029214859,
0.06127481162548065,
-0.07124098390340805,
-0.009452196769416332,
-0.019084012135863304,
-0.02937489002943039,
-0.0008841944509185851,
-0.00352788926102221,
-0.005522442515939474,
0.00863649882376194,
-0.00800306349992752,
-0.02836080826818943,
-0.010838985443115234,
0.02400084398686886,
-0.0319800041615963,
0.026354772970080376,
0.007010600063949823,
-0.012132269330322742,
0.014165125787258148,
-0.06992176920175552,
0.007806751877069473,
0.015789572149515152,
0.016113657504320145,
-0.012407842092216015,
-0.05913433060050011,
0.05412508174777031,
-0.01013200730085373,
0.00984561163932085,
0.03701629117131233,
-0.007596008479595184,
-0.0794026255607605,
-0.018651457503437996,
0.028552953153848648,
0.07722920924425125,
-0.001195299788378179,
0.008713604882359505,
0.006353245582431555,
-0.03273085877299309,
0.05285436660051346,
0.04609069600701332,
0.03836788982152939,
-0.0738755464553833,
-0.012746860273182392,
0.008264042437076569,
0.04657387733459473,
-0.04113450646400452,
0.013750509358942509,
0.015047090128064156,
-0.056547291576862335,
-0.048593372106552124,
0.020619625225663185,
-0.04597175866365433,
-0.03742413967847824,
0.009928128682076931,
-0.03560720384120941,
0.020455671474337578,
0.0363248772919178,
-0.020528025925159454,
0.008236769586801529,
-0.03097202256321907,
-0.021220818161964417,
-0.02039424702525139,
0.018411245197057724,
-0.01591598056256771,
0.017932172864675522,
0.018474359065294266,
0.0024135750718414783,
0.021893639117479324,
-0.005641302093863487,
-0.025676466524600983,
0.011752703227102757,
0.004400104749947786,
0.03288528695702553,
0.05715976655483246,
-0.009910823777318,
0.027204105630517006,
0.04337778687477112,
0.0005111751379445195,
-0.013292982243001461,
-0.01934674009680748,
0.041751451790332794,
0.053815316408872604,
-0.009995272383093834,
-0.05667334794998169,
-0.027966611087322235,
0.057776838541030884,
0.02592947520315647,
0.06269843876361847,
-0.03876211866736412,
-0.029716141521930695,
-0.011405630968511105,
-0.027578305453062057,
0.021723506972193718,
0.019069841131567955,
0.022767649963498116,
0.026457177475094795,
-0.050283052027225494,
-0.05623362958431244,
0.015664417296648026,
-0.004488283768296242,
0.028753308579325676,
-0.05351850762963295,
0.05082433298230171,
0.012991887517273426,
0.019662931561470032,
0.04467799887061119,
-0.01568596437573433,
-0.07257094234228134,
0.01652880571782589,
0.0055567435920238495,
-0.04206479713320732,
0.015238117426633835,
0.04577242583036423,
-0.006270189303904772,
-0.03228406608104706,
0.002935432828962803,
0.001379130408167839,
0.002641736064106226,
-0.011177117936313152,
-0.06864806264638901,
0.01100002322345972,
0.02787121757864952,
-0.005180438980460167,
0.07084107398986816,
0.040922652930021286,
-0.012369915843009949,
-0.07324333488941193,
0.016197582706809044,
0.003289559856057167,
-0.07834554463624954,
0.022221071645617485,
-0.03371540829539299,
0.06351493299007416,
-0.003069784492254257,
-0.03566322103142738,
-0.0436844602227211,
-0.0813223347067833,
-0.0112893246114254,
0.026272734627127647,
-0.022703276947140694,
0.05864720791578293,
0.013590876013040543,
0.005752190016210079,
-0.02563459798693657,
-0.0004658913239836693,
0.03131956607103348,
0.025418555364012718,
-0.005912493448704481,
-0.02349591627717018,
-0.012390250340104103,
-0.011845206841826439,
-0.005403890740126371,
-0.000052005922043463215,
0.03698307275772095,
0.007485642563551664,
-0.025151079520583153,
0.08505246043205261,
-0.023602236062288284,
-0.051313865929841995,
0.003542265621945262,
0.0006628049304708838,
-0.006857739295810461,
-0.021831464022397995,
-0.05010044947266579,
0.00881006196141243,
-0.012969101779162884,
-0.009167307056486607,
-0.02021859399974346,
0.04138137400150299,
-0.031551260501146317,
0.0020954206120222807,
-0.018306471407413483,
-0.018839159980416298,
-0.059689961373806,
-0.000524156610481441,
0.00902284774929285,
0.02682235836982727,
-0.0006029856158420444,
0.002311582211405039,
0.02406986430287361,
0.03479897230863571,
-0.04067671298980713,
-0.024920757859945297,
0.006034496705979109,
-0.036644089967012405,
-0.05834856629371643,
0.022795353084802628,
-0.008973103947937489,
-0.052518606185913086,
-0.012368030846118927,
-0.08429953455924988,
-0.023315854370594025,
0.013607736676931381,
-0.03202235326170921,
-0.025970252230763435,
-0.00025539929629303515,
0.009420203045010567,
-0.023473357781767845,
0.011586619541049004,
0.0033402591943740845,
-0.0174054354429245,
0.01829957216978073,
-0.023576147854328156,
0.024383876472711563,
0.049508679658174515,
-0.06700129806995392,
-0.024097679182887077,
-0.0443054735660553,
0.03277460113167763,
0.021212687715888023,
-0.0024010506458580494,
0.003925327677279711,
0.053048908710479736,
-0.0041830893605947495,
-0.028246842324733734,
0.007580211386084557,
-0.005889077205210924,
0.017321722581982613,
-0.014237366616725922,
-0.03883492574095726,
-0.03593697398900986,
-0.04519348964095116,
0.029241858050227165,
-0.052475519478321075,
-0.025067253038287163,
0.0008819673676043749,
-0.020708132535219193,
-0.005425870418548584,
-0.031984731554985046,
0.002970120869576931,
-0.05289153382182121,
-0.011896978132426739,
-0.004994972143322229
] |
<p>I have been told that trasverse wave propogates by the oscillation of medium particles in direction perpendicular to propogation.</p>
<p>Consider a wave on a taught string (x-y plane).
What is the mechanism of movement of the same sinosudial function along the string?</p>
<p>Suppose we start moving the particle on one end sinosudialy the how come the next particle also moves sinosudialy? How does elastic force between them does this work?
If we displace the particle, there is some elastic force developed which is at some angle with horizontal so the next particle should move at some angle and its vertical displacement should be less than the previous one. </p>
<p>So how come in a propogating wave all particle rise to the same height?</p> | g4630 | [
0.04817916080355644,
0.02382776327431202,
-0.005623837001621723,
-0.021678678691387177,
0.04867786914110184,
0.038068145513534546,
0.03511405363678932,
0.003392381127923727,
0.0035499955993145704,
-0.04153764247894287,
-0.017006583511829376,
0.02389044128358364,
0.04547806829214096,
-0.026051247492432594,
0.026093538850545883,
-0.01005554012954235,
0.06466768682003021,
-0.02099115587770939,
0.000443033262854442,
0.024049809202551842,
-0.016337310895323753,
0.017008114606142044,
0.004759000614285469,
-0.024563731625676155,
-0.024752162396907806,
0.016045941039919853,
0.0020648655481636524,
-0.048233311623334885,
0.03154637664556503,
-0.009135570377111435,
0.06988725811243057,
-0.024755185469985008,
0.08220832794904709,
-0.03458143398165703,
-0.002367535140365362,
0.001862996956333518,
-0.006681391038000584,
0.0014308701502159238,
0.004173568449914455,
0.04758699610829353,
-0.016287799924612045,
-0.07601403445005417,
-0.00386502081528306,
-0.0262738186866045,
0.02887316420674324,
-0.023950748145580292,
-0.012648709118366241,
0.016283243894577026,
-0.021861517801880836,
-0.03969960659742355,
-0.028404951095581055,
-0.02895462140440941,
-0.013100840151309967,
0.04299402981996536,
0.016461871564388275,
0.05500025674700737,
0.04570437967777252,
-0.04293123632669449,
0.044116608798503876,
0.010497544892132282,
0.004323746543377638,
0.06276659667491913,
0.04227537289261818,
0.030471956357359886,
0.0507289320230484,
-0.0725337341427803,
-0.07318249344825745,
0.07214219868183136,
-0.0016928848344832659,
0.026097342371940613,
0.026370853185653687,
-0.05535966902971268,
0.00879316870123148,
-0.05663464590907097,
-0.04631548002362251,
-0.020419416949152946,
0.009847905486822128,
-0.020989367738366127,
-0.050496380776166916,
-0.002354480791836977,
-0.013424929231405258,
-0.0391925647854805,
0.03637801483273506,
-0.015010116621851921,
0.03871298208832741,
-0.05733833834528923,
0.00479773199185729,
0.04937801510095596,
-0.04267216473817825,
0.027504930272698402,
0.015962544828653336,
-0.038729093968868256,
0.06605742126703262,
0.047682810574769974,
-0.024712679907679558,
-0.06673125922679901,
-0.0919518768787384,
0.13003219664096832,
-0.023479653522372246,
-0.013382012024521828,
-0.007203593384474516,
-0.0041886623948812485,
0.04748174548149109,
-0.007365910802036524,
0.02594703435897827,
0.02068367972970009,
0.05705602839589119,
-0.003380092093721032,
-0.021892718970775604,
-0.035129185765981674,
-0.030469024553894997,
-0.03023301064968109,
-0.06695245951414108,
-0.08092313259840012,
-0.01315165963023901,
-0.033070895820856094,
0.036271944642066956,
0.04568174481391907,
0.06159773841500282,
0.06117856875061989,
-0.05652065575122833,
-0.030184302479028702,
-0.009206987917423248,
0.04851653426885605,
-0.007597700227051973,
0.000046433120587607846,
0.01572086289525032,
-0.01428915560245514,
-0.02361404150724411,
-0.009218035265803337,
0.04558946192264557,
0.003736605402082205,
-0.05568215250968933,
-0.021499255672097206,
0.018492845818400383,
-0.031012972816824913,
-0.02728302963078022,
-0.00018867678591050208,
0.02386324107646942,
-0.007015622686594725,
-0.01621600054204464,
-0.04583415761590004,
0.03953411430120468,
-0.04058810696005821,
-0.015639733523130417,
0.01369045302271843,
0.023351214826107025,
-0.012679316103458405,
-0.0021533311810344458,
-0.023752260953187943,
-0.001221533166244626,
0.09251090884208679,
0.040682464838027954,
-0.005577786359935999,
0.03131965547800064,
-0.040255576372146606,
0.08625952154397964,
-0.01301359012722969,
-0.008496414870023727,
-0.025560855865478516,
0.06606375426054001,
-0.038027409464120865,
0.007247346919029951,
0.045736175030469894,
-0.07635857164859772,
0.04365235194563866,
0.00110807444434613,
-0.05046109855175018,
0.013949520885944366,
0.019216502085328102,
-0.04949231073260307,
-0.011500156484544277,
-0.01892656460404396,
0.030769065022468567,
0.005740727763622999,
0.09990975260734558,
0.004323488101363182,
-0.06730087846517563,
0.019211437553167343,
0.013648093678057194,
0.0010917545296251774,
-0.016062859445810318,
-0.02287319488823414,
-0.01068166084587574,
0.008170385845005512,
0.003806200809776783,
-0.022856634110212326,
0.017723221331834793,
-0.0372123122215271,
0.04203225299715996,
-0.0533740259706974,
-0.007096778601408005,
-0.01229995395988226,
0.011437942273914814,
-0.002966444008052349,
-0.05641474947333336,
-0.005791595205664635,
-0.024177568033337593,
-0.014940882101655006,
-0.009603062644600868,
0.008889766409993172,
0.05653436854481697,
0.09968387335538864,
-0.06279709190130234,
0.029464097693562508,
-0.015843292698264122,
0.0004437400493770838,
-0.012176373042166233,
0.01887122541666031,
0.02781854197382927,
-0.0024961051531136036,
0.009706709533929825,
0.01738738641142845,
-0.01336742751300335,
-0.03011457808315754,
-0.021426493301987648,
0.009390125051140785,
-0.01931115984916687,
-0.0022722373250871897,
0.016117138788104057,
-0.017853328958153725,
-0.02658110111951828,
0.007546863052994013,
0.017494874075055122,
-0.02636326476931572,
-0.020481035113334656,
-0.006755741313099861,
0.009623563848435879,
-0.015684938058257103,
0.05453760176897049,
-0.03312138468027115,
-0.010706780478358269,
0.03528711944818497,
-0.05216429755091667,
0.06246763840317726,
0.014489775523543358,
0.027433481067419052,
0.010571873746812344,
0.03588271886110306,
-0.021641451865434647,
0.036481823772192,
-0.03734307363629341,
-0.011846124194562435,
-0.010008499026298523,
0.051629893481731415,
-0.04026085510849953,
0.07370200753211975,
-0.011603129096329212,
-0.011443144641816616,
0.022096112370491028,
0.08110874146223068,
-0.04237768054008484,
-0.04944661632180214,
0.041849635541439056,
0.015870321542024612,
-0.025906676426529884,
-0.04544062912464142,
0.010440627112984657,
0.0528181791305542,
-0.06231812387704849,
0.0030061525758355856,
0.010989919304847717,
0.0609324611723423,
0.0056635853834450245,
-0.08277107775211334,
0.01949225924909115,
0.012381978332996368,
0.01407624315470457,
-0.03959234803915024,
-0.027341779321432114,
-0.012676460668444633,
0.020712489262223244,
-0.002251426689326763,
0.031324733048677444,
-0.0345769077539444,
0.04901989921927452,
0.023418575525283813,
-0.035504117608070374,
-0.028076499700546265,
-0.030518028885126114,
-0.004214372020214796,
0.004083066713064909,
-0.039236828684806824,
-0.016483385115861893,
0.05453282967209816,
-0.04185543209314346,
0.0025779753923416138,
-0.027887724339962006,
-0.048223067075014114,
-0.007493633311241865,
-0.05044640228152275,
-0.0017932840855792165,
0.06627065688371658,
0.04653060436248779,
-0.004104884807020426,
0.05197661370038986,
-0.004449945874512196,
-0.03806202486157417,
-0.015147790312767029,
0.014872092753648758,
-0.07177936285734177,
-0.06693881005048752,
0.019651129841804504,
-0.016797343268990517,
0.038028378039598465,
0.020199017599225044,
0.03706749156117439,
-0.04236350581049919,
-0.014600192196667194,
0.04088018462061882,
0.024119704961776733,
0.034212276339530945,
-0.022753672674298286,
-0.024099886417388916,
-0.044508714228868484,
-0.017583182081580162,
-0.036200329661369324,
-0.011267416179180145,
0.008566380478441715,
0.07293026149272919,
-0.06269372999668121,
-0.054696403443813324,
0.019923338666558266,
-0.003436542581766844,
0.008902627974748611,
0.020488141104578972,
-0.020322853699326515,
0.05201193690299988,
-0.07765943557024002,
-0.019796378910541534,
0.014523624442517757,
0.030308878049254417,
-0.0334322415292263,
-0.02501402236521244,
0.0584363155066967,
-0.028618086129426956,
0.016352474689483643,
-0.023275630548596382,
0.05037568882107735,
0.04739983379840851,
-0.029480841010808945,
-0.032982099801301956,
0.012953581288456917,
0.005083103198558092,
-0.005623426754027605,
0.03583220764994621,
-0.004655451513826847,
0.02216416969895363,
0.04183698818087578,
-0.009879427030682564,
0.018575089052319527,
0.026452695950865746,
-0.03673911467194557,
-0.007373791188001633,
0.01482450868934393,
0.055497895926237106,
0.08867613226175308,
0.032086342573165894,
0.0020262659527361393,
-0.03063792735338211,
0.025644706562161446,
0.007186415139585733,
-0.01860666275024414,
0.05829951539635658,
0.007755243685096502,
0.004598398692905903,
0.017318150028586388,
0.020406704396009445,
-0.022286102175712585,
0.01927311345934868,
-0.03265589475631714,
-0.08707509934902191,
-0.033161863684654236,
-0.037401869893074036,
-0.0283307246863842,
-0.01308615505695343,
0.014253241010010242,
-0.024350225925445557,
-0.03997674211859703,
0.04022987559437752,
-0.01909652352333069,
-0.010350609198212624,
0.015716781839728355,
-0.005024310201406479,
-0.00811727810651064,
0.09420982748270035,
-0.02358507178723812,
0.03503520041704178,
0.026890601962804794,
-0.02525968849658966,
0.02242249622941017,
-0.06776667386293411,
-0.009977278299629688,
0.003258215030655265,
0.062245823442935944,
-0.02174176089465618,
0.019877683371305466,
0.012616935186088085,
0.020059846341609955,
-0.03438865765929222,
-0.0039721643552184105,
0.020198285579681396,
-0.019757919013500214,
-0.02480662800371647,
-0.06304092705249786,
0.06758848577737808,
0.04098273813724518,
-0.009364255703985691,
-0.012895428575575352,
-0.02013264410197735,
0.034133341163396835,
0.007031007669866085,
-0.024373680353164673,
-0.05631112679839134,
-0.025171153247356415,
0.002695841947570443,
0.08506540954113007,
0.03773079067468643,
-0.03343774378299713,
0.0027768185827881098,
0.06531219929456711,
0.11190246045589447,
0.018826136365532875,
0.003998108673840761,
-0.025387972593307495,
0.09755425155162811,
0.027769573032855988,
-0.008325514383614063,
-0.022799087688326836,
-0.06394565850496292,
-0.05253681167960167,
0.02757338248193264,
0.023655617609620094,
0.025761820375919342,
-0.054856810718774796,
0.003405103925615549,
0.028583263978362083,
-0.01080702617764473,
0.03099718689918518,
-0.010788097977638245,
0.07422544062137604,
-0.0019384827464818954,
-0.03895191475749016,
-0.01721891015768051,
-0.013497653417289257,
0.0063044968992471695,
-0.01697598397731781,
-0.06163487583398819,
-0.04684709757566452,
-0.060221027582883835,
0.004133362323045731,
0.06120533123612404,
-0.039497461169958115,
-0.03405050188302994,
0.028474919497966766,
-0.0124762412160635,
0.0054381792433559895,
0.0036305978428572416,
-0.029066937044262886,
-0.08095359802246094,
-0.0388762466609478,
-0.01286905538290739,
0.002498013898730278,
0.003872312605381012,
0.0199434794485569,
-0.040018294006586075,
-0.019472341984510422,
-0.03237331286072731,
-0.033472102135419846,
0.055624980479478836,
0.05545919016003609,
-0.023078860715031624,
0.036454953253269196,
0.03358551114797592,
-0.011444924399256706,
-0.012506023980677128,
-0.030827721580863,
-0.026800159364938736,
0.037078164517879486,
-0.033048976212739944,
-0.003542800433933735,
-0.0011232999386265874,
-0.010071923956274986,
-0.029255889356136322,
-0.047403041273355484,
-0.0766477957367897,
-0.06689651310443878,
0.01620715670287609,
0.018047049641609192,
-0.0060196006670594215,
0.027455534785985947,
-0.027805043384432793,
-0.028069404885172844,
-0.027545787394046783,
-0.01403076108545065,
-0.03988742455840111,
-0.01329418271780014,
-0.018097959458827972,
-0.03371913731098175,
-0.016862191259860992,
-0.055986180901527405,
-0.03757202997803688,
0.009399347938597202,
0.026101654395461082,
-0.03245837241411209,
-0.0035194791853427887,
0.06322977691888809,
0.014446262270212173,
-0.041644275188446045,
0.019210172817111015,
0.04360518977046013,
-0.007200813852250576,
-0.03647792339324951,
-0.0037939653266221285,
0.022873463109135628,
-0.005001991521567106,
0.00960039533674717,
0.013401839882135391,
-0.018346041440963745,
0.04671597108244896,
0.01672068051993847,
0.038861677050590515,
-0.009753466583788395,
-0.02827492170035839,
0.04655725136399269,
-0.021611634641885757,
-0.08047585934400558,
0.05775769427418709,
0.019843794405460358,
-0.007236366625875235,
0.050229720771312714,
-0.008842968381941319,
0.053302161395549774,
0.03738204017281532,
-0.0033632416743785143,
-0.018883315846323967,
0.04070872813463211,
-0.04910912737250328,
-0.0005695977015420794,
-0.010628468357026577,
-0.014623429626226425,
-0.04147370904684067,
0.028054265305399895,
0.03571834787726402,
-0.03434298187494278,
0.022716807201504707,
-0.04695923253893852,
0.02473021298646927,
0.05753198266029358,
-0.024133797734975815,
-0.05684526637196541,
0.004598748870193958,
0.009355826303362846,
0.026352308690547943,
-0.013915788382291794,
0.033814385533332825,
-0.017987776547670364,
-0.06863623112440109,
0.018076879903674126,
-0.026272693648934364,
0.047685667872428894,
-0.027385951951146126,
0.01621166616678238,
0.012291288003325462,
0.0016307258047163486,
-0.02476559206843376,
0.048298127949237823,
0.006926472764462233,
0.11152373254299164,
0.0552377924323082,
-0.025803925469517708,
0.012184015475213528,
0.0123549560084939,
0.05441327765583992,
-0.0015375955263152719,
0.009703557938337326,
-0.005026604514569044,
-0.027609393000602722,
-0.047991637140512466,
0.03626514598727226,
0.025682659819722176,
-0.024853430688381195,
-0.03910350054502487,
0.014734338037669659,
-0.07086539268493652,
0.036423299461603165,
-0.046023909002542496,
-0.05901125818490982,
0.035005491226911545,
0.036178749054670334,
-0.06590148061513901,
-0.03413211554288864,
-0.03624286502599716,
0.0011178042041137815,
0.02071644924581051,
-0.017775798216462135,
0.02251458168029785,
0.054881542921066284,
0.02019587531685829,
0.047377198934555054,
0.07129713892936707,
-0.00040773945511318743,
0.026599640026688576,
-0.024461178109049797,
0.01125610526651144,
-0.010664554312825203,
0.01869192160665989,
0.029204286634922028,
0.015994207933545113,
0.058013491332530975,
-0.0056417533196508884,
0.02695331536233425,
0.00957689993083477,
0.006405928172171116,
-0.006202729418873787,
-0.06599084287881851,
0.011126803234219551,
0.0018989109667018056,
0.0023038764484226704,
-0.03314119204878807,
0.006156808231025934,
0.03346311300992966,
0.05224716663360596,
-0.014448516070842743,
0.028476236388087273,
-0.0359250083565712,
-0.03111957758665085,
-0.02448222227394581,
0.02441517822444439,
-0.028065811842679977,
0.0002860626846086234,
0.035532135516405106,
0.011315029114484787,
0.0024281505029648542,
-0.07550027221441269,
0.04093673452734947,
-0.03899358958005905,
-0.021616309881210327,
-0.009533219039440155,
-0.030781641602516174,
0.008816367015242577,
0.0724630057811737,
0.029185080900788307,
-0.0034667563159018755,
-0.013113793917000294,
0.031063171103596687,
0.00959459412842989,
0.010433114133775234,
-0.0380677804350853,
-0.00774066336452961,
0.016223959624767303,
-0.03583994135260582,
-0.01568167470395565,
0.06741901487112045,
-0.032544758170843124,
0.006900544743984938,
-0.0009160112240351737,
-0.05419088155031204,
0.015292730182409286,
-0.02871266007423401,
-0.0789867416024208,
-0.06912466883659363,
0.04359087720513344,
0.0031844123732298613,
-0.030857287347316742,
0.03603405877947807,
-0.04039107635617256,
-0.0164051353931427,
-0.004245983902364969,
0.012994742020964622,
0.011457378044724464,
-0.028663350269198418,
-0.01549603883177042,
-0.001514094416052103,
-0.003824046114459634,
0.04662963002920151,
-0.0303675327450037,
0.03376825526356697,
0.002407183637842536,
-0.016362283378839493,
0.020185187458992004,
-0.02370433695614338,
0.01805429905653,
-0.002768715610727668,
0.02872711792588234,
0.03123076632618904,
0.02909001149237156,
0.02360466681420803,
-0.018488818779587746,
-0.017522789537906647,
0.019956255331635475,
0.018680443987250328,
-0.0048876479268074036,
0.009591265581548214,
0.0031964886002242565,
-0.028260957449674606,
0.030141161754727364,
0.05999672785401344,
-0.048929452896118164,
0.002631561364978552,
-0.007068461272865534,
-0.021266238763928413,
-0.0341445654630661,
0.03864128887653351,
0.05080419033765793,
-0.059917695820331573,
-0.02564411424100399,
-0.05540646240115166,
-0.01280677504837513,
-0.045214056968688965,
-0.018370632082223892,
0.03621715307235718,
0.010592907667160034,
0.02750028856098652,
0.013809824362397194,
0.03893228620290756,
0.02543296292424202,
0.04923620820045471,
-0.00016808323562145233,
0.011744530871510506,
-0.020436039194464684,
0.0254373662173748,
0.020436210557818413,
-0.10175874829292297,
-0.01580851338803768,
0.003171090967953205,
0.035441797226667404,
-0.059733014553785324,
-0.024105826392769814,
-0.039892151951789856,
0.015306803397834301,
0.04212209954857826,
0.04451896995306015,
-0.004092230927199125,
-0.02063705027103424,
0.04049919173121452,
-0.0036046269815415144,
-0.05429909750819206,
-0.002211222192272544,
0.024326669052243233,
0.08332020044326782,
-0.016686314716935158,
-0.010066121816635132,
-0.030163345858454704,
-0.013518576510250568,
0.017641978338360786,
-0.002693604677915573,
0.06154618784785271,
-0.0011804868699982762,
-0.036399874836206436,
0.025144167244434357,
0.03070972114801407,
-0.04076051339507103,
0.06480877101421356,
0.00903912540525198,
-0.07032901048660278,
0.028608664870262146,
0.03579343482851982,
0.04313953220844269,
-0.05027955397963524,
-0.0036754258908331394,
0.02310623787343502,
0.020655207335948944,
-0.07951457053422928,
-0.0029181665740907192,
-0.010179155506193638,
-0.06312184035778046,
0.011911417357623577
] |
<p>When we send an electromagnetic short wave to the sky, it reflects due to the ionosphere effects. But if we send it horizontally, is it correct that it moves around the surface of the earth, and if it has enough energy, it can return to its first position?</p>
<p>If yes, then how could that happen?</p> | g4631 | [
0.033559221774339676,
0.03101149946451187,
-0.029719339683651924,
0.03367086499929428,
0.062325023114681244,
0.09063781052827835,
-0.004495968576520681,
0.020290663465857506,
-0.04486620053648949,
-0.06944088637828827,
-0.026180937886238098,
0.07426325231790543,
0.05046694725751877,
0.010975402779877186,
-0.028248947113752365,
0.0027115449775010347,
0.0959300771355629,
-0.022683626040816307,
0.0032591086346656084,
0.05249016359448433,
0.01561395637691021,
-0.029394572600722313,
-0.035871539264917374,
-0.0685792788863182,
-0.02216518111526966,
0.0019984047394245863,
0.0214132871478796,
-0.050437234342098236,
0.004447075538337231,
-0.040170177817344666,
0.0043946499936282635,
0.02521752566099167,
0.04199124127626419,
-0.05478177219629288,
-0.03100826032459736,
-0.022997308522462845,
-0.024216800928115845,
0.004052294883877039,
0.0026368803810328245,
0.00445979181677103,
-0.03038856014609337,
-0.03263254091143608,
0.01211780309677124,
0.02443539723753929,
0.054529618471860886,
-0.06599786132574081,
0.0335412360727787,
-0.018333077430725098,
0.03387122228741646,
-0.044959042221307755,
-0.06557870656251907,
-0.004505746066570282,
0.009426206350326538,
0.02186013199388981,
-0.009199532680213451,
0.01875315234065056,
0.039654798805713654,
-0.045785821974277496,
0.06174968183040619,
0.01282050646841526,
0.022800780832767487,
0.007876469753682613,
-0.012614338658750057,
0.008050546981394291,
0.011937325820326805,
-0.044476043432950974,
-0.11167439818382263,
-0.01709812507033348,
0.021343883126974106,
-0.008451641537249088,
0.04450739175081253,
-0.018376728519797325,
-0.06656119227409363,
-0.08253635466098785,
0.011510873213410378,
0.016392014920711517,
-0.003105130512267351,
-0.025972647592425346,
0.028998959809541702,
0.030085071921348572,
0.014152098447084427,
-0.0011892131296917796,
0.0013658195966854692,
-0.039041563868522644,
0.010181307792663574,
0.017562052235007286,
0.020698094740509987,
0.021842841058969498,
-0.008544310927391052,
-0.05388261377811432,
-0.02575746178627014,
-0.030627401545643806,
0.020065229386091232,
-0.001511639915406704,
0.013035829178988934,
-0.07464269548654556,
-0.02863932214677334,
0.046973034739494324,
-0.024466702714562416,
-0.010782928206026554,
-0.06875292956829071,
-0.033946551382541656,
-0.0482456237077713,
-0.02317255735397339,
0.0768461674451828,
0.02877998538315296,
-0.012333323247730732,
0.013060018420219421,
0.036034148186445236,
-0.012959660030901432,
-0.008361028507351875,
-0.06444820761680603,
-0.023517876863479614,
-0.042379871010780334,
-0.019059618934988976,
-0.010578365996479988,
0.03972577303647995,
-0.0023200386203825474,
0.07722188532352448,
0.10468965023756027,
0.006493480876088142,
0.008972682990133762,
0.003871413879096508,
0.07108067721128464,
-0.044543325901031494,
-0.0060380301438272,
-0.05094499513506889,
-0.0348346121609211,
0.01839889958500862,
-0.004548680502921343,
0.0014718127204105258,
0.020821910351514816,
-0.0541822724044323,
0.045258261263370514,
0.04274183511734009,
-0.03100643679499626,
-0.002946824999526143,
-0.013503037393093109,
0.005809892434626818,
0.05501672998070717,
0.06625394523143768,
-0.017548056319355965,
0.030193548649549484,
-0.07536111772060394,
-0.005780233535915613,
0.036124084144830704,
0.0013176847714930773,
-0.014371632598340511,
0.05530620366334915,
-0.06031151860952377,
-0.0378904826939106,
0.022624876350164413,
0.03520036116242409,
-0.011930182576179504,
0.013816754333674908,
-0.06778855621814728,
0.03424161672592163,
-0.00882493332028389,
0.025350691750645638,
0.0002866518625523895,
0.056123316287994385,
-0.0529114231467247,
0.008948545902967453,
0.015220200642943382,
-0.04127217456698418,
0.02696039341390133,
-0.019578900188207626,
-0.030113406479358673,
0.027611829340457916,
0.00440738070756197,
-0.07238387316465378,
0.011761347763240337,
0.03380430489778519,
0.039702530950307846,
-0.006221163552254438,
0.09702282398939133,
0.0475403256714344,
-0.010271461680531502,
0.03958035632967949,
-0.06346002966165543,
-0.058007873594760895,
0.0023865040857344866,
-0.03521651029586792,
-0.018116436898708344,
0.029939286410808563,
-0.025556806474924088,
-0.028159668669104576,
-0.02964777685701847,
-0.06784820556640625,
-0.028673872351646423,
-0.007511361967772245,
-0.02564225345849991,
-0.0021142377518117428,
0.0046159387566149235,
0.0008768436382524669,
-0.017059538513422012,
0.00155050924513489,
-0.05259709060192108,
-0.05971101298928261,
0.04100128263235092,
0.012844757176935673,
0.06288906931877136,
0.07835744321346283,
0.016556598246097565,
0.03984749689698219,
0.023437902331352234,
0.050076767802238464,
-0.009351680055260658,
0.030226795002818108,
-0.05952074006199837,
0.021911989897489548,
-0.01273136492818594,
0.025556160137057304,
0.004019253887236118,
0.0413171648979187,
0.031933337450027466,
-0.07620231062173843,
0.03829316794872284,
-0.03159162029623985,
-0.005735944025218487,
-0.06495339423418045,
0.0030816674698144197,
0.0027689943090081215,
-0.00798157136887312,
-0.020657449960708618,
0.0229018684476614,
-0.08857914805412292,
-0.018474142998456955,
-0.0024008117616176605,
-0.00519503653049469,
0.051900897175073624,
-0.029825445264577866,
-0.03340955823659897,
-0.033275045454502106,
0.06852973252534866,
0.016449017450213432,
-0.0026509365998208523,
0.008056780323386192,
-0.014069930650293827,
-0.038395535200834274,
-0.045806653797626495,
-0.023305106908082962,
-0.010318172164261341,
-0.011351642198860645,
0.0009507032809779048,
0.014543261379003525,
0.02108762413263321,
0.022895151749253273,
-0.03940585255622864,
0.0061397189274430275,
0.06606458127498627,
-0.023578327149152756,
0.019728271290659904,
0.01906660944223404,
0.0038001632783561945,
-0.06603766232728958,
-0.04801534116268158,
0.00433506490662694,
-0.013830062933266163,
-0.047080282121896744,
-0.007514619268476963,
-0.005536756478250027,
0.0450870580971241,
0.003743479959666729,
-0.023724522441625595,
-0.008936680853366852,
-0.029780277982354164,
0.02017110213637352,
-0.005224120337516069,
-0.0022121735382825136,
0.05324589088559151,
0.07812796533107758,
0.02690632827579975,
0.07586641609668732,
-0.02436385676264763,
-0.01916324533522129,
0.048010844737291336,
-0.04138042777776718,
-0.014352086000144482,
-0.015005426481366158,
-0.03295813128352165,
0.020800037309527397,
-0.03493187204003334,
-0.021150309592485428,
0.015992574393749237,
-0.024353493005037308,
-0.0623711533844471,
0.03320011496543884,
-0.03368512541055679,
0.02539205737411976,
-0.054961010813713074,
-0.01768634095788002,
0.08267015963792801,
0.04280716925859451,
-0.05625085532665253,
0.0192265622317791,
0.05493290349841118,
-0.04704325273633003,
-0.02983163669705391,
0.017755530774593353,
0.023762227967381477,
0.031009284779429436,
-0.022037694230675697,
0.0015722244279459119,
-0.0014675380662083626,
0.03432627022266388,
-0.016514800488948822,
-0.03387480974197388,
0.07445065677165985,
-0.005310357548296452,
-0.00048584950855001807,
0.11455845087766647,
-0.030481843277812004,
0.04270073026418686,
-0.04225466027855873,
-0.01713111810386181,
-0.0520721934735775,
-0.027663668617606163,
0.06879011541604996,
0.03430602699518204,
-0.07496821135282516,
-0.06912565976381302,
-0.0364191047847271,
0.02000170201063156,
0.011397358030080795,
0.04556506872177124,
-0.022021710872650146,
0.03955687955021858,
-0.054085955023765564,
0.017901470884680748,
-0.015137219801545143,
0.07163477689027786,
-0.011908349581062794,
-0.03020326793193817,
0.01978241465985775,
-0.0020017230417579412,
0.028026923537254333,
0.001518263597972691,
0.00327782123349607,
0.03460441529750824,
0.011191452853381634,
-0.013365042395889759,
-0.027739787474274635,
-0.02924569882452488,
0.05073271319270134,
0.02546646073460579,
-0.03359575569629669,
-0.028583254665136337,
-0.05970076099038124,
0.000610971124842763,
0.037466634064912796,
0.028324715793132782,
-0.03058450110256672,
-0.014520503580570221,
0.027827613055706024,
0.09757381677627563,
-0.01423540711402893,
0.00041407396201975644,
0.023919273167848587,
-0.011367949657142162,
-0.041633229702711105,
0.008866663090884686,
0.015465935692191124,
0.0060182115994393826,
0.016179516911506653,
0.03801703825592995,
-0.0479869470000267,
0.03490350767970085,
0.004352713469415903,
0.04193320497870445,
-0.03582830727100372,
-0.015674911439418793,
-0.012705899775028229,
0.020960606634616852,
-0.04338887706398964,
-0.02172003500163555,
0.04071164131164551,
-0.04203950986266136,
-0.003916924819350243,
0.019233694300055504,
-0.022538401186466217,
0.03644368425011635,
-0.01474771462380886,
-0.007971159182488918,
0.022320618852972984,
0.049804672598838806,
-0.032057493925094604,
0.0008763482910580933,
-0.010225571691989899,
-0.013710985891520977,
-0.004173004999756813,
-0.03885529562830925,
0.008730346336960793,
0.006118138786405325,
0.03437710180878639,
-0.024673733860254288,
0.03732138127088547,
-0.03133992478251457,
-0.012341133318841457,
0.03834139183163643,
0.07509560883045197,
0.011778970248997211,
-0.013885313645005226,
-0.0002812583988998085,
-0.032196566462516785,
0.05122697353363037,
0.022754518315196037,
-0.0030106310732662678,
-0.07108525186777115,
-0.008170397020876408,
-0.010079752653837204,
0.0004996795323677361,
-0.053697794675827026,
-0.03702614828944206,
0.06291760504245758,
0.030553491786122322,
0.04101116582751274,
0.0011171253863722086,
0.017077431082725525,
0.004589144140481949,
-0.0032100724056363106,
0.07616296410560608,
0.05623752623796463,
-0.016475355252623558,
-0.019707949832081795,
0.06986251473426819,
0.07107343524694443,
-0.019808311015367508,
-0.0076169357635080814,
0.01581903174519539,
-0.024784483015537262,
0.00004871649798587896,
0.0015261350199580193,
0.033114638179540634,
-0.03447141870856285,
0.018287744373083115,
0.03203253075480461,
-0.028602134436368942,
-0.033937737345695496,
0.04259650781750679,
0.07463531941175461,
-0.013493972830474377,
-0.023256564512848854,
0.02156708389520645,
-0.05560145899653435,
0.07594804465770721,
-0.01796138845384121,
-0.07663729786872864,
0.037543609738349915,
-0.0461447648704052,
-0.04077199846506119,
0.01977558247745037,
0.007909992709755898,
0.013212716206908226,
-0.02081812545657158,
0.0035514740739017725,
0.025415997952222824,
0.00752211781218648,
0.03628149628639221,
-0.0038682713638991117,
-0.018359757959842682,
0.007452585268765688,
0.052954137325286865,
0.05365403741598129,
0.06402116268873215,
-0.029981689527630806,
-0.004793807398527861,
-0.024289647117257118,
-0.0861772745847702,
0.006266482640057802,
0.008020119741559029,
0.06766331195831299,
0.03640603646636009,
0.028970593586564064,
-0.007510758470743895,
0.05241220071911812,
-0.011770686134696007,
-0.0507158488035202,
-0.003762242617085576,
-0.04779120907187462,
-0.005108517594635487,
-0.04040461406111717,
-0.005857817362993956,
0.025178059935569763,
-0.04396171495318413,
0.005949110258370638,
-0.03052389994263649,
0.03631654381752014,
-0.01670023240149021,
-0.03726765513420105,
-0.023565998300909996,
-0.049722298979759216,
-0.052984219044446945,
-0.08637121319770813,
-0.05547841265797615,
-0.024511592462658882,
-0.009280779398977757,
0.013001186773180962,
0.0014406630070880055,
-0.005560593213886023,
0.05557094141840935,
-0.008329533040523529,
-0.017786452546715736,
0.06408961862325668,
-0.0007891259156167507,
0.024477319791913033,
0.013757911510765553,
-0.01313905417919159,
-0.0213589146733284,
0.020879080519080162,
-0.0067198621109128,
-0.041181690990924835,
-0.018580198287963867,
-0.009171751327812672,
0.048244982957839966,
-0.07976624369621277,
-0.06763401627540588,
0.05303154140710831,
-0.016960343345999718,
0.05627363175153732,
0.013846968300640583,
-0.007860826328396797,
0.03622959926724434,
0.008098279125988483,
0.024146119132637978,
-0.001551824389025569,
-0.026681963354349136,
0.006760150659829378,
-0.026302998885512352,
0.05632539093494415,
0.05375329777598381,
0.06711865961551666,
0.0008769046398811042,
0.013720624148845673,
0.06190630793571472,
-0.06250128149986267,
0.025964105501770973,
0.021988967433571815,
0.05045095086097717,
-0.010912501253187656,
-0.05073446407914162,
-0.012341054156422615,
0.01696973294019699,
0.03990089148283005,
0.04233665019273758,
0.04724922403693199,
-0.02984512411057949,
0.04224139451980591,
0.03549523651599884,
-0.03758879005908966,
-0.02431284263730049,
0.015162983909249306,
-0.011739399284124374,
0.03158581629395485,
0.016509126871824265,
0.01907223090529442,
-0.03653782233595848,
-0.03771379217505455,
0.0162420142441988,
-0.04931699484586716,
0.05011013522744179,
0.05629540979862213,
-0.011275948956608772,
-0.0535896010696888,
0.04433317855000496,
-0.05130132660269737,
0.005895706359297037,
-0.006777014117687941,
0.05933646112680435,
0.008012264966964722,
0.013693947345018387,
-0.014828009530901909,
-0.00441258680075407,
-0.006151912733912468,
0.004916753154247999,
-0.01669403724372387,
-0.015113024972379208,
0.018118033185601234,
-0.04173167422413826,
-0.031147751957178116,
0.025785867124795914,
-0.029901783913373947,
0.022268211469054222,
-0.014281496405601501,
0.0008796189213171601,
-0.04465871676802635,
-0.03654206916689873,
-0.005969103425741196,
0.04460277780890465,
-0.0223842766135931,
-0.02256162278354168,
-0.008063605055212975,
0.026008905842900276,
-0.07129216194152832,
-0.021478675305843353,
-0.07501758635044098,
-0.00008155449177138507,
-0.0035617840476334095,
-0.056731197983026505,
0.026825271546840668,
0.05706911161541939,
0.011128838174045086,
0.01418820396065712,
-0.041378170251846313,
0.020147884264588356,
0.02417011559009552,
0.03099244087934494,
0.034660957753658295,
0.033166758716106415,
0.005707710515707731,
-0.027969401329755783,
-0.04306047409772873,
-0.0044731320813298225,
-0.05911214277148247,
-0.08050147444009781,
-0.008658323436975479,
0.028860026970505714,
0.00186253956053406,
0.03633769974112511,
-0.04355596750974655,
-0.03601148724555969,
-0.0017875098856166005,
-0.014394140802323818,
-0.031760621815919876,
-0.02997622825205326,
0.027912870049476624,
0.030405553057789803,
-0.020602397620677948,
0.001037510926835239,
0.023068340495228767,
-0.0015518130967393517,
0.036997292190790176,
-0.015922628343105316,
0.04230426624417305,
0.045417219400405884,
-0.0009656143374741077,
0.003906724043190479,
-0.019091911613941193,
-0.038745030760765076,
-0.005864293780177832,
-0.020883282646536827,
0.03570949658751488,
-0.032772354781627655,
0.017053473740816116,
-0.06919985264539719,
0.02784072794020176,
0.021258261054754257,
-0.01388828456401825,
-0.029513292014598846,
-0.0015360983088612556,
-0.03143152594566345,
0.0005266426596790552,
-0.023373914882540703,
-0.006513374391943216,
-0.006992385722696781,
-0.016353441402316093,
-0.024214429780840874,
0.029574494808912277,
-0.006214377470314503,
-0.02674185298383236,
-0.003827046137303114,
-0.02220829576253891,
-0.02065102942287922,
0.020363768562674522,
0.021173372864723206,
-0.0017972501227632165,
0.002118977252393961,
-0.04763070121407509,
-0.031205307692289352,
0.03355211019515991,
-0.004427413456141949,
-0.06097976863384247,
0.02730996161699295,
0.044541824609041214,
0.012165818363428116,
0.03702657297253609,
-0.03482695668935776,
-0.035198651254177094,
-0.014405136927962303,
0.03930361196398735,
0.013429712504148483,
0.015717046335339546,
-0.00789971649646759,
0.03652598336338997,
-0.017687005922198296,
0.008599202148616314,
0.007523663341999054,
0.06811061501502991,
-0.011884779669344425,
-0.047854699194431305,
0.031206006184220314,
0.08136465400457382,
0.043693069368600845,
-0.03640468418598175,
-0.004285999108105898,
-0.0248690415173769,
-0.007867277599871159,
0.04041930288076401,
-0.009041018784046173,
-0.007805017288774252,
0.01015558559447527,
-0.005004287231713533,
0.04710329696536064,
-0.015544991008937359,
0.03450801968574524,
-0.011879166588187218,
0.0040023368783295155,
-0.0412931926548481,
-0.06634934991598129,
-0.03476141765713692,
0.04535333812236786,
0.04409677907824516,
0.00857570767402649,
0.05502163991332054,
0.001417687744833529,
0.02377844601869583,
0.0035118144005537033,
0.0477832667529583,
-0.00608075549826026,
0.0068732695654034615,
-0.028460228815674782,
0.02923494391143322,
-0.005850662011653185,
-0.027607595548033714,
-0.021960362792015076,
0.057357851415872574,
-0.029794884845614433,
-0.027305902913212776,
0.07077832520008087,
-0.046853333711624146,
-0.006998260039836168,
0.05479896441102028,
-0.014776624739170074,
-0.03861300274729729,
0.04351023584604263,
0.00014583277516067028,
0.003038666909560561,
-0.03369535133242607,
0.05683276429772377,
-0.014405234716832638,
0.0056266686879098415,
0.02430766262114048,
-0.032278452068567276,
-0.021567577496170998,
-0.029005028307437897,
0.01328122615814209,
0.021016240119934082,
-0.004361280240118504,
0.006047230679541826,
-0.05503394454717636,
0.03562799096107483,
0.046466950327157974,
-0.003788871457800269,
0.03117360547184944,
0.05856073647737503,
0.03085595928132534,
-0.0029891019221395254,
0.01971052959561348,
-0.004653043579310179,
-0.010261129587888718,
-0.05441529303789139,
-0.009567616507411003,
0.03530656918883324,
-0.06768373399972916,
-0.02403574436903,
-0.07162182778120041,
-0.01889796368777752,
0.040936753153800964
] |
<p>Thermodynamic buoyancy. I have an air intake for combustion air entering into a basement furnace room. During cold weather, the air enters unchecked (no damper on pipe is allowed). I have this 5 foot vertical pipe, suspended downwards within a 2 foot high box, terminating 12" from the bottom. The cold air spills over the top of the box (combustion appliances are off at this point). How do I create a "cold air trap" like a p-trap (thermal equilibrium)? Would raising the height of the box help?</p> | g4632 | [
0.038125574588775635,
0.014976518228650093,
0.005732631776481867,
-0.00816404726356268,
-0.027391793206334114,
0.038264062255620956,
0.03496910259127617,
0.016696741804480553,
-0.06904714554548264,
-0.039429258555173874,
-0.036277804523706436,
0.03248165547847748,
0.011950341984629631,
-0.008699432015419006,
0.030612725764513016,
0.03916991874575615,
0.04664767533540726,
-0.0390305370092392,
0.005464574322104454,
-0.009511529467999935,
-0.0322737880051136,
-0.0473591685295105,
-0.03775234520435333,
-0.02441391907632351,
-0.007107269950211048,
-0.02778025157749653,
0.024154962971806526,
0.061694756150245667,
-0.03620276227593422,
0.0010243933647871017,
-0.0769193172454834,
0.014339236542582512,
-0.03812683746218681,
0.020784832537174225,
-0.05262191221117973,
0.005518965423107147,
0.08706078678369522,
0.0072424570098519325,
0.04812458157539368,
-0.09815236181020737,
0.019726082682609558,
-0.018957018852233887,
-0.017178483307361603,
0.03572598099708557,
-0.04203202575445175,
0.038087353110313416,
-0.03396185114979744,
-0.05939125269651413,
-0.002463157055899501,
0.023074887692928314,
0.018733466044068336,
-0.012296798638999462,
-0.07356565445661545,
-0.055584389716386795,
-0.03357087820768356,
-0.04920502379536629,
0.05305815488100052,
0.010748820379376411,
-0.015628740191459656,
0.01918383501470089,
-0.018580712378025055,
0.02679290622472763,
-0.004940109793096781,
-0.01143495924770832,
0.014437412843108177,
0.06603128463029861,
-0.0535673089325428,
0.011056589893996716,
-0.005409759934991598,
0.0033929534256458282,
-0.012122773565351963,
0.002894715638831258,
0.004037035629153252,
-0.03166762366890907,
-0.041740819811820984,
0.010962173342704773,
-0.057872314006090164,
0.007694684900343418,
0.10817187279462814,
-0.04647667706012726,
0.013875076547265053,
0.007899675518274307,
0.016941100358963013,
-0.03960290551185608,
0.0070580956526100636,
-0.023302027955651283,
-0.0007981743547134101,
0.02198156528174877,
-0.019257647916674614,
-0.04208262264728546,
-0.04444436728954315,
0.022966941818594933,
0.07916317135095596,
0.05391264706850052,
0.08166360855102539,
0.011316448450088501,
0.005803882144391537,
0.0335632786154747,
-0.025129184126853943,
0.010692629031836987,
-0.015428600832819939,
-0.0003436597471591085,
-0.033567674458026886,
-0.01895740069448948,
-0.06272082030773163,
0.01657571829855442,
0.03382508456707001,
0.02492799051105976,
-0.01434254553169012,
0.002937608864158392,
-0.0483570396900177,
-0.028294231742620468,
-0.06663033366203308,
0.003786548739299178,
0.016555264592170715,
-0.004403081722557545,
0.038236938416957855,
0.01247903797775507,
0.021487576887011528,
0.03200359642505646,
0.007558827754110098,
0.005066223442554474,
-0.02709307335317135,
-0.0032060483936220407,
-0.03440524637699127,
-0.07094398140907288,
-0.07099830359220505,
0.018670108169317245,
0.014722458086907864,
-0.0181037038564682,
0.011930109933018684,
-0.01925465650856495,
-0.05646282806992531,
0.03316145017743111,
0.039866723120212555,
-0.009668728336691856,
-0.030856074765324593,
0.00440759165212512,
0.027171919122338295,
0.015998484566807747,
-0.005027492064982653,
-0.019967425614595413,
-0.004316756036132574,
-0.012623815797269344,
0.0005196491838432848,
0.029155010357499123,
-0.028456468135118484,
0.03701933100819588,
-0.027648188173770905,
0.0070155030116438866,
-0.006302164867520332,
0.07746077328920364,
0.01375243067741394,
0.011463899165391922,
-0.022504575550556183,
-0.02696787193417549,
-0.0027753945905715227,
0.0055412594228982925,
0.024535734206438065,
-0.04233816638588905,
0.016958562657237053,
0.007951791398227215,
-0.0029142226558178663,
-0.034794241189956665,
-0.08589039742946625,
0.00010439793550176546,
-0.06200067326426506,
-0.07588058710098267,
0.0388537272810936,
0.036527909338474274,
-0.03675849363207817,
0.05130409821867943,
-0.002564184833317995,
0.0010868810350075364,
0.013554493896663189,
-0.014955304563045502,
0.07704219222068787,
-0.030981915071606636,
0.02839059755206108,
-0.04257786273956299,
0.019568851217627525,
0.027803799137473106,
0.03888078033924103,
-0.014173499308526516,
-0.02611100859940052,
0.007941745221614838,
0.029644770547747612,
-0.0031265586148947477,
-0.004614821635186672,
-0.024982651695609093,
0.055169906467199326,
-0.03859119117259979,
0.00739141833037138,
-0.001659914618358016,
-0.020584769546985626,
0.002180518815293908,
0.03522614762187004,
-0.05398578196763992,
-0.06977240741252899,
0.04026847705245018,
0.03590156510472298,
-0.0827077180147171,
0.08471770584583282,
-0.017434965819120407,
0.021051496267318726,
0.04988246411085129,
-0.017468946054577827,
-0.00328066642396152,
-0.046600017696619034,
-0.03351258486509323,
-0.01125164981931448,
-0.04009433090686798,
0.05964317172765732,
0.028268491849303246,
0.056492701172828674,
0.038223665207624435,
0.01358734630048275,
0.04283628240227699,
-0.001171465264633298,
-0.0031630040612071753,
0.01813916675746441,
-0.026875218376517296,
-0.023525835946202278,
-0.0018344881245866418,
-0.028299802914261818,
-0.05784156918525696,
0.029493119567632675,
-0.034558676183223724,
0.03743244335055351,
0.005485327448695898,
-0.014794952236115932,
0.028530338779091835,
0.00514507619664073,
-0.0223990511149168,
0.024928735569119453,
0.01650930754840374,
-0.01123752724379301,
0.06238850578665733,
-0.021202117204666138,
-0.010926716029644012,
-0.01721193455159664,
-0.03559660166501999,
-0.0687214657664299,
0.003394092433154583,
0.031065573915839195,
0.02830863744020462,
-0.002500009723007679,
0.005878918804228306,
-0.028177903965115547,
-0.0195311326533556,
-0.024806709960103035,
0.00572413532063365,
0.018214331939816475,
-0.07965132594108582,
-0.06865914165973663,
-0.03662167862057686,
-0.0470234639942646,
0.019654754549264908,
-0.0007084573153406382,
-0.06999565660953522,
0.012663038447499275,
-0.02556847222149372,
0.038601264357566833,
-0.010684818029403687,
-0.0813569724559784,
-0.060968998819589615,
-0.02270588092505932,
-0.031072542071342468,
-0.015126792713999748,
0.03697451949119568,
-0.007917428389191628,
-0.06346815079450607,
0.05350493639707565,
0.08237607777118683,
0.05096621811389923,
0.03536025434732437,
-0.03066311590373516,
0.014231448993086815,
0.05331684648990631,
0.013836984522640705,
0.04694078490138054,
-0.014633068814873695,
-0.013975544832646847,
0.025214025750756264,
0.051305778324604034,
-0.00006795860099373385,
-0.005983094684779644,
0.05133975297212601,
0.04783029109239578,
-0.010435707867145538,
0.05648203566670418,
-0.03405085206031799,
-0.06551224738359451,
0.05307619646191597,
-0.022744813933968544,
0.07037202268838882,
-0.006887427065521479,
0.00476883677765727,
-0.01403710339218378,
-0.03112470917403698,
-0.04091035947203636,
-0.03517397493124008,
0.026896845549345016,
-0.04280465841293335,
-0.049008890986442566,
0.003952431958168745,
0.022833671420812607,
-0.009767996147274971,
-0.00047836225712671876,
0.011345865204930305,
-0.034240685403347015,
-0.015447016805410385,
-0.013560911640524864,
0.01761799305677414,
-0.010873815976083279,
-0.013065747916698456,
-0.023662304505705833,
-0.032970160245895386,
0.029836654663085938,
0.02382749505341053,
0.005084292497485876,
-0.015916327014565468,
-0.0445970743894577,
0.0035541539546102285,
0.019449518993496895,
-0.03656833991408348,
0.02377011626958847,
-0.05119752883911133,
-0.00025731325149536133,
-0.022055912762880325,
0.07740235328674316,
0.02035946026444435,
-0.000052444014727370813,
-0.049004413187503815,
0.028620924800634384,
0.07099772244691849,
0.023893630132079124,
-0.01392796915024519,
0.024255789816379547,
-0.0023006927222013474,
-0.03196348249912262,
-0.025556819513440132,
-0.005241988226771355,
-0.04099980369210243,
-0.00792737863957882,
-0.03680533543229103,
0.05758907273411751,
0.0744226798415184,
-0.0029154878575354815,
0.026308508589863777,
-0.012176715768873692,
-0.00594024732708931,
0.010900950990617275,
-0.03336004167795181,
-0.04846461862325668,
0.03571721538901329,
0.018835553899407387,
0.009557324461638927,
-0.011088576167821884,
0.027344390749931335,
0.01161032821983099,
-0.03255055844783783,
-0.025148916989564896,
0.06811217963695526,
0.022335713729262352,
0.004798996727913618,
-0.04282182827591896,
-0.002273696009069681,
0.033768557012081146,
-0.02022194117307663,
-0.008654595352709293,
0.010193879716098309,
-0.047911375761032104,
-0.03321412205696106,
0.02000834420323372,
-0.05320458114147186,
0.047285228967666626,
0.003051919164136052,
0.01584005542099476,
0.010450298897922039,
-0.0005526504246518016,
-0.0068829902447760105,
-0.03712182492017746,
0.003188013331964612,
0.0042645581997931,
0.058333620429039,
-0.06476268917322159,
0.014763006009161472,
-0.014892365783452988,
-0.0280124731361866,
-0.04805726930499077,
0.016732240095734596,
-0.0029724740888923407,
0.04145154356956482,
0.04937337711453438,
0.02607687935233116,
-0.01721731387078762,
-0.031590864062309265,
-0.0180042814463377,
-0.019203005358576775,
0.09034845978021622,
-0.004262594506144524,
0.003916134126484394,
-0.019952017813920975,
0.02905597724020481,
0.06578395515680313,
0.05086495354771614,
-0.015618002973496914,
-0.059938181191682816,
-0.03886603191494942,
0.05151238292455673,
-0.019625555723905563,
-0.04981183260679245,
0.019500553607940674,
0.005912099499255419,
-0.009493573568761349,
0.0164620541036129,
0.03571239486336708,
0.0404338613152504,
0.016538089141249657,
0.07697447389364243,
0.06218933314085007,
-0.035796988755464554,
-0.043141067028045654,
0.010098719038069248,
0.018029293045401573,
-0.009467773139476776,
-0.03138618916273117,
-0.048721373081207275,
0.01515678595751524,
-0.011515971273183823,
0.014818424358963966,
-0.00008622854511486366,
-0.038030777126550674,
0.032838910818099976,
0.04615265130996704,
-0.030882183462381363,
-0.058162618428468704,
0.0020005889236927032,
0.05668724328279495,
0.06885526329278946,
-0.020177947357296944,
-0.01708385720849037,
-0.012177379801869392,
-0.024274250492453575,
0.015261068940162659,
-0.0009200712665915489,
-0.05974627658724785,
0.014678583480417728,
0.016097242012619972,
-0.001519455574452877,
0.008445033803582191,
0.04084312915802002,
-0.01789247617125511,
-0.019885830581188202,
0.015890099108219147,
-0.021182172000408173,
0.0016647054580971599,
-0.0037373509258031845,
-0.022811857983469963,
-0.04035995900630951,
-0.0020681130699813366,
-0.057091694325208664,
-0.05154066160321236,
0.013266538269817829,
-0.06539051979780197,
0.017223743721842766,
-0.03443199396133423,
0.00674291979521513,
0.0007803544285707176,
0.03290069103240967,
0.03104577772319317,
-0.012597191147506237,
0.05241788178682327,
0.005013579037040472,
0.08370918035507202,
0.01469324715435505,
0.010774803347885609,
0.004584798123687506,
0.010649026371538639,
0.00677036726847291,
0.016150005161762238,
-0.01929139345884323,
0.05095607042312622,
0.009793614037334919,
-0.06407880783081055,
-0.023773591965436935,
0.0356820784509182,
0.018880164250731468,
-0.004417254123836756,
-0.03336705267429352,
0.110222227871418,
-0.011575434356927872,
0.07258434593677521,
-0.024695321917533875,
-0.024573691189289093,
0.040294941514730453,
0.06794047355651855,
-0.002123500220477581,
-0.0406554713845253,
-0.0390196330845356,
-0.007166419178247452,
-0.022969862446188927,
0.009395192377269268,
-0.05344128608703613,
-0.020542114973068237,
0.011948682367801666,
0.06178425997495651,
0.010264750570058823,
-0.0030202693305909634,
0.04501192644238472,
-0.011566531844437122,
0.032663870602846146,
0.00988391600549221,
0.029364196583628654,
0.011807458475232124,
-0.005318452604115009,
-0.01405980996787548,
0.00805274210870266,
0.0013867447851225734,
0.049404725432395935,
-0.043173037469387054,
0.012296447530388832,
0.007320105563849211,
-0.024113552644848824,
0.010527328588068485,
-0.025479529052972794,
-0.01584802195429802,
0.025016719475388527,
0.0014108442701399326,
-0.0050156740471720695,
0.0038962543476372957,
0.04346837103366852,
-0.018110856413841248,
-0.03159438818693161,
-0.01906644180417061,
-0.0032399611081928015,
-0.009155991487205029,
0.004852318670600653,
0.020705290138721466,
-0.05506368726491928,
-0.022253574803471565,
0.03036799095571041,
0.014896046370267868,
0.07359550148248672,
-0.05935879424214363,
-0.007679085247218609,
0.029069554060697556,
0.09174131602048874,
0.0007251478382386267,
0.0650491714477539,
0.08154338598251343,
0.024471905082464218,
0.028484363108873367,
0.019214531406760216,
0.005299980286508799,
0.011916562914848328,
0.008361595682799816,
-0.022428300231695175,
-0.031615305691957474,
0.006828184239566326,
0.027843285351991653,
0.007473412901163101,
0.020296188071370125,
-0.014682558365166187,
0.036245834082365036,
-0.05942010134458542,
0.050312791019678116,
0.05355636775493622,
-0.039521295577287674,
0.06574422866106033,
0.018681135028600693,
0.005729735363274813,
-0.01848084107041359,
-0.008140692487359047,
0.011838617734611034,
-0.028553428128361702,
0.03395572677254677,
0.010758303105831146,
0.03797430545091629,
0.03443872556090355,
0.02762025222182274,
0.030365779995918274,
-0.023947861045598984,
-0.04821522906422615,
0.036288317292928696,
-0.046955760568380356,
-0.0003183800436090678,
-0.05218026414513588,
0.025659162551164627,
-0.0024261546786874533,
-0.08793958276510239,
-0.00839026179164648,
0.01854872517287731,
0.004041040316224098,
-0.040848974138498306,
-0.007761931046843529,
0.07431305944919586,
-0.046537160873413086,
0.07605553418397903,
-0.03769136965274811,
0.017087126150727272,
-0.009380357339978218,
-0.08726181089878082,
0.0036817570216953754,
0.062019605189561844,
0.05302126333117485,
-0.004373893607407808,
-0.015602420084178448,
0.032837122678756714,
0.043839409947395325,
-0.0006756213260814548,
0.03419901430606842,
0.02588796429336071,
0.01714964397251606,
-0.024052049964666367,
0.092215396463871,
-0.019240211695432663,
0.03393379971385002,
0.04010847583413124,
-0.04481948912143707,
-0.00211897911503911,
0.03392382711172104,
-0.04680401831865311,
0.03518995642662048,
0.010960663668811321,
-0.060020267963409424,
0.026571398600935936,
0.030638189986348152,
0.04008224233984947,
-0.00296797975897789,
0.03935423120856285,
0.019648931920528412,
-0.016739385202527046,
-0.04685990512371063,
0.06451426446437836,
-0.009024796076118946,
0.07636222243309021,
0.019287709146738052,
0.05793360620737076,
-0.008294395171105862,
0.018800856545567513,
-0.002060652244836092,
-0.008069283328950405,
-0.012766439467668533,
0.018376478925347328,
-0.059349872171878815,
0.005220747087150812,
-0.04566318169236183,
-0.05217426270246506,
-0.06017911806702614,
-0.06152252480387688,
-0.11569567024707794,
-0.032350797206163406,
0.008831511251628399,
-0.019586505368351936,
0.02029990963637829,
-0.013612832874059677,
-0.0069592841900885105,
-0.04283834248781204,
0.017067667096853256,
-0.016155710443854332,
0.0049904827028512955,
0.018663901835680008,
0.04407839477062225,
0.05024922639131546,
-0.022550249472260475,
0.00954266358166933,
0.05024755373597145,
-0.07143204659223557,
-0.013987085781991482,
-0.053068455308675766,
-0.006624192465096712,
-0.028957245871424675,
-0.022026531398296356,
-0.025751296430826187,
0.007339191157370806,
0.10040386766195297,
-0.014728521928191185,
0.010020573623478413,
-0.052234526723623276,
-0.0393897145986557,
-0.02076837234199047,
-0.0682249665260315,
0.03684021160006523,
-0.012416084297001362,
0.003129766322672367,
0.0671749860048294,
0.006005318369716406,
-0.005172352306544781,
0.001446565962396562,
0.038803379982709885,
-0.023289702832698822,
-0.014759920537471771,
-0.03706854581832886,
0.04036516323685646,
0.0035295411944389343,
-0.03681837022304535,
0.02666081301867962,
-0.02286863513290882,
0.03490900248289108,
0.05755224451422691,
-0.009432889521121979,
0.0037694259081035852,
0.00017197847773786634,
-0.027539215981960297,
0.00100602803286165,
0.06105538830161095,
-0.06880341470241547,
0.014544092118740082,
0.027679041028022766,
0.05955124273896217,
0.07292991876602173,
-0.031710490584373474,
-0.017189830541610718,
-0.0192992202937603,
-0.04861294478178024,
0.04046181961894035,
-0.031350307166576385,
0.02603432722389698,
-0.03880668431520462,
0.024226795881986618,
0.010643122717738152,
-0.017111239954829216,
0.06269507110118866,
0.0066689555533230305,
0.015920447185635567,
0.022686190903186798,
-0.05361909791827202,
-0.018933795392513275,
0.01605273224413395,
0.015666041523218155,
-0.04700006544589996,
0.04488752782344818,
-0.02575189247727394,
-0.021674202755093575,
0.030382448807358742,
-0.015141931362450123,
0.035458263009786606,
0.0034058408346027136,
0.010567924939095974,
-0.02793782390654087,
-0.03121783584356308,
-0.03863406553864479,
0.013472630642354488,
-0.02638455666601658,
-0.02854255586862564,
0.02510792575776577,
0.02283422276377678,
-0.0015859648119658232,
-0.011125246062874794,
0.004563744645565748,
0.013935343362390995,
-0.023283252492547035,
0.04451044276356697,
-0.05628903955221176,
-0.03513351455330849,
0.04968559369444847,
-0.09391333907842636,
0.014108357951045036,
-0.04075764864683151,
-0.0373910591006279,
-0.00523453950881958,
0.00028218398801982403,
-0.05093695595860481,
0.04806806892156601,
0.009362169541418552,
-0.06906107813119888
] |
<p>How is spacetime depicted in quantum field theory?
Is space and time completely separate, and time is just nature of law as in Newtonian mechanics?</p> | g4633 | [
0.01771676540374756,
0.01485398318618536,
-0.004035664722323418,
-0.021326208487153053,
-0.008771407417953014,
0.03636280074715614,
-0.026807526126503944,
-0.008146974258124828,
0.01571601815521717,
0.0012427265755832195,
0.011620290577411652,
-0.042801421135663986,
-0.02129625342786312,
0.038478996604681015,
-0.0011179809225723147,
-0.0708104595541954,
-0.00006558089808095247,
0.014989183284342289,
0.06410913169384003,
-0.04622499644756317,
0.004634401760995388,
0.017168618738651276,
0.01585311070084572,
-0.005492108874022961,
-0.02532247267663479,
-0.03540363907814026,
0.018886182457208633,
-0.004730371758341789,
-0.00058681087102741,
-0.001832280308008194,
0.02029876783490181,
0.024244558066129684,
0.02089792676270008,
-0.015184428542852402,
-0.004048140253871679,
-0.010141418315470219,
-0.018352003768086433,
0.026947425678372383,
0.027065031230449677,
-0.013458974659442902,
-0.0016494357259944081,
-0.04400494694709778,
-0.04888935387134552,
-0.026760756969451904,
-0.03484169393777847,
-0.023226503282785416,
-0.02321259304881096,
-0.001116231782361865,
-0.025310730561614037,
0.03522110357880592,
-0.03906511142849922,
0.012096988037228584,
-0.00004424567669047974,
-0.018257349729537964,
0.07340678572654724,
0.017765365540981293,
0.04930499568581581,
-0.01263271365314722,
0.1141870841383934,
0.03607368841767311,
-0.02907549776136875,
0.05156310647726059,
0.05296306684613228,
0.07205209136009216,
0.026057420298457146,
0.028325721621513367,
-0.017123112455010414,
-0.044847406446933746,
0.03479184955358505,
-0.0022593208122998476,
-0.009020295925438404,
-0.09214901179075241,
-0.030310209840536118,
-0.018794327974319458,
0.04839332774281502,
0.07772736996412277,
0.022789020091295242,
0.024535860866308212,
0.008264548145234585,
0.011607236228883266,
0.04174095019698143,
0.025713127106428146,
-0.03216788172721863,
0.021378297358751297,
0.026491066440939903,
-0.013913081958889961,
0.0016250633634626865,
-0.05772208049893379,
-0.02763141505420208,
0.06255500018596649,
-0.006518701557070017,
0.046886786818504333,
0.09494476765394211,
0.008751588873565197,
-0.05103033408522606,
-0.0206304918974638,
-0.012622812762856483,
0.030965160578489304,
-0.020067399367690086,
0.02490299940109253,
-0.02828488126397133,
0.026119960471987724,
0.05650881677865982,
-0.024031206965446472,
-0.0017066755099222064,
0.056877847760915756,
0.007777429651468992,
0.04059617593884468,
0.008659727871418,
0.0233592726290226,
-0.049511078745126724,
0.013857808895409107,
-0.03345969691872597,
0.0017881972016766667,
-0.02105211652815342,
-0.04231123626232147,
0.012593596242368221,
-0.03181275725364685,
-0.01942252553999424,
0.011734290048480034,
-0.015455064363777637,
0.04947478696703911,
0.09031941741704941,
0.01895369403064251,
-0.05267258360981941,
0.018683290109038353,
-0.01000227965414524,
-0.04477406293153763,
-0.0036996749695390463,
-0.018245132640004158,
0.010007324628531933,
0.01156044751405716,
-0.04103708267211914,
0.049053821712732315,
-0.014832897111773491,
0.0039812843315303326,
-0.02330334670841694,
-0.03448658809065819,
-0.05283717066049576,
0.01728283241391182,
0.021186072379350662,
-0.05730791389942169,
0.00008762545621721074,
-0.01794048771262169,
-0.004024649038910866,
-0.006460428703576326,
0.0015078476862981915,
-0.0018172296695411205,
0.0019577564671635628,
0.028718996793031693,
-0.03596963360905647,
0.09528158605098724,
0.04258492961525917,
-0.017084892839193344,
0.039481304585933685,
-0.049225013703107834,
0.03414502739906311,
0.015600709244608879,
-0.021525852382183075,
-0.025626033544540405,
0.03994601219892502,
0.001657875836826861,
0.041044898331165314,
0.005095407832413912,
-0.002761431969702244,
-0.0014991187490522861,
-0.0244354959577322,
-0.05733326077461243,
0.07046224176883698,
-0.03676031529903412,
0.021505888551473618,
-0.030296947807073593,
-0.024907365441322327,
0.02496834099292755,
-0.015417356044054031,
0.03687707707285881,
-0.03958304226398468,
-0.00621677516028285,
0.00002591434895293787,
0.023335937410593033,
0.024197231978178024,
0.024906540289521217,
-0.019389307126402855,
-0.061596229672431946,
-0.04331309720873833,
0.03912725672125816,
-0.007577116135507822,
0.0004236960376147181,
-0.05785127356648445,
0.0063585396856069565,
-0.03645970672369003,
-0.04364722967147827,
-0.0417124405503273,
0.035455022007226944,
0.03933257237076759,
0.004984311293810606,
-0.02828407846391201,
-0.03261590376496315,
-0.034343570470809937,
-0.013047173619270325,
-0.0032656865660101175,
0.04628841206431389,
-0.014563851058483124,
0.06946014612913132,
-0.006019486114382744,
0.018002498894929886,
-0.057558607310056686,
0.02658664993941784,
-0.05453026294708252,
-0.012849470600485802,
0.029917597770690918,
0.01202058233320713,
0.04021617770195007,
0.07298504561185837,
-0.10504838824272156,
-0.007836620323359966,
-0.03270211070775986,
0.006558287888765335,
-0.06281483918428421,
0.08314627408981323,
0.02131321281194687,
0.01747669279575348,
0.038663264364004135,
-0.015589495189487934,
-0.008729025721549988,
-0.03351346775889397,
-0.04235734045505524,
0.0041198874823749065,
-0.018606673926115036,
0.020570561289787292,
-0.0934772789478302,
-0.02570633962750435,
-0.03109791688621044,
0.031219463795423508,
0.0006399680278263986,
0.0225830040872097,
0.011080149561166763,
0.0022616260685026646,
-0.017760243266820908,
-0.03016507439315319,
-0.004473124630749226,
0.03208242729306221,
-0.00124348234385252,
0.01413083728402853,
0.03469902276992798,
-0.03231300041079521,
-0.0013687320752069354,
-0.006546754855662584,
-0.0027218861505389214,
-0.00048666345537640154,
-0.011521261185407639,
-0.024739878252148628,
-0.045484721660614014,
0.0172621738165617,
-0.010882181115448475,
0.02096036821603775,
0.03334806114435196,
-0.02375480905175209,
-0.08855322748422623,
-0.017450915649533272,
-0.022209107875823975,
-0.05840623751282692,
-0.010566996410489082,
0.05673912540078163,
-0.01924249902367592,
-0.041698355227708817,
0.036038048565387726,
0.0747227668762207,
-0.015304174274206161,
-0.010956468060612679,
-0.05129211023449898,
0.06546124070882797,
-0.003037920454517007,
-0.032685816287994385,
-0.06373731046915054,
-0.02579333819448948,
0.046140797436237335,
-0.025950556620955467,
-0.04194119945168495,
-0.019953100010752678,
0.016597533598542213,
-0.009544068947434425,
-0.06853897869586945,
0.0227082297205925,
0.012817882001399994,
-0.0765613541007042,
0.031944822520017624,
-0.0011575305834412575,
0.0012267206329852343,
0.005520304664969444,
0.032399918884038925,
0.05188540369272232,
-0.03248943015933037,
-0.037950191646814346,
-0.04340682178735733,
0.024651039391756058,
-0.001480288221500814,
-0.027221355587244034,
-0.0023594798985868692,
0.02039152942597866,
-0.03695640340447426,
-0.012633468955755234,
0.07967153191566467,
0.07958753407001495,
-0.006088363938033581,
-0.020650651305913925,
-0.006441999226808548,
-0.041727643460035324,
-0.05303636193275452,
-0.07876129448413849,
-0.014773265458643436,
0.01786366105079651,
0.059987686574459076,
-0.01431109756231308,
-0.016460852697491646,
-0.029745735228061676,
-0.051693402230739594,
-0.018401281908154488,
0.043443650007247925,
-0.0031428751535713673,
-0.016193797811865807,
-0.02738795056939125,
0.014071930199861526,
0.02901971898972988,
0.026959747076034546,
-0.025981439277529716,
0.0010512867011129856,
-0.010978973470628262,
-0.012933161109685898,
-0.02486209198832512,
-0.011909856460988522,
-0.043832890689373016,
0.0024993575643748045,
-0.008485016413033009,
-0.04432468116283417,
0.06187305226922035,
-0.0664045438170433,
-0.02395123988389969,
0.037802740931510925,
-0.028900112956762314,
0.04346710070967674,
-0.01374686136841774,
-0.03293698653578758,
0.014509801752865314,
0.024361269548535347,
0.020974142476916313,
0.026300663128495216,
-0.02637510560452938,
0.04062715545296669,
0.013763810507953167,
0.006345669273287058,
-0.016902433708310127,
0.027210433036088943,
-0.011186611838638783,
0.007794003468006849,
0.07426728308200836,
0.0380575992166996,
0.05373493209481239,
-0.003436679719015956,
-0.06940575689077377,
0.016895361244678497,
-0.010325787588953972,
0.027650145813822746,
0.030312001705169678,
0.027937298640608788,
-0.03935663029551506,
0.02348214015364647,
-0.0189353134483099,
0.023037858307361603,
0.025510558858513832,
0.039070386439561844,
0.01853819005191326,
-0.018821904435753822,
0.029457638040184975,
0.06047670915722847,
-0.04361370578408241,
-0.01590040512382984,
-0.026363583281636238,
0.020784156396985054,
-0.02036542072892189,
0.011305377818644047,
0.003953767940402031,
-0.020386287942528725,
0.04959792271256447,
0.02928660809993744,
0.042414452880620956,
-0.016332359984517097,
-0.0351492315530777,
0.023055797442793846,
0.01179246325045824,
-0.012363138608634472,
-0.04659935459494591,
-0.0203294288367033,
-0.0456312857568264,
-0.020417416468262672,
0.006756190676242113,
0.01730615645647049,
0.06751035153865814,
-0.01018567569553852,
-0.041408613324165344,
0.010651836171746254,
0.04853874444961548,
-0.012537089176476002,
0.015464559197425842,
0.032136574387550354,
0.03841240704059601,
0.01902630180120468,
-0.0728197693824768,
0.008869536221027374,
0.012391594238579273,
-0.0009914792608469725,
0.012922662310302258,
-0.018910430371761322,
-0.04813051223754883,
-0.014457951299846172,
0.04122980684041977,
0.012399711646139622,
-0.03572351858019829,
-0.0009141763439401984,
0.0182285625487566,
0.04823306202888489,
0.04567357897758484,
0.018363935872912407,
-0.024971775710582733,
-0.009150472469627857,
0.022239474579691887,
-0.015596432611346245,
0.041637539863586426,
-0.048980358988046646,
-0.031042810529470444,
0.0018493573879823089,
-0.0306746494024992,
0.0036124270409345627,
0.010528279468417168,
-0.05948146432638168,
0.02007145993411541,
-0.014987562783062458,
0.04435258358716965,
0.03774217143654823,
0.012372548691928387,
0.06129307299852371,
-0.023450857028365135,
0.04491086304187775,
0.011156642809510231,
0.002833880251273513,
0.03601383417844772,
-0.007693777792155743,
-0.05338060110807419,
-0.05503467470407486,
-0.026620112359523773,
-0.027524089440703392,
0.08212839812040329,
-0.042227841913700104,
-0.03910883516073227,
-0.041624587029218674,
-0.00008261886250693351,
-0.041522007435560226,
-0.012415803968906403,
-0.012174809351563454,
0.023263737559318542,
-0.10531803965568542,
-0.010661466978490353,
0.01174173504114151,
0.03957728296518326,
-0.016684768721461296,
0.013378570787608624,
-0.07823517173528671,
0.04678473621606827,
-0.05230644717812538,
0.05296863988041878,
0.04662024602293968,
-0.04633122310042381,
-0.026269664987921715,
-0.07735354453325272,
0.008389133028686047,
-0.007432362996041775,
0.018650364130735397,
-0.013776671141386032,
0.0034727558959275484,
-0.064334437251091,
0.07639113813638687,
-0.023475391790270805,
0.014550454914569855,
0.01140240766108036,
-0.03826986253261566,
0.03504044935107231,
0.027805844321846962,
0.01654261350631714,
-0.014840186573565006,
-0.016649512574076653,
-0.039546798914670944,
-0.026932723820209503,
0.016009997576475143,
0.03005026839673519,
-0.037441521883010864,
0.01973658800125122,
-0.0376126654446125,
-0.054177019745111465,
0.001832932815887034,
-0.025345468893647194,
-0.053749147802591324,
-0.026933301240205765,
0.006694238632917404,
0.005174263846129179,
-0.006067452486604452,
0.002764561679214239,
0.0370597243309021,
0.015962721779942513,
-0.09290798753499985,
0.041990458965301514,
0.03776213526725769,
-0.017251890152692795,
-0.06864974647760391,
0.009518271312117577,
0.0737924575805664,
-0.04669472202658653,
-0.0018032437656074762,
0.0036699033807963133,
-0.0156807079911232,
-0.01876489259302616,
-0.020143935456871986,
0.017573270946741104,
0.08082021772861481,
-0.016095755621790886,
0.061849065124988556,
0.06787095218896866,
-0.04580574110150337,
-0.01044728048145771,
-0.014485950581729412,
0.029232164844870567,
0.015424125827848911,
0.031822510063648224,
0.06546890735626221,
0.03419876471161842,
0.01722533628344536,
-0.0000098083201010013,
0.0527789406478405,
0.04272916167974472,
0.08048371225595474,
0.002068996662274003,
-0.06396637856960297,
-0.021755054593086243,
0.018991444259881973,
-0.009350095875561237,
0.020884718745946884,
0.019732695072889328,
-0.01328442431986332,
0.04033970460295677,
0.06571473926305771,
-0.022195976227521896,
-0.04915599152445793,
0.011646611616015434,
-0.026696879416704178,
0.03027595952153206,
0.015161167830228806,
0.030444957315921783,
0.02744622528553009,
-0.05429167300462723,
-0.06485015898942947,
0.031456172466278076,
0.030154669657349586,
0.06935929507017136,
-0.029114974662661552,
-0.03665158525109291,
0.01211531925946474,
0.017077043652534485,
0.044114161282777786,
0.009140410460531712,
0.039974819868803024,
-0.006842262111604214,
-0.000977864139713347,
0.018151693046092987,
0.010661441832780838,
0.0018442668952047825,
0.0005023062694817781,
-0.033897221088409424,
0.022563006728887558,
-0.05582499876618385,
-0.0568716786801815,
0.012785608880221844,
0.0025265333242714405,
-0.024217108264565468,
0.010942934080958366,
-0.07490529119968414,
-0.01653231494128704,
0.017005247995257378,
-0.004174470901489258,
0.006217403803020716,
0.041128575801849365,
0.05831427872180939,
-0.028194094076752663,
0.006413945462554693,
0.015374974347651005,
-0.03871874883770943,
0.018633214756846428,
0.015622970648109913,
0.030672481283545494,
0.03549438714981079,
0.002514464780688286,
0.050997428596019745,
-0.037546299397945404,
-0.01221956592053175,
0.002088427310809493,
-0.05607369542121887,
0.08672130852937698,
0.08143828064203262,
-0.068365678191185,
-0.03376609832048416,
0.02671768330037594,
-0.0010524013778194785,
-0.0020177613478153944,
-0.002198394387960434,
0.0019602440297603607,
0.04556000605225563,
-0.013147614896297455,
0.007525731343775988,
0.011955373920500278,
0.02684466727077961,
-0.04452848061919212,
0.04449927806854248,
0.013279215432703495,
-0.013183112256228924,
0.011965779587626457,
0.07064766436815262,
0.018009629100561142,
0.03776232525706291,
-0.02169421687722206,
0.08643170446157455,
0.009766423143446445,
-0.011679005809128284,
0.03511470928788185,
-0.015569320879876614,
0.02821492962539196,
0.05356476455926895,
0.012578466907143593,
0.01746290922164917,
-0.02743317000567913,
0.039103347808122635,
-0.0033494262024760246,
0.00200032745487988,
-0.01006496325135231,
0.0017707276856526732,
0.09155506640672684,
0.0016901764320209622,
-0.06881224364042282,
0.00432543596252799,
0.033975303173065186,
-0.03841692581772804,
-0.05217059329152107,
0.03192988038063049,
0.027601957321166992,
0.029779767617583275,
-0.07824348658323288,
0.05074594169855118,
-0.014198195189237595,
0.03338243439793587,
-0.03861048445105553,
-0.00523030199110508,
-0.018099134787917137,
-0.1111997738480568,
-0.01302396785467863,
-0.014181459322571754,
-0.06308838725090027,
-0.005036640912294388,
0.004799680784344673,
0.035566989332437515,
-0.004920627921819687,
-0.00948199350386858,
0.002372122835367918,
-0.0429309606552124,
-0.025395600125193596,
-0.06352424621582031,
0.0726037248969078,
0.06700745224952698,
-0.049766045063734055,
-0.04064657911658287,
-0.07530955970287323,
0.06739963591098785,
0.014122096821665764,
-0.025310341268777847,
-0.00906120054423809,
0.05975049361586571,
-0.009616798721253872,
0.02717144414782524,
0.024810055270791054,
-0.0054269107058644295,
0.025993671268224716,
-0.03100290521979332,
-0.011092372238636017,
0.016903165727853775,
0.03949875384569168,
-0.02055445685982704,
-0.0029652786906808615,
-0.06390216946601868,
0.06786693632602692,
0.00715977605432272,
0.09153330326080322,
-0.0299733467400074,
0.01955704763531685,
-0.0043890574015676975,
0.028278890997171402,
-0.021523579955101013,
-0.00786866620182991,
-0.025556353852152824,
0.028587572276592255,
-0.03388332203030586,
0.04540252685546875,
-0.0298711396753788,
-0.03972833976149559,
0.00835976842790842,
-0.030352957546710968,
0.049346111714839935,
-0.0031444693449884653,
0.0002020105457631871,
0.03985496610403061,
-0.03406434878706932,
-0.019237274304032326,
-0.012839632108807564,
-0.001964760012924671,
-0.06843548268079758,
0.023866519331932068,
-0.014359482564032078,
-0.01464686170220375,
-0.06439480185508728,
0.01341814361512661,
0.05521468445658684,
-0.0014376521576195955,
-0.04170564189553261,
0.008021806366741657,
-0.05985521897673607,
-0.012053485959768295,
0.0010013026185333729,
-0.0034609499853104353,
0.06266410648822784,
-0.056823451071977615,
0.038749389350414276,
-0.012902190908789635,
-0.05682414025068283,
-0.002693494549021125,
-0.02928156778216362,
-0.02049330808222294,
-0.016125258058309555,
-0.03755168616771698,
-0.02063114196062088,
-0.032890789210796356,
-0.032513197511434555,
-0.0710606724023819,
-0.010385827161371708,
0.018108049407601357,
0.018236307427287102,
-0.014533528126776218,
0.06199660897254944,
-0.03847698122262955,
0.017202312126755714,
0.04622596129775047,
-0.037759047001600266,
0.018380627036094666,
-0.029532626271247864,
0.053789857774972916,
0.02846621908247471,
0.002357227262109518,
-0.03356399014592171,
0.029708148911595345,
0.011260287836194038,
-0.032803427428007126,
-0.0005780549836345017,
0.017218220978975296,
0.028471574187278748
] |
<p>This is an ultra-soft question about relatively recent history. While reading some of Mandelstam's papers, I noticed that he cites David John Candlin consistenly whenever he does anything with Grassman path-integral. Everyone else cites Berezin.</p>
<p>So I read Candlin's 1956 paper, and I was stunned to find a complete and correct description of anticommuting variables, presented more lucidly than anywhere else, with a clear definition of Grassman integration, and a proof that it reproduces the Fermionic quantum field. This is clearly the original source of all the Grassman methods. I was stunned that the inventor of this method is quietly buried away.</p>
<p>I wrote the <a href="http://en.wikipedia.org/wiki/David_John_Candlin">Wikipedia page on the guy</a>, but I couldn't find out anything beyond the sketchy stuff I found on an old Princeton staff listing. The fellow doesn't google very well at all.</p>
<p>Here are the questions:</p>
<ul>
<li>Is he still alive? (Hello? Are you there?)</li>
<li>Did he become the experimental physicist David John Candlin in the late 1970s/early 1980s? Or is this someone else with the same name?</li>
<li>Did he get any credit for his discovery?</li>
</ul>
<p>I mean, this is one of the central tools of modern physics, it is used every day by every theorist, and the inventor is never mentioned. It's 50% of the path integral. Why the silence?</p> | g4634 | [
0.08473643660545349,
0.016100410372018814,
0.030406614765524864,
0.002107477281242609,
0.011331327259540558,
0.03416815400123596,
0.05763484537601471,
0.08406537026166916,
-0.013381043449044228,
-0.011190230026841164,
-0.03837014362215996,
-0.03520951792597771,
0.05054548755288124,
0.04197616130113602,
-0.015158296562731266,
-0.022616200149059296,
0.0020548966713249683,
0.012966186739504337,
0.021992912515997887,
-0.13376474380493164,
-0.020067531615495682,
0.01653939299285412,
0.10110507905483246,
0.02333504520356655,
-0.025211043655872345,
-0.03726261481642723,
-0.02796146646142006,
-0.07399909943342209,
-0.010861572809517384,
-0.03010370582342148,
0.029219893738627434,
-0.05372324958443642,
-0.000977946212515235,
-0.014714227057993412,
-0.05249457061290741,
-0.04487450793385506,
0.03981713205575943,
0.03930322080850601,
-0.03165028244256973,
0.035913243889808655,
-0.013415243476629257,
0.015094117261469364,
0.004891290329396725,
-0.024114495143294334,
0.0378255620598793,
0.05848999321460724,
-0.06791166961193085,
-0.007910317741334438,
-0.021129902452230453,
-0.040087610483169556,
-0.021617569029331207,
0.024534333497285843,
0.04182634875178337,
0.010943141765892506,
0.02577037923038006,
0.006695126183331013,
-0.012933346442878246,
-0.019512634724378586,
0.04168449342250824,
0.00867546908557415,
0.015859009698033333,
-0.04748539626598358,
0.008758923970162868,
-0.014845184050500393,
0.03745536506175995,
0.02883324958384037,
-0.011531837284564972,
0.014988983049988747,
0.009834937751293182,
-0.017405861988663673,
0.06661185622215271,
-0.06711386889219284,
0.003203420899808407,
-0.008565453812479973,
0.06380998343229294,
0.021484985947608948,
0.03727508708834648,
-0.011386629194021225,
0.033273983746767044,
-0.028029141947627068,
-0.0574934221804142,
-0.014277255162596703,
-0.010804317891597748,
0.01266457512974739,
0.07080095261335373,
-0.042178086936473846,
0.02887372113764286,
0.023049812763929367,
-0.008262041956186295,
0.0034545741509646177,
-0.02099919691681862,
0.034738633781671524,
0.01920444332063198,
-0.024315185844898224,
-0.024007711559534073,
-0.027110762894153595,
-0.04170067980885506,
0.016300201416015625,
-0.01081725675612688,
-0.04719090089201927,
0.010669061914086342,
-0.016186939552426338,
0.009878183715045452,
0.048810672014951706,
0.012473763898015022,
0.03348750248551369,
0.014886071905493736,
-0.05796385556459427,
0.030728930607438087,
0.03199763223528862,
-0.020786568522453308,
0.011892657727003098,
-0.07050633430480957,
-0.03966883569955826,
-0.035719409584999084,
0.0022653245832771063,
0.05201755464076996,
0.013648007996380329,
-0.010899447835981846,
0.040799833834171295,
-0.00716093135997653,
0.00511481799185276,
0.04582945257425308,
-0.012547062709927559,
-0.023264741525053978,
0.018868086859583855,
-0.031176889315247536,
0.02127317152917385,
-0.04375319927930832,
0.07745368033647537,
-0.02899756096303463,
0.03712395951151848,
0.015079016797244549,
-0.02377506159245968,
0.0382748506963253,
-0.011087760329246521,
-0.04207487031817436,
-0.00017537330859340727,
0.0013252515345811844,
0.020149363204836845,
-0.0029207386542111635,
-0.04265233129262924,
-0.007545275613665581,
0.026610979810357094,
0.03673860430717468,
0.038777194917201996,
-0.03217960521578789,
-0.029048124328255653,
-0.06640393286943436,
-0.003025280311703682,
0.056601639837026596,
0.041172467172145844,
0.05817066505551338,
-0.030880531296133995,
-0.06593228131532669,
-0.01524486392736435,
-0.027333686128258705,
-0.0513547845184803,
0.034357137978076935,
-0.013910084962844849,
0.011188768781721592,
0.01049328688532114,
0.008824431337416172,
-0.04452682286500931,
0.004676334094256163,
-0.04300520569086075,
0.003889542305842042,
-0.01963965781033039,
-0.01418091356754303,
-0.04252355918288231,
-0.025620078667998314,
0.022349078208208084,
0.022239232435822487,
0.009475412778556347,
0.0043147471733391285,
-0.002404123079031706,
-0.033802349120378494,
-0.05645434185862541,
-0.03530030697584152,
-0.009688038378953934,
-0.003835145151242614,
-0.013777936808764935,
-0.006987745873630047,
-0.01838126964867115,
-0.004623918794095516,
0.01912515237927437,
-0.015554631128907204,
-0.026300791651010513,
-0.05249977484345436,
-0.058247555047273636,
0.020872872322797775,
0.0158306285738945,
0.02625621296465397,
0.08089696615934372,
0.00867236778140068,
0.00218831654638052,
0.018207453191280365,
-0.04011837765574455,
0.015872692689299583,
0.058500584214925766,
-0.016256824135780334,
0.06389375030994415,
0.04283096641302109,
-0.07242223620414734,
0.010623198933899403,
-0.01172246690839529,
0.022951295599341393,
0.03881204500794411,
0.02322445996105671,
-0.045458514243364334,
0.029910655692219734,
0.031723275780677795,
0.03498804196715355,
-0.003821450285613537,
-0.013879110105335712,
-0.021225659176707268,
0.01594206877052784,
-0.020173517987132072,
0.013021829538047314,
0.029014678671956062,
-0.008403836749494076,
0.029804054647684097,
-0.035422977060079575,
-0.007446567993611097,
0.0013059335760772228,
0.02134839817881584,
-0.01004243828356266,
0.003047967329621315,
-0.07320800423622131,
0.041655588895082474,
-0.1183062419295311,
0.0066685122437775135,
-0.023849504068493843,
-0.0037071164697408676,
0.027314404025673866,
0.021263422444462776,
0.04938405752182007,
-0.016261862590909004,
0.04468404874205589,
0.009196602739393711,
-0.010275856591761112,
-0.031387798488140106,
-0.040526699274778366,
0.03287065774202347,
0.028325334191322327,
0.015834767371416092,
0.024064989760518074,
0.012596037238836288,
-0.02916920930147171,
-0.024889826774597168,
-0.017646901309490204,
-0.01426989771425724,
-0.0421527661383152,
0.004409224260598421,
-0.028979714959859848,
0.03249040246009827,
-0.020600415766239166,
0.01614752784371376,
0.027489908039569855,
-0.01460358314216137,
0.05218968912959099,
-0.0031867260113358498,
0.08541037142276764,
0.0196820180863142,
0.008104003965854645,
-0.07498753070831299,
-0.022480538114905357,
0.06709623336791992,
-0.014245339669287205,
0.02969258651137352,
-0.05584767833352089,
0.0748785138130188,
-0.013536167331039906,
-0.025724969804286957,
0.026993315666913986,
-0.0007503803353756666,
0.000307666341541335,
-0.012160000391304493,
0.010412310250103474,
0.0515529103577137,
-0.033045295625925064,
-0.04079999029636383,
-0.06772711873054504,
0.018506500869989395,
0.006589377298951149,
-0.01857106015086174,
0.04200936481356621,
0.005842909682542086,
-0.0015399337280541658,
-0.03709016367793083,
0.0010626568691805005,
0.01694556511938572,
-0.007813910953700542,
-0.02321563847362995,
-0.016101980581879616,
-0.012787397019565105,
-0.002173926215618849,
-0.07159809023141861,
-0.003857555566355586,
-0.006335049401968718,
0.0577426441013813,
0.00038962505641393363,
0.008894984610378742,
0.016014430671930313,
0.057802341878414154,
-0.04001699388027191,
-0.07181095331907272,
0.024235568940639496,
-0.013337936252355576,
-0.03481164202094078,
0.016438981518149376,
0.029443401843309402,
0.015770627185702324,
-0.03391628712415695,
-0.0024590916000306606,
0.02128829061985016,
0.0319376215338707,
0.030956218019127846,
0.09168940037488937,
-0.04497561976313591,
-0.06190822646021843,
-0.02059243991971016,
-0.07541225850582123,
-0.04677163437008858,
0.09264452010393143,
-0.010139173828065395,
0.012477952055633068,
0.008235449902713299,
0.011569148860871792,
-0.020168455317616463,
0.03920163959264755,
-0.03594479709863663,
-0.042693670839071274,
-0.011612198315560818,
-0.042243313044309616,
-0.10507103055715561,
-0.04915425553917885,
0.026333296671509743,
0.04660095274448395,
0.012538290582597256,
-0.03874606266617775,
-0.011145276017487049,
0.02141951397061348,
-0.011943696066737175,
-0.01655443385243416,
0.002956514712423086,
0.019757568836212158,
0.018516378477215767,
-0.015327171422541142,
0.006162105593830347,
-0.012356306426227093,
0.02975957654416561,
-0.0011082962155342102,
-0.01056424155831337,
-0.03088092803955078,
0.039561085402965546,
0.024416258558630943,
0.05896449834108353,
0.04973547160625458,
0.04198423773050308,
-0.00540181202813983,
-0.0056608677841722965,
0.03655199706554413,
-0.008950243704020977,
0.014433606527745724,
0.005550147499889135,
-0.026325903832912445,
0.033932071179151535,
-0.000298635452054441,
-0.03944528475403786,
-0.0183087345212698,
-0.029404204338788986,
0.02839457243680954,
-0.02340794913470745,
-0.05121038854122162,
-0.016043661162257195,
-0.004765632096678019,
0.09314512461423874,
-0.06283938139677048,
0.03897726535797119,
-0.018273409456014633,
0.046083953231573105,
0.023292724043130875,
-0.014898019842803478,
-0.006610190495848656,
0.014951142482459545,
-0.08406277000904083,
0.0004315931582823396,
0.00046727550216019154,
-0.018760984763503075,
0.037186846137046814,
0.01762131229043007,
0.0038851310964673758,
0.0315709188580513,
-0.030246200039982796,
0.08928540349006653,
-0.07062239944934845,
-0.015403452329337597,
0.03548052906990051,
0.0706242173910141,
-0.01676580309867859,
-0.010403847321867943,
0.02404121309518814,
0.028341127559542656,
-0.034711260348558426,
0.05580834671854973,
0.016506878659129143,
-0.017340609803795815,
0.05777802690863609,
-0.00828885193914175,
-0.0010389549424871802,
-0.011546599678695202,
0.004729174077510834,
-0.041081804782152176,
-0.01745663769543171,
-0.044805895537137985,
-0.004615244921296835,
-0.02160918153822422,
-0.01603534258902073,
-0.05598253756761551,
0.012002239935100079,
0.013800913468003273,
-0.09164634346961975,
0.0024725347757339478,
0.020529840141534805,
0.03691210225224495,
0.014418759383261204,
0.00845898687839508,
-0.03644170984625816,
-0.05791890621185303,
0.014151385053992271,
0.03675270453095436,
-0.007678184192627668,
0.004214758053421974,
-0.012762903235852718,
-0.03635551035404205,
0.022025078535079956,
0.0713595375418663,
0.0008266486111097038,
0.08613602072000504,
0.09703411161899567,
-0.0014594981912523508,
0.0037924516946077347,
-0.010967981070280075,
0.01324950810521841,
0.008765830658376217,
-0.02468869462609291,
-0.03567564859986305,
-0.017379483208060265,
-0.03200405463576317,
0.031860772520303726,
0.0003791831841226667,
-0.020251141861081123,
0.016392910853028297,
-0.00483716418966651,
-0.019331376999616623,
-0.02589869499206543,
-0.045959681272506714,
0.041659895330667496,
0.01597214676439762,
-0.04954703152179718,
0.0028304141014814377,
-0.037022046744823456,
0.00621310668066144,
0.04993307963013649,
0.0022937613539397717,
-0.05051061883568764,
-0.011156617663800716,
0.0010471651330590248,
0.045091480016708374,
0.011115974746644497,
0.04319508373737335,
0.0008665153873153031,
0.006820655893534422,
-0.029907021671533585,
-0.01517483964562416,
-0.003103303024545312,
-0.009333685971796513,
0.03147384524345398,
0.03950028494000435,
-0.01550175528973341,
-0.01439468190073967,
0.011632264591753483,
-0.03359980508685112,
0.0019963306840509176,
0.0576724112033844,
-0.04215153679251671,
0.008150466717779636,
-0.0644754022359848,
-0.029391087591648102,
0.05359285697340965,
-0.0380450114607811,
0.0552506186068058,
-0.03088913857936859,
-0.0013956357724964619,
-0.022156916558742523,
-0.009902600198984146,
-0.053935177624225616,
-0.002077209297567606,
-0.008872611448168755,
-0.05600441247224808,
0.04725654795765877,
0.030003871768712997,
-0.046415288001298904,
0.006795675028115511,
0.015649454668164253,
0.05295698344707489,
-0.00172953843139112,
0.017564823850989342,
-0.0799865871667862,
0.0038060820661485195,
0.009243179112672806,
-0.006076972000300884,
0.018279774114489555,
-0.005536392796784639,
0.028156831860542297,
0.00920645147562027,
-0.020954685285687447,
0.015324370935559273,
-0.0975634828209877,
-0.03427165746688843,
0.013304604217410088,
-0.007627090904861689,
-0.0007287965272553265,
-0.009326901286840439,
0.008083832450211048,
-0.03078487142920494,
-0.0699460357427597,
-0.013943464495241642,
0.035064175724983215,
-0.021004127338528633,
-0.02652929536998272,
-0.0061027961783111095,
0.005467891693115234,
-0.03306037560105324,
-0.03318924084305763,
-0.0048807719722390175,
0.04601611942052841,
-0.005320343188941479,
-0.01751631125807762,
-0.02650093473494053,
-0.025376111268997192,
0.030030278488993645,
0.027081213891506195,
-0.045783136039972305,
-0.042537715286016464,
-0.0015291047748178244,
-0.01557338610291481,
0.059482984244823456,
-0.06821475178003311,
-0.029515961185097694,
-0.02318001538515091,
-0.010066928341984749,
0.00114091404248029,
0.009720714762806892,
-0.012313623912632465,
-0.11306352913379669,
0.019611740484833717,
0.005012719426304102,
0.040043361485004425,
0.005875749047845602,
0.01779153198003769,
0.009648728184401989,
-0.023792386054992676,
-0.05071954056620598,
-0.042533718049526215,
-0.006354869809001684,
-0.01447995100170374,
-0.01756700500845909,
0.09548868983983994,
0.024868329986929893,
-0.018206056207418442,
-0.003983173985034227,
0.08054213225841522,
0.0361105352640152,
0.03463435918092728,
-0.01977705769240856,
-0.04083923250436783,
-0.028939787298440933,
-0.0210792887955904,
0.014831243082880974,
-0.02244909293949604,
0.02696356549859047,
-0.030925007537007332,
-0.04364167898893356,
-0.010980273596942425,
-0.05711519345641136,
-0.01424784678965807,
0.007646494545042515,
0.04449896141886711,
-0.014737808145582676,
0.01681791990995407,
0.016344163566827774,
0.01485745795071125,
-0.03340606018900871,
-0.029753757640719414,
-0.011852170340716839,
0.029287509620189667,
-0.025256402790546417,
0.019278177991509438,
0.02091992273926735,
-0.03444991633296013,
0.023744456470012665,
0.008406387642025948,
0.03872210159897804,
0.025770138949155807,
0.04981936886906624,
0.028364812955260277,
0.04215158522129059,
-0.025257272645831108,
-0.026727326214313507,
0.007571409456431866,
-0.010427327826619148,
0.03872033581137657,
-0.030811568722128868,
-0.03129458427429199,
-0.015689555555582047,
0.012558933347463608,
-0.07267121970653534,
-0.013045706786215305,
0.03430663421750069,
0.05399483069777489,
0.007095372304320335,
-0.0051134550012648106,
-0.05147436633706093,
0.04907967150211334,
0.0019029384711757302,
-0.0012715111952275038,
0.046847909688949585,
-0.01338953711092472,
-0.016112713143229485,
0.03685253486037254,
0.10678663104772568,
0.002561059780418873,
-0.027232106775045395,
0.04037126898765564,
-0.03913796693086624,
0.008914938196539879,
0.020292440429329872,
0.045515723526477814,
-0.020600322633981705,
0.0025181882083415985,
0.014231408014893532,
-0.04487910494208336,
-0.036983974277973175,
0.024297639727592468,
0.026838211342692375,
-0.05419793725013733,
-0.033340685069561005,
0.04793424531817436,
0.025672541931271553,
0.04638916626572609,
0.010499304160475731,
0.02627936378121376,
0.05271885544061661,
0.03637748956680298,
0.027157962322235107,
0.04127223417162895,
0.011410284787416458,
-0.0799981951713562,
-0.052700888365507126,
-0.004767417907714844,
-0.02399800345301628,
-0.0777272954583168,
-0.011530286632478237,
-0.012115486897528172,
0.012223663739860058,
0.00610548397526145,
0.05434741824865341,
0.02804640308022499,
-0.025098541751503944,
-0.0051156082190573215,
-0.04631631076335907,
0.024406811222434044,
-0.012545168399810791,
-0.04825372248888016,
0.01814144104719162,
0.04025198146700859,
-0.013061310164630413,
-0.02580948919057846,
-0.00457035144791007,
0.11596175283193588,
-0.04401325806975365,
-0.029367903247475624,
0.010136309079825878,
-0.04526549205183983,
-0.03172551840543747,
-0.013270586729049683,
0.015186513774096966,
0.006721369456499815,
-0.009279645048081875,
-0.02306154929101467,
-0.000575734069570899,
-0.025624142959713936,
0.014171890914440155,
0.056232232600450516,
0.02703225053846836,
0.06836384534835815,
0.01728699915111065,
0.05792868137359619,
0.09357251971960068,
-0.0338553823530674,
-0.035613417625427246,
0.07393339276313782,
0.02317325584590435,
0.006742644589394331,
-0.016922911629080772,
0.008083515800535679,
-0.06301992386579514,
0.0708996132016182,
-0.0033209447283297777,
-0.0019762669689953327,
0.03251449391245842,
0.08331184834241867,
0.005384358577430248,
0.04998990148305893,
-0.0220135860145092,
0.026611579582095146,
-0.0027797874063253403,
0.013459118083119392,
0.07576386630535126,
-0.005611927714198828,
-0.0013454837026074529,
-0.02241671085357666,
-0.007746564224362373,
-0.006765176076442003,
-0.008521625772118568,
0.019710155203938484,
0.032263725996017456,
-0.01872960664331913,
0.04065902531147003,
-0.04417030140757561,
-0.05633857101202011,
-0.02450457587838173,
-0.09061580151319504,
-0.036693453788757324,
-0.09610521793365479,
0.016698280349373817,
-0.029280053451657295,
-0.050320178270339966,
-0.0046504647471010685,
-0.06475066393613815,
0.044724855571985245,
-0.016221066936850548,
-0.006130401510745287,
-0.06324458122253418,
-0.030897246673703194,
0.014241854660212994,
0.0010949145071208477,
-0.004696482792496681,
0.058111805468797684,
0.02866741456091404,
-0.03334639221429825,
0.031151058152318,
0.07029587030410767,
0.0035865933168679476,
0.0591118149459362,
-0.004217708948999643,
0.014864909462630749,
0.03865637257695198,
0.015291424468159676,
-0.02463427558541298,
0.044188160449266434,
0.057822711765766144,
-0.0022603238467127085,
0.04913033917546272,
-0.029937414452433586,
0.0229331161826849
] |
<p>I live in Ireland where serving food on hot plates is considered “good cooking practice” to ensure the food remains warm – I come from France where I have rarely seen it done.</p>
<p>I am wondering if this practice really is useful. I assume it depends on the difference of temperature between the food and the plate, as heat won’t transfer as fast to the plate. But wouldn’t the extra time the food remains above an “acceptable” temperature threshold just be marginal?</p> | g4635 | [
0.0710025504231453,
0.05271001160144806,
0.006096933037042618,
-0.04166201129555702,
0.009509500116109848,
-0.0037269520107656717,
-0.09771756082773209,
0.04034918174147606,
-0.034498877823352814,
0.025645693764090538,
0.001108725555241108,
0.012286817654967308,
-0.0181319247931242,
0.06941960752010345,
0.042088162153959274,
-0.0068049319088459015,
0.026635102927684784,
-0.019105713814496994,
-0.018257932737469673,
0.048579223453998566,
0.0019732739310711622,
0.01937280222773552,
-0.02552332729101181,
-0.017762435600161552,
-0.1275697648525238,
-0.048565611243247986,
-0.006383166648447514,
0.005732960533350706,
-0.029138728976249695,
-0.0358230285346508,
-0.046992965042591095,
-0.018982265144586563,
0.010298340581357479,
-0.008440336212515831,
-0.017565889284014702,
0.01195192988961935,
0.023588016629219055,
-0.005445340182632208,
0.001670901314355433,
-0.03537945821881294,
0.0123698515817523,
0.03142975643277168,
0.014083067886531353,
0.040117211639881134,
0.07224783301353455,
0.03379756584763527,
-0.05083514377474785,
0.0221696849912405,
-0.005583824124187231,
0.01792294904589653,
0.03290055692195892,
-0.03752719238400459,
-0.04134734347462654,
-0.009696613065898418,
-0.02982504293322563,
-0.022450877353549004,
0.008282237686216831,
0.06497421860694885,
0.052935801446437836,
0.01789093390107155,
0.049781229346990585,
-0.0012370283948257565,
-0.01828615553677082,
-0.04970991984009743,
-0.0017010757001116872,
0.0821729451417923,
-0.04282040148973465,
0.06277097761631012,
0.05597463995218277,
0.011694744229316711,
-0.021413179114460945,
-0.01725982129573822,
-0.03788386657834053,
-0.06227697432041168,
-0.046461544930934906,
-0.0032611622009426355,
-0.02360118180513382,
-0.014201086014509201,
0.004203747492283583,
0.060186490416526794,
-0.014395765028893948,
-0.021693438291549683,
-0.03376569226384163,
0.03819776698946953,
-0.03705911710858345,
-0.005068358965218067,
0.05347716435790062,
-0.015999410301446915,
0.008314333856105804,
0.06209982559084892,
0.0285724475979805,
-0.030959606170654297,
0.0603175014257431,
0.06512413918972015,
-0.010101856663823128,
0.04053955897688866,
-0.006551526021212339,
0.0302253607660532,
-0.033649884164333344,
0.02584480121731758,
0.03593749925494194,
-0.016989044845104218,
0.03415839746594429,
0.02201213501393795,
-0.03814977779984474,
0.02019350230693817,
0.06694474071264267,
0.032631468027830124,
0.03045208938419819,
0.0017128399340435863,
-0.04224777594208717,
-0.016699034720659256,
-0.0787799060344696,
-0.047888658940792084,
-0.03967811167240143,
0.0064574554562568665,
0.052768584340810776,
0.04535742849111557,
-0.006367306690663099,
0.03718966990709305,
0.04194869473576546,
0.02347339130938053,
0.0343046709895134,
0.03586284816265106,
0.012212082743644714,
-0.023040058091282845,
-0.04455620050430298,
-0.02048381045460701,
0.0030694445595145226,
0.029196150600910187,
-0.0581473708152771,
0.021913206204771996,
-0.06144465506076813,
-0.003441652748733759,
-0.005144177470356226,
0.013611294329166412,
0.046834200620651245,
-0.019997764378786087,
-0.024917595088481903,
0.018653754144906998,
0.06339386850595474,
0.019411901012063026,
-0.03540557622909546,
-0.07332780957221985,
0.015844838693737984,
0.0581485852599144,
-0.023316770792007446,
-0.03392493352293968,
0.0268104150891304,
0.03554978221654892,
-0.00041773999691940844,
0.078779436647892,
0.045275814831256866,
0.042691539973020554,
-0.029876548796892166,
-0.019273152574896812,
-0.035864539444446564,
-0.04700521379709244,
0.08572670072317123,
0.021594278514385223,
0.027777032926678658,
-0.028026646003127098,
0.001690976321697235,
-0.06318426132202148,
-0.06034373119473457,
-0.0262216217815876,
-0.0034263653215020895,
-0.020866503939032555,
-0.04395316541194916,
0.03239265829324722,
-0.037335556000471115,
0.037103552371263504,
0.0007332240929827094,
-0.03617072105407715,
-0.009340445511043072,
-0.0675286054611206,
0.06179078295826912,
0.02822130359709263,
0.010171777568757534,
-0.031749848276376724,
-0.07990104705095291,
0.024263516068458557,
-0.01992521435022354,
-0.04908720403909683,
0.015203199349343777,
0.00566176837310195,
0.021538833156228065,
-0.0451003797352314,
-0.033754538744688034,
-0.017070772126317024,
-0.0254225917160511,
-0.04446421563625336,
0.0688006579875946,
0.01560455746948719,
-0.0038352501578629017,
-0.0009519888553768396,
-0.01664828695356846,
0.01991686038672924,
-0.00559296365827322,
0.015433859080076218,
-0.00952049158513546,
-0.02029554545879364,
0.0119762709364295,
0.018620966002345085,
-0.048529431223869324,
0.05213293805718422,
0.007562416139990091,
-0.01985539123415947,
-0.02978278137743473,
-0.0427045077085495,
-0.0438803993165493,
0.05481801927089691,
0.008629675023257732,
0.005665096454322338,
0.008198722265660763,
0.06254514306783676,
-0.025050796568393707,
0.06436976790428162,
0.0011048944434151053,
0.06041356548666954,
0.0038835133891552687,
-0.005271547939628363,
0.017204048112034798,
0.023471612483263016,
-0.0028339254204183817,
-0.011026356369256973,
-0.048058025538921356,
-0.020985320210456848,
-0.030597537755966187,
0.05961725115776062,
-0.03735631704330444,
-0.027875900268554688,
0.00335984886623919,
-0.05673958361148834,
-0.01741495169699192,
0.004417372401803732,
0.04455163702368736,
-0.0009796088561415672,
-0.01171911507844925,
0.047960687428712845,
0.0038528996519744396,
-0.06184462830424309,
-0.01580742746591568,
0.020603889599442482,
-0.010362107306718826,
-0.00004552464815787971,
-0.00258781760931015,
0.004448790103197098,
0.00636752974241972,
-0.06483353674411774,
0.02138557843863964,
0.021497508510947227,
0.031430989503860474,
0.0031610955484211445,
-0.020139198750257492,
0.012060515582561493,
-0.003703458933159709,
0.035105157643556595,
-0.026316877454519272,
0.03674944117665291,
0.04618343710899353,
0.006889659445732832,
0.005616455804556608,
-0.015191393904387951,
0.011346282437443733,
-0.0008521897834725678,
-0.07065950334072113,
0.040664978325366974,
-0.016026975587010384,
0.04539031535387039,
0.03724813461303711,
-0.012668129056692123,
-0.021641062572598457,
0.02111194282770157,
-0.007058498449623585,
-0.02297201193869114,
-0.015297477133572102,
-0.012785276398062706,
0.05772286280989647,
-0.022339139133691788,
0.03374101221561432,
-0.1091596707701683,
-0.02994099073112011,
0.003614360699430108,
-0.03245311975479126,
0.014902765862643719,
-0.04553791880607605,
0.02416243776679039,
-0.07256408035755157,
-0.029299668967723846,
-0.003163442946970463,
-0.008817700669169426,
0.05537663772702217,
-0.005897333845496178,
0.014317885972559452,
0.03226203843951225,
0.026678791269659996,
-0.07056963443756104,
-0.020991336554288864,
-0.040415208786726,
0.021595269441604614,
-0.010624569840729237,
-0.06159602850675583,
0.03122076578438282,
0.03696887567639351,
0.044913399964571,
-0.05560610443353653,
0.013742508366703987,
-0.05085816606879234,
-0.049196887761354446,
0.05907703563570976,
0.005344875156879425,
-0.054645515978336334,
0.03675733134150505,
-0.01341814175248146,
-0.009899036958813667,
-0.014128211885690689,
0.025791430845856667,
0.04551352560520172,
0.018907086923718452,
0.009195780381560326,
0.043705880641937256,
-0.005672417115420103,
0.027148820459842682,
0.030209455639123917,
0.10740583389997482,
0.03805801644921303,
-0.0042147100903093815,
-0.014745008200407028,
0.013845040462911129,
0.01413914654403925,
0.05126069486141205,
-0.03904910758137703,
-0.034729063510894775,
-0.002347387373447418,
-0.017854753881692886,
0.05686398223042488,
-0.013675093650817871,
-0.029003262519836426,
0.06807675957679749,
0.020018190145492554,
-0.010655440390110016,
0.041710175573825836,
0.013551130890846252,
0.062087442725896835,
-0.01004506554454565,
0.05593634024262428,
-0.024638405069708824,
-0.024805398657917976,
0.028364285826683044,
0.012408124282956123,
0.006727900356054306,
-0.008134412579238415,
0.004320203792303801,
-0.04213432967662811,
-0.03783578798174858,
-0.028576795011758804,
-0.023299485445022583,
-0.02073187381029129,
0.03863656893372536,
-0.009430387988686562,
0.03945821896195412,
-0.0029264986515045166,
-0.0008907088777050376,
0.013213232159614563,
0.05603664740920067,
-0.03648240119218826,
0.03822234645485878,
0.024784056469798088,
0.02020961232483387,
-0.021147621795535088,
-0.02679184079170227,
-0.000952842878177762,
0.02681603655219078,
0.021119916811585426,
0.03210075944662094,
0.015130328945815563,
0.0011868790024891496,
0.016810135915875435,
0.028102535754442215,
-0.05515265464782715,
-0.019312329590320587,
-0.001854275236837566,
-0.0030777358915656805,
0.033536653965711594,
0.007586360443383455,
0.025773487985134125,
0.0011612751986831427,
-0.0002348232374060899,
-0.03747164085507393,
0.039952345192432404,
-0.04108906537294388,
0.015128087252378464,
0.007827314548194408,
0.06784064322710037,
0.009228757582604885,
-0.028803469613194466,
-0.016675733029842377,
0.06974774599075317,
0.012751158326864243,
-0.005381077527999878,
0.005040841642767191,
0.03885107859969139,
0.024263015016913414,
-0.07471981644630432,
-0.05813112109899521,
0.035802438855171204,
-0.04142792522907257,
-0.050023965537548065,
-0.07183429598808289,
0.006049136631190777,
-0.0373457707464695,
0.029034342616796494,
0.015589232556521893,
-0.012352689169347286,
0.008294753730297089,
-0.00990215316414833,
-0.022006312385201454,
-0.034903403371572495,
-0.022173162549734116,
-0.03947756439447403,
0.022548899054527283,
-0.0053022475913167,
-0.019607191905379295,
-0.0023585285525768995,
0.06753204762935638,
0.012129359878599644,
-0.0042073349468410015,
-0.022697988897562027,
-0.003716591978445649,
0.037497565150260925,
0.0425986684858799,
-0.021196560934185982,
-0.03491191193461418,
-0.005937470588833094,
-0.010106549598276615,
-0.051526352763175964,
0.0007995475898496807,
-0.07444199919700623,
0.009046757593750954,
-0.019934816285967827,
-0.027311041951179504,
-0.029573600739240646,
0.030441636219620705,
-0.0452781617641449,
-0.0012130922405049205,
0.023673364892601967,
0.004487588070333004,
0.036394257098436356,
-0.1156219094991684,
0.00717491889372468,
0.044854648411273956,
0.003453656565397978,
0.035037584602832794,
-0.007802190724760294,
-0.0469483807682991,
0.003203009720891714,
-0.002302102278918028,
-0.05638638511300087,
-0.0067059979774057865,
-0.014518377371132374,
-0.006711131427437067,
-0.011489562690258026,
-0.012040521949529648,
-0.010429657995700836,
-0.01972973719239235,
-0.018567223101854324,
-0.0430663526058197,
-0.02520028129220009,
0.023184441030025482,
0.033405669033527374,
0.055482860654592514,
0.02503972314298153,
0.0003286947903688997,
0.008349264971911907,
0.023908983916044235,
-0.04245937615633011,
0.040433019399642944,
0.04460568726062775,
-0.017763258889317513,
-0.013625933788716793,
0.0036183767952024937,
0.0758102610707283,
0.02535353973507881,
0.006723582744598389,
-0.05779637023806572,
-0.0024034830275923014,
-0.037864118814468384,
0.05862986668944359,
0.00936210434883833,
0.030349327251315117,
0.029809072613716125,
0.00703994557261467,
0.034491412341594696,
0.009061012417078018,
-0.03970072790980339,
0.0043720826506614685,
0.013736569322645664,
-0.019082792103290558,
-0.018422115594148636,
-0.006034424528479576,
0.027707604691386223,
0.038990654051303864,
-0.00947376899421215,
-0.017627382650971413,
0.020676178857684135,
0.06946496665477753,
-0.019660748541355133,
0.013184532523155212,
0.07152101397514343,
0.06001776456832886,
-0.009508016519248486,
-0.03274448588490486,
-0.03657890483736992,
0.03332754969596863,
-0.03644178435206413,
0.017038818448781967,
-0.059282999485731125,
0.01735857129096985,
-0.04188939183950424,
0.0009391966159455478,
0.04547027498483658,
-0.009900102391839027,
0.008933805860579014,
0.02059233747422695,
-0.049221012741327286,
-0.03872447833418846,
0.019387828186154366,
-0.03488048166036606,
0.015026533044874668,
0.03446592018008232,
0.012538311071693897,
-0.031183606013655663,
0.03283288702368736,
-0.06274011731147766,
-0.014151515439152718,
-0.05353313311934471,
-0.0050902231596410275,
0.03926847130060196,
0.025148732587695122,
-0.06502410024404526,
-0.02848157472908497,
0.0759061649441719,
0.05955228954553604,
0.02446887083351612,
-0.03388179838657379,
-0.0391603447496891,
0.003140606451779604,
0.04304439574480057,
-0.015458679758012295,
-0.009370340965688229,
0.03836372122168541,
-0.023679351434111595,
-0.023278947919607162,
0.02584257163107395,
0.025220166891813278,
0.08304816484451294,
0.001154945115558803,
0.06359147280454636,
-0.016631226986646652,
0.011436332948505878,
-0.0269112940877676,
-0.004702111706137657,
0.014209880493581295,
-0.00504272012040019,
-0.038166433572769165,
-0.04201018437743187,
-0.03460158035159111,
0.0003341037954669446,
0.017594119533896446,
0.031039254739880562,
-0.025894325226545334,
0.012281152419745922,
-0.01067123468965292,
-0.057781439274549484,
0.021357376128435135,
-0.02910006232559681,
0.002207906451076269,
-0.013835243880748749,
-0.06984744966030121,
-0.03458913415670395,
0.018239296972751617,
-0.0643632709980011,
0.030918894335627556,
0.00242544524371624,
0.05375625193119049,
-0.0005453784833662212,
0.016071820631623268,
-0.022774524986743927,
-0.03285958990454674,
0.01433548890054226,
-0.030188467353582382,
-0.001867296639829874,
0.0034433347173035145,
0.07676995545625687,
-0.04201173409819603,
0.04004882276058197,
0.07406773418188095,
-0.0343850813806057,
0.04465175047516823,
0.02902238257229328,
-0.006237576249986887,
0.0008535436354577541,
-0.07527809590101242,
-0.019120432436466217,
0.03233074024319649,
0.049216825515031815,
0.020846255123615265,
0.028250237926840782,
-0.006742892786860466,
0.02845592424273491,
0.005885438993573189,
0.04748040437698364,
-0.02052467130124569,
-0.03555445745587349,
-0.04437519609928131,
-0.021698111668229103,
-0.017666231840848923,
-0.024766694754362106,
0.03235494717955589,
-0.018314873799681664,
-0.027665263041853905,
-0.05344216898083687,
-0.022789470851421356,
0.016094258055090904,
-0.03761226311326027,
-0.04223921149969101,
0.03240806981921196,
-0.017342912033200264,
-0.09090962260961533,
0.004968492314219475,
-0.06551291793584824,
-0.038167182356119156,
0.028909945860505104,
0.010233770124614239,
-0.006090252660214901,
-0.038265250623226166,
0.017639759927988052,
-0.04691721126437187,
0.016024263575673103,
-0.10119608789682388,
-0.006213259883224964,
0.03053225576877594,
0.006338386330753565,
-0.023366596549749374,
0.002105630934238434,
0.02385745383799076,
0.0549350343644619,
-0.018172675743699074,
0.01765303686261177,
0.002739184768870473,
0.02198687195777893,
-0.10831718146800995,
-0.010272313840687275,
0.05031387135386467,
-0.025061896070837975,
-0.029926087707281113,
0.010204396210610867,
-0.03131444752216339,
0.008998071774840355,
0.04724103957414627,
0.0021023063454777002,
-0.034098558127880096,
-0.01516465563327074,
0.0362943671643734,
0.0078128008171916,
-0.03871823102235794,
-0.0304881539195776,
-0.05366825312376022,
-0.010992936789989471,
0.006817142944782972,
0.022675197571516037,
0.05164734646677971,
-0.062374286353588104,
0.1194133535027504,
0.030709633603692055,
-0.007404253352433443,
-0.01537253987044096,
-0.021156007423996925,
0.03706616908311844,
-0.012012144550681114,
-0.06806281208992004,
0.003875123802572489,
0.006745426449924707,
0.012642654590308666,
-0.0011369159910827875,
0.010318460874259472,
-0.036360375583171844,
0.03344586864113808,
-0.03453580662608147,
-0.0015627524117007852,
0.03895014151930809,
0.0030902125872671604,
0.0033635294530540705,
0.02547525428235531,
0.021383807063102722,
0.05797640234231949,
-0.026692841202020645,
0.05185437202453613,
0.029809895902872086,
-0.02962004579603672,
-0.021140363067388535,
0.07201629132032394,
-0.025462398305535316,
0.07796389609575272,
0.044594813138246536,
-0.022226152941584587,
-0.029407991096377373,
-0.02606358379125595,
-0.012090262956917286,
0.02847285196185112,
0.03365115076303482,
0.036163922399282455,
0.00956293661147356,
0.012412501499056816,
-0.018468337133526802,
-0.07117617130279541,
-0.06952565163373947,
-0.021992381662130356,
0.01872330531477928,
0.018561141565442085,
-0.03755645081400871,
0.02806035429239273,
0.0015360175166279078,
0.03317246958613396,
0.027734188362956047,
-0.013587766326963902,
-0.0870988667011261,
0.07649675756692886,
-0.020982377231121063,
0.028498483821749687,
0.023090876638889313,
-0.005500011146068573,
0.03855085372924805,
-0.01962735876441002,
0.04497227072715759,
0.03115151822566986,
0.005386588629335165,
-0.02389245480298996,
0.03488243743777275,
0.04690052196383476,
0.06864461302757263,
0.018354393541812897,
-0.012266678735613823,
-0.02005910873413086,
0.0032360083423554897,
0.04096049442887306,
-0.028752200305461884,
-0.024873152375221252,
0.03729984536767006,
-0.09488372504711151,
-0.03631697967648506,
-0.08679544925689697,
0.005671029910445213,
-0.03824171423912048,
-0.02105484902858734,
-0.01590995118021965,
-0.008735882118344307,
0.01779642328619957,
0.027207134291529655,
-0.006875614635646343,
0.0036245870869606733,
-0.0015163063071668148,
-0.04426060616970062,
-0.04425433278083801,
-0.038606226444244385,
0.04176703095436096,
-0.05750586837530136
] |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/29805/richtmyer-meshkov-instability-in-mhd">Richtmyer Meshkov instability in MHD</a> </p>
</blockquote>
<p>The Richtmyer Meshkov instability in Hydrodynamics:-
1) When shock wave interacts with the contact discontinuity, it accumulates the vorticity on the CD
2) This causes the density discontinuity to curl up, and form series of vortices</p>
<p>In application of the longitudinal magnetic field with conducting fluid as the working medium,</p>
<p>1) The RM instability is suppressed
2) Series of new shocks is formed and it carries away the vorticity</p>
<p>My question is ,
what exactly happens in Magneto-Hydrodynamic system?
Why the RM instability is supressed?
How can one get the physical intuition of what is happening at the interface?</p> | g462 | [
0.02041032910346985,
0.034923404455184937,
-0.02945690043270588,
0.015794599428772926,
0.06921438127756119,
0.03778434917330742,
0.03670148551464081,
0.05146399512887001,
-0.022646889090538025,
-0.00836215540766716,
-0.05426507443189621,
0.020926736295223236,
-0.011450282298028469,
0.05148841813206673,
-0.009684314019978046,
0.03494114801287651,
-0.01932445913553238,
0.037033163011074066,
0.013090986758470535,
0.01979430951178074,
-0.0871894434094429,
0.027736827731132507,
0.04505142569541931,
-0.019501440227031708,
0.02761164680123329,
0.02870487980544567,
0.016055865213274956,
-0.0001015671732602641,
0.009003084152936935,
0.009597182273864746,
-0.01261371374130249,
0.027688341215252876,
0.06057741865515709,
-0.03977590799331665,
-0.0490364246070385,
-0.04312241077423096,
0.006013182457536459,
-0.01561429537832737,
0.025375952944159508,
-0.00043955136789008975,
0.045798156410455704,
-0.02649518847465515,
-0.04986555874347687,
-0.05856143683195114,
-0.048656120896339417,
0.03342164307832718,
-0.08081520348787308,
0.01922052539885044,
-0.06544392555952072,
0.031067855656147003,
0.04413595795631409,
-0.02088705264031887,
0.031215626746416092,
-0.007913179695606232,
0.007709689904004335,
0.012792843393981457,
0.013873415067791939,
-0.03473313897848129,
0.020085982978343964,
-0.055217888206243515,
-0.008745566010475159,
0.024367760866880417,
-0.00871527474373579,
0.004476925823837519,
0.06571075320243835,
-0.01356799341738224,
-0.008478716015815735,
0.00587235763669014,
0.03247244656085968,
0.04654131457209587,
-0.0030654133297502995,
-0.06262832880020142,
-0.033710651099681854,
-0.01957692764699459,
-0.009637277573347092,
0.023335186764597893,
-0.0009540000464767218,
0.030918359756469727,
-0.0022182173561304808,
-0.033919524401426315,
0.0013551105512306094,
0.023837130516767502,
-0.004663949366658926,
-0.03674719110131264,
-0.013641709461808205,
0.02656431496143341,
0.046519435942173004,
0.005294740665704012,
-0.003373566083610058,
-0.02575293369591236,
-0.02235940657556057,
-0.02581898123025894,
0.0046918559819459915,
0.017043963074684143,
0.012850492261350155,
0.018661243841052055,
0.00306260259822011,
0.028359368443489075,
0.010522937402129173,
0.008854914456605911,
-0.050764281302690506,
-0.05941338464617729,
-0.04973267763853073,
0.001489226589910686,
-0.011450737714767456,
0.0391806960105896,
-0.0029668649658560753,
0.08075585961341858,
0.06345514208078384,
-0.033048179000616074,
-0.015700265765190125,
-0.024090930819511414,
-0.010553102008998394,
0.023741576820611954,
0.05485466122627258,
-0.04657928645610809,
-0.007528919260948896,
0.05336104333400726,
-0.03001740388572216,
0.018302321434020996,
-0.007200800348073244,
-0.031926486641168594,
-0.050160255283117294,
0.04924295097589493,
0.03437216952443123,
-0.02130237966775894,
-0.005225477274507284,
0.00038391692214645445,
0.02986038476228714,
0.054377537220716476,
0.029055582359433174,
-0.00424333056434989,
0.015356303192675114,
-0.044128935784101486,
0.052200060337781906,
-0.0009522970649413764,
0.015480073168873787,
0.003321331227198243,
0.003673312021419406,
-0.029933927580714226,
0.05702788010239601,
-0.05272098630666733,
0.031159762293100357,
-0.07863400131464005,
0.03288866952061653,
-0.02256764844059944,
0.05971667915582657,
-0.007642699871212244,
0.0024031095672398806,
-0.0054345205426216125,
0.004792568273842335,
0.060504283756017685,
-0.02274285815656185,
-0.07783818989992142,
0.011576858349144459,
0.04297677055001259,
0.024371687322854996,
0.008953859098255634,
-0.0338541716337204,
0.014290421269834042,
0.021397413685917854,
-0.05070127174258232,
-0.025129131972789764,
0.05201021209359169,
-0.02302277646958828,
0.05044274404644966,
0.060998376458883286,
-0.0037627576384693384,
0.012518179602921009,
-0.02225370705127716,
-0.004302855581045151,
0.04005780816078186,
-0.021507445722818375,
0.06603049486875534,
0.002885027090087533,
0.02606901340186596,
0.032206177711486816,
-0.011730586178600788,
0.037386149168014526,
-0.02558683231472969,
-0.03897513076663017,
0.0032090763561427593,
0.06338343024253845,
-0.08969522267580032,
-0.0007196781225502491,
0.036194298416376114,
-0.012297969311475754,
0.030007006600499153,
-0.04261094331741333,
0.00872260332107544,
-0.009277669712901115,
-0.011551229283213615,
-0.07367482781410217,
0.06983217597007751,
0.010980045422911644,
-0.011617320589721203,
-0.00337983388453722,
-0.017280928790569305,
-0.047977227717638016,
-0.0048669069074094296,
-0.04254385083913803,
0.05748933553695679,
0.05937926098704338,
-0.01757184974849224,
-0.029298169538378716,
0.03299899771809578,
-0.005157062783837318,
-0.002130168490111828,
0.013591760769486427,
0.00041634030640125275,
0.08225314319133759,
-0.025013746693730354,
0.00518451863899827,
-0.0013974595349282026,
-0.014272202737629414,
0.02139466442167759,
0.012242959812283516,
0.007418904919177294,
-0.022592375054955482,
-0.004699775483459234,
0.00046438840217888355,
-0.034600984305143356,
-0.0244368314743042,
0.060283955186605453,
-0.01971735991537571,
-0.01775665581226349,
-0.00037972640711814165,
-0.011433862149715424,
0.015805361792445183,
-0.05081593617796898,
0.002377340802922845,
0.014914515428245068,
-0.003676197025924921,
-0.012854916974902153,
-0.009707887656986713,
0.07190727442502975,
0.051538463681936264,
-0.0019082112703472376,
0.00145331013482064,
0.04135189577937126,
-0.031963102519512177,
-0.0024161997716873884,
-0.00566359655931592,
-0.0356430746614933,
0.03253694251179695,
-0.031306181102991104,
0.06909425556659698,
0.00001954988510988187,
0.058335304260253906,
0.013894757255911827,
0.054488155990839005,
-0.06932811439037323,
0.056249141693115234,
0.011283299885690212,
0.0036425618454813957,
-0.03884156420826912,
-0.05486553907394409,
0.042201317846775055,
0.0011616869596764445,
-0.023052621632814407,
-0.0007463518995791674,
0.08945710957050323,
-0.010348796844482422,
0.019092606380581856,
-0.09223002940416336,
0.013579398393630981,
-0.025481173768639565,
0.012296212837100029,
-0.03379382938146591,
0.013441300950944424,
-0.042643480002880096,
0.043254364281892776,
-0.036129485815763474,
0.059502143412828445,
0.02200428768992424,
0.0033434864599257708,
-0.016635555773973465,
-0.005194555036723614,
0.0208775345236063,
-0.005930607672780752,
-0.0009910668013617396,
0.00714582996442914,
0.027649521827697754,
-0.054486848413944244,
-0.03081185184419155,
-0.0069411746226251125,
-0.04055539518594742,
-0.00029949756572023034,
-0.04504864290356636,
-0.028057945892214775,
-0.08594583719968796,
-0.06912973523139954,
-0.004303419031202793,
-0.033858250826597214,
-0.017368290573358536,
-0.026126066222786903,
0.01566949672996998,
0.019996091723442078,
0.0009606701205484569,
0.02376444637775421,
0.036553483456373215,
-0.002702325349673629,
-0.018177540972828865,
-0.06372472643852234,
-0.025254668667912483,
-0.006937104277312756,
-0.010245869867503643,
-0.016889741644263268,
-0.04875469207763672,
0.00634142616763711,
0.014940602704882622,
0.05901302024722099,
-0.03243253007531166,
0.03381892666220665,
-0.07656388729810715,
0.09482321888208389,
0.05054370313882828,
-0.0157485194504261,
0.03680458292365074,
0.04301164299249649,
-0.04487547650933266,
-0.04437047615647316,
-0.01767779514193535,
-0.03187226876616478,
-0.00562896765768528,
-0.0054810428991913795,
0.010944760404527187,
0.0015456350520253181,
-0.06661364436149597,
0.002416380448266864,
-0.035147421061992645,
0.03594407066702843,
0.010720617137849331,
-0.03734192997217178,
-0.0560738667845726,
0.01739511825144291,
-0.001249955384992063,
0.04934977740049362,
0.021910803392529488,
-0.0011311275884509087,
0.03413150832056999,
-0.00038858255720697343,
-0.013633311726152897,
-0.03334517031908035,
-0.032051898539066315,
0.05233923718333244,
0.021297374740242958,
0.049332134425640106,
0.010833965614438057,
-0.00849047489464283,
0.05872877314686775,
0.034373000264167786,
0.0673963725566864,
-0.06483028084039688,
-0.07127394527196884,
0.014374976977705956,
-0.03363858163356781,
-0.05776533856987953,
0.023551907390356064,
-0.013530278578400612,
-0.022133540362119675,
-0.01880974881350994,
-0.030382348224520683,
0.008397545665502548,
-0.003984791226685047,
-0.008212730288505554,
-0.0006647132686339319,
0.052388910204172134,
-0.07512781769037247,
-0.1227986216545105,
-0.029718264937400818,
-0.015989093109965324,
-0.06889369338750839,
0.02481791563332081,
0.027236122637987137,
-0.02625153958797455,
-0.030548423528671265,
0.044634804129600525,
0.0072989193722605705,
0.0238078311085701,
0.06590693444013596,
0.004589301533997059,
-0.04535403847694397,
-0.02348468266427517,
-0.009854510426521301,
0.04525823891162872,
-0.015073303133249283,
-0.008093887008726597,
-0.007704379968345165,
-0.03398263081908226,
0.02274477109313011,
0.007271823473274708,
0.05547887831926346,
0.03656703978776932,
0.04698069021105766,
-0.006307050120085478,
-0.0673997551202774,
0.026178933680057526,
0.012891230173408985,
-0.0005258079036138952,
0.017409702762961388,
-0.05331262946128845,
-0.07686068117618561,
-0.07843087613582611,
-0.015263693407177925,
0.024721108376979828,
-0.012588501907885075,
-0.0054555414244532585,
0.04250910505652428,
-0.03954128921031952,
0.07041647285223007,
-0.030217790976166725,
-0.007664076518267393,
-0.04756832495331764,
0.029037754982709885,
-0.04406309500336647,
0.039340224117040634,
0.033227890729904175,
-0.02131599746644497,
-0.04141956567764282,
-0.021966295316815376,
-0.04202141612768173,
-0.0667242556810379,
0.06777574867010117,
-0.00032321730395779014,
-0.01680465042591095,
0.026584075763821602,
0.0024289139546453953,
-0.015749545767903328,
-0.009328274987637997,
0.017418939620256424,
0.01746634766459465,
0.019907444715499878,
0.03941575810313225,
-0.04785380885004997,
-0.028461487963795662,
0.005384205374866724,
-0.005618097726255655,
-0.022895995527505875,
0.05928638577461243,
-0.007103347685188055,
-0.017307495698332787,
0.002202690578997135,
-0.030139926820993423,
0.01698409579694271,
0.02022155560553074,
0.008336374536156654,
-0.007291403133422136,
-0.0029928546864539385,
-0.018966468051075935,
-0.08499236404895782,
-0.028609350323677063,
0.012772627174854279,
0.0008927866001613438,
0.01893148198723793,
-0.003963380586355925,
-0.03199939429759979,
0.015089273452758789,
-0.020437149330973625,
-0.0420149601995945,
-0.05420731380581856,
0.023440951481461525,
-0.021695392206311226,
0.04373921453952789,
0.04469861090183258,
-0.040577713400125504,
0.015549800358712673,
-0.06299880892038345,
-0.03032078593969345,
0.014671962708234787,
0.0531478151679039,
0.01207386888563633,
0.056142352521419525,
-0.01739298366010189,
0.0926632508635521,
0.0020099622197449207,
-0.02051469124853611,
-0.047136250883340836,
-0.008394129574298859,
-0.057542309165000916,
0.07372113317251205,
0.053674619644880295,
0.03462142124772072,
0.06748765707015991,
-0.03095870092511177,
0.014828475192189217,
0.0237407386302948,
0.06089475005865097,
-0.0004655788652598858,
0.03101564198732376,
0.05021260678768158,
0.034143105149269104,
-0.01613636314868927,
0.021659014746546745,
-0.007321254815906286,
-0.01752494089305401,
0.01998462714254856,
-0.017365774139761925,
-0.10742083191871643,
-0.0232627522200346,
0.02654668129980564,
-0.07808330655097961,
-0.01855621114373207,
0.055655337870121,
-0.024167966097593307,
0.061049092561006546,
0.049280695617198944,
-0.05887524038553238,
0.0035560494288802147,
0.02021224983036518,
-0.02439233288168907,
-0.02127070724964142,
0.030940387398004532,
0.0338500514626503,
0.009392470121383667,
0.02916913665831089,
-0.00474950997158885,
0.05894917994737625,
-0.033968355506658554,
-0.010584652423858643,
0.00806218758225441,
-0.004761036951094866,
0.006492835935205221,
-0.003037999849766493,
-0.03948327153921127,
0.029149755835533142,
-0.051815904676914215,
0.01700066402554512,
0.008114942349493504,
0.03441377356648445,
0.0034707693848758936,
-0.0025342314038425684,
0.0303194597363472,
-0.007286176551133394,
-0.03426526114344597,
-0.038455214351415634,
0.1168895959854126,
0.015412009321153164,
0.011706529185175896,
0.04678803309798241,
0.04416018724441528,
-0.024596793577075005,
-0.03526107594370842,
0.041206590831279755,
-0.04055849090218544,
0.005803701467812061,
-0.02197163552045822,
0.008516873233020306,
0.05817238613963127,
-0.045670539140701294,
-0.03127465397119522,
-0.02098889648914337,
0.028148822486400604,
0.03760356456041336,
-0.016420910134911537,
-0.015005826950073242,
0.015218155458569527,
0.021225759759545326,
-0.016768410801887512,
-0.021821649745106697,
0.028831692412495613,
0.0249712485820055,
-0.057371340692043304,
0.00907253846526146,
-0.037509601563215256,
0.012822801247239113,
-0.05696859583258629,
0.0003609066770877689,
0.046126071363687515,
-0.012792483903467655,
-0.02463875152170658,
-0.0006848860066384077,
0.04861189424991608,
-0.03657490387558937,
0.06329762935638428,
0.06915459781885147,
-0.016643524169921875,
0.021980149671435356,
-0.024635761976242065,
0.021719999611377716,
-0.014905968680977821,
0.022051658481359482,
0.03604124113917351,
0.002068697474896908,
0.004798567853868008,
-0.03575880452990532,
-0.06563625484704971,
-0.04684991016983986,
-0.01681695133447647,
0.018430572003126144,
-0.020478079095482826,
0.053165748715400696,
0.035367175936698914,
0.02045411802828312,
0.00887615978717804,
0.0065093012526631355,
-0.04838338494300842,
0.010398372076451778,
-0.023744355887174606,
0.02291463501751423,
-0.03966230899095535,
-0.027304884046316147,
0.036546740680933,
0.047711580991744995,
0.036140162497758865,
-0.08691801130771637,
0.0006938736187294126,
-0.05555225536227226,
-0.011926586739718914,
0.05804293975234032,
0.029638051986694336,
-0.0050933645106852055,
-0.058042045682668686,
-0.005956409964710474,
0.012437145225703716,
-0.00573166087269783,
-0.007735188584774733,
0.018236851319670677,
-0.03199854865670204,
0.03245706856250763,
-0.014473618939518929,
-0.07734546810388565,
0.0016538649797439575,
0.0010470612905919552,
-0.0356273427605629,
0.045739542692899704,
-0.04201914742588997,
-0.09203789383172989,
0.050496917217969894,
-0.000007080660452629672,
0.05240054056048393,
0.000037157791666686535,
-0.006017221603542566,
0.07253793627023697,
0.022829344496130943,
-0.007643032353371382,
-0.03738270327448845,
-0.04961155354976654,
0.09223906695842743,
0.007398153189569712,
0.041355643421411514,
0.024517478421330452,
0.01784982904791832,
-0.00917669665068388,
-0.05735421180725098,
-0.013946427032351494,
-0.045420099049806595,
0.020767472684383392,
-0.01841643452644348,
0.0014004207914695144,
-0.0423201359808445,
-0.0010547653073444963,
-0.004109772853553295,
-0.02946162223815918,
-0.0011212363606318831,
-0.0028932110872119665,
-0.05240669101476669,
-0.035361044108867645,
0.03216402232646942,
-0.032247114926576614,
-0.016855595633387566,
0.05711730569601059,
-0.0073871673084795475,
-0.006563079543411732,
-0.003219851991161704,
0.04707416519522667,
0.03725127503275871,
-0.023062868043780327,
0.06816519796848297,
-0.01281846221536398,
0.006121849175542593,
0.022867873311042786,
0.008467106148600578,
-0.0002762764925137162,
-0.03734962269663811,
0.01447533629834652,
0.030029479414224625,
-0.0007766679627820849,
0.047908566892147064,
-0.002876234706491232,
-0.004894749261438847,
0.03288455307483673,
0.04555109888315201,
-0.018213538452982903,
0.03634803742170334,
0.004372113849967718,
0.05211351066827774,
0.03226390480995178,
0.026446513831615448,
0.02538406103849411,
0.011792941950261593,
0.027850840240716934,
-0.036792658269405365,
0.05564400181174278,
-0.00628484645858407,
-0.02374771609902382,
0.02424808032810688,
-0.017433689907193184,
-0.005605613347142935,
0.001166718197055161,
-0.008243579417467117,
0.029077129438519478,
0.027369586750864983,
0.05690871179103851,
0.010509729385375977,
0.061627473682165146,
-0.006454356946051121,
-0.01661602221429348,
0.023391449823975563,
0.05164904519915581,
0.028894169256091118,
-0.051292937248945236,
0.021878331899642944,
-0.01715249754488468,
-0.020499885082244873,
0.0010921440552920103,
-0.006638081278651953,
-0.02664487436413765,
-0.018297960981726646,
-0.03305191919207573,
-0.04324384406208992,
-0.008375151082873344,
-0.00017814102466218174,
-0.07041136920452118,
-0.0065972390584647655,
-0.014790145680308342,
0.04684893786907196,
0.00535265076905489,
-0.08849657326936722,
-0.06219858303666115,
-0.022267475724220276,
-0.027565987780690193,
-0.037240754812955856,
-0.01549708191305399,
0.013857608661055565,
-0.05342085659503937,
-0.05187271162867546,
-0.015188172459602356,
0.013325098901987076,
-0.0477977953851223,
-0.011753791011869907,
-0.08163052052259445,
0.034744080156087875,
-0.00030624232022091746,
-0.01640605367720127,
0.01390879973769188,
0.004393554292619228,
0.02791982889175415,
0.023507971316576004,
-0.047402895987033844,
0.05728748068213463,
-0.03560362011194229,
0.0013294393429532647,
-0.0030853154603391886,
0.0310093704611063,
-0.045622628182172775,
-0.04958325996994972,
-0.0008182358578778803,
0.02836242876946926,
0.04588603228330612,
0.03735185042023659,
-0.0783148780465126,
-0.0005682217888534069,
-0.04315407946705818,
0.015023372136056423,
0.021224841475486755,
-0.05002325773239136,
0.028308382257819176
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.